Research on Accurate Modeling and Test of Geometric Backlash of RV Reducer
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摘要: RV减速器几何回差指单纯由于传动元件的几何尺寸、形状与位置参数原因造成减速器输入轴反向转动时, 输出轴在转角上的滞后量。目前国内外学者研究了各种制造安装误差对几何回差的影响, 设计试验台并进行了试验。但目前对几何回差的研究中没有考虑摆线轮齿廓的修形方法及制造安装误差的方向对几何回差造成的影响, 当计入齿廓修形方法及制造安装误差的方向时, RV减速器的输出轴在不同相位时的几何回差并不相同。本文综合考虑了各零件制造及安装误差的大小及方向, 建立了RV减速器精确的几何回差模型及数学模型, 并对回差进行了仿真及试验。研究结果可用于提高减速器的传动精度, 并为传动系统各零件的公差设计提供依据。Abstract: The geometric backlash of RV reducer is the rotation angle hysteresis of output shaft when the input shaft rotation direction changed, which is caused by transmission element geometry accuracy, shape accuracy and position accuracy. The influence of various manufacturing errors and installation errors on geometric backlash has been studied and tested by many researchers. However, the current research on the geometric backlash does not consider the effect of the modification method of the cycloidal gear tooth profile and the direction of the manufacturing errors and installation errors. In fact, the manufacturing errors and installation errors have directions, and the modification methods are different, the geometrical backlash of the RV reducer is different when the output shaft is in different positions. In this paper, the size and direction of manufacturing errors and installation errors of RV reducer's parts are considered comprehensively, and the accurate geometric backlash model and mathematical model of RV reducer are established, and the geometric hysteresis was simulated and tested. The results can be used to improve the transmission precision of the reducer and provide the basis for the tolerance design of each part of the transmission system.
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Key words:
- RV reducer /
- backlash /
- transmission accuracy /
- cycloid drive
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表 1 减速器参数
参数名称 数值 针齿中心圆直径dp/mm 229 针齿直径drp/mm 10 偏心距a/mm 2.2 摆线轮齿数zc 39 摆线轮宽度/mm 18 中心轮齿数z1 21 行星轮齿数z2 42 渐开线齿轮中心距/mm 63 模数m/mm 2 压力角α/(°) 20 传动比 81 
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表 2 制造及安装误差误差
误差因素 误差/ μm 误差方向/(°) 太阳轮中心安装误差(Esz, βsz) 17 0~360 行星轮中心安装误差(Epzi, βpzi) 17 0~360 齿轮侧隙jct 11 太阳轮径向跳动误差(Est, βst) 21 0~360 行星轮径向跳动误差(Epti, βpti) 21 0~360 针轮齿槽中心圆半径偏差Rk 5 针轮齿槽圆周方向位置度偏差Pk ±5 针轮齿槽半径误差Ck 0~15 针齿半径误差Gk 0~-4 摆线轮修形引起的齿形误差Xk ±4 进刀深误差Sk ±5 分度误差Fk ±5 摆线轮径向跳动误差(Ebtj, βbtj) 6 0~360 摆线轮曲柄轴孔偏心误差(Ehji, βhji) 3 0~360 曲柄轴偏心凸轮的偏心误差(Ecji, βcji) 3 0~360 摆线轮曲柄轴孔轴承间隙u 2 行星架上曲柄轴孔偏心误差(Eai, βai) 3 0~360 行星架的装配误差(Ec, βc) 3 0~360
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表 3 RV减速器实测回差数据
减速器回差 输出轴相位角/(°) 0 30 60 90 120 150 180 210 240 270 300 330 减速器1回差/(′) 0.605 0.61 0.583 0.576 0.593 0.587 0.57 0.581 0.577 0.566 0.584 0.603 减速器2回差/(′) 0.724 0.716 0.744 0.763 0.749 0.751 0.738 0.723 0.712 0.736 0.761 0.754
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