多轴CNC机床运动优化磨齿拓扑修形面齿轮

摘要

To obtain each axis motion of a multi-axis CNC machine for grinding double crowned topological tooth geometry of face gear,a novel methodology of optimum solution for multi-axis motions was proposed by grinding disc wheel application.A theoretical model of face gear grinding with disc grinding wheel was built based on meshing theory.According to the kinematical relations of CNC machine's each axis in the grinding process,a mathematical model of actual tooth flank was established and the initial motion of each axis was obtained.Each axis motion of CNC machine was formulated by six order polynomial function approximately,and an optimization process with the objective function of tooth flank form errors minimization between actual and target tooth flanks was established.By using least squares techniques,the polynomial coefficients of multi-axis motion functions were obtained precisely.The optimization simulation and actual grinding of topological tooth flanks for face gear were developed,and the result showed that the high precision actual tooth gear could be yield by application of optimization method.%为了求解利用碟形砂轮磨齿加工拓扑修形面齿轮CNC数控机床各轴运动参数的问题,提出一种数控机床各轴运动参数的优化求解方法.依据多轴CNC机床碟形砂轮磨齿加工各轴的运动关系,建立了多轴机床磨齿实际拓扑齿面的数学模型;将机床各轴运动表示为联系参数的6阶多项式函数,以各轴运动函数的多项式系数为优化参数,并以齿面目标偏差与实际偏差的误差最小作为评价函数,建立了各轴运动参数的优化模型;利用迭代最小二乘法对模型进行求解,获得加工拓扑修形齿面各轴的运动规律.通过拓扑修形面齿轮加工优化仿真和磨齿试验,实现了高精度拓扑修形面齿轮的数控磨齿,验证了各轴运动参数优化求解的正确性.