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Reliability and life study of hydraulic solenoid valve. Part 1: A multi-physics finite element model

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This article appeared in a journal published by Elsevier. The attachedcopy is furnished to the author for internal non-commercial researchand education use, including for instruction at the authors institutionand sharing with colleagues.Other uses, including reproduction and distribution, or selling orlicensing copies, or posting to personal, institutional or third partywebsites are prohibited.In most cases authors are permitted to post their version of thearticle (e.g. in Word or Tex form) to their personal website orinstitutional repository. Authors requiring further informationregarding Elsevier’s archiving and manuscript policies areencouraged to visit:http://www.elsevier.com/copyright
Author's personal copy
Reliability and life study of hydraulic solenoid valve. Part 1:A multi-physics ﬁnite element model
S.V. Angadi
a
, R.L. Jackson
a,
*
, Song-Yul Choe
a
, G.T. Flowers
a
, J.C. Suhling
a
,Young-Kwon Chang
b
, Jung-Keol Ham
b
a
Department of Mechanical Engineering and NSF Center for Advanced Vehicle Electronics (CAVE), Auburn University, 270 Ross Hall, Auburn, AL 36849, USA
b
Korea Testing Laboratory, Seoul, South Korea
a r t i c l e i n f o
Article history:
Received 3 July 2008Accepted 2 August 2008Available online 15 August 2008
Keywords:
Automotive failuresFailure mechanismFinite element analysisThermal expansionValve failures
a b s t r a c t
A comprehensive multi-physics theoretical model of a solenoid valve used in an automo-bile transmission is constructed using the ﬁnite element method. The multi-physics modelincludes thecoupled effects of electromagnetic, thermodynamics andsolidmechanics. Theresulting ﬁnite element model of the solenoid valve provides useful information on thetemperature distribution, mechanical and thermal deformations, and stresses. The modelresults predict that the solenoid valve is susceptible to a coupled electrical–thermo-mechanical failure mechanism. The coil can generate heat which can cause compressivestress and high temperatures that in turn could fail the insulation between the coil wires.The model facilitates the characterization of the solenoid valve performance, life and reli-ability and can be used as a predictive tool in future solenoid design.
2008 Elsevier Ltd. All rights reserved.
1. Introduction
Asolenoidvalve(SV)isanelectromechanicaldeviceusedtocontroltheﬂowofgasorliquidbypassinganelectriccurrentthrough a coiled wire, thereby altering the valve position. A schematic of a SV and the cross-section of an unfailed SV areshown in Figs. 1 and 2, respectively. SVs are used in various applications ranging fromautomobiles (as in transmission con-trol, hydraulic power brake system, anti-lock brakes, tractioncontrol, etc.), aerospace and nuclear power plants to irrigationand water treatment, boom control in an agricultural vehicle. They also are widely used for domestic purposes, namely,washing machines, gardening and commercial dishwashers. Due to the extensive use of the solenoid valve it is very impor-tant to fully understand its behavior and the mechanisms which govern its reliability.To characterize and improve the overall performance (involving electromagnetic, mechanical and thermal ﬁelds) of a SV,a two part paper series is considered. In this paper (that is, Part 1), solenoid valves used in the control of automobile trans-missions are investigated to characterize their performance and reliability through theoretical modeling (i.e., multi-physicsﬁnite element modeling). The second paper will investigate the solenoid valve using experimental methods.The SV ﬁnite element model predictions are used to determine the testing methodology. Additionally, experimental testresultsofSVsarecorrelatedandvalidatedwiththeﬁniteelementmodelpredictionsandresults.Adetaileddiscussionontheexperimental test set up, experimental methodology, and the accompanying results can be found in the Part 2 paper.Mosttheoreticalmodelsofsolenoidvalvesaredesignedtoconsidertheirdynamiccharacteristicssothatacontrolschemecan be designed and optimized [1–9]. Most of these previous works do not consider the coupled thermo-mechanical
1350-6307/$ - see front matter
2008 Elsevier Ltd. All rights reserved.doi:10.1016/j.engfailanal.2008.08.011* Corresponding author. Tel.: +1 334 844 3340; fax: +1 334 844 3307.
E-mail address:
robert.jackson@eng.auburn.edu (R.L. Jackson).Engineering Failure Analysis 16 (2009) 874–887
Contents lists available at ScienceDirect
Engineering Failure Analysis
journal homepage: www.elsevier.com/locate/engfailanal
Author's personal copy
behaviorofthesolenoidvalve. However,thereareafewpast worksthat havemodeledthepseudo-staticperformanceofthesolenoid valve using ﬁnite elements and other computational methods [10,11]. The current work will develop a new multi-physics model of a solenoid valve which will consider the true coupled nature of the mechanisms that govern solenoid per-formance and reliability. In this work, the focus is made mostly on the thermo-mechanical failure mechanisms of the sole-noid valve. It should also be noticed that in many cases these various failure mechanisms do not occur independently.Several mechanisms may be initiated or progressed due to the occurrence of another mechanism. For instance, the Jouleheating could cause the solenoid temperature to rise signiﬁcantly. The seals in the solenoid could then degrade due tothe elevated temperatures, then causing the solenoid to leak and perhaps fail.
2. Modeling methodology
A multi-physics (thermal, mechanical and electro-magnetic) model of the solenoid valve (SV) is developed in the ﬁniteelement package Ansys
TM
(see Fig. 3), the results of which are discussed in the following section. The model solves the cou-pled ﬁelds of equations and thus captures the effects not normally considered by conventional uncoupled ﬁnite elementmodels. Forinstance, theheat generatedbythe solenoidcoil will be dueto Jouleheating. Thisheatingwill increasethetem-perature which will cause thermal expansion and stresses in the coil and the surrounding parts. Therefore, these differentﬁelds are coupled together and for improved accuracy, should be solved simultaneously. This results in a very powerful toolthat can be used to characterize solenoid valve performance.The mechanical ﬁeld of the problem considers the stresses and strains of the material, and how it will deform and pos-sibly fail due to over stressing. The theory of elasticityis used to model the deformations in the material. Then three dimen-sional Hooke’s law, which relates the stresses and strains, is given in cylindrical coordinates (
r
,
h
,
z
) as
Fig. 2.
Cross-section of an unfailed solenoid valve.
Fig. 1.
Schematic of solenoid valve and portion considered in model.
S.V. Angadi et al./Engineering Failure Analysis 16 (2009) 874–887
875
Author's personal copy
e
r
¼
1
E
½
r
r
m
ð
r
h
þ
r
z
Þ þ
a
D
T
ð
1
Þ
e
h
¼
1
E
½
r
h
m
ð
r
r
þ
r
z
Þ þ
a
D
T
ð
2
Þ
e
z
¼
1
E
½
r
z
m
ð
r
r
þ
r
h
Þ þ
a
D
T
ð
3
Þ
c
r
h
¼
2
ð
1
þ
m
Þ
E
s
r
h
ð
4
Þ
c
rz
¼
2
ð
1
þ
m
Þ
E
s
rz
ð
5
Þ
c
h
z
¼
2
ð
1
þ
m
Þ
E
s
h
z
ð
6
Þ
where
E
is the elastic modulus,
m
is the Poissons ratio,
r
is the normal stress,
s
is the shear stress,
e
is the normal strain,
c
isthe shear strain,
a
is the thermal expansion coefﬁcient, and
D
T
is the change in temperature of the material. In the currentanalysisthesolenoidvalvewillbemodeledasbeingaxisymmetricingeometryandloading.Foraxisymmetriccases, thedis-placement/strain relations are
c
r
h
¼
c
h
z
¼
s
r
h
¼
s
h
z
¼
u
h
¼
0
ð
7
Þ
e
r
¼
@
u
r
@
r
ð
8
Þ
e
h
¼
u
r
r
ð
9
Þ
e
z
¼
@
u
z
@
z
ð
10
Þ
c
rz
¼
@
u
r
@
z
þ
@
u
z
@
r
ð
11
Þ
where
u
is the normal displacement. The equations for continuity are also satisﬁed in the FEM software. Notice that in Eqs.(1)–(3), the strains are also dependant on the temperature of the material. Since the temperature in the solenoid valve willnot be uniform, the thermal ﬁeld must also be solved to obtain temperature.The two-dimensional steady-state heat transfer equation using cylindrical coordinates
r
and
h
is
o
2
T
o
r
2
þ
o
2
T
o
z
2
þ
1
r
o
T
o
r
þ
1
r
2
o
2
T
o
h
2
¼
1
kQ
ð
r
;
h
;
z
Þ ð
12
Þ
where
Q
(
r
,
h
) isthevolumetricheatgeneration,
T
isthetemperaturedistribution,whichmustbeperiodicorconstantaroundthecircumference.InthesolenoidvalveproblemtherewillbeseveralsourcesofheatsuchasJouleheatingandfriction.Since
Fig. 3.
A plot of the ﬁnite element mesh used to model the solenoid valve.876
S.V. Angadi et al./Engineering Failure Analysis 16 (2009) 874–887
Author's personal copy
thecontactforceontheplungersurfacesshouldbesmall, thefrictionforceshouldbesmall andthefrictionalheatingshouldbenegligible.ProbablythemostsigniﬁcantsourceofheatingwillbefromtheJouleheatingofthecoil.Therefore,thethermaland electrical ﬁelds are coupled, and the mechanical and thermal ﬁelds are coupled. The electrical and thermal ﬁelds mayalso be affected by the deformations of the solenoid, as it may affect the ﬂow of current and heat.The ﬁnite element model is a multi-physics model and so it automatically calculates the Joule heating occurring locallywithin the solenoid coil when electrical current is applied. The Joule heat generated is calculated from the equation:
Q
0
¼
Q V
¼
I
2
RV
¼
I
2
q
L A
2
L
¼
I
2
q
A
2
ð
13
Þ
where
Q
is the heat generated,
Q
0
is the volumetric heat generated,
V
is the volume,
A
is the cross-sectional area of thewire,
L
is the length of the wire,
I
is the current and
q
is the electrical resistivity. As expected, the total heat generatedincreases with the current squared (see Fig. 4). The heat generated can reach 1W or more. The Joule heat generation iscalculated over the entire surface of the solenoid. It is assumed in the current analysis that the current is distributedevenly through the cross-section of the solenoid coil. Although the heat generation is uniform, the temperature distribu-tion will not be.In addition, heat may be convected away from the solenoid valve through the air. This will be modeled as free con-vection. A more complete description of the convection modeling is given later. This is because convection is difﬁcult toanalytically model, and the current work will be empirically determined by comparison to the experimentalmeasurements.The electromagnetic, thermal and structural (that is, the directly coupledmulti-physics) modeling of the SV under inves-tigation in this work is being performed withthe measured dimensions of the actual SV product, the known applied currentdensity,andtheexpectedmaterialpropertiesofthevariousparts.However,toimprovecomputationaltimeonlyaportionof the SV will be modeled in the FEMsoftware (see Fig. 1). The resulting ﬁnite element mesh is shown in Fig. 3. The mesh was
reﬁned to satisfy mesh convergence.Multi-physicsmodelingof aSVusingAnsys
TM
givesinsight intothetemperaturedistributionandthelocationof thehigh-est temperature in the SV. It will also make predictions for the mechanical and thermal deformations and stresses due tohigh temperatures in the SV, and thus the resulting mechanical stresses and deformations on parts of the SV.Mostofthenecessarymaterialpropertiesarereadilyavailable. Thepropertiesusedforthematerialsofthesolenoidvalvein the current study are shown in Table 1.It is also important to apply realistic boundary conditions to the ﬁnite element model. Since the model considers manydifferent ﬁelds (thermal, mechanical and electromagnetic), several different sets of boundary conditions must be applied(see Fig. 5). As shown, the deﬂections in the
y
-direction are held constant on the top surfaces. One point is used to keepthe model from translating in the
x
-direction. Free convection is assumed on all the outer boundaries of the solid materials,except on the line of symmetry, where axisymmetric boundary conditions are assumed. Zero normal magnetic ﬂux is alsoassumed on all the outer boundaries.Tomodeltheconvectionofheatawayfromthesurfacesofthesolenoidvalve, theﬁniteelementmodeluses
Newton’s lawof cooling
(the following equation) to predict the heat loss due to convection (
q
):
q
¼
hA
D
T
ð
14
Þ
Fig. 4.
The ﬁnite element prediction of the Joule heating within the solenoid coil.
S.V. Angadi et al./Engineering Failure Analysis 16 (2009) 874–887
877

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