基于分形理论的机械结合部接触特性参数研究

发布时间：2018-07-17 19:37

【摘要】：接触特性参数包含接触刚度、接触阻尼和静摩擦系数、接触热阻抗和接触电阻抗等参数,对于机械结合部,前三个接触参数直接影响着整机静态特性及动态特性。一台机床中机械结合部的刚度和阻尼相对于材料本身的刚度与阻尼占据着主导地位,从而成为研究整机静动态性能的关键参数。但是由于结合部接触特性具有复杂的非线性特性,在很长的一段时间里,结合部的接触特性参数产生的机理并没有得到较透彻研究,导致从理论上精确建立机械接合部动力学模型也变得非常困难。故本文将致力于从机理上研究结合部接触特性,建立接触特性参数的解析模型,分析影响因素,为高精度的参数化建模提供一种方法,为机械结构的动态优化设计提供理论依据。本文研究的主要工作和创新点如下:提出了一种基于分形理论的结合部接触力学模型。利用改进的三维WM分形函数对接触表面进行表征,从结合部微观接触特性着手,分析了微凸体变形的弹性、弹塑性、完全塑性接触力学特性,基于Hertz接触理论和分形理论,建立了微凸体弹塑性变形阶段的接触载荷与接触面积方程,提出了微凸体接触力学模型。利用岛屿面积分布的分形理论,建立了结合部接触力学模型,并分析了分形参数及法向载荷对其作用规律。将建立的微凸体接触力学模型与四种经典的接触理论及实验数据进行对比分析,证明了本文提出的接触模型的有效性和普适性。建立了结合部法向及切向接触刚度参数的解析模型。利用微凸体接触力学模型及Mindlin球体滑移接触理论,分析得出弹性区和弹塑性区的微凸体法向及切向接触静刚度。基于分形理论,建立结合部的法向及切向静刚度参数模型。同时,研究了球体-平面动态接触的振动微分方程,推导出微凸体接触的线性化静刚度,首次建立了具有分形特征结合部的动刚度与静刚度的联系。另一方面,探索了结合部在流体润滑状态下的刚度特性,基于分形理论建立了部分膜润滑状态下粗糙面接触的平均雷诺方程,利用分离变量法得到流体平均压力解析解,推导出流体刚度,建立了包含固体接触刚度和流体刚度的结合部等效刚度参数的解析模型,并分析了各种影响因素的作用规律。研究了结合部法向及切向接触阻尼参数的解析模型。基于分形理论及Sabot振动接触理论,推导了结合部每周期法向能量损耗及存储表达式,同时联合分形理论及Mindlin理论,计算出每周期切向能量损耗及存储方程,建立结合部的法向及切向接触阻尼参数的解析模型。另一方面,研究了结合部在流体润滑状态下阻尼特性,利用部分膜润滑平均雷诺方程,解出部分膜润滑状态下接触法向流体阻尼,最终建立了包含固体接触阻尼和流体阻尼的结合部等效阻尼的解析模型,同时分析了各种影响因素的作用规律。推导了结合部静摩擦系数参数的解析模型。利用第三强度理论,解出微凸体最大静摩擦力,基于分形接触模型,建立了结合部的最大静摩擦力及静摩擦系数模型。同时,研究了结合部在流体润滑状态下的摩擦特性,基于牛顿粘性定律并结合流体平均压力解析解,推导出部分膜润滑状态下流体摩擦力表达式,建立了部分膜润滑状态下的静摩擦系数模型。最后,对试件表面进行轮廓测试分析,获取接触分形参数。对螺栓固定结合部进行了模态试验,获取谐振频率及频响函数。搭建摩擦力试验台,进行摩擦力试验,获取静摩擦系数参数。实验结果验证了本文推导的接触特性参数解析解的正确性。
[Abstract]:The contact characteristic parameters include contact stiffness, contact damping and static friction coefficient, contact thermal impedance and contact resistance resistance and other parameters. For the mechanical combination part, the first three contact parameters directly affect the static and dynamic characteristics of the whole machine. The stiffness and damping of the mechanical joint part in a machine tool are occupied by the stiffness and damping of the material itself. The leading position is the key parameter to study the static and dynamic performance of the whole machine. However, due to the complex nonlinear characteristics of the contact characteristics of the joint, the mechanism produced by the contact characteristic parameters of the joint has not been thoroughly studied in a long period of time, which leads to the precise establishment of the mechanical joint dynamic model in theory. It will become very difficult. Therefore, this article will be devoted to studying the contact characteristics of the joint from the mechanism, establishing the analytical model of the contact characteristic parameters, analyzing the influencing factors, providing a method for the high precision parameterized modeling, and providing the theoretical basis for the dynamic optimization design of the mechanical structure. The main work and innovation of this study are as follows: A model of contact mechanics based on fractal theory. The contact surface is characterized by the improved three-dimensional WM fractal function. The elastic, elastoplastic and fully plastic contact mechanical properties of the micro convex body are analyzed from the microscopic contact characteristics of the joint. Based on the Hertz contact theory and the fractal theory, the elastoplastic change of the micro convex body is established. The contact mechanics model of micro convex body is put forward by the contact load and contact area equation of the shape stage. Using the fractal theory of the area distribution of the island, the contact mechanics model of the joint is established, and the fractal parameters and the law of the normal load on it are analyzed. The contact force model of the micro convex body and the four classical contact theories and the experimental numbers will be established. According to the comparative analysis, the validity and universality of the contact model proposed in this paper are proved. An analytical model of the joint stiffness and tangential contact stiffness parameters is established. By using the contact mechanics model of the micro convex body and the sliding contact theory of Mindlin sphere, the static stiffness of the normal and tangential contact of the elastic and elastoplastic zones is obtained. Based on the fractal theory, the normal stiffness parameter model of the normal and tangential direction is established. At the same time, the vibration differential equation of the dynamic contact between the sphere and the plane is studied. The linearized static stiffness of the contact of the micro convex body is deduced. The relationship between the dynamic stiffness and the static stiffness with the fractal characteristic joint is first established. On the other hand, the joint is explored in the fluid. The average Reynolds equation of rough surface contact under partial film lubrication is established based on the fractal theory. The analytical solution of the fluid average pressure is obtained by the separation variable method. The fluid stiffness is derived, and the analytical model of the equivalent stiffness parameters of the joint with the solid contact stiffness and the fluid stiffness is established and analyzed. The analytic model of the damping parameters of the normal and tangential contact is studied. Based on the fractal theory and the Sabot vibration contact theory, the energy loss and storage expression for each cycle of the joint are derived, and the energy loss and storage of the tangential energy per cycle are calculated by combining the fractal theory and the Mindlin theory. On the other hand, the damping characteristic of the joint under the condition of fluid lubrication is studied, and the average Reynolds equation of the partial film lubrication is used to solve the damping of the contact method under the lubrication state of the partial membrane. Finally, the solid contact damping and the fluid damping are finally established. The analytical model of the equivalent damping of the combined part is analyzed and the action law of various factors is analyzed. The analytical model of the static friction coefficient of the combined part is derived. The maximum static friction force of the micro convex body is solved by the third strength theory. Based on the fractal contact model, the most large static friction force and the static friction coefficient model of the joint are established. The friction characteristics of the joint under the state of fluid lubrication are derived. Based on the Newton's law of viscosity and the analytical solution of the average pressure of the fluid, the expression of the friction force in the part of the film lubrication is derived. The static friction coefficient model in the part of the film lubrication is established. Finally, the surface of the specimen is tested and analyzed to obtain the contact fractal parameter. The modal test of the bolt fixed joint was carried out to obtain the resonant frequency and frequency response function. The friction test bench was built, the friction test was carried out, and the static friction coefficient parameters were obtained. The experimental results verify the correctness of the analytical solution of the contact characteristic parameters derived in this paper.
【学位授予单位】：华中科技大学
【学位级别】：博士
【学位授予年份】：2016
【分类号】：TH111

【相似文献】