Abstract: ［Objective］ The complexity and variability of friction in urban rail transit train disc brakes make it challenging for traditional static friction models to reveal the dynamic characteristics of the braking system. It is necessary to establish a dynamic friction model to analyze the dynamic characteristics of the disc brake system. ［Method］ Using the LuGre dynamic friction model, a two-degree-of-freedom dynamic equation for the disc brake system is established and solved by numerical analysis. The vibration response of the brake pad under different conditions is obtained, and the influence of the angular velocity, brake pressure and friction factor difference on the brake system stability is analyzed. ［Result & Conclusion］ With the increase of braking angular velocity, the brake system gradually changes from stick-slip vibration to stable vibration. When the angular velocity is higher than the critical angular velocity, the brake system amplitude increases, and the time required for the brake system to enter into the stable state also increases; as the braking pressure increases, the brake pad transitions from stable motion to stick-slip motion, and the vibration becomes complex and irregular. With the increase of braking pressure, the amplitude of the brake pad gradually increases, and the vibration intensity gets greater and greater; the amplitude increases with an increase in the friction coefficient difference. Upon comprehensive analysis, the brake system achieves optimal stability state at a friction coefficient difference of 0.2.