基于蒙特卡洛法的3D打印机定位精度分析

Analysis of Positioning Accuracy in 3D Printer Based on Monte Carlo Method

为了研究在各种误差源综合作用的条件下,FDM桌面3D打印机挤出机头相对于热床的定位精度情况,通过蒙特卡洛法对其定位精度进行评估。根据多刚体系统理论,建立3D打印机的拓扑结构模型;基于仪器精度理论,对误差向量进行综合分析,分析步进电机在运动过程中,各种误差源在x,y,z方向引入的误差向量,建立3D打印机的误差传递模型;通过蒙特卡洛法对在各种误差源综合作用的情况下打印机挤出机头的定位精度进行仿真计算。结果表明:在置信概率95%情况下,挤出机头相对于热床在x,y,z 3个方向上的定位输出及其扩展不确定度分别为x=(70±0.099)mm,y=(50±0.100)mm,z=(20±0.518)mm。该方法可用于分析影响定位精度的主要因素,进行误差补偿,提高定位精度;也可应用到精密仪器设计中用于精度分配计算,合理分配多刚体结构各环节的精度指标。

In order to study the positioning accuracy of the header of three dimensional （3D） printer with respect to the hot bed in the influence of all errors, a Monte Carlo method was used to evaluate the positioning accuracy. The topological construction model of 3D printer was built according to the multi-body system theory. Based on the instrument precision theory, an integrated error propagation model of the 3D printer was built to analyze the comprehensive effect of the various error sources, the error vector in x, y and z directions during the step motor moving was analyzed. The positioning accuracy of the header with respect to the hot bed was calculated with simulation by Monte Carlo method. The results show that within the believed 95% probability, the position outputs and the expanded uncertainty in x, y and z directions of the printer head with respect to the hot bed were calculated ： x = （70±0. 099） mm, y= （ 50±0. 100） mm, z= （20±0. 518） mm. This method can be used to analyze the main error source which influenced the positioning accuracy, and compensated it so that improving the positioning accuracy of 3D printer. This method can also be used in the precision machine design, to specify subsystem precision requirements to achieve an overall balance in the levels of accuracy index of multi-body rigid structure.