Analysis of Dynamic Characteristics of Hydraulic Transmission Lines with Distributed Parameter Model

분포정수계 유압관로 모델의 동특성 해석

Abstract

The paper deals with an approach to time domain simulation for closed end at the downstream of pipe, hydraulic lines terminating into a tank and series lines with change of cross sectional area. Time domain simulation of a fluid power systems containing hydraulic lines is very complex and difficult if the transfer functions consist of hyperbolic Bessel functions which is the case for the distributed parameter dissipative model. In this paper, the magnitudes and phases of the complex transfer functions of hydraulic lines are calculated, and the MATLAB Toolbox is used to formulate a rational polynomial approximation for these transfer functions in the frequency domain. The approximated transfer functions are accurate over a designated frequency range, and used to analyze the time domain response. This approach is usefully to simulate fluid power systems with hydraulic lines without to approximate the frequency dependent viscous friction.

Fig. 1 Schematic of a hydraulic line

Fig. 2 Closed end at the downstream of pipe

Fig. 3 Comparison of frequency response of varying line length

Fig. 4 Comparison of frequency response for H₁(s) and $\tilde{H}_1$(s) with 6th order

Fig. 5 Comparison of frequency response for H1(s) and $\tilde{H}_1$(s) with 8th order

Fig. 7 Hydraulic line terminating into a capacitance element

Fig. 6 Comparison of pressure wave forms of varying the line length

Fig. 8 Comparison of frequency response of varying the volumes of capacitance element

Fig. 9 Comparison of frequency response for H2(s) and $\tilde{H}_2$(s) 

Fig. 10 Comparison of pressure wave forms of varying the volumes of capacitance element

Fig. 11 Series lines with change of cross sectional area

Fig. 12 Comparison of frequency response of varying the ratio of radius

Fig. 13 Comparison of pressure wave forms of varying the ratio of the radius

Fig. 14 Comparison of pressure wave forms of varying the line length for ∊_r = 0.5

Fig. 15 Comparison of pressure wave forms of varying the line length for ∊_r = 1.5