车铣复合机床运动学建模及逆解计算研究

Study on kinematic modeling of turning-milling composite NC machine and inverse calculation

机床的运动学模型建立了刀具和工件之间的运动学关系,是计算机床各轴运动控制指令的基础。文章针对传统的D-H变换法、多体理论在机床运动学建模中存在的问题,提出了基于旋量理论的机床运动学建模。根据TMS-200s型车铣复合机床的结构,求出各轴的运动旋量和指数矩阵,结合刀具和工件运动链,由指数积公式求得运动学正解模型,并基于该模型完成了逆解计算;针对逆解中的多解问题,提出了对称区间与非对称区间,分析了加工中旋转轴所有可能出现的解,并根据相邻行变化角最小的原则,有效地避免了旋转轴转角突变的问题;将2种不同方法计算得到的G代码分别在仿真软件Vericut中对自由曲面进行了模拟加工。仿真结果验证了该运动学模型的正确性和逆解算法的可靠性与必要性。

The kinematic model of NC machine establishes the relationship between the tool and work-piece,and this model is the foundation of calculating the motion control instructions of each axis.This paper proposes the kinematic model of NC machine based on the screw theory,dealing with the problem of using the conventional D-H transformation method and multi-body theory.Firstly,the motion screw of each axis and exponential matrix are obtained based on the structure of TMS-200s turning-milling composite NC machine.Then,combining with the tool and work-piece chain,the forward kinematic model is constructed with the product of exponential formula.The inverse calculation is solved with this model.For the multiple results of the rotary axis,the symmetrical and asymmetrical intervals are proposed,all possible angles of rotary axis are analyzed,then with the principle of the minimum angle change between the adjacent rows,the problem of the angle mutation is effectively avoided.Finally,in order to verify the G codes obtained with two methods,a free-form surface is used to be processed.They are respectively applied in the software Vericut.The simulation results prove the accuracy of the kinematic model and the effectiveness and necessity of the algorithm of inverse calculation.