基于拟蒙特卡罗方法的三维公差综合仿真

Three Dimensional Tolerance Synthesis Simulation Based on Quasi Monte-Carlo Method

针对计算机辅助三维公差综合中蒙特卡罗仿真计算收敛速度慢以及结果不稳定的不足,提出了基于拟蒙特卡罗的三维公差综合仿真方法。在基于旋量参数和旋量矩阵的三维公差表示方法的基础上,利用机器人学中刚体坐标变换及广义逆矩阵的相关知识建立了三维公差综合仿真等式。给出了拟蒙特卡罗方法中采用Halton序列产生正态分布随机数的方法以及基于拟蒙特卡罗的三维公差综合仿真流程。最后,将所提方法应用于齿轮泵装配实例,结果表明,拟蒙特卡罗方法收敛速度快,获得的结果稳定、可靠,可以简单高效地应用于计算机辅助三维公差综合的模拟仿真。

To deal with the disadvantages of low convergence and unstable results of Monte--Carlo method in computer aided 3D tolerance synthesis, a simulation method for computer aided 3D toler- ance synthesis was proposed based on quasi Monte--Carlo method. On the basis of 3D tolerance repre- sentation of the screw parameter and spinor matrix,a 3D tolerance synthesis simulation equation was established using coordinate transform knowledge in robot kinematics of rigid body and the method of generalized inverse matrix. The procedure of generating normal distribution random number with Halton＇s sequence and the process of 3D tolerance synthesis simulation were given. Finally,an engi- neering example,gear pump, was introduced to test the proposed method. The results show that the quasi Monte--Carlo method has higher convergence rate and more stable evaluation results than those of Monte--Carlo method. Therefore, the quasi Monte--Carlo can be applied efficiently to the computer aided 3D tolerance synthesis simulation.