According to the principle of the transformation from the summary of traditional-cradle machine tool to the one of free-form machine tool-assuring the orientation between the cutter axis and the work-piece axis during the process, axis-motion formulas in the form of polynomial for free-form machine tool were fitted with the least square method. The procedure was accomplished via exemplifying No. 116 gear generator for traditional-cradle machine tool, and deducing the coordinate transformation matrixes under these two kinds of machine tool. Correctness of the procedure is validated by an example, which shows that the coordinate transformation matrixes under these two kinds of machine tool coincide, the distance between the tooth surface virtually manufactured by axis-motion formulas in the software of CATIA and the theoretical points lies in the range from Omm to 0.009mm, and the distance can be controlled to a smaller one. The influence of axis-motion error on tooth-surface error was investigated, and axis B was found to be the one influencing tooth surface most significantly. This partially provides theoretical basis for improving the manufacturing accuracy of free-form machine tool.%以No.116铣齿机为例,通过推导传统摇台型机床、Free-form型机床中的坐标变换矩阵,根据运动等效转换的原则,应用最小二乘优化原理,用多项式拟合出Free-form型机床各轴的运动方程.通过算例分析,传统摇台型机床与Free-form型机床中的坐标变换矩阵高度吻合,用各轴运动方程在CATIA软件中虚拟加工出的螺旋锥齿轮齿面与理论齿面上的点的距离在0.009mm以内,且该值可控制在0.00001mm以内,验证了该转换方法的正确性.在此基础上,分析了Free-form型机床各轴运动误差对齿面误差的影响,发现B轴为对齿面影响最大的轴,为提高Free-form型机床的制造精度提供了部分理论依据.
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