Drawing1.bmpYou are pulling yourself off track by considering the free-spinning rollers as an additional factor to consider. Actually in an initial analysis you would assume friction to be zero so you can understand the forces. If friction is zero that means your rollers rotate (spin) as they travel along the circumference of the tire. If they were restricted from turning, that would create friction, and that would create a need for additional calculations.

Simple physics and force vectors will solve your problem. The resultant force at each roller must be perpendicular to its contact point on the tire. That resultant force has a vertical component and a horizontal component. The weight on the tire is W. The vertical component of the resultant force at each roller is 1/2W. The horizontal component is what you are trying to determine (as the force from the hydraulic cylinder pulling the rollers together).

The vertical component is 1/2W. The horizontal component is determined by the amount of the vertical component and the angle from the horizontal of the resultant force.