石英振梁式重力传感器原理误差模型

Principle error model of quartz vibrating beam gravimeter sensor

为了建立石英振梁式重力传感器原理误差模型,首先,将石英振梁式重力传感器等效成转动惯量-弹性支承-阻尼系统,导出重力加速度作用条件下石英振梁式重力传感器的系统传递函数和输出差动频率公式;其次,导出由于舍掉高次项而产生的谐振频率计算误差公式和由于输出差动频率线性化处理而产生的线性化误差公式;然后,从挠性梁的加工、石英谐振器的加工和质量块的质心偏移3个方面,导出石英振梁式重力传感器加工误差公式;最后,建立石英振梁式重力传感器原理误差模型,并进行了原理误差定量计算.理论分析和原理误差定量计算表明:输出差动频率线性化误差、挠性梁的加工误差和双音叉石英谐振器的加工误差是主要原理误差,谐振频率计算误差和质量块的质心偏移是次要原理误差;石英振梁式重力传感器原理误差的数量级为6×10-7g,可以满足10-6g级的高精度重力测量要求.

The structure of the quartz vibrating beam gravimeter sensor is analyzed and the quartz vibrating beam gravimeter sensor is equivalent to the system of the moment of inertia, the stretch bearing and the damp. The transfer function and the differential frequency formula of the quartz vibrating beam gravimeter sensor under conditions of gravitational acceleration are deduced. The resonance frequency formulae of the error caused by rounding the high order terms and the differential frequency linearization are deduced. The machining error formulae of the quartz vibrating beam gravimeter sensor are deduced from the flexibility beam size, the quartz resonator size, and the mass center offset. Finally the principle error model of the quartz vibrating beam gravimeter sensor is established and the quantitative experiment is carried out. Theoretical analyses and the experimental results indicate that the error of the differential frequency linearization, the machining error of the flexibility beam size, and the quartz resonator size are the main errors, and the errors of resonance frequency calculation and mass center offset are the minor errors. The principle error magnitude is 6 × 10^-7g and the quartz vibrating beam gravimeter sensor satisfies the precise gravity measurement of the grade of 10^-6g.