测头半径对 1 级渐开线样板齿廓偏差测量的影响

按齿轮渐开线样板国家标准推荐,1 级齿轮渐开线样板的齿廓形状偏差需从展开长度 3 或 5 mm 开始计值,齿根部非计 值区间对应渐开线弧长仅为 0. 03~ 0. 18 mm,导致 1 级齿轮渐开线样板齿根部的渐开线齿廓难以精确测量。 为了能更好发挥 1 级齿轮渐开线样板的量值精准传递作用,分析了 1 级齿轮渐开线样板结构的特殊性以及测头半径对渐开线齿廓偏差测量结果 的影响,结果表明,在齿根展开角误差时,测头半径引入的测量误差会随着测头半径的增大而增大,并随着展开长度的减小而增 大,在基圆附近的测量误差可以达到齿廓偏差的 50% ~ 200% ;当仅渐开线齿面存在加工误差时,测头半径引入的测量误差和展 开长度受影响的范围会随着测头半径的增大和被测渐开线基圆半径的增大而增大,在齿根部展开长度 10% 的范围内测量误差 约齿廓形状偏差的 10% ~ 60% 。 通过选取测头半径 rp = 0. 5 和 2. 5 mm 的测头对同一齿轮渐开线样板验进行了测量实验验证了 上述结论。 研究为 1 级齿轮渐开线样板的精密制造、精密测量及使用展开长度区间选取提供了支持。

Effect of probe radius on the measurement for profile deviations of class-1 gear involute artefact

The tooth profile form deviation of class-1 gear involute artefact is evaluated from roll path length 3 or 5 mm starting with the base circle according to the Chinese national standard for gear involute artefact. The arc length corresponding to the involute is only 0. 03~ 0. 18 mm, making the root of the involute tooth profile of class-1 gear involute is difficult to be measured. To exploit the accurate transmission of the value with class-1 gear involute artefact better, the special structure of class-1 gear involute artefact and the effect of the probe radius on the measurement results of the involute profile deviation is analyzed. The following conclusions are drawn. Firstly, the measurement error introduced by probe radius increases with increasing probe radius and decreasing rolling length as the rolling angle error at the root of involute is considered, and the measurement error near the base circle can reach 50% ~ 200% of the tooth profile deviation. Secondly as the error in the machining of the involute tooth surface is considered only, the measurement error introduced by probe radius and the affected range of rolling length increases with increasing probe radius and the base radius of the involute being measured, and the measurement error is about 10% ~ 60% of the profile form deviation within the range of 10% of roll path length at the tooth root. The conclusions above are verified by measuring the same gear involute artefact with probe radius rp = 0. 5 and 2. 5 mm. The basis for the ultra-precise manufacture, measurement and the selection of the roll path length to be used of class-1 gear involute artefact is provided.