MEMS accelerometer scale factor nonlinear batch compensation test method

Abstract

The invention discloses an MEMS accelerometer scale factor nonlinear batch compensation test method. The test method comprises the following steps: establishing an accelerometer nonlinear mathematical model; designing an acceleration test batch calibration test method to carry out batch nonlinear calibration tests; establishing a compensation parameter model, and calculating various parameters of nonlinear calibration through compensation test data; carrying out batch compensation verification tests according to the various parameters; analyzing parameter consistency, and confirming fixed parameter compensation feasibility. The MEMS accelerometer combination wide-range scale factor nonlinearity can be improved, and the batch test efficiency is improved.

Description

Technical Field

[0001] The present invention relates to the field of acceleration measurement, and in particular to a batch compensation test method for nonlinearity of scale factors of MEMS accelerometers. Background Art

[0002] MEMS accelerometers are used to measure the acceleration of a carrier and output a compensated acceleration value. During use, the nonlinearity of the accelerometer's scale factor directly affects acceleration accuracy.

[0003] The centrifuge operating radius is the distance from the centrifuge's average center of gyration to the accelerometer's detection center. The accuracy of the centrifuge operating radius (accelerometer installation radius) directly affects the accelerometer's large-scale scale factor nonlinearity calibration compensation results.

[0004] Because this distance is difficult to measure accurately, actual tests typically use the 1g output value for reverse calculation. A common accelerometer centrifugal test method involves calibrating the accelerometer using the ±1g output value after a ±1g calibration, followed by a centrifugal test.

[0005] Traditional compensation test methods are inefficient and have low accuracy when used in batch tests. Summary of the Invention

[0006] In view of the above problems, the present invention is proposed to provide a MEMS accelerometer scale factor nonlinearity compensation batch test method that overcomes the above problems or at least partially solves the above problems.

[0007] According to one aspect of the present invention, a batch compensation test method for scale factor nonlinearity of a MEMS accelerometer is provided, the test method comprising:

[0008] Establish nonlinear mathematical model of accelerometer;

[0009] Design acceleration test batch test method to conduct batch nonlinear calibration test;

[0010] Establish compensation parameter model and calculate various parameters of nonlinear calibration through compensation test data;

[0011] Carry out batch compensation verification tests according to the various parameters mentioned;

[0012] Analyze parameter consistency and confirm the feasibility of fixed parameter compensation in the same batch.

[0013] Optionally, establishing a nonlinear mathematical model of the accelerometer specifically includes:

[0014] Accelerometer mathematical model:

[0015]

[0016] Where: A ind is the acceleration value indicated by the instrument, g; a i ,a o ,a p are the accelerations along the input reference axis, output reference axis, and pendulum reference axis of the accelerometer, respectively, in g; E is the output of the accelerometer, in mA, V, 1 / s, and LSB; K0 is the bias value, in g; K1 is the scale factor, in mA / g, V / g, (1 / s) / g, and LSB / g; K2 is the second-order nonlinear coefficient, in g / g 2 ; K3 is the third-order nonlinear coefficient, g / g 3 ;K ip ,K io is the cross-coupling coefficient, g / g 2 ; δ o ,δ p are the misalignment angles of the input shaft relative to the input reference axis around the output shaft and the pendulum axis, rad;

[0017] The simplified nonlinear mathematical model of the accelerometer is:

[0018]

[0019] Where: A ind is the acceleration value indicated by the instrument, g; a i is the acceleration along the accelerometer input reference axis, g; E is the accelerometer output, mA, V, 1 / s, LSB; K0 is the bias, g; K1 is the scale factor, mA / g, V / g, (1 / s) / g, LSB / g; K2 is the second-order nonlinear coefficient, g / g 2 ; K3 is the third-order nonlinear coefficient, g / g 3 .

[0020] Optionally, establishing the compensation parameter model specifically includes:

[0021] Based on the nonlinear model of the accelerometer, a compensation parameter model is established, and the various parameters of the nonlinear calibration are calculated using the calibration test data;

[0022] Fit a straight line least squares to the accelerometer input and output (x, y):

[0023] y=K·y (1) ·x+B (2)

[0024] Where x is the theoretical value of input acceleration, g; y is the output value of the accelerometer that has been calibrated at room temperature, g; y (1) is the theoretical output value of +1g / -1g after the accelerometer that has been calibrated at room temperature is installed in the centrifuge, g / g; K is the linear term coefficient obtained by fitting, g / g; B is the constant term coefficient obtained by fitting, g;

[0025] Compensate the accelerometer output according to the parameters obtained by straight line fitting:

[0026]

[0027] Where: y is the output of the accelerometer after room temperature calibration, g; y1 is the output of the accelerometer after compensation using the linear fitting parameters, g; K is the linear term coefficient obtained by fitting, g / g; B is the constant term coefficient obtained by fitting, g;

[0028] Calculate the current straight line fitting error: Δ=y1-y (1) ·x(4)

[0029] Where: x is the theoretical value of input acceleration, g; y1 is the accelerometer output after linear fitting, g; y (1) is the theoretical output value of +1g / -1g after the accelerometer that has been calibrated at room temperature is installed in the centrifuge, g / g; Δ is the linear fitting error, g;

[0030] The error Δ is fitted with the accelerometer output y1 after the straight line fitting using a third-order polynomial fit (y1, Δ):

[0031] Δ=ay1 3 +by1 2 +cy1+d (5)

[0032] Where Δ is the linear fitting error, g; y1 is the accelerometer output after linear fitting, g; a is the cubic coefficient obtained by third-order polynomial fitting, g / g 3 ; b is the quadratic term coefficient obtained by fitting the third-order polynomial, g / g 2 ; c is the coefficient of the first-order term obtained by fitting the third-order polynomial, g / g; d is the coefficient of the constant term obtained by fitting the third-order polynomial, g;

[0033] Final compensation result: y = y1 - Δ (6).

[0034] Optionally, the batch calibration test method of the designed acceleration test batch test method specifically includes:

[0035] Design the acceleration test batch calibration test method based on the working principle of the centrifuge to carry out batch nonlinear calibration test;

[0036] The principle of centrifuge calibration test is to use the principle of Newtonian mechanics to generate standard centripetal acceleration through angular motion;

[0037] The formula for calculating centripetal acceleration is:

[0038] a=ω 2 *r (1)

[0039] Where: a is the centripetal acceleration, g; ω is the angular velocity of the centrifuge, rad / s; r is the working radius of the centrifuge, m;

[0040] The working radius of a centrifuge is the distance from the average center of gyration of the centrifuge to the detection center of the accelerometer. Since the detection center of the accelerometer is inside the accelerometer, the distance between the accelerometer mounting slot on the centrifuge equipment and the center of the centrifuge table is not equal to the distance between the accelerometer detection centers. Therefore, the length cannot be accurately measured, and there is an error in the detection center of each accelerometer.

[0041] During the accelerometer centrifugal test, the accelerometer output ±1g after ±1g calibration was used for calibration. After calibration, the centrifuge angular velocity corresponding to each input acceleration value was calculated based on the actual working radius r, and then the centrifugal test was carried out. The optimized compensation method uses the output value of the 1g input point during data processing to reversely calculate the actual installation radius of each accelerometer's detection center. The actual input acceleration value of each test object is calibrated according to each installation radius.

[0042] According to the optimized compensation algorithm, batch testing does not require test personnel to perform precise calibration before each test. The fixed distance between the accelerometer mounting slot and the mean rotation center is used as the batch test working radius to ensure that the test product output is within 1g±1% when the input is 1g.

[0043] For accelerometers with the same dimensions and tooling installation conditions, the working radius shall be calibrated only during the first test, and the result shall be used as the working radius for batch tests. For accelerometers with the same dimensions and tooling installation conditions, the installation radius deviation shall be ±1%;

[0044] Data collection for scale factor nonlinear batch calibration tests: The test specimen is rigidly mounted on a precision centrifuge, with the measured axis parallel to the axis of centrifugal acceleration. Centrifuge input rate points are set, each held for 30 seconds. During the test, the accelerometer output is recorded for 20 seconds 5 seconds after reaching each acceleration point. This is used to calculate the average output acceleration of the accelerometer at each input acceleration point.

[0045] The calibration test data is processed using a data processing program, and various parameters are calculated according to the compensation parameter model algorithm.

[0046] Optionally, the accelerometer centrifugal test method is to use an accelerometer that has been calibrated to ±1g to output ±1g for calibration, specifically including:

[0047] Install the accelerometer on a three-axis turntable and complete the six-position calibration test on the turntable to obtain the ±1g accelerometer scale factor value and complete the ±1g calibration;

[0048] Then install the accelerometer on the centrifuge and set a fixed angular velocity value ω1. Use the output value a1 of the accelerometer at this time and ω1 to reversely calculate the radius r, and use r to calculate the angular velocity value ω2 corresponding to the centripetal acceleration of 1g.

[0049] Set the centrifuge input to ω2 and verify the calibration result based on whether the accelerometer output value a2 is 1g. If the calibration result deviates significantly from 1g, continue to backcalculate the radius r using the accelerometer output value a2 and ω2 until the calibration is successful.

[0050] For example, if the rotation angular rate is set to 100° / s, the accelerometer outputs the centripetal acceleration a and calculates the correct r. The angular velocity is then calculated based on r to verify that the output is 1g.

[0051] Optionally, the batch compensation verification test according to the parameters specifically includes:

[0052] Calculate various compensation parameters according to the compensation parameter model algorithm and write them into the test product;

[0053] Verification data collection: The test sample is rigidly mounted on a precision centrifuge, with the measured axis of the test sample parallel to the axis of action of the centrifugal acceleration;

[0054] Conduct verification tests according to this compensation test method and calculate indicators based on the output values ​​of the verification test accelerometer, including:

[0055] The nonlinearity index of the scale factor is calculated as the error between the output value and the least squares fitted straight line divided by the range;

[0056] The calculation formula of the scale factor nonlinear relative error is:

[0057]

[0058] Where: g n is the specified acceleration g, g; A n For the device at a given g n A0 is the value measured by the device when g=0, g; A1 is the value measured by the device when g=1, g.

[0059] Optionally, the batch compensation test according to the parameters specifically includes:

[0060] During data processing, the output value of the current 1g input point is used to reversely calculate the actual installation radius of each unit;

[0061] The actual input acceleration value of each test product is calibrated according to the installation radius of each unit, so that the accelerometer data with different installation radius in the same test can be used for accurate compensation, realizing a group of multiple tests.

[0062] The present invention provides a batch compensation test method for MEMS accelerometer scale factor nonlinearity. The test method includes: establishing a nonlinear mathematical model for the accelerometer; designing a batch acceleration test method to conduct batch nonlinear calibration tests; establishing a compensation parameter model and calculating various nonlinear calibration parameters using compensation test data; conducting batch compensation verification tests based on the various parameters; and analyzing parameter consistency to confirm the feasibility of fixed parameter compensation within the same batch. This method improves the nonlinearity of the scale factor of MEMS accelerometers with a large range and enhances batch testing efficiency.

[0063] The above description is only an overview of the technical solution of the present invention. In order to more clearly understand the technical means of the present invention, it can be implemented in accordance with the contents of the specification. In order to make the above and other purposes, features and advantages of the present invention more obvious and easy to understand, the specific implementation methods of the present invention are specifically listed below. BRIEF DESCRIPTION OF THE DRAWINGS

[0064] In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the following briefly introduces the drawings required for use in the description of the embodiments. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying any creative work.

[0065] Figure 1 A flowchart of a MEMS accelerometer scale factor nonlinearity batch compensation test method provided by an embodiment of the present invention;

[0066] Figure 2 This is a statistical diagram of the relative error of the accelerometer verification of the S1 batch of test products of the 01 type accelerometer provided in an embodiment of the present invention;

[0067] Figure 3 Schematic diagram of the deviation before and after switching between two sets of accelerometers. DETAILED DESCRIPTION

[0068] Exemplary embodiments of the present disclosure will be described in more detail below with reference to the accompanying drawings. Although exemplary embodiments of the present disclosure are shown in the accompanying drawings, it should be understood that the present disclosure can be implemented in various forms and should not be limited by the embodiments set forth herein. Rather, these embodiments are provided to enable a more thorough understanding of the present disclosure and to fully convey the scope of the present disclosure to those skilled in the art.

[0069] The terms "comprises" and "comprising" and any variations thereof in the description, embodiments, claims and drawings of the present invention are intended to cover non-exclusive inclusions, for example, including a series of steps or units.

[0070] The technical solution of the present invention is further described in detail below with reference to the accompanying drawings and embodiments.

[0071] like Figure 1 and Figure 2 A batch compensation test method for MEMS accelerometer scale factor nonlinearity is shown. The method includes: establishing a mathematical model for accelerometer nonlinearity; designing a batch acceleration test method to conduct batch nonlinearity calibration tests; establishing a compensation parameter model and calculating various nonlinearity calibration parameters using compensation test data; conducting batch compensation verification tests based on these parameters; and analyzing parameter consistency to confirm the feasibility of fixed parameter compensation within the same batch. This method improves the scale factor nonlinearity of MEMS accelerometers with a large range and enhances batch testing efficiency.

[0072] Accelerometer nonlinearity

[0073] MEMS accelerometers are used to measure the acceleration of a carrier and can output compensated acceleration values. During use, the nonlinearity of the accelerometer scale factor directly affects acceleration accuracy. This patent aims to improve the nonlinearity of the scale factor of MEMS accelerometers over a wide range and increase batch testing efficiency.

[0074] Compensation principle

[0075] The nonlinear mathematical model of the accelerometer is:

[0076]

[0077] Where: A ind is the acceleration value indicated by the instrument, g; a i is the acceleration along the accelerometer input reference axis, g; E is the accelerometer output, LSB; K0 is the bias value, g; K1 is the scale factor, LSB / g; K2 is the second-order nonlinear coefficient, g / g 2 ; K3 is the third-order nonlinear coefficient, g / g 3 ;

[0078] The calibration and compensation process is to determine more accurate parameters.

[0079] Calibration core methods, including:

[0080] The principle of centrifuge calibration test is to use Newtonian mechanics to generate standard centripetal acceleration through angular motion to calibrate the linear accelerometer.

[0081] The formula for calculating centripetal acceleration is:

[0082] a=w 2 *r (1)

[0083] Where: a is the centripetal acceleration, g; w is the angular velocity of the centrifuge, rad / s; r is the working radius of the centrifuge, m.

[0084] The centrifuge operating radius is the distance from the centrifuge's average center of gyration to the accelerometer's detection center. The accuracy of the centrifuge operating radius (accelerometer installation radius) directly affects the accelerometer's large-scale scale factor nonlinearity calibration compensation results.

[0085] Since it is difficult to measure the distance accurately, the output value under 1g is usually used for reverse calculation in actual experiments.

[0086] The commonly used centrifugal test method for accelerometers is to use an accelerometer that has been calibrated to ±1g to output ±1g for calibration, and then perform a centrifugal test.

[0087] Calculation method: Set the rotation angular rate to 100° / s, obtain the centripetal acceleration a output by the accelerometer, and calculate the accurate r using formula (1). Then calculate the set angular velocity based on r and verify whether the output is 1g.

[0088] The general test steps for large-scale calibration are:

[0089] 1. Complete the six-position calibration test of the turntable and calibrate the output under ±1g.

[0090] 2. Perform calibration test data collection: The test specimen is rigidly mounted on a precision centrifuge, with the measured axis parallel to the axis of action of the centrifugal acceleration. Set the centrifuge input rate points, each of which is maintained for 30 seconds. During the test, record the accelerometer output for 20 seconds 5 seconds after reaching each acceleration point. This is used to calculate the average output acceleration of the accelerometer at each input acceleration point.

[0091] 3. Use data processing program to process calibration test data;

[0092] 4. Write the compensation parameters into the test product.

[0093] 5. Perform verification data collection: The test specimen is rigidly mounted in a precision centrifuge, with the measured axis parallel to the axis of action of the centrifugal acceleration. Set the centrifuge input rate points, maintaining each rate point for 30 seconds. During the test, record the accelerometer output for 20 seconds 5 seconds after reaching each acceleration point. This is used to calculate the average accelerometer output acceleration at each input acceleration point.

[0094] Compensation algorithms, including:

[0095] Fit a straight line least squares to the accelerometer input and output (x, y):

[0096] y=K·y (1) ·x+B (2)

[0097] Where: x is the theoretical value of the input acceleration, g; y is the output value of the accelerometer that has been calibrated at room temperature, g; K is the linear term coefficient obtained by fitting, g / g; B is the constant term coefficient obtained by fitting, g.

[0098] Compensate the accelerometer output according to the parameters obtained by straight line fitting:

[0099]

[0100] Where y is the output of the accelerometer after room temperature calibration, in g; y1 is the output of the accelerometer after compensation using the linear fitting parameters, in g; K is the linear term coefficient obtained by fitting, in g / g; and B is the constant term coefficient obtained by fitting, in g.

[0101] Calculate the current straight line fitting error:

[0102] Δ=y1-y (1) ·x (4)

[0103] Where: x is the theoretical value of input acceleration, g; y1 is the accelerometer output after linear fitting, g; y (1) is the theoretical output value of +1g / -1g after the accelerometer that has been calibrated at room temperature is installed in the centrifuge, g / g; Δ is the linear fitting error, g.

[0104] The error Δ is fitted with the accelerometer output y1 after the straight line fitting using a third-order polynomial fit (y1, Δ):

[0105] Δ=ay1 3 +by1 2 +cy1+d (5)

[0106] Where: Δ is the linear fitting error, g; y1 is the accelerometer output after linear fitting, g; a is the cubic coefficient obtained by third-order polynomial fitting, g / g 3 ; b is the quadratic term coefficient obtained by fitting the third-order polynomial, g / g 2 ; c is the coefficient of the linear term obtained by fitting the third-order polynomial, g / g; d is the coefficient of the constant term obtained by fitting the third-order polynomial, g.

[0107] Final compensation result:

[0108] y=y1-Δ (6)

[0109] The compensation results are verified according to this compensation algorithm and the indicators are calculated.

[0110] The scale factor nonlinearity indicator is calculated as the error between the output value and the least squares fitted straight line divided by the range.

[0111] The calculation method of the relative error of the scale factor is shown in the following formula.

[0112]

[0113] Where: g n is the specified acceleration, g; A n For the device at a given g n A0 is the value measured by the device when g=0, g; A1 is the value measured by the device when g=1, g.

[0114] 01 type accelerometer scale factor nonlinearity compensation, including:

[0115] The nominal value of the nonlinear index of the original scale factor of the 01 type accelerometer is 1.3%.

[0116] According to the original data of the centrifugal calibration test, when the absolute value of the acceleration of the 01 type accelerometer is less than 9g, the error is extremely small and the linearity is good, so the third-order fitting compensation of the error is no longer required; when the absolute value of the acceleration is greater than 9g, nonlinear compensation is performed according to this method.

[0117] The verification results statistics of the 42 test products of the S1 batch of Type 01 accelerometers are shown in the figure below.

[0118] like Figure 2 As shown in the figure, the statistical diagram of the relative error of the accelerometer verification of the S1 batch of test products of type 01 accelerometer.

[0119] This verification was performed after re-disassembly and reassembly. The Y-axis showed the best overall calculation results, with nonlinearity less than 200ppm. The calculation results of individual test product indicators on the X and Z axes were outside the indicator envelope of this batch, but the nonlinearity was less than 350ppm.

[0120] Nonlinear compensation of scale factor of 02 type accelerometer

[0121] The nominal value of the original scale factor nonlinearity of the 02 accelerometer is ±0.25% (@±200g). The actual test value is >1% (@±50g).

[0122] During calibration and verification testing of six Type 02 accelerometers in batch S1, nonlinearity compensation results were calculated. The scale factor nonlinearity within 50g was <1500ppm, and the relative error was <1000ppm. The results are shown in Table 1 below.

[0123] Table 102 accelerometer 50g internal index calculation results statistics

[0124]

[0125] Batch test methods, including:

[0126] During the mass production of accelerometers, it is difficult to ensure that the installation radius and installation error of each test piece on each test centrifuge are completely consistent when testing multiple units in a batch. As a result, the actual input acceleration of each test piece under the same angular velocity input to the centrifuge has different deviations. After calibration using a fixed value [0,1,3,5…]g as the input value, the relative error of the scale factor calculated based on the ±1g output value is large, making it difficult to meet the high technical indicator requirements.

[0127] The test method of the present invention is changed to use the output value of the current 1g input point to reversely calculate the actual installation radius of each unit during data processing, and calibrate the actual input acceleration value of each test product according to the installation radius of each unit. This can achieve that the accelerometer data with different installation radii in the same test can all be used for accurate compensation, realize a group of multiple tests, save the number of tests, and improve batch production efficiency.

[0128] The optimized compensation algorithm eliminates the need for precise calibration before each batch test. The output of the test product at 1g input is guaranteed to be within ±1% of 1g, and the mounting radius deviation is ±1% for the same accelerometer dimensions and fixture installation conditions. Furthermore, according to Equation 1, other input points, such as 5g, 10g, and so on, can be multiplied by √5, √10, and so on, by the 1g rate point to obtain the corresponding input rate point. Formulas are pre-set using an Excel spreadsheet, and production test personnel automatically generate all input angular rates by pulling down and filling in the formula. Before each test, simply modify the rate value corresponding to 1g for each mounting orientation. For example, the table below shows this. For the same test product model with the same mounting method (same fixture, same axial direction), radius calculations do not need to be recalculated. Even if the mounting arrangement changes, calibration calculations and verification only need to be performed during the first test.

[0129] Theoretical input value 1g 5g 10g 15g …… Corresponding centrifuge speed a √5*a √10*a √15*a …… Theoretical input value -1g -5g -10g -15g …… Corresponding centrifuge speed b √5*b √10*b √15*b ……

[0130] Research on accelerometer combinations under different usage requirements:

[0131] According to the compensation test method, the nonlinear index of the scale factor of the MEMS accelerometer can be effectively improved, so that the accelerometer with lower cost can reach a higher index level.

[0132] Practical verification results confirm that the scale factor nonlinearity of the Type 01 accelerometer is superior to that of the Type 02 accelerometer, both before and after compensation. Furthermore, the Type 01 accelerometer's zero-bias-related indicators are superior to those of the Type 02 accelerometer. The Type 01 accelerometer has a range of ±40g, while the Type 02 accelerometer has a maximum range of ±200g.

[0133] For some larger range usage requirements, accelerometers with different characteristics can be combined to take advantage of their respective strengths. For example, the combination of type 01 accelerometer and type 02 accelerometer: the type 01 accelerometer can ensure that the indicators within a relatively small range are better, and the type 02 accelerometer can be used to meet the large range requirements and maintain a certain accuracy.

[0134] The switching rules between the two sets of accelerometers are:

[0135] 1. The default setting is 01 type accelerometer.

[0136] 2. The X, Y, and Z axes are judged separately. If the current accelerometer combination output uses the 01-type accelerometer data, it will switch to the 02-type accelerometer when the 01-type accelerometer output is greater than 38g;

[0137] 3. The X, Y, and Z axes are judged separately. If the current accelerometer combination output uses the 02-type accelerometer data, it will switch to the 01-type accelerometer when the 02-type accelerometer output is less than 36g.

[0138] Staggering the switching points can avoid data anomalies when the accelerometer is near the switching point.

[0139] The design calculates the deviation value of the current two sets of accelerometers as the offset of the accelerometer to be switched during switching, and deducts it to avoid the accelerometer combination output data jumping at the switching point. However, due to the large noise of the 02 type accelerometer, the instantaneous data error is large, or the deduction leads to a larger overall offset of the output value, such as Figure 3 shown.

[0140] Figure 3 The black line inserted in the middle is the data continued according to the output value of the type 01 accelerometer before switching. It can be seen that the data has an obvious offset after switching to the type 02 accelerometer. After about 63,700 data points, it is the stable input holding time of the centrifuge. The stable input value is 40g, and the actual calculated average output is about 40.2g.

[0141] The actual accelerometer combination is changed to a test in which both accelerometers are compensated independently. The target values ​​are both input values. When the compensation is normal, both accelerometers are close to the input value and no obvious jump occurs. The accelerometer combination no longer deducts the offset.

[0142] In actual testing, when the installation error of the accelerometer combination meets the requirements, there is no obvious offset when the accelerometer is switched.

[0143] Complete the design and implementation of an accelerometer combination with a range greater than 40g, low cost, and excellent technical indicators.

[0144] Parametric batch consistency studies, including:

[0145] Use the test parameters of the S1 batch of test products of type 01 accelerometers and the S1 batch of test products of type 02 accelerometers to find the optimal intermediate value as the fixed parameter verification.

[0146] Parameters and theoretical compensation values ​​are shown in the table below.

[0147] Compensation parameters and theoretical compensation difference table of 01 type accelerometer X axis

[0148]

[0149]

[0150]

[0151]

[0152]

[0153] Compensation parameters and theoretical compensation difference table of y-axis of 01 type accelerometer

[0154]

[0155]

[0156]

[0157]

[0158] Compensation parameters and theoretical compensation difference table of type 01 accelerometer z axis

[0159]

[0160]

[0161]

[0162]

[0163] It is found that there are certain regularities between different parameters:

[0164] The larger the linear fitting parameter K is, the larger the third-order fitting parameter a is and the smaller c is;

[0165] The larger the straight-line fitting parameter B is, the larger the third-order fitting parameter b is and the smaller d is. The straight-line fitting constant term B with a large numerical deviation is close to the opposite number of the third-order fitting constant term d, and the data with opposite signs are similar.

[0166] For a test product in this batch whose single parameter is extremely large or extremely small, the comprehensive compensation value of the entire set of parameters is not necessarily the maximum or minimum value.

[0167] The above analysis shows that calculating the average value of a single parameter as the typical value is not the optimal solution. Finally, the parameters K, B, a, b, c, and d and the parameter compensation Δ are sorted separately. After excluding the largest 1 / 3 and the smallest 1 / 3 of each parameter and the overall compensation value, the remaining test product parameters are obtained.

[0168] The X, Y, and Z axes of the same three-axis MEMS accelerometer are unrelated. Only the most typical axis in the statistical table of each axis is taken as the unit of axis. Finally, the parameters of 01-035X, 01-035Y, and 01-025Z are selected as the fixed parameters of the 01 type accelerometer for verification.

[0169] Six products with the largest difference between the theoretically calculated compensation values ​​and the individual parameters were selected for testing. The actual verification showed that the nonlinearity of the 40g internal scale factor of the Type 01 accelerometer was less than 600ppm, and the relative errors were all less than 1000ppm, which was close to the theoretical error calculation results.

[0170] Analyze the test parameters of the S1 batch 02 accelerometer test product and find the optimal intermediate value as the fixed parameter verification. The parameter table is shown below.

[0171] Type 02 accelerometer X-axis compensation parameter table and theoretical compensation difference table

[0172]

[0173]

[0174]

[0175]

[0176] Y-axis compensation parameter table and theoretical compensation difference table of type 02 accelerometer

[0177]

[0178]

[0179]

[0180]

[0181]

[0182] Z-axis compensation parameter table and theoretical compensation difference table of type 02 accelerometer

[0183]

[0184]

[0185]

[0186]

[0187] The compensation differences of the 02 accelerometers within the same batch vary greatly, with the maximum difference being about 2.5g @ 50g. It was found that there was no obvious batch consistency of the 02 accelerometers, although there were still certain patterns between different parameters:

[0188] The larger the third-order fitting parameter a is, the smaller c is;

[0189] The larger the third-order fitting parameter b is, the smaller d is;

[0190] The magnitude of the comprehensive compensation error of K, B, a, b, c, and d is inversely proportional to K (since the compensation model is original data / K);

[0191] For a test product in this batch whose single parameter is extremely large or extremely small, the comprehensive compensation value of the entire set of parameters is not necessarily the maximum or minimum value.

[0192] Combined with the above analysis, we believe that the method of calculating the average of a single parameter as a typical value is also inappropriate for this application. Furthermore, the maximum and minimum compensation delta values ​​for a batch of Type 02 accelerometers differed by >1g, exceeding the compensation delta values ​​of some test products. This indicates poor consistency and makes the fixed parameter compensation method unsuitable.

[0193] The X, Y, and Z axes of the same accelerometer combination are unrelated. Only the most typical axis in the statistical table of each axis is taken as the unit of axis. Each parameter a, b, c, d and the compensation value of the entire parameter set are sorted separately. After excluding the largest 1 / 3 and the smallest 1 / 3 of each parameter and the overall compensation value, the remaining test product parameters are verified as fixed parameters.

[0194] Ultimately, the parameters of 01-049X, 01-023Y, and 01-035Z were selected as the fixed parameters for the Type 02 accelerometer for verification. The 50g internal scale factor nonlinearity of the Type 02 accelerometer was verified to be >1% for two Z-axes and 7000 ppm for one Y-axis. The remaining scale factors were nonlinear between 2000 and 7000 ppm, indicating poor batch consistency and general effectiveness of fixed parameter compensation.

[0195] According to experimental verification, MEMS accelerometers with good batch consistency can use fixed parameters for compensation while meeting the index requirements, which greatly saves batch production time; accelerometers with poor batch consistency are not suitable for fixed parameter compensation, but the improved batch calibration compensation test method can still be used to improve the large-scale scale factor nonlinear index and batch compensation test efficiency.

[0196] Beneficial effects: The present invention improves the nonlinearity of the scale factor of a large-scale combination of MEMS accelerometers and improves the efficiency of batch testing.

[0197] The above specific implementation methods further illustrate the objectives, technical solutions and beneficial effects of the present invention in detail. It should be understood that the above are only specific implementation methods of the present invention and are not intended to limit the scope of protection of the present invention. Any modifications, equivalent substitutions, improvements, etc. made within the spirit and principles of the present invention should be included in the scope of protection of the present invention.

Claims

1. A batch compensation test method for scale factor nonlinearity of MEMS accelerometers, characterized in that: The test method includes: Establish nonlinear mathematical model of accelerometer; Design acceleration test batch test method to conduct batch nonlinear calibration test; Establish compensation parameter model and calculate various parameters of nonlinear calibration through compensation test data; Carry out batch compensation verification tests according to the various parameters mentioned; Analyze parameter consistency and confirm the feasibility of fixed parameter compensation in the same batch.

2. A MEMS accelerometer scale factor nonlinearity batch compensation test method according to claim 1, characterized in that: The establishment of the nonlinear mathematical model of the accelerometer specifically includes: Accelerometer mathematical model: Where: A ind is the acceleration value indicated by the instrument, g; a i ,a o ,a p are the accelerations along the input reference axis, output reference axis, and pendulum reference axis of the accelerometer, respectively, in g; E is the output of the accelerometer, in mA, V, 1 / s, and LSB; K0 is the bias value, in g; K1 is the scale factor, in mA / g, V / g, (1 / s) / g, and LSB / g; K2 is the second-order nonlinear coefficient, in g / g 2 ; K3 is the third-order nonlinear coefficient, g / g 3 ;K ip ,K io is the cross-coupling coefficient, g / g 2 ; δ o ,δ p are the misalignment angles of the input shaft relative to the input reference axis around the output shaft and the pendulum axis, rad; The simplified nonlinear mathematical model of the accelerometer is: Where: A ind is the acceleration value indicated by the instrument, g; a i is the acceleration along the accelerometer input reference axis, g; E is the accelerometer output, mA, V, 1 / s, LSB; K0 is the bias, g; K1 is the scale factor, mA / g, V / g, (1 / s) / g, LSB / g; K2 is the second-order nonlinear coefficient, g / g 2 ; K3 is the third-order nonlinear coefficient, g / g 3 .

3. The method for batch compensation of MEMS accelerometer scale factor nonlinearity according to claim 1, characterized in that: The establishment of the compensation parameter model specifically includes: Based on the nonlinear model of the accelerometer, a compensation parameter model is established, and the various parameters of the nonlinear calibration are calculated using the calibration test data; Fit a straight line least squares to the accelerometer input and output (x, y): y=K·y (1) ·x+B (2) Where x is the theoretical value of input acceleration, g; y is the output value of the accelerometer that has been calibrated at room temperature, g; y (1) is the theoretical output value of +1g / -1g after the accelerometer that has been calibrated at room temperature is installed in the centrifuge, g / g; K is the linear term coefficient obtained by fitting, g / g; B is the constant term coefficient obtained by fitting, g; Compensate the accelerometer output according to the parameters obtained by straight line fitting: Where: y is the output of the accelerometer after room temperature calibration, g; y1 is the output of the accelerometer after compensation using the linear fitting parameters, g; K is the linear term coefficient obtained by fitting, g / g; B is the constant term coefficient obtained by fitting, g; Calculate the current straight line fitting error: Δ=y1-y (1) ·x(4) Where: x is the theoretical value of input acceleration, g; y1 is the accelerometer output after linear fitting, g; y (1) is the theoretical output value of +1g / -1g after the accelerometer that has been calibrated at room temperature is installed in the centrifuge, g / g; Δ is the linear fitting error, g; The error Δ is fitted with the accelerometer output y1 after the straight line fitting using a third-order polynomial fit (y1, Δ): Δ=ay1 3 +by1 2 +cy1+d (5) Where Δ is the linear fitting error, g; y1 is the accelerometer output after linear fitting, g; a is the cubic coefficient obtained by third-order polynomial fitting, g / g 3 ; b is the quadratic term coefficient obtained by fitting the third-order polynomial, g / g 2 ; c is the linear term coefficient obtained by third-order polynomial fitting, g / g; d is the constant term coefficient obtained by third-order polynomial fitting, g; Final compensation result: y = y1 - Δ (6).

4. The method for batch compensation of MEMS accelerometer scale factor nonlinearity according to claim 1, characterized in that: The batch calibration test method of the designed acceleration test batch test method specifically includes: Design the acceleration test batch calibration test method based on the working principle of the centrifuge to carry out batch nonlinear calibration test; The principle of centrifuge calibration test is to use the principle of Newtonian mechanics to generate standard centripetal acceleration through angular motion; The formula for calculating centripetal acceleration is: a = ω 2 *r (1) Where: a is the centripetal acceleration, g; ω is the angular velocity of the centrifuge, rad / s; r is the working radius of the centrifuge, m; The working radius of a centrifuge is the distance from the centrifuge's average center of gyration to the accelerometer's detection center. Since the accelerometer's detection center is inside the accelerometer, the distance between the accelerometer mounting slot on the centrifuge equipment and the center of the centrifuge table is not equal to the distance between the accelerometer's detection centers. Therefore, there is an error in the detection center of each accelerometer. In the centrifugal test of the accelerometer, the accelerometer output ±1g after the ±1g calibration is completed is used for calibration. After the calibration is completed, the centrifuge setting angular velocity value corresponding to each input acceleration value is calculated based on the actual working radius r for centrifugal test; The optimized compensation method uses the output value of the 1g input point to reversely calculate the actual installation radius of each accelerometer's detection center during data processing, and calibrates the actual input acceleration value of each test product according to each installation radius. According to the optimized compensation algorithm, batch testing does not require test personnel to perform precise calibration before each test. The fixed distance between the accelerometer mounting slot and the mean rotation center is used as the batch test working radius to ensure that the test product output is within 1g±1% when the input is 1g. For accelerometers with the same dimensions and tooling installation conditions, the working radius shall be calibrated only during the first test, and the result shall be used as the working radius for batch tests. For accelerometers with the same dimensions and tooling installation conditions, the installation radius deviation shall be within ±1%. Data collection for scale factor nonlinear batch calibration tests: The test specimen is rigidly mounted on a precision centrifuge, with the measured axis parallel to the axis of centrifugal acceleration. Centrifuge input rate points are set, each held for 30 seconds. During the test, the accelerometer output is recorded for 20 seconds 5 seconds after reaching each acceleration point. This is used to calculate the average output acceleration of the accelerometer at each input acceleration point. The calibration test data is processed using a data processing program, and various parameters are calculated according to the compensation parameter model algorithm.

5. A MEMS accelerometer scale factor nonlinearity batch compensation test method according to claim 4, characterized in that: The accelerometer centrifugal test method is to use the accelerometer that has been calibrated to ±1g to output ±1g for calibration, specifically including: Install the accelerometer on a three-axis turntable and complete the six-position calibration test on the turntable to obtain the ±1g accelerometer scale factor value and complete the ±1g calibration; Then install the accelerometer on the centrifuge and set a fixed angular velocity value ω1. Use the output value a1 of the accelerometer at this time and ω1 to reversely calculate the radius r, and use r to calculate the angular velocity value ω2 corresponding to the centripetal acceleration of 1g. Set the centrifuge input to ω2 and verify the calibration result based on whether the accelerometer output value a2 is 1g. If the calibration result deviates significantly from 1g, continue to backcalculate the radius r using the accelerometer output value a2 and ω2 until the calibration is successful.

6. The method for batch compensation of MEMS accelerometer scale factor nonlinearity according to claim 1, characterized in that: The batch compensation verification test according to the parameters specifically includes: Calculate various compensation parameters according to the compensation parameter model algorithm and write them into the test product; Verification data collection: The test sample is rigidly mounted on a precision centrifuge, with the measured axis of the test sample parallel to the axis of action of the centrifugal acceleration; Conduct verification tests according to this compensation test method and calculate indicators based on the output values ​​of the verification test accelerometer, including: The nonlinearity index of the scale factor is calculated as the error between the output value and the least squares fitted straight line divided by the range; The calculation formula of the scale factor nonlinear relative error is: Where: g n is the specified acceleration g, g; A n For the device at a given g n A0 is the value measured by the device when g=0, g; A1 is the value measured by the device when g=1, g.

7. The method for batch compensation of MEMS accelerometer scale factor nonlinearity according to claim 1, characterized in that: The batch compensation test according to the parameters specifically includes: During data processing, the output value of the current 1g input point is used to reversely calculate the actual installation radius of each unit; The actual input acceleration value of each test product is calibrated according to the installation radius of each unit, so that the accelerometer data with different installation radius in the same test can be used for accurate compensation, realizing a group of multiple tests.

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