Analysis on hydraulic dynamic stiffness characteristics and experimental research of asymmetric valve-controlled asymmetric cylinder system

Hydraulic dynamic stiffness is a crucial parameter in hydraulic systems that directly affects the hydraulic natural frequency which is the lowest in hydraulic servo systems, and its magnitude directly determines 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. Moreover, conventional hydraulic dynamic stiffness models also only consider cylinder parameters, neglecting the influence of connected asymmetric valve parameters. 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.