WYLE LABORATORIES - RESEARCH STAFF 

TECHNICAL REPORT 64058-03 

ENGINEERING EVALUATION OF 

SSME DYNAMIC DATA FROM 

ENGINE TESTS AND SSV FLIGHTS 

by 

Research Staff 

A final report of 

work performed under contract NAS8-33508 

for 

NATIONAL AERONAUTICS AND SPACE ADMINISTRATION 

GEORGE C. MARSHALL SPACE FLIGHT CENTER 

MARSHALL SPACE FLIGHT CENTER, ALABAMA 35812 

February 1986 
FOREWORD 

This report was prepared by Wyle Laboratories, Scientific Services & Systems Group, 

for the George C. Marshall Space Flight Center, National Aeronautics and Space 

Administration. The work was performed under contract NAS8-33508, entitled "Dynamic 

Analysis of SSME Vibration and Pressure Data." 

Mr. T. Coffin and Mr. W. L. Swanson, of the Wyle/Huntsvjlle Research Department, 

served as Program Manager and Project Engineer, respectively, on this study. 

Messrs. T. Gardner, R. Dandridge, and Dr. J. Jong provided valuable contributions 

to SSME data analysis and component modeling tasks. Mr. W. C. Smith, MSFC/ED24 

served as Contracting Officer's Technical Representative for the study. In this 

capacity he provided valuable assistance in the coordination of test evaluation 

activities and served as a focal point for defining task requirements and priorities. 

i 
ABSTRACT 

This report summarizes an engineering evaluation of dynamic data from SSME hot 

firing tests and SSV flights. The basic objective of the study was to provide 

analyses of vibration, strain and dynamic pressure measurements in support of MSFC 

performance and reliability improvement programs. A brief description of the SSME 

test program is given and a typical test evaluation cycle reviewed. Data banks 

generated to characterize SSRlE component dynamic characteristics are described and 

statistical analyses performed on these data base measurements are discussed. 

Analytical models applied to define the dynamic behavior of SSME components (such 

as turbopump bearing elements and the flight accelerometer safety cut-off system) 

are also summarized. Appendices are included to illustrate some typical tasks 

performed under this study. 

ii 
TABLE OF CONTENTS 

Section I. Executive Summary ....................... 1-1 

Section 11. Program Review and Survey of Tasks .............. 11-1 

2.1 Background. ............................. 11-1 

2.1.1 The Space Shuttle Vehicle System ................ 11- 1 

2.1.2 The Space Shuttle Main Engines 11-2 

2.1.3 SSME Development and Acceptance Testing ........... 11-3 ................. 

2.2 Engineering Evaluation of SSME Dynamic Data. ............ 11-7 

2.2.1 Dynamic Analysis and Evaluation Considerations ......... 11-7 

2.2.2 SSME Data Base Development and Application .......... 11-8 

2.2.3 Special Considerations in Dynamic Strain Assessment ....... 11-15 

2.3 Analytical/Statistical Modeling .................... 11-20 

2.4 Concluding Remarks ......................... 11-27 

Table I. Some Topics Recently Investigated in Support of SSME Dynamic 

Evaluations ................................ 11-28 

Fascos Program Listing. .......................... 11-30 

Appendix A. Wyle Laboratories Research Staff Technical Memorandum TM 

80-8, "Evaluation of Space Shuttle Main Engine Fluid Dynamic Frequency Response Characteristics." ......................... 

Appendix B. Wyle Laboratories Research Staff Technical Memorandum TM 

84-03, "Rolling Bearing Element Rotational Speeds for the SSME High 

Pressure Fuel and LOX Turbopumps.". ................... 

. Appendix C. Wyle Laboratories Research Staff Technical Memorandum 

64058-01-TM, "Statistical Analysis of the Vibration Data for the SSME High Pressure Turbopumps During Flight." .................... 

Appendix D. Wyle Laboratories Research Staff Technical Memorandum 

64058-02-TW "Analysis of the Synchronous Vibration Levels from "High 

Running Main Impkllers" on the SSME High Pressure Oxidizer Turbopump." . . 

iii 
SECTION I 

EXECUTIVE SUMMARY 

The Space Shuttle Main Engine (SSME) system and components have been and are 

presently undergoing extensive development and certification tests, at which time 

some 250 measurements are acquired, including vibration, strain, and dynamic 

pressure at critical engine locations. Limited engine data is also recorded during 

operational flights. Under the severe temperature, pressure, and dynamic environments sustained during operation, engine systems and components have been subject to 

malfunction and failure. Over the past 13 years of SSME development, 28 major 

component failures have occurred, causing extensive damage to engine hardware and 

test. facilities, at considerable expense in cost and schedules. In addition, 

numerous off normal operations of a less severe nature have been observed. 

Detailed analysis and evaluation of the dynamic measurements obtained is mandatory 

to permit quick assess’ment of engine component condition and the initiation of 

corrective measures when necessary. A wealth of dynamic data is available to 

support this effort. Efficient performance of this task is especially critical when 

considering the high test and launch rate in progress and the significant impact of 

dynamic evaluation results on test and launch turn-around time. Dynamic analysis, 

modeling and evaluation of SSME measurements and components have been performed by 

Wyle, under NASA contract NAS8-33508, in support of these efforts. This report 

documents the results of this investigation. 

The basic objective of the effort was to provide detailed analyses and evaluation of 

vibration, dynamic pressure, and strain data available and being acquired during 

SSME tests. Additionally, analyses were performed on data obtained from Space 

Shuttle Vehicle flights. Statistical analyses were performed to characterize 

nominal and abnormal SSME component dynamic behavior under available operating 

conditions. Data banks representing component characteristics were generated and 

updated, and analyses performed to assess system response under actual and hypothesized operating conditions. This included update of the MSFC Diagnostic Data Base 

and application of the SSME Isospectral Automated Data Base System. A data base 

was also generated and updated in a format compatible with the Flight Accelerometer 

Safety Cut-Off System (FASCOS) filter characteristics to provide a basis for 

comparison of static test and flight results. FASCOS operational characteristics 

I- 1 
have recently been defined statistically through system analysis and simulation, to 

permit assessment of the system logic. 

The work was performed under three broad tasks, which are summarized as follows. 

TASK I: Analysis, Evaluation, and Documentation of SSME Dynamic Test Results 

Under this task Wyle performed analysis, evaluation and documentation of SSME 

dynamic test results. This task represented the mainstream of the contract effort 

and included data verification, analysis, evaluation, and documentation for each 

SSME ground test and additionally for SSV flight measurements. Results included 

definition of temporal and spectral characteristics observed. Subsynchronous, 

synchronous, and higher order spectral characteristics were summarized for engine 

components under all available operating conditions to characterize SSME component 

behavior. Full utilization of the SSME Isospectral Automated Data Base System was 

employed to provide inf ormative data summaries. Strain measurements were analyzed 

as above, and improved strain data reduction procedures evaluated for subsequent 

strength and fatigue analysis. Oral presentation and written summaries were 

provided to document the results of each test and flight. 

TASK 1x1: 

Dynamic Behavior 

Under this task Wyle developed, maintained, and updated the data base and statistical models of SSME component dynamic response measurements to provide characterizing profiles of observed parameter ranges, distributions, etc., under normal and 

abnormal operating conditions at available power levels. These models included 

wide-band root-mean-square values, narrow-band spectra, and band-pass results in 

the flight data format. Analytical models and computer schemes were applied to 

define the dynamic and statistical behavior of SSME components, such as bearing 

elements and the Flight Accelerometer Safety Cut-of f Systems. 

Development and Documentation of Statistical Models of SShlE Component 

The above tasks are seen to be intimately related, since promising statistical/ 

analytical models may be immediately integrated into the SSME evaluation process. 

Also, data base statistics were immediately updated as test and flight measurements 

became available. It should be noted that the above evaluations were performed 

under extremely limited time constraints consistent with test and flight schedules. 

The extent of a given investigation varied widely depending on the specific measure1-2 
ments acquired, whether or not observed engine operation was nominal, and the 

severity of any observed component malfunction of failure. 

The following section presents an overview of the study. The SSME test/measurement 

program is briefly described. Dynamic evaluation considerations are discussed. 

SSME data base development and application tasks performed under this contract are 

summarized along with analytical/statistical modeling efforts. A list of engineering investigations recently performed in support of SSME dynamic evaluations is 

presented. This table indicates the wide diversity of engineering effort required 

in accomplishing contract objectives. 

As with most test/evaluation programs, quick turnaround of investigative results 

was imperative to successful task accomplishment. These results were theref ore 

provided directly to the MSFC COTR and cognizant Program personnel through informal 

data packages and presentations. A detailed discussion of each evaluation performed 

is given in the technical progress and interim reports provided under this contract. 

Several of these reports, addressing specific task evaluations, are included as 

Appendices for reference. 
SECTION I1 

PROGRAM REVIEW AND SURVEY OF TASKS 

2.1 Backvround 

The Space Shuttle Main Engines (SSME) are required to operate under extreme temperatures with high fluid pressures and rotational pump speeds. Developmental work is 

presently in progress to uprate SSME performance, including engine certification at 

FPL (109%). The SSME and components have been subjected to extensive hot firing 

tests. Acceleration, dynamic pressure and strain data have been acquired during 

these tests and additionally from Space Shuttle Vehicle (SSV) flights. Analysis 

and evaluation of results obtained from SSME operation, to aid in the identification 

and resolution of sources of malfunction, were performed by Wyle Laboratories under 

NASA Contract NAS8-33508. Dynamic and statistical modeling to assess system 

behavior and component condition has also been accomplished. 

This section presents an overview of the Space Shuttle Vehicle (SSV) system and 

SSME in particular. The SSME test program is briefly described, and a typical SSME 

test evaluation cycle is outlined. Some methods applied by Wyle to the assessment 

of acceleration, strain and dynamic pressure measurements are discussed. A recent 

investigation of the FASCOS system is also described. 

2.1.1 The Space Shuttle Vehicle System 

The SSV is composed of the Orbiter, an External Tank (ET), which contains the ascent 

propellant to be used by the Orbiter’s three main engines, and two Solid Rocket 

Boosters (SRB). The Orbiter and SRBs are reusable; the ET is expended on each 

launch. 

A Space Shuttle mission begins with installation of the mission payload into the 

Orbiter cargo bay. The SRBs and the SSMEs fire together at liftoff. The two SRBs 

are jettisoned after burnout -- about 45 kilometers (28 miles) high -- and recovered 

for reuse by means of a parachute recovery system. The SSMEs continue to burn until 

the Orbiter is just short of orbital velocity, at which time the engines are shut 

down and the ET jettisoned. During its return through the atmosphere, the tank will 

tumble, break up and be destroyed. 

The orbital maneuvering system is used to attain the desired orbit and to make any 

subsequent maneuvers that may be needed during a mission. After orbital opera11- 1 
tions are completed, normally about seven days, deorbiting maneuvers are initiated. 

The Orbiter reenters the Earth’s atmosphere at a high angle of attack. It then 

levels into horizontal flight at low altitude for an unpowered aircraf t-type 

approach, landing at a speed of about 335 kilometers per hour (208 miles per hour). 

2A2 The Space Shuttle Main Engines 

The Orbiter vehicle main propulsion system consists of three SSMEs. The SSRlEs are 

reusable, high-performance, liquid-propellant rocket engines with variable thrust. 

They are ignited on the ground at launch and operate in parallel, with approximately 

500 seconds total firing duration. Each of the rocket engines operates at a mixture 

ratio (liquid oxygen/liquid hydrogen) of 6:1 and a chamber pressure of approximately 

3000 psia to produce a sea-level thrust of 375,000 pounds and a vacuum thrust of 

470,000 pounds. The engines are presently throttleable over a thrust range of 60 to 

109 percent of the design thrust level. This provides a higher thrust level during 

liftoff and the initial ascent phase, and allows Orbiter acceleration to be limited 

to 3 g’s during the final ascent phase. The engines are gimbaled (210.5 degrees for 

pitch and ~8.5 degrees yaw) to provide pitch, yaw, and roll control during the 

Orbiter boost phase. 

Significant to meeting performance requirements is the use of a staged combustion 

power cycle coupled with high combustion chamber pressures. In the SSME-staged 

combustion cycle, the propellants are partially burned at high pressure and relatively low temperature in the preburners, then completely combusted at high temperature and pressure in the main chamber before expanding through the high-area-ratio 

nozzle. Hydrogen fuel is used to cool all combustion devices in contact with hightemperature combustion products. An electronic engine controller automatically 

performs checkout, start, mainstage, and engine shutdown functions. Major components of the SSME are illustrated in Figure 1. A more detailed view of the SSME 

power head is shown in Figure 2. This figure provides an indication of the complexity of the SSME turbomachinery. 

11-2 
LOWSRESSURE 

F UEL OW1 \ 

~Ow-mEsstm 

HIGH-WIESSURE 

FUEL TURBOPUMP 

Low-mEssURc 

PREBURNER 

LOW-PRESSWI E 

HIGH-PRESSURE 

OXIOIZLR 

TURBOPUMP 

COOLANT * 

FIGURE 1. Space Shuttle Main Engine 

2.1.3 SSME Development and Acceptance Testing 

To validate system performance and ensure equipment reliability, the SSME and 

components have been and are presently undergoing extensive development and qualif ication tests. Testing of the engine and components is conducted at several NASA and 

contractor locations. Full scale engine test firings for development and flight 

acceptance are performed on two single-engine test stands at the National Space 

Technology Laboratories (NSTL), Bay St. Louis, Mississippi, and at one stand 

operated by Rockwell International near Santa Susana, California, with plans to 

include a development test stand at MSFC. In addition, main propulsion testing 

(MPT) is performed at NSTL on a stand designed to accommodate the Shuttle main 

propulsion system elements--the three-engine cluster, the ET, and the Orbiter 

sys tems. 

11-3 
Figure 2. Space Shuttle Main Engine Power Head 

11-4 
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Testing is being performed on a continuing basis. The length of a given test is 

dependent on specific test objectives and may run from several seconds to over 800 

seconds. Tests are generally designed to satisfy multiple specific objectives, 

which fall into two broad categories; acceptance/certification firing of flight 

hardware and development testing directed towards design verification, performance 

and reliability improvement. Test operations are controlled by a computer called 

the Command and Data Simulator (CADS) which communicates with the engine, displays 

vital measurements for on-line observation/control and initiates pre- and post-test 

procedures. 

Approximately 250 measurements are recorded on a given test including wide band 

vibration, dynamic pressure and strain at critical engine locations. Some of these 

measurements are utilized on-line as emergency cut-off indicators and all are 

recorded on magnetic tape for subsequent analysis and evaluation. Limited SSME 

vibration measurements are recorded on magnetic tape during SSV flights for evaluation with orbiter return. Typical dynamic measurements obtained during SSME 

operation are illustrated in Figure 3. 

2.2 Endneerinp Evaluation of SSME Dvnamic Data 

2.2.1 Dynamic Analysis and Evaluation Considerations 

Acceleration measurements are obtained at fuel and oxidizer turbopump locations 

during all test firings, providing an extensive vibration data - base representing 

various turbopump builds under widely differing operating conditions. Additional 

measurements are obtained on a test-specific basis, depending on performance, 

structural integrity, or rotor dynamic characteristics under evaluation. For 

example, test series have been performed with some 80 strain measurements to support 

engine nozzle and injector dynamic stress evaluations. Recent firings have also 

been conducted with internally instrumented turbopumps to define component dynamic 

load and signature characteristics. Thus it is seen that the extent of the evaluation process varies widely from test to test, even though engine performance is 

nominal. In the event of anomalous performance or component malfunction, the extent 

of this process is increased significantly. Limited turbopump measurements are also 

obtained from the three SSMEs on each SSV flight. Data bandwidths available from 

SSV flight instrumentation differ from the wide-band capability used during ground 

testing, thus the need for generating a data base of filtered ground test measure11-7 
ments to permit direct comparison with flight results. Typical engineering activities supported by Wyle in an SSME test evaluation cycle are summarized as follows. 

Data evaluation and documentation: 

- Data verification and validation 

- Events analysis 

- Temporal. and spectral correlation with operating profile and machine 

dynamic characteristics 

- Test/flight data summary 

Analytical/statistical modeling and classification: 

- 

- 

- 

- 

Develop statistical models characterizing normal and abnormal behavior 

Update SSME diagnostic data base 

Establish and update engine cut-off redlines 

Develop and apply computer programs to define SSME component dynamic 

behavior 

Failure investigation: 

- 

- 

Time/event correlations with other test parameters/observations 

Temporal and spectral comparison with structural dynamic and statistical models and associated failure modes 

- Evaluation and recommendations of probable failure/ef fect scenarios, and means of resolution. 

It should be noted that the above evaluation must be performed under extremely 

limited time constraints consistent with test and flight schedules. Also, the 

extent of a given evaluation depended on the specific measurements acquired and 

whether or not observed engine operation was nominal. 

2.2.2 SSME Data Base Development and Application 

Wyle personnel have been instrumental in the development, modification and application of the MSFC Diagnostic and Isospectral data base programs. These routines are 

used extensively in routine test evaluation and also in diagnostic investigations. 

The SSME diagnostic data base and software implemented in the last year has greatly 

facilitated the generation of quick-look performance summaries and comparisons for 

input to the SSME data reviews conducted immediately after each test, as well as the 

maintenance of historic statistical profiles. Figure 4, from Wyle TM 64058-01, 

illustrates a statistical summary of measurements obtained from the oxidizer 

11-8 
preburner pump during 141 test firings and the fuel turbopump flight data as of 

August 1985. These data represent measurements obtained under nominal engine 

operating conditions. Separate statistical definition is given for wide-band 

(composite) levels and the spectral levels at pump shaft speed (synchronous) and 

selected harmonics. Figure 5 illustrates cumulative and probability distributions 

characterizing the measurements. The cumulative distribution provides a useful tool 

for. the quick-look assessment of test results with the historical distribution of 

measurements observed over a number of test firings, and also indicates the statistical risks implied by vibration level redlines. 

A plot of the classical gamma distribution is included in these figures for reference, with parameters defined by 

G 

where 

A 

cy 

and 

- 

m 

32 

= sample mean 

= sample variance 

0 

The application of classical statistical models is desirable for data characterization since this permits continuous statistical definition and manipulation from 

discrete measurement observations. Automated optimal function definition has also 

been developed for implementation in the diagnostic data base program. Software has 

been written to assess a wide class of competing functions including the Weibull, 

Gumbel and generalized lambda distributions. 

11-9 
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STS 27 2.5 1.0 5.0 e 0.e 0.6 0.8 e 0.6 0.0 9.e 

Figure 4. Statistical Summary of High Pressure Fuel and 

Oxidizer Pump Measurements for Ground and Flight Tests 

11-10 
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Figure 5. Cumulative and Probability Distribution Plots 

for a Selected_Vibration Data Sample 

11-11 
In addition to the SSME diagnostic data base, the SSME Isospectral Data Base System 

was applied extensively. Historically, analog tapes were flown to MSFC, dubbed, 

reduced, and evaluated. Under the new system, spectra are extracted from the tapes 

every. 0.4 second for each measurement throughout each test and stored at 

NSTL/Slidell. On command, the spectral data is telemetered to MSFC via satellite. 

Based on MSFC-developed software, these preprocessed data are then manipulated and 

printed to display isoplots, bandpass trends, engine speed, etc., on user command. 

As the diagnostic data base system has made test-to-test comparisons more efficient, 

the'SSME isospectral analysis system has been a significant aid in the evaluation of 

time/amplitude/f requency trends within a test. In addition to the above preprocessed data, analog tapes are also obtained by MSFC for special-purpose time and 

frequency domain analysis. Modification of the Isospectral data base is under 

evaluation to include transmission of the Fourier coefficients (amplitude and phase) 

as well as PSD samples. This will permit immediate access to the vibration time 

history for detailed analysis, by straightforward inverse transformation. 

Figure 6 is an example of an isoplot representing a high pressure fuel turbine 

measurement throughout test 902-378. A frequency band of 60 Hz to 1310 Hz and 1310 

to 2560 Hz was selected and a spectrum plotted every 8 seconds. The displayed 

amplitude range is selectable, permitting clear representation of major spectral 

peaks or identification of low level spectral components. Interpretation obviously 

requires correlation with engine speed and other parameters. Figure 7 illustrates 

the root-mean-square acceleration time history composite, synchronous and selected 

harmonics for the same measurement. This time history is synthesized from the 

stored isospectral data by integrating over the PSDs obtained each 0.4 second during 

the test. 

II- 12 
TEST 9028370 HPFP RAD 0 

'IlnE :r&= 8.e SEC XING sa :rt! 

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Figure 6. Isoplot of a High Pressure Fuel Turbopump Measurement 

11-13 
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t I It i 

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C RHS 

(2%- 1) 

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Figure 7. Acceleration Time History of a High Pressure 

Fuel Pump Measurement and Selected Harmonic Contributions 

11-14 
A sample PSD for the same measurement is illustrated in Figure 8. An "Anomalous 

Frequency" routine was developed to track spectral components within a selected 

frequency band and relate these to the synchronous behavior. Figures 9 and 10 

illustrate the output of the procedure in the selectable frequency bands of 200-400 

Hz and 1700-2000 Hz. Another feature of the Isospectral Data Base Program is the 

cumulative speed analysis routine. Certain components on the SSME respond more 

strongly when exposed to a narrow speed range. Software was developed to track and 

evaluate the total time a particular serial number pump has accumulated in each 

speed range for a given test or series of tests. An example plot and tabulated 

values for two recent tests (Al-377 and A1-378) are shown in Figure 11. 

2.2.3 Special Considerations in Dynamic Strain Assessment 

Wide band strain measurements have generally been characterized in terms of power 

spectra and rms time histories. In special cases (such as a LOX injector post 

fatigue evaluation supported under this contract) peak strain distributions were 

estimated. More refined cycle counting techniques appeared desirable to characterize dynamic strain measurements. A cursory review of the experimental literature 

on high cycle fatigue was therefore performed. 

Miles' classical relation for fatigue under random vibration is based on an assumed 

distribution of stress or strain peak%. In a complex time history, consideration 

of adjacent peaks (and valleys) & can mask wide variations (the range) of the 

dynamic stress or strain incurred. A number of empirical cycle counting techniques 

have therefore been developed by researchers to better account for the ranges of 

stresses in a complex wave. When considering that damage has been shown to be 

roughly proportional to the sixth power of the strain range, importance of cycle 

counting and range definition techniques is underlined. 

The objective of all cycle counting methods is to relate the effect of a complex 

load, stress or strain time history to material fatigue properties obtained under 

simple cyclic loading conditions. "Overall range" counting methods have been shown 

to correlate more highly with observed fatigue life than simple peak value distributions. 

11- 15 
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11-17 
610.0 

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1988.8 

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Figure 10. Sample of Anomalous Frequency Routine Output (1700-2000 Hz) 

11-18 
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Figure 11. Sample of Cumulative Speed Analysis 

- 

11-19 
Three cycle counting techniques and associated computational algorithms appear most 

prominent in the literature for fatigue evaluation of complex strain (stress) time 

histories. These are known as the range-pair, Rainflow (or hysteresis loop closure) 

and ordered overall range (or racetrack) methods. These three procedures yield 

virtually identical results. Comp ion* schemes for implementation of these 

methods were also obtained from the references. These techniques permit significant 

data compression, in that only major strain excursions need be retained to characterize fatigue growth. The strain ranges generated as above are generally used 

concurrently with a fatigue analysis. However, the techniques may also be used 

directly in the data reduction procedure to generate strain range spectra depicting 

the number of occurrences as a function of strain range (a probability density 

approximation). Statistical definition of strain range spectra per event (such as 

engine startup) or per unit time (during constant power operation, for example) 

should constitute a valuable component fatigue life estimation tool. 

z 

23 Analvtical/Statistical Modeling 

The above discussion illustrates some capabilities of the SSME data base systems 

and software. Wyle personnel have made extensive use of this capability to define 

component test heritage and response characteristics. Numerous dynamic modeling 

investigations have also been conducted ranging from quick-look failure evaluations 

to extensive computer simulations of system behavior. As an example of these 

efforts, we summarize a recent evaluation of the SSME Flight Accelerometer Safety 

Cut-Off System (FASCOS) logic. Some additional investigations are described in the 

Appendix. 

Certification of the SSME at full power level (109%) is in progress. Implementation 

of the FASCOS system is an essential element of the certification program. The 

FASCOS is a vibration based engine condition monitor. The system continuously 

monitors accelerations measured on the SSME turbopumps during engine operation. 

Based on these measurements and assigned vibration "redlines," the FASCOS and 

engine control computer determine the "operational health" of each engine through a 

series of nonlinear operations on the vibration signals and a voting protocol. The 

outcome of the decision process (run/cut-off) is highly dependent on the redline 

values assigned to the FASCOS comparator and the (statistical) behavior of the 

monitored signals. For this reason an intensive analysis/simulation effort was 

11-20 
recently initiated by MSFC to define the FASCOS decision process as a guide to the 

assessment of redlines with respect to mission success and safety. Wyle performed 

analytical modeling and computer simulations in support of this challenging and 

significant task. 

A functional schematic of the FASCOS logic is illustrated in Figure 12. Three 

accelerometer signals are processed simultaneously to perform the required turbopump 

operational condition assessment. Major elements of the system are 

0 A filter/detection stage 

0 

0 A voting protocol based on the simultaneous state of the three comparaA comparator with time delay 

tor outputs. 

The' filter/detection stage is shown in more detail in Figure 13. This circuit 

consists of: 

0 

0 Square-law de.tector 

0 Exponential low-pass filter 

0 Square-root detector 

0 Second low-pass filter. 

Band-pass filter (approximately 50 Hz-1 KHz) 

It is seen that this nonlinear sequence of operations transforms the (possibly) 

wide-band vibration input into a slowly varying "weighted RMS" signal output which 

is fed to the comparator. 

The comparator is essentially a voltage gate with an adjustable threshold level and 

time delay required to activate the "switch." The threshold level defines the 

vibration redline which must be exceeded to initiate an output. The time delay 

precludes a threshold exceedance indication due to spurious noise sources. Transfer 

characteristics of the FASCOS comparator are illustrated in Figure 14. The output 

is seen typical of a random telegraph signal. The length of each pulse represents 

the (random) persistence time (minus delay) of the input signal above the redline 

threshold level. 

11-2 1 
Figure 12. Functional Schematic of the FASCOS 

I I 

11 

INPUT 

OUTPUT 

Figure 13. FASCOS Detection Stage and Transfer Characteristic 

11-22 
The controller periodically samples the state of the three comparator outputs and 

determines whether engine shut-down should be initiated based on a counting procedure. The voting protocol is quite simple. On a given sampling cycle a cut-off 

vote is registered only if all three controller inputs simultaneously indicate a 

redline exceedance. Shut-down is initiated only after three such Consecutive 

cycles have been observed; otherwise the voting process is reinitialized. An 

effort to demonstrate this voting process is illustrated in Figure 15, which 

indicates a sequence of events leading to a cut-off decision. 

The above qualitative description of the FASCOS system indicates a number of key 

issues to be addressed in system modeling, simulation and performance assessment, 

including 

0 Statistical characterization of the class of (random) functions representative of operational vibration signals. 

e Modeling of the nonlinear detector output to representative stochastic 

inputs. 

0 Derivation of threshold exceedance persistence time probabilities representative of the comparator operation. 

0 Estimation of joint statistical properties required to model the probability of combined level exceedance as utilized in the controller voting 

process. 

The above list is not exhaustive, but it does underline some significant technical 

considerations. At the outset, the (band-passed) vibration signals were considered 

representative of a random sine wave plus independent Gaussian noise process. This 

model admits a wide range of spectrum shapes and signal-to-noise level, and is yet 

mathematically tractable. Under this assumption a mathematical description of the 

f ilter/detection stage output (power spectrum and covariance function) was derived 

as a function of input, filter, and averaging characteristics. Limited computer 

results have demonstrated excellent agreement with empirical simulations performed 

by MSFC. The definition of threshold exceedance time persistance probabilities, to 

model the comparator output, represents a formidable theoretical problem. Several 

approximate formulations, however, have been impleniented for evaluation. These are 

called the Rice method, the method of non-correlated pulses and the quadratic 

approximation method. (See "Non-Linear Transformations of Stochastic Processes," 

11-23 
89 (2 (3 (4 4 * ‘d (2 b *‘$ t6 

INPUT OUTPUT 

Figure 14. FASCOS Comparator Transfer Characteristics 

II COMPARATOR 1 

CONTROLLER CYCLE 

TIME (Typical) It COMPARATOR 2 

II COMPARATOR 3 

“VOTES“ 1 1-0-4 1 2 )-------@-I 1’2 +O+ 1 2 3 

Figure 15. Illustration of FASCOS/Controller Voting Logic 

11-24 
by Tikhonov and Amiartov [RSIC No. QA2731, for a comparison of these techniques and 

enabling assumptions.) Persistence time probability density estimates obtained by 

these approximations are illustrated in Figure 16, for an idealized white noise plus 

sine wave input. The curves represent the persistence time distribution of the 

detected mean-square above a three sigma threshold from the average output. Basic 

assumptions employed in all three approximatio em most valid for high 

threshold-to-mean values and short time periods. A theoretical extension of the 

Rice method was developed to relax these constraints. With regards to the final 

issue above, the estimation of joint properties between vibration signals appears 

best approached through empirical simulation. In the absence of such information, 

however, bounds on system behavior may be obtained by assuming joint properties 

(total statistical dependence/independence between monitored signals, for example). 

By the above approach, a computer program was developed to define the probability 

of engine cut-off as a function of assigned redline values, turbopump vibration 

characteristics and FASCOS logic operation. Computer analyses were performed with 

the above model, based on vibration characteristics provided by MSFC, to estimate 

engine cut-off probabilities as a function of redline values. Finally, the program 

was installed on the MASSCOMP processor at the MSFC Systems Dynamics Laboratory. 

SDL personnel were provided computer program orientation at the conclusion of this 

task to permit FASCOS parameter evaluations by MSFC. A program listing of this 

analytical model is included at the end of this section. 

11-25 
4 

W 

11-26 
2.4 Concludiw Remark% 

This report provides a cursory overview of study objectives and approaches applied 

by Wyle in the performance of Contract NAS8-33508. As a test/evaluation program, 

rigid, long term task planning was neither feasible nor desirable. On the contrary, 

most tasks performed under this contract were initiated on an ad hoc basis, motivated by observed or suspected SSME component failure modes. Continued coordination 

with the MSFC COTR was therefore maintained to revise task priorities based on SSME 

test results. Consistent with stringent SSME test schedules, evaluation results 

were immediately provided the COTR in the form of presentations and informal data 

packages. A detailed chronology of these evaluations is given in the technical 

progress reports provided under this contract. To illustrate the diversity of tasks 

accomplished under this contract, some topics recently investigated by Wyle in 

support of SSME dynamic evaluations are summarized in Table I at the end of this 

section. Several representative evaluations performed under this contract are 

described in the Appendices. 

11-27 
TABLE I. SOME TOPICS RECENTLY INVESTIGATED 

IN SUPPORT OF SSME DYNAMIC EVALUATIONS 

6 Pseudoharmonic Study. Performed nonlinear coherence analysis to indicate . 

whether "apparent" harmonics were correlated with synchronous response. 

0 Pump configuration analysis. Applied linear discrimination analysis to pump 

. measurements to assess statistical difference between design conf iguraticins. 

0 Trimodal density investigation. Performed analysis and simulations to determine time series characteristics yielding three mode probability densities 

observed in turbopump measurements. 

e Source location investigation. Developed and applied analysis to estimate 

apparent source location based on geometry, wave speed and crosscorrelation 

measurements. 

0 FPB oxidizer, AS1 line accelerometer and strain gauge evaluation. 

0 MMC inlet manifold elbow strain gauge analysis for strength calculations. 

0 Developed algorithm for computer data band program: 

- 

- Cumulative distribution 

- Amplitude indian belt format 

Computer selection of PSD time slices 

o Analysis of internally instrumented pump: 

4 Transfer functions 

- Evaluation of ballpass frequencies 

- Calculation of contact angle from measured data 

a Whirl study. This required compilation of a complete history of the pumps, 

by serial number, response characteristics, and time of occurrence. 

e Rubbing model investigation. Statistical moments were derived for random 

sine wave plus noise processes with asymmetric clipping for comparison with 

observed turbopump measurements. 

0 STS-8. Investigation of AS1 line malfunction required analysis of previous 

11-28 
test data to determine whether the phenomenon could be detected on the high 

pressure pumps during ground test firings. 

Calculation of ball train frequency for high-speed ball bearing. An attempt 

was made to modify frequency equations to include the effect of varying ball 

size within a single bearing. 

High synchronous study. Evaluated maximum/minimum amplitudes by pump and 

component serial number to define statistical changes in response levels. 

Developed relationships for data extrapolation as a function of engine power 

level. 

Cumulative distribution of HPOT. Fit data to normal, Rayleigh and gamma 

distributions. Gamma was found to be best fit to empirical observations. 

Modulation investigation. The thrust was to determine the time functions 

that produce certain side-band frequencies which often appear in the data 

and are usually considered noise. A next step would be to evaluate the 

physical functions that produce such time histories. 

Results of the above investigations have been provided MSFC through technical 

progress reports, informal data packages and presentations. 

11-29 
FASCOS PROGRAM LISTING 

11-30 
D Line# 1 
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1 

1 

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1353 

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2.77 

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CONTINUE 

COW I NUE 

DO 21 I=l,NN 

IF(I.GT.NL4)GOTO 21 

w= 4 1-1 I ) *DF 

IF (W. LT. (FZ-FS 

s ( I) =s < I) +8*BW 

ELSE 

I 

IF(W. LT. IFSIN-F1). OR, (W. GT. (Fl+FSIN) - RND. W. LT. (F2+FSIN) ) )THEN 

S (I 1 =S ( I ) +4*BW*ET*R2 

ELSE 

END I F 

CaNT I NUE 

NC=E+FSIN/DF+L 

$3 ( NC) = < R*IBW*ET 1 **E!+S I NC) 

WRITE(l,*) (S(I), I=I,NN) ‘ 

VRV=S (1 ) 

IF (IFSO. EQ. 1 ) VRV-0. 

DO 478 I=S,NN 

VRV=VRV+S (I ) 

CONT I NUE 

VRV=VRV*Z*DF 

5 t r )=s< I) 

ENDIF 

SMO=S 1 ) 

IF (IFSO. EQ. 1) SIYlO=O. 

F=O 

DO 222 1=2,NN 

F=F+DF 

IF (ZFRC. E#, 1) THEN 

IF (IFFID. NE. 1) THEN 

ELSE 

END IF 

S ( I) 25 < 11 *Rl RC/ (R%RC-2+RRC*COS (Ci2*F) ) 

S(l)=S(II/Il+(C1*F)**~) 

SMO=SMO+S I ) 

RO 22 I=2,NN 

F=F+DF 

Q=PI *T+F 

s t I =s ( I )* ( (SIN (Q) /Q) **2) 

sivl0=stviu+s ( I )

CONTINUE 

ELSE 

ENDIF 

SMO=SM0*2*DF 

R&R=Z*G*BWw ( IcET) 

RR4=S~RT(O.~*SQRT14*RRR*~RR-~*~~~)~ 

SM4=RRR-RG4*RR4 

DEV I =SORT < VVV 1 

WRITE (*, 121) ZO, VVV, DEVI 

T)EV2=SQRT ( VRV > 

WRITE 19, 1221 VVV, VRV, DEW2 

DEVS=SG!RT (SMO 

WRITE (*,I231 WWI, SMU, DEV3 

REV4=SQRT ISM4) 

ioiRITE (+, 124) FIF14,SPI4, DEV4 

k2ITE (G, *I ZO, DEVl 

WRITE (6, *) VVV, DEV2 

kRITE (6, *I GMi, REV3 

11-32 
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la3 126 

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i a7 

i a9 

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186 

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130 

131 

19% 

133 

134 

135 

136 

137 

1’38 

1’33 601 

200 

201 602 

et”J2 

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306 3 

207 C 

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re 

.a .-. e- LCL 

Page Lt 

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WRITE (6, *) FIQ4, DEV4 

FORMFIT(* W&1= 3 , El& €3,’ VFIRl= ’, E16. 8, ? DEVl= ’, E1G. 8) 

FORMFIT (7 RVEZ= I E16. 8, ? VQR2= ’I, E16.8¶ ’ I)EV2= ’ , ElG. 8) 

FaRMQT[’ RVE3= 9, E16. 8,q VRR37 ?, El6. 8, DEV3= ?, E16. 8) 

FURMFIT(y RVE4= 9, E16.8, 5 VRR4= ‘, El6.8, DEV4= I &Id. 8) 

FORMRT (’ FIVES= * , E16.8,‘ VFIRS= ?, El&. 8, DEWS= ’, E16.8) 

NFFT=NN 

R43RR4 

NNP2=NFFT+2 

NNPE2=NNP2/E! 

R4S=Q4*Q4 

R4F=R4S*Q4S 

PI2=2+PI 

TIME=NFFT/FS 

DF=FS/NFFT 

DT=l/FS 

C)T2=DT*2 

DFE!=DF*Z 

XF ( IFSO. Ea. 1) S( 1) =O. 

CFILL FFT (S1 NNP2,l) 

DO 601 I=l,NNP22 

S(I)+3(2*I--l)*NFFT 

DO 602 I=I,NNPZi-2 

S(NNPe~+I)=S(NNP~2-1) 

S (NFFTi-1 1 =(3. 

S ( NFFT+2 1 =a. 

DO 3 I=ll,NStFT 

S ( I =DF%*S ( I ) 

CONT I NUE 

*******SF CQLCULQTE R4 ( T) FROM R3 < T) ********* 

RSO=S ( 1 1 

S < I 1 =-Q4S+O. S*SQRT (4*Q4F-+2*S (1 1 1 

CONTINUE 

R40=S ( 1) 

FORMRT (7 R3 (0) = 7 E16.8, ’ R4 (0)= ‘I, El6.8) 

CRLL FFT (S, NNP2, 1 ) 

DO 606 I=l,NNP22 

S < I)=S (2*1-1) *NFFT 

S (NNP22+1 1 =S (NNP2tZ-I> 

DO 4 I=l,NNMQX 

S ( I ) =S (1 ) +DTZ 

s (1) =s (1) 12. 

DO Z24 I=NNMRXtl, NFFT 

s ( I ) =o. 

WRITEI11,*) (S(I), I=l,NFFT/Z) ****** PSD CIF X4 **Si******** 

CRLL POSTR (S, NFFT/2, FC, NORDER, DF, VRHS, FS, fFE3W) 

DEVJ=SQRT VRRS) 

WRITE(*, 126)QQ4,VRRS, DEVS 

WHITE(6j, *) RQ4, DEVS 

1 

ORfG1NAL 

OF POOR QUALITY 

DO 66 1=1, NFFT 

DO GO7 I=l,NNP2i2-2 
D tine# 1 7 

1 

1 

1 

1 

1 

1 

1 

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1 

f. 

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* 

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309 123 

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311 C 

308 iea 

Page L 

ot3 : 52 : 33 

7 Mkerosoft FORTRFIN77 V3.20 t32:/84 

XR ( I ) =-DF2*XR I I) 

WRITE(12,*) (DBLE(XR(1) 1 , I=i,NOUT) 

RTTO=-X R ( 1 1 

WRITE(*, 127) RTTO 

FORMQT(’ VQRIRNCE OF SLOPE OF RMS TIME SERIES=-R”<O) = ’,E16.8) 

WRITE(*, ’ (R)’ )’ N* = EXPECT # OF UPCROSSING OF R IN TIME T9 

WRITE(*, ’ (R)’ 1’ TBQR= EXPECT PERSISTENCE TIME OF REDLINE R’ 

UP=SQRT(RTTO)/( 

UPI=l. /UP 

WRITE(*, 128)UP 

WRITE (*, 12’3) UP1 

FORMBT(’ N* = 3, F1S. 8,s * T * EXP(-0.5*R**2) 1 

FOHMRT(’ TBQR = ‘,F15.8,’ * EXP(O.S*R**i?) * ERR(R)’) 

WRITE(*,’(R)*)’ ERR(R)= Pr( X GREQTER THEN R X IS UNIT NORMRL’ 

(x-1 +a6 

WRITE (63 *) RTTO 

’TYPE 

RERL 

RERL 

RERL 

REFL 

REFIL 

REFIi 

2ERL 

RERi 

RE% 

2ERL 

RERL 

Offset P Cia55 

218 

146 

226 

150 

636 

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540 

350 

346 

142 

254 

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11-35 
IT Line# 1 

1c 

3 

’3 

4 

6 

7 

0 

3 

10 

11 

12 

I1 3 

14 

1s 

16 

17 

10 

13 

2 Cl 

231 

23 

e4 

zs 

26 

27 

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23 

30 

31 

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33 

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43 

5 0 

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59 507 

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Page 1 

OZ-i3-(3& 

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7 Microsoft FORTRRN77 V3.20 02/84 

PROGRRM PSTRR-FOR----- 3 STEP MEMORY MRRKOV MODELLING OF P.T. 

IMPLICIT RERi*S (R-H, C3-Z) 

RERL*cS R0 (50)’ Rl (50)’ VO 13’00), FVO (300)’ PSTRR (30)’ QSTQRtZO) 

RERL*B SM (3,3), TM (a), RM (31, SMK (3,3), TP(3), REDV (10) 

DIMENSION L3 (31, M3 (3) 

CHRRRCTER*l6 F1, F2, FRED, FOUT 

COMMON PI& ERR 

KK=3 

WRITE(*,’ (R)’)’ ENTER # OF REDLIN’ 

RERD {*, *) NRED 

IF (NRED. Ea. 1 1 THEN 

WRITE(*,’IR)*)’ ENTER REDLINE ( ? DEV )’ 

RERD (*, *) REDV ( 1 ) 

ELSE 

WRITE(*, ? (R)’ )’ ENTER FILNRM OF REDLINy 

RERD (*, ? (R) ’ 1 FRED 

OPEN (1 1, FILE-FRED, STRTUS=’ OLD’ ) 

RERD < 1 l, *) (REDV (I 1, 1x1, NRED) 

CLOSE ( 11 ) 

ENDIF 

WRITE (*, f (R) 9 ) ENTER INPUT R (T) R’ (TI FILNRM’ 

WRITE(*,’(R)’)’ ENTER OUTPUT INFOMRTION FILNRM ’ 

RERD (*, ’ (R) ’ 1 FE 

WRITE(*,’ (R)’ )’ ENTER OUTPUT FILNQM OF PSTFIR’ 

REFID(*,’ (R)’)FOUT 

WRITE(*,’ (Q)’>* ENTER ORDER OF RICE THE5RYsNN (NOT INCLUDE X0)’ 

RERD (*, *) NN 

WRITE(*,’ (R)’)’ ENTER # OF DRTR IN ERROR FUNCTION’ 

RERD (*, *) NERR 

WRITE (*, ’ (R)? )? 

RERE) (*, *) NVQ 

WRITE(*, ’ (R)’ 1’ ENTER MRX VRLEE OF V0 ( ? DEVCVO) f ’ 

RERD (*, *) VOMRX 

WRITE(*, ’ (a)’ ) ’ ENTER # CIF X’ 

RERD (*, *> NX 

NXiZ=NX*2 

WRITE(*, ’ (a)’ 1’ ENTER MRX VRLUE OF X ( ? DEVCX) > ’ 

RERDI*, *) XMRX 

WRITE(*,’(R)’)’ ENTER 1 FOR PRINTING INNER LOO? PRRRMETERS’ 

RERD (*, *) INNER 

CQLL SERR (ERR, NERR) 

OPEN (6, FILE=F2:, STQTUS=7 NEW’ ) 

WRITE (6, ’ (69) ’ ) ’ PROGRRM JEN3* 

WRITE (6,501) KK 

WRITE (6, SQ2)NERR 

WRITE (6,503) NN 

WRITE (6,504) NVQ 

chiRITE (6,505) VOMRX 

WRITE (6,3061 NX 

WRITE(6,507) XMQX 

FDRiviRT(, MEMORY STEP = ,, 12) 

FORMFSTI? # OF DkTk IN ERRUR FUNCTION = ’ 16) 

FORMFIT(’ ORDER c3F RICE THEORY = ’I 13) 

FORMRT(’ # OF INITIFIL SLOPE VrS = 9,X5) 

FURMRT ( MRX VkLUE OF VB = ’ , Fa. 4, ‘ DEV (VO) ’ 1 

FURMRT(’ & OF X = ’, 14) 

FiiRMRT(’ MFIX VRLLiE CF X = 3, F8.4, DEV IX) ’ ) 

RERL*B MU (20) DEL (iZO920) 3 ERR { 1005) 

REFID OC, ’ (R) ’ ) F1 

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DXl=XMRX*DEVXZ/NX 

DX2=XMRX*DEVX%/NX 

DX3=XMUX*DEVXWNX 

IF (INNER.; 

WRITE (*, 601) DZM, DEVXl, DEVXi2, DEVXS, CORlZ, COR23, COR13 

FORMUTIlX,7(E9.4,1X) > 

WRITE (*, * (R> 1 ’ BEFORE 3’3’3’ 

CORRXI -COR*COR 

QO=DXZ*DX~*DXS/ (PIZ**I. S*DS~RT(DQBS(DTM) ) ) 

>WRITE CE,,601> DZM, DEVX1, DEVX2, DEVX3, CORii3, COR23, 

1 COR13 

DO ’333 rr=i,Nvo 

DO 991 I=l,NN 

MU (I )=RED*cFI0 ( I )-VO { I I) *R1 < I) /VRRV 

RM=MU ( MM) 

DO 392 I=l,t<K 

RM(I)=MU(MM-I) 

XMINl=RM(l)-XMGX*DEVXZ 

XMIN%=RM(E!)-XMRX*DEVX2 

XMIN3=RM(3)-XM~X*DEVX3 

XMRXl=RM ( 1 ) +XMFIX*DEVX 1 

XMRX2=RM (2) +XMRX*DEVX2 

XMRX3=RM (3) +XMRX*DEVX3 

Sl=DMRXl (RED, XMINlf 

S%=DMRXl (RED, XMINZ) 

S3=DMUXl (RED, XMIN3) 

NSl=(Si-XMINl) /DX1 

NSEF(SZ-XMXN2) /ax2 

NS3= (S3-XM I N3) /DX3 

Xl=Si-DXl 

PS-0. DO 

RS=0. DO 

IF(S1,BT. XMFIX1)GOTU 100 

XI=Xl+DXl 

L!l=(Xl-RM(l)) 

Hl=Rl*Ql*SMI(l, 1) 

WKE!=E!*L!l*SMI (1, e> 

WKS=Ql*SMI (1,3) 

RZMi-RM+TP(l)*QZ 

IF (SE‘. GT, XMFIX2) GOT0 33 

X2-Si?-D X2 

X2=XWDXZ 

RZ=Xi?-RM (E!) 

Hi?=Hl+Q2*lL!E?*SMI (2,2:)+WKZ> 

WKl=E!*(WKS+G!2*SMI (2,3) 

RZM2-RZMltTP (21 *QZ 

IF (SS. GT. XMRXE!) 6070 9 

X3=S3-DX3 

x3=x 3+D x3 

G!S=XS-RM 13) 

ii3=ilE?+ ( WM 1 +t!J-*SM I ( 3,3) ) *Q3 

QZM=kZME+TP(3)*D3 

GGG=G(l‘l< t RED-RZM) /DZiyI, NERR) 

BB=DEXP (-*3/2.130) 

PS=PS+UG!*GGG 

QS=QS+QL? 

DO 33 JJ=NSl,NXF: 

DO 9 LL=NSZ,NXZ 

DO 22 IJK=NS3,NXZ 

2ilNTINtiE 

11-38 
D Line9 1 7 

178 ’3 CONTINUE 

173 ’39 CONTINUE 

180 100 PS=PS*QC)*PVO I I I ) 

181 GS=GS*RC)*PVO C I I > 

182 PSTFIR (NM) =PSTFIR (MM) +PS 

183 GSTFIR (MM) =RSTRH (MMI +G?S 

104 IF t INNER, Ea. 1) WRITE(6,602) I I, PVO ( I I ) , PS, QS, NS1, NS2, NS3, 

1 a5 

Offset P Cla55 
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DRTFIN 

DEL 

DEUX 1 

DEVX2 

DEUX3 

DEXP 

DMRX 1 

DSQRT 

DTM 

DVO 

DX1 

DX2 

DX3 

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CHFSR*16 

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INTEGERw4 

INTEGER*4 

INTEGEil*4 

INTEGER+4 

INTEGER*4 

INTEGER*4 

I NTEG&R*4 

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INTEGER*4 

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Microsoft FDRTRFIN77 US. 20 02/84 

OCnOlNIU- PAGE E3 

OF POOR QUALI’T’Y 
APPENDIX A 

M’YLE LABORATORIES - RESEARCH STAFF 

TECHNICAL MEMORANDUM TM 80-8 

EVALUATION OF SPACE SHUTTLE 

MAIN ENGINE FLUID DYNAMIC 

FREQUENCY RESPONSE CHARACTERISTICS 
ATPENDIX A 

WYLE LABORATORIES - RESEARCH STAFF 

TECHNICAL MEMORANDUM TM 80-8 

EVALUATION OF SPACE SHUTTLE 

MAIN ENGINE FLUID DYNAMIC 

FREQUENCY RESPONSE CHARACTERISTICS 

by 

T. G. GARDNER 

for 

NATIONAL AERONAUTICS AND SPACE ADMINISTRATION 

MARSHALL SPACE FLIGHT CENTER, ALABAMA 35812 

GEORGE C. MARSHALL SPACE FLiGHT CENTER 

Work Performed Under Contract Number NAS8-33508 
FOREWORD 

This report was prepared by Wyle Laboratories, Research and 

Engineering Division, Huntsville, Alabama, under NASA Contract No. NAS8-33508, for the National Aeronautics and Space 

Administration (NASA), George C. Marshal 1 Space F1 ight 

Center. The contract was administered under the technical 

direction of the Systems Dynamics Laboratory, with Mr. Harry 

Bandgren acting as the Technical Contracting Officer's 

Representative. Mr. Duron Cryder was the contract administrator for NASA. 

.. 

II 
TABLE OF CONTENTS 

- Page 

.. FOREWORD.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . II 

ABSTRACT.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . v 

SPACE SHUTTLE MAIN ENGINE SYSTEM DESCRIPTION . . . . . . . . . . . . . 1 

SPACE SHUTTLE MAIN ENGINE POGO TEST PROGRAM. . . . . . . . . . . . . 5 

POGO DATA ANALYSIS SOFTWARE. . . . . . . . . . . . . . . . . . . . . . 7 

APPENDIX A - POGO SOFTWARE FLOWCHART . . . . . . . . . . . . . . . . 17 

APPENDIX B - POGO SOFTWARE LISTING . . . . . . . . . . . . . . . . . . 41 

APPENDIX C - POGO SOFTWARE TEXT RECORDS (FILE ha). . . . . . . . . . 57 

APPENDIX D - POGO SOFTWARE TEXT BUFFERS (FILE 4b). . . . . . . . . . . 61 

APPENDIX E - POGO SOFTWARE SAMPLE OUTPUT . . . . . . . . . . . . . . 63 

... 

Ill 
EVALUATION OF SPACE SHUTTLE MAIN ENGINE 

FLUID DYNAMIC FREQUENCY RESPONSE CHARACTERISTICS 

T. G. Gardner 

ABSTRACT 

in order to determine the POGO stability characteristics of the Space 

Shuttle main engine (SSME) liquid oxygen (LOX) system, an evaluation 

of the fluid dynamic frequency response functions between elements in 

the SSME LOX system was performed, both analytically and experimentally. 

program and, more specifically, documents, as a user note, the POGO 

data analysis software. POGO refers to the effect the dynamic interaction between devices in the LOX system has on fluid/mechanical 

vibration of the system. For the experimental data evaluation, a 

software package was written for the Hewlett-Packard 5451C Fourier 

analyzer. The POGO analysis software consists of five separate segments. Each segment is stored on the 5451C disc as an individual 

program and performs its own unique function. The POGO analysis 

software includes two separate data reduction methods, a signal 

calibration, coherence or pulser signal based frequency response 

function blanking, and automatic plotting features. The 5451C a1 lows 

variable parameter transfer from program to program. This feature is 

used to an advantage and requires only minimal user interface during 

the data reduction process. Experimental results are also included. 

Comparison of experimental results with the analytical predictions 

permits adjustments to the general model in order to arrive at a 

realistic simulation of the POGO characteristics. 

This report acquaints the reader briefly with the POGO testing 

iv 
SPACE SHUTTLE MAIN ENGINE SYSTEM DESCRIPTION 

The Space Shuttle propulsion system consists of two solid rocket boosters 

(SRBS) and three main engines (SSMES). 

liquid-propellant, variable thrust rocket engines, operating at high 

temperatures, high pressures, and high rotational speeds. Each SSME 

operates at a chamber pressure of approximately 3000 psia to produce a 

sea level thrust of 375,000 pounds and vacuum thrust of 470,000 pounds 

and operates over a range from 50 to 109 percent of the rated power. 

Each engine consists of ten major components: two preburners, four 

turbopumps, the hot-gas manifold, the main injector, a heat exchanger, 

and the main combustion chamber. All other components are attached 

structurally to the hot-gas manifold, and the entire arrangement is 

called the SSME powerhead. 

The SSMEs are high-performance, 

A key to the cost effectiveness of the Space Shuttle concept is hardware 

reusabi 1 i ty. As a result, system re1 iabi 1 i ty is of paramount importance. 

The SSMEs have been subjected. to extensive hot firing and flow tests. 

Under these extreme operating conditions, system failures and malfunctions have occurred due to the self-induced dynamic environment. 

failures have ranged from subcritical wear of component bearings to 

catastrophic explosion and fire resulting from the intense pressure 

oscillations and dynamic stresses occurring in pumps, valves, and/or 

propellent lines. The components in the liquid oxygen (LOX) system 

include the low pressure oxidizer pump (LPOP), POGO suppression system 

(or accumulator), the high pressure oxidizer pump (HPOP), and the main 

combustion chamber (MCC). The LOX flows from the external tank (ET) 

through the above components and is combined with the liquid hydrogen 

(LH2) fuel at the inlet of the MCC by the main injector. 

These 

The LPOP is an axial-flow pump driven by a six-stage turbine and powered 

by the LOX. During engine startup and mainstage, the LPOP maintains 

sufficient pressure in the LOX line to permit the HPOP to operate at 

high speeds without an inducer and without cavitation, even under 

worst-case conditions. 

1 
The POGO suppressor is a gas-filled accumulator, which serves as a 

capacitance in the LOX flow circuit. 

low-frequency oscillations, transmitted from the Space Shuttle vehicle, 

from being transmitted into the HPOP and ultimately to prevent MCC 

pressure oscillations. 

startup and shutdown transients, the accumulator is filled with gaseous 

he1 ium. During normal engine operation, the heat exchanger provides 

gaseous oxygen (GO2), as the compliant medium, to the accumulator. 

system consists of a 0.6 cubic-foot accumulator, which is attached to 

the HPOP inlet duct, an internal stand pipe, helium precharge valve 

package, gaseous oxygen supply valve package, and recirculation isolaThe unit is designed to prevent 

To provide suppression protection through the 

The 

tion valves. The liquid level in the accumulator is controlled by the 

stand pipe, which is orificed to regulate the GO2 overflow over the 

engine operating power level range. Excess gaseous and liquid oxygen 

are recirculated back to the LPOP inlet through the engine oxidizer 

bleed duct. 

The HPOP consists of two single-stage centrifugal pumps on a comon 

shaft, whi-ch is directly driven by a two-s.tage hot-gas turbine. 

main pump receives oxidizer from the LPOP discharge and supplies LOX at 

increased pressure to the LPOP turbine. The HPOP turbine is powered by 

hot-gas (hydrogen-rich steam). LOX enters the HPOP main pump through 

the main pump housing and flows through an inlet with a 50-50 flow split 

into a double-entry, comnon outlet impeller. Several sets of guide 

vanes direct the flow to the impeller inlets. The impeller has four 

full and four partial blades in each half. After passing through the 

impeller, the flow is redirected into the HPOP discharge by diffuser 

vanes. The HPOP is attached to the hot-gas manifold by a flange, which 

is canted ten degrees out from the engine centerline. 

flows into the MCC. 

The 

The oxidizer then 

The MCC is a cylindrical structural chamber, which contains the burning 

propellant gases and is flange-attached to the 

MCC consists of a coolant liner, coolant inlet 

a structural jacket. The coolant liner, which 

hot-gas manifold. The 

and outlet manifolds, and 

provides the coolant 

2 
flow path of the MCC, contains 390 milled axial coolant channels, which 

are ported to the coolant inlet and outlet manifolds. 

vides an up-pass circuit for the liquid hydrogen coolant. The chamber 

jacket provides the structural strength for the MCC and is approximately 

20 inches long. The jacket is formed in two matching halves, which are 

welded together and to the coolant inlet and outlet manifolds. 

ring is also welded to the jacket at the MCC throat to provide added 

strength. 

fold of 2.96:l and is expanded to a ratio of 5:l before attaching to the 

engine nozzle. 

This network proA throat 

The MCC throat follows a contraction from the hot-gas maniIn order to validate system performance and ensure equipment reliability, 

the SSME and components have been and are presently undergoing extensive 

development and qualification tests. Testing of the engine and components 

is conducted at several NASA and contractor locations. Full-scale 

engine test firings for development and flight acceptance are performed 

on two single-engine test stands at the National Space Technology Laboratories (NSTL), Bay St. Louis, Mississippi, and one stand operated by 

Rockwell International near Santa Susana, California. In addition, main 

propulsion testing is performed at NSTL on a stand designed to accommodate the Shuttle main propulsion system element--the three-engine 

cluster, external tank, and orbiter systems. 

Testing is being performed on a continuing basis. The length of a given 

test is dependent on specific test objectives and may run from several 

seconds to over 800 seconds. During each test, comprehensive measurements are acquired to monitor system performance, including vibration, 

dynamic pressure and strain at critical engine locations. Several of 

these latter measurements are utilized on-line as emergency cutoff 

indicators, and all are recorded on magnetic tape for subsequent analysis and evaluation. 

3 

SPACE SHUTTLE MAIN ENGINE POGO TEST PROGRAM 

As part of a program to determine the POGO stability characteristics of 

the Space Shuttle Main Engine (SSME) liquid oxygen (LOX) system, POGO 

tests were conducted by Rocketdyne engineers, in California, on the A3 

SSME test stand. 

tics, frequency response functions [H(f)] between various components are 

calculated from pressure measurements taken at various locations in the 

system. To calculate the H(f)s, a known pressure signal must be applied 

to the system and the system response to this signal measured. A 

pulser was used to generate this dynamic pressure signal, with the tests 

usually including both sine sweeps and sine dwells. 

located downstream of the pulser is the low pressure oxidizer pump 

(LPOP) , fol lowed by the accumulator (or suppressor) , the high pressure 

oxidizer pump (HPOP), and the main combustion chamber (MCC). With the 

accumulator active in the system, the pulser signal is suppressed such 

that it does not reach the MCC with sufficient strength to be measured 

adequately. Consequently, tests were conducted with the accumula-tor 

active and inactive. The general system diagram below shows the relative location of these devices. Pressure measurements were made at the 

pulser, the LPOP inlet, the HPOP inlet, and the HPOP discharge. 

In order to define the system fluid dynamic characterisThe first device 

ACCUMULATOR 

The pulser sine sweeps ranged in frequency from 2 to 40 Hz. 

higher frequencies in the pulser sweep, the displacement of the pulser 

piston and the corresponding amplitude of the pressure pulse generated 

were very small. 

the line were essentially buried in the noise level and very difficult 

At the 

The amplitudes of the pressure signals further down 

5 
to measure. For the sine dwells, the magnitude of the pulsed signal can 

be increased, providing greater dynamic range in the data. The problems 

associated with the dwell testing are the increased time required to 

conduct the test and the fact that the frequency response functions can 

be defined only at the frequencies where the dwells are located. 

Because of this, a routine that will blank out invalid data in frequency 

response functions was included in the POGO analysis software. This 

blanking can be based on either the pulser signal or the coherence 

function, leaving only the frequency response function data at the 

frequencies where the pulser was operated. In the initial tests, the 

dwell frequencies were chosen at approximately 5-Hz intervals. In 

subsequent tests, the dwells were chosen closer together in order to 

better define the system frequency response. 

6 
POGO DATA ANALYSIS SOFTWARE 

For organizational purposes and because of total size, the POGO data 

analysis software is divided into five segments. Each segment is stored 

separately on the 5451C disc and runs on the 5451C as an individual 

program. 

as ten programs. This is the feature that allows these five programs to 

operate together and perform the total POGO data analysis. The software 

includes two frequency response function [H(f)] calculation routines. 

These two data reduction methods are referred to as the RATIO and DIRECT 

methods for calculating frequency response functions. In the RATIO 

technique, all H(f)s are initially referenced to the pulser. These 

H(f)s are then divided, with the resulting quotient being the H(f) 

across various combinations of devices. For example, the H(f) between 

devices 2 and 3 in the following schematic may be calculated as the 

RATIO of the H(f) between devices 1 and 3 and the H(f) between devices 1 

and 2. 

The 5451C Fourier operating system allows nesting of as many 

(f) 3/1 

= H(f)' 2/1 

" (f) 3/2 

where H(f)n,l = - Gnl and n = output, 1 = input El, 21. Here Gn, is the 

G1 1 

cross spectrum between the input and output, and Gll is the autospectrum 

of the input (pulser). 

NOTE: The POGO software outputs the autoi.(power) spectra and 

cross (power) spectra as functions normalized to the bandwidth (Af) 

or as power spectral densities (PSDs) and cross-power spectral 

densities (XPSDs). However, the 5451C calculates and uses the 

functions in their nonnormal ized form to calculate frequency 

response functions [H(f)s] and coherence functions [y2(f)s] 121. 

In the remainder of this document, all spectral functions will be 

referred to as PSDs and XPSDs regardless of their actual state of 

normal ization. The reader should understand that all H(f) and 

y2(f) calculations are made prior to normal ization. 

7 
To calculate the y2(f) that is compatible with the RATIO H(f), the 

following formula is used [3]: 

1 

- Y2 (f) 3,2 

-1 1 

JGnl l2 

11 nn 

where y2(f)n/l = G G , and n and 1 are output and input, as above [l, 

21 

To arrive at H(f)3/2 and y2(f)3/2 using the direct method involves 

calculating the frequency response function as the XPSD, between devices 

3 and 2, and divided by the PSD of device 2. The coherence is calculated as the magnitude squared of the XPSD divided by both the input and 

output PSDs. These equations are as follows: 

where G = XPSD, G22 = input PSD, and G 32 33 = output PSD. 

The POGO software also calculates frequency response functions, both 

RATIO and DIRECT, which have been blanked, based on either the coherence 

or the pulser signal. Blanking means that the frequency response function magnitude and phase are set to zero at those frequencies where the 

value of the coherence, or pulser signal, does not exceed the user set 

mini mum. 

As previously stated, the POGO analysis software consists of five segments, each of which is stored on the 5451C disc in a separate keyboard 

program file (KPF) record. They are currently stored in successive 

records (1 - 5) on the Marshall Space Flight Center, Systems Dynamics 

Lab's 5451C Fourier software disc. 

- 

- - 

8 
KEYBOARD PROGRAM FILE, RECORD 1 

KPFl contains part 1 of three parts, which perform the RATIO calculations. Part 1 sets up the data block size, calibration factors, total 

amount of data to be taken, and delta f (Af) [frequency resolution or 

bandwidth]. This information is used to calculate both the RATIO and 

DIRECT H(f)s. The 5451C has a block arithmetic mode, which allows any 

block of data to be multiplied or divided by any number. This number, 

however, must be an integer. If this number happens to be a floatingpoint - variable - parameter (VP), the 5451C simply truncates any part of 

the VP that lies to the right of the decimal. In reference to this 

problem, the POGO analysis software first multiplies each calibration 

factor by 100, then calibrates the appropriate data block, and finally 

divides the data block by 100. This allows for two decimal places in 

each calibration factor. The same type procedure is used with regard to 

the VP that holds the Af parameter, to allow for one digit to the right 

of the decimal when calculating PSDs. After the initial setup, KPFl 

reads the analog data from the tape and stores it on the ADC Throughput 

File, beginning at record 0. KPFl then retrieves this time domain data, 

two channels at a time, and calculates PSDs for each channel. KPFl also 

calculates H(f), y2(f), and XPSDs for the three pairs, LPOP/pulser, 

HPOP/pulser, and MCC/pulser. This data is stored in data blocks 12 

through 27. Program control is then transferred to KPF2, which is part 

2 of the POGO analysis software. 

KEYBOARD PROGRAM FILE, RECORD 2 

KPF2 begins the calculations for the RATIO H(f)s and y2(f)s. 

has preprogrammed keys that will perform the arithmetic necessary to 

make these calculations. The keys, however, perform what will be 

The 5451C 

referred to as block arithmetic. The 5451C stores data in blocks internal ly, in a format Hewlett-Packard cal Is floating-point-by-block. This 

means that the data block is actually a group of integers, all with a 

common scale factor. Because of this method of data handling, the 

arithmetic operation performed by the block command is not floating 

point, but is integer arithmetic. These operations involved in the 

9 
RATIO calculations are limited to a 40-dB dynamic range. 

a number, as that number approaches zero, the inverse approaches infinity. 

It becomes apparent that if there are any numbers whose value is less 

than 0.01 in a data block, any number greater than or equal to 1 will be 

more than 40 dB down when that block is inverted. The 5451C automatically scales up the block scale factor to eliminate overflowing, which 

causes any number more than 40 dB down to be set to zero. 

serious problem when doing the type of calculation involved in arriving 

at the RATIO H(f)s and y2(f)s. 

cially the y2(f) calculation, the quotient in the formulations is dominated by the small numbers in the denominator. These small numbers are 

not reliable data points, and the valid data is lost below the 40-dB 

dynamic range. 

When inverting 

This is a 

In both of these calculations, espeThe problem was solved in this program by using a floating-point arithmetic scheme in the y2(f) calculations and a combination of floatingpoint arithmetic and a filtering technique in the H(f) calculations. 

The f 1 oat i ng-poi n t scheme i nvol ves extract i ng each channel (or data 

.point) point-by-point from a data block, putting the value into a 

floating-point format (via a floating-point variable parameter) executing the arithmetic operation, and finally putting the datum back into 

the data block. A magnitude filtering technique is used in the H(f) 

calculation to eliminate a loss of data after the values are put back 

into the data block. 

filtered so that any values outside the range of - +7 are set to zero. 

This allows a polar magnitude maximum of 10. The 40-dB dynamic range 

then will be 10" to 10 . the y2(f) calculations because of the final quantity inversion in the 

formulation. All the values to be inverted, however, are scanned for 

values of identically zero before inversion. This is to eliminate any 

numbers actually going to the upper limit (infinity). 

The real and imaginary parts of the H(f) are 

1 This filtering technique is not necessary in 

The program loops through the above operation enough times to calculate 

the RATIO H(f) and y2(f) for each channel in the data block. This loop 

is nested inside a loop, which allows for all three sets of ratio 

10 
calculations to be computed. 

transfers control to part 3. 

Part 2 of the POGO analysis software then 

KEYBOARD PROGRAM FILE, RECORD 3 

KPF3 defines the variable parameter, corresponding to the ratio calculations, necessary to operate the plot routine. KPF3 also performs the 

calculations involved in the H(f) blanking routine. KPF3 has several 

entry points, which allow various operations to be performed outside the 

normal program flow. KPF2 flows into the beginning of KPF3, which jumps 

to the blanking routine. The blanking routine begins by prompting the 

user to establish whether the blanking will be based upon the y2(f) or 

the pulser PSD. The user will enter either a zero, to establish coherence blanking, or a two, to define pulser blanking. 

2) will also be used to establish which labels wi’ll be given to the 

plots of the blanked H(f)s during the plot routine. If pulser blanking 

is chosen, KPF3 will display the pulser PSD to allow the user an opportunity to view the signal and decide on the minimum value used for the 

blanking routine. If y2(f) blanking is chosen, KPF3 skips directly to 

the next step, which is a prompt, asking for the minimum value in the 

blanking routine. Next, KPF3 sets up the block that will be used for 

generating the blanked H(f). KPF3 then enters the blanking loop. This 

loop operates individually on each channel in the frequency domain data 

block. In this loop, KPF3 goes to either the pulser or y2(f) block and 

gets one channel at a time, beginning with channel one (channel zero is 

the first channel) and ending with the next to last channel in the data 

block. 

This number (0 or 

The value of this channel is compared with the values of the 

channel immediately preceding and the channel imnediately following. If 

the value of the channel in question is greatest, it is determined to be 

a local maximum. The value is then compared with the minimum value 

specified earlier by the user. 

in all three tests, it is chosen as a channel of interest. The corresponding channel in the H(f) data block is gathered into a complex variable parameter and stored in the data block that was prepared previously 

for the blanked H(f). 

consist of calculated H(f) data only at those frequencies where the 

If the value of this channel is greater 

When the loop is complete, the blanked H(f) will 

11 
pulser or y2(f) passed all the necessary tests. The remainder of the 

blanked H(f) block will be filled with zeros. Because the HP 5451C 

stores frequency domain data with both real and imaginary information in 

a combined complex channel, the blanked H(f) contains blanked phase 

information as well as blanked magnitude. KPF3 then loops three times 

to generate a blanked version of each H(f), HPOP/LPOP, MCC/HPOP, and 

MCC/LPOP. 

parameters necessary to run the plot program. Finally, KPF3 transfers 

control to KPF5, the POGO plot routine. 

KPF3 then jumps to the section that defines the variable 

KEYBOARD PROGRAM FILE, RECORD 4 

KPF4 is a single-part program, which calculates the H(f)s, HPOP/LPOP, 

MCC/HPOP, and MCC/LPOP by matching the outputs and inputs "directly" 

rather than ratioing H(f)s, which have all been referenced to the 

pulser. This program (KPF4) uses several variable parameters, which 

must have been previously defined by running the first three files 

containing the RATIO software. These variable parameters are VP1 = 

block size; VP2 = number of ADS: Throughput records; VP2000 through 

VP2003 = calibration factors for channels A through D, respectively; 

VP2004 = frequency resolution (Af); and VP2030 = minimum value for the 

blanking routine. 

Throughput File. 

disc (starting with record zero) via KPFl (RATIO software, part 1). The 

data may be written to the disc and the necessary variable parameters 

defined independently of the RATIO software. It is recommended, however, that all programs be operated in sequence. The direct POGO 

analysis saftware (KPF4) writes over the data blocks generated via the 

RATIO software. This program therefore should not be initiated until 

all the required ratio data blocks have been reproduced. These data 

blocks include all PSDs and XPSDs (ref. pulser), which are not recalculated by the DIRECT software. 

KPF4 also retrieves time domain data from the ADC 

These data must have been written previously on the 

Immediately after clearing the data 

blocks, KPF4 begins a loop that operates three times, The loop reads 

the correct data channels from the disc, Fourier transforms the data, 

calibrates the data, and calculates averaged PSDs via the special subroutine of the 5451C. KPF4 then calculates the H(f) and y2(f) from the 

12 
averaged PSD data. 

appropriate data blocks. 

The H(f), y2(f), and XPSDs are then stored in the 

(See "DIRECT POGO Program Menu," appendix C.) 

KPF4 now transfers control to KPF3 at the point where the H(f) blanking 

loop begins. 

eters that describe the location of the DIRECT H(F)s. 

blanked H(f)s are calculated using the same minimum value specified by 

the user during the RATIO calculations. If the user has entered the 

POGO software in the DIRECT calculations and wishes to change the minimum blanking value, the user simply jumps to label 43 of KPF4. 

Before jumping to KPF3, KPF4 defines the variable paramOnce in KPF3 the 

Upon returning from the blanking routine, KPF4 defines the variable 

parameters necessary to operate the POGO plot program (KPF5). 

transfers control to the plot routine. 

KPF4 then 

KEYBOARD PROGRAM FILE, RECORD 5 

KPF5 is entitled "POGO Plot Software.'' 

the RATIO and the DIRECT software. 

eters that must be defined by the respective software whose data is to 

be plotted. The program is organized into several separate routines, 

including a plot routine, a hard copy routine, a delay routine, and a 

routine that sets up and plots all the H(f)s in three different formats. 

The program sets up and automatical ly plots all the data generated by 

the respective RATIO and DIRECT programs. 

menu and allows the user to replot any of the data blocks. The plot 

program is geared to run with a Tektronics 4052 graphics terminal and a 

Tektronics hard copy unit. Because of various incompatibilities between 

the 5451C and the Tektronics terminal with respect to the time required 

to transmit plot commands and the time required to execute them, a delay 

routine is incorporated in the plot program. This subroutine simply 

counts from one to 50 and returns. The routine is called in several 

locations where a time delay between plot commands is necessary. 

This software operates with both 

KPF5 uses several variable paramThe KPF5 prints a data block 

The plot program uses several variable parameters that establish which 

program (RATIO or DIRECT) has generated the data being plotted. The 
plot program also labels each plot with test ID information in the upper 

right-hand corner of the plot. This information is stored as message 

number one in each of the text buffers one and two. Text buffer #1 is 

used for the RATIO data, while text buffer #2 is used with the DIRECT 

data. Message #1 should be changed for each new set of test data. The 

message may be changed by executing the following set of operations from 

the 5451C terminal: 

Step # Command 5451C Status 

1 Y 5403 (nl) busy 

This comnand calls text buffer nl (1 for RATIO, 2 for DIRECT) 

into the computer core and activates the editing commands. 

2 /RO 1 busy 

This command tells the 5451C to replace message #le 

3 01 busy 

4 (Test I D) busy 

5 /" busy 

This sequence of commands results in the test ID being recognized 

as message 01. The /* defines the end of the message. 

6 / busy 

This command terminates the text buffer- edit mode. 

To allow the user to enter the program flow for special purposes, the 

POGO software has many labels throughout the five KPFs. Listed below 

are the various jump commands and-their uses. 

JO1 

This command starts the POGO software, initially setting up the 

calibration factors, etc, and reading the analog data. 

J 10 1 

This command enters POGO Software Part 1 after all the initial 

values have been entered and the analog data has been stored on 

disc in the ADC Throughput File. If this command is to be executed, 

the user must first be sure that the variable parameters that contain the values for the blocksize, calibration factors, number of 

records of data, and frequency resolution (Af) are defined correctly and that the correct time domain data is stored on the ADC 

Throughput File. 

14 
J 20 2 

This command begins the RATIO calculations for H(f)s and y2(f)s. 

This command may be executed if the proper data blocks reside in 

core in the correct block numbers. The data blocks necessary are 

H (f) LPOP/Pulser Block 12 

Y2 (f) II Block 13 

H (f) HPOP/Pu 1 ser Block 14 

Block 15 

H (f) MCC/Pulser Block 16 

Y2 (f) It Block 17 

II Y2 (f) 

H 30 3 

This command may be used when the user wishes to recalculate the 

blanked RATIO frequency response functions. The user will have the 

opportunity to re-establish the type of blanking [pulser or y2(f)] 

and/or the minimum value for that blanking. 

parameters are defined and the program control is transferred to 

the plot routine. 

The RATIO autoplot 

J 31 3 

This command is preliminary to the POGO Plot Routine. This command 

enters'KPF3 and defines the variable parameters necessary to run 

the automatic plot portion of the plot routine. After these parameters are defined, program control is automatically transferred 

to the plot routine. This command should be used only when the 

user wishes to enter the autoplot routine with RATIO data blocks. 

This command might be useful if, for example, the user wants to 

change the test ID message in the RATIO text buffer after the 

POGO software has completed the data calculations. The user can 

stop program execution and edit the text buffer, then return to 

the autoplot sequence. 

J 40 4 

This command begins the DIRECT POGO Software. This should be used 

only after the RATIO program has been run, defining the appropriate variable parameters, and writing the time domain data on 

the ADC Throughput File. 

J 43 4 

This command enters KPF4 where necessary variable parameters are 

defined just prior to transferring control to the H(f) blanking 

routine in KPF3. This command will allow the user to calculate 

D I RECT blanked H (f) s. 
This command causes the computer to begin execution in KPF4 at 

the point where the variable parameters that control the autoplot routine for DIRECT data blocks are defined. Program control 

is automatically transferred to the plot routine. 

J 53 5 

This command will cause the plot program to display on the terminal the appropriate menu corresponding to the data stored in the 

data blocks. The plot program prompts the user to set the display 

scale as desired, then press the continue button to allow the program to plot the data block on the graphics terminal. 

mand is useful when the user wishes to return to the plot program 

after the machine has been idled and the plot routine pointers 

have been changed. 

This comAppendix A describes the flow of the POGO software. 

a complete list of all the program steps along with a description of 

each. 

with the POGO software. 

buffers used with the POGO software. 

output from the POGO software. 

Appendix B contains 

Appendix C contains a listing of the text record messages used 

Appendix D contains a l i s t i n g o f both text 

Appendix E contains sample data 

REFERENCES 

1. Bendat, J. S., and A. G. Piersol. Random Data: Analysis and 

Measurement Procedures. John Wiley E Sons, New York, 1971. 

2. Schiesser, W. E. Statistical Uncertainty of Frequency Response 

Determined from Random Signals. Weston-Boonshaft and Fuchs, NASA 

Bull et i n 71 1 -C2. 

3. Hewlett-Packard. 5451C Fourier Analyzer System Manual (Binder 

No. 1). Mar. 1979. 

16 

APPENDIX A 

POGO SOFTWARE FLOWCHART 

AI 

RATIO POGO SOFTWARE - PART 1 FLOWCHART 

Display the prompt and allow the 

records in the 
A2 

RAT1 0 POGO SOFTWARE - PART 1 FLOWCHART (Continued) 

Steps 132 - 136 

Initialize the AOC Throughput and 

acquire YP2 records of four channel s 

each 

Set up the variable parameters 

18 
RAT1 0 POGO SOFTWARE - PART 1 FLOWCHART (Continued) 

t 

1 Step 226 I I Initialize the off-1 ine BSFA I 

Calculate H(f) and y2(f) and store 

19 

A3 
A4 

RATIO POGO SOFTWARE - PART 1 FLOWCHART (Concluded) 

c-0 Step 377 

Loop for all 3 sets of POGO data 

I Step 383 I 

Jump to Label 20 Keyboard Program 2 

t 

20 
RATIO POGO SOFTWARE - PfiRT 2 FLOWCHART 

Start Label 20 

# 

Steps a 111-139 

Get the H(f) and y2(f) data 

21 
A6 

RATIO POGO SOFTWARE - PART 2 FLOWCHART (Continued) 

Y Invert y2( f) 1 

22 
RATIO POGO SOFTWARE - PART 2 FLOWCHART (Continued) 

Put the ratio y2(f) 

new data block 

into the 

where: H(f) = a + ib 

and H(f) =c + id 

1 

Set ImH(f) to 0 

23 
A8 

=o Loop to get all the data channels 

in the block for one set of ratio 

calculations 

RATIO POGO SOFTWARE - PART 2 FLOWCHART (Concluded) 

Q I 

1 Step 375 1 I Put the ratio H(f) into the new I data block. 2/1 

: Increment the channel counter 

Steps 393-41 2 

Jump to Label 30 in program file 3 

Step 430 <i> 

24 
POGO SOFTWARE BLANKING ROUTINE 

b Steps 5 - 23 

Set up variable parameters for ratio 

H(f) blanking; jump to label 32 

t 

Steps 31 - 91 

Jump to label 50 in 
A1 0 

POGO SOFTWARE BLANKING ROUTINE (Continued) 

coherence blanking 

Define the VP31 for pulser blanking 

Display the correct data block and ask 

the user to set the minimum blanking 

c 

Steps 148 - 155 

Define VP39 for blanking routine 

Convert the block to be blanked to 

rectangular coordinates 

Steps 168 - 179 

Clear a block and establish qualifiers 

for the blanked H(f) 

6 26 
POGO SOFTWARE BLANKING ROUTINE (Continued) 

Step 208 

Set H(f) channel to zero 

+ 

Steps 186 - 198 

Define consecutive channel counters 

in VP32, VP33, and VP34 

A Step 204 

If channel n < minimum ’> I 

/ If \ Yes 

’ Step 243. 

\channel n < channel n-wl 

A Step 251 

b 

A1 1 

27 
A1 2 

POGO SOFTWARE BLANKING ROUTINE 

Q 

(Concluded) 

Q 

Put H(f) data in the blanked data block 

Increment channel counters 

t 

I Steps 294 - 306 I I - Increment block counters I 

I I Step 313 

Loop for all H(f) data blocks 
AI 3 

DIRECT POGO SOFTWARE FLOWCHART 

Q Start Label 40 

Steps 13 - 55 

Set up variable parameters 

for program operation 

t 

Clear the data blocks prior 

to the calculations 

Step 92 

Initial ize the off-1 ine BSFA software 

I Steps 99 - 106 

Calculate the number of the 

vari ab1 e parameter containing the correct cal i bration 

factor 

29 
A1 4 DIRECT POGO SOFTWARE FLOWCHART (Continued) 

Q 

Steps 117 - 146 

Read the analog data from the disc. 

Convert the data to frequency domain, 

calibrate it, and store the input in 

Block 1 and the output in Block 2 

Step 151 

# 

Step 163 

Store the H(f)s in Blocks 8, 10, and 

12, and the y2(f)s in Blocks 9, 11, 

and 13. 

store them in 

t I Steps 233 - 239 I 

Increment the block counters 

I 

30 
DIRECT POGO SOFTWARE FLOWCHART (Concl uded) 

Loop for all three sets of H(f) 

31 
AI 6 

POGO SOFTWARE PLOT ROUTINE 

art - Label 5 

Read in the correct text buffer 

Set up the terminal as the plot device 

Step 15 

Set up to plot all log vertical plots 

in 3 decades 

tart - Plot Loo 

Determine plot label number 

c no 1 

Steps 82 - 89 

Set up the plot type, 

jump to the plot routine 

32 
POGO SOFTWARE PLOT ROUTINE (Continued) 

Step 93 

Jump to the hard copy routine 

8 Retur 

Step 101 

Decrement bl oc k counter 

I 

Step 116 I Jump to the delay routine 

33 
AI 8 

POGO SOFTWARE PLOT ROUTINE (Continued) 

Set up the plot and jump 

to the plot routine 

34 
POGO SOFTMARE PLOT ROUTINE (Continued) 

w 

Steps 266 - 273 

Set up to plot H(f) phase and 

jump to the plot routine 

Plot the selected data block along 

with data and test annotation 

35 
A20 

POGO SOFTWARE PLOT ROUTINE (Continued) 

8 Return 

Steps 277 - 283 

Label the phase plot with 

Step 288 

Jump to the hard copy routine 

Set up to plot H(f) magnitude 

36 
A2 1 

. Step 307 

Jump to the hard copy routine 

POGO SOFTWARE PLOT ROUTINE (Continued) 

r 

Step 322 

Jump to the delay routine ; 

1 Set up to plot H(f) log magnitude] 

37 
A22 

POGO SOFTWARE PLOT .ROUT1 NE (Continued) 

Step 334 I Jump to Label 52 

Return 8 

38 
POGO SOFTWARE PLOT ROUTINE (Concl uded) 

tart - Delay Routi 

a Step 381 

39 

APPENDIX B 

POGO SOFTWARE LISTING 

KEYBOARD FILE 1 - RATIO POGO SOFTWARE PART 1 

1L 0 

5 BS 4096 

9 CL 

12 CL 1 

16 CL 2 

20 CL 3 

24 CL 4 

28 CL 5 

32 CL 6 

36 Y 5814 

40 MS 34 

44 MS 14 

48 Y R 1 

53 BS 1D 

57 MS 14 

61 Y R 2000 2003 

67 Y * 2000 2000D 100 

74 Y * 2001 20010 100 

81 Y * 2002 20020 100 

88 Y * 2003 2003D 100 

95 MS 14 

99 Y R 2 

104 MS 14 

108 Y R 2004 

Label 0 

Set blocksize to 4096 

Clear blocks 0 through 6 

Call user program 5414 (blank 

terminal screen) 

Set text record pointer to zero 

(default) 

Read next text record (message #1) 

Input from terminal VPlt 

(blocksize) 

Set blocksize to. VP1 

Read next text record (message #2) 

Input from terminal VP2000, 

VP2001, VP2002, and VP2003 

(calibration factors) 

VP2000 = VP2000 * 100 

VP2001 = VP2001 * 100 

VP2002 = VP2002 * 100 

- 

VP2003 = VP2003 * 100 

Read next text record (message #3) 

Input from terminal VP2 (number 

of data acquisition loops) 

Read next text record (message #4) 

Input from terminal VP2004 (Af) 

?This means the variable of parameter 1. 

41 
02 

KEYBOARD FILE 1 - RATIO POGO SOFTWARE PART 1 (Continued) 

113 Y * 2004 2004D 10 VP2004 = VP2004 * 10 

120 MS 34 20 

125 MS 14 

129 D 

132 MS 32 

136 MS 22 4 2D 

142 L 10 

146 Y - 3 18 

Set text record pointer to 20 

Read next text record (message #7) 

Display block 0 (used as program 

pause) 

Set ADC Throughput File pointer 

to 0 

Write analog data to the ADC 

throughput file. No. of 

records = 20 (4 channels each) 

Label 10 

Set VP3 to 18 

152 Y - 4 19 Set VP4 to 19 

158 Y - 5 22 Set VP4 to 22 

164 Y - 6 23 Set VP6 to 23 

170 Y - 7 2 

176 Y - 8 12 

182 L 11 

186 CL 

189 CL 1 

193 CL 2 

197 CL 3 

201 CL 4 

205 CL 5 

209 CL 6 

9 3 213 Y - 

Set VP7 to 2 

Set VP8 to 12 

Label 11 

Clear blocks 0 through 6 

Set VP9 to 3 

219 Y A+ 10 7D 1999 VPlO = VP7 + 1999 

226 Y 47 0 0 0 Call user program 41; nl=0= 

center frequency of the band of 

interest, n2=0=width of the band 

of interest, n3=O=ADC throughput 

start record, (Initializes offline BSFA) 

233 L 12 

237 Y 45 2 0 7D 

Label 12 

Call user program 45; nl=2=block 

number where the data will be 

stored, n2=0=number of Hanni ngs 

applied to the data, n3=VP7= 

channel that will be read from 

the disc. (Off-line BSFA) 42 
KEYBOARD FILE 1 - RATIO POGO SOFTWARE PART 1 (Continued) 

244 Y 

251 * 

256 : 

261 * 

266 : 

271 SP 

277 # 

283 CH 

289 X< 

293 X> 

297 Y A+ 

303 X< 

307 X> 

311 L 

315 : 

320 * 

325 Xc 

329 X> 

333 Y A+ 

339 # 

345 Y A+ 

351 Y A+ 

358 Y A+ 

365 Y A+ 

45 

2 

2 

1 

1 

1 

12 

1 

1 

8D 

8 

2 

8D 

13 

9D 

9D 

9D 

-9D 

9 

13 

4 

5 

6 

7 

1 

-1 OD 

100 

2OOOD 

100 

2 

2D 

2 

2004D 

20 

4 

5D 

6D 

0 1 Call user program 45; nl=l 

n2=0, n3=1 

Multiply block 2 by VP(VPl0)' 

Divide block 2 by 100 

Multiply block 1 by VP2000 

Divide block 1 by 100 

Compute the average auto- and 

cross-power spectrums, where 

block nl=input data block and 

bl ock nl+1 =ou tpu t, n2=2 speci - 

fies dual channel, n3=2 specifies double precision 

2 

0 Loop through label 12 VP2 times 

2 Calculate transfer function data 

where nl=input data block, n2=2 

specifies dual channel, n3=2 

specifies double precision 

Load block 1 into block 0 

Store block 0 into block VP8 

VP8 = VP8 + 1 

Load block 2 into block 0 

Store block 0 into VP8 [y2(f)] 

Label 13 

Divide block VP9 by VP2004 

Multiply block VP9 by 20 

Load block VP9 into block 0 

Store block 0 into block VP(VP9) 

VP9 = VP9 + 1 

0 Loop through label 13 four times 

VP4 = VP4 + 1 

2 VP5 = VP5 + 2 

2 VP6 = VP6 + 2 

VP7 = VP7 + 1 

CH(f)l 

'The minus sign in front of the VP number means to use the value in the VP 

that is specified by the value of the VP given (i.e.¶ the value of the VP 

speci fi ed by VPl 0) . 

43 
KEYBOARD FILE 1 - RATIO POGO SOFTWARE PART 1 (Concluded) 

371 Y A+ 8 

377 # 11 3 0 

383 J 20 2 

388 . 

VP8 = VP8 + 1 

loop through label 11 three times 

Jump to label 20 in keyboard 

stack 2 

End 

44 
KEYBOARD FILE 2 - RATIO POGO SOFTWARE PART 2 

1L 

5 TR 

9 TR 

13 TR 

17 Y - 

23 Y - 

29 Y - 

35 Y - 

41 Y - 

47 Y - 

53 Y - 

59 Y 

65 Y 

71 Y 

- 

- 

77 Y - 

83 Y :. 

90 Y A+ 

95 Y - 

101 Y - 

107 L 

111 Y TR 

118 Y TR 

125 Y TR 

132 Y TR 

139 Y TR 

146 Y - 

152 L 

156 Y X< 

20 

12 

14 

16 

3 

4 

5 

6 

7 

8 

9 

10 

11 

12 

13 

14 

14 

15 

17 

21 

21 

21 

21 

21 

21 

0 

22 

3000 

3 

6 

7 

14 

12 

16 

14 

16 

12 

13 

15 

1D 

17 

13 

- 5D 

3D 

4D 

-1 2D 

5D 

0 

-4D 

2 

Label 20 

Convert blocks 12 ) 

to rectangul ar 

coordinates Convert blocks 14 

Convert blocks 16 1 

Set VP3 to 3 

Set VP4 to 6 

Set VP5 to 7 

Set VP6 to 14 

Set VP7 to 12 

Set VP8 to 16 

Set VP9 to 14 

Set VPlO to 16 

Set VPll to 12 

Set VP12 to 13 

Set VP13 to 15 

VP14 = VP1/2 

VP14 = VP14 + 1 

Set VP15 to 17 

Set VP17 to 13 

Label 21 

0 Get the block qualifiers from 

block VP(VP5) and put them in 

VP21 - VP25 

1 

1 

Put the block qualifiers stored 

in VP21 - VP25 into block VP3 

Put the block qualifiers into 

block VP4 

Get the block qualifiers from 

block VP(VPl2) and put them into 

VP21 - VP25 

1 Put the block qualifiers into 

block VP5 

Set VPO to 0 

Label 22 

OD Get the complex data from block 

VP(VP4), channel VPO, and put 

the values into complex VP3000 

45 
86 

KEYBOARD FILE 2 - RATIO POGO SOFTWARE PART 2 (Continued) 

163 Y X< 

170 Y X< 

177 Y Xc 

184 Y IF 

192 Y : 

199 Y If 

207 Y : 

214 Y A+ 

221 Y A226 Y : 

233 Y IF 

241 Y - 

247 Y X> 

254 Y * 

261 Y * 

268 Y * 

275 Y * 

282 Y * 

289 Y * 

296 Y A+ 

303 Y A+ 

310 Y A317 Y : 

324 Y : 

331 Y IF 

339 Y IF 

347 Y - 

3001 - 5D OD 

2005 12D OD 

2006 -12D OD 

2005 

2005 

2006 

2006 

2007 

2007 

2007 

2007 

2007 

2007 

2009 

201 0 

201 1 

201 2 

201 3 

201 4 

201 5 

201 6 

201 7 

0 7 0 

1 2005D 

0 5 0 

1 2006D 

20050 20060 

1 2007D 

0 1 2 

0 

5D OD 

2900D 

2901 D 

2901 D 

2900D 

2902D 

29031) 

201 30 

20090 

201 1D 

2902D 

2903D 

2902D 

2903D 

2902D 

2903D 

201 4D 

201 OD 

201 20 

2904 2016D 2015D 

2905 20170 2015D 

2 904 7 1 2 

2904 -7 1 1 

2904 0 

Get the complex data from block 

VP(VP5) , channel VPO and put 

them into complex VP3001 

Get the real data from block 

VP12, channel VPO and put it 

into VP2005 

Get the real data from block 

VP(VP12), channel VPO and put 

it into VP2006 

If VP2005 = 0, skip seven steps 

VP2005 = 1/VP2005 

If VP2006 = 0, skip five steps 

VP2006 = 1/VP2006 

VP2007 = VP2005 + VP2006 

VP2007 = 1/VP2007 

If VP2007 > 0, skip one step 

Set VP2007 to 0 

VP2007 = VP2007 - 1 

Put VP2007 into the real part 

of block VP5, channel WPO 

VP2009 = VP2900 * VP2902 (ac) 

VP2010 = VP2901 * VP2903 (bd) 

VP2011 = VP2901 * VP2902 (bc) 

VP2012 = VP2900 * VP2903 (ad) 

VP2013 = (VP2902)2 (c2) 

VP2014 = (VP2903)2 (d2) 

VP2015 = VP2013 + VP2014 (c2+d2) 

VP2016 = VP2009 + VP2010 (ac+bd) 

VP2017 = VP2009 - VP2012 (bc-ad) 

VP2904 = VP2016/VP2015 

VP2905 = VP2017/VP2015 i[( ] 

If VP2094 > 7, skip one step 

If VP2904 - > -7, skip one step 

Set VP2904 to 0 

[~~

(bc-ad) 

c2+d2) 

46 
B7 

KEYBOARD FILE 2 - RATIO POGO SOFTWARE PART 2 (Concluded) 

353 Y IF 2905 

361 Y IF 2905 

369 Y - 2905 

375 Y X> 3002 

382 Y A+ 0 

387 # 22 

393 Y A+ 3 

398 Y A+ 4 

405 Y A+ 5 

412 Y A+ 12 

419 # 21 

425 J 30 

430 . 

7 1 2 

-7 1 1 

0 

4D OD 

140 0 

40 2 

50 2 

12D 2 

3 0 

3 

If VP2905 > 7, skip one step 

If VP2905 - > -7, skip one step 

Set VP2905 to 0 

Put complex VP3002 into block 

VP4, channel VPO 

VPO = VPO + 1 

Loop through label 22 VP14 times 

VP3 = VP3 + 1 

VP4 = VP4 + 2 

VP5 = VP5 + 2 

VP12 = VP12 + 2 

Loop through label 21 three times 

Jump to label 30, keyboard stack 3 

End 

47 
08 

1L 

5Y - 

17 Y - 

11 Y - 

23 J 

27 L 

31 Y - 

37 Y - 

43 Y - 

49 Y - 

55 Y 

61 Y 

- 

- 

67 Y - 

73 Y - 

79 Y - 

91 Y - 

85 Y - 

97 J 

102 L 

106 MS 

191 MS 

115 Y R 

120 Y IF 

128 Y A+ 

135 X< 

139 MS 

143 Y R 

148 Y : 

155 Y A160 L 

KEYBOARD FILE 3 - RATIO POGO SOFTWARE PART 3 

30 

31 

35 

36 

32 

31 

3 

4 

5 

6 

7 

8 

9 

10 

11 

12 

13 

50 

32 

34 

14 

30 

30 

31 

31 D 

14 

20 30 

39 

39 

33 

7 

6 

3 

1 

27 

16 

14 

12 

10 

8 

6 

25 

24 

125 

5 

82 

0 

31 D 

1 OD 

Label 30 

Set VP31 to 7 

Set VP35 to 6 

Set VP36 to 3 

Jump to label 32 

Label 31 

Set VP3 to 1 

Set VP4 to 27 

Set VP5 to 16 

Set VP6 to 14 

Set VP7 to 12 

Set VP8 to 10 

Set VP9 to 8 

Set VPlO to 6 

Set VPll to 25 

Set VP12 to 24 

Set VP13 to 125 

Jump to label 50 in Keyboard 

File 5 

Label 32 

Set the text record pointer to 82 

Read next text record (type of 

bl anki ng routine 

Input from terminal VP30 

1 2 . IF VP30>0, skip 1 step 

11 VP31 = VP31 + 11 

Load blanking block (VP31) 

Read the next text record 

(minimum blanking value) 

Input from terminal VP2030 

VP39 = VP39 - 1 

Label 33 

2 VP39 = VP1/2 

164 TR 35D 

48 
B9 

KEYBOARD FILE 3 - RATIO POGO SOFTWARE PART 3 (Concluded) 

168 CL 360 

172 Y TR 21 

179 Y TR 21 

186 Y - 32 

192 Y - 33 

198 Y - 34 

204 L 34 

214 Y x< 2032 

208 Y - 3000 

221 Y X< 2033 

228 Y X< 2034 

235 Y IF 2033 

243 Y IF 2033 

251 Y IF 2033 

259 Y X< 3000 

266 Y x, 3000 

273 Y A+ 

278 Y A+ 

283 Y A+ 

288 # 

294 Y A+ 

301 Y A+ 

306 Y A+ 

313 # 

319 < 

322. 

32 

33 

34 

35 

36 

31 

34 

33 

3 5D 

361, 

0 

1 

2 

0 

310 

31D 

310 

20300 

20320 

2034D 

35D 

360 

39D 

3 5D 

31 D 

3 

0 

1 

320 

3 3D 

34D 

3 

2 

1 

33D 

338 

2 

300 

Clear block BP36 

Get the block qual if iers from 

block VP35 and put them into 

VP21 - VP25 

Put the block qualifiers stored 

in VP21-VP25 into block VP36 

Set VP32 to 0 

Set VP33 to 1 

Set VP34 to 2 

Label 34 

Set VP3000 to 0 

Get the real data from block 

VP31, channel VP32 and store it 

in VP2032 

Get the real data from block 

BP31, channel VP33 and store it 

in VP2033 

Get the real data from block 

VP31, channel VP34 and store it 

in VP2034 

-2 If VP2033<VP2030, skip 3 steps 

-2 If VP2033<VP2032, skip 2 steps 

-2 If VP2033<VP2034, skip 1 step 

Get the complex data from block 

VP35, channel VP33 and store it 

in VP3000 

Put the complex data stored in 

VP3000 into block VP36, channel 

VP33 

VP32 = VP32 + 1 

VP33 = VP33 + 1 

VP34 = VP34 + 1 

Loop through label 34 VP39 times 

VP35 = VP35 + 2 

VP36 = VP36 + 1 

VP31 = VP31 + VP3O 

Loop through label 33 three times 

Subreturn 

End 

49 
BlO 

1L 

5 x< 

9 x> 

13 Y - 

19 Y I 

25 Y - 

31 Y - 

37 Y - 

49 Y - 

55 Y - 

43 Y - 

61 L 

65 CL 

68 CL 

72 CL 

76 CL 

80 CL 

84 CL 

88 CL 

92 Y 

99 Y A+ 

106 Y A+ 

113 L 

117 Y 

124 Y 

131 * 

136 : 

141 * 

146 : 

40 

18 

20 

3 

4 

8 

10 

12 

14 

16 

18 

41 

1 

2 

3 

4 

5 

6 

41 

5 

7 

42 

45 

45 

2 

2 

1 

1 

151 SP 1 

KEYBOARD FILE 4 - DIRECT POGO SOFTMARE 

8 

14 

3 

4 

4 

2 

3 

2 

0 0 0 

-4D 1999 

-3D 1999 

2 0 - 3D 

1 0 -4D 

- 7D 

100 

- 5D 

100 

2 2 

Label 40 

Load block 18 into block 0 

Store block 0 into block 20 

Set VP3 to 8 

Set VP4 to 14 

Set VP8 to 3 

Set VPlO to 4 

Set VP12 to 4 

Set VP14 to 2 

Set VP16 to 3 

Set VP18 to 2 

Label 41 

Clear blocks. 0 through 6 

Call User Program 41, where 

nl=n2=n3=0 (Initialize offline BSFA) 

VP5 = 1999 + VP(VP4) 

VP7 = 1999 + VP(VP3) 

Label 42 

Call User Program 45; nl=2, n2=0, 

n3=VP (VP3) (of f-1 i ne BSFA) 

Call User Program 45; nl=l , n2=0 , n3=VP (VP4) 

Multiply block 2 by VP(VP7) 

Divide block 2 by 100 

Multiply block 1 by VP(VP5) 

Divide block 1 by 100 

Cal cul ate averaged 2-channeldouble precision power spectrum 

50 
157 # 

163 CH 

169 X< 

173 X> 

177 Y A+ 

183 X< 

187 X> 

191 : 

196 * 

201 : 

206 * 

211 x< 

215 X> 

219 Y A+ 

225 X< 

229 X> 

233 Y A+ 

239 Y A+ . 

245 # 

251 L 

255 Y - 

261 Y - 

267 Y - 

273 J 

278 L 

282 Y - 

288 Y - 

294 Y - 

306 Y - 

312 Y - 

318 Y - 

- 300 Y 

B11 

KEYBOARD FILE 4 - DIRECT POGO SOFTWARE (Continued) 

42 2D 

1 2 

1 

30 

3 

2 

3D 

5 20040 

5 20 

6 2004D 

6 

5 

40 

4 

6 

4D 

3 

4 

41 

43 

31 

35 

36 

32 

44 

3 

4 

5 

6 

7 

8 

9 

20 

3 

9 

8 

5 

3 

2 

19 

12 

10 

8 

8 

8 

0 Loop through label 42 VP2 times 

Calculate H(f) and y2(f) from 

the averaged power spectrum data 

Load block 1 into block 0 [H(f)] 

Store block 0 into block VP3 

VP3 = VP3 + 1 

Load block 2 into block 0 [y2(f)] 

Store block 0 in block VP3 

Divide block 5 by VP2004 

Multiply block 5 by 20 

Divide block 6 by VP2004 

Mu1 ti ply block 6 by 20 

Load block 5 into block 0 

Store block 0 in block VP4 

VP4 = VP4 + 1 

Load block 6 into block 0 

Store block 0 into block VP4 

VP3 = VP3 + 1 

VP4 = VP4 + 1 

0 Loop through label 41 three times 

Set VP31 to 9 

Set VP35 to 8 

Set VP36 to 5 

Jump to label 33 in Keyboard File 3 

Label 44 

Set VP3 to 2 

Set VP4 to 19 

Set VP5 to 12 

Set VP6 to 10 

Set VP7 to 8 

Set VP8 to 8 

Set VP9 to 8 

2 

- Label 43 

51 
91 2 

KEYBOARD FILE 4 - DIRECT POGO SOFTWARE (Concluded) 

324 Y - 10 8 

330 Y - 11 15 

336 Y - 12 58 

342 Y - 13 150 

348 J 50 5 

353 . 

Set VP10 to 8 

Set VPll to 15 

Set VP12 to 58 

Set VP13 to 150 

Jump to lable 50 in Keyboard 

File 5 (Plot Routine) 

End 

52 
1L 50 

5 Y 5838 

10 Y 5821 

15 Y 5865 

20 L 51 

24 Y 26 

30 Y IF 4 

38 Y IF 4 

46 Y IF 4 

54 Y IF 4 

62 Y IF 4 

70 Y IF 4 

78 J 110 

82 Y 5809 

- 

89 J 100 

93 J 120 

97 L 52 

101 Y A- 4 

30 

6 

3 

B13 

KEYBOARD FILE 5 - POGO PLOT ROUTINE 

40 

5D 5 0 

6D 4 0 

7D 3 0 

8D 2 0 

9D 1 0 

1 OD 1 2 

0 0 .O 

106 # 51 11D 0 

112 L 53 

116 J 130 

120 Y 5814 

124 MS 34 12D 

129 MS 14 

Label 50 

Call User Program 5838; nl=VP3 

(Read text buffer VP3 into core) 

Call User Program 5821; nl=6 

(Set up the terminal as the 

plot device) 

Call User Program 5865; nl=3 

(Set log plots to plot 3 decades, 

vertical scal e) 

Label 51 

Set VP26 to the value of VP4 

If VP4 = VP5, skip five steps 

If VP4 = VP6, skip four steps 

If VP4 = VP7, skip three steps 

If VP4 = VP8, skip two steps 

If VP4 = VP9, skip one step 

If VP4 > VP10, skip one step 

Jump to label 110 

Call User Program 5809; nl=0, 

n2=0, n3=0 (Set up to plot reall 

magnitude, linear horizontal 

scale, scale switch at 12 

o 'clock) 

Jump to label 100 

Jump to label 120 

Label 52 

VP4 = VP4 - 1 

Loop through label 51 VPl1 times 

Label 53 

Jump to label 130 

Call User Program 5814 (Blank 

the terminal screen) 

Set the text record pointer to 

VP12 

Read the next message (plot 

menu ) 

Input VP4 (data block number to 

be plotted 

133 Y R 4 

53 
81 4 

138 Y - 

144 Y IF 

152 Y IF 

160 Y A+ 

167 MS 

171 D 

175 Y 

179 J 

183 J 

187 D 

191 J 

195 L 

199 Y 

203 Y 

207 Y 

212- Y 

216 Y 

221 Y 

227 Y 

232 < 

235 L 

26 

4 

30 

26 

14 

40 

5809 

100 

120 

40 

53 

100 

581 4 

5829 

581 5 

581 6 

581 7 

5808 

581 9 

110 

239 Y IF 4 

247 Y IF 30 

KEYBOARD FILE 5 - POGO PLOT ROUTINE (Continued) 

4D Set VP26 to the value of VP4 

0 1 0 If VP30 = 0, skip 1 step 

1 OD 2 1 If VP4 - > VP10, skip 2 steps 

260 30 VP26 = VP26 + 30 

40 

26D 

975 

1 

600 

Read the next message (Set the 

scal e and press "CONTINUE" ) 

Display block VP4 

Call User Program 5809; nl=n2= 

n3=default (Set up the plot 

according to the display swi tches ) 

Jump to label 100 

Jump to label 120 

Display block VP4 

Jump to label 53 

Label 100 

Call User Program 5814 

Call User Program 5829 (Plot 

the full data block) 

Call User Program 5815; nl=\IP4 

(Plot the data from block VP4) 

Call User Program 5816 (Plot 

the defaulted axis) 

Call User Program 5817; nl=VP26 

(Label the vertical axis with 

text buffer message VP4 and the 

horizontal axis with the 

default label ) 

Call User Program 5808.; nl=970, 

n2=600 (Position the cursor to 

y=97.0% of the vertical plot 

window and x=60.0% of the 

hori zontal plot window) 

Write text buffer message #1 

Subreturn 

Label 110 

1 OD 2 1 If VP4 - > VP10, skip 2 steps 

0 1 0 If VP30 = 0, skip 1 step 

54 
KEYBOARD FILE 5 - POGO PLOT ROUTINE (Concluded) 

255 Y A+ 26 26D 30 VP26 = VP26 + 30 

262 TP 40 Convert block VP4 to polar coordi nates 

266 Y 5809 1 0 0 Call User Program 5809; nl=l , n2=0, n3=0 (Set up to plot 

imagi nary/phase , 1 i near hori - 

zontal, scale switch to 12 

0' clock) 

273 J 

277 Y 

283 Y 

288 J 

292 Y 

299 J 

303 J 

307 J 

311 TL 

315 Y 

322 J 

326 J 

330 J 

334 J 

338 L 

342 J 

346 Y 

350 < 

353 L 

100 

5808 

581 9 

120 

5809 

130 

100 

1 20 

4D 

5809 

1 30 

100 

120 

52 

120 

130 

5820 

130 

9 70 

26D 

0 

0 

130 

0 0 

0 0 

357 Y - 19 1 

363 L 131 

367 Y A+ 19 

372 # 131 50 0 

378 < 

381 . 

Jump to label 100 

Call User Program 5808; nl=970, 

n2=VP13 

Call User Program 5819; nl=VP26 

Jump to label 120 

Call User Program 5809; nl=0, 

n2=0, n3=0 

Jump to label 130 

Jump to label 100 

Jump to label 120 

Convert block VP4 to log 

polar coordinates 

Call User Program 5809; nl=O, 

n2=0, n3=0 

Jump to label 130 

Jump to label 100 

Jump to label 120 

Jump to label 52 

Label 120 

Jump to label 130 

Call User Program 5820 (Hard 

copy the terminal) 

Subreturn 

Label 130 

Set VP19 to 1 

Label 131 

VP19 = VP19 + 1 

Loop through label 131 fifty times 

Subreturn 

End 

55 

c1 

APPENDIX C 

POGO SOFTWARE TEXT RECORDS (FILE 4a) 

Line # Con tents 

Message #1 

0 

1 This is a 5451C program, written for POGO data analysis. 

2 reads 4 analog channels simultaneously and writes them directly to the 

3 disc via the ADC Throughput. The time domain data is then called from 

4 the disc and H(f)s calculated re. Pulser. H(f)s across devices are 

5 cal cul ated by ratios 28 JANUARY 80 

6 

7 

8 input signal-to-noise ratio. Then, enter Blocksize. (INTEGER LE 1024) 

9 I* 

The program 

Setup the ADC for the desired frequency resolution (Delta f), and 

Message #2 

10 

11 I" 

Enter a calibration factor for each channel. (4 - FLOATING POINT) 

Message #3 

12 Enter the number of data acquisition loops. (INTEGER) 

13 I* 

* Message #4 

14 

15 I" 

Enter Delta f as specified by the ADC. (FLOATING POINT) 

blessage #7 

20 Start the data tape. Press "CONTINUE." 

21 I* 

57 
c2 

Line # 

24 

25 

26 

27 

28 

29 

30 

31 

32 

33 

34 

35 

36 

37 

38 

39 

40 

41 

42 

43 

44 

45 

46 

47 

48 

49 

50 

51 

52 

53 

54 

55 

56 

57 

Contents 

Message #8 

RATIO POGO DATA PLOT MENU 

The program output is located in core memory as follows: 

BLOCK# 

3 

4 

5 

6 

7 

8 

9 

10 

11 

12 

13 

14 

15 

16 

17 

18 

19 

20 

21 

22 

23 

24 

25 

26 

27 

DATA 

Weighted H(f) HPOP/LPOP 

Weighted H(f) MCC/HPOP 

Weighted H(f) HCC/LPOP 

H ( f) HPOP/LPOP 

Coh(f) II 

H ( f ) NCC/HPOP 

Coh (f) 

H ( f) MCC/LPOP 

Coh(f) II 

H ( f) LPOP/Pul ser 

Coh(f) If 

H( f) HPOP/Pul ser 

Coh(f) II 

H (f) MCC/Pul ser 

Coh(f) 

PSD Pul ser 

PSD LPOP 

PSD HPOP 

PSD MCC 

Re XPSD LPOP/Pulser 

Im XPSD 

Re XPSD HPOP/Pulser 

Im XPSD 

Re XPSD MCC/Pulser 

Im XPSD 'I 

I1 

II 

II 

II 

Please enter the Block# you wish to plot. 

/* 

Message #9 

Set the scale and press "CONTINUE." 

/* 

58 
Line # 

58 

59 

60 

61 

62 

63 

64 

65 

66 

67 

68 

69 

70 

71 

72 

73 

74 

75 

76 

77 

78 

79 

80 

81 

. 82 

83 

84 

85 

86 

Con tents 

Message #10 

DIRECT POGO DATA PLOT MENU 

The program output is located in core as follows: 

BLOCK# DATA 

5 

6 

7 

8 

9 

10 

11 

12 

13 

14 

15 

16 

17 

18 

19 

Weighted H( f) HPOP/LPOP 

Weighted H( f) MCC/HPOP 

Weighted H(f) MCC/LPOP 

H ( f) HPOP/LPOP 

Coh( f) 11 

H (f ) MCC/HPOP 

Coh( f) I1 

H( f) MCC/LPOP 

Coh( f) I1 

Re XPSD HPOP/LPOP 

Im XPSD 

Re XPSD MCC/HPOP 

Im XPSD It 

Re XPSD MCC/LPOP 

Im XPSD 'I 

I1 

Please enter the block.# you wish to plot. 

/* 

Message #11 

Set the scale and press "CONTINUE". 

/* 

Message #12 

Do you want: 

/* 

Coherence blanking (enter 2) 

Pulser blanking (enter O)? 

Message #13 

Enter the minimum blanking value (floating point). 

/* 

59 

D1 

APPENDIX D 

POGO SOFTWARE TEXT BUFFERS (FILE 4b) 

Text Buffer #1 

RATIO POGO PLOT LABELS 

01 

(TEST ID) 

/* 

13 

/* 

HPOP/LPOP Ratio H (f) 

Pul ser B1 anked 

04 

/* 

MCC/HPOP Ratio H(f) 

Pul ser B1 anked 

05 

I* 

MCC/LPOP Ratio H(f). 

Pulser B1 anked 

06 

/* 

HPOP/LPOP Ratio H(f) - Polar 

07 

/* 

HPOP/LPOP Ratio Coh(f) 

08 

/* 

MCC/HPOP Ratio H(f) - Polar 

09 

/* 

MCC/HPOP Ratio Coh(f) 

10 

/* 

MCC/LPOP Ratio H(f) - Polar 

11 

/* 

MCCjLPOP Ratio Coh(f) 

61 
02 

Text Buffer #1 (Continued) 

12 

/* 

LPOP/Pulser H(f) - Polar 

13 

/* 

LPOP/Pulser Coh(f) 

14 

/* 

HPOP/Pulser H(f) - Polar 

15 

/* 

HPOP/Pulser Coh(f) 

16 

/* 

MCC/Pulser H(f) - Polar 

17 

/* 

MCC/Pulser Coh(f) 

18 

/* 

Pul ser PSD 

19 

/* 

LPOP PSD 

20 

/* 

HPOP PSD 

21 

/* 

MCC PSD 

22 

/* 

LPOP/Pul ser Real XPSD 

23 

/* 

LPOP/Pulser hag XPSD 

24 

/* 

HPOP/Pulser Real XPSD 

62 
Text Buffer #1 (Concluded) 

25 

/* 

HPOP/Pul ser Imag XPSD 

26 

/* 

MCC/Pul ser Real XPSD 

27 

/* 

MCC/Pul ser hag XPSD 

33 

/* 

HPOP/LPOP Ratio H( f) 

Coherence Blanked 

34 

MCC/HPOP Ratio H(f) 

Coherence B1 anked 

/* 

35 

/* 

MCC/LPOP Ratio H(f) 

Coherence Blanked 

Text Buffer #2 

DIRECT POGO PLOT LABELS 

01 

(TEST ID) 

/* 

05 

HPOP/LPOP Direct H( f) 

Pul ser B1 anked 

/* 

06 

MCC/HPOP Direct H( f) 

Pul ser B1 anked 

/* 

07 

/* 

MCC/LPOP Direct H( f) 

Pul ser Blanked 

63 
D4 

Text Buffer #2 (Continued) 

08 

/* 

HPOP/LPOP Direct H(f) - Polar 

09 

/* 

HPOPILPOP Direct Coh(f) 

10 

/* 

MCC/HPOP Direct H(f) - Polar 

11 

/* 

MCC/HPOP Di rect Coh ( f) 

12 

/* 

MCC/LPOP Direct H(f) - Polar 

13 

/* 

MCC/LPOP Direct Coh ( f) 

14 

/* 

HPOP/LPOP Direct Real XPSD 

15 

/* 

HPOP/LPOP Direct Imag XPSD 

16 

I* 

MCCIHPOP Direct Real XPSD 

17 

/* 

MCC/HPOP Direct Imag XPSD 

18 

/* 

MCC/LPOP Direct Rea1 XPSD 

19 

/* 

MCC/LPOP Direct Imag XPSD 

35 

/* 

HPOP/LPOP Direct H(f) 

Coherence B1 anked 

64 
.. 

Text Buffer #2 (Concluded) 

36 

I* 

MCC/HPOP Di rect H ( f) 

Co herence B1 an ked 

37 

I* 

MCC/LPOP Direct H(f) 

Coherence Blanked 

65 

El 
E2 

68 
E3 

N 

s 
E4 

I 

70 
# 

71 
E6 

72 
E7 

X 

WJ 

CI 

N 

I 

73 
E8 

74 
E9 

75 
El 0 

76 
El 1 

77 
El 2 

Q rl 

1 

d 

78 
79 
E14 , 

Q) w QI 

cr, P I 

80 
81 
El 6 

82 

E18 

84 
85 
E20 

86 
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t t I a 1 

I t . I 

cc 

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w 

t- 

.I. L I 

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Q) u) 

'llr 

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ch 

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87 
E22 

8% 
E23 
E24 

90 
91 
E26 

92 
E27 

93 
E 28 

94 
E29 

. 

. 

95 
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96 
E31 

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97 
E32 

98 
99 
100 
E35 

101 
E36 

102 
E37 

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m 

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4) 

Q 

m 

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t 

t 

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104 

E40 

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106 
E4 1 

- Is-- 

3 
E42 

108 

E44 

110 
E45 

111 
E46 

112 
E47 

L 

113 
~48 

114 

116 
E5 1 

1 

117 
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L 

118 
E53 
E54 

t 1 I 1 1 

P 

120 
E55 

121 
E56 

43 

CID 

W 

r) 

122 

N 

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E57 
E58 

124 
E59 
E60 

126 
E6 1 

ep 

L 

rp rr) 

M 

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E62 

128 
L 

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130 
E65 

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N 

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133 
134 
135 
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8 

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cp In 

r4 

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t 
E71 

137 
E72 
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139 
APPENDIX B 

WYLE LABORATORIES - RESEARCH STAFF 

TECHNICAL MEMORANDUM TM 84-03 

ROLLING BEARING ELEMENT ROTATIONAL 

SPEEDS FOR THE SSME HIGH PRESSURE 

FUELANDLOXTURBOPUMPS 
APPENDIX B 

WYLE LABORATORIES - RESEARCH STAFF 

TECHNICAL MEMORANDUM TM 84-03 

ROLLING BEARING ELEMENT ROTATIONAL SPEEDS 

FOR THE SSME HIGH PRESSURE FUEL 

AND LOX TURBOPUMPS 

by 

Wayne L. Swanson 

An interim report of 

work performed under contract NAS8-33508 

for 

NATIONAL AERONAUTICS AND SPACE ADMINISTRATION 

GEORGE C. MARSHALL SPACE FLIGHT CENTER 

MARSHALL SPACE FLIGHT CENTER, ALABAMA 35812 
POREWORD 

Wyle Laboratoriesf Scientific Services & Systems Group has prepared this 

report for the George C. Marshall Space Flight Center, National Aeronautics and Space Administration. The work was performed under contract 

NAS8-33508, entitled "Dynamic Analysis of SSME Vibration and Pressure 

Data." Technical direction and computer program coding for this study 

were provided by ED24 personnel of the Systems Dynamics Laboratory. 

2 
TABLE OF CONTENTS 

Page 

2 

4 

5 

7 

12 

17 

22 

FOREWORD.. ........................... INTRODUCTORYSUMMARY ..................... TECHNICALDISCUSSION. ...................... SPEED RATIO OF HPFTP PUMP AND TURBINE BEARINGS 

SPEED RATIO OF HPFTP THRUST BEARINGS .............. SPEED RATIO OF HPOTP TURBINE BEARINGS 

SPEED RATIO OF HPOTP PUMP END BEARINGS. 

SPEED RATIO OF HPFTP PUMP AND TURBINE BEARINGS, 3-, lo-, AND 

........ 

............. 

............ 30-DEGREEQi .......................... 

30-DEGREECti .......................... 

30-DEGREE CYi .......................... 

30-DEGREE ai .......................... 

SPEED RATIO OF HPFTP THRUST BEARINGSy 3-, lo-, 20-, AND 

SPEED RATIO OF HPOTP TURBINE BEARINGS, 3-, lo-, 20-, AND 

SPEED RATIO OF HPOTP PUMP END BEARINGS, 37 lo-, 20-, AND 

SPEED RATIO OF DIFFERENT PITCH DIAMETERS OF HPOTP TURBINE 

BEARINGS.. .......................... SPEED RATIO WITH DYNAMIC EFFECTS NEGLECTED .......... COMPUTER PROGRAM LISTING .................... INTERNALLY MEASURED BEARING FREQUENCIES OF TWO STATIC TEST 

FIRINGS.. ............................ 

27 

44 

61 

78 

95 

108 

125 

135 

3 
INTRODUCTORY SUMMARY 

This report consists of a series of charts, equations, and the computer program listing 

for determining the frequencies associated with the roller bearings of the SSME high 

pressure fuel turbopump (HPFTP) and high pressure oxygen turbopump (HPOTP). The 

frequencies are in terms of speed ratio normalized by the rotational speed of the 

shaft. Speed ratio was calculated for the cage, ball spin, outer race, and inner race 

for the different bearing parameters of the SSME HPFTP and HPOTP. 

Several methods of data presentation are provided for ease in interpretation. This 

includes charts for the change in contact angle for both the inner and outer race, 

constant inner race contact angle versus outer contact angle, and charts of inner 

contact angle equal to outer contact angle, which is only applicable for the case of 

slow rotational speed and/or applied radial load of large magnitude. 

The data from two static firing tests are also included where the cage and outer race 

frequencies were noted on internal strain gages mounted directly on the .bearing 

holder. Several attempts were made using different analysis techniques (including 

adaptive filtering, cross PSDs, etc.) to isolate these frequencies in the external 

accelerometer data. To date these efforts have not been successful. 

4 
TECHNICAL DISCUSSION 

1 The speed ratio for the cage, ball spin, and outer and inner race are defined as follows: 

Nb (1-Yf COS ai) 

1 + cos (ai-$) Outer Race Speed Ratio = 

N COS (a.-O! ) + Y' COS Cyi b 10 

1 + cos (ai-ao) Inner Race Speed Ratio = 

Ball Spin Ratio = (cos cyo + tanp sin ao) (1 + Y1 cos cy )-l 0 

where 

and 

sin CY, 

tanp = cos cLo+yl 

a! = outer raceway contact angle 

CY. = inner raceway contact angle 

Y1 = D/dm 

D = ball diameter 

0 

1 

= pitch diameter 

Nb = number of balls 

dm 

'Tedric A. Harris. Rolling Bearing Analysis, John Wiley & Sons, New York, 1966. 

5 
The bearing parameters used for this study are as follows: 

High Pressure Fuel Turbopump (HPFTP) 

Pump and turbine bearings: 

Ball diameter = 0.343750 inch 

Pitch diameter = 2.34 inches 

Number of balls = 14 

Thrust bearings: 

Ball diameter = 0.656250 inch 

Pitch diameter = 3.84 inches 

Number of balls = 13 

High Pressure Oxygen Turbopump (HPOTP) 

Turbine end bearings: 

Ball diameter = 0.50 inch 

Pitch diameters = 3.196, 3.17, 3.20, and 3.19 inches 

Number of balls = 13 

Pump end bearings: 

Ball diameter = 0.4375 inch 

Pitch diameter = 2.56 inches 

Number of balls = 13 

6 
SPEED RATIO OF 

HPFTP PUMP AND TURBINE BEARINGS 

Ball Diameter = 0.343750 inch 

Pitch Diameter = 2.34 inches 

Number of Balls = 14 

7 
8 
9 
10 
11 
SPEED RATIO OF 

HPFTP THRUST BEARINGS 

Ball Diameter = 0.656250 inch 

Pitch Diameter = 3.84 inches 

Number of Balls = 13 

12 
In 

m 
14 
a 

15 
16 
SPEED RATIO OF 

HPOTP TURBINE BEARINGS 

Ball Diameter = 0.50 inch 

Pitch Diameter = 3.196 inches 

Number of Balls = 13 
18 
19 
M 

M 

20 
21 
SPEED RATIO OF 

HPOTP PUMP END BEARINGS 

Ball Diameter = 0.4375 inch 

Pitch Diameter = 2.56 inches 

Number of Balls = 13 

22 

03 

M 

M 

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24 
25 
26 
SPEED RATIO OF 

HPPTP PUMP AND TURBINE BEARINGS 

3-, lo-, 20-, AND 30-DEGREE ai 

her mce Contact &-@e) 

Ball Diameter = 0.343750 inch 

Pitch Diameter = 2.34 inches 

Number of Balls = 14 . 

27 
28 
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43 
SPEED RATIO OF 

HPFTP THRUST BEARINGS 

3-, lo-, 20-, AND 30-DEGREE ai 

(her mce Contact Angle) 

Ball Diameter = 0.656250 inch 

Pitch Diameter = 3.84 inches 

Number of Balls’ = 13 

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SPEED RATIO OF 

HPOTP TURBINE BEARINGS 

3-, lo-, 20-, AND 30-DEGREE Qi 

(her mce contact Angle) 

Ball Diameter = 0.50 inch 

Pitch Diameter = 3.196 inches 

Number of Balls = 13 

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SPEED RATIO OF 

HPOTP PUMP END BEARINGS 

3-, lo-, 20-, AND 30-DEGREE ai 

(Inner &ace Contact Angle) 

Ball Diameter = 0.4375 inch 

Pitch Diameter = 2.56 inches 

Number.of Balls = 13 

78 
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90 
91 
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SPEED RATIO OF 

DIFFERENT PITCH DIAMETERS 

OF HPOTP TURBINE BEARJNGS 

Ball Diameter = 0.50 inch 

Pitch Diameter = 3.17, 3.19, and 3.20 inches 

Number of Balls = 13 

Inner Contact Angle = Outer Contact Angle 

9s 
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Charts of this section are for simple rolling motion, which is only applicable for the 

case of slow rotational speed and/or applied radial load of large magnitude.l The 

dynamic effects were neglected: Le., outer contact angle equal to inner contact angle. 

The equations for this case are as follows: 

Cage speed ratio = 1/2 (1 - D/d, cos 4) 

Outer race speed ratio = Nb/2 (1 - D/dm cos 4) 

Inner race speed ratio = Nb/2 (1 + D/dm cos 4) 

Ball spin ratio = 1/2 dm/D [l - (D/dm)2 cos2 41 

D = Ball diameter 

= Pitch diameter dm 

Nb = Number'of balls 

4 = Contact angle 
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I i 
INTERNALLY MEASURED BEARING FREQUENCIES 

OF TWO STATIC TEST FIRINGS 

This section includes selected data in the form of working papers for two static firing 

tests, 750-215 and 750-234. The two major points of interest are the cage frequency on 

test 750-215 and the outer race frequency on test 750-234. Of special interest is the 

beating of the bearing frequencies with the synchronous frequency of the pump. The 

data in this section is only included to illustrate or demonstrate the applicability of the 

charts of the previous sections. A comparison of the measured frequency on test 750- 

234 and the applicable chart of the HPOTP outer race speed is also shown. Several 

points of possible contact angles for the measured speed ratio are shown on the chart. 

Also included is a plot of the outer race frequency for different power levels, including 

a slow ramp down. For this test, the contact angle does not appear to be a function of 

power level. When additional data from normal bearing operation, and especially from 

bearings that have experienced damage, becomes available, it is recom mended that 

detailed analysis be performed and included in a report. 

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.. 
APPENDIX C 

WYLE LABORATORIES - RESEARCH STAFF 

TECHNICAL MEMORANDUM 64058-01-TM 

STATISTICAL ANALYSIS OF THE VIBRATION 

DATA FOR THE SSME HIGH PRESSURE 

TURBOPUMPS DURING FLIGHT 
MPENDIX C 

WYLE LABORATORIES - RESEARCH STAFF 

TECHNICAL MEMORANDUM 64058-01-TM 

STATISTICAL ANALYSIS OF THE VIBRATION 

DATA FOR THE SSME HIGH PRESSURE 

TURBOPUMPS DURING FLIGHT 

Wayne L. Swanson 

An interim report of 

work performed under contract NASS-33508 

for 

NATIONAL AERONAUTICS AND SPACE ADMINISTRATION 

GEORGE C. MARSHALL SPACE FLIGHT CENTER 

MARSHALL SPACE FLIGHT CENTER, ALABAMA 35812 
FOREWORD 

Wyle Laboratories’ Scientific Services & Systems Group prepared this report for 

the George C. Marshall Space Flight Center, National Aeronautics and Space Administration. The work was performed under contract NAS8-33508, entitled “Dynamic 

Analysis of SSME Vibration and Pressure Data.” Technical assistance and encouragement were provided by Mr. W. 6. Smith, MSFC/ED24. The special assistance of Mr. P. 

Lewallen, MSFC/ED24, is acknowledged for perf orrning numerous modifications of the 

MSFC Diagnostic Data Base Program required to adapt the routine for flight data 

analysis and documentation. The contribution of other members of ED24 and Wyle 

Laboratories Research Department is also acknowledged. 

1 
TABLEOFCONTENTS 

1.0 Introductory Summary ............................ 7 

2.0 Technical Discussion ............................. 8 

2.1 Space Shuttle Flights ......................... 8 

2.2 Measurement Location ........................ 8 

2.3 Power Profiles ............................ 14 

2.4 Mean and Standard Deviation of Vibration Measurements ....... 14 

2.4.1 Combined Data Groups .................... 14 

2.5 Formulae for Estimating Basic Engine Parameter Statistics ....... 22 

2.5.1 Background ......................... 22 

2.5.2 Combined Multiple Data Groups ................ 23 

2.5.3 Augmenting a Data Set .................... 25 

2.5.4 Deleting a Data Point ..................... 26 

2.6 Classical Distribution Functions ................... 27 

2.7 Sort Routine for Probability Density Function ............. 55 

2.8 Ratio of Synchronous to Composite ................. -57 

2.9 Turbopump Rotational Speed History . a . . a . . 64 

3.0 References .................................. 67 

4.0 Results ..................................... 69 

Flight Summary Sheets HPOTP and HPFTP 104%. 100% and 65% Power Level .... 71 

Flight Cumulative PrQbability Distributions HPOTP and HPFTP 104%. 100% and 

65% Power Level ............................. -85 

Flight Probability Density Function HPOTP and HPFTP .............. 99 

Flight Data Sheets HPFTP 104% Power Level ................... 113 

Flight Data Sheets HPOTP 104% Power Level ................... 119 

Flight Data Sheets HPFTP 100% Power Level ................... 125 

Flight Data Sheets HPOTP 100% Power Level ................... 135 

Appendix A . Vibration Data From STS Launch 27 (51-1) and 28 (51-J) . ...... 145 

2 
LIST OF FIGURES 

Figure 1 . High Pressure Oxidizer Turbopump Accelerometer Locations. Flight ... 

Figure 2 . HPOTP Accelerometer Block 135O-1 and 135O.2. Flight .......... 

Figure 3 . High Pressure Fuel Turbopump Accelerometer Locations. Flight ..... 

Figure 4 . Accelerometer Location Plane. Flight .................. 

Figure 5 . Flight Power Profile. STS-1 to STS-6 .................. Figure 6 . Flight Power Profile. STS-07 to STS-41D ................ 

Figure 7 . Flight Power Profile STS-41G to STS.51D ................ Figure 8 . Flight Power Profile. STS-41G to STS-5lF ............... 

Figure 9 . Cumulative Probability Distribution (LOX PBP RAD. Static Firing. 

Composite) Normal Overlay ........................ 

Figure 10 . Cumulative Probability Distribution (LOX PBP RAD. Static Firing. 

Composite) Rayleigh (M) Overlay ...................... 

Figure 11 . Cumulative Probability Distribution (LOX PBP RAD. Static Firing. 

Composite) Rayleigh (SD) Overlay ..................... 

Figure 12 . Cumulative Probability Distribution (LOX PBP RAD. Static Firing. 

Composite) Rayleigh (MR) Overlay ..................... 

Figure 13 . Cumulative Probability Distribution (LOX PBP RAD. Static Firing. 

Composite) Rayleigh (TC) Overlay ..................... 

Figure 14 . Cumulative Probability Distribution (LOX PBP RAD. Static Firing. 

Composite) Gamma Overlay ........................ 

Figure 15 . Probability Density (LOX PBP RAD. Static Firing. Composite) Normal 

Overlay .................................. 

Figure 16 . Probability Density (LOX PBP RAD. Static Firing. Composite) 

Rayleigh (M) Overlay ........................... 

Figure 17 . Probability Density (LOX PBP RAD. Static Firing. Composite) 

Rayleigh (SD) Overlay ........................... 

Figure 18 . Probability Density LOX PBP RAD Static Firing Composite) Rayleigh 

(MR)Overlay ............................... 

Figure 19 . Probability Density (LOX PBP RAD. Static Firing. Composite) 

Rayleigh (TC) Overlay ........................... 

Figure 20 . Probability Density (LOX PBP RAD. Static Firing. Composite) Gamma 

Overlay .................................. 

10 

11 

12 

13 

15 

16 

17 

18 

31 

32 

33 

34 

35 

36 

37 

38 

39 

40 

41 

42 

Figure 21 . 

Figure 22 . 

Figure 23 . 

Figure 24 . 

Cumulative Probability Distribution (LOX PBP RAD. Static Firing. 

Cumulative Probability Distribution (LOX PBP RAD. Static Firing. 

Cumulative Probability Distribution (LOX PBP RAD. Static Firing. 

Cumulative Probability Distribution (LOX PBP RAD. Static Firing. 

Synchronous) Normal Overlay ....................... 43 

Synchronous) Rayleigh (M) Overlay ..................... 

Synchronous) 3ayleigh (SD) Overlay .................... 45 

Synchronous) Rayleigh (MR) Overlay .................... 

44 

46 

3 
LIST OF FIGURES (Continued) 

Figure 25. Cumulative Probability Distribution (LOX PBP RAD, Static Firing, 

Synchronous) Rayleigh (TC) Overlay .................... 

Figure 26. Cumulative Probability Distribution (LOX PBP RAD, Static Firing, 

Synchronous) Gamma Overlay ....................... 

Figure 27. Probability Density (LOX PBP RAD, Static Firing, Synchronous) 

Normal Overlay .............................. Figure 28. Probability Density (LOX PBP RAD, Static Firing, Synchronous) 

Rayleigh (M) Overlay ........................... Figure 29. Probability Density (LOX PBP RAD, Static Firing, Synchronous) 

Rayleigh (SD) Overlay ........................... Figure 30. Probability Density LOX PBP RAD Static Firing Synchronous) Rayleigh 

Figure 31. Probability Density (LOX PBP RAD, Static Firing, Synchronous) 

Rayleigh (TC) Overlay. .......................... Figure 32. Probability Density (LOX PBP RAD, Static Firing, Synchronous) Gamma 

Overlay .................................. Figure 33. Probability Density of Synchronous/Composite Ratio for the HPFTP at 

100% Power Level During Flight ...................... 

Figure 34. Probability Density of Synchronous/Composite Ratio for the HPFTP at 

104% Power Level During Flight ....................... 

Figure 35. Probability Density of Synchronous/Composite Ratio for the HPOTP at 

100% Power Level During Flight ...................... 

Figure 36. Probability Density of Synchronous/Composite Ratio for the HPOTP at 

104% Power Level During Flight ...................... Figure 37. HPOTP Maximum Rotational Speed During Flight ........... 

Figure 38. HPFTP Maximum Rotational Speed During Flight ........... Figure 39. Summary of Composite Vibration Levels on the High Pressure Fuel 

Turbopump at 104% Power Level During Flight ............... 

Figure 40. Summary of Synchronous Vibration Levels on the High Pressure Fuel 

Turbopump at 104% Power Level During Flight ............... 

Figure 41. Summary of Composite Vibration Levels on the High Pressure Oxidizer 

Turbopump at 104% Power Level During Flight ............... 

Figure 42. Summary of Synchronous Vibration Levels on the High Pressure 

Oxidizer Turbopump at 104% Power Level During Flight. .......... 

Figure 43. Summary of Composite Vibration Levels on the High Pressure Fuel 

Turbopump at 100% Power Level During Flight ............... 

Figure 44. Summary of Synchronous Vibration Levels on the High Pressure Fuel 

Turbopump at 100% Power Level During Flight ............... 

Figure 45. Summary of Composite Vibration Levels on the High Pressure Oxidizer Turbopump at 100% Power Level During Flight .............. 

(MR)Overlay ............................... 

47 

48 

49 

50 

51 

52 

53 

54 

60 

61 

62 

63 

65 

66 

72 

73 

74 . 

75 

76 

77 

78 

4 
LIST OF FIGURES (Continued) 

Figure 46. Summary of Synchronous Vibration Levels on the High Pressure 

Oxidizer Turbopump at 100% Power Level During Flight ........... 

Figure 47. Summary of Composite Vibration Levels on the High Pressure Fuel 

Turbopump at 65% Power Level During Flight. ............... Figure 48. Summary of Synchronous Vibration Levels on the High Pressure Fuel 

Turbopump at 65% Power Level During Flight. ............... Figure 49. Summary of Composite Vibration Levels on the High Pressure Oxidizer 

Turbopump at 65% Power Level During Flight. ............... 

Figure 50. Summary of Synchronous Vibration Levels on the High Pressure 

Figure 51. Cumulative Distribution of Composite Vibration Levels on the High 

Figure 52. Cumulative Distribution of Synchronous Vibration Levels on the High 

Figure 53. Cumulative Distribution of Composite Vibration Levels on the High 

Figure 54. Cumulative Distribution of Synchronous Vibration Levels on the High 

Figure 55. Cumulative Fuel Distribution of Composite Vibration Levels on the 

Figure 56. Cumulative Fuel Distribution of Synchronous Vibration Levels on the 

Figure 57. Cumulative Oxidizer Distribution of Composite Vibration Levels on 

the High Pressure Oxidizer Turbopump at 100% Power Level During Flight . . 

Figure 58. Cumulative Oxidizer Distribution of Synchronous Vibration Levels on 

the High Pressure Oxidizer Turbopump at 100% Power Level During Flight . . 

Figure 59. Cumulative Fuel Distribution of Composite Vibration Levels on the 

Figure 60. Cumulative Fuel Distribution of Synchronous Vibration Levels on the 

Figure 61. Cumulative Oxidizer Distribution of Composite Vibration Levels on 

Figure 62. Cumulative Oxidizer Distribution of Synchronous Vibration Levels on 

Figure 63. Probability Density of Composite Vibration Levels on the High 

Figure 64. Probability Density of Synchronous Vibration Levels on the High 

Figure 65. Probability Density of Composite Vibration Levels on the High 

...... 

Oxidizer Turbopump at 65% Power Level During Flight 

Pressure Fuel Turbopump at 104% Power Level During Flight 

Pressure Fuel Turbopump at 104% Power Level During Flight 

Pressure Oxidizer Turbopump at 104% Power Level During Flight 

Pressure Oxidizer Turbopump at 104% Power Level During Flight 

High Pressure Oxidizer Turbopump at 100% Power Level During Flight .... 

High Pressure Oxidizer Turbopump at 100°h Power Level During Flight .... 

........... 

........ 

........ 

...... 

...... 

High Pressure Oxidizer Turbopump at 65% Power Level During Flight 

High Pressure Oxidizer Turbopump at 65% Power Level During Flight 

the High Pressure Oxidizer Turbopump at 65Oh Power Level During Flight. 

the High Pressure Oxidizer Turbopump at 65% Power Level During Flight. 

Pressure Fuel Turbopump at 104% Power Level During Flight 

Pressure Fuel Turbopump at 104% Power Level During Flight 

.... 

.... 

.. 

.. 

........ 

........ 

Pressure Oxidizer Turbopump at 104% Power Level During Flight 

79 

80 

81 

82 

83 

86 

87 

88 

89 

90 

91 

92 

93 

94 

95 

96 

97 

100 

101 

102 

5 
LIST OF FIGURES (Concluded) 

Figure 66. Probability Density of Synchronous Vibration Levels on the High 

Pressure Oxidizer Turbopump at 104% Power Level During Flight . . . . . . 

Figure 67. Probability Density of Composite Vibration Levels on the High 

Pressure Fuel Turbopump at 100% Power Level During Flight . . . . . . . 

Figure 68. Probability Density of Synchronous Vibration Levels on the High 

Pressure Fuel Turbopump at 100% Power Level During Flight . . . a e . Figure 69. Probability Density of Composite Vibration Levels on the High 

Pressure Oxidizer Turbopump at 100% Power Level During Flight . . . . . . 

Figure 70. Probability Density of Synchronous Vibration Levels on the High 

Pressure Oxidizer Turbopump at 100% Power Level During Flight . . . . . 

Figure 71. Probability Density of Composite Vibration Levels on the High 

Pressure Oxidizer Turbopump at 65% Power Level During Flight . . . . . . . 

Figure 72. Probability Density of Synchronous Vibration Levels on the High 

Pressure Oxidizer Turbopump at 65% Power Level During Flight . , - . . 

Figure 73. Probability Density of Composite Vibration Levels on the High 

Pressure Fuel Turbopump at 65% Power Level During Flight . . . . . . e e e 

Figure 74. Probability Density of Synchronous Vibration Levels on the High 

Pressure Fuel Turbopump at 65% Power Level During Flight . . . . . . . . . 

103 

104 

105 

106 

107 

108 

109 

110 

111 

6 
1.0 INTRODUCTORY SUMMARY 

This report documents the results of a statistical evaluation of RMS (root-meansquare) vibration levels measured during flight of the Space Shuttle. The data was 

recorded on-board the Orbiter, from accelerometers located on the Space Shuttle Main 

Engine (SSNIE) high pressure oxidizer turbopumps (HPOTP) and high pressure fuel 

turbopumps (HPFTP). It should be noted that the data recorded on-board the Shuttle 

vehicle has a 50-800 Hz bandpass filter and was analyzed using a 50-1000 Hz bandwidth. Therefore, any 

direct comparison of the composite vibration levels of the flight data to measurements recorded at the ground test stands without the bandpass filter will require 

the application of a small correction factor. However, the synchronous vibration 

levels will compare directly. 

Ground test data are acquired over a wider frequency range, 

The evaluation included the composite and synchronous vibration levels at 65%, 100% 

and 104% power levels. Results are presented in the form of summary sheets listing 

the mean and standard deviation for each individual measurement; plots of the 

cumulative distribution with a Gamma distribution overlay, and a plot of the density 

function. Also presented is the ratio of the synchronous to composite vibration 

levels for the high pressure fuel and oxidizer turbopumps during 100% and 104% power 

levels. 

Plots are presented of the Normal, Rayleigh, and Gamma Probability Distribution 

functions for comparison with over a thousand measured ground test data points. The 

data represents the oxidizer composite and synchronous vibration levels from ground 

static firings conducted on the Al, A2, and A3 test stands. An examination of the 

plots demonstrates the Gamma distribution function should provide reasonable 

approximations to the flight data. The application of a classical distribution is 

desirable for data characterization since this permits continuous statistical 

definition and manipulation from discrete flight measurement observations. Sketches 

are included of the accelerometer measurement locations and the power profile plots 

for each flight. 

All of the plots contained in this report are the automatic output of the menu 

driven MSFC Diagnostic Data Base Program. Details of the program are documented in 

Reference 1. 

7 
2.0 TECHNICAL DISCUSSION 

2.1 SD ace Shuttle FliPhts 

Table I summarizes the 19 flights of the Space Shuttle as of August 1985.l The data 

analysis is based upon 18 flights, since only the mean square vibration levels 

sampled at 100 msec intervals were recorded on STS-9. This type of data is not 

compatible with the analysis methods used for this report. Included in Table I are 

the launch date, Space Shuttle Vehicle identification, maximum power level during 

flight, engine serial number, HPOTP serial number, and HPFTP serial numbers. 

2.2 Measurement Location 

The measurement locations on the HPOTP are shown in Figure 1 with the block arrangements for the 135'-1 and 135'-2 locations shown in Figure 2. A few of the early 

flights had measurements located at the 180' position, while the present flight 

measurement program is standardized to 3 measurements at the 45', 135'-1 and 135'-2 

positions. No measurements during flight are located on the High Pressure Oxidizer 

Turbine (HPOT) or the low pressure oxidizer turbopumps (LPOTP). 

Figure 3 shows the measurement locations for the HPFTP. The measurement location of 

early flights was also somewhat different for the fuel turbopump than the present 

standardized plan of 3 measurements at the O', 174' and 186' positions. Data 

recqrded at 180' position on the early flights is listed at the 186O location for 

the purpose of storage in the computer data bank. In addition, a few flights 

included data at the 90' position rather than the present 0' location. No measurements are located on the high pressure fuel turbine (HPFT) end or the low pressure 

fuel turbopump (LPFTP) during flight. All measurements are in the radial direction 

for both the HPOTP and HPFTP. The relationship of the accelerometer measurement 

location plane to the SSME powerhead components is shown in Figure 4. 

Appendix A includes results from flights 27 (51-1) and 28 (51-5) which were 

not available at the time the statistical analysis was performed. The vibration 

levels of both flights were nominal and will not provide a significant change to the 

statistical values of this report. As additional flight data becomes available, 

this report will be periodically updated. 

8 
..................... dd 

..................... 

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9 
RAD - 135'-1 

RAD - 135'-2 

O0 

LOX PBP RAD 180" LOX PBP RAD 45" 

LOX PBP RAD 135" 

Figure 1. High Pressure Oxidizer Turbopump Accelerometer Locations, Flight 

10 
PBP RAD 135O-2 

Figure 2. HPOTP Accelerometer Block 135'-1 and 135O-2, Flight 

11 
RAD-00 

RAD - 

RAD - 

180" 

0" 

\ 

RAD 180" 

KZ2dA 

Figure 3. High Pressure Fuel Turbopump Accelerometer Locations, Flight 

12 
a 

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004-\L) E mhcQ -- cv, 

mm 

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ar 

13 
2.3 Power Profiles 

The power profiles for each of the 18 flights are shown in Figures 5 through 8. The 

profiles for all ground tests and flights are stored in the MSFC Diagnostic Data 

Bank for retrieval and plotting. 

Mission STS 51-F indicating the early cutoff of engine number 1 during this flight. 

It should be noted that two profiles are shown for 

2.4 Mean and Standard Deviation of Vibration Measurements 

Given a data sample of size N the mean and variance are defined by 

k = 1/N xi (Sample Mean) 

N 

a2 = 1/(N - 1) C (Sample Variance) 

N 

The standard deviation is the positive square root of the variance and defined by 

(2.4-1) 

(2,4-2) 

~~ 

SD =/" 5 (xi - k)2 (Sample Standard Deviation) (2,4-3) 

2.4.1 Combined Data Groups 

Each of the above statistics was first calculated for each measurement location and 

then combined as necessary for printout or plotting. The following is a discussion 

of procedures for combining data depending on whether the sums and the sum of 

squared terms or only the mean and standard deviation are stored. 

Assume we wish to combine the vibration levels measured on the LOX PBP 135O-1 with 

the levels measured on LOX PBP 135O-2, where the mean and standard deviation were 

calculated for each measurement. If the sums and sum of squared terms are stored 

the combined mean and standard deviation are as follows. 

Nl + N2 

14 

(24-4) 
65 

x 

R 

P 

L 

5.0, 100% 

51.0. 100% 

51.0, 65% 

70.0. 65% 

70.0, lea% 

513.0. 100% 

514.0, 65% 

TEST n DArE FULL DURATION OF .' 

STS83 / 3/22/82 520.0 SECONDS / 

100 5.0. t00X 

x 51.0, 100% 

R 51.0, 69% 

P 71.0, 65% 

L 71.0, 100% 

513.0, 100% 

515.0, 65% 

0 520.0, 65% 

65 

- TEST * 1 DATE FULL DURATION OF / 

51504 / 6/27/82 520.0 SECONDS / 

5.0, 100% 

51.0, 10@% 

57.0, 65% 

70.0, 65% 

70.0, 100% 

65 513.0. 1430% 

515.0.20 65% 651 

x 

R 

P 

L 

% 

R 

P 

L 

65 

100 I 

I-\ J

1 

._ __ __ . -- 

TEST / DATE FULL DURATION OF / 

STS05 / 11/11/92 514.0 SECONDS / 

POWFP PROFILE 

s.0, 100% 

51.0, 100% 

57.0, 65X 

70.0, 65% 

70.0, 100% 

513.0, l00X 

514.0, 65% 

n IS c) 20 514.0, 65% 

-- 

100 

x 

R 

P 

L 

65 

a* 20 

- -- - - __. __ __.- .. _- -- 

'?EST 8 / DATE FULL DURATION OF / 

STS06 / 4/3/83 505.0 SECONDS / 

POWER PROFILE 

5.0, 100% 

10.0, 100% 

13.5, 104X . 36.7, 104% 

36.7, 81% 

68.0, 81% 

68.0, 104% 

$0 450.0, 104% 

498.0, 65% 

505.0, 65% 

R 

L 

65 

___ - - .. < 2' _- ~ 

Figurc 5. Flight Power Profile, STS-I to STg6 

5.0, 100% 

51.0, 100% 

57.0, 65% 

70.8, 65% 

70.0, 100% 

515.0, 65% 

513.0. 100% 
TEST / DATE L FULL DURATION OF / 

STS07 / 6/18/03 . 505.0 SECONDS / 

5.0, 100% 

18.0. 100% 

15.0. 104% 

35,0, 104% 

35.0. 75% 

68.8. 75% , 65 68.0. 104% 

450.8, 104% 

500.0, 65% 

- 505.0, 65% 

x 

P 

P 

L 75 

- --_ -- - 

TEST n / DATE FULL IlURATIQN OF / 

SiSa8 1 2/28/01 528.0 SECONDS / 

180 5.0, 100% 

38.0. 100% 

31.0, 6BX 

67.5, 6Q% 

69.0, 100% 

470.0, 180% 

477.0, 65% 

528.0, 6511 

x 

R 

P 

0 

x 

R 

P 

L 

FULL DURATION OF / 

520.9 SECONDS / 

TEST I / DATE 

STSt 1 / 2/3/84 

08 5.0, 100% 

28.1, 100% 

32.2, 73% 

60.7, 731: 

63.1, 100% 

478.2. 180% 73 

65 514.8, 65% 

520.8, 65% 

._ - 

TEST-* / DATE FULL DURATJON / 

STSI~ 4/6/84 510.0 .SECONDS / 

5.0, 100% 1 Bl 0.6. 100% 

10.1, 104% x 

33.0, 104% a 

37.0, 65% P' 

L 50.0, 65% 

65 55.0, 104% 

500.0, 65% 

510.0, 65% 

450.0, 104% 

__ - 

:EST a / DATE FULL DURATION OF / 

STS41D / 08/30/04 521 .B SECONDS / 

POWER PROF 

0.0. 0% 

5.0, 100% 

18.7, lbB% 

P 11.1, 104% 

25.0, 104% 

L 27.0, 84% 

TInE (SECI 540 38.9, 65% 

73.0, 65% 

77.9. 104% 

465.0, 184% 

515.0, 65% 

521.0, 65% 

39.0, 84% 

B 28 

_- - ____ .. 

Figure 6. Flight Power Profile, STS-07 to STS-41D 
TEST / DATE 

STS4lC / 11/5/64 

FULL DURATION OF 

536.0 SECONDS / 

POUER PROflL 

0.0, 0% 

P 24.7, 100% 

L 26.0, 92% 

35.0, 92% 

38.0. 65% 

0 20 TINE (SEC) 540 54.0, 65% . -_ __ ~ - - .- 66.0, 65% 

69-04 100% 

80.0, 100% 

100.0, 100% 

119.0, 100% 

135.0, 100% 

240.0. 100% 

255.0, 100% 

355.0, 100% 

478.8, 180% 

530.0, 65% 

536.0, 65% 

.. 

~~GI~A~ PAGE 1s 

of: POOR QUALIn 

- -- 

TEST u DATE FULL DURATION OF ; 

STSS'A / 11/8/84 520.0 SECONDS / 

0% 

100% 

100% 

x 

P 88% 

89% 

67% 

L 

0 20 TlnE 1SECI 

- _. . 

TEST II / DATE 

STSSle / 4/38/85 

0.0, 

5.0, 

21.1, 

21.2, 

35.0, 

35.18 

74 .a. 

77.5, 

464.8, 

513.1, 

520.0, 

65% 

65% 

FULL DURATION OF-/' 

621.0 SECONDS / 

POWR PROF L 

0.0, 0% 

5.0, 100% 

25.0, 100% 

P 26.0, 84% ' 

L 34.0, 94% 

35.0. 65% 

67.0, 65% 

0 20 TIOE (SECI 540 68.0, 104% 

459.0. 104% 

515.0, 65% 

521.0, 65% 

E ~~I\-i 

POWR PROF L 

0.0, 0% 

5.0, 100% 

25.0, 100% 

P 26.0, 84% ' 

L E ~~I\-i 540 34 .O. 

0 20 TIOE (SECI 

459.0. 

515.0, 

521 .O, 

94% 

65% 

65% 

104% 

104% 

65% 

65% 
TEST 8 / DATE 

STSSlt / 06/17/85 

POU R PROFILE 

P 

L ~~~ 0 20 TIHE [SECI 548 

FULL DURATION OF / 

523.0 SECONDS / 

0.0, 

5.0, 

10.3. 

11 .O. 

25.5, 

27.0. 

37.0, 

38.0, 

75.8, 

77.0, 

462.6, 

514.0, 

523.0, 

0% 

100% 

100% 

104% 

104% 

84% 

84% 

65% 

65% 

651 

TEST a DATE / ENGIkE a / dPFPT I / HIPOPT L / EARLY CUTOFF AT / 

SiS51FE1 7/28/85 / 2023 / 2515R1 / 201QR2 / 348.7 SECONDS / 

P WER PR F L 

0.0, 0% 

5.0. 100% 

10.1, 100% 

P t1.0, 104% 

L 26.0. 104% 

27.0. 87% 

36.0. 97% 

0 20 TIBE ISECl 360 37.0. 65% 

62.0, 65% 

63.0, 104% E ~~~ 349.7, 104% 

% 

R 

P 

L 

TEST z DATE / ENClNE a / HPFPT I / *OPT a / FULL DURATION OF 

STS51FE2 / 7/28/05 / 2020 / 4202R1 / 400tR2 / 588.0 SECONDS / 

POYER PROF1 

0.1. 0% 

5.0. lB0% 

10.1. l0aX 

11.0, 104% 

26.0, 104% 

27.0, 07% 

36.0, 97% 

0 20 TIllE (SEC) 600 37.0, 65% 

62.0, 65% 

63.0. 104% 

582.0, 104% 

587.0, 91% 

988.0, 90% 

,af" ~ 

Figurc 8. Flight Powcr Profile, STS-41G to STS-SIF 

1% 
where N, and (xi), are the number of measurements and vibration value respectively 

of the LOX PBP 135'-1 location, N,, (xi), the values of the LOX PBP 135O-2 location 

and XI, is the combined mean vibration value. - 

Equation (2.4-3) for calculation of the standard deviation is modified to a format 

where the only requirement is storage of the sums. Using Equations (2.4-1) and 

(2.4-3) r 

SD 

(SD), (N-I) = c (Xi - i)2 

= c (xi2 - 2xi i + 2) N 

Since 

and 

c (XI2 = N(X)2 

N 

(SD)2 (N-I) = C (xi), - 2N(;02 + N(X), 

N 

= (xi)' - N(X)2 

N 

(2.4-5) 

and 

19 
SD 

(xi)2 - N(k)2 

- -dN N-1 

or 

SD 

(2.4-6) 

(2.4-7) 

As can be easily seen from examination of Equation (2.4-7), only the number of data 

points and the sum of xi and (xi)2 values are required for calculation of the 

standard deviation. Most hand calculators and computer programs use this method 

rather than Equations (2.4-1) and (2.4-3). Equations (2.4-1) and (2.4-3) require 

the calculation of the mean for the complete data set before the sum of the difference squared can be calculated. 

The standard deviation for the combined LOX PBP l35O-1 and LOX PBP 135'-2, assuming 

the sum of the xi and (xi)2 terms are available is 

(2.4-8) 

However, if the sums are not available the combined mean and standard deviation can 

be calculated from the individual number of data points, means and standard deviations as follows. 

From Equation (2.4-1) 

C xi = Nk 

N 

(2.4-9) 

and with Equation (2.4-4) the combined mean of the LOX PBP 135O-1 and LOX PBP 135O-2 

is 

20 
- N, x1 + N, k, 

Nl + N2 

x12 - (2.4- 10) 

where the subscripts 1 and 2 of N and 2 indicate the number of data points and mean 

of the individual data sets, respectively. 

For the calculation of the standard deviation using Equations (2.4-1), (-6), and 

(-8) 

C = (SD), (N-1) + N(X), 

N 

and substitution into Equation (2.4-8) 

(SD1J2 (N1 + N, - 1) = (SD)12 (N, - 1) + N, (i): + (SD),, (N2-1) + N2(X)2 

and the combined standard deviation of the LOX PBP 135'-1 and LOX PBP 135O-2 is 

-- -.--_-------- 

(SD)12 (N1-1) + (SD),, (N2-1) + N1 (XI), + N, (X2), - 

(2.4-1 1) SD,, = 

N, + N, - 1 v 

The procedure can be repeated if an additional data set, for example the LOX PBP RAD 

45O, is to be combined with the LOX PBP RAD 135O-1 and LOX PBP RAD 135O-2 data set. 

A more elegant derivation of the equations for combining multiple data sets, 

augmenting a data set and deleting a data point from unpublished work of Tom Coffin 

is included in the next section. A procedure for combining data based on the small 

sample size theorem for the high order moments (skewness and kurtosis) will be 

forthcoming in future documentation. 

21 
2.5 Formulae for Estimatiw Basic EnPine Parameter Statistics 

2.5.1 Background 

Given a sample of size 

defined for N and P by 

- 

m = (l/N) 

N from a population of size P, the mean and variance are 

xi 

c x. 1 

N 

P 

(Sample mean) (2.5- 1) 

(l?opuhtiun mean) (2.5-2) 

(Sample variance) (2.5-3) -2 -2 a = (l/N-l) (xi-m) 

N 

Note that for large N, 

(N/E3-1) -1, 

so formuia 3 approaches 

(for large N) (2.5-3A) 

The asymptotic convergence between formulae 2.5-3 and -3A is more strongly emphasized by 

observing that the standard deviation is the primary statistic of interest, so the 

practical deviation between formulae 2.5-3 and -3A is as 

8 { ~(~-11-1) 

Since the population of possible engine pcirameter outcomes is infinite, our statistical estimates are based on formulae 2.5-1 and’2.5-3 or -3A. 

22 
2.5.2 Combined Multiple Data Groups 

Next, assume a sample, S, consisting of three subgroups, { X 5, { Y 1 , { Z 1. Technically 

s = XUYUZ (2.5-5) 

A practical example would be to let X, Y, Z represent a parameter measured on test 

stands AI, An, %, respectively. The set S then represents the parameter variation 

giving equal weight to each test from all test stands. 

Assume also that we have computed h and a for each of these groups and wish to 

compute the same statistics for the complete set (2.5-5). It is desirable to use the 

group statistics already calculated to obtain these results, as opposed to applying 

formulae 2.5-1 and 2.5-3 on the complete data sct. More specifically, given 

compute h 6 where S is defined by formula 2.5-5. S' s' 

First, consider the mesn Gs. By formula 2.5-1, 

- mS = (l/NS) [c xi + yi+ '1 

NX NY NZ 

where NS = NX + Ny + N,. 

But also by formula 2.5-1, 

Cxi=.m xx 

NX 

so 

yi=Nm YY 

C - zi=~m zz 

NZ 

(2.54) 

(2.5 -7) 

(2.5-8) 

(2.5-9) 

23 
Or, more compactly, 

(2.5-10) 

NS = Nj. where 

j 

Next consider the variance, z:. By formula 2.5-3, 

z2 S = (l/Ns-l) I 

Expanding the first sum in brackets, 

-- -2 - 2NxmXmS+NXmS, c -2 (xi-ms) = 

and noting that by formula 2.5-3, 

the first sum in formula 2.5-11 may be written 

(2.5-1 2) 

(2.5-1 3) 

(2.5- 14) 

and an identical form follows for the remaining two sums. 

The variance of the combined data set may therefore be conveniently computed by the 

for mula 

(2.5-15) 

24 
Again, if the data groups are large (say, Ni is greater than 30), 

0 (l/NS) {XNi 5: + Ni(mi-mS) -2 

S - - 2/ 

(2.5-1 6) 

2.5.3 Augmenting a Data Set 

Often, means and variances may be computed for a set of data and a new data point 

then obtained. It is desirable to compute these statistics for the newly augmented data 

set using those already obtained (as opposed to starting anew). 

Consider a group {Xi, of size NX, for which we have already computed Ex, zx by 

formuale 2.5-1 and 2.5-3, respectively, and let 

s = {xi, x29 e) XN, (2.5-17) 

then, by formula 2.5-1, 

or simply 

- mS = (l/NX+l) (NXmX+Z) 

Finally, by formulae 2.5-3 or 2.5-11, 

i -2 as = (l/NX) 

and using 2.5-17, 

(2.5- 18) 

(2.5-19) 

(2.5-20) 

(2.5-2 I) 

2.5-19 and 2.5-21 provide the desired formulae. 

25 
2.5.4 Deleting a Data Point 

A third situation is encountered when the mean and variance for a data set have been 

computed, after which it is found that an included test result is invalid. It is then 

convenient to have formulae available to obtain the statistics for the reduced set, for 

example, neglecting the invalid data point. 

Let S, S’ represent the complete and reduced data set, respectively. 

rearranging 2.5-19, the mean for the reduced set is 

By simply 

(2.5-22) 

where Z represents the invalid data point to ,e deleted. Similarly, the desired 

variance is obtained by manipulating formula 2.5-21: 

(2.5-23) 

The above formulae are easily programmed on a small calculator for ready reference, 

and have been implemented in the diagnostic data base software for data base editing 

and update. 

26 
2.6 Classical Distribution Functions 

Three classical continuous probability distributions were selected for comparison 

with the SSME vibration data. They were the Normal, Rayleigh and Gamma functions 

and are listed as programmed in the Diagnostic Data Bank in the next paragraph. 

Since the choice of a classical probability function for a data set is arbitrary, 

additional investigations are planned to evaluate other classical distributions and 

functions of higher order. Best-Fit (Chi-square Goodness-of-Fit, Bonf erroni-Type 

Inequalities, etc,) will also be investigated. However, a visual inspection of 

Figures 9 to 32 indicates the Gamma function is reasonable for the SSME high 

pressure turbopump vibration data from static firing tests and should be applicable 

to the flight data. Plots are shown for both the composite and synchronous vibration levels. Static firing tests were utilized for the comparison, since a larger 

data base was available consisting of over 1,000 data samples. 

The application of a classical distribution is desirable for data characterization 

since this permits continuous statistical definition and manipulation from discrete 

flight measurement observations. The cumulative distribution plots provide a quicklook assessment of flight results with the historical distribution of measurements 

from previous flights. Density plots are useful for an assessment of the historical 

data scatter or dispersion around the mid-point or mean value. The density functions are shown in Figures 15 to 20 for the composite values and Figures 27 to 32 

for the synchronous values from which the cumulative distribution was calculated 

from 

N 

F(NAx) = C f(xi) 

i= 1 

(2.6-1) 

where N AX is the Grms level used in plotting. 

Normal Distribution 

Ax = l/-e 2s2 

f(x) (2.6-2) 

M - Mean Grms Level 

S - Standard Deviation 

AX - Step Size = 0.5 Grms 

27 
RavleiPh Distribution 

(2.6-3) 

AX - Step Size = 0.5 Grms 

The parameter CY of the Rayleigh density can be the mean, standard deviation, and 

the first moment or second moment of the Rayleigh function (Reference 2). A more 

detailed study and discussion of the Rayleigh density and other classical functions 

will be included in future documentation. 

Rayleigh (M) 

CY 

Rayleigh (SD) 

CY 

Rayleigh (MR) 

- 

- 

CY - - 

Rayleigh (TC) 

Mean 

Standard Deviation 

M = Mean M 

Jn/2 

S S = Standard Deviation 

J2 - n/2 

Gamma Distribution 

The Gamma distribution will be presented in more detail, since it appears to provide 

the most reasonable fit to the vibration data. It should be noted that the Gamma 

distribution contains two parameters related to both the mean and standard deviation. The four Rayleigh functions are one parameter systems and utilize the 

mean or standard deviation, but not both. The Gamma probability distribution is 

defined as 

x>o (2.6-4) 

28 
where r(r) is the Gamma, or generalized factorial function. 

The parameter h and r in terms of the mean and variance from Reference (3) are: 

- 

X 

Solving each equation for r 

r = xh 3 r = a2 A' 

or 

A = :/a2 

From the first of Equation (2.6-5) and (2.6-8) 

so 

Using Equations (2.6-4), (-8) and (-10) 

(E-1) ;tx 

- a2 xx a2 

e 

Some important 

r(n+l) = 

relationships of the Gamma function are: 

xn e -x dx, which leads to /m 0 

(n-1) 'r (n-1) 

(n-1) ! 

n! 

(2.6-5) 

(2.6-6) 

(2.6-7) 

(2.6-8) 

(2.6-9) 

(2.6-10) 

(2.6- 1 1) 

(2.6-12) 

Thus the definition as a generalized factorial function. 

29 
Therefore in terms of the mean Grms and standard deviation the Gamma density 

function is 

(mil C(m2/s2> -11 

AX (2.6- 13) - 52 m mx 

s2[m2/s2-1]! s2 

*e -*- 

f(x) = 

m - Mean Grms Level 

S - Standard Deviation 

AX - Step Size = 0.5 

Although the Gamma distribution appears to provide a reasonable fit to the data, 

some additional improvements should be investigated. These include a change in the 

class interval width, unequal class intervals and maybe some type of truncated 

Gamma or other classical function to account for the low synchronous values approaching the noise floor of the instrumentation. It may be noted F(x) and f(x) 

are not the continuous form of the cumulative probability function and probability 

density function, but represent percentiles within discrete class intervals. This 

formulation permits direct comparison between classical function approximations and 

discrete frequency distributions representing empirical measurement characteristics. 

30 
31 
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2.7 Sort Routine for Probabilitv Densitv Function 

A variation of the following quick sort routine is used in the MSFC Diagnostic Data 

Base Program to calculate the density functions. The procedure follows Reference 

4. This method requires only one data pass and therefore is basically the fastest 

most simple routine available. 

Consider the N data values for the composite, synchronous etc. for each measurement. 

The probability density function can be estimated by 

t(X) = 

where W is a narrow interval centered at x and N, is the number of data values 

which fall within the range x W/2. A general procedure to estimate f(x) can be 

obtained digitally by dividing the full range of x into an appropriate number of 

equal width class intervals. Tabulate the number of data values in each class 

interval, and divide by the product of the class interval width W and the sample 

size N. The estimate f(x) is not unique since it is dependent upon the number of 

class intervals and their width selected for the analysis. Equal class intervals of 

0.5 Grms were used in the MSFC Diagnostic Data Bank Program. The number of class 

intervals is equal to twice the maximum value of the plot with the data plotted at x 

rather than x 2 W/2. This is not in strict accordance with the above definition, 

but for data interpretation the plots show the percentage of data values less than 

or equal to x, where x is the Grms value. 

A 

A 

A general procedure for evaluation is as follows. Let K define the number of class 

intervals selected to cover the entire range of the data values from a, to b, 

Then the width of each interval is given by 

and the end point of the ith interval is 

ni - a,+iW i=O, 1,2,... K 

55 
where no = a, and nk = b, 

K+2 numbers [Nil, i = 0, 1, 2,. , . K+1, by the conditions 

The bin numbers will now be defined as a sequence of 

NO - [number of x such that x ,<no] 

Nl - [number of x such that no < x ~n,] 

Ni - [number of x such that ni-l < x 5ni] 

Nk - 

Nk+l - 

[number of x such that nk-l < x snk] 

[number of x such that x > n,] 

This procedure will sort out the N data values of x so that the bin number sequence 

[Nil satisfies 

K+ 1 

i-0 

A quick one pass method of sorting on a digital computer is to evaluate each value 

x,; n=l, 2,. . . , N in turn as follows. 

a. if x, sa,, add the integer one to No. 

Xn - ao 

W b. If a, < xn 5 b, compute I = 

then select i as the largest integer less than or equal to I, and add 

the integer one to Ni. 

C. If x, > b, add the integer one to Nk+,. 

The four output forms are histogram, percentage of data in each class interval, 

probability density estimate and probability distribution estimate. 

56 
The histogram is simply Ni without changes 

Hi Ni Histogram 

where Hi is the number of data values in each class interval. 

The second output is the sample percentage of data in each class interval defined 

for i = 0, 1, 2,. . . K+1 by 

x 100 

Ni A 

F, % = - 

N 

Percentage of Data 

The third output is the probability density estimate defined at the midpoints of the 

K class intervals in [a,, b,] by 

A 

Probability Density K 

i=l, 2, 3 . . . K 

Ni =- A Fi 

f i - - 

W N bm - a0 

and the probability distribution estimate defined at the class interval end points 

where i = 0, 1, 2, . . . , K+1. 

2.8 Ratio of Svnchronous to Comuosite 

The analysis of the ratio of synchronous to composite vibration levels measured in 

flight is documented for future reference. This data will be utilized in studies 

to relate flight to static firing data, the effect of vibration level amplitude on 

the ratio of synchronous to composite, evaluation of the FASCOS system and justification of vibration redlines. 

57 
The ratio of synchronous to composite vibration levels of Figures 33, 34, 35, and 

36 for 100% and 104% power levels were calculated using the data stored in the MSFC 

Diagnostic Data Base. Both the composite (50-1000 Hz) and synchronous vibration 

levels in the data base are derived from a sliding 11 point average (0.4 second 

PSDs) which is equal to 4.4 seconds of data during each power level. The highest* 

or maximum value of this average is then stored in the data base** to represent the 

characteristic Grms vibration level at that power level. Since the Diagnostic Data 

Base Program does not record or track the time of occurrence during the flight the 

ratio may or may not represent the same time period of the flight. However, past 

history has shown the composite and synchronous track in a reasonable manner during 

most static firing tests and flights. This pseudo ratio shown in the figures should 

therefore be fairly representative of a ratio calculated from data recorded at the 

same time period. Additional investigations are planned to evaluate the skewed 

distribution on the high pressure fuel turbopump and the appearance of a bi-modal 

type of distribution on the high pressure oxidizer turbopump. One possibility is 

the ratio of synchronous to composite is a function of the vibration level. Also 

the investigation will include a comparison with the measured static ground test 

data. 

*The vibration level stored in the Diagnostic Data Base and reported at data review 

meeting could be called the "highness" vibration level. Highness as defined in the 

Webster Dictionary "the highest of t'he nobility" with noble defined as "having 

excellent qualities; superior.". The MSFC Technical Monitor for this report has 

suggested contiguous average maximum vibration level as a descriptive term, while 

the Wyle Technical Reviewer has suggested noble vibration level. Only historical 

usage will finally define the terminology. 

**The computer also skips random clipped signals and the output data is analyzed to 

purge the data base of invalid and extreme noisy data. 

58 
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2.9 Turboourno Rotational Soeed History 

The rotational speed of the high pressure oxidizer turbopump (HPOTP) and high 

pressure fuel turbopump (HPFTP) are shown in Figures 37 and 38. The speed is 

calculated from the synchronous frequency of the measured vibration data and 

represents the maximum speed of the pump during the flight at 100% and 104% power 

levels. The notation on the plot lists the flight number STS xx, engine position 

Ex and turbopump serial number. 

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3.0 REFERENCES 

1. Lewallen, P., "SSME Vibration Data Base," (In publication MSFC/NASA TN), 1985. 

2. Papoulis, A., "Probability Random Variables and Stochastic Processes," McGrawHill Book Company, NY, 1965, p. 148. 

3. Hines, W. W. and D. C. Montgomery, "Probability and Statistics," Ronald Press 

Co., NY, 1972, p. 157. 

4. Bendet, J. S. and A. G. Pierson, "Random Data: Analysis and Measurement 

Procedures," Wiley-Interscience, NY, 197 1, p. 309. 

67 
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68 
4.0 RESULTS 

A summary of the mean vibration levels, the standard deviation, and maximum level 

measured on the SSME high pressure oxidizer and fuel turbopump during flight is 

shown in Figures 39 through 50.* The results are for the SSME operating at 104%, 

100% and 65% power levels. Statistics are for each measurement location and the 

average of all locations which represents a spatial average around the turbopump. 

Both the composite (50-1000 Hz) and synchronous vibration levels were considered in 

this investigation. 

Cumulative probability distribution plots are shown in Figures 51 through 62 with 

the classical Gamma distribution plotted as an overlay dashed line. These plots as 

discussed in Section 2.6 can provide a quick-look assessment of flight results as 

compared to this historical distribution of the previous flight data. The probability density for each power level for the oxidizer and fuel turbopumps is shown in 

Figures 63 through 74. These plots provide a quick assessment of the historical 

flight data scatter or dispersion from the mid-point or mean value whichever may be 

of interest. The tabulated data on each plot is the number of data points in each 

0.5 Grms interval. Also the number of tests is equal to the number of test samples 

rather than the number of flights. 

For future reference, flight numbers keyed into the computer are listed for the 

flights used in this analysis. The data sheets for each measurement are also 

included for reference. 

* The data of STS Launch 27 (51-1) and 28 (51-J) are included in Appendix A. 

Both flights were nominal and will not have a significant effect on the 

statistical data of Figures 39 through 74. 
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84 
FLIGHT CUMULATIVE PROBABILITY DISTRIBUTIONS 

HPOTP AND HPFTP 

104O/o, 100% AND 65% POWER LEVEL 

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FLIGHT PROBABILITY DENSITY FUNCTION 

HPOTP AND HPFTP 

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FLIGHT DATA SHEETS 

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APPENDIX A 

VIBRATION DATA FROM STS LAUNCH 27 (51-1) AND 28 (51-J) 

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APPENDIX D 

WYLE LABORATORIXS - RESEARCH STAFF 

TECHNICAL MEMORANDUM 55058-02-TM 

ANALYSIS OF THE SYNCHRONOUS VIBRATION 

LEVELS FROM "HIGH RUNNING MAIN IMPELLERS" 

ON THE SSME HIGH PRESSURE OXIDIZER TURBOPUMP 
APPEJTOIX D 

WYLE LABORATORIES - RESEARCH STAFF 

TECHNICAL MEMORANDUM 64058-02-TM 

ANALYSIS OF THE SYNCHRONOUS VIBRATION 

LEVELS FROM "HIGH RUNNING MAIN IMPELLERS" 

ON THE SSME HIGH PRESSURE OXIDIZER TURBOPUMP 

by 

Wayne L. Swanson 

An interim report of 

work performed under contract NAS8-33508 

for 

NATIONAL AERONAUTICS AND SPACE ADMINISTRATION 

GEORGE C. MARSHALL SPACE FLIGHT CENTER 

MARSHALL SPACE FLIGHT CENTER, ALABAMA 35812 
FORE WORD 

Wyle Laboratories' Scientific Services & Systems Group prepared this report for 

the George C. Marshall Space Flight Center, National Aeronautics and Space Administration. The work was performed under contract NAS8-33508, entitled "Dynamic 

Analysis of SSME Vibration and Pressure Data." Technical assistance and encouragement were provided by Mr. W. C. Smith, MSFC/ED24. The special assistance of Mr. P. 

Lewallen, MSFC/ED24, is acknowledged for modifying the MSFC Diagnostic Data Base 

Program software to calculate a unique spatial average. The contribution of other 

members of ED24 and Wyle Laboratories Research Department is also acknowledged. 

2 
TABLE OF CONTENTS 

1.0 Introduction and Conclusions ......................... 5 

2.0 Technical Discussion ............................ 7 

2.1 Diagnostic Data Base ......................... 7 

2.2 Vibration Measurement Location .................... 7 

2.4 Listing of Suspect Main Impeller .................... 29 

2.6 Random Selection of Tests ...................... 59 

2.3 Total Data Base HPOTP Synchronous Vibration ............. 29 

2.5 Synchronous Vibration Data of Six Main Impellers ........... 42 

2.7 Vibration Test History of the Six Main Impellers ............ 62 

LIST OF FIGURES 

Figure 1 . Accelerometer Location Plane HPOTP ................. 27 

Figure 2 . Major Components of HPOTP Pump .................. 28 

Figure 3 . Cumulative Distribution HPOTP-PBP Total Data Base 104% ....... 30 

Figure 4 . Probability Density HPOTP-PBP Total Data Base 104% ......... 30 

Figure 5 . Cumulative Distribution HPOTP-TURB Total Data Base 104% ...... 31 

Figure 6 . Probability Density HPOTP-TURB Total Data Base 104% ......... 31 

Figure 7 . Cumulative Distribution HPOTP-PBP Total Data Base 100Yo ....... 32 

Figure 8 . Probability Density HPOTP-PBP Total Data Base 100% ......... 32 

Figure 9 . Cumulative Distribution HPOTP-TURB Total Data Base 100% ...... 33 

Figure 10 . Probability Density HPOTP-TURB Total Data Base 100Yo ........ 33 

Figure 11 . Cumulative Distribution HPOTP-PBP Total Data Base 109% ....... 34 

Figure 12 . Probability Density HPOTP-PBP Total Data Base 109% ......... 34 

Figure 13 . Cumulative Distribution HPOTP-TURB Total Data Base 109% ..... 35 

Figure 14 . Probability Density HPOTP-TURB Total Data Base 109% ........ 35 

Figure 15 . Probability Density for HPOTP-PBP Normal Operation 104Yo ...... 45 

Figure 16 . Probability Density for HPOTP-PBP Six Main Impellers 104% ...... 45 

Figure 17 . Probability Density HPOTP-TURB Normal Operation 104% ....... 46 

Figure 18 . Probability Density HPOTP-TURB Six Main Impellers 104% ...... 46 

Figure 19 . Cumulative Distribution HPOTP-PBP Normal Operation 104% ...... 47 

Figure 20 . Cumulative Distribution HPOTP-PBP Six Main Impellers 104% ..... 47 

Figure 21 . Cumulative Distribution HPOTP-TURB Normal Operation 104% .... 48 

Figure 22 . Cumulative Distribution HPOTP-TURB Six Main Impellers 104% .... 48 

Figure 23 . Probability Density HPOTP-PBP Normal Operation 100% ........ 

Figure 24 . Probability Density HPOTP-PBP Six Main Impellers 100% ....... 50 

50 

3 
Figure 25 . Probability Density HPOTP-TURB Normal Operation 100% ....... 51 

Figure 26 . Probability Density HPOTP-TURB Six Main Impellers 100% ...... 51 

Figure 27 . Cumulative Distribution HPOTP-PBP Normal Operation 100% ...... 52 

Figure 28 . Cumulative Distribution HPOTP-PBP Six Main Impellers 100% ..... 52 

Figure 29 . Cumulative Distribution HPOTP-TURB Normal Operation 100% .... 53 

Figure 30 . Cumulative Distribution HPOTP-TURB Six Main Impellers 100% .... 53 

Figure 31 . Probability Density HPOTP-PBP Normal Operation 109% ........ 55 

Figure 32 . Probability Density HPOTP-PBP Six Main Impellers 109% ....... 55 

Figure 33 . Probability Density HPOTP-TURB Normal Operation 109% ....... 56 

Figure 34 . Probability Density HPOTP-PBP Six Main Impellers 109% ....... 56 

Figure 35 . Cumulative Distribution HPOTP-PBP Normal Operation 109% ...... 57 

Figure 36. Cumulative Distribution HPOTP-PBP Six Main Impellers 109% ..... 57 

Figure 37 . Cumulative Distribution HPOTP-TURB Normal Operation 109% .... 58 

Figure 38 . Cumulative Distribution HPOTP-TURB Six Main Impellers 109% . . ~ . 58 

Figure 39 . Cumulative Distribution HPOTP-PBP Random Selection of 29 Tests 104% 61 

Figure 40 . Probability Density HPOTP-PBP Random Selection of 29 Tests 104% . . 61 

Figure 4 1 . Synchronous Vibration Test History, Spatial Average PBP, Impeller 

S/N 2427800 ................................ 63 

Figure 42 . Synchronous Vibration Test History, Spatial Average PBP, Impeller 

Figure 43 . Synchronous Vibration Test History, Spatial Average PBP, Impeller 

Figure 44 . Synchronous Vibration Test History, Spatial Average PBP, Impeller 

Figure 45 . Synchronous Vibration Test History, Spatial Average PBP, Impeller 

Figure 46 . Synchronous Vibration Test History, Spatial Average PBP, Impeller 

S/N3134124 ................................. 64 

S/N 3134446 ................................ 65 

S/N3135444 ................................ 65 

S/N7363066 ................................ 66 

S/N 7326708 ................................ 67 

LIST OF TABLES 

Table I . SSME High Pressure Oxidizer and Fuel Turbopump Vibration Data in MSFC 

Diagnostic Data Base ........................... 8 

Table I1 . HPOP Main Impeller History . S/N 2427800 ............... 36 

Table I11 . HPOP Main Impeller History . S/N 3134124 .............. 37 

Table IV . HPOP Main Impeller History . S/N 3134446 .............. 38 

Table V . HPOP Main Impeller History . S/N 3135444 ............... 39 

Table VI . HPOP Main Impeller History . S/N 7326708 .............. 40 

Table VI1 . HPOP Main Impeller History . S/N 7363066 .............. 41 

4 
1.0 INTRODUCTION AND CONCLUSIONS 

The purpose of this report is threefold 1) to document an investigation of higher 

than expected (number of occurrences and amplitude) synchronous vibration levels on 

the high pressure oxidizer turbopump (HPOTP), 2) to illustrate the value of basic 

fundamental statistical methods of data analysis, incorporated in the MSFC Diagnostic Data Base Program, and 3) to document a data list of tests where the HPOTP 

vibration data are not contaminated by high running main impellers, whirl, instrumentation malfunctions, etc. Both the HPOTP Preburner Pump (PBP) and Turbine (TURB) 

measurements were considered in the analysis, operating at 100%, 104% and 109% power 

levels. 

The terminology "High Running Win Impellers" was applied, after the study was 

completed, to an investigation in the last quarter of 1982 and early 1983 of higher 

than expected (number and amplitude) synchronous vibration levels on the HPOTP. 

When the original study was performed the vibration data was hand plotted in a 

format similar to the plotting routines now available. using the MSFC Diagnostic Data 

Base Program. Data in this reports documents a re-evaluation and update of the 

original effort with maximum utilization of the MSFC computer program for data 

sorting, analysis and plotting. Analysis included calculation of the mean, standard 

deviation, spatial average, cumulative distribution and probability density with the 

classical Gamma distribution plotted as an overlay. Elegant and/or sophisticated 

statistical techniques were not used or required in the analysis, since visual 

methods were adequate to show a distinct difference between data groups. 

This report does not change the conclusions and results of the original study which 

indicated a strong correlation between six main impellers and the high synchronous 

vibration levels. The analysis does, however, illustrate the application of 

probability density estimates for detecting embedded measurement groups representing 

differing statistical (and likely physical) behavior. In addition, the statistical 

characterization of the vibration data provided herein represents nominal HPOTP 

operation for future reference. 
2.0 TECHNICAL DISCUSSION 

2.1 Diagnostic Data Base 

Table I is a listing of the relevant vibration measurements stored in the MSFC 

Diagnostic Data Base Program. The listing includes the test number, date of test, 

engine serial number, HPFTP serial number, HPOTP serial number and the power level 

of which the vibration data was acquired. For this analysis the number of tests at 

each power level was: 

407 tests @ 100% 

155 tests @ 104% 

234 tests @ 109%. 

These tests resulted in the following synchronous vibration data sample for analysis 

at the HPOTP preburner pump and turbine measurement locations. Each measurement 

was treated as an individual data point and therefore the results represent the 

spatial average over the transducer locations. 

Number of Power 

Data SamD le8 Level 

1299 

542 

7 12 

97 1 

348 

546 

100% 

104% 

109% 

100% 

104% 

109% 

Measurement Location 

LOX PBP RAD 45, 135-1, 135-2, 

180, 225 

LOX TURB RAD 45,90, 135 

Serial numbers of HPOTP's with the suspect main impellers discussed in Section 2.4 

are highlighted and the tests marked with an "H". Also the tests that experienced 

whirl are marked with an "SS" and the power level noted in the remarks column. 

These tests were also deleted before calculation of the statistics for normal 

turbopump operation. 

2.2 Vibration Measurement Location 

The plane in which the preburner pump and turbine accelerometers are located is 

shown in Figure 1. All accelerometers were oriented to measure the vibration in 

the radial direction. In Figure 2 the major components of the HPOTP pump section 

are identified including the main impeller. 

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2.3 Total Data Base HPOTP Synchronous Vibration 

All tests listed in Table I were used to generate the plots shown in Figures 3 to 

14. Separate plots are shown for 100%, 104%, and 109% power levels. These plots 

are the cumulative and density histograms of all the relevant synchronous Grms 

vibration data presently in the MSFC Diagnostic Data Base. Immediately obvious, 

especially at the 104% power level, is the bi-modal type of distribution which 

indicates the possibility of two different data groups. Also of note is the fact 

that a bi-modal type of distribution does not appear on the turbine end vibration 

measurements. 

In the last quarter of 1982 a major effort was instigated to evaluate the second 

group of tests Le. tests with synchronous levels greater than approximately 4 

Grms. Numerous MSFC and contractor personnel were - involved in the effort and 

investigated different facets of the problem such as imbalance, tear down inspection 

records, common components, etc. for each vibration data group. The conclusion from 

the original study was that the increased synchronous vibration levels were associated with the HPOP Main Impeller. 

2.4 . Listing of Suspect Main Impeller 

The results of the MSFC/NASA investigation specifically identified six main impellers common to the second data group of tests, i.e. tests with synchronous vibration 

levels greater than 4 Grms. A total of 33 main impellers were investigated. The 

serial numbers, tests, power levels and the serial number of the HPOTP where 

the main impeller was installed are shown in Tables I1 through VII. These tables 

are a modified version of output of a computer routine available within NASA/MSFC 

for tracking components of the SSME. 

29 
--a_-- ------ Synchronous 104% PI# CUL 12-HOU-85 

tduwber 66 tests =542 

TEST #.AS ai29i-wae8i r~2282-3d4,H31~5-~6i~ 

tlaan = 3.06 

Std dev = A19 

Step site = 0.5 

Bin Suns 

6,s) 1 47 83 118 

< 2.3) fS 45 31 29 

t 4.5)' 13 ' 7 9 16 

4 6.3) 15 17 22 13 

4 8.5) 6 1 2 1 

(12.51 0 1 

LOX PBP RkD 45 

LOX PBP RAD 135-1 

LOX PBP RAP 135-2 

Lo# PBP RAD 186 

LOX PBP RAD 225 

410.3) e i Q i 

- - - Gama Curve (8.1) 

C rtts 

Figure 3. Cumulative Distribution HPOTP-PBP Total Data Base 104Oh 

rn 

Hran = 3.66 

Std dev = 2.19 

2.5) SS 

( 4.5) 13 

6.5) 15 

8.5) 6 

(1a.5) Q i12.5) 0 

LOX PBP RCiD 

LOX PBB RCiD 

LOX PElP RRG 

LOX PBP RAP 

LOX PBP RkG 

e I 2 3 4 5 s 7 8 9 lei112 

I; rm 

Skep size = 8,s 

6iR Sufis 

t 6.5) 1 47 83 116 

45 31 25 -# 9 16 

1; 2% 13 

121 

181 

1 

4s 

135- I 

135-2 

i 80 

225 

- 

13 14 IS 

Figure 4. Probability Density HPOTP-PBP Total Data Base 104% 

30 
------ ------ Synchronous 104: PWR LUL 12-tUJ-8S 

TEST #'S A1231-1951fi22Bi ,A220?-384rfi3125-?GI g 

t4Ul.Ib~f 06 test: =348 

tleurr = 1.64 

Std dav = 0.75 

Step site = 8.5 

&in SUBS 

0.5) 8 71 95 78 

C: 2.5) 63 31 16 1 

4 4.5) 1 1 

LOX TURB Rfili 45 

LOX TURB RfiD 90 

LW TURB RIiD 135 

- - Canna Curve 40.1) 

G rtu 

Figure 5. Cumulative Distribution HPOTP-TURB Total Data Base 104% 

38 

25 

P 

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1s 

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5 

8 

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Maun = 1.64 

Std dew = 8.75 

Step size = 8.5 

Bin Suirs 

.( 8.9) 8 71 95 70 

4 2.9) 68 31 16 1 

4 4.5) 1 1 

LOX TURB Rfi# 45 

LO% TURB RAD 98 

LOX TURB RiiD 135 

Figure 6. Probability Density HPOTP-TURB Total Data Base 104% 

31 
------ ------ Synihrmaus 18% PW LitL 15-tlOV-ti5 

TEST 1.S ~119J-3952H~115-38J?H~8~~-2~~, 

IiUbIbSt-. of tests =1299 

IOU 

96 Neiln = 2.35 

Std ilev = 1.6% 

88 Step 5128 = 0.5 

Bin Suus 

0.5) 6 213 264 233 

< 2.5) 183 113 66 51 

< 4.5) 42 29 29 15 

( 6.5) 14 7 11 6 

4 8.5) 3 1 2 2 

(10.5) 4 2 z 0 

i12.5) 1 

LOX PbP RkD 45 

LOX PEP RAP 135-1 

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LO:-: PBP HAD 156 

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70 E 

R 

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30 

28 

18 

0 

c 68 

0 12 3 4 S 6f 8 9 lQi11213li15 G rHs 

Figure 7. Cumulative Distribution HPOTP-PBP Total Data Base 100% 

I 4 nStep fire = 6.5 

Bin SUIJS 

i 8.5) 6 213 264 233 

i 2,s) 183 113 66 51 

i 6.5) 14 7 11 6 

4 8.5) 3 1 2 2 

410.S) 4 2 2 a 

i12.5) 1 

LOX PBP RRG 45 

LOX PEP RRD 135-1 

LO!< PBP RAD 135-2 

LOX PBP RdD 188 

LO# PEP RAD E23 

P 

E 

R 

N 

T 

k 

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E 18 

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r J 

6 

8 12 3 15 6 7 8 9 lOil12131415 

G rnr3 

Figure 8. Probability Density HPOTP-PBP Total Data Base 100% 

32 
1 

tletirl = 1.62 

Stil dZU = 6.84 

Step jizz = 8.5 

b1n suw 

< c5.5) 18 234 Pi34 182 

( ?.Si 162 163 26 6 

r 4.5) li i 2 2 

r 6.5) 

LOX TURb RAD 45 

LlsX TURb RAG 96 

Lot-: TURB RHO 135 

Figure 10. Probability Density HPOTP-TURB Total Data Base 100°/o 

33 
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30 

20 

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c rrls 

Figure 11. Cumulative Distribution HPOTP-PBP Total Data Base 109% -_ 

Hcan = 2.72 

Std itav = 1.72 

Step site = 0.5 

1 Bin SUHS 

( 9.5) 3 78 166 97 

( 2.5) 117 87 68 32 

( 4.5) 21 26 26 12 

( 6.5) I1 6 5 6 

( 8.5) 5 2 1 I 

(.18.5i I 1 

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LOX pep RAD 135-1 

LOX pep lim m--2 

LOX pep RAD 180 

LOX PBP RAD 225 

28 

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Figure 12. Probability Density HPOTP-PBP Total Data Base 109Oh 

34 

Maan = 2.72 

Std de*/ = 1.72 

Ster, size = 0.5 

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s 

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ii rns 

Figure 13. Cumulative Distribution HPOTP-TURB Total Data Base 109% 

35 

30 

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8 1 e 3 4 5 6 7 8 9 101112131415 

G rns 

Figure 14. Probability Density HPOTP-TURB Total Data Base 109% 

Heile = 1.55 

Std ilev = 6.74 

Bin Suns 

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LOX TURB RAD 90 

LOX TUkB RAD 135 

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41 
2.5 Synchronous Vibration Data of Six Main Impellers 

The next step in the investigation was to repeat the analysis with the six main 

impeller vibration test data separated from the data sample. The results are shown 

in Figures 15 to 22 at the 104% power level. These plots present a very strong 

implication of two distinct data groups and indicate the listed six main impellers 

as very suspect. This conclusion is based upon the obvious visual difference 

between the density histograms of Figures 4, 15 and 16. No elegant statistical 

mathematical methods are required. Also it should be noted that the cumulative 

distribution after removal of the suspect main impeller data provides a much better 

fit to the classical Gamma distribution discussed in Reference 1.l Figures 23 to 38 

are the plots at 100% and 109% power level and also indicate a difference between 

groups, while not as dramatic as the 104% power level. Very little change appears 

in the LOX TURB RAD vibration cumulative distribution and probability density plots 

which is further evidence to suspect components on the preburner end of the turbopump. Since the purpose of this document is to record the results of the study, 

rather than a detailed discussion of statistical techniques and physical effects, a 

detailed analysis of each plot will not be addressed. The difference in the 

calculated mean Grms and standard deviation for.the three data groups are listed in 

Table VIIP. 

Reference 1. Swanson, W. 

for the SSME High Pressure Turbopump 

"Statistical Analysis of the Vibration Data 

During Flight," Wyle TM 64058-01 October 1985. 

42 
TABLE VIII. LOX PBP RAD SYNCHRONOUS VIBRATION LEVELS 

Total Data Base 

Mean 2.35 Grms 

Std Dev 1.69 

Data Sample 1299 

Mean 3.06 Grms 

Std Dev 2.09 

Data Sample 542 

Mean 2.72 Grms 

Std Dev 1.72 

Data Sample 712 

100% Power Level 

Six Main Impellers 

4.61 Grms 

2.16 

219 

104% Power Level 

6.57 Grms 

1.86 

111 

109% Power Level 

5.42 Grms 

2.14 

114 

Normal Operation 

1.89 Grms 

1.12 

1080 

2.09 Grms 

1.05 

412 

2.15 Grms 

1.03 

576 

. Spatial Average LOX TURB RAD Synchronous 

100% Power Level 

Total Data Base Six Main Impellers Normal Operation 

Mean 1.62 Grms 2.07 Grms 1.55 Grms 

Std Dev 0.84 1.08 0.76 

Data Sample 971 138 833 

104Oh Power Level 

Mean 1.64 Grms 1.80 Grms 1.59 Grms 

Std Dev 0.75 0.76 0.73 

Data Sample 348 61 276 

109% Power Level 

Mean 1.55 Grms 1.70 Grms 1.52 Grms 

Std Dev 0.74 

Data Sample 546 

0.82 

82 

43 

0.73 

449 
Normal HPOTP Operation 104% 

ENTER, a 1 > LIST STCltiPARP TISBLE 

2) PLOT PROERBILITY PISTRIBUTIOti 

3) PLOT PROBABILITY QENSITY 

9) SELECT FI NEW SET OF TESTS 

5) SELECT NEW DGTCI TYPE At@ PWRLVL 

6) RETURH TO MRIN 

* Six Main Impellers 104% 

TESTS USED IN THIS ANALYSIS: 

TEST #/S A1389, A1432, A1442-443, A2310, A2375-376, A3183-209, A3216-219 

44 
Heon = 2.69 

Std dev = 1,65 

Step size = 6'5 

ORIGINAL PAGE 1s 

Q POOR OUALlTY 

P 8ia Surs 

E 20 ( 0.5) 1 47 E3 103 

( 2.5) 72 41 24 19 

R 

( 4.5) 9 2 4 3 c 

< 6.5) 0 1 1 E 

H 

LOX PBP RfiG 45 T 15 

LOX PBP kAIi 135-1 I 

6 

E LOX P6P RriD 135-2 

LOX Pep RfiG 229 

Comparison 

Total Data Base 

Figure 4 

LO:-: pep RAD tm 

5 

- ~ - - GUIIII~ Curve i8.5) 

6 

C r~l3 

Figure 15. Probability Density for HPOTP-PBP Normal Operation fo4%f 

_- 

tlaila = 6.57 

Std dev = 1.56 

20 1 Step size = 6.5 

C rtis 

Figure 16. Probability Density for HPOTP-PBP Six Main Impellers 104% 

45 
38 

-4 .>E 

P 

R 

c 

E 

tt 

T 15 

A 

G 

E 

E E0 

5 

6 

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Meoa = 1.33 

Stii dev = 4.73 

Step size = 6.5 

Bin Suws 

5 0.5) 6 59 81 57 

4 2.5) 44 19 7 1 

4 4.5) 1 1 

LOX TURB RAD 45 

LOX TURB RAD 90 

LOX TURB RAO 135 

Comparison 

Total Data Base' 

Figure 6 

Genna Curve (8,Si 

3 4 5 6 7 8 9 10 11 12 13 14 19 

'C r115 

Figure 17. Probability Density HPOTP-TURB Normal Operation 104% 

25 

23 

P 

E 

R 

E 

ti 

T 

A 

C 

E 16 

c 15 

r 

8 

I. 

I\ 

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12 

7 

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Mean = 1.(30 Std dev = a.36 

Step size = 6.5 

Bin Suns 

5 0.5) 2 10 13 12 

( 2.5) 13 9 2 

LOX TURB RAG 45 

LOX TURB RAP 9% 

LOX TURB RAD 135 

v 

\ . - - - G~AN~ Curve C8.% \ 

\* 1 I I 1 I I 1 1 I 1 

3 4 5 6 7 8 9 10 11 12 13 14 1S 

C ~RI 

Figure 18. Probability Density HPOTP-TURB Six Main Impellers 104% 

46 
QRIG1NAL PAGE Is 

OF POOR QUALlt71 

1 OBr 

46 

88 

7tl E 

k 

c 66 E 

ti 

n 

t 

E 48 

3& 

20 

10 

8 

1 58 

i 

- Hear1 = G.5f 

Std dev = 1,86 

- Step size = 6.9 

Bin Sum 

8.5) e e 8 4 

4 2.5) 2 0 3 3 

4.5) 1 2 5 13 

( 6.5) 15 16 21 13 

8.51 6 1 1 

412.5) 0 f 

LOX PBF RAD 45 

i10.5) 8 1 B 1 

LO% pep HAP 135-1 

LOX pep RAD 135-2 

LOX pep R~P 180 

LUX pep NAD P~S 

- 

- 

- - Gaiwia Curve (8.1) 

l a 1 A 

0-1 2 3 4 5 6 7 8 9 lB1112131415 

/ 

I 

I.leari = 2,09 

Std dev = 1.65 

Step size = 8.5 

Bin Suws 

< 8.5) 1 47 83 185 

< 2.5) 72 41 24 19 

( 4.5) 9 2 4 3 

{ 6.5) 6 1 1 

LW. PBP RAD 45 

LOX pep RAD 135-1 

LOX pep RAD 135-2 

LOX pep RQD 188 

LO:-: pep ME! 225 

Comparison 

Total Data Base 

Figure 3 

e 

Qui 2 3 4 5 6 7 8 9 10 11 12 13 14 15 

C rw 

t I 1 I I 1 1 1 I , I I I 1 & 

Figure 19. Cumulative .Distribution HPOTP-PBP Normal Operation' 104% 

Figure 20. Cumulative Distribution HPOTP-PBP Six Main Impellers 104% 

47 
101 

90 Neaa = 1.54 

Std dzv = 0.73 

88 Step size = 8.5 

78 

Bin SUM 

8.51 6 59 81 57 

( 2.5) 44 14 7 1 

LOX TURB RirP 45 

LOX TURB RAD 90 

E 

R 

li 

T 58 t LOX TURB RAD 135 

E 4ti 

30 

26 Total Data Base 

10 

6 

E 68 ( 4.5) 1 1 

Comparison 

Figure 5 - 

- - Coma Curve (0,l) 

6 12 3 4 5 6 7 8 9 101112131415 

G rrqs 

Figure 2 1. Cumuiative Distribution HPOTP-TURB Normal Operation 104% - 

I - . Gotlnu Curve (0.1) 

I I 1 1 1 1 I I I I a l a 1 

0 i 2 3 4 5 6 7 8 9 i0lli21314l!S 

I; rr+s 

tlalln = 1=88 

Std de\t = 1.x 

Stap site = 6.5 

Birc Suns 

i 0.5; 2 16 13 12 

< 2.5) 13 4 2 

LOX TURB RirD 45 

LOX TURB RW 38 ' LOX TURB RAD 135 

Figure 22. Cumulative Distribution HPOTP-TURB Six Main Impellers 104% 

48 
Normal HPOTP Operation 100% 

ORIGINAL PAGE IS 

OF POOR QUALrrV 

Six Main Impellers 100% 

ENTER. *. 1 2 LIST STCINGARD TABLE 

22 PLOT PROBABILITY DISTRI8UTION 

3) PLOT PROBkBILITY DENSITY 

42 SELECT A NEW SET OF TESTS 

52 SELECT NEW DATA TYPE kNG PWR11JL 

6) RETURN TO t4kIt.l 

49 
I 

I 1 I 1 

b 

1 

NCilrl = 1.89 

Std dav = 1.12 

Step rite = 6.5 

Bin SUWJ 

C a.s> 6 Ell 256 226 

4 4.5) 21 4 8 1 

( 6.5) 5 i 2 B 

(18.5, 1 1 

4 2,s) 165 93 45 2% 

{ 8,s) 1 b 0 8 

3 4 5 6 7 8 9 16 11 12 13 14 15 

t rias 

LOX pep RAD 4s 

LIX Pep RAD 135-2 

LOX Pep RAG i8a 

LOX PBP RAG 135-1 

LOX PBP RAD 225 

Comparison , 

Total Data Base 

Figure 8 

Figure 23. Probability Density HPOTP-PBP Normal Operation 100% 

------ Synchronous 100% PWR LUL 21-tlOU-8J 

tiearc = 4.61 

Std drv = 2.16 

Step size = 0.5 

Bin Suns 

Nunber of tests =213 

25 

a 

P 

E 

R 

E 

I4 

T 

E 1Q 

15 

t 

LOX pep RAD 4s 

LOX PBP RAD 135-1 

LOX PBP RAG 135-2 

LOX PBP RAD 180 

LOX PBP RAD 225 

5 

a Curve (8.5) 

0 

z-@ 12 3 4 5 6 7 8 9 10111213141S 

G rns 

4 8.9) 0 2 8 7 

i 2.5) 18 26 21 23 

{ 4.5) 21 26 21 14 

< 6.5) 9 6 9 6 

< 8-5) 2 1 2 

(16.Si 3 1 2 f 

(12.5) 1 

Figure 24. Probability Density HPOTP-PBP Six Main Impellers 100% 

50 
35 

30 

P 2s 

E 

R 

C 

E 29 

ti 

T 

A 

G 15 E 

16 

5 

ct 

1 

r) 

\ 

\ 

i: 

b 

\ 

8 

\ 

10% YClF LUL 13-tWJ-85 

Wean = 1.55 

Std de+# = 8.76 

Step site = 6,s 

Bin SUHS 

{ 8.5) 18 212 255 156 

2.5) 82 83 14 4 

4.5) 4 5 

LOX TURB RAD 45 

LOX TURB RfiD 90 

LOX TURB RIlP 135 

Comparison 

Total Data Base 

Figure 10 

Figure 25. Probability Density HPOTP-TURB Normal Operation 100% 

u - -- 

25 

28 

P 

E 

R 

E 

ti 

T 

I 

C 

E 10 

c 15 

5 

0 

i 1: 

Neila = 2.b7 

Std dev = 1.06 

Step size = 0.5 

Bin Suns 

< 6.5) 

Lo)( TURB RAL; 35 

LOX TURB RAD 98 

LOX TURB RAD 135 

Figure 26. Probability Density HPOTP-TURB Six Main Impellers 100% 

51 
Synchronous 168% PCIF. LOL 18-1.1051-85 ------ ------ 

tlunber. iif tests =i€l8U 

38 HCJS = 1.89 

Std dev = 1.12 

88 Stc~ size = 6.5 

70 Bin Suas 

E 

R 0.5) 6 211 256 226 

< 2.5) 165 93 45 20 

4 4.5) 21 9 0 1 c 68 E 

H < 6.5) 5 D 2 i3 

T 56 

I 

C 

E 40 

< 8.51 t 0 B e 

(ii3.s) i i 

LO?: PBP RfiD 15 

LOX PBP RAD 135-1 

LOX PBP RAD 135-2 

38 LOX P6P RAD 188 

LOX PBP RfiD 225 

20 Comparison 

18 Figure 7 

0 

Tot21 Data Base 

- - GUPIPN Curve <ija1> 

G rm 

Figure 27. Cumulative Distribution HPOTP-PBP Normal Operation 100% 

1 OB 

90 Wean = 4.61 

Std ilev = 2.16 

80 step size = 0.5 

Bin Suns 78 

< 0.5) 8 9 8 7 

i 2.5) 18 28 21 23 

R 

i 4.5; 21 28 21 14 L' 66 E 

ti < 6.5) 9 6 9 6 

( 8.5) 2 1 2 2 

ClfLSj 3 1 2 8 T 50 

if2.S) 1 a 

G 

LOX PBP RPG 45 E de 

LOX PBP RAD 180 

LOX PBP RGG 225 

LOX pep R~D 135-1 

30 LOX PBP RAD 135-2 

20 

10 

L1 

b 

t rris 

Figure 28. Cumulative Distribution HPOTP-PBP Six Main Impellers 100% 

52 
96 Mearc = 1.55 

Std dev = 6.76 

88 Step Pize = G.5 

70 Bin Suw 

< 0.5) 18 212 255 156 

4 2.5) 82 83 14 4 

i J.Si 4 5 

LOX TURB RAD 45 

LOX TURB RAD 36 

LOX tURB R6iD 135 

E 

R 

c 60 E 

ti 

T 50 

A 

C 

E 16 

38 

20 Total Data Base 

10 

0 

Comparison 

Figure 9 

- - . Gunm Ourw (8.1) 

0 12 3 4 5 6 7 5 9 101112131413 

C rnr 

Figure 29. Cumulative Distribution HPOTP-TURB Normal Operation 100% 

------ ------. Synchronous 10BX PUR LUL 21-HOU-85 

Wunber of tests =138 

&arc = 2.67 

Std dav = i.68 

Step size = 0.5 

Bin Sums 

C 8.5) 0 22 29 26 

< 2.5) 20 20 12 2 

r 4.5) 2 f 2 2 

< 6.5) 

LOX TURB HiiO 45 

LOX TURB NAD 90 

LOX TURB HAD 135 

- __ GannQ Curve Cft.1) 

I . 1 

6 12 3 4 S 6 7 8 9 iBll1213141J 

G rns 

Figure 30. Cumulative Distribution HPOTP-TURB Six Main Impellers 100% 

53 
Normal HPOTP Operation 109% 

ENTER, 1 I 

C! 

3i 

43 

.- . 

53 

6) 

LIST STAHCJARD TABLE 

PLOT PROBABILITY DI STRIBUT ION 

PLOT PROBABILITY DENSITY 

SELECT A NEH SET OF TESTS 

SELECT tiEW GftTA T'iPE AND PWRLK 

RETURN TO MAIN 

Six Main Impellers 109% 

TESTS USEE It4 THIS ANiiLYSIS: 

ENTER.. .11 LIST STriHDtiRD TABLE 

2) PLOT PROBABILITY DISTR IeUTl ON 

3) PLOT PROBABILITY DENSITY 

42 SELECT fi NEW SET OF TESTS 

51 SELECT NEW GATA TYPE AND PWRLllL 

6; RETURH TO t.IAIN 

54 
25 

20 

P 

E 

R 

E 

H 

T 

1 

C 

E 18 

c 1s 

r J 

0 

I 

Meitn = 2.1% 

Std dev = 1.63 

Step size = ts.5 

Bin Suns 

3 4 5 6 7 8 9 10 11 12 13 14 15 

C rru 

r 8.5) 3 78 186 a8 

2.5) 189 88 63 26 

( 4.5) 13 6 2 B 

c 6,s) 1 1 

LOX PBP RfiD 45 

Loll PBP RAG 135-1 

LO# PlrP RAD 135-2 

LOX PBP RriD 225 

LO# PBP RAG tea 

Comparison 

Total Data Base 

Figure 12 . 

Figure 31. Probability Density HPOTP-PBP Normal Operation 109% 

------ Sync ttronuus 189:; PbJB LOL 15-HOW?5 

Nur.rbzr uf tests =114 

25 

28 

P 

E 

R 

E 

14 

T 

A 

G 

E 18 

c is 

c 4 

e 

l A 

0 

1 

1 

I 5 

i @.Si 

i 2.5) c 4.5) 

( 6.5) i 8.5) i10.5) 

#eua = ;.sz 

Std de\r = L.14 

Step size = 8.5 

Bin Suns 

6 

6 

16 

5 

2 

3, 

.e 

1 

3 

1 

la 

LOX PBP RClD 45 

LOX PBP RirG 135-1 

LOX PQP RirD 135-2 

LOX pep it^ le6 

LO:: pep BAD 225 

G rws 

Figure 32. Probability Density HPOTP-PBP Six Main Impellers 109% 

55 
35 

38 

P 25 

E 

R 

C 

E 28 

N 

T 

fi E 15 

1Q 

5 

0 

I 

109% PWR L!IL 14-tiO\J-85 

tJcan = 1.52 

Std $CY = 0.73 

Step size = 8.5 

Bin SUM 

C 8.5) 4 116 1147 8'3 

4 2.5) 50 22 6 0 

< 4,s 3 

LOX TURB RID 45 

L6X TURB RID 90 

LOX TURB RAD 135 

Comparison 

Total Data Base 

Figure 14 

__ Canwu Curve (8.5) 

33. Probability Density HPOTP-TURB Normal Operation 109% 

1iURh?f of tests =82 

30 - 

Mecrn = 1.76 

Stii dev = 6.82 

Step size = 6.5 

Bin SUM 

< 0.5) 1 17 23 18 

4 2.51 12 7 2 e 

4.5) 1 1 

LOX TURB RAD 45 

LOX TURB RAD 90 

LO): TURB RID 135 

Figure 34. Probability Density HPOTP-PBP Six Main Impellers 109% 

56 
so 

88 

78 E 

R 

E 

N 

56 

G 

E 48 

38 

28 

C 68 

0 

G rns 

Bin Sufis d 

I { 4 0.5) 3 78 106 158 

C 2.5) 109 80 63 26 

C 4.5) 13 6 2 0 

C 6.5) 1 1 

LOX PlrP RAD 45 

LOX PBP R(IP 135-1 

LOX PBP RAP 135-2 

LOX PBP RAP 225 

LOX PBP RAD 186 

Comparison 

Total Data Base 

Figure 11 

Figure 35. Cumulative Distribution HPOTP-PBP Normal Operation 109% 

t 96 

t 

i W but1 50 

A 

G 

E 48 

:: t 

16 

lc- -- - 

Meun = 5.42 

Btd dev = 2.14 

Step size = 8.5 J Bin Sufis 

c 8.5) e e e 9 

i 2.5) S 6 1 4 

i 4.5) 8 16 18 

6.53 9 5 3 

C 8.5) 6 2 1 

(10.53 2 2 

LOX PBP RAD 45 

LOX PBP RkD 135-2 

LOX PBP RtiP 180 

LOX PBP RAO 225 

LO): pep RAD 135-1 

/ . - - Gama Curve rCl.1) 

0 1 1 I I I I 1 I I 1 1 I I 

6 12 3 4 5 6 7 8 3 lB1l12131415 

G rms 

Figure 36. Cumulative Distribution HPOTP-PBP Six Main Impellers 109% 

57 
38 Hearc = 1.52 

Std der? = 0.73 

88 Step size = 8.5 

Bin Suns E 78 

i 8.5) 4 116 147 8s 

C 2.5) 58 22 6 8 

LO% TURB RAD 45 

LOX TURB RitO 98 

LOX TURB RAD 135 

R 

E 

N 

T 58 A 

G 

E 48 

30 

20 Total Data Base 

18 

6 

4.5) 3 c 68 

'Comparison 

Figure 13 

~ - - Gan~o Curve C0,l) 

6 12 3 4 5 6 7 8 9 101112131415 

t rRs 

Figure 37. Cumulative Distribution HPOTP-TURB Normal Operation 109% 

Meart = 1.79 

Std dev = 6.82 

Step Sit4 = 8.5 

Bir Suns 

0.5) 1 17 E3 ld 

c 2.5) 12 7 2 0 

405) 1 1 

LOX TURB RAD 45 

LOX TURB RiiD 90 

L01d TURB RAD 135 

- - - Coma Curve (8.1) 

12 3 4 5 6 7 8 9 1Oli12131415 

G rw 

Figure 38. Cumulative Distribution HPOTP-TURB Six Main Impellers 109% 

58 
2.6 Random Selechon of Tests 

A random sample of 29 tests was selected, which is the number of tests in the six 

main impeller data sample, to evaluate the effect of sample size. The same analysis 

was used for this new data group and the results are shown in Figures 39 and 40. 

While it is recognized this method of analysis is not rigorous, it seems reasonable 

to assume a random selection should have followed a relative smooth continuous type 

of distribution unless the data is from two different data groups. The distribution 

is again bi-modal and presents additional evidence that the total data sample 

consists of two different data groups. 

59 
ORIGINAL PACE tS 

CIF POOR CNJALIW 

Random Selection of 29 Tests 

60 
- 

Hean = 3.00 

Std dev = 2.18 

Step size = 8.5 

Bin Surts 

C 8.5) 6 9 16 23 

c 2.9) 11 7 re 4 

c 6.5) 2 4 4 3 

< 8,s) 2 1 

i( 4.5) B e 2 i 

I / LOX PBP RfM 45 

LOX PBP RtiD 135-1 

LOX PBP RAD 135-2 

LOX PBP RAG 180 

Lox PEP RAP 225 

~ - - Ganrw Curve (9.1) 

I I 1 I I 1 I I 1 I I 1 1 

8 12 3 4 5 6 7 0 9 101~~21314(5 

C rN5 

Figure 39. Cumulative Distribution HPOTP-PBP Random Selection of 29 Tests 104% 

25 

E0 

P 

E 

R 

E 

H 

T 

1 

G 

E ie 

c 15 

c J 

0 

81 

Mean = 3.08 

Std cle?, = 2.18 

Step size = 0.5 

Bin SUM 

< 8.51 8 9 16 23 

< 4.5) e 0 2 1 

< 6.J) 2 4 4 3 

c 2.5) ii 7 10 4 

8,J) 2 1 

LOX PBP RAD 45 

Loii PBP RbD 135-1 

LOX PBP REtD 135-2 

LOX PBP RiiD 180 

LOX PBP RiiO 225 

- - - Gama Curve (0.5) 

3 4 5 F, 7 8 9 10 11 12 13 14 15 

i; rvis 

Figure 40. Probability Density HPOTP-PBP Random Selection of 29 Tests 104% 

61 
2.7 Vibration Test History of the Six Main Impellers 

To complete this analysis, the synchronous spatial average vibration test history of 

the six main impellers is plotted. In the original study the data was hand plotted, 

and later incorporated as a routine in the MSFC Diagnostic Data Base Program. The 

output is shown in Figures 41 to 46. Listed below are the main impeller serial 

numbers, HPOTP serial number, last test and date of test. 

Main ImDeller S/N HPOTP # Last Test Date 

2427800 

3134124 

3334446 

3 135444 

7326066 

7363708 

2412 

231 1R1 

2208R 1 

02 1 OR2 

0307 

91 11R1 

A3-207 

A 1-405 

A1-432 

A3- 192 

A2-376 

A3-191 

7-21-83 

2-4-83 

1-4-84 

3-2-83 

11-1 1-83 

2-12-83 

It is beyond the scope of this study to ‘fully investigate the variation in synchronous vibration levels from test to test, pump build to pump build or verify the six 

main impellers were the sole contributor to the bi-modal distribution of the HPOTP 

synchronous vibration data. However, since the original study only main impeller 

S/N 7326708, HPOTP #0307, Test A2-375 and A2-376 (Figure 46) has deviated from the 

pattern of all the identified main impellers being associated with abnormal synchronous vibration levels. For reference, the mean, la 20, and 3u vibration 

levels for normal turbopump operation are as follows. 

HPOTP PBP RAD Spatial Average Synchronous 

100% - 104% - 109% 

Mean 1.89 Grms 2.09 Grms 2.15 Grms 

Std Dev 1.12 Grms 1.05 Grms 1.03 Grms 

Mean + 1 u 3.01 Grms 3.14 Grms 3.18 Grms 

Mean + 2 G 4.13 Grms 4.19 Grms 4.21 Grms 

Mean i- 3 u 5.25 Grms 5.24 Grms 5.24 Grms 

The vibration levels for 104% power level are shown on each plot to illustrate the 

deviation from the expected normal operation value and relationship to the sigma 

levels. 

62 
30 

20 

104% 

10 

m 

33 22 2222111' 3 1 

55 66 7%88'"7 9 9 

78 5 6. 9 3 4 5 b i 2.. 3 0 

2 

1. 

8. 

8 

R 

'1 

2 2 3 2 2 

088 1 1 

888 2 2 

R R R; 

222 

iii 3 4 

104% 

33333333333 

11111122222 

9 9 9 *9\.9 9 B 8 0 8 B 

45673901345 

2 2 2 2 2 2 '.E 2 2 2 2 

44444444444 

11 11 11 l'i 11 1 

2 2 2 2'2 2 2 2 2 2 2 

3 

2 

0 

- 

7 

I 

2 

4 

1 

2 

- 

Figure 4 1. Synchronous Vibration Test History, 

Spatial Average PBP, Impeller S/N 2427800 

63 
3q 

2rr 

104% 

1 fJ 

ni 

333333 2 .2 3 333 

4444.14 ‘6 7 6 339 

222’2’ 22 2 222 

11 2 333 

0080c10 11 1 111 

999999 11 1 111 

111i1r 

‘8 

2 

3 

1 

1 

2 

3 

1 

1 

R 

111 

1 

1 

R 

2 

3 

1 

1 

R 

Figure 42. Synchronous Vibration Test History, 

Spatial Average PBP, Impeller S/N 3134124 

64 
.1 

c 

R 

M 

s 

0 

8 

1 3322 

ole% 7 

3333'3 333 

7"T 7 888 

4;;7 9 012 5 9 o 8 9% 

2222 2 222 3 L. b. '222 

2222.2 222 2 2222 

1111 1111 1 Bo88 

2222 2 222 2 5588 

R 

1 

22 2 2 2 

22 2 2 2 

00 0 o 0 

88 8 8 8 

R 

1 

IO49 

Figure 43. Synchronous Vibration Test History, 

Spatial Average PBP, Impeller S/N 3 134446 ' 

65 
ORIGINAL 

OF POOR 

2 1 

2 3 

7 8 

7 9 

- - 

2 3 

1 3. *1 

8 0 3 

3 6 L 

3 

.Q 

1 

1 

8 

8 

2 

1 

8 

0 

1 

0 

3 

c 

0 

2 

1 

0 

Q 

1 

1 

0 

R R R 

1 1 2 

Figure -44. Synchronous Vibration Test History, 

Spatial Average PBP, Impeller S/N 3135444 

104% 

99 

11 

11 

11 

PAGE IS 

QUALITY 

Figure 45. Synchronous Vibration Test History, 

Spatial Average PBP, Impeller S/N 7363066 

66 
30 

2 il 

in 

104% 

m 

-99s 

2086) 

8234 

2EEE 

ill 

6) 

00BB 

8068 

7000 

R777 

lRRR 

lli 

- 

3 3 

8 - 

3 2 

3 

- - .. - 

3 

3 

4 4 4 

4 4 4 

2 3 4 k' 

0 0 0 0 

2 2 2 3 

0 8 

7 7 

0 8 

7 9 

3 G 

R 

S 

n 20- 

la 

m 

0 

lTTT 1 2 1 1 1 2 

Figure 46. Synchronous Vibration Test History, 

Spatial Average PBP, Impeller S/N 7326708 

67