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为了研究半球谐振子环向密度分布不均匀对输出精度的影响,首先推导了位置激励表达式,利用解微分方程的布勃诺夫-加廖尔金法建立了谐振子环向密度分布不均匀的动力学方程,然后根据动力学方程并利用平均值法推导了含有密度四次谐波误差的短时间内的漂移模型,最后根据Runge-Kutta法对系统长时间漂移进行了仿真计算,通过计算可知当密度四次谐波幅值为0.0001 kg/m3时,角位置1h内的漂移达到0.03°,因此在加工工艺过程中密度四次谐波应小于此值或采用其他方式加以补偿。
In order to study the effect of the uneven distribution of the ring-direction density of the hemispherical resonator on the output accuracy, the position excitation expression is deduced firstly. By using the method of Burinoff-Gavlel method for solving the differential equation, the power density of the resonator ring is unevenly distributed Then based on the kinetic equation and using the mean method, the drift model with the fourth harmonic error of density is deduced in a short time. Finally, the long-time drift of the system is simulated by Runge-Kutta method. Density of the fourth harmonic amplitude of 0.0001 kg / m3, the angular position of the drift within 1h reached 0.03 °, so the density of the fourth harmonic in the processing process should be less than this value or by other means to be compensated.