Reliability assessment method for RV reducers considering probability-interval hybrid uncertainties

doi:10.3785/j.issn.1006-754X.2026.05.192

Chinese Journal of Engineering Design

2026, Vol. 33

Issue (2): 265-274 DOI: 10.3785/j.issn.1006-754X.2026.05.192

Reliability and Quality Design

Reliability assessment method for RV reducers considering probability-interval hybrid uncertainties

Hongjuan XIE¹(

),Huajin LEI²,Jia WANG¹

^1.School of Electrical Engineering, Hebei University of Technology, Tianjin 300401, China
^2.Aerospace Life-Support Industries Ltd. , Aviation Industry Corporation of China, Xiangyang 441003, China

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Abstract

RV (rotate vector) reducers are widely used in complex mechanical systems such as robots. Their reliability directly affects the performance and service life of the entire system, and reliability assessment serves as a crucial foundation for reliability design and optimization. Currently, the reliability assessment for RV reducers is usually based on probability theory. However, due to the complexity of mechanical systems and the multiple sources of factors influencing reliability, it is difficult to obtain the probability distributions of all uncertain factors in practical engineering. Relying solely on probability theory makes it hard to ensure the accuracy of reliability assessment results. To address this issue, the probability-interval hybrid uncertainty theory was innovatively introduced into the reliability assessment of RV reducers. Based on the stress-strength interference theory, the multi-component failure criteria for RV reducers were established, and a new reliability assessment method for RV reducers was proposed. Specifically, a double-layer nested loop solution framework was established to solve the problem of probability-interval hybrid reliability calculation. To tackle the low efficiency of multi-dimensional hybrid reliability calculation, the modified chaos control method and the multiplicative dimensionality reduction method were respectively adopted to improve the solution efficiency of probabilistic reliability and interval uncertainty. The results of numerical examples showed that the characterization method of uncertain factors had a significant impact on the reliability assessment results. Using probability-interval hybrid uncertain parameters to describe the uncertain factors was more in line with the actual service reliability of RV reducers. The proposed method provides a new approach for the reliability evaluation of RV reducers, which can offer valuable support for the reliability design and optimization of complex equipment.

Key words： RV (rotate vector) reducer hybrid uncertainty reliability assessment failure criterion

Received: 10 September 2025 Published: 28 April 2026

CLC:

TH 132.46

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Hongjuan XIE,Huajin LEI,Jia WANG. Reliability assessment method for RV reducers considering probability-interval hybrid uncertainties. Chinese Journal of Engineering Design, 2026, 33(2): 265-274.

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https://www.zjujournals.com/gcsjxb/10.3785/j.issn.1006-754X.2026.05.192 OR https://www.zjujournals.com/gcsjxb/Y2026/V33/I2/265

考虑概率-区间混合不确定性的RV减速器可靠性评估方法

RV（rotate vector，旋转矢量）减速器广泛应用于机器人等复杂机械系统，其可靠性直接影响整机性能和使用寿命，而可靠性评估是可靠性设计与优化的重要基础。目前，RV减速器的可靠性评估通常基于概率理论。但由于机械系统的复杂性以及可靠性影响因素的多源性，在实际工程中很难获取所有不确定因素的概率分布，单纯基于概率理论难以保证可靠性评估结果的准确性。为此，创新性地将概率-区间混合不确定性理论引入RV减速器的可靠性评估中，并基于应力-强度干涉理论构建RV减速器的多部件失效准则，从而提出了一种新的RV减速器可靠性评估方法。其中，针对概率-区间混合可靠性计算问题，建立了一种双层嵌套循环求解框架；针对多维混合可靠性计算效率低的问题，分别基于修正混沌控制方法和乘法降维法，提高了概率可靠性和区间不确定性的求解效率。算例结果表明，不确定因素表征方式对可靠性评估结果存在显著影响，采用概率-区间混合不确定参量描述可靠性影响因素，更符合RV减速器服役可靠性的实际情况。所提出的方法为RV减速器的可靠性评估提供了新思路，这可为复杂装备的可靠性设计与优化提供有力支撑。

关键词： RV（rotate vector）减速器, 混合不确定性, 可靠性评估, 失效准则

Fig.1 Schematic diagram of RV reducer structure

Fig.2 Schematic diagram of limit state function in the two-dimensional plane

Fig.3 Iterative process of different probability-based reliability solving methods

Fig.4 Solution process of probability-interval hybrid reliability

Table 1 Values and distributions of relevant parameters used for contact fatigue failure analysis of planetary gear tooth surface

Table 2 Values and distributions of relevant parameters used for bending fatigue failure analysis of planetary gear tooth root

Table 3 Values and distributions of relevant parameters used for contact fatigue failure analysis of cycloidal gear tooth surface

Table 4 Calculation results of maximum failure probability for planetary gear tooth surface contact fatigue based on MCS method

Fig.5 Variation curves of maximum failure probability of planetary gear tooth surface contact fatigue with safety factor

Table 5 Calculation results of maximum failure probability of planetary gear tooth surface contact fatigue under different control parameters

Table 6 Iterative solution numbers of maximum failure probability of planetary gear tooth surface contact fatigue under different control parameters

Fig.6 Variation curves of maximum failure probability of planetary gear tooth root bending fatigue with safety factor

Table 7 Calculation results of maximum failure probability of planetary gear tooth root bending fatigue under different safety factors

Table 8 Iterative solution numbers of maximum failure probability of planetary gear tooth root bending fatigue under different safety factors

Fig.7 Variation curves of maximum failure probability of cycloidal gear tooth surface contact fatigue with safety factor

Table 9 Calculation results of maximum failure probability of cycloidal gear tooth surface contact fatigue under different safety factors

计算方法	初值条件
计算方法	$U 0 = 0.2 I Y 0 = Y c + 0.2 Y r$	$U 0 = - ? 0.2 I Y 0 = Y c - 0.2 Y r$	$U 0 = 0.4 I Y 0 = Y c + 0.4 Y r$	$U 0 = - ? 0.4 I Y 0 = Y c - ? 0.4 Y r$
相对误差/%	1.01	1.01	1.01	1.01
MCS	0.333 95	0.333 95	0.333 95	0.333 95
MCCM-MDRM	0.337 32	0.337 32	0.337 32	0.337 32

Table 10 Calculation results of maximum failure probability of cycloidal gear tooth surface contact fatigue under different initial value conditions


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