NBSIR 73-291

A Systematic Study of Vibration

Standards - Mounting Effects -

Robert S. Koyanagi, James D. Pollard, John D. Ramboz

Vibration Section, Mechanics Division

Institute for Basic Standards

National Bureau of Standards

Washington, D. C. 20234

September 1973

Final Report

Prepared for Department of Defense

Calibration Coordination Group

NBSIR 73-291

A SYSTEMATIC STUDY OF VIBRATION

STANDARDS - MOUNTING EFFECTS -

Robert S. Koyanagi, James D. Pollard, John D. Ramboz

Vibration Section, Mechanics Division

Institute for Basic Standards

National Bureau of Standards

Washington, D. C. 20234

September 1973

Final Report

Prepared for Department of Defense

Calibration Coordination Group

4 l/'

U. S. DEPARTMENT OF COMMERCE, Frederick B. Dent, Secretary

NATIONAL BUREAU OF STANDARDS, Richard W. Roberts. Director

TABLE OF CONTENTS

Page

Abstract 1

1. Introduction 2

2. Test System Description . 3

3. Test Hardware 4

3.1 Mounting Base Materials . . . 4

3.2 Insulated Studs 5

3.3 Thread Size Adaptors . .5

3.4 Test Accelerometers 6

3.5 Charge Amplifiers 6

4. Test Procedure 7 4.1 General Precautions ... 7 4.2 Test Matrix 7

5. Analysis 8

5.1 General Analysis Approach 8

5.2 Analysis of Mounting Base Materials Data. .... 8

5.3 Analysis of Insulated Stud Data 10

5.4 Analysis of Thread Adaptor Data 11

5.5 Standard Deviations for Small Data Samples .... 12

6. Measurement Results 13

6.1 General Comments on Measurement Results 13

6.2 Reference Response on Tungsten ....... 14

6.3 Results of Different Mounting Base Materials ... 15

6.4 Results of Different Insulated Studs 16

6.5 Results of Thread Size Adaptors 17

7. Conclusions 17

7.1 General Comments 17

7.2 Conclusions for Mounting Base Materials 19

7.3 Conclusion for Insulated Studs 19

7.4 Conclusions for Thread Size Adaptors 20

8. References . .21
LIST OF TABLES

Page

Table I. Characteristics of the Mounting Bases .... 22

Table II. Overall test Matrix 23

Table III. Normalized Response of Six Accelerometcrs Mounted

on Tungsten Base Material 24

Table IV. Measurement Results for Different Mounting Base

Materials 25

Table V. Measurement Results for Different Insulated Studs . 26

Table VI. Measurement Results for Thread Size Adaptors ... 27

Table VII. Summary of Measurement Results 28

^ V. LIST OF FIGURES

Figure 1. Different Mounting Base Materials 30

Figure 2. Three Typical Insulated Studs 31

Figure 3. Thread Size Adaptor Bushing and Stud 31

Figure A. Reference Response on Tungsten Base Material ... 32

Figure 5. Standard Deviation of the Reference Response on Tungsten Base Material 33

Figure 6. Measurement Results for Different Mounting Base

Materials . . .34

Figure 7. Standard Deviation for Data on Different Mounting

Base Materials 35

Figure 8. Measured Results for Different Insulated Studs . . 36

Figure 9. Standard Deviations for Data on Different Insulated

Studs 37

Figure 10. Measurement Results for Different Thread Size

Adaptors ..... 38

Figure 11. Standard Deviations for Data on Thread Size Adaptors . 39
A SYSTEMATIC STUDY OF VIBRATION STANDARDS

- MOUNTING EFFECTS -

by

Robert S. Koyanagi

James D. Pollard

John D, Ramboz

ABSTRACT

The purpose of this study was to determine the extent of the sensitivity change of laboratory quality piezoelectric accelerometers for

various mounting conditions. The mounting variables included the material

upon which the accelerometer was mounted, geometry, the use of commercial

insulated studs, and the use of mounting stud thread size adaptors. For the

stated test conditions, the effect of different materials and geometry was insignificant below about 3000 Hz. For stainless steel, beryllium, alumina,

and tungsten, the deviations were less than 0.5 percent up to 10,000 Hz. The

aluminum alloy base showed an increase of about 2 percent by 10,000 Hz. The

effect of insulated studs showed deviations beginning at about 3,000 Hz. No

significant deviation was found between the different stud thread size

adaptors

.

Note: In this study, units of acceleration are expressed in gravitational

units of g. All screws employed were fine-thread series and are designated in this paper by their screw size number of fractional

diameter in inches and the pitch in numbers of threads per inch.

This was done to facilitate communication with the intended reader.

Conversion to SI units may be accomplished using the following

relationships

1 inch = 2.540 cm; and, 1 g = 980.7 cm/s^

Keywords

:

Accelerometer calibration; mounting variable; vibration.
1. INTRODUCTION

This report describes a study of the effects of some mounting

variables on the sensitivity of selected piezoelectric accelerometers

.

The frequency range was from 100 Hz to 10,000 Hz. The mounting variables

studied were:

(1) material upon which the accelerometer is mounted,

(2) material geometry,

(3) mounting with insulated studs, and

(4) the use of thread size adaptors.

Some accelerometers exhibit a change of their sensitivity when mounting

conditions are varied. In recent years, the sensitivity to mounting torque

and to dynamic pressure has been made negligible by improved design of the

accelerometers. However, base strain sensitivity and temperature sensitivity

have remained problems for certain accelerometers. These responses may be

different in some cases even among accelerometers having the same manufacturer

and model.

Past experience shows that some accelerometers exhibit a change of

sensitivity when mounted on different materials, for example, aluminum,

stainless steel, or ceramic. These accelerometers are generally of the

compression design and are known to have base strain sensitivity.

Reasonably repeatable results can be obtained when mounted on any one material, but no good explanation is available to explain why this shift

occurs. The shift is noticed even at relatively low frequencies of the

order of 10 to 400 Hz, well below the range where the resonance phenomenon

begins. Shifts of the order of 0.5 to 1.5 percent have been observed.

When this large, a one percent calibration uncertainty is rather meaningless

unless the mounting conditions are carefully specified. Even then, one can-

-r not be certain that the conditions can be duplicated from laboratory to

laboratory. Good practice for laboratory standards would be simply to

avoid the use of such pickups as standards.

This study concentrated mainly on one model of accelerometer that is

widely accepted and used as a laboratory standard. It is important to

verify that this particular model does not suffer from the above described

problems, or if it does, to what extent. Six accelerometers of the same manufacturer and model were chosen for this work.

-2-
2. TEST SYSTEM DESCRIPTION

All the tests for this study were conducted using the Dimoff Vibration

Standard 201/203 as the vibration exciter. [1] This exciter has a reference

standard accelerometer built into the moving element. The reference standard

was calibrated by a reciprocity method during June 1971. [2]

The heart of the test system is a small digital conq)uter. [3] A software

program in the computer controlled the entire test process. The program controls

the frequencies and voltages generated by a programmable oscillator which in

turn feeds a power amplifier and then the vibration exciter. At each test

frequency there is a predetermined acceleration which is controlled by the

computer to insure constant measuring conditions through a closed-loop process.

All base material and insulated stud tests were done at 10 g peak amplitude

and at 100 Hz frequency increments between 100 and 1000 Hz, and in 500 Hz

increments between 1000 and 10,000 Hz. (An additional frequency of 1700 Hz was included because of other program considerations.) The tests for the

thread size adaptors were done at an acceleration of 5 g peak because of

increased mass of the test accelerometers

.

Accelerometer sensitivity measurements were made by comparing the

voltage output of the test accelerometer system to the voltage output of the

reference standard accelerometer system. The automated system is capable of

measuring these ratios to within a few tenths of one percent.

The waveform of each of the accelerometers' charge anqjlifier outputs

was monitored by an oscilloscope. The waveform harmonic distortion generally

did not exceed one percent. The transverse motion ratio, although not

monitored, was believed to be less than a few percent over the entire

frequency range.

Numerals in brackets refer to reference found at the end of this report.

-3-
3. TEST HARDWARE

3.1 Mounting Base Materials

To study the effects of the type of material the accelerometer is

mounted on, six washer-like mounting bases were fabricated. Table I shows

the five materials, the dimensions of the bases and gives the approximate

elastic modulus of each. The inside clearance hole was 0.490 cm disimeter,

sufficient to clear a 10-32 threaded mounting stud. Each of the base

mounting surfaces were ground flat with a surface finish of approximately

0.23 X 10 ^m rms. The materials are listed in their order of increasing

modulus

.

This geometry was selected because of symmetry, ease of fabrication

and because of past experience with similar washer-like bases. Accelerometer

sensitivity changes had been previously noted using a very similar

configuration. Figure 1 shows the bases.

The static stiffness of each of the bases was calculated using the

relationship

where k = static stiffness, N/m,

F = force, N,

e = elongation, m,

S = cross-section area, m , E = elastic (Young's) modulus, N/m^, and

Jl = thickness , m.

Substituting the dimensions into eq . 1, kj = 0.2016E and = 0.1008E

for the 0.356 cm and 0.711 cm thick bases, respectively. The static

stiffnesses are shown below for each of the bases. The values for stiffness

were rounded to the nearest whole billion and are listed in order of

k =

F SE

e (1)

-4-
increasing stiffness. (A value of E = 279 x 10^ N/m^ was used for beryllium.)

Material Static Stiffness, x lO^.N/m

Aluminum

Beryllium (0.711 cm thick) 28

Stainless Steel

Beryllium (0.356 cm thick) 56

Tungsten

Alumina 70

3.2 Insulated Studs

Insulated mounting studs are frequently used to electrically insulate

the accelerometer case from the mounting surface. Three models of

commercially available studs were tested. All were of a 10-32 stud size

on both ends. The general construction is that of a "sandwich" of a relatively stiff insulator such as fiber glass and epoxy, between the two

studded ends. Figure 2 shows typical items used. The three studs were

designated as a, 3, and y •

3.3 Thread Size Adaptors

Frequently it becomes necessary to mount an accelerometer having a 10-32 threaded hole in its base onto a surface which contains a 1/4-28

threaded hole. This is true of several of the commonly available

"piggy-back" type transfer standards. In order to accommodate several

thread sizes, adaptor studs and adaptor bushings are used.

The adaptor stud selected was made of 17-4 stainless steel with

0.343 cm length of 10-32NF2A external thread on one end and 0.635 cm

length of 1/4-28NF2A external thread on the other end.

The adaptor bushing was also made of 17-4 stainless steel and was

0.686 cm in overall length. The outside of the bushing was a 1/4-28N;F2A

external thread. Concentrically along the length axis, an internal

10-32 NF2B thread was used.

-5-
Both the adaptor stud and bushing are commercially available items.

Figure 3 shows the items used. A "piggy-back" vibration transfer standard

provided the surface having a 1/4-28 mounting hole. The transfer standard

output was used to control the acceleration level. This transfer standard

was calibrated at NBS during December 1972.

3.4 Test Accelerometers

Six accelerometers were selected to be used on the six different

mounting bases. These were a precision compression type using preloaded

quartz as the piezoelectric sensing material. The accelerometers have a mounted resonance frequency of nominally 40 kHz and weigh about 22 grams.

The diameter of their mounting surface was 1.27 cm. The moiinting hole is

10-32 which is nominally 0.356 cm deep. These accelerometers are designated A, B, C, D, E, and F for purposes of discussion.

In addition, a shear type accelerometer was also used. Preliminary

measurement revealed that "drift" due to its temperature sensitivity

masked the effects of mounting. This accelerometer was designated as G.

The same six quartz accelerometers, A through F, were used for the

insulated stud test. Several of these accelerometers, however, could not be

used because the 10-32 stud "bottomed" in the accelerometer prior to its

proper seating.

A "piggy-back" type transfer standard accelerometer was selected to

test the thread size adaptor stud and bushing. It was designated as H.

Several of the test accelerometers could not be tested because the stud

adaptor "bottomed" in the accelerometer prior to proper seating.

3.5 Charge Amplifiers

In all instances , the accelerometers were fed into charge sensing

amplifiers. For the test accelerometers A through F, the same amplifier

was used throughout. Amplifier gain was nominally 20 mV/pC. Separate

amplifiers were used for accelerometers G and H.

The frequency-gain response of the amplifier was not important, because

only changes in the test responses were being examined. Short term stability

(for the duration of the testing) was of critical importance. It was estimated that the gain stability with time was better than ±0.05 percent.

-6-
4. TEST PROCEDURE

4.1 General Precautions

When making a test assembly, all mating surfaces were thoroughly

cleaned with alcohol and coated with a thin film of medium weight

petroleum lubricating oil (viscosity of 240-500 S.U.S. at 100 degrees F)

.

The entire assembly, consisting of test accelerometer , base, stud, or bushing was mounted onto the vibration exciter. The assembly was mounted

with a torque of nominally 2 Nm (18lbf-in.). The testing of each of the

test accelerometers and each base or stud combination was done in a random

manner. After the completion of a test, the entire assembly was removed

and the next base selected at random was used. It was anticipated that

randomizing the test order would help minimize any effect due to temperature

or time drift.

The electrical connections for each accelerometer were cleaned using

dry industrial paper wipers only and the connector was securely attached.

The cable was taped to the vibration exciter base as near as possible to

the moving element without interfering with the motion. Sufficient time was allowed to permit all the electronic eqioipment to warm up.

4.2 Test Matrix

Table II shows the overall test matrix for the eight accelerometers

used, the materials, insulated studs, and the thread size adaptors.

Each of the six precision quartz accelerometers A through F were

tested on all six bases. The results using accelerometer G were unreliable

because of temperature sensitivity. Accelerometer H was a "piggy-back" type

used only for the thread size adaptor test.

Accelerometers D and E could not be used because certain of the 10-32

insulated studs "bottomed" into the accelerometer before it was properly

seated. This is shown by the absence of an "x".

Accelerometers A, D, and E also could not be -ased with the adaptor

stud because of "bottoming". This is shown by the absence of an "x" in

the "stud" column.

-7-
5. ANALYSIS

5.1 General Analysis Approach

Accelerometers A through F had a nominal sensitivity of

1 pC/g. Using a single charge amplifier for each of these six accelerometers,

the output of the amplifier was nominally 20 mV/g. It was necessary to

remove the effects of both the intrinsic frequency response of the accelerometer and charge amplifier from the results. Only the changes in response

due to the mounting variable were sought. A scheme of taking percentage

differences of the response of the same accelerometer under different

mounting conditions and group averaging was selected. Standard deviations

were also computed for the data to obtain a measure of quality for the test.

Because slightly different analysis operations had to be used for the three

different tests (i.e., materials, insulated studs, and thread adaptors) each

is discussed individually below. Data taken at frequencies below 100 Hz were

not considered. At these frequencies, the effects of the mounting variables

under investigation might be masked by other effects.

The response when mounted on the tungsten base was selected as a reference condition and was used in order to calculate the desired

percentage difference of each accelerometer ' s response when mounted on another material. Experience had indicated that this could be expected

to yield the most stable and least change in response of all the materials.

Thus, each difference is the difference between the stated material base

and the tungsten base. The percentage difference was determined from the

following expression.

5.2 Analysis of Mounting Base Materials Data

6 (M, f) = n

S (M,f) n - 1 X 100 C2)

S (W,f) n

-8-
where ^ (M, f ) = percentage difference of response between material

n M and tungsten,

S (M, f), S (W, f) = system sensitivity of accelerometer n,

n n

n = accelerometer A, B, C, D, E, or F,

M = mounting base material, for example, Al, SS , Bel,Be2, AI2O3,

and W, and

f = test frequency, in Hz.

It is important to note that the differences are determined for the different

materials, M, at specific frequencies, f , for each of six accelerometers

.

Twenty-nine frequencies were selected from 100 to 10,000 Hz. Additionally,

it can be seen from eq. 2 that <as long as the accelerometer charge amplifier

gain remains the same value from the time S (M, f) is measured to the time

n S^(W, f) is measured, the gain effectively divides out. Also, as long as the

intrinsic eharacteristics of the accelerometer remain constant with time, the

frequency response divides out. Thus, ideally all that remains is the

difference due to mounting material. Under perfect conditions, 5 (M, f ) = 0. n Because random errors exist in the measurement process, multiple measurements were made. Also, because any one accelerometer of a particular model

exhibits characteristics unique to itself, a group of six were used. The

group average was determined from

ii^(^'f>

6 (M,f) = ' (3)

N

where 6 (M,f) ~ group average for material M at frequency f , and

N = number of accelerometers tested.

The standard deviation of N measurements for any one material and

frequency was computed from

±a (M, f) =

N . r

N

^^c^M, f) - am[ f)_

N - 1

1/2

(4)

-9-
where ±o (M, f) =» standard deviation, and

C (M,f) = 5 (M, f) - 6 (M,f ). n n

(M,f) is the difference between the normalized response and the group

n average response.

If the measurement process were perfectly repeatable, ±a (M, f) = 0.

5.3 Analysis of Insulated Stud Data

The same basic approach in the analysis of the insulated stud data

was used as for the base materials discussed in Section 5.2. It was decided that the response of the accelerometers where mounted on tungsten

would be employed as a reference condition. Therefore, the percentage

differences were calculated from an equation very similar to eq. 2,

except for the notation shown in eq. 5.

6 (I, f ) =

n

S (W, £)

n

- 1 X 100 , (5)

where 6^ (I, f ) = percentage difference of response between stud I at

frequency f , and the response on tungsten at the same frequency.

S (I, f), S (W, f) = system sensitivities of accelerometer n,

n n

n = accelerometers as shown by Table II and the data below eq. 6.

The group averages were computed from eq . 6 below.

6 (I, f ) =

(6)

where 6 (I, f) = group average for the insulated stud, I, tested at

frequency, fj and

N = number of accelerometers tested for a given mounting condition,

Fur 1 = a. For I = B,

For I =

Y

,

n = A, B, C, D, F, and N = 5 n = A, B, F, and N = 3 n = A, B, C, D, F, and N = 5

See Table II

-10-
The standard deviations were computed similar to that done for the

base material analysis. Changes had to be made for the different number

of accelerometers tested. Equation 7 shows the generalized form.

±0 (I, f) = hi^p^ f) - (1/ N)[iic,(i, f)]

N - 1

where n and N are given for the different studs below eq . 6.

5.4 Analysis of Thread Adaptor Data

In order to compare the performance of the adaptor bushing and

adaptor stud, the percentage difference was calculated between the

response when using the bushing and when using the stud. This is

expressed by eq. 8 below.

6„ (q, £) = - 1 X 100

where °^ (Q, f) = percent difference of response between bushing and

stud adaptors at frequency f,

S (Qt, > f) = sensitivity when using the adaptor bushing, Q , and

n x5 B

S (Qc. > f) = sensitivity when using the adaptor stud, Q . n S

S Likewise, the average deviation was calculated from eq . 9 below.

N

6 (Q, f) = 5- A f) n~i- n ,

where n B, C, F, and N = 3.

-11-
The standard deviation was calculated by

r N

±o (Q, f) = (10)

N - 1

where C (Q, f) = 6 (Q, f) - 6 (Q, f),

n n and n is the same as for eq . 9,

5.5 Standard Deviations for Small Data Samples

Certainly the statistical meaning of standard deviation when only a few measurements are made is open to question. Any validity at all must be

considered rather lightly. It does, however, give some measure of the

quality of the measurement in a vague way. As the number of measurements

approach one pair of measurements in a set, it can be shown that the

standard deviation equals the absolute difference between the two measurements divided by the square root of 2,

?1 - C2 (11)

±a

N = 2

-12-
6. MEASUREMENT RESULTS

6.1 General Comments on Measurement Results

In all Instances, the measured data were analyzed as stated In

Section 5 and percentage deviations from a selected reference were

determined. It was necessary to select different reference quantities

for different tests. These reference quantities have been discussed

in Section 5.

The data is grouped according to the test performed. The

following groupings are presented in the order shown below:

(1) reference response on tungsten,

(2) mounting base materials,

(3) insulated studs, and

(4) thread size adaptors.

Each group contains a table of data, a plot showing percentage

deviation from the reference condition versus frequency, and a plot showing

the standard deviation of the group data versus frequency.

Plots were made in order to present the final data in a readily

readable manner* These show the extent and nature of the mounting effect

as determined by these test methods and hardware, and provide certain

assessments of the overall quality of the data.

The "FREQUENCY" axis of each plot is a two-decade logarithmic scale

from 100 Hz to 10,000 Hz. The ordinates , "AVERAGE PERCENT DEVIATION",

"PERCENT REFERENCED TO TUNGSTEN", "PERCENT REFERENCED TO ADAPTOR STUD", of

the above listed groups were plotted with the same span of -1 to +5 percent.

The ordinates "PERCENT STANDARD DEVIATION" for all the plots range from -0.5

to +2 percent. As such, the data can be more easily intercompared between

the results of the different tests.

The tabular data are given to rounded hundredths of one percent.

Usually, variations of vibration data of less than several tenths of one percent are considered excellent. The extra digits are given to indicate

the repeatability of data obtained. The control, stability and averaging

process of these tests indicate variations are generally very small

and in order of a few tenths of one percent. Exceptions are noted in the

ensuing discussions.

-13-
6.2 Reference Response on Tungsten

The responses of accelerometers A through F were measured on the base

materials given in Table I and shown in Figure 1. The data thus obtained was then

treated such that the responses on the tungsten base were used as the

reference quantity. This is shown by the denominator of eq. 2 as S^(W, f).

Because the response on tungsten was used as a reference condition, it is

desiral)le to examine the nature and quality of the reference tungsten data.

Table III gives the measured response of accelerometers A through F for

the tungsten base mounting condition. This data was normalized by dividing

the measured sensitivity by the average of the sensitivity for the five

frequencies from 100 to 500 Hz for each accelerometer , as

A (W, f) =

where (W, f) = percent difference of normalized accelerometer response.

The other terms have been previously described.

The eighth column of Table III gives the average normalized response

of the six accelerometers at each frequency and was derived by

N

!_/ (w, f)

i: n A (W, f) = , (13)

N

where A (W, f) = average of the normalized sensitivities, and

n = accelerometer A, B, C, D, E, or F , and

N = 6.

The ninth column of Tahle III gives the standard deviation of columns

A through F for each frequency.

S (W, f) n

500 - 1 X 100 (12)

(1/5)

f =100

S (W, f)

n

-14-
Figure 4 is a plot of A (W, f) versus frequency. The deviation

of the plotted data from zero is less than +0.25 percent up to a frequency of 3500 Hz. At frequencies greater than 3500 Hz, the frequency

response of the accelerometers causes the average to increase to about

+1.15 percent at 9500 Hz due to resonant rise.

Figure 5 is a plot of the standard deviation as given in Table III.

At frequencies less than about 3500 Hz, the values are near zero. The

rise at the higher frequencies is smooth and not excessive.

A small anomaly is noted at a frequency of 4000 Hz. This was

solely due to an irregularity in the data for accelerometer D. As given

In Table III, (W, 4000) = 0.95 percent, which is about 0.5 percent

or so greater than the adjacent data of S^^ (W, 3500) = 0.26 and

^^^^^ ~ ^'^^ percent. If this point had been removed from the

analysis, then A (W, 4000) would have equaled 0.32 rather than 0.43.

The probable cause of why the value of S^^ (W, 4000) was higher than

expected is not known. It was not removed from the data because

Its effect on the average was small and its subsequent effect on the

analysis can be accounted for.

Of greater concern is the anomaly noted at 10,000 Hz. The value of

(W, 10,000) for all six accelerometers suddenly decreased by about

one percent. The reason for this is unknown, but could have been the

result of poor motion or an irregularity of the sensitivity of the internal

reference standard accelerometer at 10,000 Hz.

Based on the above discussion and observations, good test results are expected with the possible exception of tests performed at 4000 and 10,000 Hz.

6.3 Results of Different Mounting Base Materials

This test was performed using accelerometers A through F as shown by

Table II and discussed in Section 3.1. The data was analyzed as described

In Section 5.2.

-15-
The results are shown in Table IV and Figures 6 and 7. All the relative

responses were smooth and near zero as desired for all frequencies up to about

3500 Hz. Above this frequency, the response when mounted on aluminum,

/) (Al, g) , begins to rise. It ultimately achieves an average rise of about

2 percent above the reference condition of tungsten mounting. The remaining

materials indicate a fairly flat response to 6000 Hz or so where they

begin to "fan" out to about ±0.5 percent at 10,000 Hz.

SlntLlaifly the standard deviation is low, not exceeding 0.25 percent

below 6000 Hz. Above 6000 Hz, scatter in the data is indicated by an increasing standard deviation of about ±0.5 percent at 10,000 Hz.

It is interesting to note the small anomaly at 4000 Hz. This is the

direct result of the irregularity of the tungsten reference response (as

previously discussed in Section 6.2) of about the same magnitude.

Additionally, there may be an indication of problems at 10,000 Hz.

Note the large range of standard deviations at 10,000 Hz from Figure 7.

6.4 Results of Different Insulated Studs

This test was performed using the accelerometers and insulated studs

as shown by Table II. The procedure is discussed in Section 3.2 and the

analysis approach in Section 5.3.

The results are shown in Table V and Figures 8 and 9. The differences

between the response when mounted on tungsten and on the insulated studs are generally small, less than about 0.25 percent up to approximately 3000 Hz.

Above 3000 Hz, the rise becomes significant. Stud y has the highest rise

of about 4 percent at 10,000 Hz, Examining the standard deviation as plotted in Figure 9, the overall values are higher than for the previous

test on different base materials. This is true especially at the high

frequencies where the values clearly rise.

-16-
6.5 Results of Thread Size Adaptors

This test was performed using the accelerometers and adaptors shown

by Table II. The procedure is discussed in Section 3.3 and the analysis

approach in Section 5.4.

The results are shown in Table VI and Figures 10 and 11. The difference

In the response between the adaptor bushing and the adaptor stud are small.

Except at frequencies of 4500 and 6500 Hz, the average difference did not

exceed 0.15 percent. It is thought that poor motion was the cause of the

apparent anomalies at 4500 and 6500 Hz. The difference should ideally be

zero. Moreover, the column average for all frequencies of the average

differences should be zero. As shown in Table VI, there was a slight

negative bias of -0.07 percent when averaging over all the frequencies.

If the anomalies at 4500 and 6500 Hz are removed from the column average,

then the bias decreases insignificantly from -0.07 to -0.06 percent. In

consideration of the average standard deviation for this test of about

±0.20 percent, the data appears to be well within an acceptable limit.

In examining the standard deviation as plotted in Figure 11, it is

reasonably low and consistent up to a frequency of 3500 Hz. At frequencies

between about 4000 and 8000 Hz, the standard deviation more than doubles

the lower frequency values. It is suspected that poor motion is the cause

of this poorer performance and that it is not related to the adaptor bushing

or stud.

7. CONCLUSIONS

7.1 General Comments

The tests performed were under tightly controlled laboratory conditions

and extra care was taken to ensure repeatable results. As such, the results

should generally be considered as the best obtainable, not particularly

typical. Furthermore, the averaging of data tends to reduce the random

component of errors and "smoothes" the results. This would not occur for

single tests.

-17-
The standard deviations derived herein were based on statistically

small samples. Additionally, statistical methods were used which presupposes that certain independence exists in the measured data; this may

not be true. However, in the lack of a more thorough and more costly test,

the results herein establish approximate bounds and limits of performance

which can be expected under similar conditions.

The standard deviations given herein are for confidence limits of ±la.

When single sets of measurements are made under less controlled conditions,

a better estimate of measurement uncertainty would probably be ±3a. It is

therefore recommended that although ±o values are given, that the reader

mentally triple the standard deviation values to develop a "feel" for a reasonable range of measurement uncertainty. Past experience indicates that

the measurements were probably no better than ±la, but no worse than ±3a.

Over the frequency range from 100 to 3000 Hz, the frequency response

was virtually flat, i.e., having less than a few tenths of one percent

difference for all mounting conditions. Because of this, it was possible

to more fully intercompare the different mounting conditions.

Table VII shows the sunmiary of all the tests performed. It is di-'/ided

into two parts. Part A deals with the average of the differences over the

frequency range. It was derived by averaging each of the "Average" columns

of Tables III, IV, V, and VI. The frequency range for the averaging for

the base mounting materials and the insulated studs was from 100 to 3000 Hz

where the response was "flat". For the thread size adaptors, the different

test permitted averaging over two frequency intervals, from 100 to 3000 Hz

and 100 to 10,000 Hz.

Part B of Table VII deals with the average of the standard deviations

over the indicated frequency ranges. It was derived by averaging each of

the "Standard Deviation"(±a) columns of Tables III, IV, V, and VI. Because

the standard deviation is not a direct function of the frequency response,

averaging could be done over the whole range. It was, however, subdivided

into ranges of 100 to 3000 Hz, 3500 to 10,000 Hz, and the whole range of

100 to 10,000 Hz. (The exception was for the tungsten mounting base material

where it was a function of the frequency response. See Section 5 . 2 for a description of the analysis.)

-18-
7.2 Conclusions for Mounting Base Materials

The measured differences were small for all the materials tested over

a frequency range from 100 to 3000 Hz. The aluminum alloy base showed

an increase of about 2 percent at 10,000 Hz. The other materials

showed deviations of less than 0.5 percent up to 10,000 Hz. The largest mean values of the average difference in the frequency range of 100 to

3000 Hz was about +0.10 percent. This is shown in Table VII, Part A.

The mean value of the average standard deviation was about ±0.10

percent over the frequency range from 100 to 3000 Hz and about ±0.20 percent

over the frequency range from 3500 to 10,000 Hz. This is shown in Table VII,

Part B.A conservative estimate of the change of accelerometer sensitivity

in the frequency range from 100 Hz to 3000 Hz is ±0.30 percent and for the

frequency range from 3500 to 10,000 Hz is ±0.6 percent (excluding the aluminum

base material from the latter) . These nunfcers represent a ±3o standard

deviation envelope.

7.3 Conclusion for Insulated Studs

The measured differences in response were small in the frequency range

from 100 to 3000 Hz. Above 3000 Hz, the response begins to rise. For stud

Y, the rise was approximately 4 percent at 10,000 Hz. The other two studs were somev/hat less. The standard deviation also increased with an increasing

frequency. This is generally true for instances where measurements are made

on the "skirts" of a mechanical resonance.

In the frequency range from 100 to 3000 Hz, the standard deviation was

about ±0.20 percent and in the range from 3500 to 10,000 Hz was about ±0.35

percent. This is shown in Table VII. It is expected that accelerometers of

the type tested could be calibrated on a specific insulated Stud to within

an additional uncertainty of ±0.6 percent from 100 to 3000 Hz and ±1.0 percent

from 3500 to 10,000 Hz. These uncertainties would be due to the insulated

stud and should be added to other sources of error. Any phenomena (such as

-19-
aging, temperature change, or fracture of the epoxy) which changes the

dynamic characteristics of the Insulated stud Increases the uncertainty.

A study of the stability of the insulated stud was beyond the scope of this

investigation.

7.4 Conclusions for Thread Size Adaptors

The measured difference between the response when using adaptor studs

and adaptor bushings was small and within expected measurement uncertainties.

This is shown in Table VII. The measured standard deviation for the

frequency range from 100 to 3000 Hz was about ±0.11 percent and about ±0.31

percent over the frequency range from 3500 to 10,000 Hz.

In consideration of the test conditions, no measureable difference is

thought to exist between the use of a 10-32 to 1/4-28 adaptor bushing and

adaptor stud.

-20-
8. REFERENCES

1. Dimoff, T. , "Electro dynamic 'Vibration Standard With a Ceramic

Moving Element" , Journal of the Acoustical Society of America,

Vol. 40, No. 3, Sept. 1966, pp. 671-676.

2. Payne, B. F. , "Absolute Calibration of Vibration Generators With

Time Sharing Con^uter as an Integral Part of System", Shock and

Vibration Symposium Bulletin No. 36, Part 6, February 196 7,

pp. 183-194.

3. Payne, B. F. , "An Automated Precision Calibration System for

Accelerometers" , Instrument Society of America 17th National

Aerospace Instrumentation Symposium, May 1971 (Las Vegas, Nevada).

-21-
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-22-
TABLE II. Overall Test Matrix

Mounting Base Materials^ Insulated Studs Thread Size

Adaptors

A 1 ss oej. DC Z Ai2U3 w 6 Y Bushing Stud

Test

Accelerometers

A AV X X AY AY X

VA

\rA X

B X A X A YA X X X X X X

C Y X AY X X AY A YA VA

VA

D X X X X X X X X [X]

E X X X X X X [X]

F X X X X X X X X X X X

(X) (X) (X) (X) (X) (X)

H X X

^Sce Table I for material symbols.

Values obtained by the tests in parenthesis were not xised in the final

results because of unreliable data. See text for explanafions

.

c Values obtained by the bushing tests in brackets were not losed because

corresponding data was not available for the stud. See text for explanations.

-23-
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-24-

I

,1/
TABLE IV. Measurement Results for Different Mounting Base Materials

(Data derived from eqs. 3 and ^.)

Frequency

Hz

Mounting Base Materials

Al SS Bel Be2 AI2O3

Ave- a Ave

a Ave- a Ave. a Avea Inn .08 .06 .04 . 16 . 11 . 14 . 10 . 11 .08 . 16

or\r> zUU — .01 . 15 .03 . 13 . 13 . 10 .09 . 11 .09 .11

JUU .00 .05 .07 . 17 . 16 . 15 . 13 . 11 . 10 .13

A nn ^UU .04 .06 .02 . 19 . 12 . 10 .05 .09 .08 .09

50U .03 .05 .03 . 14 . 11 . 10 .06 .08 .06 .09

oUU .06 .04 .02 . 15 .08 .08 .04 .08 .04 .09

/uu .01 .02 -.01 . 13 . 10 .08 .04 r\ —7 .07 .03 .07

oUU .05 .08 .03 . 14 . 11 .07 .07 .07 .04 . 11

yuu .03 .03 .03 . 14 . 11 .06 .07 . 11 . 04 .09

lUUtJ .05 .03 .06 . 16 . 11 .09 .08 .08 .07 . 11

IjUU .04 . 04 .01 . 21 . 11 .08 .06 . 11 .07 .09

1 /Uu .05 .05 .03 . 16 . 13 .07 . 05 .06 .07 f\ 0 .08

ZUUU .03 . 10 .01 . 16 .05 .05 .03 .08 .06 .08

Z jUU . 11 . 04 -.01 . 16 . 06 r\ o .08 .01 .07 .02 .07

JvJUU . 12 . 09 .03 . 18 .05 .09 .05 .09 .06 . 10

jjUV .19 O .08 .04 . 15 .01 . 04 .02 .07 .01 .05

Annn .27 .11 -.14 .27 -.09 .22 -.06 .26 .10 .24

4 JUVJ . Jz .18 .09 .08 .01 .08 .05 .06 .03 .01

juuu .36 . zy n Q

. Do . 1/ - . Oo . 10 -.01 . 10 -.01 . 11

.45 .27 .06 .09 -.06 .06 .02 .10 .00 .07

6000 .46 .19 .08 .17 -.06 .06 .05 .06 .01 .08

6500 .57 .35 .12 .26 -.10 .11 .02 .13 .00 .10

7000 / \J\J\J . 71 .34 .14 .30 -.12 .11 .00 .11 .00 .10

7500 .97 .38 .18 .18 -.18 .14 -.02 .20 -.06 .17

8000 .97 .32 .16 .21 -.28 .18 -.11 .23 -.11 .16

8500 1 .11 .41 .26 .28 -.36 .24 -.10 .30 -.11 .20

9000 1 . 21 .33 .28 .35 -.43 .28 -.14 .39 -.19 .23

9500 1 .34 .16 .44 .40 -.43 .38 -.05 .49 -.05 .27

10000 2 .01 1.92 .42 .45 -.18 .48 -.02 .67 -.04 .23

-25-
V. Measurement Results for Different Insulated Studs

(Data derived from eqs. 6 and 7)

Freq uency

Insulated Studs

Hz

Stud a Stud e Stuc VT Ave. a Ave- a Ave- a 100 .05 . 20 . 16 . 27 .05 . 30

200 - 05 . 17 . 18 .23 -.02 23

300 .02 . 18 . 28 . 28 .04 .27

400 -.13 . 16 . 18 . 14 -.09 . 24

500 -.07 . 18 . 18 .19 -.02 .26

600 -.12 . 15 .13 . 19 -.13 . 24

700 -.11 .15 .13 .12 -.10 .24

800 -.09 .14 . 18 . 17 -.06 .26

900 -. 11 . 14 .20 . 17 -.05 . 23

1000 -.09 . 16 .19 . 18 -.04 . 25

1500 -.02 . 15 .21 . 16 .05 .25

1700 -.01 . 12 . 24 . 18 .04 .24

2000 .04 . 15 .18 . 15 . 10 . 24

2500 .07 . 13 .24 .13 .21 .24

3000 .23 . 18 . 29 . 17 . 40 . 25

3500 . 36 .09 .37 .15 .56 . 24

4000 . 33 . 30 .40 . 16 .62 .29

4500 . 71 . 12 .48 . 13 . 86 .19

5000 .68 .24 .52 .07 .98 32

5500 .87 .11 .61 .22 1.34 .30

6000 1.04 . 21 . 72 . 12 1.61 .40

6500 1. 25 .27 .87 .12 1.92 .48

7000 1.46 .35 1.05 .16 2.24 .50

7500 1.89 .29 1.21 .32 2.71 .53

8000 2.14 .42 1.49 .37 3.07 .70

8500 2.42 .42 1.63 .33 3.51 .75

9000 2. 73 .71 1.72 .41 3.95 .92

9500 3.62 .66 2.41 .30 3.79 1.06

10000 2.79 .60 2.08 .52 4.40 .97

-26-
TABLE VI. Measurement Results for Thread Size Adaptors

(Data derived from eqs. 9 and 10.)

Freq uency

Hz

rrU

100

200 00 . 20

"^00 ~f\J\J 02 • xv/ TO

400 - 07 • XX11

500 -.06 . 12

600 -.05 .08

700 -.08 . 14

800 - 05 . 10

900 - 05 .08

1000 -.06 .07

-L1500 ^ \J\J - 05 05

1700 - 03 • 14X ^ 2000 - 06 07

2500 - 07 07

- 06 • Xv/ 10 - 05 • x^

AOOO . J

/ 53

1 / • 71/ X soon

- 08

6000 -.06 .48

6500 -.34 .51

7000 -. 15 . 36

7500 -.07 .24

8000 -.07 .16

8500 -.10 .13

9000 -.10 .09

9500 -.08 .10

10000 -.10 .13

-27-
TABLE VII. Summary of Measurement Results, all values given

in percent. (See Sections 5 and 7 for explanation

of the derivation of values. Table I gives

materials description.)

Frequency

Range , Hz

Mounting Base Materials Insulated Studs Thread

Size

Al SS Bel Be 2 AI2O3 W a 3 Y ^^daptors

Part A. Mean value of the average differences.

100 - 3000 + .05 + .03 + .10 + .06 + .06 + .07 -.03 + .20 +.03 -.05

3500 - 10,000 + .16 -.17 -.03 -.03 -.09

Part B. Mean value of the average of standard deviation

100 - 3000 ±.05 ±.16 ±.09 ±.09 ±.10 ±.06 ±.16 ±.18 ±.25 ±.11

3500 - 10,000 ±.38 ±.24 ±.18 ±.21 ±.14 ±.34 ±.24 ±.48 ±.31

100 - 10,000 ±.21 ±.20 ±.13 ±.15 ±.12 ±.25 ±.21 ±.36 ±.20

-28-
FIGURES

-29-
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-31-
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U i 0? P r, OF COMM. BIBLIOGRAPHIC DATA

SHEFET

1. PL:iiL!''Al RiN OR WlA-'OK'l NO. NBSIR 7 3-291

2. Gi>v 'r Act c-s.s ion No.3. Ki-c- 1 p i-.'.it '.s Aci;L-.>^.-.ion Nn.

4. TITLK AND SL I^ l lTLt;

"A SYSTEMATIC STUDY OF VIBRATION TRANSFER STANDARDS - MOUNTING EFFECTS"

5. Publication Dnte September 19 7 3

6, Performing Organ i zac ion Code

7. AlTHORiS)

Robert S. Koyanagi James D. Pollard John D. Ramboz

8. i-'jrforming Organ. Report No. NBS IR 73-291

9. PERFORMING ORGANIZATION NAME AND ADDRESS

NATIONAL BUREAU OF STANDARDS

DEPARTMENT OF COMMERCE

WASHiriGTON, D.C. 20234

10. Projecr/Task/Work Unit No. 2130426

11. Contract /Grant No.

12. Sponsoring Organization Name and Complete Address (Street, City, State, ZIP)

Department of Defense

Calibration Coordination Group

13. Type of Report & Period Covered

f mai

14. Sponsoring Agency Code

15. SUPPLEMENTARY NOTES

16. .ABSTRACT (A 200-word or less (actual summary of most significant in formation. If document includes a significant

bibliography or literature survey, mention it here.) The purpose of this study was to determine the extent of th.e sensitivity change

of laboratory quality piezoelectric accelerometers for various mounting conditions.

The mounting variables included the material upon which the accelerometer was mounted,

geometry, the use of commercial insulated studs, and the use of mounting stud thread

size adaptors. For the stated test conditions, the effect of different materials and

geometry was insignificant below about 3000 Hz. For stainless steel, beryllium,

alumina, and tungsten, the deviations were less than 0.5 percent up to 10,000 Hz. The

aluminum alloy base showed an increase of about 2 percent at 10,000 Hz. The effect

of insulated studs showed deviations beginning at about 3,000 Hz. No significant

deviation xvas found between the different stud thread size adaptors.

17. KcY 'AORDS (six to twelve entries; alphabetical order; capitalize only the first letter of the first key Hord unless a proper

na/r.e,- separated by semicolons)

Acceleration calibration, mounting variable, vibration.

18. AVAILABILITY [1_ Unlimited 19. SECURITY CLASS 21. NO. OF PAGES

(THIS REPORT)

!XX P'^r Official Distribution. Do Not Release to NTIS 28

UNCLASSIFIED

I Order From Sup. of Doc, U.S. Government Printing Office 20. SECURITY CLASS 22. Price

Washington, D.C. 20402. SD Cat. No. CH (THIS PAGE)

' Orde; i rom National Technical Information Service (NTIS^

Spr:i'.gfiel.l, \'irginia 22151 L^NCLASSIFIED

USCOMM-DC ZiCiZ-P'A

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