A Novel Method for Measuring Three-Axis Dynamic Centrifugal Acceleration Field: the Matrix Transformation Method

Abstract When a three-axis dynamic centrifuge is used to test the performance of inertial equipment (accelerometer, gyroscope, gyro-accelerometer, etc.), accurate estimating of the acceleration at the sensing position of the tested sensors is a key step. To solve the problem of the lack of relevant suitable methods, first, the principle of rigid body kinematics is used to prove that the acceleration of each point on a rigid body changes linearly with respect to the position. Subsequently, a matrix transformation method for accurately measuring the acceleration field on the three-axis dynamic centrifuge is presented. In this method, the distribution law (expressed by a 3×3 matrix) of the acceleration field is calculated based on the measured acceleration at multiple positions. After that the acceleration estimation value at any point on the centrifuge can be calculated. Finally, the uncertainty of the estimated acceleration value is analysed, and a verification experiment is carried out. The results show that the accuracy of this method is mainly limited by the accuracy of the acceleration measurements. The preliminary verification experiment system shows that the mean deviation of the estimated value error obtained by this method is less than 0.024 g, the standard uncertainty is less than 0.015 g, the left and right endpoints of the 95% probability inclusion interval are less than -0.026 g and 0.036 g, respectively, and the half width of the interval is less than 0.028 g. In all, this paper provides a powerful tool for examining the precision performance of inertial equipment on a three-axis dynamic centrifuge, and can also be used for calibration of this kind of centrifuge.