ai-aerospace/ams_data_full_2000-2020 huggingface dataset:
© 2016 Sierra Nevada Corporation   371  GSFC -STD-7000 (General Environmental Verification Standard (GEVS)) . Figure 12 compares the  proposed test levels  (i.e., Final Modified Profile , plot 4 ) with GEVS and other historical profile s. These  comparisons  highlight  the strategic reduction in test input  levels at frequencies greater than 350 Hz and  contrast s the proposed profile to those associated with unsuccessful SADA tests . 

The proposed test profile met most criteria and was ultimately approved by the review community. The 350-Hz roll -off was selected because it was safely under the approximate 650- Hz natural frequency of the  SADA but well above (and inclusive of) significant response expected at the SADA during launch and spacecraft level tests. The profile also included a transition at 600 Hz from a straight to a kneed ramp.   This transition kept the test levels above GEVS minimum workmanship requirements and mitigated   concerns voiced during force- limiting tests when input significantly dropped below GEVS at the notched  frequency ( Figure 10).  

   Figure 12.  Final Tailored Vibration Profile Comparison

 The final modified profile did fall  slightly short of  the design goal to demonstrate analytical margin against  6-sigma dynamic load events  but the team felt the risk of gapping remained very low . Brush force margin  against an estimated 5.5-sigma load event still represented a very l ow likelihood of occurrence and the  design included additional inherent force margin against brush movement out and away from an assigned  groove if brush gapping did occur.  This modified profile was validated when SADAs  built for the follow -on  program  passed all required protoflight testing, including slip ring electrical isolation and resistance  checks, without issues. Review of post -test 3D radiographic brush block and rotor images similar to  Figure 6 confirmed all brushes were properly aligned and positioned within assigned rotor grooves  after  exposure to the modified test profile.  

Summary    The combination of increased minimum brush preload and testing to a modifie d random vibration test  profile ultimately  resulted in the successful completion of the SADA protoflight test program.  This final  success was a result of efforts from analysts, designers, and the entire review community starting with the  discovery of the initial fault through to the successful delivery of several sets of hardware. During this  process, significant insights were gained that will help mitigate the recurrence of similar problems in future designs.    650Hz – SADA First Lateral Mode  800Hz – SADA First Axial Mode
373 High -Performance  Reaction Wheel  Optimization  for Fine-Pointing   Space Platforms :  Minimizing Induced  Vibration  Effects on   Jitter  Performance plus Less ons Learned from Hubble Space   Telescope for Current and Future Spacecraft  Applications  

Martin D. Hasha* 

Abstract  

The Hubbl e Space Telescope (HST) applies  large -diameter  optics  (2.5-m primary  mirror)  for diffractionlimited resolution spanning an extended wavelength range (~100 -2500 nm). Its Pointing Control System  (PCS)  Reaction W heel Assemblies  (RWAs ), in the Support Systems Module (SSM) , acquired  an  unprecedented set of high-sensitivity Induced Vibratio n (IV) data for 5 flight -certified RWAs : dwell ing at set   rotation rates . Focused on 4 key ratios, f orce and moment  harmonic values  (in 3 local principal directions )  are extracted in the RWA  operating range (0-3000 RPM) . The IV test data, obtained under ambient lab  conditions , are investigated  in detail,  evaluated,  compiled,  and curve- fitted; variational  trends , core causes,   and unforeseen anomalies  are addressed. In aggregate, these values  constitute a statisti cally-valid basis   to quantify  ground  test-to-test variations and facilitate  extrapolations  to on-orbit conditions. Accumulated   knowledge of bearing- rotor vibrational  sources, corr esponding harmonic contributions, and salient  elements   of IV key varia bility fac tors are discussed. An evolved methodology  is presented for absolute assessment s  and relativ e comparisons  of mac ro-level IV signal magnitude due to micro- level construction- assembly  geometric  details/ imperfections stemming from  both elect rical drive and primary  bearing design   parameter s. Based upon studies of  same- size/similar -design momentum wheels ’ IV changes, upper  estimates due to transitions  from ground test s to orbital conditions  are derived. Recommended HST RWA  choices are discussed relative  to system  optimization /tradeoffs of  Line- Of-Sight (LOS) vector-pointing focal - plane error  driven by  higher  IV transmissibilities through low-damped structural dynamics  that stimulate  optical  elements . Unique analytical  disturbance results  for orbital  HST accelerations are described   applicable to  micro gravity efforts . Conclusions, lessons learned, historical context /insights , and  perspectives  on future applications  are given ; these previously unpublished data and findings  represents a  valuable resource for fine-pointing spacecraft or space- based platforms using RWAs , Control Moment  Gyros (CMGs) , Momentum Wheels, or other ball-bearing- based rotational  units . 

Figure 1.  HST Deployed Configuration Cutaway  & PCS Block Diagram  Highlighting  RWAs1,2                                                       * Lockheed Martin Space Systems Company, Sunnyvale, CA  

Procee dings of the 43rd Aerospace Mechanisms Symposium, NASA Ames Research Center, May 4-6, 2016
375 charact erizations; subsequently prompting additional analytical studies to minimize HST LOS jitter impacts  as described herein.  

PCS analyses originally showed RWA orbital rotation rate predictions of up to 5 Hz (4 RWAs operating);  with a potential reach to 10 Hz  (600 RPM) under rare unfavorable pointing attitudes. However, estimates  later climbed to ~20 Hz (1200 RPM) considering the additive effects of:  1) higher -than- normal solar -cycle  activity (where Earth’s ionosphere expands causing higher atmospheric drag t orque), 2) lowest -possible  orbit altitude forecasts (from later -than- expected Space Shuttle service mission/boosts originally planned  to occur ~5 years), and 3) assuring mission capabilities in the unlikely event of an RWA or magnetic torquer failure. Note that, due to RWA criticality, HST studies have been undertaken to find approaches to maintain  stability if up to 2 RWAs fail 7. Above worst -case rates and margins set upper bounds for LOS jitter studies.   Table 2.  Spacecraft LOS  Error Control Methods,  Pointing Accuracies/Stabilities , & Examples5  Spacecraft Pointing Accuracy Approximations Obtained via Various  System Approaches/Architecture Implementations  Spacecraft Relative Approximate Pointing  Accuracy Requirement Level   Pointing/Stability Performance Sensors (each step  down includes data/improvement from above)  Pointing  Accuracy (arc sec,  3σ)   Two Star Trackers  60-100   Adding Gyros  30-60 Typical Commercial Stabilized Satellite   Co-locate attitude sensors with instrument  3-30  Geoeye2 & SIM   Improving Star Catalog  1-3  Widefield Infrared Survey Explorer (WISE)   Using Instrument to Sense Orientation or Using  Fine Guidance Sensors  0.1-1.0  Reference Spacecraft & A2100 Variants    SIRTF & Deep Impact Spacecraft Flyby   Fast-Steering Mirrors/Advanced Isolation Systems  0.003- 0.1  Kepler    Extrasolar Planetary Imaging Coronagraph  (EPIC)   Systematic Managing /Reduction of al l Pointing Error  Sources + Interferometric Star Sensor in Op tical Path    + Source -Structural Mode Separation/Decoupling  Sub-milli -arcsec   Hubble Space Telescope  

Figure 2.  RWAs (2 of 4 ) in HST SSM Locations  & Diagram of Local Principal   Directions/Orientations   Vehicle   Principal Axes
376   Figure 3 .  HST SSM  PCS Pointing Error Budget & LOS Notional Disturbance -Managed  Elements3,8 

RWA Fundamental Mechanical Noise Vibrational Disturbances  Relevant  to HST Induced Jitter    RWA IV noise characteristics fundamentally  emanate from intrinsic  core/ assembly  imperfect ions, but can  change  due to  micro -effect  combinations;  e.g., bearing surface lubricant  re-distribution over time can create   small non-deterministic detectable deviations . Dynamic fine-balancing is a proven approach to minimize  IV;  specifically  at basic rotation rates  (i.e., 1.0 harmonic  ratio). IV macro- characterization is not normally  of  much concern except for predicting end-of-life issues  in many  rotating assembly  applications;  but much   more critical when applied to  highly sensitive transducer/sensor  platform s. Although judicious drive  motor  current monitoring can track  long- term bearing friction  changes /instabilities , it cannot reliably detec t nor  correlate well to  small IV changes along  RWA  force/moment axes . Detailed, in- situ, and statistically -valid  data are needed to quantitatively ascertain maximum expected IV levels  and bound  variations/ uncertainties ; more specifically, design- specific root sources, secondary empirical  manifestations, trends /correlation, and externally -imposed conditions that can directly impact  jitter limits,  system allocations , and margins . The effort  documented here was first  driven solely to enable HST jitter  verification efforts for comparison versus  specified  top-level limits  and sub- level budgets, since acquired IV  data are simply  input sources for  jitter modeling/analysis forcing- functions. However, due t o discovery  of  jitter’s hyper -sensitivity to IV , it became clear  after gaining significantly more detailed analytical data   (discussed below)  that contributions  from harmonic s and ground -to-orbital transition s must  also be  known/bounded for credible on- orbit predictions.  Prior to data compilation, wide speculative ranges  (i.e.,  orders -of-magnitude) existed regarding possible worst -case changes  due to relativel y modest  effects .  Alternately, if  variability  found can challenge IV measured under highly  benign lab and handling situations ,  what unforeseen excessive  IV might  result  from much more severe disturbing effects ( e.g.,  temperature/ pressure changes , or launch- ascent vibrations ).
377 

Figure 4 .  RWA Local Principal  IV Directions (Shown o n Isolators) &  Cutaway   Mechanical  Features9 

Fundamental RWA IV Disturbance Characterization:  Accompanied b y Higher Harmonics    Prior  program experience clearly demonstrated that RWA  fine-balancing  methods  – along with significant  margins (vs. required limits ), performed at minimum -detection levels on high- stiffness  test fixtures at  rated  design speed  (e.g., 3000 RPM)  with repeated  trial-and-error reductions,  were  successful . At first , because   HST RWA imbalance/IV is  specified across  a range of predicted on-orbit operating  speeds, basic 3-axis IV  force amplitude data was measured and reported at  agreed- to increments  of 500 RPM . As RWA IV  verification occur red (circa 1984)  flight unit  acceptance test data were requested. A dditionally,  to compare  value trending versus  precursor E ngineering Evaluation Unit that supported HST  proposal effort s’  fundamental performance analyses, spectral plots (force -amplitude -vs-frequency ) at select ed 200 RPM  increments  were obtained. It was noted that,  while attaining required  fine-balance levels  with significant  margins  (i.e., 1.0 radial force harmonic) , additional  RWA high- amplitude IV peaks  (Fig. 5) became   prominent ( not suppressed by fine-balancing ), the first indicator  of prominent  harmonic  content amplitudes  that tower over  primary IV  (~10 times  balanc ed 1.0 harmonic  level). At the  time, high- frequency   harmonics /ratios  were seen as an interesting curiosity  and not explicitly  addressed or enveloped in jitter  analytical assessments . PCS experts  were not concerned because this IV content was  so far beyond  practical  active control limits.  

Figure 5.  Typical RWA IV (800 RPM /13.33 Hz) & Waterfall -Style ( Slowly Increasing  Speed ) Plots 9
381 grade/limit , a maximum allowable residual unbalance (e.g., in g-mm/kg ) is determined for the rotor mass  and prescribed  service/ reference speed. N ote that maximum allowable  residual unbalance calculations  assume  that rotor mass is evenly distribu ted about t he center -of-gravity  and along the shaft between  bearings . For reference, a typical  (~10 lb(mass) rotor) spacecraft RWA static balance limit  is 0.007  oz(mass)-in;  equating to 44 µ-inch (1.1 µ-m) unbalance offset . HST’s large RWA (44 lb (mass) rotor) spec limit is  13.4 µinch (0.34 µ-m). One RWA’s post -environment  IV test resulted in 2.5 µ-inch (0.063 µ-m), an 80% margin.      Figure 7.  Rotating Mass Unbalance Parameters &  ISO Standard  1940  Balance Quality Grades15 

Output sinusoidal centrifugal force amplitude  (Fcf) is related to  rotor unbalance  parameter s by the following :  Fcf  = M∗d∗ω2= M∗d∗(2𝜋𝜋𝜋𝜋 )2= M∗d∗�2𝜋𝜋𝑛𝑛 60�2

Where  M is rotor mass, d  is effective distance between rotor  center -of-rotation and center -of-gravity/mass,  (Cg), and operating rotation  rate is given by n  (RPM) , f (Hz),  or ω ( angular velocity in radians/second). For  a designated ISO Standard 19 40 Balance Quality Grade, the fundamental  relationships are:    e=𝜐𝜐 1000∗ω=𝜐𝜐 1000∗2𝜋𝜋𝜋𝜋=𝜐𝜐 1000∗2𝜋𝜋∗𝑛𝑛 60   Where e is specific residual unbalance (gm-mm/kg) /displacement  (µm), υ is balance grade ( based on  angular rate and relatable to effective radius d via rotor mass ); rate parameter s are as above.  Resulting   RWA  unbalance (1.0-ratio) IV propagates  at a frequen cy matching the commanded rotation frequency . 

IV-Related Em pirical Findings  Relative to Bearing  Geometries and Geometric Imperfections    Since IV char acterization  stem s from fundamental bearing design aspects , geometric  parameters lead to  IV ratios/relationships. For example, HST RWA bearings ( a tailored variant of commercially available 304H - type angular contact ball bearings) have design dimensions shown in Table 3 relative to Figure 8. 

Figure 8  and Table 3.  304H  & Comparable  101H -Series Bearing Basic Design  Parameter Values [9]  d  Cg  Fcf  n ,ω  BEARING PARAMETER  304H  NOM. VALUES  101-TYPE NOM. VALUES   Inner Bore (d IB) 20mm (0.7874 inch)  12mm (0.4723  inch)   Outer Diameter (D OD) 52mm (2.0472 inch)  28mm (1.024  inch)   Pitch Circle Diam. (D PC) 35.6mm (1.402 inch)  20.2mm (0.796  inch)   Ball Diameter ( DB) 11.1mm ( 0.438 inch)  4.7mm ( 0.1875  inch)   Number of Balls ( N) 8 10  Contact Angle (α CA) 18.6 degrees  15.0 degrees   Material  52100 CEVM  52100 CEVM   Tolerance Class  ABEC 9  ABEC 9   Max. Runout Allowed  .0012 mm (.000047")  .0012 mm (.000047")   Bearing Configuration  2  DF Duplex Pairs  2  DF Duplex Pairs
391 narrow  for ESTR ). An ESTR has a precise frequency output  during slow -speed recording at 1.375 Hz;  repeatedly reconfirmed in on-orbit tests18,19. Telemetry data are bandpass filtered (1.1- 1.5 Hz) via  a  Blackman window for each principal  HST axis (V1, V2, and V3) . Bandpass rates are then different iated for  each Solar Array orbital event type, producing RSU angular accelerations. Results are multiplied  by the  distance to the HST C.G. to obtain an equivalent loc al linear acceleration at 3 specific locations. R ootmean- squared (RMS) values  (over time)  are then computed for each orbi tal disturbance period.  As a  specific reference, worst -case -maximum computed acceleration  for the known ESTR  input  primary  frequency  (i.e., 41 inches -per-second recording rate) is 0.75 µ g (axially ) and 0.49 µ g (radially ). 

Once the on-orbit model is correlated for the ESTR  known reference source, RWA inputs  are applied. Since  ground- to-orbit additive RWA IV variability cannot be known with certainty, worst -case as -tested IV forces   and moment s (with  4 key  harmonic ratios; 1.0, 2.0, 2.8, and 5.6) define input amplitudes ; derived from   computed coefficients14. Periodic ( i.e., pure sinusoidal) tim e histories are created for each RWA harmonic  for 2 different rotation rates: 3 Hz (nominal on- orbit ma ximum) and 10 Hz (typical -4-wheel case/ condition  upper bound). Individ ual time histories for  the 4 key harmonics are combined by direct addition,  no time - phasing nor dithering is done to simulate random phasing.  Time histories are combined simultaneously at  an RWA rotor source (for all local DOFs ) in the HST on -orbit dynamic FEM . Resulting frequency -domain  response, i.e., Fast-Fourier Transforms  (FFTs),  are developed; 2 typical  input -output examples (10 Hz  RWA) of response at the SSM Equipment Bay  (EB) (V2 direction) and RSU (V1 direction)  are shown in  Figure 1 120. Note domin ant modal ( i.e., non-optical here) transmissibilities  at 10, 20, 28, and 52 H z:   isolation system damped resonances are present . Also note that, summed results  are primarily dominated  by rigid body responses to the set force/moment RWA inputs, with the additive structural response being  minimal (further confirmation that the RWA isolation system is performing as intended) . Summary  HST  results are listed in Tables 13 and 14 . Note  that this was a first on-orbit reference confirmation leading to   the level of challenge present ed in attaining  low microgravity limits for  the International Space Station12. 

Figure 11 .  HST Mi crogravity -Related  Acceleration Response - Examples at EB (V2) & RSU  (V1)20     Table 13.  HST On -Orbit Acceleration Results; ESTR 1.375 Hz Input d uring Solar Array Transition s (4)20  HST Prin.  Direction  EON   Event  MIDN  Settling  EOD   Event  MIDD  Settling   V1RMS 0.49 µg  0.49 µg  0.66 µg  0.65 µg   V2RMS 0.03 µg  0.02 µg  0.04 µg  0.02 µg   V3RMS 0.09 µg  0.05 µg  0.12 µg  0.05 µg
393   Figure 12: General (Scalable) Cost Proportions for Typical NASA Spacecraft and Large Satellite  System -Missions21,22. 

Estimated ACS -related costs have limited utility unless the scope ( i.e., actual size) of a particular RWA unit  is better quanti fied. An established tool for  SE parametric cost analysis applies  multiple -program  data to  create Cost Estimating Relation ships (CERs) for the size/performance needed and historical  known- costs  (adding development -related factors). RWA CER equations have been determined,  however, they depend  on unit mass, whereas per -axis maximum angular momentum capability drives basic tradeoffs. Therefore,  as a bridge, a relationship between mass and angular momentum is established (with good overall correlation) 22,23. Note that this relationship encompasses RWAs from ~3- 300 kg, so is relevant for medium - to-large satellites, but needs revision for micro/ small -sat applications24. To assess future capabilities, the  connection from RWA angular momentum to mass to CER (Figure 1 3) was validated by  comparisons with  recent (circa 2014) known inertia wheel procurement costs to substantiate  lower and high bounds ; cost  analysis sources show an RWA range of roughly 1.5- 5.0% of satellite procurement costs25, a typical range  for RWA per -set costs are approximately 3- 4% of overall satellite procurement costs26. 

Figure 13 .  RWA Angular Momentum Sizing & Cost -Estimating -Relationship Projection22,23,24,25   Note that  a wide variety of programmatic factors ( e.g., small or singular procurements, design qualification  for a particular mis sion-environments, quality control -related requirements, special testing, added  documentation and particular added program requirements, etc.) raise s costs: higher range/limit  of values.  Alternately, larger  contract buys (often an impedi ment with high- performance spacecraft), minimal testing,  minimal doc umentation, and low procurement over head can drive costs towards  lower bounds.  

   Key: Payload        Structure       TCS      EPS      TT&C        ADC/ACS      Propulsion 21.7 %5.3 % 28.3 %4.5 %5.8 %4.4 %Larger Satellites [Up To Several Tons Mass (15)] 30.1 % 0 10 20 30 40 50 60 RWA Unit Mass (kg)RWA Unit Cost (2014 dollars/1000)High Range Low Range350 300 250 200150 100 50 0RWA Unit Cost Vs. Size (Mass) y = 0.1595x + 2.1556 R² = 0.9696 01020304050 0 50 100 150 200 250 300RWA Mass Vs. Angular Momentum Design Rated/Specified Angular Momentum  [N -m-s]Mass (Including Drive Electronics)  [kg]
396 18. Camino, T. S., “HST Solar Array Feathering Test II Test Report”, Engineering Memorandum SPS 648,  LMSC, July 1991.   19. Camino, T. S., Hasha M. D., “Structural G Level Accelerations at 1.0 and 100.0 inches from CG of HST during Solar Array Fe athering Test II to be used as a Demonstration for Space Station” , Engineering Memo  Communication, September 1991.   20. Sills, J. W., Hasha, M. D., “Derived Structural Acceler ations for the HST Due to  Reacti on Wheel Harmonic  Steady State Inputs and Engineering/Science Tape Recorders Telemetry Data, Interdepartmental  Communication Report, LMSC, 16 September 1991.   21. Guerra, Lisa, “Cost Estimating Module –  Space Systems Engineering Version 1.0”, Course Materials  Developed under  NASA Explora tion Systems Mission Directorate in association with the University of Texas  at Austin, 2010.   22. Aas, C. , Zandbergen, B.T.C. , Hamann, R.J., Gill, E.K.A., “ SCALES – A System Level Tool for Conceptual  Design of Nano-  and Microsatellites ”, 7th IAA Symposium  on Small Satellites for Earth Obser vation, Berlin,  Germany, May 4 -8, 2009.     23. Larson, W.J., Wertz, J.R., “ Space Miss ion Analysis and Design”  or “SMAD” , 3rd Ed. , Microcosm Press &  Springer, 1999.   24. Aas, C. L. O. , Zandbergen, B.  T. C. , Hamann, R.J., Gill, E .K. A., “Development of a System Level Tool for  Conceptual Design of Small Satellites”, 7 th Annual Conference on Systems Engineering research 2009  (CSER 2009), April 20- 23, 2009 .  25. Aerospace Corp. Small Satellite Cost Model Ver 7.4, CER via www.coursehero.com \Georgia  State/ASTR \ASTR 630 0 [homework 7 -  page 4 of 13].   26. Comparisons with Internal Engineering Assessments, Internal Guidelines Discussion between D.  Anderson and M. Hasha, September 1, 2015.