Titanium alloys are widely used in aviation because of their excellent properties， such as high specific strength， high specific stiffness and strong plasticity. However， these characteristics also bring big challenges to the high precision hole making operation. Vibration is proved to be an effective way to solve the problem. In this paper， a vibration drilling test bench is set up. Through the vibration drilling dynamics test of titanium alloys， it is found that the system has nonlinear vibration characteristics like a hard spring. The key dynamic parameters and dynamic models of the system are obtained by dynamic modeling and experimental parameter estimation. The nonlinear average analysis of the dynamic model is carried out during the near-resonance operation. The average equation is calculated and the results show that the amplitude-frequency characteristics agree with the measurements， which proves the correctness of the dynamic model. Based on the nonlinear characteristics of the system and the near-resonance operation， a large range of steady vibration is observed under low excitation， and the stable and efficient vibration chip breaking and drilling operation are realized. It shows that the vibration drilling process is more stable， the power consumption is lower and the hole quality can be better by skillfully using the nonlinear cutting process through proper dynamic design.