等强度变截面构件可靠性分析与设计
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摘要
随着经济危机到来和石油资源匮乏,机械产品越来越趋向省油、可靠、更加经济实用,传统的机械设计已不能满足要求,而建立在概率和统计基础上的可靠性设计越来越受到重视,其中可靠性设计的灵敏度分析是研究设计参数变化对可靠性的影响,而基于灵敏度分析的稳健设计使设计参数的变化对设计产品质量的影响不敏感即稳健。因此研究等强度变截面构件灵敏度分析与设计具有现实的工程意义。
本文基于可靠性摄动分析法、Edgeworth级数以及相应的经验修正公式,研究了随机变量间相关系数的可靠性灵敏度,讨论了随机变量(协)方差以及相关系数可靠性灵敏度的正负性及其决定条件;给出了随机变量服从正态分布和任意分布时的可靠性灵敏度计算公式,拓展了可靠性灵敏度设计的研究范围;并将可靠性灵敏度分析方法与稳健设计方法相结合,通过将可靠性灵敏度函数结合到可靠性优化设计的目标函数中,将可靠性稳健设计问题归结为满足可靠性要求的多目标优化设计问题,实现了基于可靠性灵敏度分析的稳健设计。最后通过数值算例说明可靠性灵敏度分析方法以及可靠性稳健设计方法的实用性和有效性。
Present,Reliability technology has been applying into each field of the mechanical engineering,it is generally recognized that products are indeterminate. For example, material date and dimension date provided may be not completely consistent with that of real strueture, some hypothesis,for convenience and simplifieation,make the caleulation model is not the same as the real strueture. Application of the reliability design and reliability-based design for mechanical products can save a lot of human and material resources,raise design standards,shorten the design cycle, Therefore,The research on reliability of the uncertain systems is very important for design purposes. With the development of reliability design, it will play a more important role.
It is possible that many failure modes have emergence during the struetural serviee period. For example, dead load strength failure, Stiffness failure and fatigue failure. However in many cases,Reliability analysis of products of strength failure,Stiffness failure and fatigue failure is respectively considered. Therefore, it’ll be much more accordant to consider uncertain factors in the mechanical products design. The reliability analysis of mechanical structures can help the designer to establish acceptable tolerances on mechanical structures and to govern the fluctuations of the system parameters for safe operations. In the end, the reasonable products could be designed with enough reliability and little cost. Due to design parameters and structural parameters are uncertain, current mechanical structures design practice tends to account for the uncertainties, which include geometry parameters, material properties, loadings, etc.
With the process and development of society, more and more attention is paid to the reliability of products.In mechanical analysis of the reliability of products ,the influence characters and degree of different design parameters to reliability of the mechanical structures are different, it is necessary to do reliability-based sensitivity analysis to make sure the influence of design parameters to reliability of the mechanical structures, Therefore, reliability-based sensitivity analysis techniques have become an important part of reliability design. Reliability-based design, reliability-based optimization design and robust design are very advanced ideas. They have extensive application prospects on account of significance in improving product quality and making performance stability. The reliability-based design and the reliability-based optimization design utilize reliability theory to deal with uncertainties, and robust design attempts to make the variations of mechanical structures are insensitive to variations of design variables. The aforementioned methods are all very effective to improve design level of the mechanical structures. These methods have usually been used separately in different design stages for different purposes. Therefore, it is essential to combine the reliability-based design theory, reliability-based optimization design method, the reliability sensitivity analysis technique and the robust design method and to develop a reliability-based robust design approach, the reliability-based robust design will play a more important role.in the future machine design.
On the basis of summarizing the reliability-based design theory, reliability-based optimization design method ,the reliability-based sensitivity design method and the idea of robust design ,the reliability-based sensitivity of correlation coefficients among the random variants obeying Gaussian and arbitrary distributions was studied; the reliability-based sensitivity design methods of the uniform strength variable cross-section component was proposed; then the reliability-based mechanical and structural robust design based on the reliability-based sensitivity was realized.
The main productions obtained from this paper are following as:
1.This paper, based on preliminary studies, We explicate the engineering background, the aim and meaning of the research, summed up the reliability of the design sensitivity of various theories and methods ,the variation law for reliability-based sensitivity of cross-section the uniform strength components are studied, a method on the reliability and sensitivity of cross-section the uniform strength mechanical components are proposed. Random variables in the basic probabilistic characteristics of certain circumstances, we can get the information of the cross-section the uniform strength mechanical commponents on the reliability-based sensitivity quickly and accurately. This paper studies variation law of utility reliability sensitivity under the normal conditions and the arbitrary distribution parameters, and the sensitivity of the variation law .The numerical method of reliability-based sensitivity design was studied from the level of the mean, the variance (covariance) and the correlation coefficients of basic random variants obeying Gaussian and arbitrary distributions. The influences of variance (covariance) and correlation coefficients of basic random variants on reliability of mechanical structures are discussed. The positive and negative characters and its determinative conditions of the reliability-based sensitivity of variance (covariance) and correlation coefficients were analyzed. The reliability-based sensitivity design theory is made much more perfect. Gave the analysis chart, the application field of reliability-based robust design is developed well.
2.On the basis of the reliability-based optimization design theory, the reliability sensitivity analysis technique and the robust design method, the reliability-based robust design of mechanical structures is discussed based on the reliability-based optimization model. A mathematical model of reliability-based robust design was established according to such an idea that reliability-based robust design problem was equalized to multi-objective optimization problem satisfying the reliability constrictions by including the reliability-based sensitivity functions to the objective functions of reliability-based optimization design model. And used the reliability design theory in the uniform strength variable cross-section component design. Gave the design example in the uniform strength variable cross-section component design. The stiffness reliability-based robust design attempts to make the reliability variations of structure are insensitive to variations in design variables in the stage of design, which can minimize the effect of variations without eliminating the causes. When the stiffness reliability-based robust design approach is applied to mechanical structures design, the method is very useful and effective to improve quality and reliability of mechanical structures. The application field of reliability-based robust design is developed well.
本文基于可靠性摄动分析法、Edgeworth级数以及相应的经验修正公式,研究了随机变量间相关系数的可靠性灵敏度,讨论了随机变量(协)方差以及相关系数可靠性灵敏度的正负性及其决定条件;给出了随机变量服从正态分布和任意分布时的可靠性灵敏度计算公式,拓展了可靠性灵敏度设计的研究范围;并将可靠性灵敏度分析方法与稳健设计方法相结合,通过将可靠性灵敏度函数结合到可靠性优化设计的目标函数中,将可靠性稳健设计问题归结为满足可靠性要求的多目标优化设计问题,实现了基于可靠性灵敏度分析的稳健设计。最后通过数值算例说明可靠性灵敏度分析方法以及可靠性稳健设计方法的实用性和有效性。
Present,Reliability technology has been applying into each field of the mechanical engineering,it is generally recognized that products are indeterminate. For example, material date and dimension date provided may be not completely consistent with that of real strueture, some hypothesis,for convenience and simplifieation,make the caleulation model is not the same as the real strueture. Application of the reliability design and reliability-based design for mechanical products can save a lot of human and material resources,raise design standards,shorten the design cycle, Therefore,The research on reliability of the uncertain systems is very important for design purposes. With the development of reliability design, it will play a more important role.
It is possible that many failure modes have emergence during the struetural serviee period. For example, dead load strength failure, Stiffness failure and fatigue failure. However in many cases,Reliability analysis of products of strength failure,Stiffness failure and fatigue failure is respectively considered. Therefore, it’ll be much more accordant to consider uncertain factors in the mechanical products design. The reliability analysis of mechanical structures can help the designer to establish acceptable tolerances on mechanical structures and to govern the fluctuations of the system parameters for safe operations. In the end, the reasonable products could be designed with enough reliability and little cost. Due to design parameters and structural parameters are uncertain, current mechanical structures design practice tends to account for the uncertainties, which include geometry parameters, material properties, loadings, etc.
With the process and development of society, more and more attention is paid to the reliability of products.In mechanical analysis of the reliability of products ,the influence characters and degree of different design parameters to reliability of the mechanical structures are different, it is necessary to do reliability-based sensitivity analysis to make sure the influence of design parameters to reliability of the mechanical structures, Therefore, reliability-based sensitivity analysis techniques have become an important part of reliability design. Reliability-based design, reliability-based optimization design and robust design are very advanced ideas. They have extensive application prospects on account of significance in improving product quality and making performance stability. The reliability-based design and the reliability-based optimization design utilize reliability theory to deal with uncertainties, and robust design attempts to make the variations of mechanical structures are insensitive to variations of design variables. The aforementioned methods are all very effective to improve design level of the mechanical structures. These methods have usually been used separately in different design stages for different purposes. Therefore, it is essential to combine the reliability-based design theory, reliability-based optimization design method, the reliability sensitivity analysis technique and the robust design method and to develop a reliability-based robust design approach, the reliability-based robust design will play a more important role.in the future machine design.
On the basis of summarizing the reliability-based design theory, reliability-based optimization design method ,the reliability-based sensitivity design method and the idea of robust design ,the reliability-based sensitivity of correlation coefficients among the random variants obeying Gaussian and arbitrary distributions was studied; the reliability-based sensitivity design methods of the uniform strength variable cross-section component was proposed; then the reliability-based mechanical and structural robust design based on the reliability-based sensitivity was realized.
The main productions obtained from this paper are following as:
1.This paper, based on preliminary studies, We explicate the engineering background, the aim and meaning of the research, summed up the reliability of the design sensitivity of various theories and methods ,the variation law for reliability-based sensitivity of cross-section the uniform strength components are studied, a method on the reliability and sensitivity of cross-section the uniform strength mechanical components are proposed. Random variables in the basic probabilistic characteristics of certain circumstances, we can get the information of the cross-section the uniform strength mechanical commponents on the reliability-based sensitivity quickly and accurately. This paper studies variation law of utility reliability sensitivity under the normal conditions and the arbitrary distribution parameters, and the sensitivity of the variation law .The numerical method of reliability-based sensitivity design was studied from the level of the mean, the variance (covariance) and the correlation coefficients of basic random variants obeying Gaussian and arbitrary distributions. The influences of variance (covariance) and correlation coefficients of basic random variants on reliability of mechanical structures are discussed. The positive and negative characters and its determinative conditions of the reliability-based sensitivity of variance (covariance) and correlation coefficients were analyzed. The reliability-based sensitivity design theory is made much more perfect. Gave the analysis chart, the application field of reliability-based robust design is developed well.
2.On the basis of the reliability-based optimization design theory, the reliability sensitivity analysis technique and the robust design method, the reliability-based robust design of mechanical structures is discussed based on the reliability-based optimization model. A mathematical model of reliability-based robust design was established according to such an idea that reliability-based robust design problem was equalized to multi-objective optimization problem satisfying the reliability constrictions by including the reliability-based sensitivity functions to the objective functions of reliability-based optimization design model. And used the reliability design theory in the uniform strength variable cross-section component design. Gave the design example in the uniform strength variable cross-section component design. The stiffness reliability-based robust design attempts to make the reliability variations of structure are insensitive to variations in design variables in the stage of design, which can minimize the effect of variations without eliminating the causes. When the stiffness reliability-based robust design approach is applied to mechanical structures design, the method is very useful and effective to improve quality and reliability of mechanical structures. The application field of reliability-based robust design is developed well.
引文
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