The model of the braking system with dry friction we focus on is a six-dimensional autonomous Filippov system.The discontinuity-induced bifurcations(DIBs) involving periodic orbit of this system are investigated in this paper.The route to chaos is found numerically, including periodic doubling cascade.A key anal.vtical tool called improved Poincaré Map is presented here for the first time to investigate the periodic doubling cascade.It shows that the analytical results agree with numerical predictions.