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Nonsmooth Quasistatic Modeling of Hydraulic Actuators

This article presents a quasistatic model of a hydraulic actuator driven by a four-valve independent metering circuit. The presented model describes the quasistatic balance between the velocity and force and that between the flowrate and the pressure. In such balanced states, the pressure difference across each valve determines the oil flowrate through the valve, the oil flowrate into the actuator determines the velocity of the actuator, and the pressures in the actuator chambers are algebraically related to the external force acting on the actuator. Based on these relations, we derive a set of quasistatic representations, which analytically relates the control valve openings, the actuator velocity, and the external force. This analytical expression is written with nonsmooth functions, of which the return values are set-valued instead of single-valued. We also show a method of incorporating the obtained nonsmooth quasistatic model into multibody simulators, in which a virtual viscoelastic element is used to mimic transient responses. In addition, the proposed model is extended to include a regeneration pipeline and to deal with a collection of actuators driven by a single pump.