Abstract: Theory of self-excited vibration belongs to the study on the theory of limit cycles. Almost all of scholars only studied the possible appearance or disappearance of a limit cycle surrounding a singular point. A new mathematical model with clearance is presented. It is not satisfied general condition for existence of a stable limit cycle. Because there is a singular segmental line, this equation is called generalized Lienard equation. Authors give two theorems about the existence and uniqueness of stable limit cycle of this equation, then the numerical computation can be used to solve generalized Lienard equation, some new conclusins are obtained which are useful for self-excited vibration of mechanical engineering.

Key words: Clearance, Mechanical system, Segmental line, Self-excited vibration