The roller deformation in the roller bearings is determined by the relative motion of the shaft and the outer races at the roller location. When the bearing has misalignment, this relative motion needs to be adjusted for the parallel misalignment u0 and angular misalignment θ0 to calculate the actual roller deformation. Let the displacement of the inner race at its center be ui and its tilt θi, and the displacement of the outer race at its center be uo with tilt θo. Then, the net relative motion of the inner and outer races including the effect of misalignment can be written as:

Here, rrc is the position of the roller center relative to the center of the bearing. The roller force is a function of the roller deformation, which in case of misalignment is given by the above expression.