Dynamic reliability analysis of gear transmission system based on sparse grid numerical integration and saddle-point approximation method
Junhua Chen
College of Mechanical Engineering, Nanjing University of Science and Technology, Nanjing, Jiangsu, P.R. China
Search for more papers by this authorCorresponding Author
Longmiao Chen
College of Mechanical Engineering, Nanjing University of Science and Technology, Nanjing, Jiangsu, P.R. China
Correspondence
Longmiao Chen, College of Mechanical Engineering, Nanjing University of Science and Technology, Nanjing, Jiangsu 210000, P.R. China
Email: [email protected]
Search for more papers by this authorLinfang Qian
College of Mechanical Engineering, Nanjing University of Science and Technology, Nanjing, Jiangsu, P.R. China
Northwest Institute of mechanical and electrical engineering, Xianyang, China
Search for more papers by this authorGuangsong Chen
College of Mechanical Engineering, Nanjing University of Science and Technology, Nanjing, Jiangsu, P.R. China
Search for more papers by this authorWei Miao
College of Mechanical Engineering, Nanjing University of Science and Technology, Nanjing, Jiangsu, P.R. China
Search for more papers by this authorJunhua Chen
College of Mechanical Engineering, Nanjing University of Science and Technology, Nanjing, Jiangsu, P.R. China
Search for more papers by this authorCorresponding Author
Longmiao Chen
College of Mechanical Engineering, Nanjing University of Science and Technology, Nanjing, Jiangsu, P.R. China
Correspondence
Longmiao Chen, College of Mechanical Engineering, Nanjing University of Science and Technology, Nanjing, Jiangsu 210000, P.R. China
Email: [email protected]
Search for more papers by this authorLinfang Qian
College of Mechanical Engineering, Nanjing University of Science and Technology, Nanjing, Jiangsu, P.R. China
Northwest Institute of mechanical and electrical engineering, Xianyang, China
Search for more papers by this authorGuangsong Chen
College of Mechanical Engineering, Nanjing University of Science and Technology, Nanjing, Jiangsu, P.R. China
Search for more papers by this authorWei Miao
College of Mechanical Engineering, Nanjing University of Science and Technology, Nanjing, Jiangsu, P.R. China
Search for more papers by this authorAbstract
Gear systems are widely used in various mechanical transmission systems. This paper aims to develop an effective and practical method for dynamic reliability analysis of gear transmission system. The proposed method can comprehensively evaluate the dynamic reliability of gear transmission system by adopting the fourth-moment SPA method. First, a nonlinear dynamics model of a single-stage spur gear transmission system is established, which simultaneously takes into account the nonlinear backlash, time-varying meshing stiffness, and static transmission error. After that, a dynamic reliability model for the tooth surface contact fatigue failure of gear system is established with the uncertainty of the motion, structure, and material parameters using stress-strength interference (SSI) theory. To be specific, the sparse grid numerical integration (SGNI) method is applied to solve the statistical characteristic parameters of the dynamic reliability of the system. The probability distribution of the performance function is obtained with the fourth-moment SPA method. Test examples show that the results of the proposed method are consistent with the results obtained by the Monte Carlo simulation (MCS) and superior to the maximum entropy with fractional moments (ME-FM) method, which verifies the effectiveness of this approach. Finally, the dynamic reliability of the gear transmission system with respect to load times is evaluated.
Open Research
DATA AVAILABILITY STATEMENT
Research data are not shared.
REFERENCES
- 1Sheng RY, Wang Y, Zhang LN. Study on the nonlinear dynamics of a single-stage gear vibro-impact system. Appl Mech Mater. 2014; 697: 161-167. https://doi.org/10.4028/www.scientific.net/amm.697.161
10.4028/www.scientific.net/amm.697.161 Google Scholar
- 2Ma J, Chen G, Ji L, Qian L, Dong S. A general methodology to establish the contact force model for complex contacting surfaces. Mech Syst Signal Process. 2020; 140:106678. https://doi.org/10.1016/j.ymssp.2020.106678
- 3Guerine A, El Hami A. Uncertainty Analysis of One Stage Gear System using Interval Analysis Method. Colloq. Inf. Sci. Technol. Cist; 2017: 670-674. https://doi.org/10.1109/CIST.2016.7804970
- 4Zhou D, Zhang XF, Yang Z, Zhang YM. Vibration reliability analysis on tractive transmission system of shearer. J China Coal Soc. 2015; 40: 2546-2551.
- 5Rice OS. Mathematical analysis of random noise. Bell Syst Tech J. 1994; 23: 282-332.
10.1002/j.1538-7305.1944.tb00874.x Google Scholar
- 6Hmqa B, Tha B, Hzha B. A single-loop strategy for time-variant system reliability analysis under multiple failure modes - Science Direct. Mech Syst Signal Process; 148. n.d.
- 7Hu Z, Du X. Time-dependent reliability analysis with joint upcrossing rates. Struct Multidiscip Optim. 2013; 48: 893-907.
- 8Hu Z, Li H, Du X, Chandrashekhara K. Simulation-based time-dependent reliability analysis for composite hydrokinetic turbine blades. Struct Multidiscip Optim. 2013; 47: 765-781.
- 9Zhang J, Du X. Time-dependent reliability analysis for function generator mechanisms. J Mech Des. 2011; 133.
- 10Wang L, Liu J, Li Y. The optimal controller design framework for PID-based vibration active control systems via non-probabilistic time-dependent reliability measure. ISA Trans. 2020; 105: 129-145. https://doi.org/10.1016/J.ISATRA.2020.06.007
- 11Wang L, Liu J, Yang C, Wu D. A novel interval dynamic reliability computation approach for the risk evaluation of vibration active control systems based on PID controllers. Appl Math Model. 2021; 92: 422-446. https://doi.org/10.1016/J.APM.2020.11.007
- 12Wang L, Liu Y, Liu Y. An inverse method for distributed dynamic load identification of structures with interval uncertainties. Adv Eng Softw. 2019; 131: 77-89. https://doi.org/10.1016/j.advengsoft.2019.02.003
- 13Jiang C, Huang XP, Han X, Zhang DQ. A time-variant reliability analysis method based on stochastic process discretization. J Mech Des. 2014; 136:91009.
- 14Zhang D, Han X, Jiang C, Liu J, Li Q. Time-variant reliability analysis through response surface method. J Mech Des. 2017; 139:41404.
- 15Zhang D, Xu H, Chao J, et al., Time-dependent system reliability analysis method based on the outcrossing rate. 11th Word Congr. Struct. Multidisciplinary Optim. 2015.
- 16Zhang DQ, Han X, Jiang C, Liu J, Long XY. The interval PHI2 analysis method for time-dependent reliability. Sci Sin Astron. 2015; 45:054601.
- 17Deng J, Gu D, Li X, Yue ZQ. Structural reliability analysis for implicit performance functions using artificial neural network. Struct Saf. 2005; 27: 25-48. https://doi.org/10.1016/J.STRUSAFE.2004.03.004
- 18Bosio A, Bernardi P, Ruospo A, Sanchez E, A reliability analysis of a deep neural network. LATS 2019 - 20th IEEE Lat. Am. Test Symp; 2019: 1-6. https://doi.org/10.1109/LATW.2019.8704548
10.1109/LATW.2019.8704548 Google Scholar
- 19Tang J, Qian L, Chen G. A gradient continuous smoothed GFEM for heat transfer and thermoelasticity analyses. Acta Mech. 2021; 2021: 1-29. https://doi.org/10.1007/S00707-021-03018-0
10.1007/S00707?021?03018?0 Google Scholar
- 20Deng C, Miao J, Ma Y, Wei B, Feng Y, Reliability analysis of chatter stability for milling process system with uncertainties based on neural network and fourth moment method. 2019; 58: 2732-2750. https://doi.org/10.1080/00207543.2019.1636327
10.1080/00207543.2019.1636327 Google Scholar
- 21Guo X, Dias D, Carvajal C, Peyras L, Breul P. Reliability analysis of embankment dam sliding stability using the sparse polynomial chaos expansion. Eng Struct. 2018; 174: 295-307. https://doi.org/10.1016/J.ENGSTRUCT.2018.07.053
- 22He W, Hao P, Li G. A novel approach for reliability analysis with correlated variables based on the concepts of entropy and polynomial chaos expansion. Mech Syst Signal Process. 2020; 146. https://doi.org/10.1016/J.YMSSP.2020.106980
- 23Dong S, Ma J, Su Z, Li C. Robust circular marker localization under non-uniform illuminations based on homomorphic filtering. Measurement. 2021; 170:108700. https://doi.org/10.1016/J.MEASUREMENT.2020.108700
- 24Hawchar L, El Soueidy CP, Schoefs F. Principal component analysis and polynomial chaos expansion for time-variant reliability problems. Reliab Eng Syst Saf. 2017; 167: 406-416. https://doi.org/10.1016/J.RESS.2017.06.024
- 25Yun W, Lu Z, Zhou Y, Jiang X. AK-SYSi: an improved adaptive Kriging model for system reliability analysis with multiple failure modes by a refined U learning function. Struct Multidiscip Optim. 2018; 59: 263-278. https://doi.org/10.1007/S00158-018-2067-3
- 26Yang X, Mi C, Deng D, Liu Y. A system reliability analysis method combining active learning Kriging model with adaptive size of candidate points. Struct Multidiscip Optim. 2019; 60: 137-150. https://doi.org/10.1007/S00158-019-02205-X
- 27Qian HM, Huang HZ, Li YF. A novel single-loop procedure for time-variant reliability analysis based on Kriging model. Appl Math Model. 2019; 75: 735-748. https://doi.org/10.1016/J.APM.2019.07.006
- 28Wang Z, Wang P. A new approach for reliability analysis with time-variant performance characteristics. Reliab Eng Syst Saf. 2013; 115: 70-81.
- 29Li M, Bai G, Wang Z. Time-variant reliability-based design optimization using sequential kriging modeling. Struct Multidiscip Optim. 2018; 58: 1051-1065.
- 30Du X. System reliability analysis with saddlepoint approximation. Struct Multidiscip Optim. 2010; 42: 193-208.
- 31Du X. Time-dependent mechanism reliability analysis with envelope functions and first-order approximation. J Mech Des. 2014; 136:81010.
- 32Pandey MD, Zhang X. System reliability analysis of the robotic manipulator with random joint clearances. Mech Mach Theory. 2012; 58: 137-152. https://doi.org/10.1016/J.MECHMACHTHEORY.2012.08.009
- 33Zhang X, Pandey MD. An efficient method for system reliability analysis of planar mechanisms. Proc Inst Mech Eng Part C J Mech Eng Sci. 2013; 227: 373-386. https://doi.org/10.1177/0954406212448341
- 34Zhang X, Pandey MD, Zhang Y. Computationally efficient reliability analysis of mechanisms based on a multiplicative dimensional reduction method. J Mech Des Trans ASME. 2014; 136. https://doi.org/10.1115/1.4026270
- 35Qian H-M, Huang T, Huang H-Z. Time-dependent reliability model of structures under different stochastic loads. ASCE-ASME J Risk Uncert Eng Syst Part B Mech Eng. 2020; 6. https://doi.org/10.1115/1.4045252
10.1115/1.4045252 Google Scholar
- 36Daniels HE. Saddlepoint approximations in statistics. Ann Math Stat. 1954: 631-650.
10.1214/aoms/1177728652 Google Scholar
- 37Du X, Sudjianto A. First order saddlepoint approximation for reliability analysis. AIAA J. 2004; 42: 1199-1207.
10.2514/1.3877 Google Scholar
- 38Du X. Saddlepoint approximation for sequential optimization and reliability analysis. J Mech Des. 2008; 130: 842-849.
- 39Meng D, Huang HZ, Wang Z, Xiao NC, Zhang XL. Mean-value first-order saddlepoint approximation based collaborative optimization for multidisciplinary problems under aleatory uncertainty. J Mech Sci Technol. 2014; 28: 3925-3935.
- 40Guo S. An efficient third-moment saddlepoint approximation for probabilistic uncertainty analysis and reliability evaluation of structures. Appl Math Model. 2014; 38: 221-232.
- 41Lu H, Cao S, Zhu Z, Zhang Y. An improved high order moment-based saddlepoint approximation method for reliability analysis. Appl Math Model. 2020; 82: 836-847. https://doi.org/10.1016/j.apm.2020.02.006
- 42He J, Gao S, Gong J. A sparse grid stochastic collocation method for structural reliability analysis. Struct Saf. 2014; 51: 29-34.
- 43Shui W, Zhonglai M, Debiao. Time-variant reliability assessment for multiple failure modes and temporal parameters. Struct Multidiscip Optim. 2018; 58: 1705-1717.
- 44Smolyak SA. Quadrature and interpolation formulas for tensor products of certain classes of functions. Dokl. Akad. Nauk. Russian Academy of Sciences; 1963: 1042-1045.
- 45Di Z, Xufang Z, Yimin Z. Dynamic reliability analysis for planetary gear system in shearer mechanisms. Mech Mach Theory. 2016; 105: 244-259.
- 46Siyu C, Jinyuan T, Caiwang L, Qibo W. Nonlinear dynamic characteristics of geared rotor bearing systems with dynamic backlash and friction. Mech Mach Theory. 2011; 46: 466-478.
- 47Tobe T, Sato K, Takatsu N. Statistical analysis of dynamic loads on spur gear teeth: experimental study. Bull JSME. 1977; 20: 1315-1320.
10.1299/jsme1958.20.1315 Google Scholar
- 48Dong S, Ma J, Su Z, Li C. Robust circular marker localization under non-uniform illuminations based on homomorphic filtering. Measurement. 2021; 170:108700. https://doi.org/10.1016/j.measurement.2020.108700
- 49Yang J. Vibration analysis on multi-mesh gear-trains under combined deterministic and random excitations. Mech Mach Theory. 2013; 59: 20-33.
- 50 National Gear Standardization Technical Committee. Calculation Methods of Load Capacity for Involute Cylindrical Gears: GB/T 3480-1997. National Gear Standardization Technical Committee; 1997: 29-31.
- 51Ma J, Dong S, Chen G, Peng P, Qian L. A data-driven normal contact force model based on artificial neural network for complex contacting surfaces. Mech Syst Signal Process. 2021; 156:107612.
- 52Runfang L, Zeguang T, Tengjiao L. Numerical simulation for inner dynamic excitation of gearing. J Mech Transm. 2001; 25:.
- 53Pu L, Minggan J. Machine Design. Higher Education Press; 2001.
- 54Kendall MG, Stuart A. The Advanced Theory of Statistics. Distribution Theory; 1977.
- 55Lugannani R, Rice S. Saddle point approximation for the distribution of the sum of independent random variables. Adv Appl Probab. 1980; 12: 475-490.
- 56Gerstner T, Griebel M. Numerical integration using sparse grids. Numer Algorithms. 1998; 18: 209.
- 57Xiong F, Xiong Y, Greene S, Chen W, Yang S, A new sparse grid based method for uncertainty propagation. In: Int. Des. Eng. Tech. Conf. Comput. Inf. Eng. Conf.; 2009: 1205-1215.
- 58Wang Z, Xie L, Li B. Reliability model of failure-dependent system with frequency of loading taken into account. J Northeast Univ Nat Sci. 2007; 28: 704.
- 59Liu X. Research on Dynamic Analysis and Reliability of the Gear Coupled Rotor System with Multi-Parallel Shafts. Northeast University; 2013.
- 60Wang Z, Kang R, Xie L, Failure rate model of components with the number of load application as life parameter. In: 2009 8th Int. Conf. Reliab. Maintainab. Saf., IEEE; 2009: 241-244.
- 61Qi Z, Jing Z, Wu C, Xu Z, Lyu SK. The evaluation of contact fatigue strength for 20MnCr5 carburized gear. Int J Precis Eng Manuf. 2014; 15: 117-121.
- 62Wei S, Han Q, Chu F. Review on research of uncertain dynamics for gear system. J Mech Eng. 2016; 52: 1.
- 63Lee I, Noh Y, Yoo D. A novel second-order reliability method (SORM) using noncentral or generalized chi-squared distributions. J Mech Des Trans ASME. 2012; 134. https://doi.org/10.1115/1.4007391
- 64Huang X, Li Y, Zhang Y, Zhang X. A new direct second-order reliability analysis method. Appl Math Model. 2018; 55. https://doi.org/10.1016/j.apm.2017.10.026
