Dynamic Engaging Characteristics of Wet Clutch in Automatic Transmission

LIU Yan－fang(劉艷芳)，GUO Wei(郭 偉)，ZHANG Jing(張 婧)，XU Xiang－yang(徐向陽(yáng))

1 School of Transportation Science＆Engineering，Beihang University，Beijing 100191，China

2 International Education College，Hefei University，Hefei 230001，China

3 National PCAT Engineering Research Center，Weifang 2612206，China

Dynamic Engaging Characteristics of Wet Clutch in Automatic Transmission

LIU Yan－fang(劉艷芳)1*，GUO Wei(郭 偉)1，3，ZHANG Jing(張 婧)2，XU Xiang－yang(徐向陽(yáng))1

1 School of Transportation Science＆Engineering，Beihang University，Beijing 100191，China

2 International Education College，Hefei University，Hefei 230001，China

3 National PCAT Engineering Research Center，Weifang 2612206，China

Wetclutch isan importantshifting componentin automatic transmission，and its properties will affect the gear shift performance．By comparing the calculated and test results，the static friction torque model was proved to be capable of describing the real pressure and torque only in the situation of high-energy engagement．Therefore，a dynamic torque model was proposed on basis of hydrodynamic properties between friction surfaces，in which the clutch engagement was divided into three phases for hydrodynamic lubrication，mixed lubrication， and mechanicalcontact．The proposed dynamic torque model was validated by comparing the calculated and test results．The effects of temperature，pressure，and pressure changing rate of automatic transmission fluid(ATF)on the clutch torque were analyzed．Based on these results，the clutchto-clutch torque control during shifting in automatic transmission was optimized，and as a result，the shifting comfort was significantly improved since the problems such as the fluctuation and sudden drop of the engine rotating speed during shifting were eliminated．

automatic transmission; wet clutch; dynamic characteristics;torque control;friction

Introduction

Hydraulic automatic transmission with wet clutches is widely used owing to its smooth shift．By engaging or opening some clutches，a new gear is shifted so as to change the power flow in automatic transmission and satisfy the vehicle's torque and speed requirements．The shift quality is determined by the friction torque of wet clutches，and thus it is necessary to build up a precise model to describe the dynamic clutch torque during shifting．

Berger et al．proposed a finite element model［1］and an analytical solution［2］to model the torque response of the grooved wet clutch during engagement．Yang et al．［3］proposed an axial symmetric model to describe the heat transfer in a wet clutch．The temperature prediction based on the above models is consistent favorably with experimental measurements．Jang and Khonsari［4］put forward a comprehensive Reynolds equation considering thepermeability，roughness，wavinessofthe friction material，and the deformability and centrifugal force in wet clutches．Experimental methods are commonly used to characterize wet clutches．The aeration at high rotational speed was confirmed by experiment［5］．It was pointed out that the deficit of the fluid film was due to the cavitations and gas entering from inner radius of clutches［6］．However，the pressure can barely be enough low for cavitations at clutch speed less than 4000 r/min，and the deficit of the fluid film starts from the out radius．

Static torque model is often used in clutch control．An adaptive temperature compensation method based on the static torque model was proposed to reduce the shift shock under low temperature［7］．The oncoming clutch speed slip can be controlled with fuzzy logic，which is used to optimize the target fill pressure in fill phase and shorten the shifting time［8－10］．

In this paper，the static toque model is tested by experiment first．Based on the Reynolds equation，the dynamic clutch torque model is built up，which is proved to be capable of precisely describing the dynamic characteristics of clutch torque during the course of engagement．According to the dynamic characteristics，a pressure correction method is proposed based on the transmission end of line test when the clutch is engaging．The optimized pressure control is adjusted to reduce the transmission's shift impact and shift time．

1 Structure and Working Principle of Clutch

Figure 1 shows the basic structure of a wet clutch in automatic transmissions．The hydraulic system of automatic transmission feeds oil from the hole into the cylinder．The piston is pulled to overcome the resistance of the return spring and the friction force until the gap between friction discs is eliminated and the clutch is engaged;and vice versa．Because of the friction between clutch discs，the torque is transmitted．Therefore，the pressure force on clutch friction discs can be calculated as:

where P is the pressure of active oil cylinder;S is the area of piston;FCFAand FCFBare the centrifugal forces of the active and balance cylinders，respectively;k is the stiffness of the return spring;Fsealis the friction force of sealing materials;Δx is the displacement;and sgn()is the sign function．

Fig．1 Schematic of a wet clutch in an automatic transmission

2 The Static Torque Model of Clutch

According to coulomb friction law，the friction torquebetween friction and steel discs can be calculated as:

where N is the number of friction surfaces;Fappis the pressure force;μ is the friction coefficient described with Stribeck's equation［11］;Rmis the equivalent frictional radius;Roand Riare the externaland internaldiameters of friction surface，respectively．

To verify the above model，three types of tests are completed considering the variations of initial clutch slip ω0，the oil pressure rise time Δt，and the final apply pressure Papp1．Figure 2 shows the data of calculated and experimental torque．Clearly，there is a delay between the real torque and the calculated torque，which can be reduced by increasing the clutch pressure during the engagement with small clutch slip(Figs．2 (a)and(d))．The large difference between the calculated and experimental torques is due to the low applied pressure(Fig．2 (a))，because the oil between the clutch discs cannot be extruded in a short time．Then the friction characteristics are quite different by comparing the clutch condition with complete contact．The real torque is obviously overshoot with large clutch slip(low pressure)or high pressure changing rate(Figs．2(b) and(c))．The calculated static torque matches the real torque well at high clutch pressure(Figs．2(d)，(e)，and(f))．The calculated torque matches the real torque well at low pressure changing rate(Figs．2(c)and(f))．Therefore，it can be deduced that the static torque model of clutch is suitable only for high－energy engagement since the hydrodynamic characteristics of the automatic transmission fluid(ATF)in clutch discs are neglected．Therefore，a more accurate dynamic clutch model is required to characterize the real clutch torque．

Fig．2 Comparison of the calculated clutch torque with the static torque model with experimental data

3 The Dynamic Torque Model of Clutch

While a wet clutch is open and has relative rotational speed，there are fluid films between clutch discs，which lead to resistance forces．With the pressure Fappshown in Fig．3，the clutch starts to engage and the clutch torque varies with the thickness of the fluid film［12］．

Initially，the film thickness is so large that there is only viscous friction between discs．With the clutch discs pressed increasingly tighter，the fluid between discs will be exhausted gradually，which leads to larger viscous friction．The above process is called hydrodynamic lubrication phase．

When the fluid film thickness reaches the friction disc's coarse surface and when there is relative rotational speed between discs，the clutch torque would be dominated by coarse contact friction and viscous friction．This above process is called the mixed lubrication phase．

When there is no relative rotational speed，there is only contact friction that can generate clutch torque，and this process is called the mechanical contact phase．

The delay and overshoot of torque would occur in the dynamic lubrication phase and the mixed lubrication phase．

Thus，the clutch torque T is the sum of the viscosity torque Tvand the contact torque Tc:

Fig．3 Schematic of plate－type wet clutch

To calculate the changing rate of fluid film thickness，two assumptions are used here．

(1)The thickness of the fluid film is constant within normal contact area，and the pressure in the grooves is equal to zero．

(2)The temperature of ATF is constant within normal clutch contact area，and the kinematic viscosity is irrelative withpolar coordinates r and θ．

Thus，the changing rate of fluid film thickness in this phase can be described by Reynolds equation，

where h is the thickness of fluid film，Φ is the osmosis of friction material，φ(h)is the flow factor，η is the dynamic viscosity of ATF，θ2is the angle of ungrooved friction discs (Fig．3)，Ngis the number of grooves for each clutch disc，A is the area of friction plates，d is the thickness of friction materials (Fig．3)，Q is the fluid flow，pc(h)is the contact pressure，ηBJis the Beavars－Joseph coefficient，and erf()is the error function．

According to the Greenwood and Williamson model［13］，pc(h)can be expressed as:

where E is the Young modulus of friction material，ρ is the asperity density，σ is the standard deviation of roughness，and β is the asperity tip radius，and erfc()is complementary error function．

The viscosity torque can be expressed as

where φfand φfsare Patir factor and Cheng factor，respectively; Nfis the number of friction surfaces;and r2and r1are the outside and the inside radiuses，respectively．

The contact torque can be expressed as

where μcis the sliding friction coefficient．

4 Simulation and Discussion

Figure 4 shows the calculated fluid film thickness during the course of clutch engagement under varying pressure and viscosity of ATF．Obviously，the film thickness decreases quickly in the hydrodynamic lubrication phase(PP*)and then gradually in the mixed lubrication phase(PM*)，and finally keeps constant in the mechanical contact phase(PC*)．Larger pressure or viscosity both can lead to smaller film thickness．With varying pressure and viscosity of ATF，the duration of each phase isspecific，which infectsthe clutch torque significantly．

Fig．4 Thickness of the fluid film during the course of engaging a clutch

Figure 5 shows the calculated clutch torque in three phases marked as I－III when engaging a clutch．In phase I，there is no asperity contact，so the clutch torque is equal to the viscosity torque although it is small．The viscosity torque increases slightly even with the severe reduction of fluid film thickness and thus the clutch slip decreases slightly too．In phase II，in addition to the viscosity friction，there is also asperity contact which leads to quick growth of the contact torque until reaching the steady state．The viscosity torque would peak first，which leads to an overshoot of the clutch torque，and then decrease gradually because of the changing of fluid film thickness．Under the increasing clutch torque，the clutch slip decreases significantly till it becomes very small．In phase III，the clutch is engaged completely and there is only the contact friction torque．

Fig．5 Clutch torque when engaging a clutch

5 Test Validation

To verify the above model，experiment is conducted by an SAE#2 machine Greening Inc．，which considers different engaging conditions．Figure 6 illustrates both the calculated and the experimental clutch torques．In Fig．6，ω0is the initial clutch slip，Δt is the pressure ramp time，and τ is the ATF temperature．Obviously，the dynamic model predicts the torque precisely for all conditions while the static models are different．

Fig．6 Simulation and test validations of the clutch torque under different engaging conditions

Comparing Figs．6(a)，(d)，and(g)with Figs．6(b)，(e)，and(h)，a significant torque overshoot appears which will increase with higher pressure ramp rate．Meanwhile，a higher pressure ramp rate would lead to shorter time delay．Larger pressure would decrease the clutch slip of clutch quickly．However，the real torque was unstable initially(Figs．6(g)，(h)，and(i))．Comparing with Fig．5，the torque also has an overshoot in the phase II because of the characteristics of viscosity torque．The torque delay at the beginning of pressure ramp－up originates from the oil film compression speed，which can affect the viscosity torque．Higher temperature can reduce the viscosity of ATF and thus slow down the increase of the viscosity torque．Thus，the overshoot torque in Figs．6(c)，(g)，and(i)is more smooth．Higher viscosity torque appears with larger initial clutch slip and thus the total clutch torque increases more quickly than that with smaller clutch slip．Therefore，it can be deduced that the clutch torque can be significantly affected by temperature，pressure force and clutch slip，and thus these parameters must be considered in clutch torque prediction so as to improve the control accuracy．

6 Optimization ofClutch-to-Clutch Torque Control

Gear shifting of automatic transmission is operated by engaging one on－coming clutch and opening one off－going clutch［14－16］．Figure 7 shows the equivalent driveline，in which C1 is the low－gear clutch and C2 is the high－gear clutch．Figure 8 shows the speed and torque characteristics of the power－on upshift type．The shift process is generally divided into a fill phase to eliminate the gap，a torque phase to transfer the turbine torque from C1 to C2，and a speed phase to synchronize C2．The clutch－to－clutch power on up－shifting is controlled by filling the oncoming clutch C2 while ramping down the pressure of the off－going clutch C1．Because the engine torque is active，a torque has to be reduced by the engine to let C2 pull down the engine speed．The torque capacity and pressure of C2 and C1 are controlled by the closed loop proportion integration differentiation(PID)system with reference to the clutch slip speed．Except for the fill phase for C2 because zero torque is required，all the command torque is calculated based on the engine toque and clutch slip．To make the engine speed change smoothly，the real clutch torque should follow the commandtorque．Otherwise，the engines may flare and tire up，causing poor shift quality．Therefore，the torque－to－pressure relationship is very important for ensuring high shift quality．

Fig．7 Equivalent scheme of the driveline

Fig．8 Speed and torque characteristics of power－on up－shift type

6．1 Test of transmission clutch torque-pressure characteristics

The clutch torque－pressure characteristics(T2P curve)are important for controlling the clutch of automatic transmission，which can be obtained by the test rig．Massive heat would be produced when there is high－pressure and high－speed difference，which may burn out the clutch within short time，so it is usually difficult to test under this condition．The T2P characteristics of clutches can be achieved by the comprehensive dynamic test bench in Fig．9．This test bench consists of one input motor and two output motors which can be controlled separately．The test steps are as follows:

(1)lock up two clutches and open the third clutch(tested clutch);

(2)set the input motor to 2000 r/min，and set the output motor to a certain speed which makes the clutch slip at 40 r/min (small slip);

(3)increase the control pressure to the clutch，and record the clutch's pressure and the input motor torque;

(4)according to the transmission structure，the input motor torque can be equivalent to the clutch torque．The clutch T2P characteristics can be obtained．

Fig．9 Comprehensive dynamic test bench for automatic transmission

Figure 10 shows the experimental T2P curves for C1 at 80℃．With increasing pressure，two different pressure rates are used．Low pressure rate is used to check the clutch kiss point pressure．Kiss point pressure is the pressure that can eliminate the clutch gap and start the clutch to transfer torque along with the increasing pressure．It can be checked by detecting the inflection point(point A)of input torque because the viscosity torque Tvand the contact torque Tcwill increase fast(Fig．5)．High pressure rate is used to check the T2P characteristics．The test results in Fig．10(b)show that the clutch T2P characteristic is linear in fixed clutch slip and stable pressure change．This T2P test data can be the base curve for the clutch control．

Fig．10 Test result for clutch T2P characteristics

6．2 Clutch torque control

According to Fig．6，the pressure change rate and clutch slip can affect the clutch transfer torque．Therefore，these two factors should be considered for the clutch control pressure．Otherwise the shift quality may be influenced．Figure 11 shows the clutch control results with and without correction during shifting．During the clutch oil fill stage，the slip of oncoming clutch C1 is large while its pressure is still small．If clutch pressure increases too fast，the clutch torque would fluctuate and affect the engine load(Figs．6(g)－(i))，thus affecting the shift quality(curve En2 in Fig．11)．In torque exchange stage，pressure P2 for engaging clutch increases linearly so quickly that the torque is overshot，which leads to sudden rise of engine load and thus sudden drop of engine speed(curve En2)．To optimize the clutch torque control，the pressure correction offset based on pressure change rate and clutch slip is added during the pressure control．The pressure offset correction map is shown in Fig．12．P'is the pressure change rate during the shifting．If the clutch slip and P'are larger，the pressure offset correction value is also larger．The final optimized pressure offset can be obtained from the vehicle calibration test．The engine speed En1 is stable and does not cause tie－up or judder during the shifting according to clutch pressure correction P1(Fig．11)．With the pressure correction，the clutch transfer torque can respond to the pressure control more accurately and stably，which will makethe engine load match with the engine input torque and improve the shift quality．

Fig．11 Clutch control results during shift

Fig．12 Pressure offset correction MAP for varying clutch slip and pressure rate

7 Conclusions

(1)The static model for prediction of wet clutch torque is suitable only for the engaging condition with high clutch slip and pressure．

(2)By characterizing the fluid flow during the course of engaging a wet clutch with three phases:fluid lubrication，mixed lubrication，and mechanical contact phase，a dynamic model is proposed to predict the clutch torque．

(3)Based on the dynamic characteristics of clutch torque，the clutch pressure controlwasmodified，and thusthe fluctuation and sudden drop of engine speed could be eliminated and the shift quality be improved．

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U463．22

A

1672－5220(2015)03－0357－06

date:2013－11－19

National Science and Technology Support Program，China(No．2011BAG09B00)

*Correspondence should be addressed to LIU Yan－fang，E－mail:liuyf@buaa．edu．cn