Three degrees of freedom (3-DOF) Helmholtz resonator which consists of three cylindrical necks and cavities connected in series (neck-cavity-neck-cavity-neck-cavity) is suitable to reduce flow pulsation in hydraulic system. A novel lumped parameter model (LPM) of 3-DOF Helmholtz resonator in hydraulic system is developed which considers the viscous friction loss of hydraulic fluid in the necks. Applying the Newton's second law of motion to the equivalent mechanical model of the resonator, closed-form expression of transmission loss and resonance frequency is presented. Based on the LPM, an optimal design method which employs rotate vector optimization method (RVOM) is proposed. The purpose of the optimal design is to search the resonator's unknown parameters so that its resonance frequencies can coincide with the pump-induced flow pulsation harmonics respectively. The optimal design method is realized to design 3-DOF Helmholtz resonator for a certain type of aviation piston pump hydraulic system. The optimization result shows the feasibility of this method, and the simulation under optimum parameters reveals that the LPM can get the same precision as transfer matrix method (TMM).
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