机械疲劳寿命预测与可靠性设计关键技术研究
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摘要
在汽车、工程机械、矿山机械、特种装备等关乎国计民生的诸多领域，其中机械结构关键零部件的疲劳损伤寿命预测与可靠度计算，多年以来一直是众多专家学者的研究热点。在疲劳损伤寿命预测方面，一般采用Miner准则、Coten-Dolan准则进行；而在可靠性设计方面，则是基于应力-强度理论的传统力学模型。然而，由于损伤模型中经验系数的存在以及传统计算方法的单一性，导致了疲劳寿命与可靠性优化的计算结果与真实值之间的偏离，在实际工作中产生安全隐患。因此，如何提高疲劳寿命预测与可靠性计算结果的准确性，并开展科学合理且有效的研究工作，就显得非常紧迫与必要。
本文追踪国内外的相关研究进展，在Miner准则、Manson准则的基础上，提出了一种基于虚拟区间长度等分的改进疲劳损伤寿命分析模型，并与可靠度的高精求解结合起来，考虑到可靠性稳健元素，通过模糊数学理论和粒子群算法，对系统可靠性的稳健优化设计方法开展进一步研究。研究工作的创新点主要体现在以下方面：
1)提出一种虚拟区间长度等分的疲劳损伤寿命计算模型。在传统Miner准则基础上，将疲劳载荷谱的加载工作应力/区间/频数进行虚拟化等分，建立了一种改进的疲劳损伤模型，并从理论层面证明其疲劳寿命的收敛性。通过与疲劳寿命仿真分析的计算结果比较，说明了虚拟区间长度等分模型计算结果的可信性，有效克服了Miner准则计算公式中经验系数所导致的计算结果不准确性，体现了改进损伤模型的先进与合理。
2)曼森-哈尔福德损伤模型的改进研究。为提高疲劳寿命预测的准确性，对其模型计算公式中的拐点系数与幂指数等经验数据进行研究，探索其对疲劳损伤寿命计算结果的影响，并对其取值范围进行优化与理论研究。研究表明：改进的曼森-哈尔福德模型的疲劳寿命预测结果的准确性得到了提高，但与基于虚拟区间长度等分损伤模型相比较，还存在差距。
3)可靠度高精求解模型与计算方法研究。根据已有的疲劳损伤寿命模型研究成果，在可靠度-应力-寿命（P-S-N）基本理论基础上，考虑到疲劳加载工作应力与强度参数的不确定性，分别建立起基于随机参数概率密度分布的干涉区间积分方法、梯形法则与辛普森法则的三种可靠度计算数学模型，并实现可靠度的高精求解方法研究。结果表明：与传统计算方法比较，有效地提高了可靠度求解的计算精度和效率。
4)基于可靠性的模糊多目标优化设计。在可靠度高精求解方法的基础上，考虑到疲劳工作应力、材料强度等参数的随机性，运用模糊数学的理论与方法，建立起基于可靠性的模糊多目标优化设计数学模型，多目标模糊函数适应值之间采用加权系数进行处理，并对加权系数取值开展了有效地研究。研究成果体现在多目标约束优化中引入了可靠性设计元素，算例表明，研究方法简单、实用，可以直接得到系统设计信息。
5)基于改进粒子群算法（PSO）的可靠性稳健优化。提出了动态加速常数因子和速度自适应因子的两种改进PSO算法，结合可靠性与稳健设计理念，建立多目标的可靠性稳健优化设计数学模型，并实现数值求解。研究成果主要体现在改进的粒子群算法与可靠性稳健设计的有效结合，实现了机械系统可靠性的鲁棒设计。本课题的研究成果，可以很好的应用到车辆、工程机械、矿山装备等关乎国计民生的重大领域之中。应用算例表明，本课题的研究成果，具有较强的工程应用背景。
For many years, Life prediction involving fatigue and reliability assessment ofkey structure parts have been the research hot spot for experts and scholars, in manyfields concerning national welfare and the people's daily life such as automobile,engineering machinery, mining machinery, special equipment, etc. In the research offatigue damage life, computational prediction is usually applied with Miner andCoten-Dolan criteria. In the meanwhile, traditional mechanical models based on thestress-strength principle are used in current researches concerning reliabilitydesign.Nevertheless, due to the applications of experience factors in damage modelsand uniqueness of traditional calculation method, the deviation between the fatiguereliability calculation results and the real value has been resulted. Therefore, how toimprove the accuracy and feasibility of the research about the fatigue prediction andreliability calculation then carry out of the scientific and effective research is veryurgent and necessary.
Based on conclusions of related research at home and abroad, also Miner andManson principle, an improved fatigue life prediction model combined with reliabilitycalculation of high accuracy were proposed and improved concerning robustoptimization design in this paper, through fuzzy mathematics and PSO inconsideration of robust optimization design.
The main innovation points of the work include：
(1) A new fatigue life calculation method has been put forward. Based on theMiner standards, modified fatigue damage model is built by the virtualization toworking stress loading/interval/frequency and the convergence is confirmed throughtheoretical derivations. Compared with simulation analysis results of fatigue life, themain work gives clear evidences to the dependability about the equal classification ofvirtual interval length model. It overcomes the inaccuracy of the calculation due toexperience factors in Miner principle and embodies advances and rationality of themodified model.
(2) The research of the improved Manson-Halford fatigue damage model hasbeen made. To improve the accuracy of fatigue life prediction, the research about theexperience data such as inflection point coefficient and power exponent in the modelis carried out. As a result, the influence of the experience data on the fatigue damagecalculation results is obtained and the value span is dicussed. The research shows that the accuracy of the improved Manson-Halford fatigue damage model is advanced butinferior to which of the equal classification of virtual interval length model.
(3) The research for reliability and high precision mathematic calculation modeland algorithm has been proposed. According to the existing fatigue damage life model,based on reliability-stress-life principle, interference interval integration method,trapezoidal law and the rules of the Simpson three reliability calculation mathematicalmodel are established based on the random parameter probability density distributionconsidering the fatigue loading work stress and the uncertainty of the strengthparameter, then related algorithm about reliability with high accuracy is studied. Theresearch results manifest that the accuracy and efficiency of the new method has beenimproved effectively in comparation with existing methods.
(4) The research of the reliability design based on the fatigue load has been made.With the high accuracy calculation methods of reliability, considering the randomnessof parameters about the fatigue work stress, strength of materials, the fuzzy multipleobjective optimization design mathematical model based on reliability is built and theadaptive values of fuzzy multiple objective function are handled through weightingcoefficients with further effective research. The example of the research resultsembodied in the reliability design elements of multiple objective constraintoptimizations shows that it is simple and practicable to obtain the system designinformation through the research method.
(5) The research of reliability robust design based on improved Particle SwarmOptimization algorithm (PSO) has been made. Particle swarm algorithm belongs tothe advanced evolution algorithm. In the foundation based on the reliabilityoptimization design, two improved PSO algorithms about the dynamic accelerateconstant factor and the speed of the adaptive factor are proposed to build the multipleobjective reliability robust optimization design mathematical model for the numericalsolution. The main research work lies in the realization of the robust design aboutmechanical system through the effective combination of modified PSO and reliabilityrobust design.
The research achievements of this topic could be well applied in many fieldsconcerning national welfare and the people's livelihood such as vehicles, engineeringmachinery, mining equipment, etc. Experimental results show the strong engineeringbackground of the research.
本文追踪国内外的相关研究进展，在Miner准则、Manson准则的基础上，提出了一种基于虚拟区间长度等分的改进疲劳损伤寿命分析模型，并与可靠度的高精求解结合起来，考虑到可靠性稳健元素，通过模糊数学理论和粒子群算法，对系统可靠性的稳健优化设计方法开展进一步研究。研究工作的创新点主要体现在以下方面：
1)提出一种虚拟区间长度等分的疲劳损伤寿命计算模型。在传统Miner准则基础上，将疲劳载荷谱的加载工作应力/区间/频数进行虚拟化等分，建立了一种改进的疲劳损伤模型，并从理论层面证明其疲劳寿命的收敛性。通过与疲劳寿命仿真分析的计算结果比较，说明了虚拟区间长度等分模型计算结果的可信性，有效克服了Miner准则计算公式中经验系数所导致的计算结果不准确性，体现了改进损伤模型的先进与合理。
2)曼森-哈尔福德损伤模型的改进研究。为提高疲劳寿命预测的准确性，对其模型计算公式中的拐点系数与幂指数等经验数据进行研究，探索其对疲劳损伤寿命计算结果的影响，并对其取值范围进行优化与理论研究。研究表明：改进的曼森-哈尔福德模型的疲劳寿命预测结果的准确性得到了提高，但与基于虚拟区间长度等分损伤模型相比较，还存在差距。
3)可靠度高精求解模型与计算方法研究。根据已有的疲劳损伤寿命模型研究成果，在可靠度-应力-寿命（P-S-N）基本理论基础上，考虑到疲劳加载工作应力与强度参数的不确定性，分别建立起基于随机参数概率密度分布的干涉区间积分方法、梯形法则与辛普森法则的三种可靠度计算数学模型，并实现可靠度的高精求解方法研究。结果表明：与传统计算方法比较，有效地提高了可靠度求解的计算精度和效率。
4)基于可靠性的模糊多目标优化设计。在可靠度高精求解方法的基础上，考虑到疲劳工作应力、材料强度等参数的随机性，运用模糊数学的理论与方法，建立起基于可靠性的模糊多目标优化设计数学模型，多目标模糊函数适应值之间采用加权系数进行处理，并对加权系数取值开展了有效地研究。研究成果体现在多目标约束优化中引入了可靠性设计元素，算例表明，研究方法简单、实用，可以直接得到系统设计信息。
5)基于改进粒子群算法（PSO）的可靠性稳健优化。提出了动态加速常数因子和速度自适应因子的两种改进PSO算法，结合可靠性与稳健设计理念，建立多目标的可靠性稳健优化设计数学模型，并实现数值求解。研究成果主要体现在改进的粒子群算法与可靠性稳健设计的有效结合，实现了机械系统可靠性的鲁棒设计。本课题的研究成果，可以很好的应用到车辆、工程机械、矿山装备等关乎国计民生的重大领域之中。应用算例表明，本课题的研究成果，具有较强的工程应用背景。
For many years, Life prediction involving fatigue and reliability assessment ofkey structure parts have been the research hot spot for experts and scholars, in manyfields concerning national welfare and the people's daily life such as automobile,engineering machinery, mining machinery, special equipment, etc. In the research offatigue damage life, computational prediction is usually applied with Miner andCoten-Dolan criteria. In the meanwhile, traditional mechanical models based on thestress-strength principle are used in current researches concerning reliabilitydesign.Nevertheless, due to the applications of experience factors in damage modelsand uniqueness of traditional calculation method, the deviation between the fatiguereliability calculation results and the real value has been resulted. Therefore, how toimprove the accuracy and feasibility of the research about the fatigue prediction andreliability calculation then carry out of the scientific and effective research is veryurgent and necessary.
Based on conclusions of related research at home and abroad, also Miner andManson principle, an improved fatigue life prediction model combined with reliabilitycalculation of high accuracy were proposed and improved concerning robustoptimization design in this paper, through fuzzy mathematics and PSO inconsideration of robust optimization design.
The main innovation points of the work include：
(1) A new fatigue life calculation method has been put forward. Based on theMiner standards, modified fatigue damage model is built by the virtualization toworking stress loading/interval/frequency and the convergence is confirmed throughtheoretical derivations. Compared with simulation analysis results of fatigue life, themain work gives clear evidences to the dependability about the equal classification ofvirtual interval length model. It overcomes the inaccuracy of the calculation due toexperience factors in Miner principle and embodies advances and rationality of themodified model.
(2) The research of the improved Manson-Halford fatigue damage model hasbeen made. To improve the accuracy of fatigue life prediction, the research about theexperience data such as inflection point coefficient and power exponent in the modelis carried out. As a result, the influence of the experience data on the fatigue damagecalculation results is obtained and the value span is dicussed. The research shows that the accuracy of the improved Manson-Halford fatigue damage model is advanced butinferior to which of the equal classification of virtual interval length model.
(3) The research for reliability and high precision mathematic calculation modeland algorithm has been proposed. According to the existing fatigue damage life model,based on reliability-stress-life principle, interference interval integration method,trapezoidal law and the rules of the Simpson three reliability calculation mathematicalmodel are established based on the random parameter probability density distributionconsidering the fatigue loading work stress and the uncertainty of the strengthparameter, then related algorithm about reliability with high accuracy is studied. Theresearch results manifest that the accuracy and efficiency of the new method has beenimproved effectively in comparation with existing methods.
(4) The research of the reliability design based on the fatigue load has been made.With the high accuracy calculation methods of reliability, considering the randomnessof parameters about the fatigue work stress, strength of materials, the fuzzy multipleobjective optimization design mathematical model based on reliability is built and theadaptive values of fuzzy multiple objective function are handled through weightingcoefficients with further effective research. The example of the research resultsembodied in the reliability design elements of multiple objective constraintoptimizations shows that it is simple and practicable to obtain the system designinformation through the research method.
(5) The research of reliability robust design based on improved Particle SwarmOptimization algorithm (PSO) has been made. Particle swarm algorithm belongs tothe advanced evolution algorithm. In the foundation based on the reliabilityoptimization design, two improved PSO algorithms about the dynamic accelerateconstant factor and the speed of the adaptive factor are proposed to build the multipleobjective reliability robust optimization design mathematical model for the numericalsolution. The main research work lies in the realization of the robust design aboutmechanical system through the effective combination of modified PSO and reliabilityrobust design.
The research achievements of this topic could be well applied in many fieldsconcerning national welfare and the people's livelihood such as vehicles, engineeringmachinery, mining equipment, etc. Experimental results show the strong engineeringbackground of the research.
引文
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