首先,设计齿廓、齿向修形曲线,经过3次B样条拟合为拓扑修形曲面,并与理论齿面叠加设计修形齿面;其次,根据成形磨削过程中砂轮与齿轮之间的运动关系,推导成形砂轮与齿面的接触条件方程,计算砂轮的廓形点,再通过3次B样条拟合得到精确的砂轮轴向廓形曲线;然后,建立成形砂轮磨削斜齿轮5轴联动Free-Form型数控磨齿机模型,根据砂轮位矢的等效转换,推导各轴运动关系;接着,建立基于数控机床各轴敏感性分析的齿面修正模型,用6阶多项式表示各轴的运动,判断砂轮与齿面的接触状态,确定磨削齿面的误差,并分析各系数扰动对齿面误差的影响;最后,以齿面误差平方和最小为目标函数,通过粒子群优化方法,得到机床运动参数.结果表明,以齿廓修形齿面反算砂轮截形进行5轴数控成形磨齿加工,可有效降低磨削误差.
In this paper,first,a modified tooth surface was represented by a sum of two vector functions that determined the theoretical tooth surface and the deviation surface,which was fitted by B-spline based on the tooth surface grid established by a profile and a longitudinal deviation curve.Next,according to the motion relationship between the grinding wheel and the gear in the grinding process of helical gear,the wheel is formulated as B-spline curves using a curve fitting technique by deducing the meshing equations.Then,a model of five-axis Free-Form CNC grinding machine was established and the kinematic relationships among the axes were derived based on the equivalence of wheel position vector.Moreover,an error correction model based on a sensitivity analysis was put forward,and each axis of the grinding machine was formulated as a six-order polynomial,and then a sensitivity analysis of disturbed polynomial coefficients on the topographic flank errors was carried out by estimating the wheel contact status.Finally,by using the minimum squared error as the objective function,kinematic parameters of the machine tool are obtained via the PSO optimization.The results show that the five-axis CNC grinding machining,which is based on the back calculation of grinding wheel section with modified tooth surface,decreases the grinding error effectively.