分析了机械系统渐发性故障和突发性故障的不同的数学内涵，从非线性动力学角度说明了导致突发性故障的两种机制，论述了突变理论用于突发性故障描述的可能性及应用方式．建立了动静件径向摩擦转子系统振动状态突变的数学模型．为机械系统突发性故障的阐释、描述、诊断与预测提供依据． The different mathematic connotations of progressive failure and sudden failure of mechanical system are analyzed. Two mechanisms that lead to sudden failure are described from the point of view of nonlinear dynamics, and the possible application of mutation theory to sudden failure description Sex and application methods. A mathematical model of sudden change of vibration state of dynamic and static radial friction rotor system was established. It provides the basis for explaining, describing, diagnosing and forecasting sudden failure of mechanical system.