Transmission Characteristics of Fluidborne Pressure Ripples in Finite-Length Hydraulic Flexible Hoses

Abstract

The paper is concerned with the development of an analytical model for the transmission characteristics of fluidborne pressure ripples in hydraulic flexible hoses with finite length under anchored end conditions, as an extension to the previous researches for the hoses with relatively long length[1, 2]. The model is obtained in transfer matrix form relating the pressure and flow ripples at hose upstream and downstream, by considering the effect of possible longitudinal resonance of the hose in addition to the anisotropic viscoelasticity of the hose wall and the coupled vibration of the hose and the fluid. It is applied to predict the transfer matrix parameters of the hoses with different lengths. By the comparison of the predicted and measured results, it is shown that the model yields fairly good results in a frequency range up to around 3kHz and even may accurately predict what existing models failed to predict, i.e., the influence of longitudinal resonance of the hose wall on the wave propagation of fluid in the hose. KEY WORDS Fluid power systems, Flexible hose, Pressure ripple, Wave propagation, Viscoelasticity NOMENCLATURE a, b,h: inside, average radii, and thickness of hose wall Br: Bessel function ratio, Br(z)=2.11(z)l[zio(z)] c: sonic velocity in fluid in rigid pipe Eo: average Young modulus of hose fittings Ex,Ee: longitudinal and circumferential components of normal Young modulus of hose wall Ex*,Ee*: longitudinal and circumferential components of complex Young modulus of hose wall P1,P2: pressure ripples at hose upstream and downstream Q1,Q2: flow ripples at hose upstream and downstream r: radial coordinate ro: inner radius of a reference pipe (=9.8 mm) s: Laplace operator U: axial displacement of hose wall Vr, Vx: radial and axial components of fluid velocity W, W': real & apparent radial displacements of hose wall