Abstract: The negative and associative dampings, acting on hydraulic cylinder running at low speeds, results in a complex nonlinear vibration and restricts the equipment precision performance. A nonlinear model of hydraulic cylinders is proposed by considering friction negative and associative dampings. A perturbation theory is employed for solving this nonlinear model to obtain a pulsating rate expression. And then, the coupling effects of negative and associative dampings on the cylinder vibration amplitude and frequency are studied. The results showed that: It is an opposite and competitive relationship between these two dampings because negative one promotes vibration while associative one suppresses vibration. When running velocity is below 0.61 times of Stribeck velocity v_s, the vibration gradually increases because its negative effect increases while its associative effect decreases; When running velocity exceeds 0.71v_s, the vibration gradually decreases until to zero because its negative effect decreases while its associative effect firstly increases and then decreases to zero; When running velocity is between 0.61v_s and 0.71v_s, its negative effect reach to its maximum while its associative effect reach to its minimum, resulting in diverging of vibration amplitude and decreasing of fluctuation frequency, which finally forms a spike impulse. The investigation revealed nonlinear characteristic of hydraulic cylinder under low speed condition and provided a theoretical foundation for stable operation and control of hydraulic system.

Key words: vibration, shock, friction, damping, hydraulic cylinder