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，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 deter-mined the theoretical tooth surface and the deviation surface,which was fitted by B- spline based on the tooth sur-face grid established by a profile and a longitudinal deviation curve.Next,according to the motion relationship be-tween the grinding wheel and the gear in the grinding process of helical gear,the wheel is formulated as B- splinecurves using a curve fitting technique by deducing the meshing equations.Then,a model of five- axis Free- FormCNC grinding machine was established and the kinematic relationships among the axes were derived based on the e-quivalence of wheel position vector.Moreover,an error correction model based on a sensitivity analysis was put for-ward,and each axis of the grinding machine was formulated as a six- order polynomial,and then a sensitivity analy-sis of disturbed polynomial coefficients on the topographic flank errors was carried out by estimating the wheel con-tact status.Finally,by using the minimum squared error as the objective function,kinematic parameters of the ma-chine 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 grindingerror effectively.