In this paper, a dynamic brake model has been constructed by incorporating the brake rotor's speed and the brake normal force as excitation sources. By introducing two permissible errors (e_1,2), a novel computation algorithm is proposed to reduce the ill-conditioning, arising from the nonlinear friction. Its validation illustrates the proposed method, using double-changed time-steps and smarter adaptive time-step reduced method, is more reliable than other integral equation solvers with a higher accuracy as well as less computation time. Moreover, the influences of external excitations on the dynamic characteristic of the brake system are also analyzed, and an estimation for the occurrence of unstable vibration is investigated. The results demonstrate the different contributions of the two external excitations on the dynamic characteristic. The brake system has more unstable vibration at a higher brake normal force and a lower brake rotor's speed with small fluctuation. Furthermore, the higher brake rotor's speed could generate more positive damping effect, which could reduce and suppress the occurrence of the sick-slip vibrations. In practice, these instabilities can be minimized by appropriate selection of the two external, which can be adjusted according to the advanced working requirements.