基于极值响应面法的柔性机构可靠性优化设计

Optimized reliability design for flexible mechanisms based on the extremum response surface method

为建立柔性机构可靠性优化设计的理论与方法.用传统方法进行柔性机构截面尺寸的初步设计,将模态综合法与柔性多体系统动力学相结合,建立柔性机构拉格朗日形式的动力学微分方程,用蒙特卡罗法抽取柔性机构输入参数随机样本,并对每个样本求解动力学微分方程,得到对应的位移、速度、加速度在分析时域内的响应,在此基础上求出对应的动态应力和挠度响应.将不同输入样本对应的应力和变形输出响应在分析时域内的最大值的全体作为新的输出(极值)响应,构造极值响应面函数.以材料密度、弹性模量、许用刚度、强度和构件截面尺寸为随机变量,以构件尺寸为设计变量,以机构质量为目标函数,以设计变量表示的可靠性指标为约束函数,对柔性机构进行可靠性优化设计.实例计算表明,该设计方法在满足可靠性要求的情况下使得机构的质量最小.

The aim of the following research was to establish a new theory and method of reliability optimization for flexible mechanisms. Firstly, cross section dimensions of flexible mechanisms were predesigned by traditional methods. Secondly, Lagrange dynamics differential equations of the flexible mechanisms were established by using the modal integrated method and the flexible multi-body system dynamics method. Subsequently, by using the Monte Carlo Method （MCM）, the random sample values of the input parameters were obtained and Lagrange dynamics differential equations were solved for each random sample value which revealed the response of their displacement, speed, and acceleration within the analysis time domain. On this basis, dynamic stress points and deflection responses were obtained. By taking the entire maximum values of the stress points and deflections as new output responses, the extremum response surface function （ERSF） was established. With material density, elastic modulus, allowable stiffness, intensity and section size of structure parts as random variables, component size as a design variable, mechanism mass as an objective function, and reliability indices expressed by a design variable as the restriction function, the flexible mechanism was carried out with optimized design reliability. The calculation results of the real example show that the method allows the minimum mass of the mechanism under the condition of meeting the reliability requirement.