考虑表面多尺度几何特征的三维多层结构接触响应研究

Research on the Contact Responses of Three⁃Dimensional Multilayer Structures Considering Multiscale Geometric Characteristics of Surfaces

航空发动机叶盘结构服役于高温、高转速的恶劣环境,使得叶片与轮盘非连续界面之间的涂层接触力学行为复杂,影响整体动力学性态.本文基于三维弹性理论建立了一种基于多层半空间体的接触模型,研究多层结构粗糙表面间的接触响应规律.采用数学解析形式将粗糙表面形貌分解为微观、介观和宏观多层级几何轮廓,引入Papkovich-Neuber势函数(P-N势函数),结合傅里叶积分变换法和影响系数法,构建了多层接触的边值问题,应用共轭梯度算法得到接触频响函数解.通过典型多层接触问题的解析解和有限元结果对比,验证了模型的可靠性;进一步研究了不同弹性模量、泊松比及摩擦系数下层内的应力场、位移场变化规律,为研究涂层系统表面粗糙界面的接触响应提供了一种可行而有效的方法.

The aero-engine blade disc works in the harsh environment of high temperature and high speed,which affect the mechanical behavior of the coating contact of the discontinuous blade-disk interfaces and the overall dynamic properties.In this paper,based on the three-dimensional elasticity theory,a contact model based on a multilayer half-space body is developed to investigate the contact responses between rough surfaces of multilayer structures.First,rough surface topography is decomposed into micro,mesoscopic and macro multi-level geometric profiles by explicit expression.Then,based on the Papkovich-Neuber potential function(P-N potential function),Fourier integral transform method and the influence coefficient method,a boundary constraint model for the multilayer contact problem is constrcuted,and is solved using a conjugate gradient algorithm.Finally,the reliability of the model is verified by comparing it with the analytical solution and the finite element results.Furthermore,a parametric study is performed to investigate the influcences of elastic modulus,Poisson's ratio and friction coefficient on the stress and displacement fields.This work provides a feasible and effective approach to study the contact response of rough interfaces of the coating systems.