For the study of hollow shaft cutting under compound frequency vibration， it is extremely important to establish the relationship among cutting life， geometry parameters of hollow shaft and loaded state. The stress intensity factor（SIF） is derived at the crack tip of a V-groove hollow shaft. Its dynamic model is established based on the built-in dual-frequency vibration system. So the constant amplitude nominal stress at the V-shaped incision is obtained plotting the stress spectrum， and the SIF value at the V-shaped incision of the hollow shaft under the compond frequency vibration is obtained. Based on the SIF superposition principle and the fatigue crack life formula， the cutting life model of the hollow shaft under the compound frequency is generalized. Analysis model and design the experiments， the experimental results are consistent with the model laws.