Transmission accuracy reliability analysis and parameter optimization of RV reducer considering cycloid gear wear

doi:10.3785/j.issn.1006-754X.2022.00.081

Chin J Eng Design

2022, Vol. 29

Issue (6): 739-747 DOI: 10.3785/j.issn.1006-754X.2022.00.081

Design for Quality

Transmission accuracy reliability analysis and parameter optimization of RV reducer considering cycloid gear wear

Jiang LIU¹(

),Zheng-ming XIAO¹(

),Long-long ZHANG¹,Wei-biao LIU²

^1.School of Mechanical and Electrical Engineering, Kunming University of Science and Technology, Kunming 650500, China
^2.Yunnan Kunming Iron & Steel Heavy Equipment Manufacturing Group Co. , Ltd. , Kunming 650501, China

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Abstract

In view of the problem that the transmission accuracy of RV (rotate vector) reducer decreased due to the wear of its parts in the working process, a dynamic reliability model of the transmission accuracy of RV reducer considering the wear of cycloid wheel was established, the reliability of transmission accuracy was analyzed, and the tolerance of key parts and the modification parameters of cycloid wheel were optimized. Taking a heavy-load RV reducer as the research object, the wear depth of cycloidal gear was calculated by using Archard wear formula, the distribution of gear tooth profile wear was analyzed, and the wear amount was predicted by using Gaussian process regression model based on numerical simulation data; the reliability model of RV reducer transmission accuracy with dynamic wear was established, and its dynamic reliability was solved by Monte Carlo method; an optimization model was established with the dynamic reliability of transmission accuracy as the constraint condition, the minimum machining cost and the minimum maximum wear in the rated life cycle as the optimization objectives, and the optimal solution was obtained adopting multi-objective genetic algorithm. The results showed that after optimization, the wear of cycloidal gear was slightly increased, and the machining cost of reducer was obviously reduced; the reliability of transmission accuracy of the reducer had been significantly improved, and the reliability within the rated life of 6 000 h met expected requirements. The research results can provide reference for the design of high-precision RV reducer.

Key words： RV (rotate vector) reducer cycloidal gear wear transmission accuracy dynamic reliability multi-objective optimization

Received: 25 February 2022 Published: 06 January 2023

CLC:

TH 132.46

Corresponding Authors: Zheng-ming XIAO E-mail: 1695898727@qq.com;suzem@sina.com

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Cite this article:

Jiang LIU,Zheng-ming XIAO,Long-long ZHANG,Wei-biao LIU. Transmission accuracy reliability analysis and parameter optimization of RV reducer considering cycloid gear wear. Chin J Eng Design, 2022, 29(6): 739-747.

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https://www.zjujournals.com/gcsjxb/10.3785/j.issn.1006-754X.2022.00.081 OR https://www.zjujournals.com/gcsjxb/Y2022/V29/I6/739

考虑摆线轮磨损的RV减速器传动精度可靠性分析与参数优化

针对RV （rotate vector）减速器在工作过程中存在的零件磨损导致传动精度下降的问题，建立了考虑摆线轮磨损的RV减速器传动精度动态可靠性模型，进行传动精度可靠性分析，并对关键零件的公差以及摆线轮的修形参数进行优化设计。以某重载RV减速器为研究对象，利用Archard磨损公式对摆线轮的磨损深度进行计算，分析轮齿齿廓磨损的分布情况，并基于数值仿真数据利用高斯过程回归模型预测磨损量；建立了含动态磨损的RV减速器传动精度可靠性模型，用蒙特卡洛法求解其动态可靠度；建立了以传动精度动态可靠度为约束条件，以加工成本最低、额定寿命周期内最大磨损量最小为优化目标的优化模型，采用多目标遗传算法求得最优解。结果表明；优化后摆线轮的磨损量略微增大，而减速器的加工成本明显降低；优化后减速器传动精度可靠度得到明显提高，在额定寿命6 000 h内的可靠度满足预期要求。研究结果可以为高精度RV减速器的设计提供参考。

关键词： RV （rotate vector）减速器, 摆线轮磨损, 传动精度, 动态可靠度, 多目标优化

Table 1 Parameters of a RV reducer

Fig.1 Force on cycloidal gear with different modification amount

Fig.2 Wear amount of cycloidal gear with different modification amount

Fig.3 Comparison between simulation value and prediction value of cycloidal gear wear

序号 $j$	误差因素	法向侧隙	灵敏度指数
1	公法线平均长度偏差 $E w$	$- E w ① c o s θ$	-0.037
2	齿圈径向跳动误差 $Δ f r$	$2 Δ f r t a n θ$	0.025
3	中心距误差 $Δ f a$	$2 Δ f a t a n θ$	0.025
4	等距修形量Δr_rp	$2 Δ r r p$	1.56
5	移距修形量Δr_p	$- 2 Δ r p 1 - K 12$	-1
6	针齿中心圆半径误差 $δ r p$	$2 δ r p 1 - K 12$	1
7	针齿半径误差 $δ r r p$	$- 2 δ r r p$	-1.56
8	针齿销孔配合间隙 $δ J$	$δ J$	0.78
9	摆线轮齿圈径向圆跳动误差 $Δ F r$	$12 Δ F r$	0.39
10	针齿销孔圆周位置度 $δ t$	$2 K 1 δ t$	1.20
11	摆线轮齿廓累积误差 $F p k$	$- K 1 F p k$	-0.60
12	等距修形误差 $δ Δ r r p$	$2 δ Δ r r p$	1.56
13	移距修形误差 $δ Δ r p$	$- 2 δ Δ r p 1 - K 12$	-1
14	偏心距误差 $δ a$	$2 k n δ a$ ^②	0.00016
15	摆线轮齿廓磨损 $δ w$	$2 δ w$	1.56
16	曲柄轴承间隙 $Δ r$	$Δ r$	1.06

Table 2 Normal backlash caused by RV reducer error factor and sensitivity index of each error

参数	数值	分布特征	参数	数值	分布特征
$E w$	$- 0.049 - 0.086$	正态	$δ t$	±0.005	正态
$Δ f r$	0.014	瑞利	$F p k$	0.015	正态
$Δ f a$	±0.01	正态	$δ Δ r r p$	±0.001	正态
$δ r p$	±0.0025	正态	$δ Δ r p$	±0.002	正态
$δ r r p$	$- 0.0075 ? - 0.0087$	正态	$δ a$	±0.002	正态
$δ J$	$+ 0.010 ? + 0.005$	正态	$Δ r$	$+ 0.004 ? + 0.001$	正态
$Δ F r$	0.009	瑞利

Table 3 Deviation value and distribution characteristics of error term of RV reducer

Fig.4 Backlash simulation diagram of RV reducer

Fig.5 Variation curve of accuracy reliability of RV reducer with working time

参数	下限值	上限值	参数	下限值	上限值
$Δ r r p$	-0.053	0.011	$Δ F r$	0.009	0.0017
$Δ r p$	-0.057	0.007	$δ t$	0.005	0.009
$δ r p$	0.0025	0.005	$F p k$	0.015	0.030
$δ r r p$	-0.010	-0.006	$δ Δ r r p$	0.001	0.003
$δ J$	0.005	0.020	$δ Δ r p$	0.001	0.003

Table 4 Value range of optimization parameters of RV reducer

Fig.6 Pareto frontal solution set for multi-objective optimization of RV reducer

参数	优化1	优化2	参数	优化1	优化2
$Δ r r p$	-0.028 7	-0.034 7	$Δ F r$	0.014 5	0.012 3
$Δ r p$	-0.032 7	-0.038 7	$δ t$	±0.008 5	±0.007 9
$δ r p$	±0.004 5	±0.004 1	$F p k$	0.027 3	0.028 1
$δ r r p$	-0.006 2 -0.008 2	-0.007 3 -0.008 4	$δ Δ r r p$	±0.002 8	±0.002 6
$δ J$	+0.013 0 +0.005 5	+0.015 1 +0.007 1	$δ Δ r p$	±0.002 9	±0.002 7

Table 5 Parameters of RV reducer after optimization

Fig.7 Comparison of transmission accuracy reliability of RV reducer before and after optimization


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