Analysis on Hydraulic Dynamic Stiffness Characteristics and Experimental Research of Asymmetric Valve-Controlled Asymmetric Cylinder System

Asymmetric cylinders are widely utilized due to their simple structure and high load-carrying capacity. However, their structural asymmetry leads to significant differences in performance between the piston’s extension and retraction motions. Additionally, Hydraulic dynamic stiffness directly influences the hydraulic natural frequency, which is the lowest frequency in servo systems and thus governs the system’s dynamic response speed. Traditional nonlinear modeling of asymmetric valve-controlled asymmetric cylinder systems（AVCACS）relies on a unified transfer function for both extension and retraction, failing to account for the cylinder’s motion asymmetry. Additionally, load pressure and load flow are defined exclusively based on the extension motion, overlooking load force variations during retraction. Moreover, conventional hydraulic dynamic stiffness models also only consider cylinder parameters, neglecting the influence of connected asymmetric valve parameters, thus failing to accurately reflect the dynamic stiffness variation mechanism. To address these limitations, this study proposes a novel segmented transfer function model. Grounded in the motion asymmetry of the cylinder piston and the power matching principle of valve-controlled cylinders, the model defines forward and reverse load pressure/flow separately and establishes the corresponding mathematical model for AVCACS. It analyzes the effects of system parameters including piston position, rod-to-cap area ratio（RTCAR），and valve port area gradient ratio（VPAGR）on hydraulic dynamic stiffness. Special focus is placed on the minimum hydraulic dynamic stiffness, which limits the system’s dynamic response speed. Additionally, a comparison is conducted on the minimum forward and reverse hydraulic stiffness of AVCACS under the condition of complete matching between the valve orifice area gradient and piston area. Theoretical and experimental results demonstrate that as the matching coefficient increases, the minimum forward hydraulic dynamic stiffness increases, the minimum reverse hydraulic dynamic stiffness first decreases slightly and then increases, and the minimum reverse hydraulic dynamic stiffness is always greater than the minimum forward hydraulic dynamic stiffness, when the matching coefficient equals 1 (symmetric valve-controlled symmetric cylinder), the minimum forward and reverse hydraulic dynamic stiffness values are equal. Compared with traditional hydraulic stiffness models, the segmented transfer function model exhibits greater generality and accuracy. It provides a more precise theoretical basis for the design of control strategies in valve-controlled cylinder systems.