圆锥微凸体在粗糙表面接触分析中的应用
Application of Conical Asperity in Contact Analysis of Rough Surfaces

为了从微观角度研究粗糙表面的法向接触特性,构建了一种具有圆锥微凸体的有限元分析模型。对反双曲余弦应力进行定积分,获得了作用在单个圆锥接触区域的总法向弹性接触力;给出了圆锥顶点法向变形量与接触半径之间的拟合公式。数值模拟表明:反双曲余弦应力在锥尖处(接触区域的中心)有一个自然对数奇点,但作用在单个圆锥接触区域的总法向弹性接触力有边界;单个圆锥的法向弹性接触载荷随着半顶角的增加先增大后减小;结合部整体的法向接触载荷随着表面粗糙度的减小而增大;当法向最大变形量明显增大时,结合部整体的法向接触载荷随着法向最大变形量的增加仅有微小的增加;半顶角越大,单个圆锥的法向接触刚度也越大;随着圆锥顶点法向变形量的增加,单个圆锥的法向接触刚度先略微减小,而后保持不变;法向临界变形量较小时,结合部整体的法向接触刚度随着法向临界变形量的增加而近似于线性增大;表面粗糙度越小,结合部整体的法向接触刚度增加得越明显;法向临界变形量较大时,结合部整体的法向接触刚度趋于不变。
A finite element analysis model with conical asperity is proposed to investigate the normal contact characters of rough surfaces in the micro perspective. The total normal elastic contact force acting on the single？？cone contact region is obtained through definite integrate of the inverse hyperbolic cosine stress. A formula fitting the normal deformation of cone tip and the contact radius is given. Digital simulations show that although the inverse hyperbolic cosine stress has a natural logarithmic singular spot at the tip of the cone (at the center of the contact region), the total normal elastic contact force acting on the single？？cone contact domain is bounded. The normal elastic contact load on single cone increases at first and then decreases with the increase of the half apex angle. The joint interface’s total normal contact load increases with the decrease of the surface roughness. When the normal maximal deformation increases very evidently, the increase of the total normal contact load on joint interface is very small. The larger the half apex angle is, the larger the single？？cone normal contact stiffness becomes. When the normal deformation of the cone tip increases, the single？？cone normal contact stiffness slightly decreases at first and then keeps constant. When the normal critical deformation is smaller, the joint interface’s total normal contact stiffness has an approximate linear increase with the increase of the normal critical deformation. The smaller the surface roughness is, the more evidently the joint interface’s total normal contact stiffness increases. When the normal critical deformation is larger, the joint interface’s whole normal contact stiffness approaches constant