Hybrid Time-variant Reliability Analysis of Harmonic Gear Drive Based on Monotonic Function Method
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摘要: 由于数据匮乏与性能退化,谐波减速器的可靠性呈现出显著的概率-区间不确定性混合与时变特征。针对这一问题,提出一种混合时变可靠性分析的单调函数法。首先,基于应力-强度干涉理论构建谐波减速器的混合时变可靠性模型;其次,通过分析可靠性模型动态响应关于时间变量的单调性,以消去时间变量的影响;进一步结合偏导数判断可靠性模型响应关于区间变量的单调性,将概率-区间混合可靠性转换为概率静态可靠性,然后利用蒙特卡罗法求解谐波减速器的可靠度。结果表明:所提方法有效降低了计算复杂性,并准确反映出谐波减速器可靠性的动态变化过程。Abstract: Due to limited data and performance degeneration, the reliability of harmonic gear drive involves probability-interval hybrid uncertainty and has distinct time-variant characteristic. In order to solve these problems more effectively, a monotonic function method (MFM) for hybrid time-variant reliability analysis is proposed. Firstly, hybrid time-variant reliability model of harmonic gear drive is built up with the stress-strength interference theory; secondly, the effect of time is eliminated by analyzing the monotonicity of reliability model dynamic response with respect to time variable; thirdly, the monotonicity of reliability model response about interval variable is judged by partial derivative, and the probability-interval hybrid reliability is transform into the probabilistic time-invariant reliability. Then, the reliability of harmonic gear drive is calculated by Monte Carlo method. Reliability analysis result for an engineering example shows that MFM reduces computational complexity effectively, and reflects reliability dynamic change process of harmonic gear drive accurately.
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Key words:
- harmonic gear drive /
- reliability /
- time-variant /
- hybrid /
- monotonicity /
- uncertainty
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表 1 谐波减速器不确定性变量分布情况
不确定变量 分布类型 参数1 参数2 σ/MPa 区间变量 216 276 K 正态分布 1.0×10-7 1.0×10-8 E1/MPa 正态分布 209 000 20 900 υ1 正态分布 0.295 0.029 5 E2/MPa 正态分布 206 000 20 600 υ2 正态分布 0.3 0.03 注: 随机变量, 参数1、2分别对应均值与标准差; 区间变量则分别对应下界和上界。 -
[1] 官浩, 王安宇, 吴鸿涛. 谐波减速器寿命分布可靠性模型[J]. 机械设计与研究, 2016, 32(6): 46-48 https://www.cnki.com.cn/Article/CJFDTOTAL-JSYY201606015.htmGUAN H, WANG A Y, WU H T. Study of life distribution reliability model for harmonic driver[J]. Machine Design and Research, 2016, 32(6): 46-48 (in Chinese) https://www.cnki.com.cn/Article/CJFDTOTAL-JSYY201606015.htm [2] 王俊, 王家序, 程美玲, 等. 空间谐波减速器的可靠性研究[J]. 机械传动, 2013, 37(12): 1-4 https://www.cnki.com.cn/Article/CJFDTOTAL-JXCD201312002.htmWANG J, WANG J X, CHENG M L, et al. Study on the reliability of space harmonic reducer[J]. Journal of Mechanical Transmission, 2013, 37(12): 1-4 (in Chinese) https://www.cnki.com.cn/Article/CJFDTOTAL-JXCD201312002.htm [3] 张金洋, 张建国, 彭文胜, 等. 基于PCE的谐波减速器动态精度不确定性分析[J]. 北京航空航天大学学报, 2018, 44(5): 1056-1065 https://www.cnki.com.cn/Article/CJFDTOTAL-BJHK201805019.htmZHANG J Y, ZHANG J G, PENG W S, et al. Dynamic accuracy uncertainty analysis of harmonic reducer based on PCE[J]. Journal of Beijing University of Aeronautics and Astronautics, 2018, 44(5): 1056-1065 (in Chinese) https://www.cnki.com.cn/Article/CJFDTOTAL-BJHK201805019.htm [4] 马天政, 秦代成, 张义民. 基于遗传算法的谐波齿轮可靠性优化设计[J]. 工程设计学报, 2011, 18(4): 246-250 doi: 10.3785/j.issn.1006-754X.2011.04.003MA T Z, QIN D C, ZHANG Y M. Reliability-based optimization of harmonic gears using genetic algorithm[J]. Journal of Engineering Design, 2011, 18(4): 246-250 (in Chinese) doi: 10.3785/j.issn.1006-754X.2011.04.003 [5] 孙静怡, 张建国, 彭文胜, 等. 基于区间仿射响应面的非概率可靠性分析[J]. 计算机集成制造系统, 2018, 24(11): 2734-2742 https://www.cnki.com.cn/Article/CJFDTOTAL-JSJJ201811008.htmSUN J Y, ZHANG J G, PENG W S, et al. Non-probabilistic reliability analysis method based on interval affine response surface[J]. Computer Integrated Manufacturing Systems, 2018, 24(11): 2734-2742 (in Chinese) https://www.cnki.com.cn/Article/CJFDTOTAL-JSJJ201811008.htm [6] YANG X F, LIU Y S, GAO Y, et al. An active learning Kriging model for hybrid reliability analysis with both random and interval variables[J]. Structural and Multidisciplinary Optimization, 2015, 51(5): 1003-1016 doi: 10.1007/s00158-014-1189-5 [7] 杜丽, 肖宁聪, 黄洪钟, 等. 认知不确定性的谐波齿轮减速器可靠性分析研究[J]. 电子科技大学学报, 2011, 40(3): 470-475 doi: 10.3969/j.issn.1001-0548.2011.03.028DU L, XIAO N C, HUANG H Z, et al. Reliability analysis approach of harmonic drive under epistemic uncertainty[J]. Journal of University of Electronic Science and Technology of China, 2011, 40(3): 470-475 (in Chinese) doi: 10.3969/j.issn.1001-0548.2011.03.028 [8] ANARIEU-RENAUD C, SUDRET B, LEMAIRE M. The PHI2 method: a way to compute time-variant reliability[J]. Reliability Engineering & System Safety, 2004, 84(1): 75-86 http://www.sciencedirect.com/science/article/pii/S0951832003002321 [9] 高明君, 张国义, 高家一, 等. 基于强度退化的机构模糊动态可靠性分析方法[J]. 强度与环境, 2015, 42(1): 54-62 doi: 10.3969/j.issn.1006-3919.2015.01.008GAO M J, ZHANG G Y, GAO J Y, et al. Fuzzy time-variant reliability analysis method for mechanisms based on strength degradation[J]. Structure & Environment Engineering, 2015, 42(1): 54-62 (in Chinese) doi: 10.3969/j.issn.1006-3919.2015.01.008 [10] ARCHARD J F. Contact and rubbing of flat surfaces[J]. Journal of Applied Physics, 1953;24(8): 981-988 doi: 10.1063/1.1721448 [11] 徐俊杰, 忻展红. 基于两阶段策略的粒子群优化[J]. 北京邮电大学学报, 2007, 30(1): 136-139 doi: 10.3969/j.issn.1007-5321.2007.01.030XU J J, XIN Z H. Particle swarm optimization based on a two-stage strategy[J]. Journal of Beijing University of Posts and Telecommunications, 2007, 30(1): 136-139 (in Chinese) doi: 10.3969/j.issn.1007-5321.2007.01.030