CALIBRATION OF SENSORS

Abstract: A plurality of seismic sensors calibration method (100) includes: an assembling so that sensors are coupled with each sensor positioned with its axis of sensitivity in a different spatial direction calibration system step (105), a rotating sensors step (110), a measuring sensors output signals step (115), a sensor output signal processing step (120) and a storing calibration coefficient(s) step (125).

Description: CALIBRATION OF SENSORS Background of the Invention The present disclosure relates generally to a method of calibrating a plurality of sensors, and in particular to a three-axis sensor. In deploying sensors, calibration coefficients are used to correct the sensors for variations or errors in gain, offset, non-linearity, misahgnment of the proof masses, cross-axis coupling, temperature, or other environmental factors and to provide more accurate seismic data. Some limitations of current calibration methods include no automatic calibration, no conversion of data to internationally accepted scientific units, no permanent storage of the data, and no universal usage by any and all seismic software. The present invention is directed to overcoming or at least minimizing some of the limitations of the existing methods of calibrating sensors. Summary of the Invention According to one aspect of the invention, a method of calibrating a plurality of seismic sensors, each sensor having an axis of sensitivity, is provided that includes: coupling the sensors with each sensor positioned with its axis of sensitivity in a different spatial direction; rotating the sensors; measuring one or more output signals from the sensors; processing the output signals from the sensors; and storing one or more calibration coefficients. Brief Description of the Drawings Fig. 1 is a block diagram illustrating an embodiment of a method for calibrating a plurality of sensors. Fig. 2A is a schematic view of an embodiment of a calibration system for use in the method of Fig. 1. Fig. 2B is a schematic view of an embodiment of the sensors of the calibration system of Fig. 2A. Fig. 2C is a schematic view of an embodiment of the controller of the calibration system of Fig. 2A. Fig. 3 is a schematic view of rotating the sensors and measuring output from the sensors of the calibration method of Fig. 1. Fig. 4 is a schematic view of a preferred embodiment for processing output from the sensors and storing calibration coefficients to the sensors of the calibration method of Fig. 1. Detailed Description of the Illustrative Embodiments 5 Several embodiments of a method for calibrating a plurality of sensors are provided. The sensors are calibrated to correct for variations or errors in gain, offset, non-linearity, misalignment of the proof masses, cross-axis coupling, temperature, or other environmental factors and to provide more accurate seismic data. In a preferred embodiment, a system for calibration 10 includes a plurality of sensors and a controller. The sensors are cahbrated by rotating the sensors, obtaining data from the sensors, calculating the calibration coefficients for the sensors, and storing the calibration coefficients. The controller gathers the sensor data and calculates the calibration coefficients. The controller preferably includes a computer data acquisition 15 system and a computer software program. Referring initially to Fig. 1, a preferred embodiment of a method 100 for calibrating a plurality of seismic sensors includes: (1) assembling a calibration system in step 105; (2) rotating the sensors in step 110; (3) measuring output from the sensors in step 115; (4) processing output from the sensors in step 20 120; and (5) storing one or more calibration coefficients in step 125. In a preferred embodiment, the steps 105, 110, 115, and 120 of the method 100 preferably incorporate the methods disclosed in the Institute of Electrical and Electronic Engineers Specification IEEE 337-1972 for the IEEE Standard Specification Format Guide and Test Procedure for Linear, Single-Axis, 25 Pendulous, Analog Torque Balance Acclerometer, attached as Appendix A. Referring to Fig. 2A, in step 105, a calibration system 200 preferably includes a plurality of sensors 205 and a controller 210. In a preferred embodiment, the calibration system 200 includes a first sensor 205a, a second sensor 205b, and a third sensor 205c. The sensors 205 are preferably coupled 30 to the controller 210 by one or more communication interfaces 215. In a preferred embodiment, the calibration system 200 includes a first communication interface 215a, a second communication interface 215b, and a third communication interface 215c. The first sensor 205a is preferably coupled to the controller 210 by the first communication interface 215a. The second sensor 205b is preferably coupled to the controller 210 by the second communication interface 215b. The third sensor 205c is preferably coupled to 5 the controller 210 by the third communication interface 215c. The communication interfaces 215 may, for example, be parallel. In a preferred embodiment, the communication interfaces 215 are serial in order to optimally provide reduced wiring complexity. The first sensor 205a preferably includes an axis of sensitivity 220. The 10 axis of sensitivity 220 is preferably approximately parallel to the x-axis. The first sensor 205a is preferably coupled to the second sensor 205b and the third sensor 205c to maintain the axis of sensitivity 220 parallel to the x-axis. The second sensor 205b preferably includes an axis of sensitivity 225. The axis of sensitivity 225 is preferably approximately parallel to the y-axis. The second 15 sensor 205b is preferably coupled to the first sensor 205a and the third sensor 205c to maintain the axis of sensitivity 225 parallel to the y-axis. The third sensor 205c preferably includes an axis of sensitivity 230. The axis of sensitivity 230 is preferably approximately parallel to the z-axis. The third sensor 205c is preferably coupled to the first sensor 205a and the second sensor 20 205b to maintain the axis of sensitivity 230 parallel to the z-axis. More generally, the axis of sensitivity 220 is in a first direction, the axis of sensitivity 225 is in a second direction, and the axis of sensitivity 230 is in a third direction and the directions need not be orthogonal to one another when the sensors 205 are coupled. 25 Referring to Fig. 2B, each of the sensors 205 preferably include a seismic sensor 235 and an application specific integrated circuit ("ASIC") 240. The design and operation of the seismic sensor 235 and the ASIC 240 are preferably substantially as disclosed in the following copending U. S. Patent Applications Serial No. , Attorney Docket No. 14737.737, filed on , 30 Serial No. , Attorney Docket No. 14737.739, filed on , and Serial No. 08/935,093, Attorney Docket No. IOS011, filed on September 25, 1997, the contents of which are incorporated herein by reference. The ASIC 240 preferably further includes a local non-volatile memory 245. The local nonvolatile memory 245 may be, for example, PROM, EPROM, EEPROM, flash memory or traditional NVM. In a preferred embodiment, the local non-volatile memory 245 is EEPROM in order to optimally providepermanent reprogrammable data storage. Referring to Fig. 2C, the controller 210 preferably includes a computer data acquisition system 250 and a computer software program 255. The controller 210 may, for example, be a mechanical fixture and a PC. In a preferred embodiment, the controller 210 is a motor driven rotation stage in order to optimally provide better repeatability and automation in the method 100. The computer data acquisition system 250 may, for example, be a voltmeter. In a preferred embodiment, the computer data acquisition system 250 is PC-based using counter A/D, D/A and digital I/O boards in order to optimally provide automation. The computer software program 255 may be, for example, C code. In a preferred embodiment the computer software program 255 is a commercial package utilizing graphical user interfaces in order to optimally provide ease of programming, debugging and usage. Referring to Fig. 3, in step 110, the sensors 205 are preferably rotated around the x-axis, the y-axis and the z-axis. The sensors 205 may, for example, be rotated at angle increments ranging from about 30 to 90 degrees. In a preferred embodiment, the sensors 205 are rotated at angle increments ranging from about 45 to 90 degrees in order to optimally provide the minimum required accuracy. In step 115, the sensors 205 preferably transmit one or more output signals 305 to the computer data acquisition system 250 of the controller 210 as the corresponding sensors 205 are rotated. In a preferred embodiment, a first output signal 305a, a second output signal 305b, and a third output signal 305c are transmitted from the first sensor 205a, the second sensor 205b, and the third sensor 205c, respectively. The computer data acquisition system 250 of the controller 210 preferably stores the output signals 305 from the corresponding sensors 205. The output signals 305 are preferably measured at each angle the corresponding sensors 205 are rotated about in step 110. Referring to Fig. 4, in step 120, the output signals 305 from the corresponding sensors 205 are preferably processed by the computer software program 255 of the controller 210. The computer software program 255 ofthe controller 210 preferably calculates one or more calibration coefficients 405 from the outputs 305 of the sensors 205. In a preferred embodiment, a first calibration coefficient 405a, a second calibration coefficient 405b, and a third calibration coefficient 405c are generated for the first sensor 205a, the second sensor 205b, and the third sensor 205c, respectively, to the controller 210. In step 125, the calibration coefficients 405 are stored. The calibration coefficients may be stored, for example, in the local non-volatile memory 245 or an external database. In a preferred embodiment, the calibration coefficients are stored in the local non-volatile memory 245 of the corresponding sensor 205 in order to optimally provide storage of data in the cahbrated unit. The first calibration coefficient 405a, the second calibration coefficient 405b, and the third calibration coefficient 405c are preferably downloaded to the first sensor 205a, the second sensor 205b, and the third sensor 205c, respectively. A method of calibrating a plurality of seismic sensors, with each sensor having an axis of sensitivity, has been described that includes coupling the sensors, with each sensor positioned with its axis of sensitivity in a different spatial direction, rotating the sensors, measuring the output signals from the sensors, processing the output signals from the sensors, and storing one or more calibration coefficients. In a preferred embodiment, the sensors comprise micro-machined accelerometers. In a preferred embodiment, coupling the sensors with each sensor positioned with its axis of sensitivity in a different spatial direction includes couphng the sensors with the axes of sensitivity in the x-direction, the y-direction, and the z-direction. In a preferred embodiment, rotating the sensors includes rotating the sensors about the x-axis, the y-axis and the z-axis. In a preferred embodiment, measuring output from the sensors includes measuring the output signals from the sensors at one or more angles of rotation. In a preferred embodiment, processing output from the sensors includes calculating one or more calibration coefficients from the measured output signals of the sensors. In a preferred embodiment, each sensor further includes a corresponding ASIC having a local non-volatile memory. In a preferred embodiment, storing one or more calibration coefficients to the sensors includes storing the corresponding calibration coefficients to the corresponding local non-volatile memories in the corresponding ASIC. In a preferred embodiment, storing one or more calibration coefficients to the sensors includes storing the corresponding calibration coefficients to an external database. In a preferred embodiment, coupling, rotating, measuring, and processing are provided in accordance with the Institute of Electrical and Electronic Engineers Specification IEEE 337-1972 for the IEEE Standard Specification Format Guide and Test Procedure for Linear, Single-Axis, Pendulous, Analog Torque Balance Acclerometer. Although illustrative embodiments of the invention have been shown and described, a wide range of modification, changes and substitution is contemplated in the foregoing disclosure. In some instances, some features of the present invention may be employed without a corresponding use of the other features. Accordingly, it is appropriate that the appended claims be construed broadly and in a manner consistent with the scope of the invention. APPENDIX A IEEE Standard Specification Format Guide and Test Procedure for Linear, Single-Axis, Pendulous, Analog Torque Balance Acclerometer IEEE Standard Specification Format Guide and Test Procedure for Linear, Single- Axis, Pendulous, Analog Torque Balance Accelerometer Sponsor Gyro and Accelerometer Panel of the IEEE Aerospace Electronics Systems Group β Copyright 1971 by The Institute of Electrical and Electronics Engineers, Inc. No part of this publication may be reproduced in any form. in an electronic retrieval system or otherwise. without the prior written permission of the publisher. IEEE Standards Committee B. B. Barrow. Chairman J. Forster, Vice Chairman S. I. Sherr, Secretary S. J. Angello J. A. Goetz R. H. Rose. II E. C. Barnes A. D. Hasley S. V. Soanes F. K. Becker G. E. Hertig L. Van Rooij W. H. Cook A. R. Hileman R. V. Wachter W. H. Devenish H. Lance B. O. Weinschel C. J. Essel D. T. Michael C. E. White R. F. Estoppey J. B. Owens W. T. Wintringham Foreword (This Foreword is not a part of IEEE Std 337-1972. Specification Format Guide and Test Procedure for Linear. Single- Axis. Pendulous. Analog Tσrαue Balance Accelerometer.) This standard was prepared by the Gyro and Accelerometer Panel of the Aerospace Electronics Systems Group of the Institute of Electrical and Electronics Engineers. It consists of two parts. Part I is a specification format guide for the preparation of an accelerometer specification. It provides a common meeting ground of terminology and practice for manufacturers and users. The user is cautioned not to overspecify; only those parameters that are required to guarantee proper instrument performance in the specific application should be controlled. In general, the specification should contain only those requirements that can be verified by test or inspection. Parameters in addition to those given in this standard are not precluded. Appendix A presents a discussion of the dynamic response of the instrument when operating in either the open or the closed loop mode. Figures 1. 2. Al and A2 are to be used as a guide for the preparation of specific figures or drawings. Part II is a compilation of recommended procedures for testing an accelerometer. These procedures, including test conditions to be considered, are derived from those currently in use. For a specific application, the test procedure should reflect the requirements of the specifications: therefore, not all tests outlined in this document need be included, nor are additional tests precluded. In some cases, alternative methods for measuring performance characteristics have been included or indicated. Blank spaces in the text of this document permit the insertion of specific parameter values and their tolerances. Brackets are used to enclose alternative choices of dimensional units, signs, axes, etc. Boxed statements are included for information only and are not part of the specification or test procedures. The symbols used conform to IEEE Std 260-1967. Letter Symbols for Units Used in Electrical Science and Electrical Engineering. In this document, the symbol g is used to denote a unit of acceleration equal in magnitude to the local value of gravity at the test site or other specified value of gravity. This symbol is thus distinguished from g, which is the letter symbol for gram. The user should note that the forcing function for most of the tests described in this document is the local gravity vector. Since the magnitude of the gravity vector varies with location, it is necessary to normalize the measured coefficients to a selected standard value of g when comparing data obtained at different test locations. The attractive force of gravity acting on the proof mass of an earth-bound accelerometer is equivalent in effect to the inertia or reaction force due to an upward acceleration of one g. The accelerometer considered in this document is a linear, single-axis, non-gyroscopic, analog torque balance, pendulous accelerometer with permanent magnet torquer. Refer to Ac celerometer System Diagram on the next page. The analog electronics of the torque balance capture loop are considered to be part of the test equipment. The accelerometer is normally used as a sensing element to provide an electrical signal proportional to acceleration. An acceleration applied along the input axis causes the proof mass to deflect. The pickoff error signal caused by this motion is utilized in the capture loop to produce a restoring torque. When static equilibrium is reached, the reaction force of the proof mass to acceleration is exactly balanced by the restoring torque. The current required by the torquer to maintain this equilibrium condition is approximately proportional to the applied acceleration, and provides the accelerometer output. The IEEE will maintain this document current with the state of the technology. Comments are invited on this document as are suggestions for additional material. These should be addressed to: Secretary IEEE Standards Committee The Institute of Electrical and Electronics Engineers. Inc. 345 East 47 Street New York, N. Y. 10017 PENDULOUS AXIS OUTPUT AXIS I ► INPUT AXIS , PENDULOUS AXIS CROSS PRODUCT OF I NPUT A XIS AND PENDULOUS AX IS = OUTPUT AX IS Accelerometer System Diagram The major contributors to this document were the following: A. T. Campbell. Chairman. 1965 C. O. Swanson. Chairman, 1968 A. M. Leeking. Chairman. 1966 H. A. Dinter, Chairman. 1969 R. B. Clark, Chairman. 1967 N. F. Sinnott. Chairman. 1970 M. D. Mobley. Chairman. 1971 W. E. Bachman H. L. Gubbins G. H. Neugebauer C. E. Bosson J. E. Hardie R. C. Peters R. M. Burrows J. G. Hawkins T. M. Rankin J. R. Cash F. J. Hellings H. F. Rickman R. A. Crawford K. W. Homb H. RogaU J. W. Davies C. E. Huriburt L. M. Ross H. B. Diamond J. V. Johnston R. C. Royce J. DiGiroiamo J. H. Jordan S. J. Sor«er K. E. Eggers K. J. Klaπnan C. B. Strang E. G. Fotou J. L. Luber M. Taylor H. A. Fredine K G. Mengersen C. I. Thornburg T. A. Fuhπnan F. B. Mikoleit R. L. Van Alstine K. N. Green G. E. Morrison B. J. Wiraber In addition, there were more than 130 others who attended meetings of the Gyro and Accelerometer Panel and helped create this standard. Contents Part I — Standard Specification Format SECTION PAGE 1. Scope . . . 9 2. Applicable Documents 9 2.1 Specifications 9 2.2 Standards 9 2.3 Drawings 9 2.4 Bulletins 9 2.5 Other Publications 9 3. Requirements 9 3.1 Description 9 3.2 General Requirements 9 3.2.1 Precedence 9 3.2.2 Definitions 9 3.3 Performance . . . , 10 3.3.1 Operating Temperature 10 3.3.2 Pickoff Characteristics 10 3.3.3 Reference Constants 10 3.3.4 Pendulum Elastic Restraint 10 3.3.5 Input Limits 10 3.3.6 Overload Capacity 10 3.3.7 Capture Electronics 10 3.3.8 Accelerometer Bias 11 3.3.9 Accelerometer Scale Factor 11 3.3.10 Nonlinearity 12 3.3.11 Torquer Polarity 12 3.3.12 Self-Test Torquer Characteristics 12 3.3.13 Input-Axis Misalignment 12 3.3.14 Cross Coupling 12 3.3.15 Frequency Response 12 3.3.16 Warmup Time 12 3.3.17 Threshold 12 3.3.18 Resolution 13 3.3.19 Turn-On Hysteresis 13 3.3.20 Life 13 3.4 Mechanical Requirements 13 3.4.1 Exterior Surfaces 13 3.4.2 Dimensions - 13 3.4.3 Accelerometer Axes 13 3.4.4 Weight 13 3.4.5 Seal 13 3.4.6 Identification of Product 13 3.5 Electrical Requirements 14 3.5.1 - Electrical Schematic 14 3.5.2 Excitation 15 3.5.3 Impedances 15 3.5.4 Insulation Resistance 16 SECTION PAGE 3.5.5 Dielectric Strength . 16 3.5.6 Electromagnetic Interference 16 3.5.7 Magnetic Flux Leakage 16 3.6 Environmental Requirements .16 3.6.1 Nonoperative Environment . 16 3.6.2 Operative Environment . .17 3.7 Reliability . . . 18 3.7.1 Reliability Program 18 3.7.2 Mean Time Between Failure . . . . . . . 18 4. Quality Assurance . . . . . 18 4.1 Classification of Tests . . . . . 18 4.2 Acceptance Tests . . . . 18 4.3 Qualification Tests 19 4.4 Reliability Tests . 20 4.5 Test Conditions and Equipment 20 4.6 Test Methods . 20 4.6.1 Nonoperative Tests .20 4.6.2 Operative Open-Loop Tests 20 4.6.3 Operative Closed-Loop Tests 20 4.6.4 Environmental Tests 20 4.7 Data Submittal 21 5. Preparation for Delivery 21 6. Notes . . . 21 6.1 Intended Use . . . . 21 6.2 Ordering Data 21 6.3 Model Equation 21 Part II — Standard Test Procedure 7. Scope . 22 8. Description . 22 9. Test Conditions and Equipment . . 22 9.1 Standard Test Conditions 22 9.1.1 Ambient Environment 22 9.1.2 Installation Requirements 22 9.1.3 Electrical Requirements 22 9.2 Test Equipment . . 23 9.2.1 General Requirements 23 9.2.2 Description of Test Equipment 23 9.3 Starting Procedure ,. 23 9.3.1 Operative Open-Loop Tests 23 9.3.2 Operative Closed-Loop Tests 23 10. Test Procedure 23 10.1 Nonoperative Tests 23 10.1.1 Examination of Product _ 23 10.1.2 Weight 23 10.1.3 Test Setup 23 10.1.4 Impedance 24 SECTION PAGE 10.1.5 Dielectric Strength . 24 10.1.6 Insulation Resistance .24 10.1.7 Seal . . .25 10.1.8 Temperature Sensor Characteristics . 25 10.1.9 Power Stress . 26 10.2 Operative Open-Loop Tests . 26 10.2.1 Test Setup 26 10.2.2 Electrical Null 27 10.2.3 Pickoff Characteristics . . . 27 10.2.4 Torquer and Self-Test Torquer Polarity 27 10.2.5 Frequency Response 28 10.3 Operative Closed-Loop Tests 28 10.3.1 Test Setup 28 10.3.2 Scale Factor and Bias 29 10.3.3 Pickoff Scale Factor and Pendulum Elastic Restraint . . . . 30 10.3.4 Input Axis Misalignment 32 10.3.5 Static Multipoint Test 32 10.3.6 Turn-On Hysteresis 33 10.3.7 Threshold and Resolution . 34 10.3.8 Warmup Time . .34 10.3.9 Self-Test Torquer Scale Factor. .35 10.3.10 Short Term Stability 35 10.3.11 Long Term Stability . 36 10.3.12 Reapeatability . . . 36 10.3.13 Sensitivity . 36 10.3.14 Centrifuge Input Range Test . 38 10.3.15 Precision Centrifuge Test. . 38 10.3.16 Life, Storage 39 10.3.17 Life, Operating . . . . . 39 10.4 Environmental Tests . . . . . 41 FIGURES Fig 1 Dimensions . 14 Fig 2 Electrical Schematic 15 Fig 3 Test Circuit for the Measurement of Pickoff Scale Factor and Pendulum Elastic Restraint . . . . 31 Fig 4 Suggested Accelerometer Environment and Test Combinations . 40 APPENDIXES Appendix A Accelerometer Dynamic Equations 42 Al Introduction . 42 A2 Open-Loop Operation 42 A3 Closed-Loop Operation . ≠ 42 Appendix B Static Multipoint Test ' . 43 Bl Introduction . 43 B2 Model Equation 43 B3 Test Procedure — Mounting Position 1 43 B4 Test Procedure — Mounting Position 2 46 B5 Best Estimate of Model Equation Coefficients 47 FIGURES Fig Al Block Diagram for Open-Loop Operation 42 Fig A2 Block Diagram for Closed-Loop Operation 43 IEEE Standard Specification Format Guide and Test Procedure for Linear, Single- Axis, Pendulous, Analog Torque Balance Accelerometer Part I — Standard Specification Format 1. Scope 2.3 Drawings 2.3.1 Government This specification defines the requirements 2.3.2 Industry/Technical for a linear, single-axis, pendulous, analog 2.3.3 Company torque balance accelerometer. The instru¬ 2.4 Bulletins ment is equipped with a permanent magnet 2.4.1 Government torquer and is used as a sensing element to provide an electrical signal proportional to 2.4.2 Industry/Technical acceleration. The torque balance electronics 2.4.3 Company are not considered to be part of the instru2.5 Other Publications ment. Other applicable documents should be 2. Applicable Documents listed in appropriate categories. The following documents of the issue in effect on date of invitation for bids or request for proposal form a part of the specification to the extent specified herein. In the event of any 3. Requirements conflict between the requirements of this doc3.1 Description. The accelerometer is a linument and the listed documents, the requireear, single-axis, non-gyroscopic, analog torque ments of this document shall govern. balance, pendulous device with permanent magnet torquer. It is normally used as a Give identification number, title, date sensing element to provide an electrical signal of issue, and revision letter of each listed proportional to acceleration. The analog elecdocument. tronics used in the torque balance capture loop are considered to be part of the test 2.1 Specifications 2.1.1 Government equipment. 2.1.2 Industry/Technical 3.2 General Requirements 2.1.3 Company 3.2.1 Precedence. In the event of conflict among the purchase agreement, this specifica¬ 2.2 Standards tion, and other documents referred to herein, 2.2.1 Government the order of precedence shall be as follows: 2.2.2 Industry/Technical ( 1) Purchase agreement 2.2.2.1 Aerospace Industries Associ¬ (2) This specification and its applicable ation, Standard Accelerometer Terminology, drawings EETC Report 30, June 1965 ' (3) Other applicable documents 2.2.2.2 IEEE Std 260-1967. Letter Symbols for Units Used in Electrical Science and Electrical Engineering List other applicable documents in or¬ 2.2.3 Company der of precedence: see Section 2. 1 Available from: National Standards Association. Ine 1321 Fourteenth Street. NW 3.2.2 Definitions. The following document Washington. DC 20005 defines terminology used in this specification: Aerospace Industries Association. Standard " 3.3.3 Reference Constants. Nominal values Accelerometer Terminology, EETC Report of these constants are listed for reference only. 30. June 1965. They are not specified as they may vary 3.3 Performance within the framework of the specification and 3.3.1 Operating Temperature. The operbecause they are difficult or impossible to ating temperature, as indicated by the temmeasure independently in a complete acpe rature sensor [ on . within ] the accelerometer. celerometer. shall be ± ° C. ( 1 ) Moment of inertia of pendulum about the output axis g - cm - (2 ) Pendulosity g - cm Section 3.3.1 is applicable only to an (3) Damping coefficient dyn • cm • s accelerometer with its own temperature (4) Damping ratio control. (5) Torquer scale factor dyn • cm/mA (6) Proof mass g 3.3.2 Pickoff Characteristics 3.3.2.1 Scale Factor. The pickoff scale 3.3.4 Pendulum Elastic Restraint. The penfactor shall be ■ = V/rad. dulum elastic restraint K τ shall be = g/rad for pendulum displacements In some cases it may be desirable to within the range of 0 ± " (seconds specify the pickoff linearity. plane angle). Pendulum elastic restraint includes all 3.3.2.2 Phase. When the angular disrestraints such as flex lead spring replacement of the proof mass about the output straint, pivot spring restraint, and pickoff axis is positive, the output voltage measured reaction torque restraint but it does not from terminal (high) to terminal include the principal restraint (rebalance (low) shall (lead, lag) the pickoff extorque supplied by the servo loop). K τ is citation by ± β . Similarly. related to K e of Appendix A by the followwhen the angular displacement of the proof ing relationship: K τ = AT e /(980 x pendumass about the output axis is negative, the losity). output voltage (high to low) shall [ lag, lead ] the pickoff excitation by ± β . The pickoff excitation shall be applied to 3.3.5 Input Limits. The input limits shall terminals (high) and (low). be ■ = g. These requirements shall be met for all output voltages greater than V. The input limits need not be sym¬ 3.3.2.3 Electrical Null. The minimum metrical about the null. electrical output shall not exceed V rms. 3.3.6 Overload Capacity. Th e ac¬ In some cases, it may be desirable to celerometer shall perform within specification specify the fundamental, its harmonics, requirements after an acceleration of g and quadrature. has been applied along the [ axis, axes ] for seconds a total of times. 3.3.'7 Capture Electronics. The capture 3.3.2.4 Maximum Output. The maxelectronics, which is a part of the test equipimum output voltage for proof-mass rotation ment, shall have characteristics as follows. in each direction shall be ± V 3.3.7.1 Input Characteristics rms. ( 1) Source impedance ± l+. -li * Ω The output limits need not be sym(2) Input frequency — Hz metrical about the null. (3) Input impedance « (4) Input voltage, maximum V [ac. 3.3.8.3 Long- Term Stability. The best fit dc ] slope of the bias determined over a period of (5) Input voltage, quadrature days of continuous operation shall be [rms, peak to peak ] less than g/day. The standard de¬ (6) Input voltage. harmonics viation of the bias data points from the best fit [rms, peak to peak] line shall be less than g. Bias measure¬ (7) Input phase angle (relative to reference ments shall be made times per day and voltage) ± β at least [ minutes, hours ] apart. 3.3.7.2 Output Characteristics The unbiased estimate of the standard (1) Load impedance ** - _ deviation may be substituted for the stan¬ . - ] J * « dard deviation. Alternate ways of speci¬ (2) Output impedance fying short-term or long-term stability or 1 - . - ]j * « both may be used, for example, peak-to- (3) Polarity positive with ( in-phase. out- peak deviation. of- phase] input (4) Voltage range - ± V to - ± V 3.3.8.4 Repeatability. The rms deviation (5) Current range -r ± mA of the bias from the mean of measureto - ±- m A ments shall be less than g. Between (6) With grounded input, the output shall successive measurements, the accelerometer be within • * • V dc and V rms shall be cooled to β C for at least maximum hours. (7) Quadrature rejection shall be greater than dB The cool-down time should be sufficient (8) Noise shall be less than mV rms to attain thermal equilibrium. Other con¬ 0 to Hz for all input conditions of ditions for repeatability may be specified, Section 3.3.7.1 such as turn-off with the accelerometer (9) Gain K A ± . V dc/ V rms maintained at operating temperature. with the above specified output load impedance ( 10) Frequency response 3.3.8.5 Sensitivity. The absolute value of the sensitivity coefficients of the bias to variations from the standard test conditions of Describe the transfer function or the Section 4.5 shall not exceed the limits listed gain and phase characteristics, or both. below: Specify tolerances compatible with the ( 1 ) Pickoff excitation voltage g/V application. (2) Pickoff excitation frequency g ϋz It also may be desirable to specify short- (3) Operating temperature g ° C circuit protection, overload protection, (4) External magnetic fields g/T and removal of load protection in this (5) Pressure g/(N/m* ) section if required. (6) Ambient temperature g/° C 3.3.9 Accelerometer Scale Factor 3.3.8 Accelerometer Bias 3.3.9.1 Scale Factor and Tolerance. The 3.3.8.1 A bsolute Value. The absolute scale factor shall be ± value of the bias Ko shall not exceed g. output units/g. 3.3.8.2 Short-Term Stability. The standard deviation of the bias from its mean value The desired form of the output should as determined over a period of [hours, be specified, for example, V or mA. days ] of continuous operation shall be less than g. Bias measurements shall be made times per day and at least 3.3.9.2 Short-Term Stability. The stan¬ [ minutes, hours ] apart. dard deviation of the scale factor from its mean value as determined over a period of and the third-order nonlinearity coefficient (hours, days] of continuous operation Ks shall be less than gig- and shall be less than output units/g. Scale g/g 3 , respectively. factor measurements shall be made 3.3.11 Torquer Polarity. With a voltage aptimes per day and at least [minutes. plied between terminal (high) and hours] apart. terminal (low), the pickoff output volt¬ 3.3.9.3 Long-Term Stability. The best fit age shall be ( in-phase, out-of-phase ] with slope of the scale factor determined over a respect to the pickoff excitation voltage. period of days of continuous operation 3.3.12 Self -Test Torquer Characteristics shall be less than (output units g) per 3.3.12.1 Self- Test Torquer Scale Factor. day. The standard deviation of the scale facThe self-test torquer scale factor shall be tor data points from the best fit line shall be ± mA/g. less than output units/g. Scale factor 3.3.12.2 Self-Test Torquer Polarity. measurements shall be made times per With a voltage applied between terminal day and at least [minutes, hours ] (high) and terminal (low), the apart. pickoff output voltage shall be [ in-phase. out- of-phase ] with respect to the pickoff ex¬ The unbiased estimate of the standard citation voltage. deviation may be substituted for the stan3.3.13 Input-Axis Misalignment. The absodard deviation. Alternate ways of specilute value of the input-axis misalignment ά p fying short-term or long term stability, or about the pendulous axis shall be less than both, may be used, for example, peak-to- [ rad. g/cross g]. peak deviation. The absolute value of the input-axis misalignment έo about the output axis shall be less than [ rad, g/cross g\. 3.3.9.4 Repeatability. The rms deviation of the scale factor from the mean of In some applications it may be desirable measurements shall be less than outto specify the input-axis misalignment put units/g. Between successive measurestability or sensitivity, or both. ments, the accelerometer shall be cooled to β C for at least hours. 3.3.14 Cross Coupling. The absolute value The cool-down time should be sufficient of the cross-coupling coefficients ip , K * 0 to attain thermal equilibrium. Other conshall be less than (g/g)/cross g. ditions for repeatability may be specified, 3.3.15 Frequency Response. The open-loop such as turn-off with the accelerometer frequency response shall conform to the folmaintained at operating temperature. lowing requirements: ( 1) The input frequency corresponding to a phase lag of 45 * shall be less than * Hz 3.3.9.5 Sensitivity. The absolute value of (2) The input frequency corresponding to a the sensitivity coefficient of the scale factor to phase lag of 135 * shall be between and variations from the standard test conditions Hz of Section 4.5 shall not exceed the limits listed below: In some cases it may be desirable to (1) Pickoff excitation voltage percent V specify the phase versus frequency char¬ (2) Pickoff excitation acteristics. frequency percent/Hz (3) Operating temperature percent * C (4) External magnetic fields percent T 3.3.16 Warmup Time. The output of the (5) Pressure percent/(N/m 2 ) accelerometer shall be within . output (6) Ambient temperature percent * C units of its steady-state value in no more than minutes after starting up from _ > C. 3.3.10 Nonlinearity. The absolute values of 3.3.17 Threshold. The threshold shall be the second-order nonlinearity coefficient K-ι less than g. 3.3.18 Resolution. The resolution shall be 3.4.5 Seal less than g- 3.3.19 Turn-On Hysteresis. The absolute In general, only one of the two methods value of the turn-on hysteresis shall be less given below would be specified. than g- ( 1) Fluid Filled. The accelerometer shall be 3.3.20 Life sealed such that no fluid leakage is detected 3.3.20.1 Operating Life. Under the operunder power magnification after being ating environment conditions specified in subjected to an external vacuum at = Section 3.6.2. the unit shall be capable of torr. and an accelerometer temoperating and performing within the requireperature of ± β C for a minments of this specification for a period of at imum period of . .minutes. least hours. 3.3.20.2 Storage Life. Under the non- In some cases, other procedures may be operating environment conditions specified in more appropriate, such as the use of fluoSection 3.6.1. the life of the instrument shall rescent tracers in the fluid to facilitate be greater than years. leak detection, or weight loss may be measured to indicate leakage. 3.4 Mechanical Requirements 3.4.1 Exterior Surfaces. All exterior sur(2) Gas Filled. The accelerometer shall be faces must withstand the environment herein sealed such that the maximum gas leakage specified and the handling expected in the shall not exceed cm ] of helium per normal course of operation, testing, and mainsecond or equivalent, measured at standard tenance without deterioration which causes conditions, during a minimum period of nonconformance to this specification. minutes that the accelerometer is being subjected to a vacuum of * Additional requirements controlling torr at a temperature of ±± * C. surface finish, protective treatment, metOr als, dissimilar metals, workmanship, etc. may be designated by the procuring orgaThe accelerometer shall be sealed such that nization. there shall be no flow of bubbles during a period of minutes when the accelerometer is placed in a bath of 3.4.2 Dimensions. The outline, mounting having a viscosity of centistokes at dimensions and location of the center of grav* C. ity shall conform to Fig 1. 3.4.3 Accelerometer Axes. The input, penTracer gases may be added to the fill gas dulous, and output reference axes and their in order to facilitate leak detection. positive directions shall be defined by external In the bubble test, care must be taken to markings and by reference mounting [surface, distinguish bubbles due to leakage from surfaces ] as indicated in Fig 1. The location of those due to absorbed gases on the outer the center of gravity of the accelerometer surface. (CG A ) and the location of the center of gravity of the proof mass (CG M ) are also given. 3.4.6 Identification of Product. The acThe positive directions of the axes shall be celerometer shall be marked on the surface such that the cross product of input axis and with the following information: pendulous axis shall be along the output axis. ( 1) Name of component 3.4.4 Weight. The weight shall be * (2) Model number [g, kg. oz. IbJ. (3) Stock number (4) Part number (5) Contract number If appropriate, maximum weight only (6) Unit serial number need be specified. When accessories such as cable or connector are to be included in (7) Manufacturer's name or symbol the weight, the specification shall so The purchase agreement may require state. other or additional identification. CG A = CENTER OF GRAVITY A OF THE ACCELEROMETER CG = CENTER OF GRAVITY OF THE PROOF MASS THE REFERENCE MOUNTING SURFACES X AND Y ARE USED FOR LOCATING THE INPUT REFERENCE AXIS Give nominal dimensions and tolerances. It is not intended that this sample drawing offer specific information, but it is to be used as a guide. The accelerometer may be cylindrical, square, etc. Fig 1 Dimensions 3.5 Electrical Requirements shall be 3.5.1 Electrical Schematic. The ac(1) Frequency. Hz celerometer electrical circuits shall be as (2) [Voltage. Current] * [V. shown in Fig 2. mA ] " 3.5.2 Excitation (3) Maximum (voltage, current ] waveform 3.5.2.1 Pickoff. The pickoff excitation distortion percent PICKOFF VARIABLE TORQUER CASE RELUCTANCE GROUNO EXCITATION SIGNAL AUXILIARY AND ALTERNATE CIRCUITS Fig 2 Electrical Schematic ( 4) Source impedance . -Ω 3.5.2.3 Temperature Sensor. The temperature sensor excitation shall be Specify wave shape if other than sinu( 1 ) Frequency * -= Hz soidal. (2) Voltage * ± V 3.5.2.4 Self-Test Torquer. The self-test torquer excitation shall be: 3.5.2.2 Heaters. The heater excitations ( 1 ) Maximum input [ voltage, current ] shall be as follows: [V. mA ] ( 1) Warmup Heater (2) Electrical noise shall not exceed Frequency . Hz mV ' Voltage ■ » (3) Source impedance ± Q Current .A maximum 3.5.3 Impedances. The impedances shall Type of control is conform to the following specifications when (2) Control Heater the unit is at the operating temperature. Frequency ±. Hz 3.5.3.1 Pickoff Voltage ± — (1) The pickoff input impedance shall be Current A maximum * [ +. - ]/ * n Type of control is at the specified excitation and output load (2) The output load impedance shall be 3.5.6 Electromagnetic Interference. The ± Ω electromagnetic interference shall be in accor¬ (3) The output impedance shall be dance with t ( -i- , - ) j ± Ω with In the United States, a common stanthe specified pickoff excitation dard is MIL-STD-461. 3.5.3.2 Heaters. The warmup heater resistance shall be ± Ω and the 3.5.7 Magnetic Flux Leakage. The magnetinductance shall be less than H. ic flux leakage shall not exceed T at a The control heater resistance shall be distance of cm from the accelerometer ± Ω and the inductance shall in any direction. be less than H. 3.6 Environmental Requirements. The envi¬ 3.5.3.3 Temperature Sensor. The temronmental conditions listed in this section are perature sensor resistance shall be ± those to which the instrument may be subΩ and the temperature coefficient jected during storage, transportation, and shall be [ + . - ] ± Ω/*C at handling or operation, or both. The equip" C. ment shall be designed to survive these envi¬ 3.5.3.4 Torquer. The torquer impedance ronments and to successfully complete the shall be ± [ + , - ] j -± environmental tests specified in Section 4. Ω when measured at a frequency of 3.6.1 Nonoperative Environment. The folHz. lowing conditions, occurring separately or in combination, may be encountered during In some cases, it may be desirable to transportation and handling, or storage, or specify the dc resistance or the impedance both. The accelerometer shall conform to all at several frequencies. the requirements of Section 3.3 after exposure to any reasonable combinations of the specified service conditions. 3.5.3.5 Self-Test Torquer. The self-test torquer resistance shall be ± Ω. Where appropriate, the environment 3.5.4 Insulation Resistance. The insulation specified must be adjusted for the protecresistance between isolated circuits and betion afforded by packaging. tween the accelerometer case and circuits isolated from the case shall not be less than 3.6.1.1 Temperature and Thermal RadiMΩ measured at * V ation. Ambient temperature may vary from a dc applied for. seconds. minimum of * C to a maximum of * C under unsheltered ground condi¬ Lower voltages may be specified for tions. Areas exposed to direct sunlight shall be certain elements, such as the pickoff inconsidered as unsheltered conditions. put to output. The time specified should 3.6.1.2 Vibration allow for time constants of RFI filters, if Describe the vibration environment. any. For sinusoidal vibration, include the specific vibration amplitude versus frequency, duration, or sweep rate and axes of 3.5.5 Dielectric Strength. The leakage curapplication. For random vibration, specirent shall not exceed mA when fy power spectral density (provide figure if ± V rms. Hz are applied complex), tolerance, bandwidth, peak acbetween isolated circuits and between the celeration level, total rms acceleration, accelerometer case and circuits isolated from duration, and axes of application. the case for *-** seconds. 3.6.1.3 Mechanical Shock Lower voltages may be specified for certain elements, such as the pickoff in- Specify the shock wave shape, duration pui to output. For some cases lower voltof the pulse, tolerances, number of shocks, ages may be specified for subsequent tests. and axes of application. 3.6.1.4 Thermal Shock. • C to 3.6.2 Operative Environment. The follow" C. The heating and cooling rates of ing conditions, occurring separately or in the ambient environment shall be approxicombination, may be encountered during opmately * C/s. eration. The accelerometer shall conform to all the requirements of Section 3.3 during, For cyclic conditions, specify temunless otherwise specified, and after exposure perature limits for each level, dwell times, to any reasonable combination of the specified and sequence. service conditions. 3.6.2.1 Thermal 3.6.1.5 Pressure. [N/m 2 . lbf/in 2 ] It may be impractical or impossible to to . [N/m -. lbf in * ]. The rate of change make meaningful measurements during of pressure shall be nominally exposure to some environmental condi¬ [ (N/m 2 )/s. (lbf/in 2 )/sJ. tions; under other environmental conditions a degraded performance may be al¬ If appropriate, pressure may be exlowed. The procuring organization should pressed in terms of altitude and rate of specify such deviations in the section climb. which specifies the environment. 3.6.1.6 Fungus 3.6.2.1.1 Temperature (High and Low). Ambient temperature may vary from " C to * C under sheltered conditions (pro¬ Specify fungus organisms, length of extected from direct sunlight). posure, and temperature and humidity 3.6.2.1.2 Thermal Shock. β C to conditions during exposure. " C. The heating and cooling rates of the ambient environment shall be approximately *C/s. 3.6.1.7 Humidity. Relative humidity from 0 to 100 percent with conditions such For cyclic conditions, specify temthat condensation may take place in the form perature limits for each level, dwell times, of water or frost. and sequence. 3.6.1.8 Salt Spray. percent salt solution for hours. 3.6.1.9 Magnetic Fields 3.6.2.1.3 Other Other thermal conditions which may Define magnitudes, directions of fields affect performance shall be specified, for with respect to each axis, and duration. If example, equivalent heat sink, radiant exposure to fields resulting from alterenergy from surrounding surfaces, power nating current is desired, specify intensity dissipation, and type of atmosphere. versus frequency. 3.6.2.2 Vibration 3.6.1.10 Sand and Dust ( g m \ Describe the vibration environment. g/ft 3 ] at a velocity of ± _ Im/s. For sinusoidal vibration, include the speft/min ] for hours. Relative humidity cific vibration amplitude versus frequennot to exceed . . percent. cy, duration or sweep rate, and axes of 3.6.1.11 Other application. For random vibration, specify power spectral density (provide figure if Include any other appropriate non- complex), tolerance, bandwidth, peak acoperative environmental conditions such celeration level, total rms acceleration, as acoustic noise, rain, air currents, etc. duration, and axes of application. 3.6.2L3 Mechanical Shock 3.7 Reliability 3.7.1 Reliability Program. The reliability program shall be in accordance with Specify the shock wave shape, duration of the pulse, tolerances, number of shocks, and axes of application. In the United States, a commonly used standard is MIL-STD-785. 3.6.2.4 Pressure. (N/m'. lbf/in 2 ] to . [N/m 1 . lbf/n 2 l. The rate of change 3.7.2 Mean Time Between Failure. The of pressure shall be nominally . MTBF shall be a minimum of hours [ (N/m -)/s. (lbf in - )/sl. with a lower confidence limit of percent. If appropriate, pressure may be expressed in terms of altitude and rate of climb. 3.6.2.5 Humidity. The operative relative 4. Quality Assurance humidity shall be percent maximum. 3.6.2.6 Acoustic Noise All tests governed by this specification shall be conducted in accordance with detailed test Describe the acoustic noise environprocedures prepared by the contractor and ment. Supply the specific noise spectrum approved by the procuring organization. in dB versus frequency, tolerance, band4.1 Classification of Tests. The inspection width, peak level, and duration. Use a and testing of the accelerometer shall be clas0-dB reference of 0.0002 dyn/cmA sified as follows. ( 1) Acceptance Tests. Acceptance tests are 3.6.2.7 Electromagnetic Interference those performed on accelerometers submitted for acceptance under contract Specify the requirements. In the United (2) Qualification Tests. Qualification tests States, compliance with MIL STD-826 are those performed on samples submitted for and MIL-E-6051 of latest issue is usually qualification as a satisfactory product considered adequate. (3) Reliability Tests. Reliability tests are those performed to demonstrate the level of 3.6.2.8 Magnetic Fields reliability and to assure the ability to maintain, with a certain confidence, the assessed Define magnitudes, directions of fields reliability with respect to each axis, and duration. If exposure to fields resulting from alternating current is desired, specify intensity versus frequency. 4.2 Acceptance Tests. Acceptance tests shall consist of individual and sample tests. 3.6.2.9 Acceleration 4.2.1 Individual Tests. Each accelerometer shall be subjected to the following tests de¬ Specify the maximum acceleration scribed under Section 4.6. Test Methods. along each of the three axes and the duration. The list of individual tests shall be specified by the procuring organization 3.6.2.10 Other based on the requirements. The number or type of individual tests specified is at Include any other appropriate operthe discretion of the procuring organizaative environmental conditions such as tion. Those tests frequently specified as fungus, salt spray, nuclear radiation, etc. individual tests are listed below. (1) Section 4.6.1.1, Examination of ProdThe procuring organization shall speciuct fy those tests which shall be performed on (2) Section 4.6.1.3, Impedance accelerometers selected in accordance (3) Section 4.6.1.4. Dielectric Strength with the sampling plan. Section 4.2.2.1. (4) Section 4.6.1.5, Insulation Resistance Those tests frequently specified for (5) Section 4.6.1.6. Seal sample tests are listed below. Sampling- (6) Section 4.6.2.1. Electrical Null plan units may be used for delivery unless (7) Section 4.6.2.2. Pickoff Characteristics the procuring organization specifies life (8) Section 4.6.2.3. Torquer and Self-Test tests or other destructive tests under the Torquer Polarity Tests sampling plan. (9) Section 4.6.2.4, Frequency Response (1) Individual tests listed in Section 4.2.1 (10) Section 4.6.3.1. Scale Factor and Bias (2) Section 4.6.1.2. Weight ( 11 ) Section 4.6.3.3, Input-Axis Mis(3) Section 4.6.1.7, Temperature Sensor alignment Characteristics (12) Section 4.6.3.5, Turn-On Hysteresis (4) Section 4.6.1.8. Power Stress ( 13) Section 4.6.3.8. Self-Test Torquer (5) Section 4.6.3.2. Pickoff Scale Factor Scale Factor and Pendulum Elastic Restraint (14) Section 4.6.3.9, Short-Term Stability (6) Section 4.6.3.4. Static Multipoint (15) Section 4.6.3.11. Repeatability (7) Section 4.6.3.6. Threshold and Resolu¬ ( 16) Section 4.6.3.13, Centrifuge Input tion Range Test (8) Section 4.6.3.7, Warmup Time ( 9) Section 4.6.3.14. Precision Centrifuge There are other individual tests which Test are not generally specified but which may ( 10) Section 4.6.4.3, Acceleration be included, and there are some listed ( 11) Section 4.6.4.4, Temperature (High, above which may be deleted depending on Low) the requirements of the specific appli4.2.3 Rejection and Retest. When a unit cation. from the production run fails to meet the specification requirements, the procuring organization shall be notified of the failure. The cause of the failure shall be determined, and 4.2.2 Sampling Plan and Tests rejection and retest shall be accomplished in 4.2.2.1 Sampling Plan. Accelerometers accordance with the following plan. [ Describe selected per ( describe sampling method ] shall rejection and retest plan. ] After corrections be subjected to the tests specified in Section have been made, the complete test under 4.2.2.2. which failure occurred and also any tests which might be affected by the corrective measures taken, shall be defined and ap¬ This paragraph is intended to designate proved by the procuring organization. The a sampling plan whereby samples are peunit shall complete the retest without further riodically selected for more complete failure before it will be considered to have tests, if required. Sampling plans are at passed the test. For operational and producthe discretion of the procuring organization reasons, individual tests may be contintion based upon usage, size of contract, ued pending the investigation of the failure. individual requirements, etc. 4.2.4 Defects in Accepted Items. The inves¬ In the United States, selection accordtigation of a test failure could indicate that ing to MIL-STD-105 is common. defects may exist in items already accepted. If so. the manufacturer shall fully advise the procuring organization of defects likely to be 4.2.2.2 Sample Tests. Accelerometers sefound and of methods for correcting them. lected in accordance with Section 4.2.2.1 shall 4.3 Qualification Tests be subjected to the following tests described 4.3.1 Qualification Test Samples. A pre- under Section 4.6. Test Methods. production sample of accelerometers manufactured in accordance with the require4.6 Test Methods ments of this specification shall be subjected to qualification tests specified herein. The Instructions for performing specified procuring organization may designate an intests in this section are detailed in Section dependent facility at which one or more of 10 of this standard. When a test is specithese tests may be performed. fied, the complete test method shall be If the product is later modified in any way, detailed in this specification, including the modified form shall be subjected to and requirements to be met after test to deterpass those qualification tests designated by mine satisfactory performance. A test the procuring organization. method should not be listed in Section 4.6 The qualification test samples shall be idenunless a requirement exists in Section 3 of tified with the manufacturer's own part numthis specification. ber and any other information required by the procuring organization. 4.3.2 Qualification Tests 4.6.1 Nonoperative Tests 4.6.1.1 Examination of Product The procuring organization shall speci4.6.1.2 Weight fy from Section 4.6. Test Methods, those 4.6.1.3 Impedance tests which shall be performed on the 4.6.1.4 Dielectric Strength qualification test samples. It is usual to 4.6.1.5 Insulation Resistance require all the individual tests as listed in 4.6.1.6 Seal Section 4.2.1, selected sample tests from 4.6.1.7 Temperature Sensor CharacterSection 4.2.2.2. sensitivity test from Secistics tion 4.6.3.12. long-term stability from 4.6.1.8 Power Stress Section 4.6.3.10. and all of the environ4.6.2 Operative Open-Loop Tests mental tests in Section 4.6.4. 4.6.2.1 Electrical Null 4.6.2.2 Pickoff Characteristics 4.4 Reliability Tests. The MTBF require4.6.2.3 Torquer and Self-Test Torquer ments of Section 3.7.2 shall be demonstrated Polarity by testing production units for 4.6.2.4 Frequency Response hours minimum each and a minimum time of 4.6.3 Operative Closed-Loop Tests hours combined. 4.6.3.1 Scale Factor and Bias Other methods of demonstration test4.6.3.2 Pickoff Scale Factor and Penduing may be selected at the discretion of the lum Elastic Restraint procuring organization. A demonstration 4.6.3.3 Input-Axis Misalignment test plan shall be prepared to define test 4.6.3.4 Static Multipoint conditions, types of tests, failures, etc. In 4.6.3.5 Turn-On Hysteresis some cases it may be desirable to combine 4.6.3.6 Threshold and Resolution the reliability tests with the life tests of 4.6.3.7 Warmup Time Sections 4.6.4.17 and 4.6.4.18. 4.6.3.8 Self-Test Torquer Scale Factor 4.6.3.9 Short-Term Stability 4.5 Test Conditions and Equipment 4.6.3.10 Long-Term Stability 4.6.3.11 Repeatability The procuring organization shall speci4.6.3.12 Sensitivity fy from Section 9 of this standard the 4.6.3.13 Centrifuge Input Range nominal test conditions and the test 4.6.3.14 Precision Centrifuge equipment required. The test equipment 4.6.4 Environmental Tests shall be listed by name and model, part 4.6.4.1 Vibration number, or performance requirements. 4.6.4.2 Mechanical Shock The conditions shall apply to all tests 4.6.4.3 Acceleration unless otherwise specified. When a test 4.6.4.4 Temperature (High, Low) condition is specified, the complete test 4.6.4.5 Thermal Shock conditions shall be detailed in this specifi¬ 4.6.4.6 Thermal Radiation cation. 4.6.4.7 Pressure (High. Low) 4.6.4.8 Acoustic Noise 4.6.4.9 Electromagnetic Interference l ιnd - -E- = K + α. + K 2 a, z + λ',α, 3 + δ , 4.6.4.10 Magnetic Fields + λ'. p βjαp — δ p α c + A' 10 α,α 0 4.6.4.11 Magnetic Flux Leakage where 4.6.4.12 Fungus A ind = acceleration indicated by the ac¬ 4.6.4.13 Humidity celerometer in g 4.6.4.14 Salt Spray E = accelerometer output in accelerometer 4.6.4.15 Sand and Dust output units 4.6.4.16 Nuclear Radiation α* = Applied acceleration component along 4.6.4.17 Life. Storage the positive input reference axis in g (see Note 4.6.4.18 Life, Operating below) 4.7 Data Submittal <ip - applied acceleration component along the positive pendulous reference axis, in g (see The format for all data organization Note below) and the method of submittal shall be α o = applied acceleration component along specified. the positive output reference axis, in g (see Note below) 5. Preparation for Delivery Kt> = bias, in g K \ = scale factor, in output units per g Give detailed procedures for (1) preserKi = second-order nonlinearity coefficient, vation and packaging. (2) packing, and (3) in gig 2 marking of shipping containers. A comKi = third-order nonlinearity coefficient, in mon United States specification covering gig 3 preservation and packaging is MIL- ■5o . -5 p = misalignment of the input axis P-116. Other organizations use different with respect to the input reference axis about " supporting documents. the output and pendulous axes, respectively, in radians 6. Notes R ip • -^ io = cross-coupling coefficients, in 6.1 Intended Use (g/g)/cross g. that is, gig z NOTE: Applied acceleration refers only to non- Describe application if it is considered eravitational acceleration since an accelerometer cannot necessary or helpful. sense the acceleration of free fall. The attractive force of Eravity acting on the proof mass of an earthbound accelerometer is equivalent in effect to the inertia or reac¬ 6.2 Ordering Data tion force due to an upward acceleration of 1 £ Procuring documents should specify The coefficients of the model equation the title, number, and date of this specifimay be functions of other variables such cation. In addition, the following, or other as voltage, temperature, time, angular veitems, should be specified as applicable: locity, etc. ( 1) Level of packaging and packing deSome of the above terms may be deleted sired or others added as appropriate for the (2) Mode of shipment required type of accelerometer and its applications. (3) Sampling-plan tests if any Only a sufficient number of terms should (4) Number of preproduction samples be used that will adequately describe the to be submitted for qualification testing response of the accelerometer. (5) Data package In those cases where the forcing function is the local gravity vector, it should 6.3 Model Equation be noted that the magnitude of gravity The model equation of the accelerometer is varies with location, including effect of defined as a series which mathematically realtitude, and it is necessary to normalize lates the accelerometer output to the comthe measured coefficients to a standard ponents of acceleration applied parallel and value of gravity when comparing data normal to the accelerometer's input reference obtained at different test locations. axis. Part II — Standard Test Procedure 7. Scope List types of radiation and applicable intensity limits. This test procedure describes the test requirements for . (model number, part number, change letter (if any), other identi9.1.1.4 Vibration. Total acceleration fication ], manufactured by (name, g rms over the frequency range of address ]. to Hz. Above limits normally apply to each of 8. Description the three axes of the accelerometer coordinate system. The accelerometer considered in this document is a linear, single-axis, non-gyroscopic, analog torque balance, pendulous device with 9.1.2 Installation Requirements permanent magnet torquer. It is normally used as a sensing element to provide an electrical signal proportional to acceleration. The The mounting [fixture, fixtures ] should analog electronics used in the torque balance be designed to reasonably simulate the capture loop are considered to be part of the application conditions and should be carefully specified. test equipment. 9. Test Conditions and 9.1.2.1 Operating Temperature. The opEquipment erating temperature, as indicated by the temperature sensor [on. withinl the accel¬ 9.1 Standard Test Conditions erometer. shall be ± * C. 9.1.1 Ambient Environment. The conditions listed below define the requirements for In some applications, careful considthe environment in the immediate vicinity of eration should be given to the magnitude the instrument. They are not intended as of thermal gradients existing across the environmental tests, which are described in accelerometer. Section 10.4. 9.1.1.1 A tmospheric Conditions ( 1 ) Pressure ± ( N/m 2 . 9.1.2.2 Mechanical Conditions. The test lbf/in 2 ] unit should be mounted in such a way that the (2) Ambient temperature ± ? C alignment of its three reference axes with (3) Relative humidity to respect to the axes of the test fixture is mainpercent tained within " under all specified test 9.1.1.2 Magnetic Field conditions. The three reference axes of the (1) Horizontal component T. maxtest unit are those defined by external case imum markings and mounting [surface, surfaces) as (2) Vertical component T, maxindicated in Fig 1. imum ,9.1.3 Electrical Requirements 9.1.3.1 Electrical Circuits. The ac¬ In some applications, careful considcelerometer electrical circuits shall be as eration should be given to the magnitude shown in Fig 2. of ac magnetic fields. 9.1.3.2 Pickoff Excitation. Frequency ± Hz. (Voltage, Current] 9.1.1.3 Radiation. All tests are to be per* [V, mA ]. Maximum ( voltformed under radiation conditions as listed age, current } waveform distortion perbelow. cent. Source impedance ± Ω. Specify wave shape if other than sinu9.2.2 Description of Test Equipment soidal. All special-purpose and commercial test 9.1.3.3 Self-Test Torquer. Maximum inequipment shall be listed by name, model, put [voltage, current ] * (V, part number, or performance requiremA ]. Electrical noise shall not exceed ment. mV. Source impedance = Ω. 9.1.3.4 Warmup Heater. Frequency 9.3 Starting Procedure ± Hz. Voltage ± 9.3.1 Operative Open-Loop Tests _ V. Current. . A maximum. Type 9.3.2 Operative Closed-Loop Tests of control is. . 1.3.5 Con trol Heater. Frequency _ = Hz. Voltage = State sequence of operations in Sec¬ . V. Current. tions 9.3.1 and 9.3.2 required to bring A maximum. Type of control is . accelerometer and test equipment to operating conditions. With a proportional temperature control, consideration should be given to its 10. Test Procedure gain (W / β C). The hysteresis associated with thermostatic-type controls should be 10.1 Nonoperative Tests. These procedures specified. are intended to assure the conformance of the accelerometer to the mechanical and electrical requirements. 9.1.3.6 Temperature Sensor. Frequency 10.1.1 Examination of Product. The ac± Hz. Voltage -s celerometer shall be examined visually for V. proper identification, surface finish, defects in 9.1.3.7 Interconnections workmanship, and dimensional conformance ( 1 ) Opera tive Open -Loop Tests. Interto the outline drawing connections, test points, and grounding shall 10.1.2 Weight. Measure the weight of the be as specified on schematic diagram accelerometer. The weight shall be at ( 2) Operative Closed-Loop Tests. Inter(g. kg. oz. lb ]. connections, test points, and grounding shall be as specified on schematic diagram . When accessories such as cable or connector are to be included in the weight, Voltage gradients between the acthey should be specified. celerometer case and internal circuitry may produce extraneous torques on the proof mass and should be given careful 10.1.3 Test Setup consideration. ( 1) Unless otherwise specified, all non- operative tests shall be performed in a normal laboratory environment as described in Sec¬ 9.2 Test Equipment tion 9.1.1 9.2.1 General Requirements ( 2) The accelerometer shall be mounted on a simple mounting fixture that will minimize the chances for accidental mechanical dam¬ The selection of test equipment should age be based on accuracy requirements compatible with the performance specifica(3) The electrical leads, if required, shall be tions. Similarly, the bandpass of the meabrought out to a junction box or equivalent suring devices should be chosen so as to device that will minimize the chance of acciprovide information within the frequency dental electrical damage due to shorting spectrum of interest for the tests. across leads, etc. Terminal designations are shown in Fig 2 Care must be taken in the choice of the (5) The resistance of the temperature senjunction box and the size and length of sor shall be ± Ω at • C leads in order to avoid affecting the char- (6) The impedance of the torquer shall be acteristics of the accelerometer circuits. . [ + . - ]; Ω 10.1.4 Impedance (7) The resistance of the self-test torquer 10.1.4.1 Purpose. The purpose of this shall be ± Ω test is to measure the impedance of the accelerometer's electrical circuits. In some cases it may be desirable to 10.1.4.2 Test Equipment. The following conduct the impedance test at operating test equipment specified in Section 9.2 is temperature. required for this test: Impedance measuring equipment 10.1.5 Dielectric Strength Resistance measuring equipment 10.1.5.1 Purpose. The purpose of this 10.1.4.3 Test Setup. The test setup shall test is to ascertain that the accelerometer be in accordance with Section 10.1.3. circuits can operate safely at their rated volt¬ 10.1.4.4 Test Procedure. Measure the age and withstand overvoltage due to switchimpedances of each circuit listed below. ing, surges, etc. by monitoring the leakage (1) Pickoff current between isolated circuits and between Input impedance of the pickoff between the accelerometer case and circuits isolated terminals and at ± from the accelerometer case. Hz 10.1.5.2 Test Equipment. The following Output impedance of the pickoff between test equipment specified in Section 9.2 is terminals and at * required for this test: Hz Adjustable ac high-voltage source equipped (2) Heaters with voltage- and current-measuring capabili¬ Impedance of the warmup heater between ties. terminals and at ± 10.1.5.3 Test Setup. The test setup shall Hz be in accordance with Section 10.1.3. Impedance of the control heater between 10.1.5.4 Test Procedure. Apply terminals and at * = V rms at Hz between muHz tually isolated circuits and between each cir-. (3) Temperature Sensor. Resistance of the cuit and the accelerometer case. The test temperature sensor between terminals voltage shall be raised from zero to the speciand fied value as uniformly as possible, at a rate of (4) Torquer. Impedance of the torquer beV rms per second. The test voltage tween terminals and at shall then be gradually reduced to zero. Dur± Hz ing each test the current meter shall be mon¬ (5) Self-Test Torquer. Resistance of the itored for leakage current and the result self-test torquer between terminals recorded. and 10.1.5.5 Test Results. The leakage cur¬ 10.1.4.5 Test Results rent shall not exceed mA. (1) The input impedance of the pickoff 10.1.6 Insulation Resistance shall be ± ( + , - ] j * 10.1.6.1 Purpose. The purpose of this Ω test is ' to measure the insulation resistance (2) The output impedance of the pickoff between isolated circuits and between the shall be ± ( +. - ] j ± accelerometer case and circuits isolated from the case. (3) The resistance of the warmup heater 10.1.6.2 Test Equipment. The following shall be ± Ω and the intest equipment specified in Section 9.2 is ductance shall be less than H required for this test: (4) The resistance of the control heater Megohmmeter shall be ± Ω and the in10.1.6.3 Test Setup. The test setup shall ductance shall be less than H be in accordance with Section 10.1.3. 10.1.6.4 Test Procedure. Apply perature for a period of . minutes. The V dc for a period of — presence or absence of a flow of bubbles after seconds between mutually isolated minutes shall be noted. Care must be circuits and between each circuit and the taken to distinguish bubbles due to leakage accelerometer case. Record the minimum refrom those due to absorbed gases on the outer sistance readings. surface. 10.1.7.5 Test Results 10.1.6.5 Test Results. The minimum in¬ (1) Fluid- Filled Accelerometer. There shall sulation resistance shall not be less than M Ω. be no evidence of leakage. (2) Gas-Filled Accelerometer. The mea¬ 10.1.7 Seal sured leak rate shall not exceed cm 3 helium per second or equivalent at standard This procedure is written to accommoconditions. date either fluid- or gas-filled instruOr ments. The appropriate subsections, below, should be chosen. There shall be no flow of bubbles after minutes. 10.1.7.1 Purpose. The purpose of this test is to determine that the accelerometer is In some cases other procedures may be properly sealed. more appropriate, such as the use of fluo¬ 10.1.7.2 Test Equipment. The following rescent tracers in fluids or the measuretest equipment specified in Section 9.2 is ment of weight loss. required for this test: ( 1 ) Fluid- Filled A ccelerometer Binocular microscope 10.1.8 Temperature Sensor Characteristics Vacuum enclosure 10.1.8.1 Purpose. The purpose of this (2) Gas-Filled Accelerometer test is to determine the accelerometer tem¬ Leak detector or immersion fluid (speciperature sensor resistance and temperature fy ) coefficient at operating temperature. Vacuum enclosure 10.1.8.2 Test Equipmen t. The following 10.1.7.3 Test Setup. The test setup shall test equipment specified in Section 9.2 is be in accordance with Section 10.1.3. (2). required for this test: 10.1.7.4 Test Procedure Temperature-controlled oven (1) Fluid-Filled Accelerometer. After thorResistance measuring equipment ough cleaning of all surfaces, the accel10.1.8.3 Test Setup. The accelerometer erometer shall be placed in a vacuum enshall be placed in a temperature-controlled closure at * *- * torr and at an oven. All accelerometer circuits shall be de- accelerometer temperature of =- *■ energized. β C for a minimum period of minutes. 10.1.8.4 Test Procedure The accelerometer shall then be removed and (1) Resistance at Operating Temperature. visually examined for evidence of leakage at a Stabilize the accelerometer temperature at magnification of * * C (normal operating tem¬ (2) Gas-Filled Accelerometer. The acperature). Measure the resistance of the temcelerometer shall be placed in a vacuum enperature sensor using the resistance measurclosure at ± torr and **-* ing equipment. The power applied to the * C accelerometer temperature. Extemperature sensor shall be ± W. ternal gas leakage shall then be measured (2) Temperature Coefficient. Repeat Step using a leak detector. (1) for the following accelerometer temperatures: and =fc * C Or The accelerometer shall ' be submerged in fluid Select temperatures above and below and placed in a vacuum enclosure at ± the operating temperature. torr and ± * C tem 10.1.8.5 Test Results. The resistance of the precision resistor and the pickoff primary. the sensor at the nominal operating temRecord the voltage across the pickoff primary perature shall be ± Ω. From and across the precision resistor after the off-nominal temperature data compute seconds. Remove the applied voltage. the change in resistance per unit temperature. (5) Apply ± V dc across the The result shall be ± Ω/ β C. series combination of the precision resistor and the torquer. Record the voltage across the If the accelerometer utilizes a thermo- torquer and across the precision resistor after seconds. Remove the applied voltage. static temperature control instead of a resistive sensor, the temperature at which 10.1.9.5 Test Results. The voltage readings shall be as follows. the device opens on a rising temperature ( 1) Warmup Heater Winding and closes on a falling temperature should be measured. The rate of temperature Voltage across warmup heater V change should also be specified. Voltage across resistor V (2) Control Heater Voltage across control heater 10.1.9 Power Stress V 10.1.9.1 Purpose. The purpose of this Voltage across resistor * V test is to assure circuit integrity under condi(3) Pickoff tions of maximum power dissipation. Voltage across pickoff . ÷ V 10.1.9.2 Test Equipment Required. The Voltage across resistor . V following test equipment specified in Section (4) Torquer 9.2 is required for these tests: Voltage across torquer V Accelerometer mounting fixture Voltage across resistor . V Pickoff power supply Temperature control amplifier Rms voltmeter Care must be taken in the selection of Ac voltage supply voltage levels, exposure time periods, and Precision resistor mounting provisions. Dc voltmeter Dc voltage supply 10.1.9.3 Test Setup. The test setup shall 10.2 Operative Open-Loop Tests. These tests be in accordance with Section 10.1.3. are intended to determine the pertinent open- 10.1.9.4 Test Procedure loop characteristics prior to operating the ( 1) Apply ± V at Hz instrument in the closed-loop mode. across the series combination of the precision 10.2.1 Test Setup resistor and the warmup heater. Record the ( 1 ) Unless otherwise specified, the acvoltage across the precision resistor and across celerometer shall be operated under the stanthe warmup heater winding after secdard test conditions of Section 9.1 for operonds. Remove the applied voltage. ative open-loop tests (2) Apply ± V at Hz (2) With the rotation axis of the dividing across the series combination of the precision head horizontal within ' (minutes •— resistor and across the control heater. Record plane angle), attach the mounting fixture to the voltage across the precision resistor and the face plate of the dividing head so that the across the control heater winding after accelerometer when mounted will satisfy the seconds. Remove the applied voltage. requirements of (3) (3) Activate the temperature control loop (3) With the dividing head set at 0* ± and allow the instrument to reach operating ('. '], mount the accelerometer on the temperature before proceeding with the folreference mounting [surface, surfaces] so that lowing tests. the input reference axis is horizontal within (4) Connect a δ resistor across the [', '], the positive pendulous axis pickoff secondary. Apply ± V points downward, the output reference axis is at Hz across the series combination of parallel to the rotation axis of the head with- in ('. "1. and the positive input refer10.2.3.4 Test Procedure ence axis points upward when the head is (1) Rotate the dividing head in the positive rotated to the 90° position direction (increasing angle) from the 0* posi¬ (4) The accelerometer and test equipment tion until a pickoff output of * shall be brought to operating condition in V rms is attained. Measure and record the accordance with the procedure of Section phase angle of the output voltage with respect 9.3.1. to the pickoff excitation (5) The accelerometer and the immediate (2) Continue rotating the dividing head in environment (including the dividing head) the positive direction until the maximum outshall be allowed to reach thermal equilibrium put voltage is reached. Measure and record before proceeding with the test the rms output voltage 10.2.2 Electrical Null (3) Return the dividing head to the 0* posi¬ 10.2.2.1 Purpose. The purpose of this tion and repeat the above procedure for the test is to determine the minimum output negative direction of rotation voltage of the pickoff. 10.2.3.5 Test Results 10.2.2.2 Test Equipment Required. The ( 1) For the positive direction of rotation, following test equipment specified in Section the pickoff output voltage shall [lead, lag] the 9.2 is required for these tests: pickoff excitation by * -= * Dividing head and mounting fixture (2) For the negative direction of rotation, Pickoff power supply the pickoff output voltage shall [lag. lead ] the Temperature control amplifier pickoff excitation by ± * Ac rms voltmeter (3) The maximum rms output voltage in Oscilloscope each case shall be greater than V. 10.2.2.3 Test Setup. The test setup shall 10.2.4 Torquer and Self -Test Torquer Pobe in accordance with Section 10.2.1. larity 10.2.2.4 Test Procedure. Rotate the di10.2.4.1 Purpose. The purpose of these viding head until the minimum rms output tests is to determine the relationship between voltage is obtained. Measure and record the specified currents applied to the torquer and voltage. self-test torquer coils and the resulting pendu¬ 10.2.2.5 Test Results. The minimum lum motion as evidenced by the pickoff outoutput shall be less than V rms. put. 10.2.4.2 Test Equipment Required. The In some cases it may be desirable to following test equipment specified in Section measure the fundamental, its harmonics, 9.2 is required for these tests: and quadrature. Dividing head and mounting fixture Pickoff power supply Temperature control amplifier 10.2.3 Pickoff Characteristics Dc voltmeter 10.2.3.1 Purpose. The purpose of this Phase angle voltmeter test is to determine the phase relationships Oscilloscope among the pickoff excitation, input acceleraDc current supply tion, and output voltage, and also the max10.2.4.3 Test Setup. The test setup shall imum pickoff voltage. be in accordance with Section 10.2.1. 10.2.3.2 Test Equipment Required. The 10.2.4.4 Test Procedure following test equipment specified in Section (1) Connect the dc current supply to the 9.2 is required for these tests: torquer such that terminal is positive Dividing head and mounting fixture with respect to terminal for positive Pickoff power supply torquing. Increase the current to ± Temperature control amplifier A Rms voltmeter Phase angle voltmeter Specify a test current which will not Oscilloscope damage the accelerometer but is sufficient 10.2.3.3 Test Setup. The test setup shall to drive the pendulum against the stop. be in accordance with Section 10.2.1. (2) Measure and record the phase of the resistor and the torquer. Measure and record pickoff output voltage relative to the pickoff the voltage across the resistor, the demod ¬ excitation ulator output, and the phase angle between (3) Repeat Step (2) with the torquer current these two voltages reversed (2) Repeat the above step for the following (4) Connect the dc supply to the self-test frequencies: Hz. Hz • • • torquer so that terminal is positive Hz with respect to terminal Increase the 10.2.5.5 Test Results. Calculate the ratio current to ± A in dB of the demodulator output voltage to (5) Measure and record the phase of the the input voltage measured across the resistor. pickoff output voltage relative to the pickoff Plot the phase and gain versus frequency on a excitation semilog chart. Determine Λ and fi, the fre¬ (6) Repeat Step (5) with the self-test torquencies corresponding to phase shifts of 45 ° quer current reversed and 135 *, respectively. 10.2.4.5 Test Results The value of Λ shall be less than (1) From Section 10.2.4.4(2) the pickoff outHz. put voltage shall (lead, lag] the pickoff exThe value of ft shall be between and citation voltage by * -= * Hz. (2) From Section 10.2.4.4(3) the pickoff output voltage shall [lag, lead ] the pickoff exThe frequency characteristics of the citation voltage by * * amplifier/demodulator must be consid¬ (3) From Section 10.2.4.4 (5) the pickoff outered (and if necessary compensated for) put voltage shall [lead, lag ] the pickoff exwhen performing this test. citation Note that generally the undamped nat¬ (4) From Section 10.2.4.4(6) the pickoff outural frequency is put voltage shall (lag, lead ] the pickoff excitation /- = τ r 2 10.2.5 Frequency Response 10.3 Operative Closed-Loop Tests. These 10.2.5.1 Purpose. The purpose of this tests are intended to determine the closed- test is to determine the accelerometer open- loop performance characteristics. loop frequency response. 10.2.5.2 Test Equipment Required. The following test equipment specified in Section In the tests which follow, the ac9.2 is required for these tests: celerometer output measurement test equipmen t and techniq ue may sig¬ Dividing head and mounting fixture nificantly influence the test results and Pickoff power supply therefore should be carefully specified. Temperature control amplifier Rms voltmeter Phase angle voltmeter 10.3.1 Test Setup Oscilloscope 10.3.1.1 Mounting Position I Signal generator Amplifier/demodulator ( 1) Unless otherwise specified, the accelerometer shall be operated under the stanPrecision current-sensing resistor dard test conditions of Section 9.1 for oper¬ 10.2.5.3 Test Setup. The test setup shall ative closed-loop tests be in accordance with Section 10.2.1 except (2) With the rotation axis of the dividing that the amplifier/demodulator shall be conhead horizontal within ". attach the nected to the pickoff output. mounting fixture to the face plate of the 10.2.5.4 Test Procedure dividing head so that the accelerometer when (1) Rotate the dividing head until the demounted will satisfy the requirements of (3) modulator output is nulled within V. (3) With the dividing head set at 0* ± Apply a sinusoidal signal of ± ". mount the accelerometer on the V and ± Hz across a series reference mounting [surface, surfaces ] so the combination of the precision current-sensing input reference axis is horizontal within _____", the positive pendulous reference axis 10.3.2.2 Test Equipment. The following points upward, the output reference axis is equipment specified in Section 9.2 is required parallel to the rotation axis of the head within for this test: '.. and the positive input reference axis Dividing head and mounting fixture points upward when the head is rotated to the Electronic equipment required to operate 90 β position the accelerometer and to measure its output (4) The accelerometer and test equipment 10.3.2.3 Test Setup. The test setup shall shall be brought to operating condition in be in accordance with Section 10.3.1.1. accordance with the procedure of Section 10.3.2.4 Test Procedure 9.3.2 ( 1) Rotate the dividing head to the 90* (5) With the dividing head set at 90* . the position (input reference axis up) within accelerometer and the immediate environ'. Record the accelerometer output as ment (including the dividing head) shall be E allowed to reach thermal equilibrium as evi(2) Rotate the dividing head to the 270* denced by the stability of the accelerometer position (input reference axis down) within output being within output units for '.. Record the accelerometer output as measurements spaced minutes £.»o apart before proceeding with the test (3) Calculate Kx and Ko using the following 10.3.1.2 Mounting Position 2 algebraic equations: ( 1 ) Unless otherwise specified, the accelerometer shall be operated under the stan90 ~ " *^270 Λ] = 5 output units/g (Eq 1) dard test conditions of Section 9.1 for operative closed-loop tests E 90 + E 2 to (2) With the rotation axis of the dividing (Eq 2) head horizontal within * , attach the mounting fixture to the face plate so that the accelerometer when mounted will satisfy the The apparent bias and scale factor obrequirements of (3) tained by the above method include the (3) With the dividing head set at 0* ± effects of the second-order term K2 and * . mount the accelerometer on the the third-order term Kz. respectively. See reference mounting [surface, surfaces ] so that Appendix B. the input reference axis is horizontal within An alternate method of measuring bias ". the positive output reference axis is to obtain accelerometer outputs at the points downward, the pendulous reference other two cardinal positions. This value axis is parallel to the rotation axis of the head represents the bias with (nominally) no within ', and the positive input referacceleration applied along the input axis, ence axis points upward when the head is and is rotated to the 90" position (4) The accelerometer and test equipment E 0 + £, 80 shall be brought to operating condition in K a 2* ! accordance with the procedure of Section 9.3.2 where £0 and £ιβo are the accelerometer (5) With the dividing head set at 90* . the outputs measured in the two horizontal accelerometer and the immediate environpositions. The two positions must be 180° ment (including the dividing head) shall be - apart within 1 * for each 2.5 μg allowable allowed to reach thermal equilibrium as eviuncertainty in the bias measurement. denced by the stability of the accelerometer output being within output units for measurements spaced minutes apart before proceeding with the test 10.3.2.5 Test Results. The apparent 10.3.2 Scale Factor and Bias scale factor and apparent bias shall conform 10.3.2.1 Purpose. The purpose of this to the following requirements: test is to determine the apparent bias Ko and « ± output units g the apparent scale factor K \ | oj≤ g 10.3.3 Pickoff Scale Factor and Pendulum (3) Decrease the output of the dc supply to Elastic Restraint zero. Reverse its polarity and increase its 10.3.3.1 Purpose. The purpose of these output to the same voltage to offset the pendutests is to determine the pickoff voltage lum in the negative direction - θ . Measure change and the pendulum elastic restraint and record the accelerometer output as £b change as functions of pendulum angular disand measure the pickoff in-phase output as placement. V b (4) Rotate the dividing head 180 * ± * . Turn on the dc voltage supply and increase Pickoff Scale Factor. The pickoff scale its output to the same voltage as in Step (1). factor is the output voltage change as a Measure and record the accelerometer output function of pendulum displacement. reading as E e and measure the pickoff output Pendulum Elastic Restraint. This inin-phase voltage as V c cludes all restraints such as flex lead (5) Utilizing the procedure described in spring restraints, pivot spring restraints, Step (3), reverse the output of the dc supply and pickoff reaction torque restraints, but and measure and record the accelerometer it does not include the principal restraint output as E and measure the pickoff in- (rebalance torque supplied by the servo phase output as Vd loop). 10.3.3.5 Test Results (1) Calculate the input axis deviation 7 about the output axis for each of the two 10.3.3.2 Test Equipment Required. The modes of operation using the following equafollowing test equipment specified in Section tions: 9.2 is required for these tests: Dividing head and mounting fixture _ E - E 1 Electronic equipment required to operate rad 7 * β 2K t the accelerometer and to measure its output Phase angle voltmeter £» - £- Dc voltmeter 7- β rad 2K, Variable dc power supply 10.3.3.3 Test Setup. The test setup shall be in accordance with Section 10.3.1.1. except where Kι is the nominal accelerometer scale that the electrical connections shall be modifactor in output units g fied to conform to Fig 3. (2) Compute the pendulum elastic restraint 10.3.3.4 Test Procedure K t and the pickoff scale factor K^ using the (1) Reduce the capture electronics gain to following equations: ± V dc/V rms. Position the dividing head at 0* (input axis nominally κ f(E. + £„ ) - (£„ + £. )! ϊ horizontal). Turn on the dc voltage supply and increase its output to ± V which will displace the pendulum a suitable amount about the positive output axis direcV/rad tion + θ T* β 7- e (2) Measure and record the accelerometer output as E Λ and the pickoff output in-phase (3) The values calculated in (2). shall meet voltage as V a the following requirements: K τ - ± g/rad K po - * V /rad The amplifier must be operating in its nonsaturated region. Sets of points may An alternate method of conducting this be taken at varying displacements to detest is to -sum an ac voltage with the termine pickoff and elastic restraint linpickoff output voltage to effectively shift earity. the pickoff null position. Fig 3 Test Circuit for Measurement of Pickoff Scale Factor and Pendulum Elastic Restraint 10.3.4 Input-Axis Misalignment 10.3.4.1 Purpose. The purpose of this The misalignment angles as obtained test is to determine the misalignment of the above include angular errors of the input axis with respect to the input reference mounting fixture, dividing head errors, axis (IRA). The IRA is defined by external and errors in mounting as well as the marks or mounting [surface, surfaces] or both, misalignment between the input referon the accelerometer case. ence axis and the input axis. There is no 10.3.4.2 Test Equipment. The following way of distinguishing between a mistest equipment specified in Section 9.2 is alignment and a cross axis sensitivity. An required for this test: alternate method is to align the IRA Dividing head and mounting fixture parallel to the horizontal dividing head Electronic equipment required to operate rotation axis, and to obtain measures of the accelerometer and to measure its output indicated acceleration at each of the four 10.3.4.3 Test Setup — Moun ting Posicardinal case positions. tion 1. The test setup shall be in accordance with Section 10.3.1.1. 10.3.4.7 Test Results. The values of -J o 10.3.4.4 Test Procedure — Mounting Poand ό p shall meet the following requirements: sition 1 (1) With the dividing head set at 0" , record the accelerometer output as Eo (2) Rotate the dividing head 180* ± An alternative method is to specify the and record the accelerometer output as E iw (3) Calculate the misalignment angle δo total misalignment angle: using the following equation: δ , δ 0 2 + δ 10.3.5 Static Multipoint £Q ~ *El80 , 10.3.5.1 Purpose. The purpose of the static multipoint test is to determine the coefficients of the assumed model equation by where & o is the misalignment angle of the a series of measurements in a 1-g field. input axis with respect to the input reference axis about the output reference axis, in radi¬ See Appendix B for a discussion on the ans and is the nominal scale factor, in static multipoint test and the data reducoutput units/g tion procedure. 10.3.4.5 Test Setup — Moun ting Position 2. The test setup shall be in accordance with Section 10.3.1.2. 10.3.4.6 Test Procedure -— Mounting Po10.3.5.2 Test Equipment. The following sition 2 test equipment specified in Section 9.2 is (1) With the dividing head set at 0* , record required for this test: the accelerometer output as E o Dividing head and mounting fixture (2) Rotate the dividing head 180* ± !. Electronic equipment required to operate and record the accelerometer output as E ■ * • the accelerometer and to measure its output (3) Calculate the misalignment angle <5 P 10.3.5.3 Test Setup — Mounting Posiusing the following equation: tion I. The test setup shall be in accordance with Section 10.3.1.1. 10.3.5.4 Test Procedure — Mounting Po¬ ■ El 80 ~ EQ sition I. At each head angle θ = 0* . θ n , 2 β n . δ p = rad 2K • ■ • . k β n t • • • , (π-1) θ„ . take and record measurements of the accelerometer where -5 P is the misalignment angle of the output E kp . where θ „ - 360/π. n and k are input axis with respect to the input reference integers, n - , and 0 ≤ k ≤ n-1. The axis about the pendulous reference axis, in dividing head angles shall be set within radians n is the number of test positions and its (3) The standard deviation of the residuals choice is usually based on statistical conshall not exceed g siderations. Depending upon the desired test accuracy and the output characteristics of 10.3.6 Turn-On Hysteresis the particular accelerometer. the follow10.3.6.1 Purpose. The purpose of this ing items should be specified: test is to determine the displacement hys¬ (1) Sequence of dividing head positions teresis associated with moving the pendulum (2) Instrument settling time allowed at from either stop to the operating null position each position as a result of power turn-on. (3) Number of individual measurements at each position The test will be conducted using reduc¬ (4) Averaging interval associated with tions in loop gain in lieu of power turn-on . each measurement to preclude any dithering effects from a (5) Dividing head accuracy sudden loop closure. (6) Pier stability 10.3.5.5 Test Setup — Mounting Posi10.3.6.2 Test Equipment. The following tion 2. The test setup shall be in accordance test equipment specified in Section 9.2 is with Section 10.3.1.2. required for this test: 10.3.5.6 Test Procedure — Mounting PoDividing head and mounting fixture sition 2. At head angles θ = 0 * . θ n . 2Θ„ , ■ ■ ■ , Electronic equipment required to operate kθ n . • - *. , (n- 1) θ n . take and record the accelerometer and to measure its output measurements of the accelerometer output 10.3.6.3 Test Setup. The test setup shall E ko . where θ n = 360/n. /J and k are integers, n be in accordance with Section 10.3.1.1. except = , and O ≤ k≤ n-1. The dividing head that the torquing loop shall be open. angles shall be set within ". 10.3.6.4 Test Procedure 10.3.5.7 Test Results (1) Rotate the dividing head to the 0° posi¬ ( 1 ) From the above test data taken in the tion and close the loop two mounting positions, compute the best (2) Rotate the dividing head to the 90* estimate of each of the model equation position coefficients, the uncertainties of the coeffi(3) Measure the accelerometer output Et cients, and the unbiased estimate of the stan(4) Reduce the servo loop gain smoothly, dard deviation of the residuals allowing the pendulum to move to the stop ( 5) Smoothly reestablish the normal servo Specify the data reduction procedure or loop gain and measure the accelerometer outthe data reduction program to be used. put E( See Appendix B for suggested data reduc(6) Repeat Steps (2) through (5), except tion procedures. that the dividing head shall be rotated from the 0* position to the 270* position (pendulum falls to the other stop) (2) The best estimate of the model equation (7) Repeat Steps of (2) through (6) coefficients and their uncertainties shall contimes form to the following requirements: Estimated Maximum The angle of the accelerometer with Coefficient Value Uncertainty Units respect to the gravity vector may be varied to provide less than 1 g along the input axis if desired. /g 10.3.6.5 Test Results (1) Calculate the turn-on hysteresis for each set of data. Use the accelerometer's nom inal scale factor for Kι E. - E, eration levels of * 0.5 g and ± 1.0 g instead of 0 tf v - g. The angular increments at ± 0.5 g are to be * " and at ± 1.0 g the angular in¬ (2) For each test, the absolute value of the crements are to be ± '. [mean, median ] determination shall not exceed - g Other or additional input acceleration levels may be utilized if desired. The above test provides a measure of the variation in output associated with power turn -on or loop closure. Another 10.3.7.5 Test Results type of hysteresis is the variation in out( 1) Compu tation. Divide the individual put, at a given input, resulting from exreadings by the nominal scale factor. Deterercising the pendulous mass within its mine the output change (in g units) at each operating range (similar to magnetic hysreference input acceleration level teresis). To determine this characteristic, (2) Threshold. The absolute value of the current injection or a similar technique smallest change in the accelerometer output may be employed to swing the pendulum recorded in Section 10.3.7.4 (1) shall exceed back and forth through its operating g range, without moving the instrument (3) Resolution. The absolute value of the case. A plot of the restoring current versus smallest change in the accelerometer output the driving current on an X- Y recorder recorded in Section 10.3.7.4 (2) shall exceed will produce a hysteresis loop, the maxg imum opening of which is the operating hysteresis. The relationship of the resolution (or threshold) to the input reference angle and the angular increment is 10.3.7 Threshold and Resolution 10.3.7.1 Purpose. The purpose of this ΔA md = — = g cos θ Aθ test is to determine if the changes in instrument output are greater than the specified values for given acceleration level changes. where: 10.3.7.2 Test Equipment. The following ΔA ind = desired resolution (or threshtest equipment specified in Section 9.2 is old) required for this test: 0 - angle between the positive input Dividing head and mounting fixture axis and the horizontal such that g sin d = Electronic equipment required to operate reference input acceleration the accelerometer and to measure its output Δfl . angular increment in θ. in radians 10.3.7.3 Test Setup. The test setup shall The minimum threshold and resolution be in accordance with Section 10.3.1.1. responses are usually specified to be great¬ 10.3.7.4 Test Procedures er than 50 percent of the expected output ( 1) Threshold using the nominal scale factor. (a) Rotate the dividing head to the 0* position (zero g) within " (b) Rotate the dividing head + " 10.3.8 Warmup Time and record the accelerometer output 10.3.8.1 Purpose. The purpose of this (c) Rotate the dividing head - " test is to determine the time required for the from the 0* position and record the acaccelerometer output to come within a specicelerometer output fied value of the steady state or final indicated (d) Repeat Steps (b) and (c) output following power turn-on in a specified times ambient environment. (2) Resolution. Repeat Steps (a) through 10.3.8.2 Test Equipment. The following (d) of Section 10.3.7.4( 1). except that the test equipment specified in Section 9.2 is dividing head is rotated to induce input accelrequired for this test: O 00/55652 41 Dividing head and mounting fixture Electronic equipment required to operate Specify a current which will not damthe accelerometer and to measure its output age the accelerometer nor cause the pen¬ Equipment required to establish the specdulum to hit a stop. ified ambient environment 10.3.8.3 Test Setup. The test setup shall (2) Reverse the polarity of the applied self- be in accordance with Sections 10.3.1.2 (1). test torquer current. Record the accel(2). and (3) only, except that the initial amerometer output as £ j bient temperature shall be room temperature. (3) Calculate the self-test torquer scale fac¬ 10.3.8.4 Test Procedure tor K s by (1) Set the dividing head at 0° 2/, K x (2) Establish the ambient thermal environK, = mA/g ment at ± β C. Allow E h - £, minutes for the instrument to reach thermal where equilibrium K s = self-test scale factor, in mA/g (3) Energize the accelerometer and test Is = self-test current, in mA equipment as quickly as possible in accor£h . £ j ■ accelerometer outputs, in output dance with Sections 9.1.1 and 9.3.2 units (4) Record the accelerometer output as a Ri = accelerometer scale factor obtained function of time until a steady state is reached from Section 10.3.2. in output units/g 10.3.8.5 Test Results 10.3.9.5 Test Results. The self-test tor¬ ( 1) Plot the value of the accelerometer outquer scale factor shall be = put as a function of time mA/g. (2) The output obtained from the test shall 10.3.10 Short-Term Stability be within output units of the steady- 10.3.10.1 Purpose. The purpose of this state value at the end of minutes test is to determine the short-term stability of the accelerometer bias Ko and scale factor . In all cases, the initial thermal ambient 10.3.10.2 Test Equipmen t. The followenvironment and thermal mounting coning test equipment specified in Section 9.2 is ditions must be carefully specified. Care required for this test: must be taken to ensure that the specified Dividing head and mounting fixture thermal environment does not affect the Electronic equipment required to operate dividing head positioning accuracy. For the accelerometer and to measure its output some applications, other orientations 10.3.10.3 Test Setup. The test setup may be specified. shall be in accordance with Section 10.3.1.1. 10.3.10.4 Test Procedure 10.3.9 Self-Test Torquer Scale Factor ( 1 ) Stabilize the accelerometer at the stan¬ 10.3.9.1 Purpose. The purpose of this dard operating conditions specified in Section test is to determine the scale factor of the self- 9.1 test torquer. (2) Determine and record the bias and scale 10.3.9.2 Test Equipment. The following factor using the procedure of Section 10.3.2.4 test equipment specified in Section 9.2 is (3) Repeat Step (2) times per day for required for this test: [ hours, days ] of continuous operation. Dividing head and mounting fixture Measurements to be made at least Electronic equipment required to operate [ minutes, hours ] apart the accelerometer and to measure its output 10.3.10.5 Test Results. Determine the Dc current supply standard deviation of the bias and scale factor 10.3.9.3 Test Setup. The test setup shall from their mean values obtained in Section be in accordance with Section 10.3.1.1. except 10.3.10.4. that the dividing head shall be set at 0*. (1) The short-term standard deviation of 10.3.9.4 Test Procedure the bias shall be less than g ( 1 ) Apply A dc to the (2) The short-term standard deviation of self-test torquer winding. Record the acthe scale factor shall be less than celerometer output as E output units g In some applications it may be desirable In some applications, it may be desirto modify the test to determine the stabilable to modify the test to determine the ity of additional parameters such as instability of additional parameters such as put-axis misalignment. input-axis misalignment. Other criteria for establishing stability may be utilized such as the unbiased estimate of the standard deviation, curve 10.3.12 Repeatability fitting for trend determinations, or com10.3.12.1 Purpose. The purpose of this puter analyses to determine the autotest is to determine the repeatability of the correlation times. bias Ko and the scale factor K \ with cool downs to the specified temperature. 10.3.12.2 Test Equipment. The following test equipment specified in Section 9.2 is required for this test: 10.3.11 Long-Term Stability Dividing head and mounting fixture 10.3.11.1 Purpose. The purpose of this Electronic equipment required to operate test is to determine the long-term stability of the accelerometer and to measure its output the accelerometer bias Ko and scale factor K 10.3.12.3 Test Setup. The test setup 10.3.11.2 Test Equipment. The followshall be in accordance with Section 10.3.1.1. ing test equipment specified in Section 9.2 is 10.3.12.4 Test Procedure required for this test: ( 1) Stabilize the accelerometer at the stan¬ Dividing head and mounting fixture dard operating conditions specified in Section Electronic equipment required to operate 10.3.1.1 the accelerometer and to measure its output (2) Determine and record the bias and scale 10.3.11.3 Test Setup. The test setup factor using the procedure of Section 10.3.2.4 shall be in accordance with Section 10.3.1.1. (3) Deenergize and cool the accelerometer 10.3.11.4 Test Procedure to ± * C. Soak at least (1) Stabilize the accelerometer at the stanhours dard operating conditions specified in Section (4) Repeat Steps ( 1). (2). and (3) . 9.1 times (2) Determine and record the bias and scale 10.3.12.5 Test Results factor using the procedure of Section 10.3.2.4 ( 1) The rms deviation of the bias measure¬ (3) Repeat Step (2) times per day for ments from the mean value shall not exceed days of continuous operation. Meag surements to be made at least [ min(2) The rms deviation of the scale factor utes, hours ] apart. measurements from the mean value shall not 10.3.11.5 Test Results. Obtain the best exceed output units/g fit linear curves to the bias and scale factor data points of Section 10.3.11.4 by the method Other changes in environmental condiof least squares. Determine the standard detions may be specified as desired. viation of the data points from the best fit lines. ( 1) The slope of the best fit bias line shall 10.3.13 Sensitivity not exceed g/day 10.3.13.1 Purpose. The purpose of the (2) The standard deviation of the bias data sensitivity test is to determine the changes in points from the best fit line shall be less than accelerometer scale factor K \ and bias Ro g caused by variations in the following: (3) The slope of the best fit scale factor line (1) Pickoff excitation voltage shall not exceed output units g per (2) Pickoff excitation frequency day (3) Ambient temperature (4) The standard deviation of the scale fac(4) External magnetic fields tor data points from the best fit line shall be (5) Pressure less than output units/g (6) Operating temperature For some applications it may be desir(1) The scale factor sensitivity with variable to increase or reduce the number of ations of pickoff excitation voltage is test conditions to be varied and to test for 100 (K l Λ - K lh ) the sensitivity of other accelerometer percent/V parameters such as input-axis misKι (V* - V„ ) alignment. where: 10.3.13.2 Test Equipment. The followV Λ > maximum pickoff excitation ing test equipment specified in Section 9.2 is Vb = minimum pickoff excitation required for this test: i = scale factor measured with V Λ ap¬ Dividing head and mounting fixture plied Electronic equipment required to operate Kι b = scale factor measured with V 0 apthe accelerometer and to measure its output plied Equipment required to produce the exK\ > nominal scale factor citation variations and environmental ( 2) The bias sensitivity with variations of changes pickoff excitation is 10.3.13.3 Test Setup. The test setup shall be in accordance with Section 10.3.1.1. Ko* K{ Ob 10.3.13.4 Test Procedure *7V This test is performed by varying each where: parameter ind ividually while mainK oa * bias measured with V t applied taining all other test conditions constant K ob - bias measured with V b applied per the requirements of Section 9.1. An example is presented below. Determ ine the other sensitivity Pickoff Excitation Voltage coefficients in a similar manner. ( 1) Determine the accelerometer scale factor and bias per Section 10.3.2 with the pickoff excitation increased to * V ( 2) Decrease the pickoff excitation to (3) The sensitivity coefficients shall be ± V and repeat the test equal to or less than the following limits: Other Parameter Variations. Repeat Parameter Sensitivity the test described in Section 10.3.13.4 (1) Scale Factor Bias for each parameter listed in Section Pickoff excitation . percent/V glV 10.3.13.1. voltage Select the appro priate parameter Pickoff excitation . percent/Hz g/Hz frequency change for each test. Operating temper. percent/ C __*/°C Generally the conditions of environature mental exposure should be specified such External magnetic . percent/T g/T fields as rate of temperature and pressure Pressure percent/(N/m z ) g/(N/m z ) changes and the direction of the magnetic Ambient tempera. percent/°C g C fields. Care must be taken to separate or ture eliminate the effect of changes in test equipment characteristics caused by variations in environment. Note that if a particular sensitivity is nonlinear, the result obtained from the 10.3.13.5 Test Results above procedure can be misleading. It may be desirable to obtain more data The test data shall be reduced in order points in order to determine such characto determine the sensitivity coefficients. teristics as linearity, maximum slope, or An example of an accelerometer sensihysteresis. tivity coefficient calculation is as follows. 10.3.14 Centrifuge Input Range 10.3.14.7 Test Results. The absolute val¬ 10.3.14.1 Purpose. The purpose of this ues of the accelerometer outputs from the two test is to establish that the instrument input tests shall each be ± output acceleration range is equal to or greater than units. The pickoff voltages shall each be less the specified value. than V rms. 10.3.14.2 Test Equipment. The follow10.3.15 Precision Centrifuge ing equipment specified in Section 9.2 is re10.3.15.1 Purpose. The purpose of this quired for this test: test is to determine the magnitude of the Mounting fixture nonlinear acceleration-sensitive model equa¬ Electronic equipment required to operate tion coefficients Ki and Kt. the accelerometer and to measure its output Centrifuge Precision centrifuge tests are usually 10.3.14.3 Test Setup — Mounting Posinot required for instruments with low tion A input ranges (for example, less than ± 2 ( 1) Unless otherwise specified, the acg ) . celerometer shall be operated under the stan¬ 10.3.15.2 Test Equipment. Same as Secdard test conditions of Section 9.2 for opertion 10.3.14.2, except use a precision cenative closed-loop tests trifuge and timing equipment to measure the (2) The axis of rotation of the centrifuge centrifuge period. shall be vertical within 10.3.15.3 Test Setup — Mounting Posi¬ (3) Attach the accelerometer to the mounttion A ing fixture on the centrifuge arm with the ( 1 ) Unless otherwise specified, the acinput reference axis normal to the centrifuge celerometer shall be operated under the stanaxis within ' and pointing toward the dard test conditions of Section 9.2 for operrotation axis (positive input acceleration). Deative closed-loop tests termine and record the nominal radius from (2) The axis of rotation of the centrifuge the centrifuge axis to the proof mass center of gravity within inches. shall be vertical within " (3) Attach the accelerometer to the mount¬ (4) Starting Procedure ing fixture on the centrifuge arm with the input reference axis normal to the centrifuge State sequence of operations required to axis within ' and pointing toward the bring accelerometer and test equipment rotation axis (positive input acceleration). Deto operating conditions. termine and record the nominal radius from the centrifuge axis to the proof mass center of (5) The accelerometer and the immediate gravity environment shall be allowed to reach ther(4) Starting Procedure mal equilibrium as evidenced by the stability of the accelerometer output within State sequence of operations required to output units for measurements spaced bring accelerometer and test equipment minutes apart before proceeding with to operating conditions. the test 10.3.14.4 Test Procedure — Mounting 10.3.15.4 Test Procedure — Mounting Position A Position A ( 1 ) Apply a centripetal acceleration of (1) Set the centrifuge angular rate to a ± g value equivalent to a centripetal acceleration (2) Record the accelerometer output and at the accelerometer proof mass of g. the rms pickoff output voltage nominally 10.3.14.5 Test Setup — Mounting Posi(2) Measure the accelerometer output and tion B. Same as Section 10.3.14.3. except that the centrifuge period simultaneously and the direction of the input reference axis shall record be reversed (negative input acceleration). (3) Repeat Steps (1) and (2) at nominal 10.3.14.6 Test Procedure — Mounting centripetal acceleration levels of . Position B. Same as Section 10.3.14.4. . . • • • . and g 10.3.15.5 Test Setup — Mounting Posi10.3.16 Life, Storage tion B. Same as Section 10.3.15.3, except that 10.3.16.1 Purpose. The purpose of this the direction of the input reference axis shall test is to demonstrate storage life of the acbe reversed (negative input acceleration). celerometer. 10.3.15.6 Test Procedure — Mounting Position B. Same as Section 10.3.15.4. 10.3.16.2 Test Equipment. The following test equipment specified in Section 9.2 is Additional orientations of the acrequired for this test: celerometer with respect to the centripetal acceleration vector may be speciDividing head and mounting fixture fied, if desired, in order to determine the Electronic equipment required to operate cross-coupling or other model equation the accelerometer and to measure its output coefficients. 10.3.16.3 Test Setup. The setup for 10.3.15.7 Test Results. Perform a rechecking the accelerometer at the beginning gression analysis of the input versus indicated and end of the test period shall be in accoracceleration data in order to obtain values of dance with Section 10.3.1.1. the nonlinear acceleration-sensitive model 10.3.16.4 Test Procedure equation coefficients and the test residuals. The resulting coefficients shall conform to the ( 1) Determine the bias and scale factor following: using the procedure of Section 10.3.2 K 2 ≤ gig 2 K 3 ≤ gig' and so on. I2J_ The standard deviation of the residuals Specify the storage environment which shall be less than g. may include periodic subjection to vibra¬ The measurement precision is directly tion, shock, temperature cycling, and/or related to the test accuracy desired, and other nonoperating environmental condicareful attention must be given to these tions. Specify storage time and any proconsiderations when designing a centective packaging requirements. trifuge test. In some cases it may be necessary to measure the arm compliance (arm bending and change in arm length) which occurs between the test acceleration lev(3) At the end of the storage period, again els. Equipment to perform these measuredetermine the bias and scale factor. ments is usually provided as part of the centrifuge apparatus. The test procedure or the regression analysis, or both, must If desired, periodic measurements of be designed to minimize the impact of performance parameters during storage these effects as well as uncompensated life may be specified. changes in centrifuge radius and accelerometer attitude relative to gravity which might occur between the positive (input axis in) and negative (input axis 10.3.16.5 Test Results. The bias and out) halves of the test. If these effects are scale factor values for all measurements shall not removed or compensated for. large meet the following requirements: errors in the derived values of the model equation coefficients can occur. Examine the residuals (differences be units/g tween the actual data points and the 10.3.17 Life, Operating fitted curves) in order to verify that the model equation utilized reasonably re10.3.17.1 Purpose. The purpose of this flects the accelerometer response. test is to demonstrate the operating life of the accelerometer. CODE: 0 ■ Accelerometer ta l l conducted during epeclfled environment, and N • Accelerometer teet conducted before and after epeclfled environment and eccelerome r la oparatlnf or non-operallng aa applicable. accelerometer not operated during environment. S • Speclel leel deeorlbed In environment. (■ • Accelerometer leal conducted before and after epeclfled envlronmeni, and accelerometer operated during environment. P a Toete performed perlodtceily ee epeclfled In Paragraph 4.4.3. Fig 4 Suggested Accelerometer Environmental and Test Combinations 10.3.17.2 Test Equipment. The follow10.4.3 Test Procedure and Results ing test equipment specified in Section 9.2 is required for this test: Detail the procedure for the control of Dividing head and mounting fixture the environment, including tolerances Electronic equipment required to operate and rates of change, integrated with the the accelerometer and to measure its output procedure for the accelerometer test. Cau¬ 10.3.17.3 Test Setup. The test setup tion notes on overload limits on the envishall be in accordance with Section 10.3.1.1. ronmental intensity applied to the ac¬ 10.3.17.4 Test Procedure. Every celerometer can be specified if required. days for (days, months ] measure the Compliance with the specification perbias, scale factor, and misalignment angle formance requirements should be demonusing the procedure of Section 10.3.2 and strated prior to, during if appropriate, and 10.3.4 in mounting position 1. upon completion of the environmental 10.3.17.5 Test Results. The bias, scale test sequence. factor, and misalignment angle shall meet the Procedures for most environmental following requirements: tests are well covered by existing industry, government, and military documents IRoJ ≤. - g such as MIL-E-5272, Environmental Kx - . .-fc . output units g Testing, Aeronautical and Associated 1*0. ≤ . _ rad Equipment. Rather than duplicate samples of existing procedures, this standard provides assistance in selecting the ac¬ 10.4 Environmental Tests celerometer parameters which will be 10.4.1 Purpose. The purpose of these tests most important to measure in each enviis to verify that the accelerometer performs as ronment. (See Fig 4.) This selection is specified when subjected to environments outmade based on the expected environmenside of the standard operating conditions, but tal sensitivities of the accelerometer and within the specified environmental limits. the cost-effectiveness of the testing. 10.4.2 Test Equipment. The following test The application of the accelerometer equipment from Section 9.2 must be included will determine which tests, or comfor each environmental test: bination of tests, are to be performed, and their sequence. The figure is intended as a Equipment for providing the specified enguide for selection of the accelerometer vironment test which should be conducted in associ¬ Means of measurement of environment ation with the environmental tests that and time are chosen dependent on the application Adaptation of accelerometer to environof the accelerometer. In some cases it may mental equipment such as special holding be desirable to combine environments in fixtures, cables, etc. order to simulate the expected operating Equipment for each accelerometer test, conditions. chosen from Sections 10.1. 10.2. and 10.3. Appendix A Accelerometer Dynamic Equations Al. Introduction K t = pendulum elastic restraint, in dyn • cm/rad This Appendix presents the equations and •K o (s) = pickoff transfer function, in V/rad block diagrams of the dynamic response of the K A (s) = torque balance electronics transfer accelerometer when operating in both the function, in V dc/V rms open- and closed-loop modes. In each case, an r 4 (s) = Laplace transform of driving idealized linear second-order model is astorque, in dyn • cm sumed for the accelerometer pendulum. Sp o (s) - Laplace transform of angular displacement of pendulum with re¬ where where t ( (t) = applied voltage, in volts a(t) = applied acceleration along input axis V, (s) = Laplace transform of i * - (t) ing V a (s) = Laplace transform of output voltA(s) = Laplace transform of a(t) age, in volts P = pendulosity in g • cm K t = torquer scale factor, in dyn • cm/A T t (s) - Laplace transform of capture torque R = torquer resistance, in ohms in dyn • cm L = torquer inductance, in henrys Te(s) = Laplace transform of error torque s = Laplace operator in dyn • cm J - moment of inertia of pendulum about output axis, in g • cm 2 All other symbols have the same definition C - damping torque coefficient, in dyn as in Eq Al. All effects of the model equation • cm/(rad/s) error coefficients have been neglected. Fi Al Block Diagram for Open-Loop Operation Appendix B Static Multipoint Test Bl. Introduction K 2 = second-order nonlinearity coeffi¬ A short discussion on the static multipoint cient in g/g 2 test is presented herewith with emphasis on a K3 = third-order nonlinearity coefficient suggested data reduction procedure. The proin g/g 3 cedure is based on the method of least squares. δ 0 , δp = misalignments of the input axis It gives a best estimate of each of the acwith respect to the input reference celerometer performance coefficients, the unaxis about the output reference certainties of these coefficients, and it proand pendulous reference axes, revides a criterion for determining if a coeffispectively in radians cient is statistically significant. ϋfip.-Kio = cross-coupling coefficients in (g/g)/ cross g B2. Model Equation The misalignment angles include angular The model equation represents the response errors of the mounting fixture, dividing head of the accelerometer to applied accelerations errors, and errors in mounting as well as along and normal to the input axis. The misalignment of the input axis with respect to following model equation is assumed in the the input reference axis. There is no way of analysis: distinguishing between a misalignment and a linear cross axis sensitivity. + α, + K 2 o. 2 + #*,<-, 3 + δ Some of the above terms may be deleted or l ιnd Es. = K 0 o "p others added as appropriate for the type of δ p α 0 + K ιv a,a v + K^a^ a (Eq Bl) accelerometer and its applications. Only a sufficient number of terms should be used that where will adequately describe the response of the Ai d = acceleration indicated by the ac accelerometer. where •"ind acceleration indicated by the accelerometer in g accelerometer output in output B3. Test Procedure — units Mounting Position 1 αj,α p n = applied acceleration components along the positive input, penduB3.1 Mounting Position 1. With the axis of lous, and output references axes, the dividing head in a horizontal position and respectively in g the head set at its 0* position, mount the K 0 bias in accelerometer so that its output reference axis K scale factor in output uni s/g is parallel to the axis of the dividing head, the Fig A2 Block Diagram for Closed-Loop Operation input reference axis is horizontal, the positive eration components in units of the local gravpendulous reference axis points upward, and ity vector g as functions of table angle are the positive input reference axis points upward when the head is rotated to the 90° a* = sin kβ„ a p = cos kθ n position. *° = ° (Eq B2) B3.2 Data Taking — Mounting Position 1. At each head angle β ■ = 0', θ „ , 2Θ „ . • . - , kθn, • • • , where (n -1) θ „ , take and record several measurek β n - dividing head angle, in degrees, k = 0. 1. 2. • • • , π-l ments of the accelerometer output -E kp . where β n = 360/π, n and k are integers, and 0 It should be noted that *5 p and K o of the model equation Bl are not exercised in ≤ k ≤ n-1. The number n of head angles at mounting position 1, since ao - 0. which measurements of accelerometer output are to be made is based on statistical considSubstituting Eqs B2 in Eq Bl and using erations. In general, n should be at least equal well-known trigonometric identities and small-angle approximations, Eq Bl may be to twice the number of model equation expressed by the following Fourier series: coefficients to be determined. Though it is necessary to have equally spaced head angles, E kp = 0 0 + 0 ! sin kθ„ + α 2 sin 2kθ „ the specified sequence need not be in numer¬ + o 3 sin 3kθ„ + 0ι cos fe0 n + β 2 cos 2Λ0 „ ical order. It is quite possible to have occasional "wild" (Eq B3) data points in a series of readings which may where be due to operator errors in recording the data E k f) = expected value of the accelerometer (such as transposition of numbers), or they output at head angle θ = kθ „ may be due to a power line or other unusual transient, or they may be true members of the o-o ~ Ki \Ko + ~ K ) statistical population. For example, in a Gaussian distribution of the errors around the α, = ^ (1 + ^) mean, one may expect three readings out of a 1000 to have an error greater than three times the standard deviation from the mean. Since α 2 = 2" *^ι *^ip (Eq B4) the usual sample is only three to five readings at each head angle, a single "wild" point α 3 ~ £ κ ι κ . could cause a large error in the estimate of the 0ι " K 1 δ c model equation coefficients. In order to reduce the possibility of a large error in the β 2 = - \ κ l κ L 2 estimated values of the coefficients, it is quite common to use the median value at each head Those values of the Fourier coefficients angle. However, if the number of readings q which will best fit all the data points are per head angle multiplied by the number of determined by the method of least squares. head angle positions n is large compared to The residual (the measured value less the the number of unknown coefficients, a single expected or best fit value of the output) at "wild" point will have very little effect on the head angle θ -= kθ „ is estimated value of the coefficients. The equations derived below are intended for use only r k ■ E kv ' — (α 0 + a x sin kθ„ + β 2 sin 2k θ„ with the median reading, or the mean of the + α 3 sin 3k θ„ + β t cos fcβ,, + β 2 cos 2k θ „) readings at each head angle. If all the data at each head angle are used, it is important that (Eq B5) exactly the same number of readings be taken where at every head angle and that the equations r k = E kp — £ fcp = residual at head angle below be modified appropriately. k θ„ , in output units •Ekp = measured value of accelerometer out¬ B3.3 Fourier Analysis — Mounting Position put at head angle kθ„, in output 1. In the above mounting position, the accel- units The sum of the squares of the residuals is If desired for convenience, an approximate n — 1 n — 1 value of may be used on the right-hand side of Eqs B8 without any significant loss of k ∑-0 r * 2 ■ * ∑»0 L' B ' ,p ~ (α ° + αι sin * βn accuracy. + α 2 sin 2Λ 6>„ + α 3 sin 3k θ„ B3.5 Standard Deviation of Residuals — Mounting Position 1. The standard deviation + /?ι cos ft 0 n + β 2 cos 2ft 0„ )J 2 (Eq B6) of the residuals is a measure of the fit of the Fourier series. Eq B3. to the test data. The In the method of least squares, the sum of the unbiased estimate of the standard deviation of squares of the residuals is minimized. This is the residuals for mounting position 1 is done by taking the partial derivative of Eq B6 with respect to each of the unknown Fourier π— I coefficients, in turn, and setting each derivative equal to zero. Six normal equations k Σ' O '*' (Eq B9) are thus obtained from which the six Fourier n—m coefficients are determined. Because the head where angles are equally spaced, most of the sums Ot - unbiased estimate of the standard that appear in the normal equations are equal deviation of the residuals in output units to zero. Solving the normal equations for the n - number of head angle positions Fourier coefficients, it is found that TΛ - number of Fourier coefficients From Eq B3 it is seen that m = 6 for the assumed model equation. The sum of the α o " TT Σ E *v squares of the residuals in Eq B9 can be fc - 0 determined from Eq B6 which may be put into n — 1 _ 2 the following more convenient form: a-i ~ n £ kp sin kθ n * Σ- 0 n — 1 n — I n — I _ 2 α 2 ~ n £ kp sin 2kθ„ " * ∑«o * kp 2 -f (2α 0 = + α, * -o * -0 n — 1 (Eq B7) _ 2 α 3 ~ n Σ £ kp sin 3kθ„ + α 2 z + α 3 z + 0 ! * + 3 2 z ) (Eq BlO) * - 0 n — 1 Eq B7 may be substituted in Eq BIO if it is _ 2 01 n £ kp cos kθ„ found to be more convenient for programming * Σ» 0 the data reduction. n — 1 _ 2 B3.6 Uncertainties of Fourier Coefficients — 02 n p cos 2ft0 „ Mounting Position 1. The unbiased estimates f Σ £ k c « 0 of the uncertainty of the Fourier coefficient «o is B3.4 Model Equation Coefficients — Mounting Position 1. Solve Eqs B4 for the best fit (Eq Bll) values of the model equation coefficients in •3(o 0 ) terms of the Fourier coefficients. -».v The unbiased estimate of the uncertainty of ϋTj = x + 3α 3 each of the other Fourier coefficients is Ko = (a 0 + β 2 )/K 1 K 2 *= -20 2 /£- &<α,) - σ(β j ) - & r γ , ; - . lt 2 , or 3 (Eq B12) (Eq Bδ) *3 = -4a 3 /K x s β - øi/i-r, For some accelerometers, the Fourier ■Si. - 2α 2 /X. coefficients due to the nonlinear or cross acceleration terms, or both, may be too small to measure by a static multipoint test in a 1-g accelerometer so that its pendulous reference field, and the values obtained are largely the axis is parallel to the axis of the dividing head, result of noise in the measurement. Using the the input reference axis is horizontal, the Student's t statistic and n-m ≥ 8, we can be positive output reference axis points downapproximately 95 percent confident that a ward, and the positive input reference axis Fourier coefficient is not significantly differpoints upward when the head is rotated to fctie ent from zero if its absolute value is smaller 90° position. than twice the uncertainty obtained in Eq Bll or B12, whichever is appropriate. It is B4.2 Data Taking — M«uating Position 2. At obvious from Eqs B7 that setting one Fourier each head angle θ = 0" , θ a , 2θn , • • - . k$ n . coefficient equal to zero does not affect the ■ - - , (n-l)θn , take and record several measurevalue of the others. However, setting a Fourier ments of the accelerometer output E k β . where coefficient equal to zero does affect Eq B8 θn - 360/π. n and ft are integers, and 0 ≤ ft ≤ through B12 because of the increase in the n-1. The value of n must be the same as that residuals and the decrease in m. New values of used in mounting position 1. the uncertainties must be calculated if one or B4.3 Fourier Analysis — Mounting Position more Fourier coefficients are set equal to zero 2. In this mounting position, the acceleration because they are not significantly different components in units ofthe local gravity vector from zero. g as functions of table angle are B3.7 Uncertainties of Model Equation Oj = sin kθ „ Coefficients — Mounting Position 1. The uncertainties of the model equation coefficients σ p = 0 (Eq B14) may be expressed in terms of the uncertainties α 0 = — cos kθ , of the best estimate of the Fourier coefficients. Based on Eqs B8. it can be shown that It should be noted that δ 0 and K i p of Eq 1 σ. are not exercised in mounting position 2 since β C£β> - [ -)-* | --f [f] a p - 0. Substituting Eqs B14 in Eq Bl. we obtain the following Fourier series: σ(/ ϊ ) - [σ 2 (α, ) * 9σ 2 (α 3 )] - σ t [~ •Eito = α o + &ι sin kθ n + α 2 sin 2ftθ „ σ(K 2 ) - K σ(β 2 ) - j- ] (Eq B13) + α 3 sin 3fcθ „ + β r cos ftø - + β 2 cos 2ft0„ <*., .- . 4 . „ σ r T321 2 (Eq B15) I ^ where *σ. ) -^- *< ι>-^ [!] 2 E \u, *> expected value of the accelerometer output at head angle θ - kθ„ a 0 = K λ (K 0 + K 2 ) If any of the Fourier coefficients in Eq B3 are zero. Eqs B13 should be modified accordingly. B4. Test Procedure — (Eq B16) Mounting Position 2 «3 = - *l*3 B4.1 Mounting Position 2. With the axis of øi = -Ki δ.p the dividing head in a horizontal position and the head set at its 0° position, mount the 02 = ~ 2 " ^1*^2 Note that Fourier coefficients of Eqs B15 and mounting positions. For example, the best B16 are. in general, different from those of Eq estimate of R 2 is B3 and B4 which are derived from data taken in mounting position 1. K - 2 - - -1J Eqs B5 through B7 hold for mounting posi2T (K 2 + X 2 ) tion 2 except that the subscripts "p" and "o" where should be interchanged wherever they appear. K 2 = average value of K 2 K 2 = value of K 2 determined from posi¬ B4.4 Model Equation Coefficients — Mounting tion 1 Position 2. Solve Eqs B16 for the best fit values of the K' 2 = value of K 2 determined from posimodel equation coefficients in terms of the tion 2 Fourier coefficients which are derived from (Eq B18) data taken in mounting position 2. If desired for convenience, an approximate The model equation coefficients δ 0 and K ip value of K \ may be used on the right-hand and their uncertainties are determined only in side of Eqs B17 without any significant loss of mounting position 1. The coefficients δ p and accuracy. K \ 0 and their uncertainties are determined only in mounting position 2. Therefore, no B4.5 Uncertainties of Model Equation averaging process is involved for these four Coefficients — Mounting Position 2. The uncoefficients. certainties of the model equation coefficients As previously stated, the standard deviation determined from mounting position 2 may be of the residuals is a measure of the fit of the found by use of Eq B9 through B13 except Fourier series to the test data. The best estithat subscripts "p" and "o" should be intermate of the standard deviation of the residuchanged wherever they appear. als (expressed in units of g rather than output units) for the best fit model equation, as determined by the above procedures using the B5. Best Estimate of Model two mounting positions, is very nearly equal Equation Coefficients to The best estimate for each of the model 2 equation coefficients Ro. K \. Kι. and K* is the a • 2 + . σ « r ι B20) average of those determined from the two O τ * (Eq *l

Claims: Claims 1. A method of calibrating a plurality of seismic sensors, each sensor having an axis of sensitivity, comprising: coupling the sensors with each sensor positioned with its axis of sensitivity in a different spatial direction; rotating the sensors; measuring one or more output signals from the sensors; processing the output signals from the sensors; and storing one or more calibration coefficients. 2. The method of claim 1, wherein the sensors comprise micro-machined accelerometers. 3. The method of claim 1, wherein coupling the sensors with each sensor positioned with its axis of sensitivity in a different spatial direction comprises, coupling the sensors with the axes of sensitivity in: a first direction; a second direction; and a third direction. 4. The method of claim 1, wherein rotating the sensors comprises, rotating the sensors about the x-axis, the y-axis and the z-axis. 5. The method of claim 1, wherein measuring one or more output signals from the sensors comprises, measuring the output signals from the sensors at one or more angles of rotation. 6. The method of claim 1, wherein processing the output signals from the sensors comprises, calculating one or more calibration coefficients from the measured output signals of the sensors. 7. The method of claim 1, wherein each sensor further includes a corresponding ASIC having a local non- volatile memory; and wherein storing one or more calibration coefficients includes storing the corresponding calibration coefficients to the corresponding local non- volatile memories in the corresponding ASIC. 8. The method of claim 1, wherein storing one or more calibration coefficients includes storing the corresponding cahbration coefficients to an external database. 9. The method of claim 1, wherein coupling, rotating, measuring, and processing are provided in accordance with the Institute of Electrical and Electronic Engineers Specification IEEE 337-1972 for the IEEE Standard Specification Format Guide and Test Procedure for Linear, Single-Axis, Pendulous, Analog Torque Balance Acclerometer.

Inventors: GANNON JEFFREY C, PHAM HAI T, RAGAN GLEN, WILSON DAVID, GANNON, JEFFREY, C., PHAM, HAI, T., RAGAN, GLEN, WILSON, DAVID
Applicants: GANNON JEFFREY C, INPUT OUTPUT INC, PHAM HAI T, RAGAN GLEN, WILSON DAVID, GANNON, JEFFREY, C., INPUT/OUTPUT, INC., PHAM, HAI, T., RAGAN, GLEN, WILSON, DAVID
Application year: 2000
Main classification: G01V13
IPC codes: G01D11, G01D18, G01H1, G01L27, G01N1, G01P1, G01P15, G01P21, G01V1, H01L21, H01L29, H05K5