Research ArticleFriction Characteristics of Synchronization ProcessBased on Tribo-Thermodynamics

Hao Yan,1 Zhaoping Xu ,1 Juntang Yuan,1 Liang Liu,1 Cao Tan,2 and Wenqing Ge2

1School of Mechanical Engineering, Nanjing University of Science and Technology, Nanjing 210094, China2School of Transportation and Vehicle Engineering, Shandong University of Technology, Zibo 255000, China

Correspondence should be addressed to Zhaoping Xu; xuzhaoping@njust.edu.cn

Received 11 April 2018; Revised 26 June 2018; Accepted 4 July 2018; Published 7 August 2018

Academic Editor: David Holec

Copyright © 2018HaoYan et al.,is is an open access article distributed under the Creative CommonsAttribution License, whichpermits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

In order to improve the shift control accuracy and shift quality, the temperature and friction coefficient changing regularities ofa friction cone during the synchronization process were investigated. ,e thermal-structural coupling model was establishedthrough tribo-thermodynamic analysis. ,e relevant experiment was carried out as well. ,e results show that the error betweenthe experimental and simulated results is within 3%. Besides, the maximum temperature of the synchronous ring friction surfaceincreases 1.8°C for every additional 50N of shift force, while increases 1.1°C for every additional 200 r/min shift speed difference.Moreover, the friction coefficient declines rapidly first and then tends to be stable slowly during the synchronization process. ,eresult of friction coefficient changing regularity lays a good theoretical basis for establishing an effective friction coefficientcompensation control strategy.

1. Introduction

Transmission is an important part of the transmissionsystem and has been regarded as the focus of technologicalinnovation for a long time [1, 2].,e shift speed difference iseliminated by the interaction of a synchronizer friction coneduring the synchronous shift phase. ,e heat generated byfriction will change material surface energy and lattice re-sistance, so that the friction coefficient between frictioncones will change and the shift control accuracy of trans-mission will be influenced [3].

Currently, lots of researches to improve the automatictransmission’s control accuracy have been proposed [1–3].,e friction surface temperature and the friction coefficientof the friction cone are the critical influences on the shiftcontrol accuracy and shift quality. In the literature [4–6], thetemperature changing regularities of the friction surfaceunder different working conditions were analyzed by sim-ulation and experiment. ,e influence of temperature onsynchronizer working performance was verified. In theliterature [7, 8], the friction and heat generation process ofthe synchronizer with different friction coefficients were

analyzed by simulation. ,e results show that the greater thefriction coefficient is, within a certain range, the higher thetemperature between the friction surfaces is. ,e frictioncharacteristics of the synchronizer were preliminary studiedin the above literatures. However, the influence of frictionheat and friction coefficient on the accuracy of synchronousshift control was rarely considered during the synchroni-zation process.

,e friction coefficient of the synchronizer friction coneis an important index in the synchronizer. Li et al. presenta model of predicting wear in the friction lining of a wetclutch and introduces that the wear mechanism is related tothermal degradation [9, 10]. Marklund and Larsson developa friction model which takes temperature, speed, andnominal pressure into account of the wet clutch duringboundary lubrication conditions [11, 12]. ,e investigationof temperature and friction coefficient during the syn-chronization process will lay a good theoretical basis forestablishing a control strategy for automotive transmissiondesigners.

,is paper is organized as follows. Section 2 describesthe existing problem of the locking ring synchronizer.

HindawiAdvances in Materials Science and EngineeringVolume 2018, Article ID 8467921, 9 pageshttps://doi.org/10.1155/2018/8467921

�e thermal-structural coupling model is establishedthrough tribo-thermodynamic analysis in Section 3. �eestablished model is veri�ed by experiments in Section 4.�e analysis of results is carried out in Section 5. �is paperis concluded in Section 6.

2. Problem Description

2.1. Structure and Operating Principle. �e locking ringsynchronizer of automated mechanical transmission is theresearch object in this paper. �e schematic diagram of thelocking ring synchronizer is shown in Figure 1, whichconsists of a synchromesh sliding sleeve, a splined hub,a synchronous ring, a target ring gear, and a locating slider.�e material parameters are shown in Table 1.

During the synchronization process, the synchronousring is under an axial shift force. �e speed di�erence be-tween the synchronous output shaft and the input shaft iseliminated by the friction torque between synchronousring’s inner cone and target ring gear’s friction cone toachieve a smooth and fast shift. �us, the friction surfacetemperature and the friction coe�cient of the friction coneare the critical in�uences on the shift control accuracy andshift quality.

2.2. Heat Resource Analysis. In the actual synchronizationprocess, the synchronous force is only the catalyst for energytransfer and transformation of the transmission system. Allthe work done by the friction torque is converted into ir-reversible heat loss, which is the primary heat source of thesynchronizer [13]. Divide synchronizer friction pair surfacesinto microelements, and denote one of them as dA. �enormal pressure between synchronizer friction pair surfacesis p, and then the friction dF on the area dA is

dF � μpdA, (1)

where μ is the friction coe�cient between friction surfaces.Under the in�uence of friction dF, the moving distancewithin dt is

ds � ω(t)r dt, (2)

where r is the average radius of the friction cone. Assumingthat all the work done by friction dF converts to heat [14],the heat produced in dt is

dQ � dF ds � μprω(t)dAdt. (3)

�e heat �ux function on synchronizer friction pairsurfaces is

q(r, t) � dQ

(dAdt)� μprω(t). (4)

According to the operating parameters, the heat �ux inputfunction of the synchronizer friction pair is determined to be(3200000− 6400000 × t) W/m2·s. Meanwhile, ignoring theheat is taken away by oil in the synchronizer ring threadgroove, the heat generated by the metal friction pair iscompletely absorbed by the synchronizer ring and target gear

ring. So that the heat is all assigned to the synchronizerring and the target ring gear conical surface. �e distri-bution of the heat �ux between the synchronizer ring andthe conical surface is related to their material propertiesdirectly. According to the relevant conclusions [15, 16],the heat �ux distribution ratio between upper and lowerspecimens is

k �qpqd�

������λpcpρpλdcdρd

√

, (5)

where subscripts p and d stand for the material properties ofthe synchronizer ring and target gear ring, λ is the thermalconductivity, c is the speci�c heat capacity, and ρ is thedensity. According to Table 1, by substituting (5), the heat�ux distribution coe�cient of the synchronizer ring is 51%,which of the target gear ring is 49%.

3. Thermal-Structural Coupling Model

3.1.HeatTransferModeling. In Cartesian coordinates, takeany microelement on the surface of the friction pair asthe research object. According to the law of conservationof energy, the heat balance relationship of microelementsin unit time is analyzed [17, 19]. Select �rst gear forsecond gear as the typical working condition of thermal-structural coupling analysis of the synchronizer, andcalculate the boundary conditions in the synchroniza-tion process. �e temperature of friction pair surfaceschanges with time. As for the transient heat conductionproblem [13], to solve the problem of temperature �elddistribution without internal heat source, the heatconduction equation is

Synchromeshsliding sleeve

Splinedhub

Locatingslider

Synchronousring

Target ringgear

Figure 1: �e structure of lock ring synchronizer.

Table 1: Primary material parameters.

Parameters (room temperature) 45 Steel QSn4-3Density ρ (kg·m−3) 7890 8800Elastic modulus E (GPa) 209 1100Poisson ratio (μo) 0.27 0.33�ermal conductivity λ (W·m−2·K−1) 48.15 47Speci�c heat capacity c (J·kg−1·K−1) 450 380�ermal expansion coe�cient (1°C−1) 1.08e−5 1.8e−5

2 Advances in Materials Science and Engineering

ρc

λzT

zt�

z2T

zx2 +z2T

zy2 +z2T

zz2 , (6)

where T is the thermodynamic temperature. ,e thermalconduction differential equation is a general expression todescribe the conduction process but does not involvea specific conduction process. For solving the specificthermal conduction differential equation, declaration con-ditions are needed to obtain a unique solution.

,e heat flux is affected by parameters such as speed,pressure, and friction coefficient, and it is time dependent. Itis an unsteady heat conduction process, which accords withthe second boundary condition. For convection heat transferboundary conditions, the convective heat transfer coefficientequation and the operational environment temperature areknown, and the real-time convective heat transfer coefficientat the synchronizer boundary can be obtained, whichbelonged to the third boundary condition.

,e convective heat transfer coefficient mainly dependson fluid states, the physical properties of fluid, the geo-metrical factors of the heat transfer surface, the cause of flow,and whether the fluid has a phase change [17]. ,e con-vective heat transfer coefficient is calculated as follows:

hcon �Nuλair

l, (7)

where Nu is the Nusselt number, λair is the air thermalconductivity, and l is the characteristic length of the heattransfer surface. Convective heat transfer is divided intothree categories: (1) forced convection heat transfer; (2)natural convection heat transfer; and (3) mixed convectionheat transfer. ,e convection heat transfer manner is usuallydetermined by the value of Gr/Re2 in engineering [18]. ,eGrashof number Gr is calculated as follows:

Gr �gαvΔtl3

η2air, (8)

where g is the acceleration of gravity, Δt is the temperaturedifference between thermal conductivity object and theenvironment, and ηair is the kinematic viscosity of air innormal temperature. When v is the velocity, the Reynoldsnumber Re is calculated as follows:

Re �]l

ηair. (9)

In order to simplify the calculation of thermo-structuralcoupling analysis of the synchronization process, the targetring gear is assumed to be stationary and the synchronizerring is rotating.,e speed of the synchronizer ring is equal tothe speed difference between the two ends of the synchro-nizer during the actual synchronization process. Hence,there is no relative motion between the target ring gear andthe surrounding air. ,ere is a natural convection heattransfer between the target ring gear surface and the air [19].,e surface shape of the target ring gear friction cone iscylindrical vertical wall, and air flow is laminar. ,e Nusseltnumber for natural convection heat transfer is calculated asfollows:

Nu � 0.68 +0.67(Ra)1/4

[1 +(0.492/Pr)]4/9, (10)

where Pr is the Prandtl number and Ra is the Rayleighnumber. Ra is calculated as

Ra � Gr · Pr. (11)

When the synchronous ring speed is 200 r/min, theReynolds number is 186.67, the Grashof number is 1563, andGr/Re2 is 0.045. ,ere is a forced convection heat transferbetween the synchronizer ring surface and the air becauseGr/Re2 is less than 0.1 [19]. Besides, the speed between thetwo ends of the synchronizer is more than 200 r/min duringthe synchronization process. Substituting the results of theGrashof number calculated into (11), the Rayleigh number11095.8 can be obtained. Nusselt number 6.08 can be ob-tained by substituting the Rayleigh number into (10). Finally,the free convection heat transfer coefficient (hcon) of thetarget gear ring is 6.08 W/m2·K.

C is the coefficient of the constant term. ,e Nusseltnumber of forced convection heat transfer is calculated asfollows:

Nu � CRe1/2Pr1/3. (12)

Similarly, the forced convection heat transfer coefficient(hcon) of the synchronizer ring is 28.96 W/m2·K.

3.2. 3D Finite Element Model. ,e thermo-structural cou-pling modeling based on 3D finite element method iscarried out through the above theoretical analysis. Firstly,a three-dimensional model of the synchronizer is estab-lished based on CATIA. ,en, the target ring gear is 45Steel as material, and the synchronous ring is copper alloy(QSn4-3) [20]. ,eir primary material parameters areshown in Table 1.

Moreover, the mesh model of the target ring gear andsynchronous ring is shown in Figure 2, as well as theboundary conditions. Besides, the selection of the boundarycondition has been explained in Section 3.1. ,e boundaries1 and 6 are friction interfaces. ,e heat resource is applied tofriction interfaces. ,e boundary 2–5 of the synchronousring is the forced convection heat transfer boundary, whilethe boundary 7–9 of the target ring gear is the naturalconvection heat transfer boundary.

4. Experimental Verification

4.1. Experimental Setup. In order to verify the accuracy ofthe thermal-structural coupling model and investigatefriction coefficient change regularities of the friction cone,the synchronization process is researched by the friction andwear test bench. ,e schematic of the experimental setup isshown in Figure 3.

,e experimental setup of the synchronizer mainlyconsists of a three-phase asynchronous motor (Y90L-4) thatsimulates input shaft speed, an inertia simulator at inputshaft (the range of rotational inertia 0.04∼0.09 kg·m2), a gearshift simulator, a linear actuator (AUM5-S2) that simulates

Advances in Materials Science and Engineering 3

shift force, and a support for target ring gear. To verify themodel, following signals are acquired from the experimentsetup: a thermal infrared imager (Optris PI 450), a dis-placement sensor (WYDC-15D), and a torque-speed sensor(JN338-300A) with a 0.1% FS and 300 N·m(5000 r/min)measuring range. Besides, a controller and a host computerare needed to control the experimental process and collectdata. Set the required inertia value and speed di�erencebefore test. Open the three-phase asynchronous motor todrive input shaft by the controller. When the feedback signalfrom the torque-speed transducer reaches to predeterminedspeed value, turn o� the three-phase asynchronous motorand turn on the linear actuator. �e required shift force isprovided through the linear actuator. �e host computerreceives the feedback signal from each sensor to realize real-time control during the synchronization process. �e photoof the experimental setup is shown in Figure 4.

�e test bench adopts a ring-ring friction pair structure,and the size of the test specimen is basically the same as thesize of the car synchronizer. According to the actual syn-chronization process, adjust the speed and the shift force, so

that the test operation is closer to the real synchronizationprocess. �e tests were carried out at room temperature.�ere must be no strong light around specimens; otherwise,re�ection may cause inaccurate measurements. �e relevantparameters of the synchronizer ring and the target gear ringare shown in Table 2.

4.2. Model Veri�cation. Take the condition that the syn-chronous load is 195N and the speed di�erence is1000 r/min as an example. �e temperature distribution ofthe synchronizer measured by the infrared thermal imager ata certain time is shown in Figure 5.

�e temperature measuring areas 1 and 2 (1× 1mm2)measure the change of maximum temperature on the fric-tional cone during the synchronization process. Tempera-ture measuring area 3 measures the change of averagetemperature on the target gear ring liner cone. In the rightcorner of Figure 6, 21.67°C represents the average temper-ature in the temperature measuring area 3. In order to verifythe accuracy of the simulation results, the experimental and

Target ringgearAA

Synchronousring

(a)

A-A7

8

9

65

4

3

2 1

(b)

Figure 2:�emesh generation and boundary conditions of the synchronizer. 1, 6: heat resource (friction interfaces); 2–5: forced convectionheat transfer boundary; 7–9: natural convection heat transfer boundary.

Hostcomputer

Controller Displacementsensor

Thermalinfraredimager Gear shift simulator

SynchronizerShifting forkLinearactuator

Drivingmotor

Torque andspeedsensor

Inertiasimulator

Synchronousring

Target ringgear Support

Electric connectionMechanical connection

Figure 3: Schematic of experimental setup.

4 Advances in Materials Science and Engineering

simulated results of maximum temperature on the frictionalcone during the synchronization process are shown inFigure 7.

�ere are errors between the experimental and simulatedresults of the friction cone temperature �eld during thesynchronization process. �e error between the experi-mental and simulated results is controlled within 3%, whichveri�es the accuracy of thermo-structural coupling analysis.�ere are two main reasons that lead to the error. Firstly, thewear-resistant treatment is not applied to the friction cone of

synchronous ring and target gear ring in the experimentalstudy.�ere are microbulges on the friction cone, so that theactual friction contact area is less than the ideal contact area.Secondly, the forced convection heat transfer coe�cient ofthe synchronous ring friction cone is related to speed,according to formulas (9) and (13). �e slower the rotationalspeed is, the smaller the convection heat transfer coe�cientis. However, the convective heat transfer coe�cient of thesynchronous ring surface is set to a constant value insimulation, while the convective heat transfer coe�cient of

Linear actuator anddisplacement sensor

Synchronizer

Testbench

Inertia simulatorTorque and speedsensor

Three-phaseasynchronous motor

Controller Host computerThermal infrared

imager

Figure 4: Schematic of experimental setup.

Table 2: Speci�cation parameters.

Parameters Synchronizer ring Target gear ringMaterial QSn4-3 45 SteelInner diameter (external diameter) (mm) 13 26Min external diameter (min inner diameter) (mm) 20 20Max external diameter (max inner diameter) (mm) 21 21Axial length (mm) 8 28

Target ringgear

Measuring area 3 averagetemperature 19.67°C

Measuring area 3

Measuring area 1

Measuring area 2

Support

Synchronousring

Figure 5: �e thermal imagery taken by thermal imager.

Advances in Materials Science and Engineering 5

the synchronous ring surface is changing all the time duringthe practical tests.

5. Results and Discussion

5.1. Temperature Rise Analysis. Take the condition that thesynchronous load is 195N and the speed di�erence is1000 r/min as an example. �e highest temperaturechanging regularities of friction surface through the thermo-structural coupling analysis is shown in Figure 8. �etemperature of the target gear ring and synchronous ring atdi�erent time is shown in Figures 6 and 9, respectively.

�e maximum temperature changing regularities of thesynchronizer ring and target gear ring are the same. �etemperature increases �rst and then decreases. At the initialstage of friction, the energy of heat �ux density input is

greater than the energy of heat conduction and convectiveheat transfer taken away, and the temperature increasesspeedily. With the decrease of speed di�erence at both endsof the synchronizer, heat �ux and convective heat transfercoe�cient of the friction cone decreases gradually. Whenthe energy of heat �ux density input is equal to the energytaken away, the temperature of the synchronizer ringfriction cone reaches to the maximum. As the speed dif-ference at both ends of the synchronizer decreases con-tinuously, the temperature of the synchronizer ring frictionsurface reduces gradually until the end of the synchroni-zation process.

At the initial stage of friction, the maximum temperatureof the target gear ring friction cone appears at both ends ofthe contact surface. �en the maximum temperature of thefriction cone appears only at the larger round end of surface

Min

Max

27.8827.0027.1325.2524.3823.5022.6321.7520.8820.00

(a)

Min

Max

53.9850.2146.4542.6838.9235.1531.3927.6223.8520.42

(b)

Min

Max

50.5247.2143.8940.5737.2333.9430.6227.3023.9920.67

(c)

Min

Max

41.7839.5837.3835.1632.9530.7528.5426.3324.1221.94

(d)

Figure 6: Surface temperature distribution of the target gear ring. (a) t� 0.035 s, (b) t� 0.678 s, (c) t� 1.143 s, and (d) t� 1.5 s.

1.51.20.90.60.30.019

20

21

22

23

24

25

26

Erro

r (%

)

Tem

pera

ture

(T/°C

)

Time (t/s)

–2

0

2

4

6

8

Experimental resultsSimulation resultsError

Figure 7: Comparison of experimental and simulated results.

1.51.20.90.60.30.019

20

21

22

23

24

25

26

Tem

pera

ture

(T/°C

)

Time (t/s)

Target ring gearSynchronous ring

Decreasing areaIncreasing area

The highest temperature

Figure 8: �e highest temperature changing regularities of frictionsurface.

6 Advances in Materials Science and Engineering

with the friction process.�e temperature distribution of thefriction cone tends to be uniform gradually. Note that theenergy dissipation through heat conduction on the frictionsurface is the main determinant of the gear ring temperaturerise, instead of convective heat transfer.

�e maximum temperature of the synchronizer ringinner cone appears at all ring gears at the initial stage offriction. �en the maximum temperature of the synchro-nizer ring appears only at the smallest ring gear with thefriction process. �erefore, the smaller the inner diameter ofsynchronizer ring gear is, the thicker the ring gear is. So thatthe energy dissipation of ring gear surface with smaller innerdiameter is slower through heat conduction, and the tem-perature is higher than the ring gear surface with biggerinner diameter.

�e temperature of friction surface under di�erentworking conditions is shown in Figure 10. �e maximumtemperature of friction surface increases about 1.8°C forevery additional 50N of the synchronous load. While themaximum temperature of friction surface increases about1.1°C for every additional 200 r/min shift speed di�erencebetween the two ends of the synchronizer.

5.2. FrictionCoe�cientAnalysis. �e torque of the friction isobtained from torque-speed sensor under di�erent workingconditions, and the friction coe�cient is calculated asfollows:

μ �TS sin αFS · R

, (13)

where TS is the cone torque, FS is the shifting force, α is thehalf-cone angle, and R is the cone radius. Hence, friction

coe�cient changing regularities of the friction cone underdi�erent working conditions are shown in Figure 11.

�e friction coe�cient changing regularities of thefriction cone are the same under di�erent conditions ba-sically. �e friction coe�cient declines rapidly �rst and thentends to be stable slowly during the synchronization process.�e experimental data about friction coe�cient have �uc-tuations because of the coaxiality of test bench and sur-rounding electromagnetic interference. �e analysis offriction coe�cient changing regularity lays the foundationfor establishing an e�ective friction coe�cient compensa-tion control strategy.

Min

Max32.3230.9529.5828.2126.8425.4724.1022.7421.3720.00

(a)

Min

Max 61.9957.3852.7848.4843.5838.9834.3829.7925.1920.59

(b)

Max

Min

55.5251.9248.3144.7041.1037.4933.8930.2826.6723.07

(c)

Min

Max42.8840.9939.0937.2035.3133.4131.5229.6227.7325.84

(d)

Figure 9: Surface temperature distribution of the synchronous ring. (a) t� 0.035 s, (b) t� 0.678 s, (c) t� 1.143 s, and (d) t� 1.5 s.

25020015010022

23

24

25

26

27

28

The h

ighe

st te

mpe

ratu

re (T

/°C)

Synchronous load (N)

Temperature versus speed difference,synchronous load = 195 NTemperature versus synchronous load,speed difference = 1000 r/min

Speed difference (v/(r/min))12001000800600

Figure 10: Variation law of temperature under di�erent workingconditions.

Advances in Materials Science and Engineering 7

6. Conclusions

In order to improve the shift quality further, the frictioncoe�cient changing regularities of the friction cone and thetemperature rise of friction surface during the synchroni-zation process were investigated. �e thermal-structural cou-pling model was established through tribo-thermodynamicanalysis. �e relevant experiment was carried out as well. Mainresults are summarized as follows:

(1) �e error between the experimental and simulatedresults is controlled within 3%, which veri�es theaccuracy of the thermo-structural coupling model.

(2) �e maximum temperature of synchronous ringfriction surface increases 1.8°C for every additional50N of shift force, while increases 1.1°C for everyadditional 200 r/min shift speed di�erence.

(3) �e friction coe�cient declines rapidly �rstly andthen tends to be stable slowly during the synchro-nization process. �e result of friction coe�cientchanging regularity lays a good theoretical basis forestablishing an e�ective friction coe�cient com-pensation control strategy.

Data Availability

�e data used to support the �ndings of this study areavailable from the corresponding author upon request.

Conflicts of Interest

�e authors declare that they have no con�icts of interest.

Acknowledgments

�is work was supported by the National Natural ScienceFoundation of China (Grant no. 51505263); Six Talent PeaksProject in Jiangsu Province, China (Grant no. XNYQC-010);and the Natural Science Foundation of Shandong Province,China (Grant no. ZR2016EL15).

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Fric

tion

coef

ficie

nt (μ

)

Time (t/s)

95 N-1000 r/min

195 N-600 r/min195 N-800 r/min

0.052

0.054

0.056

0.058

2.52.01.51.00.50.0

Stable value

Figure 11: Variation law of friction coe�cient of the friction coneunder di�erent working conditions.

8 Advances in Materials Science and Engineering

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