中文摘要：

根据面齿轮、圆柱齿轮及蜗杆砂轮三者同时啮合的原理，推导面齿轮磨削用蜗杆砂轮的齿面方程。基于某型5轴数控机床模型，建立利用标准双锥面金刚滚轮修整蜗杆砂轮曲面的非线性接触方程。通过分解砂轮修整过程，将砂轮曲面的5坐标修整运动转化为一系列的3坐标连续运动。依据面齿轮与蜗杆砂轮间的共轭关系，导出面齿轮齿面偏差的砂轮修整补偿计算公式。试验表明，采用该方法磨削面齿轮其齿形偏差与齿距偏差能够达到国标GB11365—89中规定相同尺寸锥齿轮的6级精度水平。另外，该方法减少了同时联动的数控轴数，从而降低了对机床的数控精度要求。

英文摘要：

The tooth surface equations of the grinding worm are deduced according to the principle of meshing simultaneously of the surfaces of face gear, spur gear and worm grinding wheel. A set of nonlinear contact equations is established for dressing grinding worm with standard double cone dressing wheel based on a kind of 5-axis CNC machine tools. The complicated dressing process for grinding worm with 5 coordinates is transformed into a series of motion with only 3 coordinates, through decomposition for the process. The compensation calculation formula for dressing grinding wheel is derived, based on the conjugate relationship of face gear and the worm grinding wheel. The experiment proves that the tooth profile deviation and pitch deviation of face gear grinded by this method can reach level 6 precision in China standard GBl1365-89 for the same size of bevel gear. In addition, this method reduces the number of simultaneous linkage CNC axis, which reduces accuracy requirement for the numerical control of the machine tool.