粗糙表面弹塑性接触连续光滑指数函数模型与法向接触刚度研究
Research on Continuous Smooth Exponential Model of Elastic？？Plastic Contact and Normal Contact Stiffness of Rough Surface

针对微凸体在完全弹性、弹塑性和完全塑性变形阶段接触载荷和接触面积的不连续、跳跃和不光滑,以及平均接触压力的不单调问题,提出了一种新颖的近似指数形式的解析模型。在此基础上,利用分形理论进一步建立了粗糙表面在三阶段接触时的法向接触刚度和法向接触载荷与真实接触面积之间的解析模型,并进行了无量纲化处理。仿真分析了分形维数D、塑性指数Φ以及无量纲分形粗糙度参数G*对无量纲法向接触刚度K*n和无量纲法向接触载荷F*n的影响规律,并分析了K*n随F*n的变化规律。模型的仿真结果表明:K*n和F*n都随着无量纲真实接触面积A*r的增大而增大;随Φ的增大或G*的减小,K*n和F*n的增速都变大;F*n的增速随D的变化是先减小后增大,而K*n的增速是指数增大;K*n随F*n的增大而增大,在D从1.1到1.9的变化过程中,K*n随F*n的增速是先增大后减小,在D>1？？51时,随着G*的减小,K*n随F*n的增速明显变大。利用法向接触刚度模型计算了哑铃模型的固有频率,计算结果与实验结果比较一致,验证了模型的准确性。
A novel approximate exponential analytical model of asperity elastic？？plastic contact is developed. The proposed model can solve the problem of discontinuous, leap and unsmooth contact load and contact area in three separated phases, i.e. perfectly elastic phase, elastic？？plastic phase and fully plastic phase, and can also deal with the problem of non？？monotone of average contact pressure in the elastic？？plastic phase. The analytical model between the contact stiffness or contact pressure of rough surface and the real contact area in the three phases is further established by the fractal theory. The dimensionless normal contact stiffness K*n and dimensionless normal contact load F*n are obtained. The influences of fractal dimension D, plastic index Φ and dimensionless fractal roughness parameter G* on K*n or F*n are simulated and analyzed, and the change of K*n with F*n is also simulated and analyzed. The results show that K*n and F*n increase with increasing dimensionless real contact area A*r; the increasing rate of K*n and F*n are enhanced with the increase of Φ or decrease of G*. The increasing rate of F*n decreases first and then increases with D, while the increasing rate of K*n shows an exponential increase. K*n increases with F*n. When D changes from 1.1 to 1.9, the increasing rate of K*n increases first and then decreases with F*n. When D>1.51, the value of K*n/F*n obviously increases with the decrease of G*. The natural frequencies of the dumbbell model are calculated by the normal contact stiffness model and compared with the experimental one, verifying the accuracy of the proposed model