Reduced-Order Modeling of Elastomer-Based Constant-Flow Regulators With Experimental Validation

Abstract Constant-flow regulators are widely used in compact hydraulic systems to maintain stable flow rates under varying supply pressures. In elastomer-based regulators, pressure-induced deformation of a compliant element modifies the effective throttling area and thereby regulates hydraulic resistance. Predictive modelling of this behavior is challenging because the coupled deformation–flow process involves geometric nonlinearity, pressure-dependent contact conditions, and evolving flow restriction geometry. This study presents an experimentally calibrated reduced-order model for predicting the flow–pressure characteristics of elastomer-based constant-flow regulators used in solenoid inlet valves. The formulation combines an orifice-based hydraulic representation with a lumped-parameter energy model of elastomer deformation that determines discrete pillar loading configurations governing the effective throttling gap geometry. The deformation of the elastomer element is represented by equivalent indentation and tensile stiffnessparameters identified through targeted experiments using a single adjustable regulator specimen. The modelling framework is applied to determine the pillar height configuration required to achieve a target flow rate of 7 L/min over an operating pressure range of 1–10 bar. Model predictions agree with experimental measurements within ±5% across the regulation regime. The proposed reduced-order formulation provides a computationally efficient alternative to detailed CFD?FEM simulations for engineering analysis and design of elastomer-based passive flow regulators.