卡尔曼滤波在精密机床装配过程误差状态估计中的应用
Kalman Filter with Applications to Assembly Accuracy State Estimation for Precision Machine Tool

针对精密机床装配偏差控制问题,在借鉴多工位装配中薄壁件装配偏差控制方法的基础上,建立了精密机床装配过程中偏差传递的状态空间模型,并提出了一种利用卡尔曼滤波实现对装配误差进行最优估计的新方法。首先,根据机床结构建立基准传递链,将零件关键特征在基础坐标系中位姿误差定义为状态变量,引入状态空间方程描述装配过程中的偏差传递,实现对装配工艺过程的数学表达。然后,基于状态空间模型,将当前装入零件加工误差作为系统输入误差,以当前装配步的测量结果为观测值,通过卡尔曼滤波计算装配误差最优估计值以及相应协方差矩阵,实现装配过程中装配误差的估计。最后,应用该方法对精密坐标镗床装配过程进行计算,结果表明:与传统公差分析计算方差相比,经过卡尔曼滤波计算得到最终装配状态估计误差的方差减小了63％,说明该方法用于评价装配过程中偏差累积是有效的,能为优化装配工艺和机床装配调整工艺提供有效
In terms of variation control strategy for sheet components assembly, a state space model (SSM) of variation propagation for precision machine tools in assembly process is established and a new method for optimally estimating assembling error by Kalman filter is proposed. Datum flow chain (DFC) of the machine is set up according to the machine topology, and the position and orientation error of key character of the part in DFC is defined as state variable. The SSM is introduced to describe the variation propagation and accumulation of assembly process to acquire the mathematical expression. The optimal estimation and corresponding covariance matrix of assembly error can be calculated by Kalman filter method, which synthesizes the measuring results of current assembly step. The suggested approach is applied to the assembly process in a precision machining center. The results show that the variances of estimation errors at final assembly step are reduced significantly by 63％ using Kalman filter method compared with ones from the traditional tolerance analysis