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Numerical and experimental nonlinear dynamics of a proportional pressure-regulating valve

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Abstract

A novel direct proportional pressure-regulating valve is presented in this paper, and its working principle is introduced. The pressure of feedback chamber is controlled by two orifices. The lumped parameter double-mass dynamic model considering both the spool mass and the plunger mass is established. The model consists of the subsystem models with hydraulic fluid dynamic, valve mechanic and electromagnetic. The numerical model is validated through experiments. With the model, the spool and pressure dynamics are analysed by comparing the changes of the simulation parameters. The effects of orifice diameters, lap, spring stiffness, viscous damping coefficient on the stability of spool and pressure are investigated. The results show that a fixed relationship between the orifice diameters of the valve can be achieved. A larger overlap is beneficial to improve the stability of the spool. It is aimed to propose a parametric design method for the valve optimization.

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Abbreviations

A in :

Valve flow area of inlet

A out :

Valve flow area of outlet

A pi :

Piston cross-sectional area

B oil :

Oil bulk modulus

C in :

Flow coefficient of inlet

C out :

Flow coefficient of outlet

C p :

Viscous damping coefficient of plunger

c ps :

Equivalent contact coefficient of viscous friction

C s :

Viscous damping coefficient of spool

d pi :

Diameter of piston

d in :

Diameter of orifice 1

d out :

Diameter of orifice 2

d s :

Diameter of spool

F c :

Contact force between the plunger and the spool

F e :

Electromagnetic forces

F pd :

Damping force

F sp :

Hydraulic force

F ss :

Spring force

i :

Input current

k :

Spring stiffness

K b :

Induction back-EMF coefficient

K i :

Current–force gain

K ps :

Equivalent contact stiffness

K x :

Displacement–force gain

L :

Inductance of the coil

m p :

Plunger mass

m s :

Spool mass

p A :

Pressure of port A

p sp :

Feedback chamber pressure

Q :

Instantaneous flow

Q in :

Flow rate of inlet orifices

Q out :

Flow rate of outlet orifices

R c :

Internal resistance of the coil

s 1 :

Underlap

s 2 :

Overlap

t :

Time

V :

Instantaneous volume

V 0 :

Initial volume of the feedback chamber

x gap :

Gap between the spool and the plunger

x gap0 :

Initial gap when the valve closes

x s :

Spool displacement

x s0 :

Spring pre-compression

μ 0 :

Input voltage

ρ :

Oil density

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Acknowledgements

This work is supported by the National Natural Science Foundation of China (Grant No. U1864210).

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Authors and Affiliations

  1. National Key Laboratory of Vehicular Transmission, Beijing Institute of Technology, Room 412, Building 9, Beijing, 100081, People’s Republic of China

    Wei Wu, Chunhui Wei, Junjie Zhou, Jibin Hu & Shihua Yuan

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  1. Wei Wu
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  2. Chunhui Wei
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Correspondence to Wei Wu.

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Wu, W., Wei, C., Zhou, J. et al. Numerical and experimental nonlinear dynamics of a proportional pressure-regulating valve. Nonlinear Dyn 103, 1415–1425 (2021). https://doi.org/10.1007/s11071-020-06125-0

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  • DOI: https://doi.org/10.1007/s11071-020-06125-0

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