Calculating Wear on Shifter Pad of Gearbox

If this is a vehicle transmission then either the shifter is maladjusted or the operator rests his/her hand on the shifter while in operation, check the end point stops of the shifter they are probably causing a coutinuous load due to the positive stop being too tight. As far as the calculation goes I would not concern myself with that. Repair the problem and the symtoms will go away.

Wear is directly related to the shear stress in the sliding zone. It is not enough to give the force all geometrical data must be available for an evaluation.

Could give more information and if possible picture of worn parts ?

The synchronization force should as well be checked if it is really in correct relation to the process (condition when commuting, dimensions and possible frictions aso).

I have opened transmissions with >>200,000 miles on them and found no significant wear in that area. If you are achieving proper hydrodynamic lubrication between the moving parts, there should be zero wear. I suspect that either the lubricating oil is being wiped away during shifting and not available to maintain a film between the parts, or the transmissions are being dry shifted excessively. Perhaps to test this theory, you might want to install a small pump to force lubricate the sliding joint whenever shifting occurs.

Possibly the wrong lubrication? Or one that is too cheap/not a true equivalent to the recommended?