measurement and evaluation methods for an …tableofcontents page foreword iii abstract 1 1....

NBS

PUBLICATIONS

NBSIR 81-2337

Measurement and EvaluationMethods for an AngularAccelerometer

A11100 cn i4ti4^

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—

U.S. DEPARTMENT OF COMMERCENational Bureau of Standards

National Engineering Laboratory

Center for Electronics and Electrical Engineering

Electrosystems Division

Washington, DC 20234

January 1 981

Final Report

Issued August 1 981

Under Department of Transportation Reimbursable AgreementDOT-HS-0-021 93IA

c

100

. U56

81-2337

1981

c. 2

Prepared for:

Department of Transportation

national Highway Traffic Safety Administration400 Seventh St., S.W.i/Vashington, DC 20590

NATIONAL BURBA

O

OF STANDARDSUBfiABT

MEASUREMENT AND EVALUATIONMETHODS FOR AN ANGULARACCELEROMETER

NBSIR 81-2337OCT 1 4 J987

/W Cull. _ &>Qtfoo

/?o. %/-23S 7

John D. Ramboz

U.S. DEPARTMENT OF COMMERCENational Bureau of Standards

National Engineering Laboratory

Center for Electronics and Electrical Engineering

Electrosystems Division

Washington, DC 20234

January 1 981

Final Report

Issued August 1 981

Under Department of Transportation Reimbursable AgreementDOT-HS-9-021 93IA

Prepared for:

Department of Transportation

National Highway Traffic Safety Administration

400 Seventh St., S.W.Washington, DC 20590

U.S. DEPARTMENT OF COMMERCE, Malcolm Baldrige, Secretary

NATIONAL BUREAU OF STANDARDS, Ernest Ambler, Director

*&£X}K — ' •

Foreword

Work described herein was performed for the National HighwayTraffic Safety Administration (NHTSA) of the Department of Trans-portation (DoT) under an Interagency Reimbursable AgreementDoT-HS -9-021 93IA . The NBS Cost Center for this project was 7223403 .

Laboratory efforts commenced on October 1, 1980 and were completedon December 30, 1980. The DoT/NHTSA Technical Contract Monitor wasMr . Mark Haffner

.

The tests performed and discussed in this report are abbreviatedmeasurements to assess the principal operating characteristics of a

newly developed angular accelerometer. Time and funding constraintsrequired that only selected fundamental measurements could be made.As a result of these measurements, satisfactory performance wasindicated and further consideration should be given to additionalwork for the development and testing of this type of transducer.Because of the limited testing, this conclusion is preliminary.Further testing should be done in order to reach final conclusionsas to the overall performance for the intended DoT application.

Certain commercial equipment, instruments, or materials areidentified in this report in order to adequately specify the experi-mental procedure. In no case does such identification implyrecommendation or endorsement by the National Bureau of Standards,nor does it imply that the material or equipment identified is

necessarily the best available for the purpose.

TABLE OF CONTENTS

Page

Foreword iii

Abstract 1

1 . INTRODUCTION 1

2. ACCELEROMETER SPECIFICATIONS AND PHYSICAL DESCRIPTION .. 2

2.1 Angular Acceleration Sensitivity 3

2 .2 Frequency Response 3

2.3 Amplitude Linearity 5

2.4 Transverse Axis Angular Sensitivity 5

2.5 Linear Acceleration Sensitivity 5

2.5.1 Linear Acceleration Sensitivity Parallel toSensing Axis 5

2.5.2 Linear Acceleration Sensitivity Perpendicularto Sensing Axis 5

2.6 Physical Description 6

3. LABORATORY MEASUREMENTS 6

3.1 Resistance Measurements 7

3.2 Angular Acceleration 8

3.2.1 Test Philosophy 8

3.2.2 Electrical Excitation Power Configuration . . 8

3.2.3 Laboratory Instrumentation. Amplifiers, andFilters 8

3.2.4 Angular Acceleration Generation 8

3.2.5 Test Measurements 12

3 .2 .5 .1 Angular Acceleration Sensitivity ... 12

3 .2 .5 .2 Amplitude Linearity Measurements ... 14

3.3 Transverse Axis Angular Sensitivity ........ 143.4 Linear Acceleration Testing 16

3.4.1 Test Philosophy 16

3.4.2 Linear Sensitivity Parallel to SensitiveAxis 17

3.4.3 Linear Sensitivity Perpendicular to SensitiveAxis 18

3 .4 .4 Other Effects 20

IV

TABLE OF CONTENTS (cont.)

Page

3.5 Measurement Uncertainties 21

3.5.1 Bridge Voltage Excitation 21

3.5.2 Signal Voltage Measurement . .213.5.3 Amplifier Gain and Filter Response 21

3.5.4 Acceleration Determinations 22

3.5.5 Computation and Arithmetic Errors 22

3 .5 .6 Other Error Sources 23

3.5.7 Combined Uncertainties 23

4. CONCLUSIONS 24

5. ACKNOWLEDGMENTS 25

6. REFERENCES 25

APPENDIX A A-l

APPENDIX B B-l

v

TABLE OF CONTENTS (cont.)

Page

3.5 Measurement Uncertainties 21

3.5.1 Bridge Voltage Excitation 21

3.5.2 Signal Voltage Measurement .213.5.3 Amplifier Gain and Filter Response 21

3.5.4 Acceleration Determinations .223.5.5 Computation and Arithmetic Errors 22

3 .5 .6 Other Error Sources 23

3.5.7 Combined Uncertainties 23

4. CONCLUSIONS 24

5. ACKNOWLEDGMENTS 25

6. REFERENCES 25

APPENDIX A A-l

APPENDIX B B-l

v

MEASUREMENT AND EVALUATION METHODSFOR

AN ANGULAR ACCELEROMETER

John D. Ramboz

A transducer which measures angular accelerationalong one axis was investigated to assess three of its

performance characteristics, viz., sensitivity factor,amplitude linearity, and response to linear (non-angular)input accelerations. Accelerometer specifications and

response theory are presented. Test philosophy andmethodology are discussed along with measurement results.Tests were conducted over a frequency range from 1 .5 to100 Hz and over an acceleration range from 64 to 5000 rad/s^

.

Generally, the performance observed was in agreement withthe manufacturer' s preliminary specifications.

Key words: angular acceleration; angular accelerometer;calibration; instrumentation; measurement; shock andvibration

.

1 . INTRODUCTION

The Department of Transportation, National Highway TrafficSafety Administration (DoT/NHTSA), Biomechanics Branch is studyingthe mechanisms of human head impact injury and is developing injurytolerance criteria. An understanding of these mechanisms and use ofthe tolerance criteria will be of immediate benefit to automotiveoccupant protection and protection headgear design. These are intendedto contribute to the established national goal of improved highwaysafety

.

The measurement of angular head motions during impact has poseda serious challenge to available instrumentation. To date, thisdifficult measurement has not been successfully performed withoutlarge errors and ambiguities. Measurement methods in the past haverelied on either photographic techniques or the derivation of angularmotions from linear motion measurements. Neither technique has

proven totally satisfactory and is, in any instance, very laborious.

In an attempt to establish head injury criteria, a programwhich employs athletic boxers is being pursued by the DoT. Headmotions will be measured and analyzed along with qualified biomedical

1

observations. Correlation between the measured data and apparent"injury" will lead to a threshold criteria useful in automobileoccupant safety

.

Transducer attachment to the boxer's head will be made by incor-porating the instrumentation, including a multichannel FM transmitter,in the orthodontic mouthpiece. Thus, with the mouthpiece tightlygripped between the teeth, three-dimensional head motion can be

sensed and data transmitted to a ringside receiver and recorder

.

This approach is feasible only if a suitably small and accuratetransducer is available to sense the head motions.

A newly developed transducer [1]P which senses angular acceler-ation is being investigated for possible use in the "mouthpiece."Its small size, ruggedness, and frequency response make it attractiveto consider for this application. A preliminary set of measurementswas desired to ascertain the fundamental operating characteristicsof this transducer. Based on the preliminary findings, a decisioncan then be made as to whether to invest additional resources for an

in-depth evaluation of such an accelerometer.

The tests performed and discussed herein are designed to determinethe angular-acceleration sensitivity factor (i.e., transfer function),the frequency response, amplitude linearity, transverse sensitivity,and linear acceleration sensitivity. These were felt to be the mostimportant of the parameters and could be assessed with hardware andmethods already available. Programmatic constraints on time and fundsnecessitated a brief, but meaningful, set of tests. These are describedin this report. However, to characterize fully the transducer'sperformance, additional tests would be required, but were not performedat this time.

2. ACCELEROMETER SPECIFICATIONS AND PHYSICAL DESCRIPTION

The angular accelerometer available for testing was a developmentalprototype and, as such, may not have had all the engineering refinementsincorporated into its design. However, it was deemed worthwhile to

test it at this stage of its development in order to determine its

feasibility for use in the DoT "mouthpiece" configuration.

The manufacturer's preliminary specifications which accompaniedthe accelerometer are reproduced in appendix A. The parameters of

key interest in this phase of the investigation are listed as follows:

1

Numbers in brackets refer to the references listed at the end of

this report.

2

1 . Sensitivity,2. Frequency response,3 . Ampl i tude 1 i neari ty

,

4. Transverse-axis angular sensitivity, and5. Linear acceleration sensitivity.

Each of these parameters is briefly discussed and interpreted.

2.1 Angular Acceleration Sensitivity

The sensitivity factor for the transducer is the mechanical -to

-

electrical transfer function. As such, the transfer function is a

complex ratio of the electrical output divided by the mechanical

input. The electrical output is voltage and the mechanical input is

angular acceleration in units of radians per unit time squared, or

rad/s^ . The accelerometer transduction element contains an electricalfour-arm Wheatstone bridge where all four arms are active strainsensing elements. The sensitivity factor is, therefore, a functionof the bridge excitation voltage which is specified as 10 volts dc

.

With the specified excitation voltage, the angular accelerationsensitivity factor is given in appendix A as "5.7 yV« s^/rad

."

Generally, it is accepted practice to give associated test conditionsfor which the sensitivity applies, such as frequency and accelerationamplitude. No such information was supplied, therefore, the valueof 5.7 yV«s2/rad is interpreted as a nominal value. Phaseresponse is inferred by the resonance frequency and damping factorand is discussed in the following section.

2 .2 Frequency Response

The frequency response specification is given as "flat (to)

within 1 dB to approximately 700 Hz." Transducers having a straingage type sensing element usually have "dc response" (a frequency ofzero hertz), however, because of a small, pressure-equalizing, bleedorifice in this design, the unit does not have dc response. Discussionwith the manufacturer disclosed that the response at the low end ofthe spectrum is thought to roll off somewhere near 1 Hz or less [2],Neither the manufacturer nor NBS has made measurements at this timeto assess the low-frequency roll-off.

The nonlinear response with frequency is caused by thetransducer's natural mechanical resonance which is given as about2600 Hz. The rate of sensitivity increase as a function of frequencybelow the natural resonance is controlled by the damping. The prelim-inary specifications state that the "phase response" is "typical ofan undamped system." With near zero damping, the response typicallyincreases by about 4% to 6% at 20% of the resonance frequency. In

this instance, one-fifth of the resonance is about 520 Hz.

Assuming that the transducer exhibits the typical behavior of other

types of accelerometers, i .e ., the mechanical resonant system can be

3

represented as a second-order, single-degree-of-freedom, spring-mass,lightly damped system, the response R can be predicted by the followingrelationship [3] where w is the angular stimulus frequency and wn is thenatural mechanical resonance.

R =

/(I - w2/a)n2

)2 + (2£a)/wn )

2. ( 1 )

Further assuming a typical value for the fraction of criticaldamping of 5 = 0.01 (i.e., mechanical Q = 50)2, expectedresponse is shown in figures 1A and IB. The maximum response riseis consistent with the assumed mechanical Q of 50 as shown by figure 1A.

Figure IB shows the same function with the frequency one decade lessthan in figure 1A and also with the ordinate being greatly expanded.The computed rise at 700 Hz is about +7.8% (or +0.65 dB) as comparedto the preliminary specification of +12% (+1 dB). It appears thatthe preliminary specification is conservative or that the dampingfactor may not be as assumed. The rise at 100 Hz is approximately+0.15% and at 300 Hz is approximately +1.3%. It is anticipated thatthe frequency spectrum of the angular acceleration to be measured in

the final application (i.e., boxer's head motions) will not containfrequencies greater than several hundred hertz. This overall responseis adequate to satisfy the demands for the transient bandwidth ofthe expected in measurement application.

The phase lag of the electrical output as compared to themechanical input is predicted by [3]

<t>= tan"'1

2£ - (w/u^)

1 - ( u/up

)

2_

( 2 )

Again, assigning values of resonance frequency of 2600 Hz andthe fraction of critical damping of 0.01, the phase lags are 0.03°

at 100 Hz, 0.13° at 300 Hz and 0.33° at 700 Hz. These are sufficientlysmall so as to be of no practical concern for the expected measurementappl i cat ion.

^The damping factor is related to mechanical Q by the relationship

C = 1/2Q. A mechanical Q of 30 to 100 is typical of most lightlydamped accelerometer designs, therefore, Q = 50 is a reasonableapproximation for purposes of these calculations.

2.3

Amplitude Linearity

The preliminary specifications give the amplitude linearityspecification for this angular accelerometer as "...less than 1

percent nonlinearity..." This is interpreted as: the deviation at

any amplitude from a least-squares linear-fit to the data within thetransducer's range will be less than one percent of the reading.

This is illustrated in figure 2.

2.4

Transverse Axis Angular Sensitivity

The preliminary specification for the response to transverseangular acceleration (i.e., input angular acceleration perpendicularto the sensing axis) is given as "3% maximum, 2% typical." Thisapplies for all frequencies and amplitudes throughout the transducer'soperating ranges.

2.5

Linear Acceleration Sensitivity

The response to linear input acceleration is given under twoconditions: parallel to and perpendicular to the angular sensing axis.

2.5.1 Linear Acceleration Sensitivity Parallel toSensing Axis

The preliminary specifications give the linear accelerationsensitivity parallel to the sensing axis as "2.5 rad/(s^»g) fromdc to * 50 Hz, increasing directly with frequency above « 50 Hz at

about 0.05 rad/(s 2 *g*Hz). " This is shown graphically in

figure 3. This can be expressed as

2.5

rad/(s 2 *g), 0 Hz < f < 50 Hz, and

0.5 rad/(s 2 *g*Hz), f > 50 Hz .

Where plotted versus frequency, the linear sensitivity appears constantabove 50 Hz if the ordinate units are rad/(s^*g»Hz). Below a frequencyof 50 Hz, the function increases as (1/f) because the specificationcontains no frequency term. This lower portion represents a constantresponse of 2.5 rad/(s^*g).

2.5.2 Linear Acceleration Sensitivity Perpendicular toSensing Axis

The sensitivity for input linear acceleration which is perpendicularto the angular sensing axis "increases directly with frequency (at a

rate of) 0.04 to 0.05 rad/(s^*g*Hz). " This is shown in figure 3

by the dashed line below 50 Hz.

5

2.6 Physical Description

Figure 4 shows a photograph of the accelerometer. It is approxi-mately 3 cm long with 0.5 inch hex faces to facilitate mounting.The integral mounting post is a UNF 1/4-28 external thread. Withoutthe connecting cable, the accelerometer's center-of-gravity wasmeasured on a knife edge as approximately 8.9 mm (0.35 in.) from the

base. The manufacturer gave [2] the location as about 7.6 mm(0.30 in.) from the base. The illustration of figure 4 shows the

location for the center-of-gravity for the orthogonal planes and is

located symmetrically on the cylindrical axis of the accelerometer.The measured mass of the accelerometer (without the electrical cableand connector-^) was 16.5 ±0.1 grams.

The electrical connections were made through a supplied cablehaving a miniature six-pin connector. The "pig-tail" leads are colorcoded and were tagged with the following information:

Cable Lead Tagged Information Comment

RedBlackWhiteGreen

"Input +"

"Input"Output +"

"Output -"

Bridge excitationBridge excitationSignal output, high

Signal output, low

The principle of operation in its simplest form can be describedas a liquid filled torus having an intercepting diaphragm. As the torus

is accelerated about an axis perpendicular to the toroidal plane, a

differential pressure is exerted on the diaphragm. Strain gages aremounted on the diaphragm and hence sense the differential pressurewhich, in turn, is directly proportional to the angular acceleration.

3. LABORATORY MEASUREMENTS

The laboratory measurements selected for this assessment can be

divided into three sets:

A. Transducer resistance measurements,B. Angular acceleration measurements, and

C. Linear acceleration measurements.

The resistance measurements were preliminary to all the othersto ensure that all leads and transduction elements were intact. The

angular acceleration measurements were designed to assess the most

%or mass considerations, the accelerometer is measured alone. The

connector has a mass of about 1 gram. In most applications, onlya portion of the cable dynamically loads the accelerometer as effectivemass; generally about 2 cm of cable length ( i . e . , about 0.5 gram) is

added to account for the cable's effective mass.

6

important transducer parameter, its angular sensitivity factor,

along with the frequency response and amplitude linearity. The

linear acceleration measurements were designed to evaluate the

transducer's output when rectilinear motion is applied to the angularaccelerometer. Ideally, the output should be zero under the latterconditions and any output is interpreted as an error.

This section contains descriptions and discussions of the testphilosophy, test systems and apparatus special fixtures, test procedures,data collection and presentation, and data analysis and discussion.Measurement results of weight and center-of-gravity were given in

section 2.6 of this report

.

3.1 Resistance Measurements

The "lead-to-lead" resistance was measured for an unmountedaccelerometer to ensure that no damage had occurred in the leads,connector, and transducer gages. A dc digital ohmmeter was used to

measure the resistances. The resistance was measured with the ohmmeterleads in a "forward" and "reversed" position to check for any possible"polarity" effects. Table 1 gives the measurement results. The

resistance ranged from about 1200 to 1670 ohms. There was no apparentohmmeter-lead reversal effect; the "reversed" reading agreed withthe "forward" reading to within 0.2 ohm in the worst case. Theresistance from the shield to any other lead was an open circuitinsofar as the ohmmeter reading indicated. The resistance from the

"pig-tail" end of the shield wire and the transducer case was approxi-mately 0.5 ohm.

The computed current drain with a 10 V dc excitation voltageapplied between the ±INPUT leads would be 5.991 mA. The measuredcurrent with 10.000 V dc applied was 5.912 mA, or a difference fromthe computed value of about -1 .3%. The accelerometer was held in a

hand for several minutes and the current monitored; the "warm" currentwas 5.879 mA (about 0.6% lower than the previous ambient temperaturecurrent) . This would indicate that the overall resistance betweenthe ±INPUT leads was temperature sensitive and that self-heatingand external environmental heating can be expected to cause resistancechanges of perhaps several percent. The temperature coefficient ofbridge resistance was obtained from the manufacturer [4] as approximately+0.7% per degree C (0.4% per degree F) as measured at any pair ofdiametric points on the bridge.

With ±10 V dc applied between the ±INPUT leads, the dc

offset (bridge unbalance) voltage was measured as 9.22 mV underambient laboratory temperature conditions. This indicates that theelectrical balance of the strain gage bridge elements is rather good(within about 0.09%). The unbalance as a function of temperaturewas not measured, but should be if further testing is performed at a

1 a ter time .

7

3.2

Angular Acceleration

3.2.1 Test Philosophy

With a known angular acceleration applied to the transduceralong its sensitive axis, the accelerometer's transfer function(i.e., sensitivity factor) can be determined by measuring its electricaloutput. This simple relationship is shown below.

Sensitivity Factor =Voltage Output

Acceleration Input

The units of the sensitivity factor are volts per unit angular acceler-ation, or V/( rad/s2 ). The preferred form of expressing these unitsis V«s2 «rad“' and will be used throughout this report.

Further, the sensitivity factor is directly proportional to thebridge excitation voltage. For all of the measurements made herein,the bridge excitation voltage was nominally 10 V dc.

3.2.2

Electrical Excitation Power Configuration

The electrical excitation for the resistance bridge was suppliedfrom two separate adjustable and regulated sources. This is shownschematically in figure 5. The two power sources were connected in

series so that the sum of the two voltages is the bridge excitationvoltage, nominally 10 V dc. The center connection of the sources is

connected to the system ground. For nominally equal bridge resistanceand no input angular acceleration, the bridge output voltage is zero.Because the four bridge arms are not all exactly equal, there is a

small residual unbalance (offset) voltage. The two power supplieswere adjusted so that the sum of their two voltages always equaled10 V dc and the two output voltages to ground were opposite andequal. This procedure thus minimizes the dc voltages at the outputterminals of the bridge. This was necessary to avoid dc overloadingof sensitive amplifiers used in the measurement of the small ac

signal outputs.

3.2.3

Laboratory Instrumentation, Amplifiers, and Filters

The electrical output from the accelerometer is a small ac

voltage from a source impedance of about 1500 ohms. Even withmoderately good shielding and low noise power supplies, noise andhum (i.e., 60 Hz related components) make accurate measurementsdifficult. The nominal sensitivity given for the accelerometer was5.7 uV«s 2 *rad“l. The test acceleration amplitudes to be usedranged from about 64 to 5000 rad/s 2 peak. (Details of the inputacceleration are discussed in a later portion of this report.)Multiplying the sensitivity and the angular accelerations provides

8

estimates of the voltages to be measured. For sinusoidal inputaccelerations, the output voltages could be expected to range fromabout 0.26 to 20.1 mV rms . To ensure adequate precision and accuracy,the voltage measurement resolution and uncertainties should be a

fraction of a percent; this requires that low-level ac signals(at low frequencies at times) must be known to within a few microvolts.

Narrow band amplifiers were used as is shown in figure 6. The

output of the accelerometer was fed into a preamplifier/filter withdifferential inputs. Low noise gains of nominally 200 or 500

were achieved in the first amplifier. Some band-pass filtering wasalso achieved in this preamplifier. Its output fed two cascadedfilters, each having nominally 0 dB gain (unity gain). These filters,identified as "filter A" and "filter B" in figure 6, could be configuredas low-pass, high-pass, band-pass, or band-reject filters. The

output of filter B was connected to a digital measuring system whichmeasured and oscilloscopically displayed the signal .

Because the measurement system includes amplifiers and filters,the response of the external system must be removed from the measure-ment to assess the transducer performance . This is shown as

Transducer SignalMeasured Signal

External Gain

Because the gain settings of each of the amplifiers and filters wereonly known nominally, and further modified by the "skirt response"of the filters, system gain had to be measured for each of the gain-and filter-setting combinations used in the measurements.

3.2.4 Angular Acceleration Generation

The input angular acceleration to the accelerometer was generatedby a dual spin-axis rate-table (DSART). This device consists of twomotor-driven platforms whose rotational axes are perpendicular andintersect. The main platform is oriented horizontally and rotatesabout a vertical axis. Mounted on this horizontal platform is a

second motor and platform whose axis is oriented horizontally.Figure 7 shows a simplified drawing of the DSART platforms. Each ofthe two motors is independently controllable and each of the angularvelocities is measurable. When both motors are rotating at a constantspeed, an angular acceleration is generated about the vertical axiswhich is sinusoidal and predicted from

a(t) = w-|W2 sin(a)2t + 62), (3)

9

where a(t) is the angular acceleration, wi is the angularvelocity of the horizontal platform, u

>

2

is the angular velocityof the second platform, and t is a generalized unit of time. Thephase angle 62 is the angle between some arbitrary rotationalreference position on the upper platform and the accelerometer sensingaxis, and is generally selected such that 02

= 0 and can thus be

neglected. An accelerometer mounted on the upper platform, suchthat its sensitive axis is perpendicular to the upper motor's horizontalaxis, will experience input angular acceleration as described by eq (3).

(References 5 through 7 give details of the DSART operation and theory.)

The lower main platform is servo-controlled so that its angularvelocity is constant and is selected by a set of thumbwheel switcheson the DSART 's front panel. It incorporates an optically sensed,multi-slit disc in the velocity sensing servo-control circuit. Thevelocity is selectable over a range from 0.0001 to 3200 °/s (about1.7 urad/s to 56 ra d/s).

The upper motor is not servo-controlled and its velocity is setmanually by a multi-turn control. The velocity is sensed by a 60-toothcircular gear and the output from the magnetic pickup is fed into anelectronic counter. The counter reading is in units of revolutionsper minute (rpm) when the counter is gated at 1 second. Greatervelocity revolution can be obtained by gating the counter to 10 or100 seconds.

As given by eq (3), the peak amplitude of the angular accelerationis calculated by the product of the two angular velocities, w| ando)2 . Because the two velocities are in mixed, non-metric units,a factor is needed to convert the product of degrees per second andrevolutions per minute to radians per second squared. (The factoralso accounts for the two factors of 2 tt .

)

Hence,

where v-| is the angular velocity of the lower platform in unitsof degrees per second and V2 is the velocity of the upper platformin units of revolutions per minute. For convenience, the angularaccelerations, ap^, are peak accelerations and hereafter will be

designated as a, without any subscripts.

Table 2 shows the angular velocities needed to generate theangular accelerations at specified frequencies. Note from eq (3)

that the sinusoidal frequency of the acceleration is determined bythe velocity of the upper motor, as

(4)

10

Hz,(5)

Vof = —

60

where V2 is in units of rpm. The frequencies shown in table 2

were selected so that they are evenly spaced on a logarithmic scale.

The upper motor loses velocity stability at rates below about100 rpm (10.5 rad/s); its maximum velocity is specified as 6000 rpm(628 rad/s). Therefore, the maximum usable frequency range overwhich the DSART operates is about 1.67 to 100 Hz. The maximum angularacceleration, because of bearing loading forces, is 7896 rad/s 2

peak4

. These limiting parameters (i.e*, v-. = 3200 °/s,v2max

= 6000 rpm, ancl “max= ^896 rad/s^) then set the limits of

operation for the DSART. The values shown in table 2 are all withinthese limits and can be derived from eqs (4) and (5).

In practice, all the frequencies and accelerations may not be

obtainable because of problems of unbalance, noise, hum pickup,mechanical resonances, wave distortions, or motor heating. Balancingbecomes a critical and limiting factor as the test frequencies increase(i.e., as V 2 increases). Mechanical vibration and, hence, mechanical"noise" results from unbalanced conditions. Two-plane balancing is

required on each end of the rotating test specimen, usually with weightincrements as small as 0.5 gram.

At low velocities of the upper motor, the driving torque is verysmall. Under these conditions, interactive forces between the mainplatform's rotation and the upper motor's rotation cause coupledtorques to exist which can distort the desired sinusoidal motion;that is to say that the upper motor cannot maintain a constantangular velocity but is modulated by gyroscopically coupled torqueswhich exist because of the lower platform's rotation. When distortedmotions occur, the peak value of angular acceleration can no longerbe predicted simply by eq (4).

The slip rings used to conduct the signal from the rotatingplatform are also a source of electrical noise. The lower rings arelow-noise, mercury-wetted rings; the upper rings have simple dual

carbon brushes. The latter are orders of magnitude more noisy thanthe mercury-wetted rings. The noise from the carbon brushes tendsto be in bursts of high frequency signals, the bursts being synchro-nized with the rotation of the upper motor. Electronic filtering is

relatively effective in minimizing the brush/ring noise.

4The manufacturer limits the maximum operating acceleration by

specifying that the product of the two angular velocities in rpmshall not exceed 720 000 (rpm) 2

.

11

Sixty hertz pickup hum is also a source of noise whichcontaminates the acceleration-generated transducer signal. Theprincipal source of 60-Hz hum is from inadequate shielding and thelocation of wiring within the DSART cabinet. The wiring passesclose to a power transformer within the DSART frame. Electronicfiltering can be effective in attenuating these hum components atmost frequencies of test; however, acceleration tests at 50 Hz werenot possible because the filters could not be adjusted to providesufficient attenuation at 60 Hz.

3.2.5 Test Measurements

3. 2. 5.1 Angular Acceleration Sensitivity

The angular accelerometer to be tested was mounted onto theupper rotating platform of the DSART illustrated in figure 7. Thecenter-of-gravity of the accelerometer was located approximately 3 mmabove the horizontal axis of the upper platform and was in line withthe vertical axis of the lower platform. The cable was coiled andsecured to the upper platform to prevent any whipping action. Theupper platform was balanced so that minimum unbalanced vibrationoccurred over the rotational speeds from about 100 to 6000 rpm.

As shown in figure 6, cascaded filters and amplifiers were usedto minimize the noise and to increase the signal voltage to a levelsuitable for digital measurement. Because the filter settings wereoften close to the test frequencies, the amplifier gain response wason the filter "skirts" and the nominal gains as indicated by theamplifier settings were not accurate enough for these measurements.Therefore, the cascaded gains were measured at each of the testfrequencies and the gain slope with frequency determined. In practice,an exact frequency could not be set accurately nor maintained formore than short periods because of the speed variations and drifts of

the upper DSART motor. The velocity, V 2 , could be measured butwould differ slightly from the nominal setting. It was thus necessaryto make slight frequency corrections to the amplifier/filter gains.Table 3 gives the nominal test frequencies, the measured gain, thegain slope, and the filter settings.

The signal outputs from the amplifiers and filters went into a

digital measuring system with averaging and data processing capabilities.Random components of noise, jitter, and some distortions were removedfrom the signal by ensemble averaging of a number of waveforms. Thenumber of ensembles ranged from 10 to 100, but usually numbered 25 or50. The ensemble averaging has the effect of a low-pass filter.

After averaging the signal, it was integrated over a wholenumber of sinusoidal cycles to determine and remove by calculationany dc voltage components contributed by the amplifiers. The rms

value of the waveform was determined and used as a basis for calculatingthe transducer sensitivity. As shown in section 4.2.1 of this report.

12

the sensitivity is the ratio of the electrical output divided by the

mechanical input. The sensitivity factor, S, was computed by the use

of the following relationships:

{?_ 5400 E yV«s2 *rad"l, (6)

tt2v,v0 H [1 + 0.01 c ( f - f )]

1 2 n t n

where E is the rms voltage output from filter B, H n is the measuredgain at the nominal frequency, c is the gain slope in units of percentper hertz and the other parameters are as previously described. Thefactor of /Z is a simple conversion from rms voltage to peak voltagefor a sinusoidal waveform; this is necessary inasmuch as the accelerationis in peak units. The frequencies, f^ and fn , are the test frequencyand the nominal frequency, respectively. The bridge excitation voltagewas maintained at 10 V dc for all the measurements.

At each test frequency and acceleration, a minimum of threemeasurements were taken to compute the sensitivity factor. In someinstances considerably more than three sets of data were taken.

Figures 8 through 17 show the results graphically with themeasured sensitivity plotted versus frequency. The measured pointsare represented by an asterisk (*) and the group average frequencyand average sensitivity are shown by the symbol "0." The left-handordinate is the measured sensitivity plotted from 5 to 6 yV*s 2 *rad”l

;

the right ordinate is the percentage deviation referenced to valueof sensitivity of 5.529 yV«s 2 *rad

-'. (This value was chosen

from an early set of data at 15 Hz and at 1000 rad/s 2 because thescatter in data is small at these operating conditions. The valueis arbitrary and has no special significance, but serves as a commonlevel for comparison purposes.)

The accompanying tables of appendix B for the figures B-l throughB-l 0 give the average frequency, average sensitivity, the percentagedeviation, and the number of measurements for each of the data setsby frequency. Figure 8 is the summary of all the angular accelerationsensitivity measurements for accelerations from 64 to 5000 rad/s2 .

Overall, there are 229 measurements that are summarized in figure 8.

For example, at a frequency of 70 Hz, there are 62 data points plotted.

The average of the data as plotted in figure 8 indicates thatthe transducer frequency response is relatively "flat" to withinabout ±2.5% over a frequency range from 1.5 to 70 Hz. There is a

general trend for the data to have an apparent increase in sensitivityas frequency increases. The reasons for this are unknown. Theoretically,the sensitivity rise should not be more than a small fraction of onepercent at 100 Hz (see fig. IB). Without further testing, one cannotstate that the rise is a result of transducer performance, but rather

13

could be a result of systematic error in the measurement apparatusor procedure.

3 .2 .5 .2 Amplitude Linearity Measurements

The data collected and presented in the previous section (angularacceleration sensitivity) were regrouped and analyzed for amplituderesponse. The data at each acceleration amplitude was averaged toget a single value regardless of frequency. This is plotted andshown by figure 9. The averaged data are shown by the plottingsymbol "1 ." The straight, sloped line is a first degree regressionfit to these data. The fit line is difficult to detect because itis very close to the data, however, a slight difference can be seenat 2000 rad/s 2

. Figure 10 shows the same data in terms of deviationfrom the mean accelerometer sensitivity (slope of fit curve of fig. 9)

rather than accelerometer output voltage. Here, the differencesbetween the measured and fit values are more apparent. The maximumdifference allowable by the preliminary specification is ±1%

(see appendix A and section 2.3 of this report). Table 4 givestabular results in terms of the measured accelerometer sensitivity.The column headed percentage deviation should be less than ±1% to

meet the specifications. The largest difference measured was approxi-mately -1 .27% at 500 rad/s 2

.

It should be noted that other effects are present and "contaminate"the data to an unknown amount. For example, there was no attempt toseparate the frequency response effect from the amplitude responsewhen examining the amplitude linearity. With the present data, the

frequency effect, which is included, has the tendency to make theamplitude linearity appear worse than it would be at a single frequency.Data from the test frequencies of 70 and 100 Hz are included in thisanalysis. It was seen from the angular acceleration sensitivitythat the tests at 70 and 100 Hz tended to be of a greater-than -expectedsensitivity. It is believed that this same "data rise" at these twofrequencies may have "biased" the linear fit slightly higher than it

should be. Therefore, the value of -1 .27% deviation at 500 rad/s 2

is probably not as significant as it would first appear. Furthermore,other measurement uncertainties are associated with each of thedatum points shown which could easily account for the apparent "greater-than-specification" deviation

.

It should also be further noted that the analysis was accomplishedand acceleration data were taken at only 10% of the transducer'sfull scale of 50 000 rad/s2 ; no statement can be made concerningthe response for acceleration amplitudes between the 5000 rad/s^level to which testing was done and the full-scale range of 50 000

rad/s2 .

3.3 Transverse Axis Angular Sensitivity

The sensitivity of the accelerometer to angular accelerations appliedin a direction which is transverse to the main sensing axis was not

14

performed directly. Indirect measurements of the influence of a

transverse angular sensitivity on the performance are discussed below.

With the accelerometer mounted on the DSART upper platform as

previously described, a component of transverse angular motion is

present by the fundamental operation of the DSART. Equation (3)

shows a phase term, 62, which, for the previous set of measurements,was set to zero. When set to zero, the mechanical rotational referenceposition is aligned in the same direction as the accelerometer sensingaxis. Under these conditions, a second component of angular accelerationexists on the upper platform which is in quadrature, i.e., it occursat a mechanical rotation of 90° later. This component has the sameangular acceleration, sinusoidal amplitude, w-ju^, but a phase angleof tt/2 rads or 90°. Thus there exists, by the fundamental operation,a quadrature motion (i.e., transverse) which is of the same amplitudeas the main, in-phase angular acceleration. So while the accelerometeris sensing the "in-axis" angular acceleration generated by the DSART,

it is also simultaneously experiencing a transverse angular accelerationof equal amplitude (i.e., 100% transverse input).

In theory, if the accelerometer' s phase response is accuratelymeasured, and the in-phase and quadrature-phase components resolved,then the transverse sensitivity could be measured; the transversesensitivity would be the quadrature-phase component. This, in practice,however, is not easy. Phase shifts in the measuring system andtransducer have to be carefully determined. For example, if thetransverse sensitivity were at a typical value of 2% of the mainangular sensitivity, the phase shift in response due to 100% transverseinput as described above calculates to be only 1 .1°. Phase shiftsdue to the accelerometer resonance (see eq (2)) and, more importantly,due to the amplifiers and filters would have to be known very precisely.This is especially difficult when the filters are used at frequenciesnear their cutoff frequencies.

A second method was considered, but the lack of time did notallow it to be tried. If the accel erometer sensing axis were alignedin the same direction as the rotational axis of the upper platform,then, ideally, the angular acceleration in this direction would be

zero. The accelerometer would experience 100% transverse inputmotion from the main acceleration vector of the upper platform.Again, ideally, the output measured under these conditions representsthe transverse sensitivity of the transducer. This assumes, ofcourse, perfect alignments of the accelerometer mounting, DSARTrotational axes, etc. It also assumes that the velocity, a>2,

of the upper platform is perfectly constant, and that no variationsin velocity occur over a one revolution. Observation has shown thelater condition is not true because of coupled gyroscopic torquesbetween the two rotating systems, namely, the lower and upper platformsand their drive systems. The upper platform does not maintain a

15

constant velocity, especially at low velocities when waveform distortionis easily observable. Velocity variations of the upper platform areindeed angular accelerations in that axis. At higher velocities,the electric drive motor develops sufficient torque to overcome thegyroscopic coupled torques. Also, the angular momentum is muchgreater which tends to "smooth out" the variations in angular velocity.

It should be kept in mind that the angular transverse sensitivityis a small quantity, i.e., about 2% of the main sensitivity; therefore,signals in the order of 2/1 00 of 5 uV*s2 *rad"^ are being sought.This alone represents a difficult measurement. Moreover, the gyro-scopically coupled torques occur at the same period (or frequency)as the transverse acceleration input vector to the accelerometer,since both are directly related to the rotational velocity of theupper platform. Hence one cannot easily separate the effects oftrue transverse response and upper platform velocity variation (i.e.,angular accelerations). Transverse sensitivity would better be

performed on a specially designed apparatus expressly made for thepurpose.

3.4 Linear Acceleration Testing

3.4.1 Test Philosophy

Two specifications for linear vibration sensitivity are givenby the preliminary specifications; one for input vibration parallelto the angular accelerometer's sensing axis, and the second forvibration perpendicular to the angular sensing axis. These specifi-cations were discussed in section 2.5 of this report.

The ideal angular accelerometer would have zero output forpurely rectilinear input vibration. Any accelerometer output underthese conditions represents an error. Testing for these angularaccelerometer characteristics is complicated by the fact that purerectilinear motion does not exist on even the best of linear vibrationexciters (shakers). Cross axis motion as well as rocking modesalways are present to some finite level; the rocking modes generateangular accelerations. Furthermore, the rocking modes change withfrequency, drive amplitude, position, direction, mass, and sometimestemperature and time. It is, therefore, not only a difficult measure-ment, but one that often has little meaning unless extreme care has

been taken by very elaborately accounting for rocking modes of thelinear exciter.

The fixture to which the accelerometer was mounted was made andmounted so that it and the accelerometer represented a momentbalanced load to the exciter, i.e., the exciter was driving its

linear acceleration vector through the effective center-of-gravityof the fixture and accelerometer combined. The fixture was a 2.5 cmcube-shaped block of aluminum machined square so that perpendicularitywas ensured. A UNF 1/4-28 hole was tapped to accommodate the integral

16

mounting stud of the accelerometer (see fig. 4). Various UNF 10-32

threaded holes were located so that the block could be attached to

the linear exciter in a balanced manner.

The electrical and instrumentation hookups were the same aspreviously described for the angular acceleration tests (see section3.2.2). The filters were set for a band-pass configuration as follows(see fig. 6): preampl ifier/fil ter gain was 1000 and filters set to3-Hz high pass, 10-kHz low pass; filters A and B gains were 0 dB andfilters set to 5-Hz high pass and 2-kHz low pass, respectively.Therefore, the overall gain was nominally 1000 (+30 dB) with a bandpass of approximately 5 to 2000 Hz. Because measurements were takenat least one octave away from each of the band limits, gain measurementswere not made as they were for the angular acceleration tests.Furthermore, accuracy was not paramount for these linear accelerationtests so accurate gain was not necessary.

3.4.2 Linear Sensitivity Parallel to Sensitive Axis

The accelerometer was mounted on the linear vibration exciterso that the linear sinusoidal acceleration vector was alignedparallel to the angular acceleration sensitivity axis. Linear acceler-ations were servo-controlled to a constant peak amplitude of nominally50 m/s 2 (5 g peak). The test frequencies were manually selectedand ranged from about 25 Hz to 1000 Hz.

The linear sensitivity is referenced to the angular sensitivityby the following relationship.

S£ = ^2E_ rad/(s 2 *g),,

A*HSa (7)

where

OS£ is the linear acceleration sensitivity in units of rad/(s »g)

(same units as given in the preliminary specifications),

E is the rms output voltage from the amplifier and filters(the term /7 converts the rms values to a peak value).

A^ is the linear acceleration test amplitude in units of"g" (1 g = 9.80665 m/s 2 ),

H is the composite amplifier gain, and

Sa is the angular acceleration sensitivity factor in unitsof uV»

s

2 *rad"'

.

17

For these tests, the following parameters were set:

7A£ = 5 g peak (approximately 50 m/s )

,

H = 1000 (+30 dB), and

Sg

= 5.529 pV*s *rad"“ as determined from the angularacceleration sensitivity.

Table 5 gives the measurement results over a frequency rangefrom about 25 to 700 Hz. A rocking mode resonance in the exciterprevented measurements at higher frequencies. Figure 11 shows theresults graphically along with the preliminary specification whichis also plotted.

Because of the angular accelerations present in the linearexciter's motion (rocking modes), this data may not represent thetrue response of the accelerometer, but rather the combined responseof the exciter and the accelerometer. The rocking motion addsvectorially to the linear sensitivity since the exciter's rocking or"contamination components" could either add to or subtract from thetrue response. This is probably the cause of the "peak-valley"response seen at 200 and 300 Hz in figure 11. Further, the rise in

response beyond 700 Hz is very probably due to a known rocking resonancein the exciter near 1000 Hz. Even so, the measurement results indicatethat the linear acceleration sensitivity parallel to the angular sensingaxis is low and probably within the manufacturer's preliminaryspecifications.

3.4.3 Linear Sensitivity Perpendicular to Sensitive Axis

The accelerometer was mounted on the adaptor block which was,in turn, mounted onto the vibration exciter so that the linearsinusoidal acceleration vector was aligned perpendicular to theangular accelerometer's sensitive axis. As before, the linear acceler-ations were servo-controlled to a peak amplitude of 50 m/s^ (5 g peak).The frequencies were manually selected and ranged from 100 to 1000 Hz.

The linear sensitivity perpendicular to the angular sensingaxis is referenced to the angular sensitivity by the followingrelationship.

5' = 4^ = rad/(s 2 °g»Hz) ,^

18

where

S' is the linear acceleration sensitivity in units of

rad/(s 2# g*Hz) (same units as given in the preliminaryspecifications)

,

E is the rms output voltage from the amplifiers and filters(the factor of /2 converts the rms voltage to peak voltage),

Ao is the linear acceleration test amplitude in units of"g" (1 g = 9.80665 m/s 2

),

H is the composite amplifier gain,

Sa is the angular acceleration sensitivity factor in unitsof yV*s2 *rad‘l, and

f is the test frequency in Hz.

For these tests, the following parameters were selected:

OAj, = 5 g peak (approximately 50 m/s ),

H = 1000 (+30 dB) or as noted in table 7, and

Sa = 5.529 pV •s^*rad”l

.

Equation (8) is the same as eq (7) except for the new term offrequency, f, in the denominator.

When the angular accelerometer is mounted in the configurationas described, the angular sensing axis is perpendicular to the linearacceleration vector, however, rocking motions on the exciter ( i . e.

,

angular accelerations) are aligned with the angular sensing axis.The importance of this cannot be overstated inasmuch as very small

rocking motions are directly sensed by the angular accelerometer.In order to perform this measurement satisfactorily, one would haveto ensure that the exciter's rocking motions were indeed extremelysmall. For example, at A^ = 5 g and at f = 100 Hz, the rockingmode angular acceleration would have to be less than about 2.5 rad/s 2

in order to have negligible effect on the linear sensitivity measurement;this is considered to be a low angular acceleration. Another way toillustrate these small motions in a way more familiar to those workingwith rectilinear vibration is to relate an equivalent angular acceler-ation in terms of a linear acceleration. If, as in the case above,the angular acceleration were to be limited to 2.5 rad/s 2 at 100 Hz on

a vibration exciter having a table about 7.5 cm (3 in.) in diameter,the maximum permissible difference in vertical linear accelerations

19

between the two edges of the table could be only about 0.00004 g peak,small indeed, and would in itself represent a difficult measurement.

The measurements given below represent a first attempt at obtainingsome measure of linear sensitivity. Because of the above rockingmode considerations and restraints, good quality measurements couldnot be obtained. Time and funds did not permit the development of a

method by which better measurements could be achieved. Table 6 givesthe measurement results over a frequency range from 100 to 700 Hz.

Figure 12 shows these results graphically.

One set of measurements was taken and evaluated by the use ofeq (8). The accelerometer's angular axis was oriented in an approximate"cross-trunion" direction on the exciter. A second set was done by

rotating the accelerometer 90° about its angular sensitive axis andthe measurements repeated. The results of both sets of data as

measured are two to four times greater than the preliminary specifi-cations, however, it is felt that under these test conditions, thefault likely lies with the testing exciter and method, and not withthe accelerometer. The fact that the results are this close to thespecification is regarded as a probable indication that the acceler-ometer's linear sensitivity is low and in the order of the preliminaryspecification ( i . e . ,

0.05 rad/(s^*g*Hz))

.

3.4.4 Other Effects

While performing the measurements for the linear sensitivitywith the acceleration perpendicular to the angular sensing axis (seesection 4.4.3), distortion was observed in the waveform. Nominally,the waveform should have been sinusoidal, however, higher orderharmonics were present.

A swept frequency response was made over the frequency rangefrom about 200 to 3000 Hz and is shown in figure 13. The unfilteredaccelerometer output is plotted versus frequency. The output waslow and relatively flat at the lower end of the spectrum up to frequencyof about 1425 Hz. Several resonance rises are noted about 1425 Hz,

the most notable being at a frequency of about 2160 Hz. This resonancewas traced to the connector and top of the accelerometer case.

Dwelling at this frequency, large effects could be seen on this high

Q resonance by lightly touching the connector. This resonant motion,probably coupled through the electrical leads, caused an output from

the strain gage sensing elements.

Because this resonance is such a high Q, it can easily be excitedby subharmonically related accelerations which can have the effectof seriously distorting the waveform. In the present accelerometerpackaging configuration, this may cause application measurementproblems. If, however, the transducer is repackaged for the DoTapplication in a miniature triaxial configuration, then this casetop/connector resonance would not likely exist. Any new configurationshould be tested to ensure that similar resonances do not exist.

20

3.5 Measurement Uncertainties

The uncertainties in the measurement process stem from varioussources, some of which are evaluatable, but others which are moredifficult to ascertain. A rigorous error analysis was not performedinasmuch as to do so could consume more effort than did the measurementsthemselves. The errors which are more obvious and evaluatable are

discussed below and combined to obtain some reasonable measure of

uncertainty in connection to the data shown previously.3.5.1

Bridge Voltage Excitation

The output voltage from the four-arm Wheatstone bridge withinthe transducer is directly proportional to the bridge excitationvoltage and, moreover, uncertainty of the output voltage is directlyproportional to uncertainty of the excitation voltage. The voltagewas adjustable and measurable to within a resolution of ±0.02%

with an additional uncertainty of ±0.05% in the voltage magnitude.Voltage drops in the short leads and connections were neglected.Therefore, the total estimated uncertainty in the bridge excitationvoltage is ±0.07% worst case (direct addition) and ±0.054%(rounded to ±0.05%) root-sum-squared (rss).

3.5.2

Signal Voltage Measurement

The amplified and filtered output voltage was measured with a

digital processing oscilloscope whose digitizing resolution was 10 bits;this translates to approximately ±0.1% of a full-scale digitalword of 1 bit in 1024 bits. The ranging sequence was in a 1-2-5

scheme where it would be possible to measure at 2/5 of full scalebefore being able to down range to the next lower scale. Thiseffectively makes the measuring resolution 2.5 times less than atfull scale, or 2 .5 x (±0.1%) = ±0.25% of reading. It is estimatedthat the integration process for dc voltage removal is accomplishedto within ±0.05%. The rms voltage integration, squaring, summing,etc., is done to within ±0.1%. the ranging, gain, and referencevoltage is known to within ±0.1% and the readout resolution is to

five digits making its uncertainty about ±0.01%. Thus the overallvoltage measuring uncertainty is estimated to be ±0.51% worst caseand ±0.29% root-sum-squared.

3.5.3

Amplifier Gain and Filter Response

The amplifier gain was determined using a precision Kel vin-Varleydivider whose setting resolution (because of noise and drift) wasabout 5 parts in 2000, or ±0.25% of setting. (The uncertaintiesassociated with the divider ratio are in the order of a few partsper million (ppm) and are completely overshadowed by the lack ofresolution due to system noise.)

21

The gain as a function of frequency was determined over a narrowband (usually a few hertz) around a nominal frequency to determinethe gain slope with frequency. Referring to eq (6) (section 3 .2 .5 .1

of this report), two other terms are seen, namely, the gain slope andfrequency difference. Analysis of gain measurement data led to the

conclusion that the overall effects of gain measurement, frequency, gainslope, noise, and drifts yielded an uncertainty of about ±0.75%worst case and about ±0.43% root-sum-squared.

3.5.4 Acceleration Determinations

The angular acceleration generated by the DSART is principallya function of the two angular velocities, v-j and V 2 , as shownin eq (6). The velocity, v-j, of the lower platform has a settingaccuracy of ±0.25%, a "wow and flutter" specification of 0.1% at1/10 of full-scale range, and a stability specification of ±0.1%.These combine to be ±0.45% worst case and ±0.29% root-sum-squared

.

The velocity, V2, of the upper platform is measured by useof a 60-tooth tachometer utilizing an electronic counter. At frequencyof 1 .5 Hz (90 rpm) , the counter resolution over a 10-second countergate time is ±1 part in 900, or about ±0.1%. Examination of thedata indicates that drifts and other instabilities account for approx-imately ±0.48% uncertainties. Combining these sources of error,the worst case uncertainty is estimated as ±0.59% and ±0.49% forthe root-sum-squared estimated uncertainty.

The angular acceleration is the product of the two angularvelocities, therefore, the uncertainty in acceleration is approximatelythe sum of the uncertainties of each of the velocities. Combiningthese uncertainties leads to an estimate of the uncertainty forangular acceleration of ±1 .04% worst case and ±0.74% root-sum-squared .

There are other sources of error in the acceleration predictionsuch as nonsinusoidal waveform distortion, or rocking motions of theDSART mechanisms which appear as angular accelerations; these effectsare not evaluated here. However, some of the influences that thosesources have on the uncertainty have been included in the final

uncertainty value andareshown in section 3.5.7. In some instances,these "other sources" of uncertainty may not necessarily be small in

comparison to those values given above. (If future work is performedusing this hardware, efforts should be made to evaluate such errorsand, if possible, reduce them.)

3.5.5 Computation and Arithmetic Errors

Calculations were performed digitally to 20-bit precision andread to 4 decimal places. Final values are reported and discussedto 3 decimal places, therefore, rounding errors can be interpretedas ±1/2 part in 550 parts, or about ±0.09% of the typical sensitivityreading.

3 .5 .6 Other Error Sources

There are a number of sources of additional errors leading tomeasurement uncertainty. A few of the more elusive parameters are noiseand hum, nonsinusoidal distortion, cross-axis excitation and response,temperature changes, DSART rocking motions, etc. These sourcescould represent difficult and complex error relationships which areinterdependent on frequency, acceleration, temperature, and mountingposition as well as other now unknown quantities. In order to get a

first order assessment of these effects, the scatter of the sensitivitymeasurement results was briefly analyzed. Because it is believedthat the amplitude nonlinearities are small, the analysis was doneon a frequency-by-frequency basis. Statistically, an estimate ofthe standard deviation was calculated for each set of data by frequency.The results are shown in table 7. The estimated standard deviationdid not exceed ±3.5% for the 229 sets of data analyzed. Thisvalue is a measure of the scatter in the measurement process as a

result of some of the sources discussed previously as well as someof the effects such as noise, distortion, cross-axis excitation,etc., which were not assigned values of uncertainty. For this analysis,a value of ±3.5% uncertainty is included in the error analysis toaccount for the observed scatter due to unevaluatable causes.

3.5.7 Combined Uncertainties

The uncertainties discussed above are summarized below. The"symbols" refer to the parameters as given in eq (6). The uncertaintiesgiven are for the worst case combinations.

Symbol Source of Uncertainty ± Uncertainty %

- Bridge excitation voltage 0.07

E Measured voltage, rms 0.51

H,c, (ft -fn ) Amplifier gain, gain slopeand frequency difference

0.75

VI, v2 Arithmetic calculations andround-off

0.09

a Applied angular acceleration 1 .04

- Scatter and other effects 3.5

Worst case sumRoot-sum-squared

±5 .96%

±3 .76%

The worst case combination is about ±6% whileestimate is about ±4%. In examining the foregoingin figure 18, most of the data falls within a band

the root-sum-squareddata as summarizedof ±6% except

23

perhaps the data at 100 Hz. It is felt that other causes were affectingthis data, to an extent beyond the error analysis. Overall, anestimated uncertainty of ±6% is acceptable as a realistic value in

lack of a more thorough analysis.

All of the parameters listed above except the last, “scatter andother effects," are uncertainties which pertain to the test andcalibration equipment, and not to the performance of the accelerometer.A portion of the accelerometer's measurement uncertainty is includedin the 3.5% value of scatter and other effects, but just how muchcannot be stated at this time. Although a value of 6% was assignedas an estimate of overall uncertainty surrounding the entire measurementprocess, it should be emphasized that the accelerometer' s contributionis a fraction of the 6% under the conditions that these data wereobtained.

4. CONCLUSIONS

Three of the more important transducer parameters were testedto obtain a measure of performance and to fundamentally characterizethe accelerometer. These parameters were:

(1) Angular acceleration sensitivity as a function of frequency,

(2) Angular acceleration amplitude linearity, and

(3) Linear acceleration sensitivity response.

The angular acceleration sensitivity was measured over a frequencyrange from about 1.5 to 100 Hz and an acceleration amplitude rangefrom about 64 to 5000 rad/s2 . The mean sensitivity as describedin this report was 5.53 uV*s2 /rad at a reference frequencyof 15 Hz. Deviations of the sensitivity with frequency over a rangefrom 1.5 to 70 Hz was about -1.5 to +2.5% referenced to the 15-Hzmean value.

The angular acceleration amplitude linearity was measured over an

acceleration range from about 64 to 5000 rad/s2 . The maximum deviationbetween the measured data and a zero-based, best-fit, straight line wasabout -1.27%, a moderate portion of which can be attributed to

uncertainties in making the measurement and analyzing the data.

The linear acceleration sensitivity was measured both parallel

to and perpendicular to the angular sensing axis. In the firstinstance, measurements indicated performance was within the preliminaryspecifications as given by the manufacturer. In the second instance,

the measurement is much more difficult and rocking motions of thevibration exciter ( i . e .

,

angular accelerations) contaminate the data

so that good measurements could not be achieved. However, theresults were well within an order of magnitude of being within thepreliminary specifications and are small, even though a good measurecould not be done.

24

Overall, based on the limited measurement results obtained andfrom the observed performance, it is felt that the quality is probablyadequate for the current DoT application of measuring angular headmotions. However, the accelerometer packaging configuration must be

changed and adapted to the DoT application which would then requireadditional testing to ensure that the transducer performance wasmaintained.

Future testing should be done at a greater depth ( i . e. , morethoroughly), other parameters tested, and an attempt made to reducethe overall measurement uncertainties.

5. ACKNOWLEDGMENTS

Appreciation is given to Mark Haffner, the DoT/NHTSA technicalcontract monitor, for his support and guidance concerning the ultimateapplication for the type accelerometer and also for his probingquestions regarding transducer operation and testing methodology.Thanks are extended to Bob Sill of Endevco regarding details of theaccelerometer design and construction as well as interpretation ofsome of the specifications. Thanks also to several NBS co-workerswho contributed suggestions.

6. REFERENCES

[1] Endevco angular accelerometer, model 7302, serial no. 102prototype.

[2] Personal communication with R. Sill of Endevco, October 14, 1980.

[3] Harris, C. M., Crede, C. E., "Shock and Vibration Handbook,"Second Edition, McGraw-Hill, New York, 1976, p. 2-9.

[4] Personal communication with R. Sill of Endevco, November 17, 1980.

[5] Ramboz, J. D., Angular Acceleration Generation Using a DualSpin-Axis Rate-Table. Nat. Bur. Stand. (U.S.) NBSIR 81-xxxx,being prepared.

[6] McCuskey, S. W., "Introduction to Advanced Dynamics," Addison-Wesley, Reading, Mass., 1959, pp. 120-124.

[7] "Handbook of Instructions, 1100 series. Rate Tables," GeniscoTechnology Corporation, Compton, Calif., June 1, 1973.

25

Table 1 - Transducer gage resistance measurements;values are in units of kilohms.

Red meter lead

+INPUT -INPUT +0UTPUT -OUTPUT SHIELD

Black

meter

lead

+INPUT -- 1.66 1.32 1.27 00

-INPUT 1.67 — 1.26 1.21 00

+0UTPUT 1.32 1.26 -- 1.66 00

-OUTPUT 1.27 1.21 1.66 -- 00

SHIELD 00 00 00 00 --

26

Table

2-

Angular

velocities

v,

and

v~

for

calculated

peak

acceleration,

78961

1

1

1

1

1

0

1

1

1 !

00<3-

001440 1029

720

0 00 cu 000 1 1 1 | 0 0 CO r— CO0 1 l 1 § 0 0 r— cu 03 IDr-'. CO r“

0 CO r^»

0 1 0 1 | 8 1 CO 03 000 1 1 1 | 1 1 00 O I''. inID c 1

<T3

(1> O 0 0 CU ID(/) CL O 1 1 0 1 1 cu 1

—

LD inO 0 1 1 1 1 0 in C3 ID

o CU ID CO r—<S)

(

—

-a03 O cu ID O r— ins_ O 0 0 0 8 8 CO r— CO 00 ID

>, O 1 1 1 1 1 cu in CO+-> r* CO —

’

•r— a>u "Oo 13

+-> O ID cu r^. r—cu O 1 1 0 8 CO cu r— 03 i->.

> O 1 1 1 | r"- 00 03 m CO cu

s-fO

CLE<0

CO CXI 1

n c O in ID 00 in ,

—

cucn 0 O 1 1 1 0 cu r— 0 10 ID 00c O 1 1 1 ID CO CO ID CO CU r—<C +J CO CU 1

—

1

—

03S—

oOJ O 0 CO CO CO ^3" cu O cu

4- cu O 1 C\J 0 1

—

0 0 00 CO •

+-> u O 1 0 CO CO 03 ID CO r— r— r—<T3 u 1 CO 1—

-

1 03i

—

03D_

s_

c 03 O in O cu 1 ID CO cu r— ID•r— O co cu r— in in 0 in • • •

rtf 13 in i'-- m 03 10 CO r— I— in LO2: 03 C\J l 03 ID

C

0 CO 0 ID ID 00 CO 0 ID ID COin ID ID LO cu CO LO • • • •

00 CO 1"- co CO 1— ID in CO cu1 r-- CO cu

0 I''. CO 000 • • •

1— 1—

’

0in 03 ID

ID0 • •

m in 0CO

E >>S- u +->

QJ O -r- cvj E 0 O O 0 0 0 0 O 0 0cl<+- a Q_ 0 00 O cu 0 0 0 O 0 0CL 4-> O S- r— CO ID 03 00 0 cu 0ZD ra 1

—

1 00 IDO)

a_ >

+-> c

r

c-.(/) d) N 10 CO ld C'. O in 0 0 0 Ocu s- m r— 1

—

CO in O1— Ll_ r—

27

rpm

x

-rr/30

=

rad/s

°/s

x

tt/

180

=

rad/s

Table 3 - Measured gains and gain slope corrections for the cascadedfilters and amplifiers used for the angular acceleration sensitivity

measurements. (LP = low pass, HP = high pass)

Nominal

^FrequencyHz

l

1.5

2

3

j3

5

I

)

15

j 15i

15

1

15

30

30

70

70

70

100

11i

l P.ainFilter Settings

\

NominalGain

MeasuredGain

\ Slope

I %/HzPreamp.

Hz|

Filter AHz

! Filter B

Hz

500 500.001

0.00 .03HP/30LP|

1 5LP 15LP

500 413.87j

-1.64 .03HP/3LP 4LP j 4LP|

500 498.75 -0.201 .03HP/30LP 1 5LP 15LP

200 199.32 -0.401 .03HP/30LP 15LP 15LP

500 493.91 -0.640 .03HP/30P 15LP 1 5LP

500 484.49 -1.064 .03HP/30LP 1 5LP 15LP

500 498.50 -0.149 .03HP/100LP 30LP 30LP

500 491.88 -0.439 .03HP/100LP 30LP 30LP

500 479.24 +0.144 3HP/100LP 30LP 30LP

200 196.62 -0.432 .03HP/100LP 30LP 30LP

200 190.49 +0.467 3HP/100LP 30LP 30LP

500 474.84 -0.496 3HP/100LP 55LP 55LP

200 188.14 -0.545 3HP/100LP 55LP 55LP

500 379.35 +2.714 3HP/300LP 60HP 60HP

500 428.63 +2.056 3HP/300LP 60HP 150LP

200 171.17 +2.89 3HP/300LP 60HP 150LP

500 449.68 -0.698 3HP/300LP 65HP 150LP

28

Table 4 - Amplitude linearity data over 10 percent of the

acceleration full-scale range of 50 000 rad/s^.Reference sensitivity was 5.53 yV*s 2/rad;

% deviation is deviation between fitvalue and measured value

Accelerationrad/s^

Meas. SensitivityyV • s 2/rad

% Deviation

64 5.486 -0.80100 5.472 -1.05

250 5.503 -0.49500 5.46 -1.27

1000 5.531 +0.022000 5.498 -0.583000 5.567 +0.674000 5.575 +0.81

5000 5.573 +0.78

29

Table 5 - Linear acceleration sensitivityparallel to the angular acceleration

sensitive axis

FrequencyHz

|

Linear Sensitivityrad/s2»g

Preliminary Spec.rad/s2.g

24.5|

0.66 ! 2.5

50 0.80 2.5

100 2.10 5.0

S

150 4.2 7.5;

rooo 8.4 10.0 1

j

|

250 3.0 12.58

300 12.6 15.0j

350 17.5 17.5

400 22. 8* 20.0

500 29.

0

a 25.0

600 37.

4

a 30.0

700»

45.

0

a 35.0

aThis value contains angular acceleration componentsdue to the rocking motion of the vibrator exciterand is therefore greater than the "pure linear response."The exact amount is unknown, but shown to indicate a

trend in the linear acceleration response with frequency.

30

Table 6 - Linear acceleration sensitivity perpendicularto the angular acceleration sensitive axis for

two positions; see text for explanation

FrequencyHz

Linear Sensi tivityc , rad/s2«g*Hz

Position 1 Position 2

100 0.180 0.089

150 0.112 0.055

200 0.121 0.059

250 0.109 0.054

300 0.180 0.090

350 0.199 0.100

400 0.204 0.102

500 0.149 0.075

600 0.186b —700 0. 277a >b

aGain, H, was set to 500 rather than 1000.

^Harmonic distortion present in waveform.cValues shown also have a vector component includeddue to rocking motion (i.e., exciter angularacceleration) causing values to be larger than thetrue linear response.

31

Table 7 - Results of the analysis for an

estimate of standard deviation calculatedfrom 229 data sets. See figure 18 for

a plot of the data

Freq. , Hz No. of Meas.

Estimated% Std. Dev.

j

1 9 1 • 1 I

3 9 1.5

5 15 1.0i

7 18 3.3|

|

10 21 3.2

15 42 1.3

30 295

1.0

70 62 3.2

100l

24 3.1

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AMPLITUDE

LINEARITY

SPECIFICATION

***

35

Figure

2.

Angular

acceleration

amplitude

linearity

preliminary

specification.

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36

FREQUENCY,

Hz

37

angular

accelerometer.

NOTE

POWER SUPPLIES AJUSTED TO NOMINALLY 5 VOLTS EACH.

Figure 5. Transducer bridge elements and split power supplies toforce output residual voltage to near zero volts.

38

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39

Figure

6.

Accelerometer,

amplifiers.

40

Figure

7.

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elements

of

the

dual

spin-axis

rate-

table

(DSART).

Angular

accelerometer

to

be

calibrated

is

mounted

on

the

upper

rotating

platform.

09-DEC-80

08:43:54

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41

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43

Figure

9.

Angular

acceleration

measurement

data

results

for

the

amplitude

linearity;

accelerometer

output

vs.

acceleration

Note

straight

line

also

plotted.

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46

Figure

12.

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sensitivity

measurement

results

perpendicular

to

the

angular

sensitivity

axis.

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shown

for

two

orientations

of

the

accel

erome

te

r

about

its

sensing

axis.

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are

approximate

and

are

"contaminated"

with

rocking

motion

of

the

exciter.

Figure 13. Resonant response of the acce 1 e romete r when excitedby linear acceleration pe rpendi cul ar to the angular sensingaxis.

47

APPENDIX A

Preliminary Specification

7302 Angular Accelerometer S/N 102

Sensitivity

Full Scale

Frequency Response

Phase Response

Mounted Resonant Frequency

Linear Acceleration Sensitivity

Parallel to mounting surface:

Parallel to transducer axis:

5.7 yV-sec 2/radian with 10 V

excitation

50 000 rad/sec 2

Flat within 1 dB to approximately 700 Hz

Typical of undamped system

2600 Hz

Increases directly with frequency

rad0.04 to 0.05

sec 2 - G - Hz

2.5 rad/sec 2 - G from dc to«50 Hz,

increasing directly with frequencyabove « 50 Hz at about 0.05 rad/sec 2 - G - Hz

Transverse Axis Angular Sensitivity 3% maximum, 2% typical

Shock Limits

Angular

Linear

Amplitude Linearity

« 500,000 rad/sec 2

« 5000 G's

Less than 1% nonl i neari-ty

Temperature +10% at 25°F-15% at 1 75°F

Physical Description

Electrical Connection

Maximum Mounting Torque

15 grams, 3 cm long, stainless steel

case with 1/2" hex faces, 1/4 x 28

mounting post

Six-pin receptacle

One foot-pound

A-l

APPENDIX B

FREQUENCY RESPONSE MEASUREMENT DATA

B-l

08-DEC-80

09:32:57

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08-DEC-80

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09-DEC-80

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Figure

B-3B.

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acceleration

measurement

results*

frequency

at

an

acceleration

of

250

rad/s

2

09-OEC-80

10.24:20

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Figure

B-4A.

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measurement

results;

sensitivity

vs.

frequency

at

an

acceleration

of

500

rad/s

2.

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NBS-114A (rev. 2-eo

U.S. DEPT. OF COMM.

4.

BIBLIOGRAPHIC DATASHEET (See instructions)

TITLE AND SUBTITLE

PUBLICATION OR 2

REPORT NO.. Performing Organ. Report No. 3.

NBSIR 81-2337

Publication Date

August 1981

Measurement and Evaluation Methods for an Angular Accelerometer

5. AUTHOR(S)

John D. Ramboz

6. PERFORMING ORGANIZATION (If joint or other than NBS, see instructions) 7. Contract/Grant No.

NATIONAL BUREAU OF STANDARDSDEPARTMENT OF COMMERCEWASHINGTON, D.C. 20234

8

9. SPONSORING ORGANIZATION NAME AND COMPLETE ADDRESS (Street, City, State, ZIP)

D0T-HS-9-021 93IA. Type of Report & Period Covered

Final Report

8/1/80 - 12/30/80

Department of Trans porta ti onNational Highway Traffic Safety Administration400 Seventh St . , S . W

.

Washington, D.C. 2059010. SUPPLEMENTARY NOTES

~| Document describes a computer program; SF-185, FIPS Software Summary, is attached.

11. ABSTRACT (A 200-word or less factual summary of most significant information. If document includes a significantbibliography or literature survey, mention it here)

A transducer which measures angular accelerationalong one axis was investigated to assess three of itsperformance characteristics, viz., sensitivity factor,amplitude linearity, and response to linear ( non-angul ar

)

input accelerations. Accelerometer specifications andresponse theory are presented. Test philosophy andmethodology are discussed along with measurement results.Tests were conducted over a frequency range from 1.5 to

100 Hz and an acceleration range from 64 to 5000 rad/s^.Generally, the performance observed was in agreement withthe manufacturer's preliminary specifications.

12. KEY WORDS (Six to twelve entries; alphabetical order; capitalize only proper names; and separate key words by semicolons)

Angular acceleration; angular accelerometer; calibration;instrumentation; measurement; shock and vibration.

13. AVAILABILITY 14. NO. OFPRINTED PAGES

(_}(JUnlimited

| |

For Official Distribution. Do Not Release to NTIS 78

1 1 Order From Superintendent of Documents, U.S. Government Printing Office, Washington, D.C.15. Price20402.

[325 Order From National Technical Information Service (NTIS), Springfield, VA. 22161 $9.50

USCOMM-DC 6043-P80