Friction Characteristics of Synchronization Process Based on Tribo-Thermodynamics

In order to improve the shift control accuracy and shift quality, the temperature and friction coefficient changing regularities of a friction cone during the synchronization process were investigated. ,e thermal-structural coupling model was established through tribo-thermodynamic analysis. ,e relevant experiment was carried out as well. ,e results show that the error between the experimental and simulated results is within 3%. Besides, the maximum temperature of the synchronous ring friction surface increases 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. ,e result of friction coefficient changing regularity lays a good theoretical basis for establishing an effective friction coefficient compensation control strategy.


Introduction
Transmission is an important part of the transmission system and has been regarded as the focus of technological innovation for a long time [1,2].e shift speed difference is eliminated by the interaction of a synchronizer friction cone during the synchronous shift phase.e heat generated by friction will change material surface energy and lattice resistance, so that the friction coefficient between friction cones will change and the shift control accuracy of transmission will be influenced [3].
e friction surface temperature and the friction coefficient of the friction cone are the critical influences on the shift control accuracy and shift quality.In the literature [4][5][6], the temperature changing regularities of the friction surface under different working conditions were analyzed by simulation and experiment.e influence of temperature on synchronizer working performance was verified.In the literature [7,8], the friction and heat generation process of the synchronizer with different friction coefficients were analyzed by simulation.e results show that the greater the friction coefficient is, within a certain range, the higher the temperature between the friction surfaces is.
e friction characteristics of the synchronizer were preliminary studied in the above literatures.However, the influence of friction heat and friction coefficient on the accuracy of synchronous shift control was rarely considered during the synchronization process.
e friction coefficient of the synchronizer friction cone is an important index in the synchronizer.Li et al. present a model of predicting wear in the friction lining of a wet clutch and introduces that the wear mechanism is related to thermal degradation [9,10].Marklund and Larsson develop a friction model which takes temperature, speed, and nominal pressure into account of the wet clutch during boundary lubrication conditions [11,12].e investigation of temperature and friction coefficient during the synchronization process will lay a good theoretical basis for establishing a control strategy for automotive transmission designers.
is paper is organized as follows.Section 2 describes the existing problem of the locking ring synchronizer.e analysis of results is carried out in Section 5. is paper is concluded in Section 6. e locking ring synchronizer of automated mechanical transmission is the research object in this paper.e schematic diagram of the locking ring synchronizer is shown in Figure 1, which consists of a synchromesh sliding sleeve, a splined hub, a synchronous ring, a target ring gear, and a locating slider.

Problem Description
e material parameters are shown in Table 1.
During the synchronization process, the synchronous ring is under an axial shift force.e speed di erence between the synchronous output shaft and the input shaft is eliminated by the friction torque between synchronous ring's inner cone and target ring gear's friction cone to achieve a smooth and fast shift.us, the friction surface temperature and the friction coe cient of the friction cone are the critical in uences on the shift control accuracy and shift quality.

Heat Resource Analysis.
In the actual synchronization process, the synchronous force is only the catalyst for energy transfer and transformation of the transmission system.All the work done by the friction torque is converted into irreversible heat loss, which is the primary heat source of the synchronizer [13].Divide synchronizer friction pair surfaces into microelements, and denote one of them as dA.e normal pressure between synchronizer friction pair surfaces is p, and then the friction dF on the area dA is where μ is the friction coe cient between friction surfaces.Under the in uence of friction dF, the moving distance within dt is where r is the average radius of the friction cone.Assuming that all the work done by friction dF converts to heat [14], the heat produced in dt is dQ dF ds μprω(t)dA dt. ( e heat ux function on synchronizer friction pair surfaces is According to the operating parameters, the heat ux input function of the synchronizer friction pair is determined to be (3200000 − 6400000 × t) W/m 2 •s.Meanwhile, ignoring the heat is taken away by oil in the synchronizer ring thread groove, the heat generated by the metal friction pair is completely absorbed by the synchronizer ring and target gear ring.So that the heat is all assigned to the synchronizer ring and the target ring gear conical surface.e distribution of the heat ux between the synchronizer ring and the conical surface is related to their material properties directly.According to the relevant conclusions [15,16], the heat ux distribution ratio between upper and lower specimens is where subscripts p and d stand for the material properties of the synchronizer ring and target gear ring, λ is the thermal conductivity, c is the speci c heat capacity, and ρ is the density.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%.

Thermal-Structural Coupling Model
3.1.Heat Transfer Modeling.In Cartesian coordinates, take any microelement on the surface of the friction pair as the research object.According to the law of conservation of energy, the heat balance relationship of microelements in unit time is analyzed [17,19].Select rst gear for second gear as the typical working condition of thermalstructural coupling analysis of the synchronizer, and calculate the boundary conditions in the synchronization process.
e temperature of friction pair surfaces changes with time.As for the transient heat conduction problem [13], to solve the problem of temperature eld distribution without internal heat source, the heat conduction equation is Advances in Materials Science and Engineering ρc λ where T is the thermodynamic temperature.e thermal conduction differential equation is a general expression to describe the conduction process but does not involve a specific conduction process.For solving the specific thermal conduction differential equation, declaration conditions 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.It is an unsteady heat conduction process, which accords with the second boundary condition.For convection heat transfer boundary conditions, the convective heat transfer coefficient equation and the operational environment temperature are known, and the real-time convective heat transfer coefficient at the synchronizer boundary can be obtained, which belonged to the third boundary condition.
e convective heat transfer coefficient mainly depends on fluid states, the physical properties of fluid, the geometrical factors of the heat transfer surface, the cause of flow, and whether the fluid has a phase change [17].e convective heat transfer coefficient is calculated as follows: where Nu is the Nusselt number, λ air is the air thermal conductivity, and l is the characteristic length of the heat transfer surface.Convective heat transfer is divided into three categories: (1) forced convection heat transfer; (2) natural convection heat transfer; and (3) mixed convection heat transfer.e convection heat transfer manner is usually determined by the value of Gr/Re 2 in engineering [18].e Grashof number Gr is calculated as follows: where g is the acceleration of gravity, Δt is the temperature difference between thermal conductivity object and the environment, and η air is the kinematic viscosity of air in normal temperature.When v is the velocity, the Reynolds number Re is calculated as follows: In order to simplify the calculation of thermo-structural coupling analysis of the synchronization process, the target ring gear is assumed to be stationary and the synchronizer ring is rotating.e speed of the synchronizer ring is equal to the speed difference between the two ends of the synchronizer during the actual synchronization process.Hence, there is no relative motion between the target ring gear and the surrounding air.
ere is a natural convection heat transfer between the target ring gear surface and the air [19].
e surface shape of the target ring gear friction cone is cylindrical vertical wall, and air flow is laminar.e Nusselt number for natural convection heat transfer is calculated as follows: where Pr is the Prandtl number and Ra is the Rayleigh number.Ra is calculated as When the synchronous ring speed is 200 r/min, the Reynolds number is 186.67, the Grashof number is 1563, and Gr/Re 2 is 0.045.ere is a forced convection heat transfer between the synchronizer ring surface and the air because Gr/Re 2 is less than 0.1 [19].Besides, the speed between the two ends of the synchronizer is more than 200 r/min during the synchronization process.Substituting the results of the Grashof number calculated into (11), the Rayleigh number 11095.8 can be obtained.Nusselt number 6.08 can be obtained by substituting the Rayleigh number into (10).Finally, the free convection heat transfer coefficient (h con ) of the target gear ring is 6.08 W/m 2 •K.
C is the coefficient of the constant term.e Nusselt number of forced convection heat transfer is calculated as follows: Similarly, the forced convection heat transfer coefficient (h con ) of the synchronizer ring is 28.96W/m 2 •K.

3D Finite Element Model.
e thermo-structural coupling modeling based on 3D finite element method is carried out through the above theoretical analysis.Firstly, a three-dimensional model of the synchronizer is established based on CATIA.en, the target ring gear is 45 Steel as material, and the synchronous ring is copper alloy (QSn4-3) [20].
eir primary material parameters are shown in Table 1.
Moreover, the mesh model of the target ring gear and synchronous ring is shown in Figure 2, as well as the boundary conditions.Besides, the selection of the boundary condition has been explained in Section 3.1.e boundaries 1 and 6 are friction interfaces.e heat resource is applied to friction interfaces.e boundary 2-5 of the synchronous ring is the forced convection heat transfer boundary, while the boundary 7-9 of the target ring gear is the natural convection heat transfer boundary.

Experimental Verification
4.1.Experimental Setup.In order to verify the accuracy of the thermal-structural coupling model and investigate friction coefficient change regularities of the friction cone, the synchronization process is researched by the friction and wear test bench.e schematic of the experimental setup is shown in Figure 3.
e experimental setup of the synchronizer mainly consists of a three-phase asynchronous motor (Y90L-4) that simulates input shaft speed, an inertia simulator at input shaft (the range of rotational inertia 0.04∼0.09kg•m 2 ), a gear shift simulator, a linear actuator (AUM5-S2) that simulates Advances in Materials Science and Engineering shift force, and a support for target ring gear.To verify the model, following signals are acquired from the experiment setup: a thermal infrared imager (Optris PI 450), a displacement 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 computer are needed to control the experimental process and collect data.Set the required inertia value and speed di erence before test.Open the three-phase asynchronous motor to drive input shaft by the controller.When the feedback signal from the torque-speed transducer reaches to predetermined speed value, turn o the three-phase asynchronous motor and turn on the linear actuator.e required shift force is provided through the linear actuator.
e host computer receives the feedback signal from each sensor to realize realtime control during the synchronization process.e photo of 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 the size of the car synchronizer.According to the actual synchronization process, adjust the speed and the shift force, so that the test operation is closer to the real synchronization process.e tests were carried out at room temperature.
ere must be no strong light around specimens; otherwise, re ection may cause inaccurate measurements.e relevant parameters of the synchronizer ring and the target gear ring are shown in Table 2.

Model Veri cation.
Take the condition that the synchronous load is 195 N and the speed di erence is 1000 r/min as an example.e temperature distribution of the synchronizer measured by the infrared thermal imager at a certain time is shown in Figure 5.
e temperature measuring areas 1 and 2 (1 × 1 mm 2 ) measure the change of maximum temperature on the frictional cone during the synchronization process.Temperature measuring area 3 measures the change of average temperature on the target gear ring liner cone.In the right corner of Figure 6, 21.67 °C represents the average temperature in the temperature measuring area 3.In order to verify the accuracy of the simulation results, the experimental and  e error between the experimental and simulated results is controlled within 3%, which veri es the accuracy of thermo-structural coupling analysis.
ere are two main reasons that lead to the error.Firstly, the wear-resistant treatment is not applied to the friction cone of synchronous ring and target gear ring in the experimental study.ere are microbulges on the friction cone, so that the actual friction contact area is less than the ideal contact area.Secondly, the forced convection heat transfer coe cient of the synchronous ring friction cone is related to speed, according to formulas ( 9) and ( 13).e slower the rotational speed is, the smaller the convection heat transfer coe cient is.However, the convective heat transfer coe cient of the synchronous ring surface is set to a constant value in simulation, while the convective heat transfer coe cient of the synchronous ring surface is changing all the time during the practical tests.

Results and Discussion
5.1.Temperature Rise Analysis.Take the condition that the synchronous load is 195 N and the speed di erence is 1000 r/min as an example.e highest temperature changing regularities of friction surface through the thermostructural coupling analysis is shown in Figure 8. e temperature of the target gear ring and synchronous ring at di erent time is shown in Figures 6 and 9, respectively.e maximum temperature changing regularities of the synchronizer ring and target gear ring are the same.e temperature increases rst and then decreases.At the initial stage of friction, the energy of heat ux density input is greater than the energy of heat conduction and convective heat transfer taken away, and the temperature increases speedily.With the decrease of speed di erence at both ends of the synchronizer, heat ux and convective heat transfer coe cient of the friction cone decreases gradually.When the energy of heat ux density input is equal to the energy taken away, the temperature of the synchronizer ring friction cone reaches to the maximum.As the speed difference at both ends of the synchronizer decreases continuously, the temperature of the synchronizer ring friction surface reduces gradually until the end of the synchronization process.
At the initial stage of friction, the maximum temperature of the target gear ring friction cone appears at both ends of the contact surface.en the maximum temperature of the friction cone appears only at the larger round end of surface    6 Advances in Materials Science and Engineering with the friction process.e temperature distribution of the friction cone tends to be uniform gradually.Note that the energy dissipation through heat conduction on the friction surface is the main determinant of the gear ring temperature rise, instead of convective heat transfer.e maximum temperature of the synchronizer ring inner cone appears at all ring gears at the initial stage of friction.en the maximum temperature of the synchronizer ring appears only at the smallest ring gear with the friction process.erefore, the smaller the inner diameter of synchronizer ring gear is, the thicker the ring gear is.So that the energy dissipation of ring gear surface with smaller inner diameter is slower through heat conduction, and the temperature is higher than the ring gear surface with bigger inner diameter.
e temperature of friction surface under di erent working conditions is shown in Figure 10.e maximum temperature of friction surface increases about 1.8 °C for every additional 50 N of the synchronous load.While the maximum temperature of friction surface increases about 1.1 °C for every additional 200 r/min shift speed di erence between the two ends of the synchronizer.

Friction Coe cient Analysis.
e torque of the friction is obtained from torque-speed sensor under di erent working conditions, and the friction coe cient is calculated as follows: where T S is the cone torque, F S is the shifting force, α is the half-cone angle, and R is the cone radius.Hence, friction coe cient changing regularities of the friction cone under di erent working conditions are shown in Figure 11.e friction coe cient changing regularities of the friction cone are the same under di erent conditions basically.e friction coe cient declines rapidly rst and then tends to be stable slowly during the synchronization process.
e experimental data about friction coe cient have uctuations because of the coaxiality of test bench and surrounding electromagnetic interference.e analysis of friction coe cient changing regularity lays the foundation for establishing an e ective friction coe cient compensation control strategy.

Conclusions
In order to improve the shift quality further, the friction coe cient changing regularities of the friction cone and the temperature rise of friction surface during the synchronization process were investigated.e thermal-structural coupling model was established through tribo-thermodynamic analysis.e relevant experiment was carried out as well.Main results are summarized as follows: (1) e error between the experimental and simulated results is controlled within 3%, which veri es the accuracy of the thermo-structural coupling model.(2) e maximum temperature of synchronous ring friction surface increases 1.8 °C for every additional 50 N of shift force, while increases 1.1 °C for every additional 200 r/min shift speed di erence.(3) e friction coe cient declines rapidly rstly and then tends to be stable slowly during the synchronization process.e result of friction coe cient changing regularity lays a good theoretical basis for establishing an e ective friction coe cient compensation control strategy.
e thermal-structural coupling model is established through tribo-thermodynamic analysis in Section 3. e established model is veri ed by experiments in Section 4.

Figure 1 :
Figure 1: e structure of lock ring synchronizer.

Figure 6 :
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.

Figure 7 :
Figure 7: Comparison of experimental and simulated results.

Figure 8 :
Figure 8: e highest temperature changing regularities of friction surface.

FrictionFigure 11 :
Figure 11: Variation law of friction coe cient of the friction cone under di erent working conditions.