Abstract: It was difficult to achieve high-precision machining of internal beveloid gears with standard shaper cutters by inclining the shaper-arbor with respect to the gear axis or slotting angle optimization method. A design method of special gear shaper cutters was proposed for precision machining internal beveloid gears. The tooth profile equation of the gear shaper cutters included both of geometric parameters of the cutters and the slotting angles. The tool profile equations were derived based on the meshing principle, the mathematical models of the gear shapers were established, and the parameter optimization processes of the shaper cutters were given. The profile errors of different machining methods were compared and analyzed, and the influences of design parameter changes on profile errors were studied. The results show that the proposed method may effectively reduce the tooth profile errors under various design parameters, and the designed cutters may achieve the precision machining of internal beveloid gears by linear slotting according to the optimal slotting angle, without the needs to transform the machine tool, which is easy to promote.

Key words: internal beveloid gear, shaper cutter, profile error, involute

摘要： 针对标准插齿刀通过斜插法或插削角优化法难以实现变齿厚内齿轮高精度加工的问题，提出了一种精密加工变齿厚内齿轮的专用插齿刀设计方法。该插齿刀齿廓方程同时包含刀具几何参数和插削角工艺参数。基于啮合原理推导了刀具齿廓方程，建立了插齿刀切削刃数学模型，给出了插齿刀切削刃参数优化流程。对比分析了不同加工方法的齿形误差，研究了设计参数变化对齿形误差的影响规律。结果表明,所提出的方法在各种设计参数下均能有效减小齿形误差，设计出的刀具按优化倾角做直线插削即可实现变齿厚内齿轮的精密加工，无需对机床进行改造，易于推广。

关键词: 变齿厚内齿轮, 插齿刀, 齿形误差, 渐开线