一种半球谐振陀螺谐振子动力学建模方法

摘要

The accurate and complete dynamic model for the hemispherical shell resonator is the basis of error analysis of the Hemispherical Resonator Gyro (HRG).A dynamic modeling method for the hemispherical shell resonator is proposed based on the thin shell theory of elasticity.First,the deformation geometry equation for the hemispherical shell resonator is derived based on the elasticity geometry equation for the thin shell.Second,based on the improvement of calculation accuracy of force analysis,the physical equation for the hemispherical shell resonator is developed.After an analysis of the force equilibrium relationship for the middle surface of the resonator,the equilibrium differential equation for the resonator is obtained.Finally,based on the above dynamic analysis of the whole resonator,the dynamic equation for the resonator is established.After an analysis of the external load forms of the resonator,the second-order resonant dynamic model for the resonator is obtained by using the Bubnov-Galerkin method,and the expressions for the proportion coefficients and second-order resonant frequency of the resonator are also obtained.Comparison shows that the calculation results are consistent with the measured data,proving the accuracy of the dynamic model proposed.%准确完备的半球谐振陀螺(HRG)谐振子动力学模型是陀螺误差分析的基础.为建立半球壳谐振子动力学模型,基于弹性力学薄壳理论,提出了一种谐振子动力学建模方法.首先,在薄壳的弹性力学几何方程基础上,推导了半球壳谐振子的变形几何方程.其次,在提高受力分析计算精度的基础上,推导了半球壳谐振子的物理方程.然后,分析了谐振子中面的受力平衡关系,推导了谐振子的平衡微分方程.最后,基于以上对整个谐振子的动力学分析,建立了谐振子动力学方程.根据谐振子的不同外载荷形式,利用布勃诺夫-伽辽金法求解得到谐振子2阶谐振状态动力学模型,并得到了谐振子比例系数和2阶谐振频率的表达式.通过对比验证可以看出,参数计算值与实测数据结果一致,证明了所建立的动力学模型的准确性.