机械可靠性英文文献及翻译.doc

Mechanical Reliability SimulationJianfeng Xu, Yalian Xie, Dan XuShanghai Institute of Process Automation Instrumentation Shanghai, PRCAbstractThis article provides a numerical method to simulate the reliability of a complicated mechanical system with multiple input random parameters. The method bases on the theory of mechanical reliability and uses a commercial FEM software, ANSYS. The quantitative reliability of the mechanical system is obtained by Monte Carlo simulation. The method is verified by theoretical analysis and is applied to a real structure. This method has prevented the tedious mathematical calculation and is more economical than experimental methods. It can be used as a complement of traditional experimental methods.KeywordsMechanical Reliability; Finite ElementMethod; Monte Carlo SimulationI. INTRODUCTIONBased on the national standard GB/T 3187-1994 1, reliability has been defined as “the probability that a product will satisfactorily perform its intended function under given circumstances for a specified period of time”. Reliability has been viewed as one of the most critical parameters for the products. For example, it is said in US that reliability will be the focus of competition for the future products. Most Japanese companies take more reliable product as their main objective for company development. Therefore, to accurately predict the reliability of the product, and to optimize the design based on the reliability requirements is very meaningful.Generally a mechanical system is composed by many parts. A systems reliability is determined by many parameters, such as the number of components, the quality of the components and also how those components are assembled. It is also related to the material properties, manufacturing technologies, dimension tolerances and so on. Most of the referencescurrently available are focused on the theoretical derivation for reliability calculation, however, due the complexity, it requires tedious mathematical calculation. Another method to obtain the reliability of a system is by experiments, which requires enough samples and testing time, thus the experimental method can only be applicable to those most critical systems.This article uses mechanical strength reliability as an example, illustrates how FEM can be applied to the reliability simulation. The method employs commercial FEM software, ANSYS, and takes advantage of the integrated Monte Carlo simulation function. A simple example is analyzed to verify the correctness of the method. The verified method is then applied to a real structure to obtain the quantitative reliability of a complex system with multiple input random parameters.II. STRENGTH-STRESS INTERFERENCE THEORYNormally the structural maximum stress and the material strength are distributed with certain probability density. Figure 1 shows an example of the distribution, inwhich f ( ) and g( s) represent the maximum stressand material strength, respectively. In Figure 1(a), sinceg( s) is always larger than f ( ) , the reliability of the structure is 1. However, in Figure 1(b), it is notguaranteed that g( s) be larger than f ( ) . There is aninterference zone in the distribution, as shown in the shaded area and zoomed in Figure 2. Thus the reliability of the structure is less than 1. Based on the mathematical derivation, the reliability can be calculated by integration with the distribution.978-1-61284-666-8/11$26.00 2011 IEEE1147R = P( s) = + f ( ) + g( s)ds df ( )g(s)III. METHOD DESCRIPTIONThe commercial FEM package ANSYS has a PDS (Probabilistic Design Simulation) module 2. The module defines dimension, material properties and other parameters as random variables with certain distributions. The output stress and displacement can be defined as results variables. Samples are collected based on Monte(a)f ( )(b)g(s)Carlo method to obtain the distribution of output variables.With the PDS module, a suitable analysis file should be firstly generated to define the simulation process and to define the input and output variables. If necessary, correlation between input parameters can also be defined. Monte Carlo method is then employed to collect enough samples for simulation. Since each run is independent, theFigure 1 Stress and strength distributiong(s) f ( )Figure 2 Stress-strength interference zoneTo create analysis file and to define parametersTo define the input random parameters and distributionsTo define correlations between inputTo define output random variablesTo define method for probabilistic simulationResponse surface simulationResults reviewFigure 3. Flow chart for strengthmethod is suitable for parallel run to save time. Generally 50200 samples are collected in Monte Carlo method to insure the correctness of the results. In some cases, the output variable is a smooth function of the random input variables. In such cases, the response can be approximately evaluated by a mathematical function. By assessing the coefficients in the function with the sampling points and runs, response surface can be determined and numerous runs can be conducted to obtain better distributions with limited time. Basically the flowchart to simulate the strength reliability with ANSYS can be shown in Figure 3, in which the dashed steps indicate they are optional.IV.VERIFICATIONS AND APPLICATIONSThe correctness of the method is verified by a tension rod which is an example in the reference 3. Thetension P N(29400,441)N , material strengthS N(1054.48,41.36) Nmm2 , radius of the rodr N(3.195,0.016)mm , theoretical calculationshows the reliability of the rod is 0.999.1148reliability of a pressure vessel. The shape and parameter distributions are shown in Figure 6.Bar elementPFigure 4. FEM model(a) Monte Carlo Simulation(b) Response Surface SimulationFigure 5. Histogram of strength-stress differenceWith ANSYS, the rod is modeled as a bar element which is fixed in on end. The tension is applied at the other end. The axial stress is calculated in ANSYS. The tension force, radius and material strength are defined as random input variables in PDS. The output variable is defined as the difference between the strength and maximum stress. A value less than 0 indicate a strength failure. One hundred samples are collected with Monte Carlo method. Results show that the difference approximately follows a normal distribution with normal 137.73N and variance 45.42N. Later on, response surface are obtained based on the previous samples and 10000 runs are conducted. The normal and variance can be better obtained as 137.65N and 44.52N, respectively. From which it is concluded that the reliability of the rod is 0.9988 and 0.9990 with the two methods. This result matches well with the theoretical calculation which demonstrates the correctness of the method. Figure 4 shows the FEM model, and Figure 5 is the histogram of the strength-stress difference, where KPa is unit.The method is then applied to analyze therLFixedr U1990,2010mm L U9990,10010mmThickness U7.5,8.5mmPressure U2800,3200KPa YoungsModule N(200,10)GPa YieldStres N(1000,50)MPaFigure 6 Pressure VesselIn PDS module, the random input parameters are defined in accordance with Figure 6. With 50 Monte Carlo sampling points, the simulation shows that the difference between strength and stress can be approximately described as a normal distributionN (229.22,67.251)MPa . A further response surfacesimulation demonstrates that the difference match the distribution as N (228.86,65.823)MPa , as shown inFigure 7. From these distributions, the reliability of the1149pressure vessel can obtained as 0.99967 and 0.99974,respectively.(a) Monte Carlo Simulation(b) Response Surface SimulationFigure 7. Strength-stress deviation histogram of pressure vesselV. CONCLUSIONSFEM and Monte Carlo simulation method can be integrated to obtain the mechanical reliability of a complex structure with multiple input random parameters. Although this article considers only the static cases, the method can also be applied to dynamic cases with suitable analysis file.The method described in this article prevents tedious mathematical calculation. The structure reliability can be obtained with less time and money. This method can be a complement of the traditional experimental methods.REFERENCES1 Reliability and Maintainability terms, GB/T 3187-942 ANSYS Help, ANSYS Corp3 Liu P., Basic of Reliability Engineering, Metrology Press, 2002中文翻译：机械可靠性仿真Jianfeng Xu, Yalian Xie, Dan Xu上海工业自动化仪表研究所上海，中华人民共和国摘要：本文提供了一种多输入随机参数模拟复杂机械系统的可靠性计算方法。该方法基于可靠性理论，采用商业有限元软件ANSYS。机械系统的可靠性定量是通过蒙特卡罗模拟。该方法是通过理论分析验证和实际应用的结构。该方法避免了繁琐的数学计算和比实验方法更经济。它可以作为传统实验方法的一种补充。关键词：机械可靠性；有限元；蒙特卡罗仿真方法。一、引言根据国家标准GBT 3187-1994 1 ，可靠性被定义为“在一定的条件下在指定的一段时间内，一个产品很好地履行其预期的功能的概率”。可靠性一直被看作是一个产品的最重要的参数。例如，据说在美国，可靠性将是今后产品竞争的焦点。大多数日本企业以更可靠的产品作为公司发展的主要目标。因此，为了准确地预测产品的可靠性，并优化基于可靠性要求的设计是非常有意义的。一般的机械系统是由许多部分。一个系统的可靠性取决于许多参数，如组件的数量，质量的部件和这些部件组装。这也与材料的性质，相关的制造技术，尺寸公差等有关。大多数现有的文献主要集中在可靠性理论推导计算，然而，由于它的复杂性，需要繁琐的数学计算。还有一种实验法来获得系统的可靠性试验，需要足够的样本和测试时间，因此，实验方法只能适用于那些最重要的系统。本文采用机械强度可靠性为例，说明了有限元法可以应用于可靠性仿真。该方法采用商业有限元软件，ANSYS，并利用Monte Carlo模拟功能集成。一个简单的实例分析验证了该方法的正确性。这种验证的方法随后便应用到实际结构，来获得多输入随机参数的一个复杂系统的可靠性定量。二、拉压干涉理论。通常情况下，结构的最大应力和材料强度的分布有一定的概率密度。图1显示的分布的一个例子，在f ( )和g( s)分别代表最大应力和材料强度的情况下。图1（a）中因为g( s)总是大于f ( )，结构的可靠度是1。然而，在图1（b），它是不能保证g( s)大于f ( )。图中分布着一个干扰区，如图所示，在阴影区域和放大的图2。因此，结构的可靠度小于1。基于数学推导的可靠性，可以按照分布做一体化计算。R = P( s) = + f ( ) + g( s)ds df ( )g(s)(a)f ( )g(s)（b）图1 拉压分布g(s) f ( )图2 拉压干扰区创建分析文件并定义参数定义输入随机变量以及分配定义输入数据之间的相关性定义输出随机变量定义概率模拟方法响应面模拟结论综述图3 拉力流程图三、描述方法商业有限元软件ANSYS有PDS（概率设计仿真）模块 2 。该模块定义尺寸，材料特性和其他参数作为具有一定分布的随机变量。输出力和位移可以被定义为结果变量。样品的采集是基于Monte Carlo方法得到输出变量的分布。借助于PDS模块，一个合适的分析文件应首先生成定义仿真过程和定义输入和输出变量。如果需要，输入参数之间的相关性也可以定义。然后采用蒙特卡罗方法收集足够的样本进行仿真。由于每个