According to the geometric model of spindle deformation,the total displacement relation of the front end of the spindle is obtained,and the optimum bearing span of the spindle is determined according to the minimum displacement of the front end.By means of numerical integration,the nonlinear dynamic response of the rotor system with the optimal span support is given,and the influence of rotational speed on the system dynamic response is analyzed by using axial trajectory diagram,phase portraits and Poincaré map.The results show that the rotor bearing system has good stability when it is running under the optimum support span.