The forced state of the ball-screw of machine tool feeding system is analyzed. The ball-screw is simplified as Timoshenko beam and the differential equation of motion for the ball-screw is built. To obtain the axial vibration equation,the differential equation of motion is simplified using the assumed mode method. Axial vibration equation is in form of Duffing equation and has the characteristics of nonlinearity. The numerical simulation of Duffing equation is proceeded by MATLAB / Simulink. The effect of screw length,exciting force and damping coefficient are researched,and the axial vibration phase track diagram and Poincare section are obtained. The stability and period of the axial vibration are analyzed. The limit cycle of phase track diagram is enclosed. Axial vibration has two type-center singularity distributions on both sides of the origin. The singularity attracts vibration to reach a stable state,and Poincare section shows that axial vibration appears chaotic motion and quasi periodic motion or periodic motion. Singularity position changes with the vibration system parameters,while the distribution doesn’ t change. The period of the vibration is enhanced with increasing frequency and damping coefficient. Test of the feeding system ball-screw axial vibration exists chaos movement. This paper provides a certain theoretical basis for the dynamic characteristic analysis of machine feeding system ball-screw and optimization of structural parameters. The forced state of the ball-screw of the machine tool feeding system is analyzed. The ball-screw is simplified as Timoshenko beam and the differential equation of motion for the ball-screw is built. To obtain the axial vibration equation, the differential equation of The numerical simulation of Duffing equation is proceeded by MATLAB / Simulink. The effect of screw length, exciting force and damping coefficient are The limit cycle of phase track diagram is enclosed. The limit cycle of phase track diagram is enclosed. Axial vibration has two type-center singularity distributions on both sides of the origin. The singularity attracts vibration to reach a stable state, and Poincare section shows that axial vibration appears chaotic motion and quas Singularity position changes with the vibration system parameters, while the distribution does not change. The period of the vibration is enhanced with increasing frequency and damping coefficient. Test of the feeding system ball-screw axial vibration exists chaos movement. This paper provides a certain theoretical basis for the dynamic characteristic analysis of machine feeding system ball-screw and optimization of structural parameters.