中文摘要：

基于ZK蜗杆的齿廓方程，建立了齿廓测量误差的数学模型．在蜗杆参数确定的情况下，齿廓测量误差Z是测头偏置量yo的函数，给出了ZK蜗杆齿廓测量误差曲线，并研究了该曲线的特点．同时研究了在不同模数、头数和分度圆直径下测头偏置量对齿廓测量误差的影响规律．根据测量仪器精度确定原则，可以由被测蜗杆的精度等级来确定允许的测头最大偏置量．最后研究了齿廓近似测量的原理误差，举例说明了齿廓近似测量的可行性，对ZK蜗杆齿廓精密测量具有指导意义．

英文摘要：

Based on a tooth profile equation for DIN standard ZK type worm gears, a mathematical model of tooth profile measurement errors was established. Given the worm parameters, error measuring the tooth profile, or fz, is the function of probe offset value y0. A curve for tooth profile measuring error was derived and its properties were studied. At the same time, the influence of the probe＇s offset on tooth profile measuring error was analyzed, using different modules, numbers of threads, and pitch circle diameters. According to the principles determining device precision, the maximal probe offset value was defined by precision of worm measurement . Finally, the principle error in a tooth profile＇s approximate measurement was analyzed, and an example was given to explain the feasibility of improving a tooth profile＇s approximate measurement. The study can provide guidance for more precise measurements of the tooth profiles of ZK type worm gears.