response characteristics of dynamic torque for wet clutch ...2021/02/06 · h drdθ, t c z π 0 b a...

Research ArticleResponse Characteristics of Dynamic Torque for Wet ClutchEngagement A Numerical and Experimental Study

Zhigang Zhang 12 Ling Zou 1 Hang Liu 1 Jin Feng 1 and Zhige Chen 1

1Key Laboratory of Advanced Manufacturing Technology for Automobile Parts Ministry of EducationChongqing University of Technology Chongqing 400054 China2Ningbo Shenglong Group Co Ltd Ningbo 315104 China

Correspondence should be addressed to Zhigang Zhang zhangzhigangcquteducn

Received 6 February 2021 Revised 28 April 2021 Accepted 8 May 2021 Published 18 May 2021

Academic Editor Dario Richiedei

Copyright copy 2021 Zhigang Zhang et al(is is an open access article distributed under the Creative CommonsAttribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

To determine the factors affecting the dynamic transmitted torque response characteristics of the wet clutch the oil film pressurethe asperity contact pressure the applied pressure and the dynamic transmitted torque model were established using the fourth-order RungendashKutta numerical method to couple the oil film thickness and the speed difference to obtain the change curve of thejoint pressure and the transmitted torque (e established model was used to study the influence of the pressure hysteresis timelubricant viscosity friction lining permeability friction pair equivalent elastic modulus and surface combined roughness RMS onthe dynamic transmitted torque response during the wet clutch engagement (e results indicate that the longer the pressurehysteresis time the smaller the permeability of the friction lining the smaller the equivalent elastic modulus the greater surfacecombined roughness RMS the more delayed the response of the transmitted torque and the smaller the level of jerk of the wetclutch engagement Also the lower the lubricant viscosity the greater the permeability of the friction lining and the smaller theequivalent elastic modulus is and the greater surface combined roughness RMS is the more sensitive the transmitted torqueresponse is to pressure response changes

1 Introduction

As a core component of vehicle transmission systems thewet clutch plays a critical role in vehicle starting and gearshifting processes It is widely used in premium sedansheavy-duty vehicles and crawler vehicles [1] In the workingprocess of the wet clutch the dynamic transmission oftorque highly depends on the hydraulic pressure acting onthe piston for compression of the separator plate and thefriction disk of friction pairs Studying the regulation of thetransmitted torque during wet clutch engagement signifi-cantly affects the detail and optimization of the developedcontrol strategy which further determines the startingstability of the vehicle and the sensing of frustration duringgear shifting Concurrently it significantly impacts thesliding friction power of the wet clutch during vehiclestarting and gear shifting (e variation in dynamic trans-mitted torque of the wet clutch mainly depends on its torque

response characteristics [2] Consequently the effects ofvarious factors on the dynamic transmitted torque responseof the wet clutch are analyzed on the basis of the frictiontransmission mechanism of the wet clutch which is of greatsignificance for obtaining the optimal wet clutch controlstrategy

Existing domestic and international research on the wetclutch has mainly focused on the modeling of wet clutchengagement characteristics analysis of thermal character-istics and control optimization Gao et al [3] performedexperiments to investigate the surface asperity height dis-tribution model of the paper-based friction disk and sub-sequently modeled and simulated the wet clutch engagementcharacteristics via a surface asperity height distributionmodel [4] A three-dimensional finite element model and aheat conduction model of the friction pair were establishedin which the influence of the groove was considered Liuet al [1] established a mathematical model of the wet clutch

HindawiShock and VibrationVolume 2021 Article ID 5522998 9 pageshttpsdoiorg10115520215522998

engagement by analyzing the engagement of the wet clutchapplying the one-dimensional average Reynolds equationand the rough surface elastic contact model(e effect of wetclutch engagement pressure on viscous torque rough fric-tion torque and transmitted torque during the engagementis studied Yu et al [5] studied the friction torque charac-teristics of a paper-based wet clutch based on the modifiedReynolds equation Reference [6] discussed the influence ofengagement pressure lubricating oil working temperaturefriction coefficient and other factors on the transmittedtorque of the wet clutch during the working engagementChen [7] did clutch engagement tests under differentworking conditions and studied the influence of engagementoil pressure on speed and the influence of engagement oilpressure and speed on torque Chen studied the torquetransmission characteristics of a clutch with a single frictionpair and proposed the concept of equivalent friction coef-ficient Simulation results show that increasing viscosity ordecreasing surface roughness can lead to smooth incre-mental torque Increasing control oil pressure can reduceengagement time but the peak of power loss will increaseDecreasing Yongrsquos modulus can delay response of asperitycontact torque and increase engagement time [8]

Miyagawa et al [9] conducted heat-fluid-solid couplinganalysis to study the wet clutch engagement characteristicsdeveloped the wet clutch engagement characteristic modeland studied the influence of groove type on the engagementcharacteristics of friction pairs Reference [10] has tried tostudy the torque transmission characteristics in radialmagnetorheological (MR) clutch discs with different grooveprofiles Jang et al [4] developed a thermodynamic model toanalyze the torque response of a wet clutch with differentgroove patterns and showed that thermal effects criticallyimpact the engagement time and torque response Reference[11] established a multiphysics coupling clutch thermody-namic model analyzed the generation and change mecha-nism of viscous torque and contact torque during clutchengagement and studied the influence of lubricating oiltemperature on friction torque characteristics Depratereet al [12] applied a bilevel iterative learning control strategyto control wet clutch engagement in an optimal manner andobserved that the engagement quality was adequate Ref-erence [13] proposed a new adaptive control method ofclutch torque which mainly focused on the relationshipbetween dry clutch and actuator piston pressure and clutchtorque However response characteristics of torque in wetclutch engagement from the standpoint of the frictiontransmission mechanism of the wet clutch have scarcelybeen investigated

In this study on the basis of the analysis of the wet clutchfriction transmission mechanism a dynamic transmittedtorque model of the wet clutch is proposed and the factorsinfluencing the torque response characteristics of the wetclutch are analyzed via numerical simulations and experi-mental methods

2 Friction Transmission Mechanism ofWet Clutch

According to the mechanisms of applied force and trans-mitted torque of the wet clutch the wet clutch engagementprocess can be divided into three stages [14] the fluidsqueezing stage boundary lubrication stage and mechanicalcontact stage In the fluid squeezing stage transmittedtorque is composed of hydrodynamic torque of the auto-matic transmission fluid (ATF) oil film In the boundarylubrication stage the transmitted torque is composed ofhydrodynamic torque of the ATF oil film and the asperitycontact torque of friction pairs With wet clutch engage-ment contact pressure and friction torque of asperitiesgradually play a dominant role In the mechanical contactstage the transmitted torque is only composed of asperityfriction torque (e friction transmission mechanism in wetclutch engagement is modeled as follows

21 Model of Oil Film Pressure Wet clutch engagement canbe simplified as per the physical model shown in Figure 1Friction pairs are filled with lubricant before wet clutchengagement and the friction disk and separator plate areseparated by the oil film(e angular velocity of friction diskand separator plate are ω2 and ω1 respectively then frictionpairs are compressed gradually via the applied pressure PsCombined with the axial symmetric characteristics of thewet clutch friction pairs the governing equation of the forcesupported by the oil film in cylindrical coordinate system isderived using the PatirndashCheng average Reynolds equation[15 16]

ddr

rφr h3

+ 12Φ d1113872 1113873dPh

dr1113890 1113891 12 ηr

dhT

dt (1)

where φr is the radial flow factor h is the film thickness of theoil Φ is the permeability of the friction lining d is thethickness of the friction lining Ph is the average pressure ofthe oil film η is the dynamic viscosity of the oil film and hT

is the average clearance of the friction pairsLet us assume that the surface asperity height of the

friction disk and separator plate are subject to Gaussiandistribution of zero average value (en the relationshipbetween the average clearance of friction pairs hT and oilfilm thickness h can be described as [17]

dhT

dt 05 1 + erf

h2

radicσ

1113888 11138891113890 11138911113896 1113897dh

dt (2)

Assume that

g(h) 05 1 + erfh2

radicσ

1113888 11138891113890 1113891 (3)

where σ is the RMS roughness of the friction pairs and erf isthe Gaussian error function

2 Shock and Vibration

On combination of the oil film boundary condition atthe inner and outer diameters of the friction pairs the oilfilm pressure in the radial distribution can be obtained as[17]

Ph(r) 3η

φr h3

+ 12Φ d1113872 1113873r2

+b2

minus a2

2 ln(ab)ln

r

bminus b

21113890 1113891g(h)

dh

dt

(4)

22 Model of Asperity Contact Pressure Let us assume thatthe surface asperity heights of the friction pairs are subject toGaussian distribution combined with G-W elastic contactmodel (en the real contact area Ac between the asperitiesof the friction pairs in the wet clutch is obtained by [18 19]

Ac πλcσ12π

radic eminus (h

2

radicσ)2

+h

σ(g(h) minus 1)1113890 1113891 (5)

where λ is the asperity density and c is the asperity tip radius(erefore the asperity contact pressure of friction pairs

in the wet clutch Pc is expressed by

Pc Eδ (6)

where E is the equivalent elasticity modulus of friction pairsand δ is the real contact area ratio (δ AcAn) which is usedto characterize the relationship between the real contact areaand the nominal contact area (An) of the friction pairs

23 Model of Applied Pressure During wet clutch engage-ment the applied pressure is not a fixed value but graduallyreaches the set value in a short period of time controlled bythe hydraulic system (e applied pressure acting on thefriction pairs can be obtained by fitting the applied pressuretest data [11]

Ps Po 1 minus exp minust

ts1113888 11138891113888 1113889 (7)

where Po is the set value of pressure and ts is the hysteresistime of pressure

24Model ofDynamicTransmittedTorque According to theengagement of the wet clutch the applied pressure is suc-cessively carried by the oil film and asperities and the forcebalance during wet clutch engagement can be obtained as

π b2

minus a2

1113872 1113873Ps (1 minus δ)BPh dA + δBPc dA (8)

where a and b are the inner and outer radii of the frictionpairs respectively

Owing to different load carriers in wet clutch engage-ment the mechanism of transmitted torque is also trans-formed gradually from the viscous torque of oil filmTv to thefriction torque of asperities Tc (e torque can be obtainedfrom the torque balance condition in wet clutch engagementby using

T (1 minus δ)Tv + δTc (9)

where

Tv 11139462π

01113946

b

a(1 minus δ) φf minus φfs1113872 1113873

r3ηωrel

hdr dθ

Tc 11139462π

01113946

b

aδfcPcr

2 dr dθ

T I middotdωrel

dt

(10)

where φf and φfs are the factors given by PatirndashCheng[20 21] ωrel is the relative angular velocity between theseparator plates and friction disks and fc is the frictioncoefficient of the asperity contact

3 Numerical Simulations and Analysis

(e force and torque balance equations are solved via in-tegration using the RungendashKutta method to obtain the oilfilm thickness hi and relative angular velocity of the frictionpairs ωi

rel for each time increment i (e step of numericalintegration is 0001 s and the iteration termination condi-tion corresponds to the point at which the relative angularvelocity between the separator plates and friction disks is lessthan 0001 rads (en the viscous torque of the oil filmfriction torque of the asperities and total torque transmittedby the wet clutch can be obtained using the oil film thicknessand rate of relative angular velocity variation In the sim-ulation it is assumed that the angular velocity of the sep-arator plate is always zero and the initial angular velocity ofthe friction disk is ω0 (e friction disks gradually compressagainst the separator plates under the applied pressure untilthe angular velocity of the friction disks satisfies the iterativetermination condition By this time the engagement of thewet clutch is completed

To facilitate analysis of the influence law of lubricantviscosity friction lining permeability equivalent elasticmodulus of the friction pairs and surface roughness RMS onresponse time of torque in the wet clutch the pressureresponse time (ΔtP) and torque response time (ΔtT) aredefined as shown in Figure 2 Here ΔtP is defined as the

Separator plateFriction plate

ATF

P3 Psr

z

Figure 1 Physical model of wet clutch engagement

Shock and Vibration 3

time period when the value of applied pressure is between10 and 90 of the stable value and the torque responsetime ΔtT is defined as the time period when the value ofapplied pressure is between 50 of the stable value and thetorque is 90 of transmitted torque

To investigate the effect of lubricant viscosity frictionlining permeability equivalent elastic modulus of the fric-tion pairs and surface roughness RMS on response time oftorque in the wet clutch five groups of pressure hysteresistimes are taken as 002 s 004 s 006 s 008 s and 01 s re-spectively (e corresponding pressure response times are0044 s 0088 s 0132 s 0176 s and 022 s according toformula (6) and the definition of pressure response time(en the effect of pressure hysteresis time lubricant vis-cosity permeability of friction lining equivalent elasticmodulus of friction pairs and surface roughness RMS ontorque response time are studied respectively based on thedynamic torque model of the wet clutch (e initial con-ditions for the simulation are listed in Table 1

31 Effect of Pressure Hysteresis Time (e effect of pressurehysteresis time ts on applied pressure Ps and transmittedtorque T during wet clutch engagement is shown in Figure 3(is figure indicates that by increasing the pressure hys-teresis time the applied pressure and transmitted torquetake more time to reach stable values and the response timeof the applied pressure and transmitted torque are bothextended However the change in pressure hysteresis timeimposes only a minor influence on the stable value of thetransmitted torque Appropriately reducing the pressurehysteresis time can accelerate the response of the trans-mission torque shorten the wet clutch engagement timeand increase the impact force of wet clutch engagement

32 Effect of Lubricant Viscosity It can be understood fromthe simulation results shown in Figure 4 that the pressureresponse time and the transmitted torque response timehave a positive correlation and the lubricant with a lowerviscosity demonstrates more sensitivity of transmitted tor-que response time to pressure response time In contrastwith the increase in lubricant viscosity the sensitivity oftransmitted torque response time to pressure response timereduces (is is owing to the resistance caused by squeezingoil film increasing with the increase in lubricant viscosityduring the engagement of the wet clutch Consequently theduration for which the oil film remains between the sepa-rator plate and the friction disk increases Further thetransmitting torque response time is insensitive to the

times105

∆tp

∆tT

0

2

4

6

8

10

Pres

sure

(Pa)

0

20

40

60

80

100

Torq

ue

01 02 03 04 05 06 07 08 09 1 11 120Time (s)

PressureTorque

Figure 2 Definition of response time for pressure and torque

Table 1 Initial conditions for simulation

Parameters ValueInner radius of friction pairs am 0064Outer radius of friction pairs bm 0085Friction lining thickness dm 0001Surface roughness σm 841times 10ndash6

Friction material permeability Φm2 4times10ndash12

Equivalent elasticity modulus EPa 27times107

Asperity density λm2 7times107

Asperity tip radius Rm 8times10ndash4

Initial film thickness hom 88times10ndash5

Lubricant viscosity ηPamiddots 00681Maximum applied pressure PoPa 6times105

Initial angular velocity ωorads 1000Moment of inertia Ikgmiddotm2 056

02Time (s)

times105

ts = 001sts = 005sts = 01s

0

1

2

3

4

5

6

7

8

Pres

sure

(Pa)

0

10

20

30

40

50

60

70

80

Torq

ue (N

m)

03 04 05 06 07 08 09 1 11 120 01

PressurePressurePressure

TorqueTorqueTorque

Figure 3 Effect of pressure hysteresis time on torque responsetime


change in pressure response time under high lubricantviscosity in wet clutch engagement and vice versa

When the pressure response time is short under thesame pressure response time as the viscosity of the lubri-cating oil is greater the torque response time is longer thetransmission torque rises more smoothly and the level ofjerk of the wet clutch engagement is smaller (is is becausein the squeeze stage the greater the viscosity of the lubri-cating oil the greater the viscous resistance of the lubricatingoil penetrating into the friction lining or being squeezed outalong the friction surface so the longer the squeeze stagelasts the slower the transmitted torque response is

Conversely when the pressure response time is relativelylong under the same pressure response time as the viscosityof the lubricating oil is greater the torque response time isshorter the transmission torque rises faster and the level ofjerk of the wet clutch engagement is greater When thepressure response time is relatively long as the viscosity ofthe lubricating oil changes the flow inertia of the coolinglubricating oil has less influence and the centrifugal force onthe cooling lubricating oil in the separation gap is thedominant factor (erefore when designing a wet clutchpressure response time and lubricating oil viscosity must beconsidered at the same time

33 Effect of Friction Lining Permeability Figure 5 demon-strates the variation in torque response time due to differentfriction lining permeability It is found that with the in-crease in the permeability of friction lining torque responsetime under the same pressure response time is reduced (isis because the higher the permeability of the friction lining isthe easier the lubricant permeates into the porous structure

of the friction lining As a result the duration of the fluidsqueezing stage is shortened and the torque response time isreduced (e greater the permeability of the friction liningthe faster the torque response time under the same pressureresponse time which indicates that the faster the transmittedtorque rises the greater the level of jerk of the wet clutchengagement is

Further the higher the permeability of the friction liningis the more sensitive the torque response time to pressureresponse time is and vice versa (is is because the hy-drodynamic pressure effect is easily formed between thefriction pairs when the permeability of friction linings is lowwhich weakens the effect of pressure response time variationon the transmitted torque response

34 Effect of Equivalent Elastic Modulus (e effect of dif-ferent equivalent elastic modulus on torque response time isillustrated in Figure 6 It can be seen from Figure 6 that withthe increase in equivalent elastic modulus of friction pairstorque response time is reduced slightly under the samepressure response time With a fixed elastic modulus torqueresponse time is increased with the increase in pressureresponse time(is is because in the same pressure responsetime the larger the equivalent elastic modulus is the largerthe bearing force generated by the same deformation and thelarger friction torque of asperities will be Meanwhile thethickness of the oil film between friction pairs becomeslarger when the equivalent elastic modulus increases so theviscous torque of oil film becomes smaller which results in afaster response of transmitted torque As the equivalentelastic modulus increases the torque response time

004

006

008

01

012

014

016

018

02

Tor

que r

espo

nse t

ime (

s)

006 008 01 012 014 016 018 02 022004Pressure response time (s)

η = 00381Pamiddotsη = 00681Pamiddotsη = 00981Pamiddots

Figure 4 Effect of lubricant viscosities on torque response time

006 008 01 012 014 016 018 02 022004 Pressure response time (s)

0

005

01

015

02

025

03

Torq

ue re

spon

se ti

me (

s)

Ф = 04 times 10ndash12m2



Figure 5 Effect of friction lining permeability on torque responsetime


decreases slightly under the same pressure response timeindicating that the faster the transmitted torque rises thegreater the level of jerk of the wet clutch engagement is

35 Effect of Surface Combined Roughness RMS It can becomprehended from Figure 7 that by increasing the surfacecombined roughness RMS of friction pairs the torque re-sponse time corresponding to the same pressure responsetime is increased(e reason for this is that with the increaseof surface combined roughness RMS of friction pairs thecontact of asperities proceeds in advance the force sup-ported by oil film drops the shear flow factor is reduced thenumber of the asperities in contact becomes less and thefriction torque of asperities is reduced thus the transmittedtorque response time increases As the surface combinedroughness RMS increases the torque response time isslightly longer under the same pressure response time thetransmitted torque rises slowly and the level of jerk of thewet clutch engagement is smaller Moreover the higher thesurface combined roughness RMS of friction pairs is themore sensitive the response of transmitted torque to thechange of pressure response will be

4 Test Verification

To validate the simulation results the response character-istics of transmitted torque of wet clutch are tested using thewet clutch comprehensive performance test rig and thespecifications and materials of the friction pairs used in thetest are consistent with what was used in the numericalsimulation which is shown in Figure 8 In the test the

separator plates were mounted on the outer hub and thefriction disks were mounted on the inner hub of clutchfollowing which the outer hub was fixed by the torque metersuch that the separator plates were fixed Furthermore theinner hub of clutch was connected with an inertia flywheeldriven by the motor to determine the rotation of frictiondisks (e working principle of the bench is as follows Firstthe speed of active end is set to a constant value and then theIPC (Industrial Personal Computer) controls the hydraulicsystem according to the set pressure curve and applies theengaging pressure to the friction pair of the wet clutch untilthe displacement of the friction plate of the drive end is zeroDuring the entire test process the change regulation oftransmitted torque and pressure in engagement weremeasured and recorded at a 1 kHz sampling frequency usingthe test system in real time as shown in Figure 9

To ensure the comparability between the test and sim-ulation results PID parameters of clutch hydraulic controlsystem on the test rig were adjusted repeatedly before themeasurement to understand the control of different pressureresponse time which includes 0044 s 0088 s 0132 s0176 s and 022 s in each work condition of the test

Due to the limitations of test conditions only the in-fluence law of lubricant viscosity and surface combinedroughness RMS of friction disk on the response charac-teristics of transmitted torque for wet clutch was tested andverified To investigate the effect of lubricant viscosity thetest was performed to assess the transmitted torque responsetime with respect to different pressure response times of thewet clutch with lubricant temperatures of 40degC 80degC and110degC (e comparison between test results and simulationresults is shown in Figure 10 It can be seen from the figure

σ = 441 times 10ndash6mσ = 641 times 10ndash6mσ = 841 times 10ndash6m


004

006

008

01

012

014

016

Tor

que r

espo

nse t

ime (

s)

Figure 7 Effect of surface combined roughness RMS on torqueresponse time


E = 27 times 107PaE = 54 times 107PaE = 81 times 107Pa

004

006

008

01

012

014

016

Tor

que r

espo

nse t

ime (

s)

Figure 6 Effect of equivalent elastic modulus on torque responsetime


that the simulation results are highly consistent with the testresults but the response time during the test is longer thanthat during the simulation (is is mainly due to the flowwhose lubricant viscosity decreases with the increase of shearstress that is shear thinning flow

Moreover the test was performed to assess the trans-mitting torque response time under different pressure re-sponse time with new friction disk new friction disk inrunning-in period and worn friction disk with lubricanttemperature of 40degC to evaluate the effect of surface com-bined roughness RMS on response time of transmittingtorque the results are shown in Figure 11 (e effect of testand simulation roughness RMS on the response time of thetransmitted torque is shown in Figure 11 It can be seen from

the figure that the test results and the simulation results havegood consistency but there are also certain deviations (isis mainly because the friction disk used has a smaller rangewhen sampling but the overall roughness shown by thewhole is deviated from the simulation roughness

(rough the experiment of viscosity and roughness it isproved that the simulation analysis model in this paper is

Test box

Separator plateSeparator plate

Inertia flywheel

Torque meter

IPCAD

Motor

ABB

Hydraulic system

Friction disk

(a)

Inertiaflywheel

Test box

Torquemeter

Hydraulicsystem

Motor

(b)

Figure 8 Wet clutch comprehensive performance test rig (a) Test rig principle (b) Test rig picture

Pressure

Torque

6

5

4

3

2

1

00 01 02 03 04 05 06 07 08

Engagement time (s)

Pres

sure

(Pa)

1101009080706050403020100

Torq

ue (N

m)

times105

Figure 9 Response characteristics of torque for wet clutch 006 008 01 012 014 016 018 02 022004 Pressure response time (s)

110degCη = 00381Pamiddots

η = 00681Pamiddots

80degC


004

006

008

01

012

014

016

018

02 T

orqu

e res

pons

e tim

e (s)

Figure 10 Test results of effect of lubricant viscosities on torqueresponse time


reliable and can be used to analyze the change law of thedynamic transmitted torque response characteristics of thewet clutch

5 Conclusions

For the engagement of the wet clutch four models of the oilfilm pressure the asperity contact pressure the appliedpressure and the dynamic transmitted torque model areestablished Based on the mathematical model establishedthe simulation analysis method was used to study the in-fluence of the pressure hysteresis time lubricant viscosityfriction lining permeability friction pair equivalent elasticmodulus and surface combined roughness RMS on thedynamic transmitted torque response characteristics duringthe wet clutch engagement Further a wet clutch compre-hensive performance test bench was used to verify the law ofthe influence of lubricant viscosity and surface combinedroughness RMS on the transmitted torque response time andto verify the validity of the established mathematical model(e result shows the following

(1) (e longer the pressure hysteresis time the moredelayed the response of transmitted torque and thesmaller the level of jerk of the wet clutch engagement

(2) (e lower the lubricant viscosity is the more sen-sitive the transmitted torque response is to thepressure response time and the pressure responsetime has a great influence on the transmitted torqueresponse time of different lubricant viscosities

(3) (e greater the permeability of the friction lining isthe faster the transmitted torque response is themore sensitive it is to pressure response changes the

shorter the time for the wet clutch to engage is andthe greater the level of jerk is

(4) (e smaller the equivalent elastic modulus is theslower the transmitted torque response is the moresensitive it is to pressure response changes thelonger the time for the wet clutch to engage is andthe smaller the level of jerk is

(5) (e greater the surface combined roughness RMS isthe slower the transmitted torque response is themore sensitive it is to pressure response changes isand the smaller the level of jerk of wet clutch en-gagement is

(6) Due to the limitations of test conditions only theinfluence of lubricant viscosity and surface com-bined roughness RMS of friction disk on thetransmitted torque response characteristics for wetclutch was tested and verified (is verifies thecorrectness of the simulation analysis and shows thatthe simulation analysis model in this paper is reli-able and it can be used to analyze the change law ofthe dynamic transmitted torque response charac-teristics of the wet clutch and further experimentalresearch on other influencing factors can be carriedout in the future

Data Availability

(e data used to support the findings of this study are in-cluded within the article

Conflicts of Interest

(e authors declare that they have no conflicts of interest

Acknowledgments

(is paper was supported by Chongqing Research Programof Basic Research and Frontier Technology (nocstc2017jcyjAX0143) China Postdoctoral Science Founda-tion (no 2020M681808) and the Postdoctoral ResearchPreferred Fund Project of Zhejiang Province (noZJ2020080)

References

[1] X C Liu Z G Zhang X H Shi et al ldquoEffect of engagementpressure on engagement characteristics of wet clutchrdquo Journalof Chongqing University of Technology (Natural Science)vol 4 no 1 pp 7ndash11 2015

[2] Y Yang C L Robert and F Tamotsu ldquoPrediction of torqueresponse during the engagement of wet friction clutchrdquo SAETechnical Paper Warrendale PA USA 981097 1998

[3] H Gao G C Barber and M Shillor ldquoNumerical simulationof engagement of a wet clutch with skewed surface rough-nessrdquo Journal of Tribology vol 124 no 2 pp 305ndash312 2002

[4] J Y Jang M M Khonsari and R Maki ldquo(ree-dimensionalthermohydrodynamic analysis of a wet clutch with consid-eration of grooved friction surfacesrdquo Journal of Tribologyvol 133 no 1 Article ID 011703 2011


004

006

008

01

012

014

016

Tor

que r

espo

nse t

ime (

s)

Worn friction diskσ = 441 times 10ndash6m

σ = 641 times 10ndash6m

Running-in friction disk

New friction diskσ = 841 times 10ndash6m

Figure 11 Test results of effect of surface roughness on torqueresponse time


[5] L Yu B Ma M Chen H Li J Liu and L Zheng ldquoNumericaland experimental studies on the characteristics of frictiontorque based on wet paper-based clutchesrdquo Tribology Inter-national vol 131 no 1 pp 541ndash551 2018

[6] L C Yang Simulation Study on Torque Characteristics ofMulti-Plate Wet Clutch Jilin University Changchun China2015 in Chinese

[7] H Chen ldquo(e effect of wet clutch engagement oil pressure onspeed and torquerdquo Equipment Management and Mainte-nance vol 13 no 1 pp 53ndash55 2018

[8] M Chen B Ma G Li et al ldquoStudy on torque characteristics ofmulti-plate wet clutches during engagementrdquo Journal ofHuazhong University of Science and Technology (Natural ScienceEdition) vol 42 no 5 pp 34ndash39 2014

[9] M Miyagawa M Ogawa Y Okano H Hara S Sasaki andK Okui ldquoNumerical simulation of temperature and torquecurve of multidisk wet clutch with radial and circumferentialgroovesrdquo Tribology Online vol 4 no 1 pp 17ndash21 2009

[10] M K(akur and C Sarkar ldquoInvestigation of different grooveprofile effects on torque transmission in shear mode mag-netorheological clutch numerical simulation and experi-mental studyrdquo Journal of Tribology vol 143 no 9 pp 1ndash102020

[11] L Yu B Ma M Chen et al ldquoInfluence of the temperature oflubricating oil on the friction torque of cu-based wet clutchrdquoJournal of Mechanical Engineering vol 56 no 20 pp 155ndash1632020

[12] B Depraetere G Pinte W Symens and J Swevers ldquoA two-level iterative learning control scheme for the engagement ofwet clutchesrdquo Mechatronics vol 21 no 3 pp 501ndash508 2011

[13] J Park and S Choi ldquoAdaptive control method of clutchtorque during clutch slip engagementrdquo in Proceedings fo the2020 American Control Conference (ACC) July 2020

[14] Z Zhang X Zhou L Shen and Y-J Li ldquoSimulation andexperiment on dynamic engagement characteristics of wetclutchrdquo China Journal of Highway and Transport vol 23no 3 pp 115ndash120 2010

[15] P Zagrodzki and S A Truncone ldquoGeneration of hot spots in awet multidisk clutch during short-term engagementrdquo Wearvol 254 no 5-6 pp 474ndash491 2003

[16] F Meng Q J Wang D Hua and S Liu ldquoA simple method tocalculate contact factor used in average flflow modelrdquo Journalof Tribology vol 132 no 2 pp 483ndash485 2010

[17] Y Chen Research on Temperature Characteristics and Aer-mal Failure of Wet Multi-Disk Clutch Chongqing UniversityTechnology Chongqing China 2019 in Chinese

[18] Z Y Li ldquoModeling and simulation of dual clutch joint startcontrol of wet DCTrdquo Mechanical Transmission vol 43 no 1pp 109ndash113 2019

[19] Q L Wang ldquoResearch on transient characteristic of stressfifield of the friction pair during soft start-up process ofhydro-viscous driverdquo Mechanical Transmission vol 43pp 32ndash37 2019

[20] N Patir and H S Cheng ldquoApplication of average flflowmodelto lubrication between rough sliding surfacesrdquo Journal ofTribology vol 101 no 2 pp 229-230 1979

[21] X B Shang Aeoretical Analysis and Experimental Study onEngagement Process of Wet Clutch Zhejiang UniversityHangzhou China 2019 in Chinese


engagement by analyzing the engagement of the wet clutchapplying the one-dimensional average Reynolds equationand the rough surface elastic contact model(e effect of wetclutch engagement pressure on viscous torque rough fric-tion torque and transmitted torque during the engagementis studied Yu et al [5] studied the friction torque charac-teristics of a paper-based wet clutch based on the modifiedReynolds equation Reference [6] discussed the influence ofengagement pressure lubricating oil working temperaturefriction coefficient and other factors on the transmittedtorque of the wet clutch during the working engagementChen [7] did clutch engagement tests under differentworking conditions and studied the influence of engagementoil pressure on speed and the influence of engagement oilpressure and speed on torque Chen studied the torquetransmission characteristics of a clutch with a single frictionpair and proposed the concept of equivalent friction coef-ficient Simulation results show that increasing viscosity ordecreasing surface roughness can lead to smooth incre-mental torque Increasing control oil pressure can reduceengagement time but the peak of power loss will increaseDecreasing Yongrsquos modulus can delay response of asperitycontact torque and increase engagement time [8]

Miyagawa et al [9] conducted heat-fluid-solid couplinganalysis to study the wet clutch engagement characteristicsdeveloped the wet clutch engagement characteristic modeland studied the influence of groove type on the engagementcharacteristics of friction pairs Reference [10] has tried tostudy the torque transmission characteristics in radialmagnetorheological (MR) clutch discs with different grooveprofiles Jang et al [4] developed a thermodynamic model toanalyze the torque response of a wet clutch with differentgroove patterns and showed that thermal effects criticallyimpact the engagement time and torque response Reference[11] established a multiphysics coupling clutch thermody-namic model analyzed the generation and change mecha-nism of viscous torque and contact torque during clutchengagement and studied the influence of lubricating oiltemperature on friction torque characteristics Depratereet al [12] applied a bilevel iterative learning control strategyto control wet clutch engagement in an optimal manner andobserved that the engagement quality was adequate Ref-erence [13] proposed a new adaptive control method ofclutch torque which mainly focused on the relationshipbetween dry clutch and actuator piston pressure and clutchtorque However response characteristics of torque in wetclutch engagement from the standpoint of the frictiontransmission mechanism of the wet clutch have scarcelybeen investigated

In this study on the basis of the analysis of the wet clutchfriction transmission mechanism a dynamic transmittedtorque model of the wet clutch is proposed and the factorsinfluencing the torque response characteristics of the wetclutch are analyzed via numerical simulations and experi-mental methods

2 Friction Transmission Mechanism ofWet Clutch

According to the mechanisms of applied force and trans-mitted torque of the wet clutch the wet clutch engagementprocess can be divided into three stages [14] the fluidsqueezing stage boundary lubrication stage and mechanicalcontact stage In the fluid squeezing stage transmittedtorque is composed of hydrodynamic torque of the auto-matic transmission fluid (ATF) oil film In the boundarylubrication stage the transmitted torque is composed ofhydrodynamic torque of the ATF oil film and the asperitycontact torque of friction pairs With wet clutch engage-ment contact pressure and friction torque of asperitiesgradually play a dominant role In the mechanical contactstage the transmitted torque is only composed of asperityfriction torque (e friction transmission mechanism in wetclutch engagement is modeled as follows

21 Model of Oil Film Pressure Wet clutch engagement canbe simplified as per the physical model shown in Figure 1Friction pairs are filled with lubricant before wet clutchengagement and the friction disk and separator plate areseparated by the oil film(e angular velocity of friction diskand separator plate are ω2 and ω1 respectively then frictionpairs are compressed gradually via the applied pressure PsCombined with the axial symmetric characteristics of thewet clutch friction pairs the governing equation of the forcesupported by the oil film in cylindrical coordinate system isderived using the PatirndashCheng average Reynolds equation[15 16]

ddr

rφr h3

+ 12Φ d1113872 1113873dPh

dr1113890 1113891 12 ηr

dhT

dt (1)

where φr is the radial flow factor h is the film thickness of theoil Φ is the permeability of the friction lining d is thethickness of the friction lining Ph is the average pressure ofthe oil film η is the dynamic viscosity of the oil film and hT

is the average clearance of the friction pairsLet us assume that the surface asperity height of the

friction disk and separator plate are subject to Gaussiandistribution of zero average value (en the relationshipbetween the average clearance of friction pairs hT and oilfilm thickness h can be described as [17]

dhT

dt 05 1 + erf

h2

radicσ

1113888 11138891113890 11138911113896 1113897dh

dt (2)

Assume that

g(h) 05 1 + erfh2

radicσ

1113888 11138891113890 1113891 (3)

where σ is the RMS roughness of the friction pairs and erf isthe Gaussian error function



Ph(r) 3η

φr h3

+ 12Φ d1113872 1113873r2

+b2

minus a2

2 ln(ab)ln

r

bminus b

21113890 1113891g(h)

dh

dt

(4)


Ac πλcσ12π

radic eminus (h

2

radicσ)2

+h

σ(g(h) minus 1)1113890 1113891 (5)



Pc Eδ (6)




ts1113888 11138891113888 1113889 (7)



π b2

minus a2





where

Tv 11139462π

01113946

b


r3ηωrel

hdr dθ

Tc 11139462π

01113946

b

aδfcPcr

2 dr dθ

T I middotdωrel

dt

(10)







ATF

P3 Psr

z







times105

∆tp

∆tT

0

2

4

6

8

10

Pres

sure

(Pa)

0

20

40

60

80

100

Torq

ue

01 02 03 04 05 06 07 08 09 1 11 120Time (s)

PressureTorque











02Time (s)

times105

ts = 001sts = 005sts = 01s

0

1

2

3

4

5

6

7

8

Pres

sure

(Pa)

0

10

20

30

40

50

60

70

80

Torq

ue (N

m)

03 04 05 06 07 08 09 1 11 120 01


TorqueTorqueTorque










004

006

008

01

012

014

016

018

02

Tor

que r

espo

nse t

ime (

s)





0

005

01

015

02

025

03

Torq

ue re

spon

se ti

me (

s)








4 Test Verification







004

006

008

01

012

014

016

Tor

que r

espo

nse t

ime (

s)




004

006

008

01

012

014

016

Tor

que r

espo

nse t

ime (

s)







Test box


Inertia flywheel

Torque meter

IPCAD

Motor

ABB

Hydraulic system

Friction disk

(a)

Inertiaflywheel

Test box

Torquemeter

Hydraulicsystem

Motor

(b)


Pressure

Torque

6

5

4

3

2

1

00 01 02 03 04 05 06 07 08

Engagement time (s)

Pres

sure

(Pa)

1101009080706050403020100

Torq

ue (N

m)

times105



η = 00681Pamiddots

80degC


004

006

008

01

012

014

016

018

02 T

orqu

e res

pons

e tim

e (s)




5 Conclusions









Data Availability




Acknowledgments


References






004

006

008

01

012

014

016

Tor

que r

espo

nse t

ime (

s)


























Ph(r) 3η

φr h3

+ 12Φ d1113872 1113873r2

+b2

minus a2

2 ln(ab)ln

r

bminus b

21113890 1113891g(h)

dh

dt

(4)


Ac πλcσ12π

radic eminus (h

2

radicσ)2

+h

σ(g(h) minus 1)1113890 1113891 (5)



Pc Eδ (6)




ts1113888 11138891113888 1113889 (7)



π b2

minus a2





where

Tv 11139462π

01113946

b


r3ηωrel

hdr dθ

Tc 11139462π

01113946

b

aδfcPcr

2 dr dθ

T I middotdωrel

dt

(10)







ATF

P3 Psr

z







times105

∆tp

∆tT

0

2

4

6

8

10

Pres

sure

(Pa)

0

20

40

60

80

100

Torq

ue

01 02 03 04 05 06 07 08 09 1 11 120Time (s)

PressureTorque











02Time (s)

times105

ts = 001sts = 005sts = 01s

0

1

2

3

4

5

6

7

8

Pres

sure

(Pa)

0

10

20

30

40

50

60

70

80

Torq

ue (N

m)

03 04 05 06 07 08 09 1 11 120 01


TorqueTorqueTorque










004

006

008

01

012

014

016

018

02

Tor

que r

espo

nse t

ime (

s)





0

005

01

015

02

025

03

Torq

ue re

spon

se ti

me (

s)








4 Test Verification







004

006

008

01

012

014

016

Tor

que r

espo

nse t

ime (

s)




004

006

008

01

012

014

016

Tor

que r

espo

nse t

ime (

s)







Test box


Inertia flywheel

Torque meter

IPCAD

Motor

ABB

Hydraulic system

Friction disk

(a)

Inertiaflywheel

Test box

Torquemeter

Hydraulicsystem

Motor

(b)


Pressure

Torque

6

5

4

3

2

1

00 01 02 03 04 05 06 07 08

Engagement time (s)

Pres

sure

(Pa)

1101009080706050403020100

Torq

ue (N

m)

times105



η = 00681Pamiddots

80degC


004

006

008

01

012

014

016

018

02 T

orqu

e res

pons

e tim

e (s)




5 Conclusions









Data Availability




Acknowledgments


References






004

006

008

01

012

014

016

Tor

que r

espo

nse t

ime (

s)





























times105

∆tp

∆tT

0

2

4

6

8

10

Pres

sure

(Pa)

0

20

40

60

80

100

Torq

ue

01 02 03 04 05 06 07 08 09 1 11 120Time (s)

PressureTorque











02Time (s)

times105

ts = 001sts = 005sts = 01s

0

1

2

3

4

5

6

7

8

Pres

sure

(Pa)

0

10

20

30

40

50

60

70

80

Torq

ue (N

m)

03 04 05 06 07 08 09 1 11 120 01


TorqueTorqueTorque










004

006

008

01

012

014

016

018

02

Tor

que r

espo

nse t

ime (

s)





0

005

01

015

02

025

03

Torq

ue re

spon

se ti

me (

s)








4 Test Verification







004

006

008

01

012

014

016

Tor

que r

espo

nse t

ime (

s)




004

006

008

01

012

014

016

Tor

que r

espo

nse t

ime (

s)







Test box


Inertia flywheel

Torque meter

IPCAD

Motor

ABB

Hydraulic system

Friction disk

(a)

Inertiaflywheel

Test box

Torquemeter

Hydraulicsystem

Motor

(b)


Pressure

Torque

6

5

4

3

2

1

00 01 02 03 04 05 06 07 08

Engagement time (s)

Pres

sure

(Pa)

1101009080706050403020100

Torq

ue (N

m)

times105



η = 00681Pamiddots

80degC


004

006

008

01

012

014

016

018

02 T

orqu

e res

pons

e tim

e (s)




5 Conclusions









Data Availability




Acknowledgments


References






004

006

008

01

012

014

016

Tor

que r

espo

nse t

ime (

s)
































004

006

008

01

012

014

016

018

02

Tor

que r

espo

nse t

ime (

s)





0

005

01

015

02

025

03

Torq

ue re

spon

se ti

me (

s)








4 Test Verification







004

006

008

01

012

014

016

Tor

que r

espo

nse t

ime (

s)




004

006

008

01

012

014

016

Tor

que r

espo

nse t

ime (

s)







Test box


Inertia flywheel

Torque meter

IPCAD

Motor

ABB

Hydraulic system

Friction disk

(a)

Inertiaflywheel

Test box

Torquemeter

Hydraulicsystem

Motor

(b)


Pressure

Torque

6

5

4

3

2

1

00 01 02 03 04 05 06 07 08

Engagement time (s)

Pres

sure

(Pa)

1101009080706050403020100

Torq

ue (N

m)

times105



η = 00681Pamiddots

80degC


004

006

008

01

012

014

016

018

02 T

orqu

e res

pons

e tim

e (s)




5 Conclusions









Data Availability




Acknowledgments


References






004

006

008

01

012

014

016

Tor

que r

espo

nse t

ime (

s)



























4 Test Verification







004

006

008

01

012

014

016

Tor

que r

espo

nse t

ime (

s)




004

006

008

01

012

014

016

Tor

que r

espo

nse t

ime (

s)







Test box


Inertia flywheel

Torque meter

IPCAD

Motor

ABB

Hydraulic system

Friction disk

(a)

Inertiaflywheel

Test box

Torquemeter

Hydraulicsystem

Motor

(b)


Pressure

Torque

6

5

4

3

2

1

00 01 02 03 04 05 06 07 08

Engagement time (s)

Pres

sure

(Pa)

1101009080706050403020100

Torq

ue (N

m)

times105



η = 00681Pamiddots

80degC


004

006

008

01

012

014

016

018

02 T

orqu

e res

pons

e tim

e (s)




5 Conclusions









Data Availability




Acknowledgments


References






004

006

008

01

012

014

016

Tor

que r

espo

nse t

ime (

s)





























Test box


Inertia flywheel

Torque meter

IPCAD

Motor

ABB

Hydraulic system

Friction disk

(a)

Inertiaflywheel

Test box

Torquemeter

Hydraulicsystem

Motor

(b)


Pressure

Torque

6

5

4

3

2

1

00 01 02 03 04 05 06 07 08

Engagement time (s)

Pres

sure

(Pa)

1101009080706050403020100

Torq

ue (N

m)

times105



η = 00681Pamiddots

80degC


004

006

008

01

012

014

016

018

02 T

orqu

e res

pons

e tim

e (s)




5 Conclusions









Data Availability




Acknowledgments


References






004

006

008

01

012

014

016

Tor

que r

espo

nse t

ime (

s)


























5 Conclusions









Data Availability




Acknowledgments


References






004

006

008

01

012

014

016

Tor

que r

espo

nse t

ime (

s)

























response characteristics of dynamic torque for wet clutch ...2021/02/06 · h drdθ, t c z π 0 b a...

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