关键词: Duffing方程, Lienard方程, Van Der Pol方程, 非线性动态特征, 跳跃现象, 液压缸, 自激振动

Abstract: In terms of nonlinear dynamics, the actions of nonlinear spring force and nonlinear frictional force on dynamic characteristics of moving hydraulic cylinder are emphatically studied by means of theoretical analysis and experimental verification. Varying regularities of spring stiffness with piston displacement controlled by three types of hydraulic throttle-governing circuits are obtained. Soft spring property or hard spring property shown separately by above different working situations are found. The conclusions that the effect of nonlinear spring can be described by Duffing equation, the effect of nonlinear frictional force can be described by Van Der Pol equation, and their coupling effect can be described by Lienard equation are achieved. The reasons why hydraulic cylinder creeps in lower velocity are common acting results of the jump phenomenon caused by soft spring property and the self-excited vibration caused by nonlinear frictional force in specific working situation are expressed. Solutions of the equations are of different patterns in terms of different working conditions. All above illustrate that the nonlinear characteristics of moving hydraulic cylinder are complicated and changeable.

Key words: Duffing equation, Hydraulic cylinder, Jump phenomenon, Lienard equation, Nonlinear dynamic characteristics, Self-excited vibration, Van Der Pol equation