Abstract: Based on the concept of ‘Optimum Range of the Crowning Value’, a crowning design method according to thermal EHL theory was proposed for the optimum logarithmic profile roller. The axial pressure distribution index and axial filmthickness distribution index were defined, and satisfactory axial pressure and filmthickness distribution could be realized by restricting the allowable value of the two indexes mentioned above. Moreover, the lower bound and upper limit of the optimum range of the crowning value were corresponding to the allowable value of the axial filmthickness distribution index and the axial pressure distribution index separately. Using this method, the relationship between the crowing modification index and the working conditions was studied. It was concluded that the lower bound of the optimum range of the crowning value? increased with the increase of applied load when the load was low, while it reached a stable value when the load was heavy; the upper limit of the optimum range of the crowning value? increased with the increase of the applied load. however, the influence of the velocity parameter on the optimum range of the crowning value ?was not pronounced.