First of all - are you mowing in 4WD or with the loader attached? I have one tractor with R1's and another with R4's and neither will mess up the grass unless I'm in 4WD or have the loader on and make sharp turns. If the ground is very moist, I can sometimes cut the wheels hard enough to do some minor damage to the grass.
There have been similar discussions here, and I believe the soil composition also plays a role in this...................chim