An isotropic, thermoelastic half-space is at rest when a rigid sphere is pressed into the surface and translated along a straight path over the surface with constant speed. The speed is rapid but subcritical, and translation is opposed by surface friction and accompanied by thermal convection. A dynamic steady state ensues, so that the contact zone assumes a constant shape that translates at the same speed as the sphere. An analytical solution, based on robust asymptotic expressions in integral transform space, is developed. The roles of sliding friction and thermal convection on solution form are identified. Examination of the solution shows in particular that in the absence of convection, contact zone geometry is self-similar whether or not friction exists. If convection is accounted for, self-similarity is lost.

当刚性球体被压入表面并沿直线路径以恒定速度平移时，各向同性的热弹性半空间处于静止状态。速度快但亚临界，平移与表面摩擦相反，并伴有热对流。随之而来的是动态稳态，因此接触区呈现恒定形状，以与球体相同的速度平移。开发了一种基于积分变换空间中稳健渐近表达式的解析解。确定了滑动摩擦和热对流对溶液形式的作用。对解决方案的检查特别表明，在没有对流的情况下，无论是否存在摩擦，接触区几何形状都是自相似的。如果考虑对流，自相似性就会丢失。