安装误差对直齿标准齿轮螺旋线偏差的影响规律

在齿轮螺旋线的实际测量过程中, 不同轮齿的螺旋线倾斜偏差经常会出现较大差异。为提高齿轮螺旋线偏差的测量精度, 分别研究了芯轴和齿轮安装误差对齿轮螺旋线偏差的影响规律。首先分别建立了芯轴安装偏心和倾斜误差及齿轮安装偏心和偏摆误差对齿轮螺旋线形状偏差和倾斜偏差影响的数学模型, 然后制作了平垫圈(1#、4#)和楔角误差分别5.5 μm/45 mm(2#)和11.9 μm/45 mm (3#)的楔形垫圈, 用于进行齿轮螺旋线偏差的精密测试实验。得到如下结果: 采用2#楔形垫圈时, 螺旋线倾斜偏差fHβ的最大值与理论模型相差0.17 μm, 相对误差为7%; 采用3#楔形垫圈时, 螺旋线倾斜偏差fHβ的最大值与理论模型相差0.06 μm, 相对误差为1%; 而两次试验中齿轮螺旋线的形状偏差ffβ基本不变。实验结果表明: 齿轮安装偏摆误差对螺旋线偏差的实测结果与理论值基本吻合, 从而验证了所建数学模型的准确性。依据本文所建螺旋线的数学模型, 得到通过调整齿轮安装偏摆误差补偿各齿轮螺旋线倾斜偏差差异的误差补偿方法。本文研究对于研制高精度标准齿轮具有重要研究意义。

Abstract

In the measurement practice of gear helix deviation, there is phenomenon that big difference often appears between helix deviations for different gear teeth. In order to improve the measurement accuracy of gear helix deviation, influence laws of installation error of mandrel and gear on gear helix deviation were respectively researched. Firstly, mathematical models of influences of mandrel installation eccentricity and tilt error as well as gear installation eccentricity and deflection error on gear helix deviation were respectively established. Then precision test experiment of gear helix deviation was conducted by using manufactured flat washer (1#, 4#) and tilt washers with tilt errors respectively of 5.5 μm/45 mm (2#) and 11.9 μm/45 mm (3#). The following result was achieved: the difference of maximum for helix slope deviation fHβ and theoretical model was 0.17 μm and relative error was 7% to adopt 2# tilt washer; the difference of maximum for helix slope deviation fHβ and theoretical model was 0.06μm and relative error was 1% to adopt 3# tilt washer; while shape deviation ffβ of gear helix was basically fixed in the two tests. Experimental result indicates that measured result of deflection error of gear installation on helix deviation is basically the same as theoretical value to verify accuracy of established mathematical model. Error compensation method of compensating helix slope deviation difference through adjusting deflection error of gear installation according to established mathematical model is proposed, which is of important research meaning to develop high precision gear artifact.

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安装误差对直齿标准齿轮螺旋线偏差的影响规律

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