基于响应面法的机床螺栓结合部刚度辨识与动力学建模

为了研究结合部刚度参数间的耦合关系对机床结合部动态性能的影响，基于响应面函数的选型建立了广义模态固有频率与结合部动刚度耦合和非耦合的函数模型。响应面函数辨识法以结合部模态固有频率这一关键动力学性能为指标，研究了结合部动态特性与结合部刚度参数的数学关系。基于结合部单、双对节点有限元建模方式，结合中心复合实验设计方案和响应面方法理论，分别对两种建模方式建立响应面函数辨识模型。以响应函数模型的响应值与实验测得值的最小二乘法为优化目标，结合非线性规划与遗传算法实现结合部刚度参数的辨识。其中通过响应面函数二次多项式的选型显现多对节点间的刚度耦合关系，揭示了参数间的耦合关系对结合部动力学的影响。为验证此理论和方法的可靠性，以一螺栓结合部为研究对象，制定有限元动力学仿真分析的实验设计方案和采集了刚度组合点，并计算每一组采样点的前11阶模态固有频率。以有限元分析的数据为基础，建立反映螺栓结合部刚度间耦合关系的2次多项式响应面函数，并通过计算响应面模型质量评价指标验证了该模型的有效性。对比分析多刚度耦合、不耦合和单刚度的有限元模型预测精度，结果显示，多刚度耦合的有限元模型在固有频率、振型方面均具有较好预测效果，前11阶模态固有频率平均误差仅为1.6%，论证了考虑刚度间耦合关系的必要性和方法的可行性。

Stiffness Identification and Dynamic Modeling of Machine Tool Bolt Joints Based on Response Surface Method

In order to analyze the effect of coupling relationship between joint stiffness parameters on the dynamic performance of machine tool bolt joints surface, a response surface method which is based on the theory of response surface statistics was proposed to fit the natural frequency of generalized modal states and the dynamic stiffness of the joints. In this method, the natural frequency was taken as the critical index to describe the object dynamic characteristics, with which the mathematic relationship between dynamic characteristics and the stiffness parameters between the joints were analyzed. The response surface model of predicating the varying dynamic characteristics with the finite element models of single and two nodes was established by central composite experiment design and response surface method theory. The least square method with the response function and the experimental test value were taken as the optimization objective, the nonlinear programming and genetic algorithm were combined to realize the stiffness parameter identification of the joint part. The type of response surface function expression was selected to display the stiffness coupling relationship between multiple pairs of nodes, and the influence with the coupling of stiffness on the dynamics of components was revealed. In order to verify the feasibility of the method, one bolt assembly was taken as the research object. The central composite experiment was designed to determine the different combination values of the stiffness between the joints, and the natural frequencies related to the first 11 orders were acquired by conducting the modal analyses with the ANSYS software. Utilizing the acquired dynamic data, a second-order polynomial response surface model was established to describe the connections between the stiffness and the natural frequencies. The accuracy of the established model was validated after calculating the valuating indexes, the influence of the coupling of stiffness on the dynamic characteristics of the components was analyzed, and the effects of multiple rigidness coupling, uncoupling and single stiffness on the dynamic performance of structures were compared and analyzed. The results showed that the dynamic modeling simulation with multi-stiffness coupling is in good agreement with the modal frequency and mode of vibration measured in the test. The first 11 mean modal frequency error is only 1.6%, which proves the necessity of considering the coupling relation between equivalent stiffness.