二维随机载荷作用下疲劳寿命的研究
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摘要
基于Goodman公式和Miner损伤定则,提出了一种考虑载荷均值影响的二维随机载荷作用下疲劳寿命的计算方法。在此基础上以幅值和均值均符合正态分布的随机载荷为研究对象,推导出了其当量载荷的概率密度函数和等效载荷的数学模型,采用Gauss-Legendre求积公式进行积分运算,对该载荷作用下的疲劳寿命进行了研究。分析了等效载荷随载荷均值和幅值不同分布参数变化而变化的规律,并与不考虑载荷均值的一维随机载荷作用下的等效载荷进行了对比。研究结果表明:载荷均值μm的正负变化对等效载荷产生明显的影响,负的μm导致等效载荷降低,甚至低于一维随机载荷作用下的等效载荷;而正的μm会导致等效载荷迅速增大以至到远大于一维随机载荷作用的等效载荷;当μm=0时,二维随机载荷则略高于一维随机载荷作用的等效载荷。
Based on Goodman formula and Miner damage rule,a calculation method of fatigue life was presented under two dimension random stresses considering influences of mean stress.The mathematical models of the probability density function of equivalent stress and the equivalent stress of two dimension random stress were deduced whose mean stress and stress amplitude followed Gaussian distribution.By integrating with Gauss-Legendre integration formula,the fatigue life was studied under the stress.The change regulations of the equivalent stress with the change of the distribution parameters of mean stress and stress amplitude were analyzed.The equivalent stress was compared with that under one dimension random stress not considering influences of mean stress.The results show:with positive and negative direction changing of the mean values of mean stress"μm",the equivalent stress will be influenced obviously.Negativeμm will result in equivalent stress reduction,even less than it under one dimension conditions.Positiveμm will result in rapidly increase of equivalent stress,even greater than it under one dimension conditions.Whenμm =0,the equivalent stress under two dimension is a little more than it under one dimension conditions.
Based on Goodman formula and Miner damage rule,a calculation method of fatigue life was presented under two dimension random stresses considering influences of mean stress.The mathematical models of the probability density function of equivalent stress and the equivalent stress of two dimension random stress were deduced whose mean stress and stress amplitude followed Gaussian distribution.By integrating with Gauss-Legendre integration formula,the fatigue life was studied under the stress.The change regulations of the equivalent stress with the change of the distribution parameters of mean stress and stress amplitude were analyzed.The equivalent stress was compared with that under one dimension random stress not considering influences of mean stress.The results show:with positive and negative direction changing of the mean values of mean stress"μm",the equivalent stress will be influenced obviously.Negativeμm will result in equivalent stress reduction,even less than it under one dimension conditions.Positiveμm will result in rapidly increase of equivalent stress,even greater than it under one dimension conditions.Whenμm =0,the equivalent stress under two dimension is a little more than it under one dimension conditions.
引文
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[2]胡建军,许洪斌,祖世华,等.服从正态分布随机载荷作用下齿轮弯曲疲劳试验研究[J].中国机械工程,2013,24(12):1572-1575.HU Jianjun,XU Hongbin,ZU Shihua,et al.Experimental Study of Gear Bending Fatigue Strength under Random Load with Gaussian Normal Distribution[J].China Mechanical Engineering,2013,24(12):1572-1575.
[3]武滢,谢里阳.随机载荷作用下疲劳寿命分布预测模型[J].工程设计学报,2010,17(6):435-438.WU Ying,XIE Liyang.Prediction on Probability Distribution of Fatigue Life under Spectrum Loading[J].Journal of Engineering Design,2010,17(6):435-438.
[4]郭虎,陈文华,樊晓燕.汽车试验场可靠性试验强化系数的研究[J].机械工程学报,2004,40(10):73-76.GUO Hu,CHEN Wenhua,FAN Xiaoyan.Reseachof Enhancement Coefficient of Automobile Reliability Enhancement Test on Proving Ground[J].Chinese Journal of Mechanical Engineering,2004,40(10):73-76.
[5]王正,王增全,何洪.随机载荷循环作用下的机械结构疲劳寿命预测模型[J].中国机械工程,2012,23(1):98-101.WANG Zheng,WANG Zengquan,HE Hong.Predicting Model for Fatigue Life of Mechanical Structures under Random Cyclic Loads[J].China Mechanical Engineering,2012,23(1):98-101.
[6]陈欣,项昌乐,郑慕侨.车辆传动系多工况随机载荷谱的统计处理方法[J].汽车工程,1999,21(4):232-237.CHEN Xin,XIANG Changle,ZHENG Muqiao.Statistical Methods for Random Load Spectrum of Vehicle Transmission under Multiple Working Conditions[J].Automotive Engineering,1999,21(4):232-237.
[7]SCHIJVE J.Fatigue of Structures and Materials[M].Boston:Kluwer Academic Publishers,2001.
[8]姚卫星.结构疲劳寿命分析[M].北京:国防工业出版社,2003.YAO Weixing.Constructure Fatigue Life Analysis[M].Beijing:National Defence Industry Press,2003.
[9]SURESH S.Fatigue of Materials[M].2nd ed.Cambridg:Cambridge University Press,1998.
[10]徐灏.概率疲劳[M].沈阳:东北大学出版社,1993.XU Hao.Probability Fatigue[M].Shenyang:Dongbei University Press,1993.
[11]郑修麟,王泓,鄢君辉,等.材料疲劳理论与工程应用[M].北京:科学出版社,2013.ZHENG Xiulin,WANG Hong,YAN Junhui,et al.Material Fatigue Theory and Engineering Application[M].Beijing:Science Press,2013.
[12]郑修麟.金属疲劳的定量理论[M].西安:西北工业大学出版社,1994.ZHENG Xiulin.Quantitative Theory of Metal Material[M].Xi’an:Northwest Polytechnical University Press,1994.
[13]郑修麟,凌超,吕宝桐,等.低碳低合金钢及焊接件的寿命估算[J].机械强度,1993,15(3):70-75.ZHENG Xiulin,LING Chao,LYU Baotong,et al.Life Pridiction of Low Carbon Low Alloy Steels and Welded Elements[J].Journal of Mechanical Strength,1993,15(3):70-75.
[14]盛骤,谢式千,潘承毅.概率论与数理统计[M].北京:高等教育出版社,2008.SHENG Zhou,XIE Shiqian,PAN Chengyi.Probability Theory and Mathematical Statistics[M].Beijing:Higher Education Press,2008.
[15]李庆扬,王能超,易大义.数值分析[M].北京:清华大学出版社,2008.LI Qingyang,WANG Nengchao,YI Dayi.Numerical Analysis[M].Bejing:Tsinghua University Press,2008.
[16]张立民.循环加载与随机加载对疲劳损伤等效性的研究[J].强度与环境,1997(3),9-10.ZHANG Limin.Study of Equivalent about Fatigue Damage under Cyclic and Random Load[J].Structure&Environment Engineering,1997(3),9-10.