when a large scale lathe is machining a big size irregular shaped work piece like crankshaft, the spindle system of the lathe can hardly operate in the desired constant rotating speed, because of gravitational unbalance torque arisen from the eccentric unbalance weight of the work piece. Consequently, rotating speed changes and torsional vibration of the spindle can make machining accuracy worse. To analyze the torsional vibrations, 3 different lumped parameter models for the spindle system with geared transmission were derived. And the gravitational unbalance torque was also represented mathematically. Because the gravitational unbalance torque is related with the torsional vibration itself, the system with unbalanced work piece become a nonlinear self excited vibrating system. We solved the equations of motion by using Runge-Kutta method of the MATLAB.