Research Papers

The Modeling of Electrohydraulic Proportional Valves

[+] Author and Article Information
Davide Cristofori

Maha Fluid Power Research Center,  Purdue University, 1500 Kepner Drive, Lafayette, IN 47905dcristof@purdue.edu

Andrea Vacca

Maha Fluid Power Research Center,  Purdue University, 1500 Kepner Drive, Lafayette, IN 47905avacca@purdue.edu

J. Dyn. Sys., Meas., Control 134(2), 021008 (Dec 30, 2011) (13 pages) doi:10.1115/1.4005362 History: Received October 07, 2010; Revised September 20, 2011; Published December 30, 2011; Online December 30, 2011

The present work describes the modeling of a proportional relief valve actuated by an electromagnet. Two models were developed and compared each other: a detailed nonlinear model and its linearized version. The modeling approach presented has a general nature and can be applied to various types of electrohydraulic proportional valves (EHPV). The comparison between nonlinear and linear model results shows the limits of the linear approximation to study the real component. Substantially, the nonlinear model is composed by three submodels: the fluid-dynamic model (for the evaluation of the main flow features), the mechanical model (which solves the mobile body motion), and the electromagnetic model (which evaluates the magnetic forces and the electric transient). All submodels are based on a lumped parameter (LP) approach and they implement a specific set of nonlinear equations. However, to carefully model the main electromagnetic phenomena that characterize the proportional electromagnet behavior (including: magnetic losses, fringing effects, and magnetic saturation), a finite element analysis (FEA) 3D model was developed by the authors. The LP electromagnetic model is based on a particular use of the FEA 3D model steady state results. A series of transient simulations were performed through the FEA 3D model in order to quantify the effect of the eddy currents and to determine a second order transfer function used in the linear model to describe the electromagnet dynamics. The remaining parts of the linear model are obtained by linearizing the nonlinear model equations. The FEA 3D model was experimentally validated in steady-state conditions, while the results of the overall model of the valve were verified in both steady-state and dynamic conditions.

Copyright © 2012 by American Society of Mechanical Engineers
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Figure 1

The modeled valve: (a) Picture; (b) ISO symbol; (c) Simplified schematic: 1. Valve body; 2. Poppet; 3. Armature; 4. Magnetically conductive core.; 5. Coil; 6. Nonmagnetically conductive ring; 7. Spring.

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Figure 2

Schematic representation of the developed model

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Figure 3

Representation of the coordinate system, the control volumes and their relative connections through orifices

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Figure 4

(b-h) characteristic of the soft ferromagnetic material used for the proportional valve taken as reference

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Figure 5

Electric scheme of the electromagnet

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Figure 6

The anhysteretic FMx curve is approximately obtained as mean value between the curve for increasing (FMx(imin→imax))) and decreasing (FMx(imax→imin))) current

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Figure 7

The empirical correction curve is obtained as difference between the anhysteretic curve and the hysteretic curves

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Figure 8

Block diagram of the electromagnetic submodel (proportional amplifier and LP electromagnet model)

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Figure 9

3D mesh of the FEA proportional electromagnet model (air mesh is not represented): (a) external core; (b) internal core; (c) nonmagnetic ring; (d) armature

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Figure 10

Map of the magnetic flux density and detail of the axial air gap area. The magnetic flux vectors are schematically represented in case of: (b) large, (c) small air gap

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Figure 11

Axial magnetic force for an input step for versus Effect of different material of the non magnetic ring. (a) Full transient; (b) Zoom which highlights the slowdown in the magnet caused by the bronze and copper ring

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Figure 12

Radial magnetic force evaluated through the 3D FEA model respect to the electric current i and the armature stroke XS

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Figure 13

Electromagnet transient in case of XS = 0 mm

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Figure 14

Empirical technique to obtain, known the step response, the time constant of an overdamped 2nd order system

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Figure 15

Simplified block diagram of the linear model

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Figure 16

Graphical representation of the nonlinear model in the AMESim® software environment

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Figure 17

Picture and scheme of the apparatus used to characterize the electromagnet

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Figure 18

Comparison between modeled and measured FMx (in case of XS = 0.2 and 2.0 mm)

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Figure 19

Comparison between modeled and measured FMx (in case of i = 0.5 and 1.5 A)

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Figure 20

Picture and scheme of the hydraulic system used to characterize the valve

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Figure 21

Schematic of the hydraulic system used to characterize the valve

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Figure 22

Operating test T1 (openings, x = 0.5, 0.6, 0.7 mm)

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Figure 23

Operating test T2 (i = 0.0, 0.5, 1.0 A)

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Figure 24

Comparison between experimental and simulated pin, as a function of i, for a constant Qin (cases: 1.4, 5.5 l/min)

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Figure 25

Scheme of the hydraulic system model

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Figure 26

Transient inlet port pressure after a step variation of the dc value from 0% to 35%

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Figure 27

Inlet port pressure transient after a step variation of the dc value from 35% to 0%

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Figure 28

Transient FF,x and Qin in the simulation of Fig. 2. (a) Composite plot; (b) Detailed view of time 0.25 for normalized stroke and flow; (c) detailed view of time 0.25 for normalized friction



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