Probabilistic Fatigue Life Prediction Model for Filled Natural Rubber under Constant Amplitude Loading

doi:10.3969/j.issn.1004-132X.2024.08.004

Abstract

Abstract: A conditional probability distribution model was proposed to quantify the distribution law of rubber fatigue life under arbitrary strain levels. The uniaxial tensile fatigue tests of rubber under different strain levels were carried out. The distribution law of rubber fatigue life was analyzed, and the parameter values of the probability distribution model were determined by a great likelihood estimation method. The least squares method was used to fit the functional relationship between strain level and parameter values of the probability distribution model, and then the conditional probability distribution model was established. The rubber fatigue reliability assessment was carried out, and the rubber P-ε-N model was established. The validity of the rubber P-ε-N model was verified by comparison with the measured lifetimes.

Key words: rubber, fatigue life, probability distribution, P-ε-N model, reliability

摘要： 建立一种条件概率分布模型来描述任意应变水平下的橡胶疲劳寿命分布规律。开展了不同应变水平下的橡胶单轴拉伸疲劳试验，分析了橡胶疲劳寿命的分布规律，并采用极大似然估计法确定了橡胶疲劳寿命概率分布模型的参数值。采用最小二乘法拟合了应变水平与概率分布模型参数值之间的函数关系，并建立了条件概率的分布模型。开展了橡胶疲劳可靠度的评估，建立了橡胶P-ε-N模型，通过与实测寿命的比较，验证了橡胶P-ε-N模型的有效性。

关键词: 橡胶, 疲劳寿命, 概率分布, P-ε-N模型, 可靠度

CLC Number:

TQ333

LIU Xiangnan1, 2, XU Jingwei1. Probabilistic Fatigue Life Prediction Model for Filled Natural Rubber under Constant Amplitude Loading[J]. China Mechanical Engineering, 2024, 35(08): 1366-1372.

刘湘楠1, 2, 许靖伟1. 恒幅载荷下填充天然橡胶概率疲劳寿命预测模型[J]. 中国机械工程, 2024, 35(08): 1366-1372.

References

［1］LIU Xiangnan, ZHAO Xuezhi, LIU Xiaoang, et al. A Load Spectrum Editing Method of Time-frequency for Rubber Isolators Based on the Continuous Wavelet Transform［J］. Measurement, 2022, 198:111374.
［2］段小成, 上官文斌, 王小莉, 等. 变幅载荷下填充型天然橡胶疲劳试验与预测方法研究［J］. 机械工程学报, 2016, 52(14):58-66.
DUAN Xiaocheng, SHANGGUAN Wenbin, WANG Xiaoli, et al. Experiment and Fatigue Life Prediction of Filled Natural Rubber under Variable Amplitude Loading Conditions［J］. Journal of Mechanical Engineering, 2016, 52(14):58-66.
［3］王昊, 危银涛, 王静. 橡胶材料疲劳寿命影响因素及研究方法综述［J］. 橡胶工业, 2020, 67(10):723-735.
WANG Hao, WEI Yintao, WANG Jing. Influencing Factors and Research Methods of Rubber Material Fatigue Life［J］. China Rubber Industry, 2020, 67(10):723-735.
［4］上官文斌, 段小成, 刘泰凯, 等. 不同损伤参量对橡胶隔振器疲劳寿命预测结果影响的研究［J］. 机械工程学报, 2016, 52(2):116-126.
SHANGGUAN Wenbin, DUAN Xiaocheng, LIU Taikai, et al. Study on the Effect of Different Damage Parameters on the Predicting Fatigue Life of Rubber Isolators［J］. Journal of Mechanical Engineering, 2016, 52(2):116-126.
［5］王小莉, 上官文斌, 刘泰凯, 等. 填充橡胶材料单轴拉伸疲劳试验及疲劳寿命模型研究［J］. 机械工程学报, 2013, 49(14):65-73.
WANG Xiaoli, SHANGGUAN Wenbin, LIU Taikai, et al. Experiment of Uniaxial Tension Fatigue and Modeling of Fatigue Life for Filled Natural Rubbers［J］. Journal of Mechanical Engineering, 2013, 49(14):65-73.
［6］丁智平, 陈吉平, 宋传江, 等. 橡胶弹性减振元件疲劳裂纹扩展寿命分析［J］. 机械工程学报, 2010, 46(22):58-64.
DING Zhiping, CHEN Jiping, SONG Chuanjiang, et al. Analysis of Fatigue Crack Growth Life for Rubber Vibration Damper［J］. Journal of Mechanical Engineering, 2010, 46(22):58-64.
［7］王小莉, 上官文斌, 曾祥坤, 等. 基于开裂能密度及裂纹扩展特性的橡胶隔振器疲劳特性预测［J］. 振动与冲击, 2016, 35(6):70-74.
WANG Xiaoli, SHANGGUAN Wenbin, ZENG Xiangkun, et al. A Method to Predict Fatigue Performances of Rubber Isolator Based on the Cracking Energy Density and the Fatigue Crack Growth Characteristic of Rubber Material［J］. Journal of Vibration and Shock, 2016, 35(6):70-74.
［8］LIU Xiangnan, SHANGGUAN Wenbin, ZHAO Xuezhi. ProbabilisticFatigue Life Prediction Model of Natural Rubber Components Based on the Expanded Sample Data［J］. International Journal of Fatigue, 2022, 163:107034.
［9］王小莉, 彭肖阳, 刘湘楠, 等. 防振橡胶材料疲劳寿命可靠性分布模型研究［J］. 机械强度, 2022, 44(6):1335-1342.
WANG Xiaoli, PENG Xiaoyang, LIU Xiangnan, et al. Study on Reliability Distribution Models of Fatigue Life of Anti-vibration Rubber Materials［J］. Journal of Mechanical Strength, 2022, 44(6):1335-1342.
［10］荣继纲, 黄友剑, 卜继玲, 等. 隔振橡胶材料基于简单应变模式的蠕变特性研究［J］. 橡胶工业, 2022, 69(7):506-511.
RONG Jigang, HUANG Youjian, BU Jiling, et al. Research on Creep Characteristic of Damping Rubber Material on Simple Strain Mode［J］. China Rubber Industry, 2022, 69(7):506-511.
［11］LIU Xiangnan, SHANGGUAN Wenbin, ZHAO Xuezhi. Residual Fatigue Life Prediction of Natural Rubber Components under Variable Amplitude Loads［J］. International Journal of Fatigue, 2022, 165:107199.
［12］吕向飞, 黄帅. 考虑应变比影响的车用隔振橡胶疲劳寿命预测方法［J］. 噪声与振动控制, 2021, 41(6):211-214.
LYU Xiangfei, HUANG Shuai. Fatigue Life Prediction Method of Vibration Isolation Rubber for Vehicles Considering the Influence of Strain Ratios［J］. Noise and Vibration Control, 2021, 41(6):211-214.
［13］赵丙峰, 廖鼎, 朱顺鹏, 等. 机械结构概率疲劳寿命预测研究进展［J］. 机械工程学报, 2021, 57(16):173-184.
ZHAO Bingfeng, LIAO Ding, ZHU Shunpeng, et al. Probabilistic Fatigue Life Prediction of Mechanical Structures:State of the Art［J］. Journal of Mechanical Engineering, 2021, 57(16):173-184.
［14］唐圣金, 郭晓松, 周召发, 等. 步进应力加速退化试验的建模与剩余寿命估计［J］. 机械工程学报, 2014, 50(16):33-40.
TANG Shengjin, GUO Xiaosong, ZHOU Zhaofa, et al. Step Stress Accelerated Degradation Process Modeling and Remaining Useful Life Estimation［J］. Journal of Mechanical Engineering, 2014, 50(16):33-40.
［15］GAO Jianxiong, YUAN Yiping, XU Rongxia. A Framework for Fatigue Life Prediction of Materials under the Multi-level Cyclic Loading［J］. Engineering Failure Analysis, 2021, 127:105496.
［16］LIU Xiangnan, ZHAO Xuezhi, LIU Xiaoang. A Unified Probabilistic Fatigue Life Prediction Model for Natural Rubber Components Considering Strain Ratio Effect［J］. Fatigue & Fracture of Engineering Materials & Structures, 2023, 46(4):1473-1487.
［17］刘俭辉, 赵贺, 冉勇, 等. 基于临界面理论的多轴等效应变疲劳寿命预估模型［J］. 中国机械工程, 2022, 33(15):1821-1827.
LIU Jianhui, ZHAO He, RAN Yong, et al. Multiaxial Equivalent Strain Fatigue Life Prediction Model Based on Critical Plane Theory［J］. China Mechanical Engineering, 2022, 33(15):1821-1827.

[1]	ZU Haiying, SUN Jinshan, YE Weidong, LI Daqi. Study on Dynamic Mechanics Characteristics and Fatigue Life Prediction of Single PCPs [J]. China Mechanical Engineering, 2024, 35(08): 1358-1365.
[2]	QI Jinping1, 2, 3, LIU Xiaoyu1, FENG Hong1, LI Hongwei1, YAN Daqiang4. Modeling and Reliability Analysis of Wheel Two-stage Degradation of High-speed Trains [J]. China Mechanical Engineering, 2024, 35(08): 1390-1396.
[3]	. Fatigue Life Prediction of Multiple Unit Axle Considering Wheel Polygon [J]. China Mechanical Engineering, 2024, 35(07): 1299-1307.
[4]	DONG Zhibo1, LI Chengkun1, WANG Chengcheng1, HAN Fang1, ZHANG Zhihang1, TENG Junfei2, LYU Yanlong2. Study on Influence Rules of Residual Stress on Thermal Fatigue Life of GH3230 Laminate Welds [J]. China Mechanical Engineering, 2024, 35(06): 1097-1102.
[5]	SONG Haizheng1, 2, ZHOU Changcong1, 2, LI Lei1, 2, LIN Huagang1, 2, YUE Zhufeng1, 2. An Estimation Method of Failure Probability Function Based on AK-MCS-K [J]. China Mechanical Engineering, 2024, 35(05): 784-791.
[6]	ZHANG Wei1, 2, XIE Jun1, DU Yanbin1, RAN Yan3, ZHANG Genbao3, 4. A Reliability Allocation Method for Meta-action of Mechanical Products Considering Double Uncertainty [J]. China Mechanical Engineering, 2024, 35(05): 802-810.
[7]	FENG Hong1, QI Jinping2, LIU Xiaoyu1, LI Hongwei1, YAN Daqiang3, FU Lusheng3. Reliability Modeling for Multi-correlation Degradation Considering Random Variable Failure Threshold [J]. China Mechanical Engineering, 2024, 35(05): 811-820.
[8]	LI Jian1, 2, WANG Hongwei3, MU Zongyi3, DU Yanbin1, RAN Yan4. Research on Reliability Allocation Method for Mechanical Systems Considering Performance Stability [J]. China Mechanical Engineering, 2024, 35(05): 821-828,850.
[9]	GUAN Cunhe1, 2, XU Gaobin1, 2, JIANG Jingqi1, 2, WANG Huanzhang1, 2, CHEN Xing1, 2, MA Yuanming1, 2 . Reliability Modeling and Analysis of Micro Accelerometers under Multi-load Environments [J]. China Mechanical Engineering, 2024, 35(05): 860-868.
[10]	WANG Zheng, MA Tongling, WANG Bowen, GU Meidan. Heat Exchange Micro-tube Vibration Analysis and Reliability Evaluation Methods for Diaphragm Micro-channel Pre-coolers [J]. China Mechanical Engineering, 2024, 35(05): 869-876,885.
[11]	YAN Lijun1, LI Guangqi1, LIU Qin2, GAO Jingzhou1, SONG Huabin1, LUO Xiaoping1. Research on Reliability-based Design Optimization of Larger-caliber Artillery Ammunition Coordinator Mechanisms [J]. China Mechanical Engineering, 2024, 35(05): 877-885.
[12]	QIAN Ping, CHEN Chi, CHEN Wenhua, WU Shanqi, GUO Mingda. Accelerated Test Verification and Evaluation of Storage Reliability Statistical Model of Polyurethane Sealing Elements for Electrical Connectors [J]. China Mechanical Engineering, 2024, 35(05): 886-894.
[13]	SHEN Minmin, SHI Rui, GUO Pengfei, YANG Yang, YANG Xiaodong, YANG Jihou. Study on Vibration and Fatigue of Distributed Connection Structures of Reusable Aircrafts [J]. China Mechanical Engineering, 2024, 35(01): 45-55.
[14]	GAO Jin, CUI Haibing, FAN Tao, LI Ang, DU Zunfeng. A Structural Reliability Calculation Method Based on Adaptive Kriging Ensemble Model [J]. China Mechanical Engineering, 2024, 35(01): 83-92.
[15]	GOU Ruijie, ZHANG Xiaofeng, ZHANG Hongbin, YAO Jun, LI Xun. Effects of Tool Wear on Milling Surface Integrity and Fatigue Properties of Allvac 718Plus Superalloy [J]. China Mechanical Engineering, 2023, 34(24): 2920-2926.