A high-precision measuring method for acceleration field of dynamic centrifuge

Abstract

The application relates to a high-precision measurement method of an acceleration field of a dynamic centrifuge, and belongs to the technical field of mechanical environment testing and measurement. On the premise that the dynamic centrifuge can be regarded as a rigid body, according to the principle that the acceleration of each point on the rigid body linearly changes with position, the specific coefficient of the linear change can be solved by using the actual measurement values of the accelerations of multiple points on the dynamic centrifuge, so that the acceleration measurement value of a sensitive position of a test piece on the dynamic centrifuge is obtained. The partial derivative analysis of the mathematical formula corresponding to the calculation process can obtain the uncertainty of the measurement value. By using the method, an acceleration field measurement system with simple structure, convenient installation, convenient operation and high precision can be designed, and the high-precision measurement of the acceleration field on various dynamic centrifuges such as single-shaft, double-shaft and three-shaft dynamic centrifuges is suitable.

Description

Technical Field

[0001] This invention belongs to the field of mechanical environment testing and measurement technology, specifically relating to a high-precision method for calculating the acceleration field of a dynamic centrifuge. Background Technology

[0002] Inertial devices such as accelerometers are crucial components of aircraft, and their accuracy significantly impacts the navigation precision of these vehicles. Therefore, in the past, precision centrifuges were used to create high-precision acceleration environments for evaluating these inertial devices. However, considering that precision centrifuges cannot simulate the actual flight acceleration environment—a three-dimensional dynamic acceleration environment—the Institute of Overall Engineering of the China Academy of Engineering Physics developed a triaxial dynamic centrifuge, providing a more realistic flight acceleration environment for evaluating these inertial devices. Currently, this device can generate a three-dimensional dynamic acceleration environment at the device's control point with a loading accuracy of ±0.4g. However, this accuracy is still insufficient for verifying the precision of high-precision accelerometers; furthermore, in experiments, accelerometers and other test pieces cannot be accurately installed at the device's control point. Given the gradient of the acceleration field on the dynamic centrifuge, resulting in different accelerations at different points, the acceleration value at the control point cannot be directly used to represent the acceleration value at the test piece. Therefore, there is an urgent need to develop a high-precision method for calculating the acceleration field on a dynamic centrifuge, so as to obtain a high-precision calculated value of the acceleration at the specimen, and at the same time give the uncertainty of the calculated value, thereby verifying the accuracy performance of inertial devices such as accelerators. In addition, after the development of this method, the acceleration at the control point of the dynamic centrifuge can also be calculated with high precision, thereby realizing the calibration of the equipment and ensuring that the acceleration environmental conditions provided by the dynamic centrifugation test equipment are true and reliable.

[0003] Currently, the general approach to calculating the acceleration field on a dynamic centrifuge is as follows: A mathematical model for acceleration calculation is derived using multi-rigid-body kinematics. Then, the motion parameters and dimensions of each axis of the dynamic centrifuge, as well as the installation position and attitude of the specimen, are measured. Finally, these parameters are input into the mathematical model to calculate the acceleration at the specimen. Because this method relies on various parameters of the dynamic centrifuge, it is simply referred to as the "parametric method."

[0004] When using the parametric method, in order to calculate the acceleration with high accuracy, factors such as the dynamic axial deviation of the centrifuge spindle, the parallelism error between the centrifuge spindle and the outer frame shaft, the perpendicularity error between the outer frame shaft and the inner frame shaft, and the dynamic radius of the centrifuge need to be considered. The functional form of the acceleration expression at the specimen is as follows.

[0005] (1)

[0006] In the formula, These represent the angular velocity and angular acceleration of the main shaft, respectively. These represent the rotation angle, angular velocity, and angular acceleration of the outer frame, respectively. These represent the rotation angle, angular velocity, and angular acceleration of the inner frame, respectively. These represent the position and orientation of the sensitive location of the specimen relative to the center point of the inner frame, respectively, and R represents the static distance (i.e., static radius) of the center point of the inner frame from the main axis. Let R be the change in R during the centrifuge's operation. These represent the dynamic attitude deflections of the main shaft, outer frame shaft, and inner frame shaft during the operation of the centrifuge, respectively. These deflections determine errors such as the dynamic axial deflection of the centrifuge main shaft, the parallelism error between the main shaft and the outer frame shaft, and the perpendicularity error between the outer frame shaft and the inner frame shaft. It is evident that using the parametric method to perform high-precision calculations of acceleration at the specimen presents the following challenges:

[0007] 1) The mathematical modeling is exceptionally complex: there are as many as 22 parameters, which leads to more complex uncertainty analysis formulas;

[0008] 2) Dynamic radius during centrifuge operation Dynamic attitude deflection of each axis High-precision quantitative analysis is difficult to perform in all of them, and they are also difficult to measure due to the lack of measurement benchmarks;

[0009] 3) Specimen installation location ,attitude High-precision measurement values ​​are difficult to obtain due to the lack of measurement benchmarks;

[0010] 4) High-precision measurement of angular velocity and angular acceleration of each shaft is difficult: Considering the installation error of the centrifuge encoder, the encoder scale has a certain degree of non-uniformity, making it difficult to accurately analyze the measurement error of angular velocity and angular acceleration of each shaft. Summary of the Invention

[0011] The purpose of this invention is to provide a high-precision calculation method for the acceleration field of a dynamic centrifuge, which solves the technical problems existing in the prior art. Specifically, when using the parametric method to perform high-precision calculation of the acceleration field on a dynamic centrifuge, the uncertainty analysis faces two major challenges: extremely complex theoretical modeling and extremely high engineering implementation difficulty.

[0012] To achieve the above objectives, the technical solution of the present invention is as follows:

[0013] Assuming the dynamic centrifuge can be considered a rigid body, based on the principle that the acceleration of each point on the rigid body changes linearly with respect to position, the specific coefficient of this linear change can be calculated using the measured acceleration values ​​of multiple points on the dynamic centrifuge, thereby obtaining the measured acceleration value at the sensitive location of the specimen on the dynamic centrifuge; then, by performing partial derivative analysis on the mathematical formula corresponding to this calculation process, the uncertainty of the measured value can be obtained.

[0014] The characteristics of this method are: considering that all types of dynamic centrifuges can be regarded as rigid bodies, this calculation method is applicable to the high-precision calculation of acceleration fields on various types of dynamic centrifuges such as single-axis, dual-axis, and triaxial centrifuges.

[0015] Furthermore, the acceleration at each point on the dynamic centrifuge with respect to position... Linear change can be reduced to the following formula:

[0016] (2)

[0017] In the formula Let M be the acceleration at point M. Let be the acceleration at point 0. This represents the position vector of the sensitive location M of the specimen relative to the sensitive location 0 of the accelerometer. K is the acceleration field distribution coefficient matrix of the rigid body; therefore, K can be calculated by using the measured acceleration values ​​at multiple points on the dynamic centrifuge, and then K can be substituted into equation (2) to obtain the measured acceleration value at any point M on the dynamic centrifuge.

[0018] Furthermore, K is calculated based on the measured acceleration values ​​at multiple points on the dynamic centrifuge; the core algorithm for calculating K is as follows:

[0019] (3)

[0020] (4)

[0021] (5)

[0022] In the formula, In =0, i, j, k, where i, j, k represent the sensitive position measurement results of the accelerometer at positions 0, i, j, and k, respectively. These represent the position vectors from the accelerometer's 0-sensitive position to its i, j, and k-sensitive positions in the block coordinate system f( Figure 1 The projection of the matrix into the coordinate system (o-xyz); the superscript "T" indicates the matrix transpose; the superscript "-1" indicates the matrix inverse. Elements of K;

[0023] Then, based on the position and attitude of the specimen coordinate system s (representing the position and attitude of the sensitive element of the specimen) relative to the f system, the acceleration measurement value at the sensitive position of the specimen can be obtained as follows:

[0024] (6)

[0025] In the formula, This represents the direction cosine matrix from the f-system to the s-system. This indicates the measurement result of accelerometer 0. This represents the position vector of the sensitive location M of the specimen relative to the sensitive location 0 of the accelerometer, i.e., projected onto the f frame; the calculated acceleration value can be seen. Determined by the following measurements:

[0026] 1) The sensitive positions of the accelerometer at 0, i, j, and k are... , , , , , , , , , , , ;

[0027] 2) The sensitive positions of accelerometers 0, i, j, k relative to the f system, i.e., x0, y0, z0, x i y i z i x j y j z j x k y k z k ;

[0028] 3) The position and orientation of the specimen relative to the f system, i.e., x M y M z M θ x θ y θ z .

[0029] Furthermore, an algorithm for solving the uncertainty of acceleration measurements at sensitive locations on a dynamic centrifuge specimen:

[0030] The partial derivative of equation (6) is obtained using numerical methods, i.e.

[0031] (7)

[0032] Thus, by using equations (6) and (7), the effect of each measurement error on the measured acceleration value can be calculated. Influence coefficient Thus, all influence coefficients are obtained. Then, the acceleration measurement value can be obtained. The error calculation formula is as follows:

[0033] (8)

[0034] Taking into account various measurement errors As independent random variables, the acceleration measurement value can be obtained based on the properties of variance. The variance is as follows:

[0035] (9)

[0036] In the formula This represents the variance of the random variable v.

[0037] Furthermore, with multiple accelerometers, the acceleration at sensitive locations on the specimen is measured multiple times, and the optimal measured value of the acceleration is obtained using the basic principles of probability theory.

[0038] With the addition of an accelerometer, using the new accelerometer to... Calculations were performed; for every four additional accelerometers, one more accelerometer can be added. The calculated value;

[0039] Two data points were obtained using two sets of accelerometers (four in each set). Calculated value The variances are respectively ;but The optimal measured values ​​and variances are as follows:

[0040] (10)

[0041] In the formula The proof is as follows:

[0042]

[0043] Therefore hour, The variance of the measured value is minimized. ;

[0044] Similarly, this can be extended to the case of more accelerometers for calculation. The optimal measured values ​​and their variances. For example, n values ​​were obtained using n groups of accelerometers (4 accelerometers per group). Calculated value The variances are respectively The optimal calculated value is obtained by using formula (10) to calculate the first two calculated values. and its variance Then, using formula (10) according to , and , The optimal calculated value can be obtained from the first three calculated values. and its variance ; and so on, it can be seen that by repeatedly using formula (10), the optimal measurement value can be calculated for n sets of accelerometers.

[0045] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0046] One of the advantages of this scheme is that, under the premise that the dynamic centrifuge can be regarded as a rigid body, based on the principle that the acceleration of each point on the rigid body changes linearly with respect to position, the specific coefficient of this linear change can be calculated using the measured acceleration values ​​of multiple points on the dynamic centrifuge, thereby obtaining the measured acceleration values ​​at sensitive locations of the specimen on the dynamic centrifuge. Furthermore, by performing partial derivative analysis on the mathematical formula corresponding to this calculation process, the uncertainty of the measured value can be obtained. Using this method, a simple, easy-to-install, convenient-to-operate, and highly accurate acceleration field measurement system can be designed, suitable for high-precision measurement of acceleration fields on various types of dynamic centrifuges, including single-axis, dual-axis, and triaxial centrifuges. Attached Figure Description

[0047] Figure 1 This is a schematic diagram of a cube and a high-precision accelerometer mounted on it, representing a specific embodiment of the present invention. A coordinate system o-xyz is established on the cube, denoted as the cube coordinate system f. Point M can be any point on the cube and does not necessarily have to be at the position shown in the figure.

[0048] Figure 2 This is a schematic diagram of an acceleration field measurement system according to a specific embodiment of the present invention.

[0049] Among them, 1 is the precision-machined block; 2 is the high-precision accelerometer (4 in total: at 0, i, j, k); 3 is the accelerometer signal line, which needs to be connected to the data acquisition system; 4 is the precision positioning angle on the precision-machined block; and 5 is the block coordinate system f. Detailed Implementation

[0050] The following description, in conjunction with the appendix of the present invention, Figure 1 -Appendix Figure 2 The technical solutions in the embodiments of the present invention are clearly and completely described herein. Obviously, the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative effort are within the scope of protection of the present invention.

[0051] Example:

[0052] Method for calculating acceleration at sensitive locations on the specimen:

[0053] Acceleration of points on a rigid body with respect to position Linear change can be reduced to the following formula:

[0054] (2)

[0055] In the formula Let M be the acceleration at point M. Let be the acceleration at point 0. This represents the position vector of the sensitive location M of the specimen relative to the sensitive location 0 of the accelerometer. Let K be the acceleration field distribution coefficient matrix of the rigid body. Therefore, K can be calculated using the measured acceleration values ​​at four points on the dynamic centrifuge (considered as a rigid body). Then, substituting K into equation (2) will yield the calculated acceleration value at any point M on the dynamic centrifuge. The core algorithm for calculating K is shown in equations (3) to (5).

[0056] (3) (4)

[0057] (5)

[0058] In the formula, In =0, i, j, k, where i, j, k represent the sensitive position measurement results of the accelerometer at positions 0, i, j, and k, respectively. These represent the position vectors from the accelerometer's 0-sensitive position to its i, j, and k-sensitive positions (projected onto the block coordinate system f, i.e., ...). Figure 1 The coordinate system in the matrix is ​​o-xyz; the superscript "T" indicates the matrix transpose; the superscript "-1" indicates the matrix inverse. The elements of K.

[0059] Then, based on the position and attitude of the specimen coordinate system s (representing the position and attitude of the sensitive element of the specimen) relative to the f system, the acceleration measurement value at the sensitive location of the specimen can be obtained as follows:

[0060] (6)

[0061] In the formula, This represents the direction cosine matrix from the f-system to the s-system. This indicates the measurement result of accelerometer 0. This represents the position vector (projected onto the f frame) of the sensitive location M of the specimen relative to the sensitive location 0 of the accelerometer. The calculated acceleration value is visible. The following measurements determine the sensitive positions of the accelerometer: 1) the positions of accelerometer 0, i, j, and k. , , , , , , , , , , , ;2) The sensitive positions of accelerometers 0, i, j, k relative to the f system, i.e., x0, y0, z0, x i y i z i x j y j z j x k y k z k 3) The position and orientation of the specimen relative to the f system, i.e., x M y M z M θ x θ y θ z .

[0062] Uncertainty analysis of acceleration measurement values:

[0063] In order to calculate the acceleration values To analyze the uncertainty, it is necessary to... Take the first-order partial derivative with respect to each measurement value. Considering that formula (6) is too complex ( Since both K and K are 3×3 matrices, and the expression for each element of K is extremely complex, direct partial derivative analysis would yield exceptionally complex formulas. This not only makes it difficult to obtain the correct formulas but also places an excessive workload on computer programming and is prone to errors. Therefore, this patent suggests using numerical methods to calculate partial derivatives, i.e.

[0064] (7)

[0065] Thus, by using equations (6) and (7), the effect of each measurement error on the calculated acceleration value can be determined. Influence coefficient This avoids complex formula derivations and is easy to implement in programming. All influence coefficients are thus obtained. Then, the acceleration measurement value can be obtained. The error calculation formula is as follows:

[0066] (8)

[0067] Taking into account various measurement errors As independent random variables, the acceleration measurement value can be obtained based on the properties of variance. The variance is as follows

[0068] (9)

[0069] In the formula This represents the variance of the random variable v.

[0070] Methods to further improve the accuracy of acceleration measurement:

[0071] The above provides the calculated acceleration values ​​at the specimen location using four accelerometers. And the method for calculating its variance. Considering the appendix... Figure 1 More accelerometers can be placed on the Chinese block, thus enabling the measurement of... Performing multiple calculations and then appropriately processing the calculated values ​​can improve the accuracy of the calculations. This will be explained below.

[0072] With the addition of an accelerometer, the new accelerometer can be used to... Calculations were performed. Each additional four accelerometers would add one [accelerometer / mechanism]. The calculated values. For example, two accelerometers (4 in each group) were used to obtain two... Calculated value The variances are respectively ;but The optimal measured values ​​and variances are respectively

[0073] (10)

[0074] In the formula The proof is as follows:

[0075]

[0076] Therefore hour, The variance of the measured value is minimized. .

[0077] Clearly, this approach can be extended to more accelerometer cases for calculation. The optimal measured values ​​and their variances. For example, n values ​​were obtained using n groups of accelerometers (4 accelerometers per group). Calculated value The variances are respectively The optimal calculated value is obtained by using formula (10) to calculate the first two calculated values. and its variance Then, using formula (10) according to , and , The optimal calculated value can be obtained from the first three calculated values. and its variance ; and so on, it can be seen that by repeatedly using formula (10), the optimal measurement value can be calculated for n sets of accelerometers.

[0078] In summary, the error in the acceleration calculation values ​​obtained by this method is related to the following factors: 1) the uncertainty of the specimen position and attitude measurement values; 2) the uncertainty of the accelerometer measurement results; and 3) the uncertainty of the accelerometer installation position and attitude measurement values. Since these measurement results are all traceable, the uncertainty analysis of this method has a solid foundation.

[0079] In this method, the accelerometer is mounted on a block because the block provides a reference for measuring position and attitude. This not only facilitates the measurement of the accelerometer's mounting position and attitude but also makes it easier to measure the position and attitude of the specimen relative to the block. In fact, this method does not require the accelerometer to be mounted on a block. As long as it is convenient for measuring the position and attitude of the accelerometer and the specimen, the mounting base of the accelerometer can be of other shapes. At that time, this method can be used to perform high-precision calculation of the acceleration at the sensitive element of the specimen (see equations (3) to (6)) and give the uncertainty of the calculated value (see equations (8) and (9)). In addition, the number of accelerometers can be increased so that the acceleration at K and the specimen can be calculated multiple times, thereby improving the calculation accuracy, as shown in equation (10).

[0080] Engineering implementation of this calculation method:

[0081] Appendix Figure 2 Here is an engineering example of this method: 1 is a precision-machined block, 2 is four high-precision accelerometers (located at 0, i, j, and k), 3 is the accelerometer signal cable, which needs to be connected to the data acquisition system, 4 is the precision positioning angle on the precision-machined block for precise accelerometer installation, and 5 is the block coordinate system f. Therefore, this method can be used to design an acceleration field measurement system that is simple in structure, easy to install, convenient to operate, and highly accurate.

[0082] The above are preferred embodiments of the present invention. Any changes made to the technical solution of the present invention that do not exceed the scope of the technical solution of the present invention shall fall within the protection scope of the present invention.

Claims

1. A high-precision method for calculating the acceleration field of a dynamic centrifuge, characterized in that, The distribution law of the acceleration field with respect to position on the dynamic centrifuge is described by the acceleration field distribution coefficient matrix K. Then, the acceleration at the sensitive position of the specimen is inferred from the measured acceleration value at a certain base point. The acceleration of each point on a dynamic centrifuge with respect to position Linear change can be reduced to the following formula: （2） In the formula Let M be the acceleration at point M. Let be the acceleration at point 0. This represents the position vector of the sensitive location M of the specimen relative to the sensitive location 0 of the accelerometer. K is the acceleration field distribution coefficient matrix of the rigid body; therefore, K can be calculated by using the measured acceleration values ​​at multiple points on the dynamic centrifuge, and then K can be substituted into equation (2) to obtain the measured acceleration value at any point M on the dynamic centrifuge. K is calculated based on the measured acceleration values ​​at multiple points on a dynamic centrifuge; the core algorithm for calculating K is as follows: （3） （4） （5） In the formula, In =0, i, j, k, where i, j, k represent the sensitive position measurement results of the accelerometer at positions 0, i, j, and k, respectively. These represent the projections of the position vectors from the accelerometer's 0-sensitive position to its i, j, and k-sensitive positions into the block coordinate system f; the superscript "T" indicates matrix transpose; the superscript "-1" indicates the matrix inverse. The elements of K.

2. The high-precision calculation method for the acceleration field of a dynamic centrifuge as described in claim 1, characterized in that, After obtaining K, the acceleration measurement value at the sensitive location of the specimen is calculated as follows: Based on the position and attitude of the specimen coordinate system s relative to the f system, the acceleration measurement value at the sensitive location of the specimen can be obtained: （6） In the formula, This represents the direction cosine matrix from the f-frame to the s-frame, i.e., projected onto the f-frame; the calculated acceleration values ​​are visible. Determined by the following measurements: 1) The sensitive positions of the accelerometer at 0, i, j, and k are... , , , , , , , , , , , ; 2) The sensitive positions of accelerometers 0, i, j, k relative to the f system, i.e., x0, y0, z0, x i y i z i x j y j z j x k y k z k ; 3) The position and orientation of the specimen relative to the f system, i.e., x M y M z M θ x θ y θ z .

3. The high-precision calculation method for the acceleration field of a dynamic centrifuge as described in claim 2, characterized in that, The algorithm for solving the uncertainty of acceleration measurements at sensitive locations on a specimen in a dynamic centrifuge is as follows: The partial derivative of equation (6) is obtained using numerical methods, i.e. （7） Thus, by using equations (6) and (7), the effect of each measurement error on the measured acceleration value can be calculated. Influence coefficient Thus, all influence coefficients are obtained. Then, the acceleration measurement value can be obtained. The error calculation formula is as follows: （8） Taking into account various measurement errors As independent random variables, the acceleration measurement value can be obtained based on the properties of variance. The variance is as follows: （9） In the formula This represents the variance of the random variable v.

4. The high-precision calculation method for the acceleration field of a dynamic centrifuge as described in claim 3, characterized in that, With multiple accelerometers, the acceleration at the sensitive location of the specimen is measured multiple times, and the optimal measured value of the acceleration is obtained by using the basic principles of probability theory. With the addition of an accelerometer, using the new accelerometer to... Calculations were performed; for every four additional accelerometers, one more accelerometer can be added. The calculated value; Two accelerometers were used to obtain two data points. Calculated value The variances are respectively ;but The optimal measured values ​​and variances are as follows: （10） In the formula The proof is as follows: ； Therefore hour, The variance of the measured value is minimized. ; Similarly, this can be extended to the case of more accelerometers for calculation. The optimal measured value and its variance; n values ​​obtained from n sets of accelerometers. Calculated value The variances are respectively The optimal calculated value is obtained by using formula (10) to calculate the first two calculated values. and its variance Then, using formula (10) according to , and , The optimal calculated value can be obtained from the first three calculated values. and its variance ; and so on, it can be seen that by repeatedly using formula (10), the optimal measurement value can be calculated for n sets of accelerometers.

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