Calculations of Relative Velocity in Abrasive Wear Systems Employing Laps of Constant Radius of Curvature

A rigid spherical lap and rigid part in extended contact can only be spheres coincident to within the dimension of the intervening abrasive. Their only motion with respect to each while maintaining contact are their individual rotations. If the axes of these two rotations are noncoincident, they define a plane. If the axes are moving with respect to each other, this movement can be regarded as a rotational vector in a direction orthogonal to the plane defined by the two axes above, and this vector can be added to either of the two rotations described above or apportioned between them to define a reference frame. This demonstrates that at any moment there are actually only two independent rotations. For those familiar with vector algebra, the velocity of either sphere at any point on its surface can be described as the vector or cross product of its rotational vector with the radius vector of the point, i.e. V→=ω→×R→. This discussion of the changing relationship between the rotational axes is also a precise description of a part stroked across a lap.