dynamic analysis and control of the clutch filling process in clutch-to-clutch transmissions

Research ArticleDynamic Analysis and Control of the Clutch Filling Process inClutch-to-Clutch Transmissions

Wei Guo,1 Yanfang Liu,1 Jing Zhang,2 and Xiangyang Xu1

1 School of Transportation Science & Engineering, Beijing University of Aeronautics and Astronautics, Beijing 100191, China2 International Academy, Hefei University, Anhui 230601, China

Correspondence should be addressed to Yanfang Liu; [email protected]

Received 20 February 2014; Revised 14 May 2014; Accepted 18 May 2014; Published 23 June 2014

Academic Editor: Yunhua Li

Copyright 2014 Wei Guo et al.This is an open access article distributed under the Creative Commons Attribution License, whichpermits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Clutch fill control in clutch-to-clutch transmissions influences shift quality considerably. An oncoming clutch should be appliedsynchronously with the release of an offgoing clutch to shift gear smoothly; therefore, the gap between the piston and clutch platesshould be eliminated when the torque capacity is near zero at the end of the clutch fill phase. Open-loop control is typicallyimplemented for the clutch fill because of the cost of pressure sensor. Low control precision causes underfill or overfill to occur,deteriorating shift quality. In this paper, amathematicalmodel of an electrohydraulic clutch shift control system is presented. Specialdynamic characteristic parameters for optimal clutch fill control are subsequently proposed. An automatic method for predictinginitial fill control parameters is proposed to eliminate distinct discrepancies among transmissions caused by manufacturing orassembling errors. To prevent underfill and overfill, a fuzzy adaptive control method is proposed, in which clutch fill controlparameters are adjusted self-adaptively and continually. Road vehicle test results proved that applying the fuzzy adaptive methodensures the consistency of shift quality even after the transmissions status is changed.

1. Introduction

Automatic transmissions are used to transfer the power of anengine smoothly and effectively to vehicle wheels at optimaltransmission ratios according to performance requirementsand economic demand. Figure 1 shows a two-dimensionalstructural diagramof an 8-speed automatic transmissionwithfive shift elements, namely, a brake 1 and four clutches 14, which are engaged or separated by the electrohydrauliccontrol system of transmissions. To shift from one gear toanother in an automatic transmission, one clutch must bereleased and another must be applied synchronously, whichis called a clutch-to-clutch shift [1, 2]. With the developmentof six-speed transmissions or even more speeds nowadays,considerable time and effort has been made to study theclutch-to-clutch shift control technology [1, 3, 4]. Asyn-chronous clutch control would cause power interruption oroverconstraint [5].Therefore, the gap between the piston andclutch plates for the oncoming clutch should be eliminatedwhen the clutch torque capacity is near zero at the end ofthe clutch fill phase [6, 7]. Nowadays most clutch torque

models do not take hydraulic dynamic characteristics intoaccount [8]. To optimize the engagement of clutches, clutchfill is usually formulated as an optimization problem. Open-loop clutch pressure control was proposed as a solution bymeans of dynamic programming algorithm for cost reasons[6]. However, this controlmethod requires precision trackingof the input pressure. Relative experiments were proposedand the experimental results were used for optimal control ofclutch fill process [9]. Low control precision causes underfillor overfill to occur, deteriorating shift quality.

Most automatic transmissions use the electrohydraulicdriving pattern, in which the shifting elements are controlledseparately. Figure 2 shows a partial electrohydraulic controlsystem for a single clutch and a torque convertor. The mainline pressure CV, is provided by an oil pump, which ismechanically connected with the engine output shaft. A flowregulation valve (indicated by number 1) is used to dischargeredundant fluid flow, especially at a high rotation speed, andto prevent the pressure and fluid flow in the main hydrauliccircuit from exceeding the limitation. A pressure-regulatingvalve (indicated by number 5) is used to regulate the pressure

Hindawi Publishing CorporationMathematical Problems in EngineeringVolume 2014, Article ID 293637, 14 pageshttp://dx.doi.org/10.1155/2014/293637

http://dx.doi.org/10.1155/2014/293637

2 Mathematical Problems in Engineering

B1C4

C3 C1

Outputleft

Outputright

C2

Torqueconvertor

Differential

Input

Figure 1: Schematic diagram of an 8-speed automatic transmission.

1

2

345

6

7

8

9

10

Lubrication

12

11

13

(1) Flow control valve(2) Solenoid valve(3) Shift valve(4) Oil duct(5) Pressure-regulating valve(6) Pump(7) Filter

(8) Tank(9) Solenoid valve(10) Control value(11) Disc spring(12) Piston(13) Clutch friction disc

B

TC

PCV,P

PCV,A

PCU

PSV,V

PSV,K

Figure 2: A partial electrohydraulic control system for a singleclutch.

in the main hydraulic circuit to satisfy the pressure demandsSV, for all shift valves control; here 5 bar is preferred whichis realized by the dimensions of the pressure-regulating valve.The clutch piston chamber pressures are jointly controlledby a solenoid valve (indicated by number 2) and a shiftvalve (indicated by number 3). By controlling the electriccurrent of the solenoid valve, the pilot pressure SV, of theshift valve can be regulated. The pilot pressure determinesthe position of the shift valve spool and thereby determinesthe pressure and fluid flow in the clutch piston chamber.When the clutch piston chamber pressure increases, once thefrictional resistance and the return spring force are overcome,the clutch piston starts to move rightward until the gap iseliminated and then force is applied. To prevent overfill orunderfill, the fill phase is controlled to end before a presettime. To reduce the cost of transmission sensors, no pressuresensors are assembled for clutches; consequently, obtainingthe feedback pressure for closed-loop control is difficult.Moreover, because of the strong nonlinear pressure charac-teristics of solenoid valves and the response delay, obtainingprecise target pressure by controlling the current is difficult.Furthermore, the clutch pressure response differs based onthe status of transmissions, such as the tolerance and wearof parts. Therefore, building an open-loop clutch pressurecontrol model for clutch fill phase based on the dynamicpressure characteristics of electrohydraulic clutch controlsystems is necessary to satisfy the requirements of clutch filltime andmaximal fluid flow. Previous models have primarilydepended on car test results, which cannot be adapted tocomplex working environments. After transmissions run foran extensive period, wear inevitably occurs.Therefore, a fuzzyadaptive fill control method, which was proven to be capableof improving the shift quality effectively, is proposed in thispaper.

2. Model of Hydraulic Clutch ShiftControl Unit

Figure 3 shows a clutch hydraulic control unit, in which theclutch piston chamber pressure is controlled by a solenoidvalve and a shift control valve mainly. The solenoid valvecontrols the pilot pressure SV, at port of the shift valve tocontrol the position of the valve spool and change the openingarea of port , thereby regulating the clutch piston chamberpressure CU. Port is connected to the main line pressureCV, of this system, and port is used for discharging theclutch cylinder. The pressure CV, at port is controlledby a limp home valve, and there is no pressure in normalmodes. Pressure response in failure modes is not discussedhere. Orifice is used to control the total fluid flow intothe solenoid valve and the shift valve. Here some symbolsand subscripts are appointed in advance for computationalconvenience; see Nomenclature.

2.1. Dynamic Model of a Solenoid Valve. Figure 4 showsthe structural diagram of a normally open high-speed pro-portional solenoid valve [7], mainly composed of a coil,armature, return spring, and valve spool. The coil produces

Mathematical Problems in Engineering 3

V

APT

D

C

B

1

2

3PSV,V

PSV,C = 0

PSV,K = 5 bar

PCV,P PCV,A

PCU

(1) Clutch control solenoid valve(2) Shift valve(3) Clutch

Figure 3: Schematic diagram of a hydraulic clutch control unit.

electromagnetic force and overcomes the resistance of thereturn spring, and the armature drives the valve spool tomove in the axial direction of the spool, thereby regulatingthe opening area of the valve and, subsequently, the pressure.

According to the laws established by Newton, the dynam-ic equation of the valve spool can be described as

SVSV + SVSV + SV (SV + 0SV) = SV. (1)

The electromagnetic subsystem of the solenoid valve canbe simplified into a series connection of resistive and induc-tive components [10]. The electromagnetic force is calculatedusing

SV = 2

SV, (2)

where the dynamic equation of the electric circuit is writtenas

SV =(SV SVSV VSVSV)

SV. (3)

During the movement of the valve spool, the dynamicequation for the hydraulic subsystem is expressed as

SV, = CdSVSV, (SV) 2

SV,. (4)

2.2. DynamicModel of a ShiftValve. Figure 5 shows the struc-tural diagram of a shift control valve with double spools. Forconvenience, the symbol

1

represents the pilot spool and

2

the main valve spool. When the electric control systemfails to provide pilot pressure at port , the safety pressureat port still can control the main spool

2

to ensure theclutch pressure which can be supplied from port. There aresectional area differences in chambers II and III.

1 2 3

4 5

Flow out

Flow in

(1) Coil (2) Armature (3) Valve spool

(4) Spring(5) Strainer

K

T

Figure 4: Structural diagram of a variable-force solenoid valve.

A

T PV C D

m1 m2

ds

I

P: InletV: Pilot portC: Limp home portA: Outlet

D: Pressure regulation portT: Discharging portIIII: Chambers

II III IV

Figure 5: Structure of the shift valve.

According to the laws established by Newton, the dynam-ic equations of the valve spools are described as

CV,1

CV,1

= SV,CV,I CV,CV,II

2

1

, (5)

CV,2

CV,2

+ CVCV,2

+ CV (CV,2

+ 0CV,2

)

= CV,CV,II + 2

1

CV,CV,III CV,CV,IV,

(6)

where CV,III = CV,III CV,III is the sectional area differ-ence of chamber III.

Because of the movement of the main spool, the relation-ship between the pressure and fluid flow of the shift controlvalve at all ports can be expressed as

CV, = sign (CV, CV,)CdCV

CV, (CV,2

)2

CV, CV,,

CV, = CdCVCV, (CV,2

)2

CV,,


CV, = sign (SV, SV,)Cd

2

SV, SV, SV,,

(7)

SV, =CV

0CV,I + CV,1

CV,I(CV, CV,

1

CV,I) , (8)

CV, =CV

0CV,IV CV,2

CV,IV(CV, + CV,

2

CV,IV) .

(9)

2.3. DynamicModel of the Clutch Fill Phase. Automatic trans-mission fluid (ATF) flows from port of the shift valve intothe clutch chamber through pipes in gear structure of thetransmission. For convenience, the symbols and are theequivalent length and radius of these, respectively;

is theequivalent centrifugal pressure in the piston chamber causedby rotational speed of the clutch, calculated in [11]. Withthe function of the increasing inlet pressure, after the returnspring force and friction force of the clutch are overcome, thepiston starts tomove rightward until the gap is eliminated andthen force is applied.

According to the laws established by Newton, thedynamic equations of the clutch piston are described as

CUCU = CU (CU + ) seal CU (CU + 0CU)

CUCU (CU < ) ,

APP = CU (CU + ) seal

CU ( + 0CU) (CU = ) .

(10)

The fluid flow into the clutch piston chamber throughpipes and the piston chamber pressure can be expressed as

CU =

4

8(CV, CU) +

leakCU , (11)

CU =CU

0CU + CUCU(CU CUCU) . (12)

The sealing force seal is defined as

seal

=

{{{{

{{{{

{

(seal (CU + ) + ) tanh(

)

(CU

> 0.1mm/s)

(CU + ) + (CU

0.1mm/s) .

(13)

The static viscous friction stick can be computed usingthe Kanopp stick-slip model [12]. This viscous friction isgenerally ignored in dynamic models [13]. However, in theclutch fill phase, the pressure of ATF fluid is low and,thus, a large proportion of viscous friction exists. From theperspective of numerical computation, the friction of the Oseal ring is assumed to be equal to stick when the velocity of

the clutch piston is under 0.1mm/s. When this occurs, stickis the force used to balance the piston, and its acceleration is0. Therefore, this viscous friction is the maximal limit value.Once the friction exceeds this limitation, the piston starts tomove.

2.4. Clutch Pressure Characteristics. By combining (1)(12),the clutch piston chamber pressure response can be simu-lated. Figure 6(a) shows the pressure response when applyingthe step current command. The simulation results indicatedthat the clutch piston chamber pressure is initially 310mA.Therefore, a calculated pilot pressure of at least 0.6 bar isrequired to overcome the resistance of the shift valve spool.When the small step control is applied, the clutch pressureincreases with step to approximately 0.28 bar. If the pressureis not sufficiently high to overcome the resistance of theshift valve spool, then the clutch pressure does not respondto the current step, the so-called loss of step. When largestep current control is applied, the clutch pressure overshootsor oscillates, but it rapidly stabilizes because of systemdamping (II in Figure 6(a)); clearly, the stabilizing time ofthe shift valve is shorter than that of the solenoid valve.Based on Figure 6(a), the steady characteristics of the clutchpiston chamber pressure, exhibited when the control currentincreases, can be obtained, as illustrated in Figure 6(b), whichshows that hysteresis exists.

3. Optimization of Clutch FillControl Parameters

3.1. Selection of Control Parameters. Theobjective of clutch fillcontrol is to stably eliminate the gap between the piston andclutch plates within a preset time.The ideal piston velocity inthe clutch fill phase is shown in Figure 7. In the early periodfrom0 to2, the piston velocity is nearly zero, and the deadvolume of the clutch cylinders is first filled with ATF fluid.Consequently, the piston velocity is low within a short periodfrom 1 to 2, rapidly increases to the maximum within theperiod from2 to3, ismaintained from3 to4, andfinallydecreases from 4 to 5, and the clutch is engaged.

Figure 8 shows two methods for clutch fill pressurecontrol based on the piston motion shown in Figure 7: trian-gle fill and square fill. pre, FP, and FTP are the prefillpressure, fast fill pressure, and stable fill torque pressure,respectively. FTP is the pressure when the clutch transfers asmall torque. In practice, based on characteristic curves, suchas pressure versus current curves, the target pressure can betransformed into the control current of the solenoid valve.Therefore, analysis of the target pressure and the real pressureis necessary for optimizing clutch fill control. According toFigures 7 and 8, the clutch fill phase is divided into threestages.

(1) Prefill Stage. The prefill stage shown in Figure 8 ensuresthat the dead volume in the clutch cylinder (Figure 2) is filledwithATFfluid and an initial amount of pressure. At this stage,because of the sealing force, the piston velocity is extremelylow.


10 30 50 70 900

200

400

600

800

1000

1200

0 20 40 60 800

10

20

Time (s)

Clut

ch p

ress

ure (

bar)

Con

trol c

urre

nt (m

A)

I

I

II

II

(a)

Control current (mA)

Clut

ch p

ress

ure (

bar)

200 400 600 800 10000

5

10

15

20

a b c d

DownUpper

I

I

(b)

Figure 6: Simulation results for the step response of the system.

Time (s)

0T5T1T0 T2 T3 T4

Maximum

xC

U(m

m/s

)

Figure 7: Ideal piston velocity.

(2) Fast Fill Stage. This stage is the most crucial and difficultstage, corresponding to the period from 2 to 3 in Figure 7.The triangle fill method can be used to increase the pressurepeak substantially and enhance the piston velocity. However,applying this method also increases the instability of thefill phase, and an excessively high pressure peak increasesthe demand for systemic fluid flow, thereby affecting themain pressure supply. Regarding the square fill method, thepressure response is relatively slow but stabler than thatproduced when applying the triangle fill method.

(3) Stable Fill Stage. At this stage, the piston is driven stablyto eliminate the gap between clutch plates, corresponding tothe period from 3 to 5 in Figure 7. The control currentis generally unvarying in this process. As the piston moves,the elasticity of the wave spring gradually increases and, thus,the pressure gradually increases until the piston stopsmovingwhen the gap is completely eliminated.

Four parameters listed in Figure 8 were selected as clutchfill control parameters: fast fill pressure FP, rapid fill timeII, stable fill pressure FTP, and prefill pressure pre. Theseparameters were used to determine the variation in the clutch

Pres

sure

(bar

)Fill

Time (s)0

Triangle fill

Square fill

A

Ppre

PFP

PFTP

TIIITII

TI

II III

II III

I PrefillFast fillStable fill

I

Figure 8: Design of clutch fill control pressure.

fill pressure and the movement of the piston; thus, the clutchfill control was optimized by optimizing these parameters.

3.2. Influence of Clutch System Parameters on Clutch Fill-ing. The aforementioned equations indicate that numerousparameters affect the clutch fill process. The consistencyof several parameters, such as the number of coils in thesolenoid valve, the magnetic resistance, and the sectional sizeof the valve core, is maintained during assembly. However,the consistency of other parameters, such as the springstiffness and preload force, main supply pressure, ATF fluidtemperature, and sealing force, is impossible to maintain,which causes differences in the oil fill results. Therefore, theeffects of these parameters on the clutch fill phase should be


analyzed and controlled to optimize the open-loop clutch fillcontrol.

Based on the aforementioned (5)(12), the influence ofthese parameters on filling the clutch under the same targetoil fill pressure was simulated, as shown in Figure 9.

(1) ATF Fluid Temperature . Figure 9(a) shows the clutchpiston chamber pressures at various temperatures. The tem-perature of the ATF fluid directly affects its viscosity; thus,the resistance of motion increases at low temperatures.In addition, the contraction of components contributes tochanges in the tolerance clearance. These factors slow clutchfill. As shown in Figure 9(a), when the temperature is below20

C, the pressure response is extremely slow at the fast oilfill stage and stable oil fill stage. As the temperature increases,the speed of the oil fill response and the peak pressureclearly increase. At high temperatures, such as 120C, theclutch piston chamber pressure rapidly reaches the kiss-pointpressure, but this process may cause overfill and shiftingimpact to occur. Therefore, clutch fill control parametersshould be adjusted based on temperature to meet the shiftquality requirements at various temperatures.

(2) Main Oil Pressure CV,. Equation (8) indicates that themain supply pressure affects the flow of the system and that itis directly related to the rotation speed of the engine; thus, themain supply pressure considerably influences the clutch fillperformance. Figure 9(b) shows the simulated clutch pistonchamber pressure under various main supply pressures.Underfill clearly occurs between 5 and 10 bar, whereas overfilloccurs at 20 bar. Therefore, the influence of the main supplypressure should be considered; in other words, the clutchfill intensity should be reduced to prevent overfill at highpressures and increased to prevent underfill at low pressures.

(3) Spring Stiffness CU and Preload 0CU. Tolerances existbecause of both manufacture and assembly of return springsin clutches, which are mainly reflected in the stiffness andpreload of the return springs. These two parameters deter-mine the spring resistance that occurswhen the pistonmoves.A strong resistance causes the clutch to reach the kiss pointunder high pressure and over a long time. Although this timecan be shortened when the resistance is weak, shortening thetime may cause the piston to move too fast and thereby affectthe shift quality. Figures 9(c) and 9(d) show the simulationresults for clutch fill pressure at various spring stiffness andpreload values. Clearly, increased spring stiffness and preloadresult in a high maximal fill pressure and a low pressurechange rate during the rapid fill stage.

(4) Static Frictional Resistance Coefficient

. The static fric-tional resistance coefficient affects the maximal static frictionthatmust be overcomewhen the piston is static ormoving at alow speed.This coefficient and the preload 0CU jointly affectthe pressure when the piston starts to move.The larger the

is, the higher the peak pressure is during the rapid fill stage(Figure 9(e)). However, if

and 0CU are extremely small,then the acceleration of the clutch piston becomes extremelyhigh, easily causing a piston movement bump to occur. If thepiston speed reduces to a certain level, then double-peak fill

occurs because of the static friction (Figure 9(e)), resulting inunderfill; therefore, the clutch cannot reach the kiss point.

(5) Sealing Resistance Coefficient seal. Figure 9(f) showsthe effects of the sealing resistance coefficient seal of theclutch cylinder. The influence of the tolerance of seal onclutch fill pressure is relatively small compared with that ofother parameters. The resistance caused by seal influencesthe acceleration of the piston. Thus, a high speed clearlyaffects resistance. Therefore, seal can magnify the effects oftemperature, piston preload, piston stiffness, andmain supplypressure on the speed of the piston.

3.3. Optimization of Clutch Fill Control Parameters. Since themanufacturing tolerance, assembly tolerance, and workingconditions also affect clutch fill pressure, clutch fill controlshould cover all types of qualified tolerance and normalworking conditions.

3.3.1. Prefill Pressure. Prefill pressure pre is included toensure that the pipes in the gear structure of the transmissionsbetween the shift valve and clutch piston are filled with fluidand is not high to the extent that the resistance required tomove the piston is overcome. Therefore, pre should not betoo high to overfill when using clutches with low resistance.Moreover, the minimum prefill pressure should avoid thedropping downward of ATF oil of the rotating clutch. The oilflow must be completed in the prefill time I. Furthermorethe prefill time is generally limited to theminimum shift time.The constraint condition on pre and I can be defined as

I max

0

(CV, leakCU ) = 0CU +

2

,

I max = 0.1 shift,

I = (1 I) I min + II max,

pre maxCU = (stick)min + (CU0CU)min,

pre min = ,

pre = (1 pre) pre min + pre pre max.

(14)

3.3.2. Fast Fill Pressure and Time. The fast fill stage is theperiod when the piston accelerates after overcoming all typesof resistance. The fast fill pressure and time affect the fillspeed and stable fill pressure status. Figure 10(a) shows thesimulation results for varying target pressures. Increasing thefast fill pressure enhances the clutch pressure response speedand increases the fill pressure at the initial stage. The time forthe clutch pressure to reach the target value is shortened withincreasing the fill pressure. However, pressure fluctuationoccurs during the third and fourth fill process because thepiston speed is still extremely high when the gap betweenclutch plates is eliminated. The ATF fluid cannot absorb allof the remaining energy instantly; therefore, the pressurefluctuation occurs inevitably.


00.80.60.40.20.0

4

3

2

1

Fill

pres

sure

(bar

)

= 110C

= 60C

= 60C

= 20C

= 20C

Time (s)

(a)

0 0.80.60.40.20.0

4

3

2

1

PCV,P = 20 bar

PCV,P = 15 barPCV,P = 15 bar

PCV,P = 10 barPCV,P = 5 bar

Time (s)

Fill

pres

sure

(bar

)

(b)

00.80.60.40.20.0

4

3

2

1

kCU = 80nm/mmkCU = 91nm/mmkCU = 91nm/mm

kCU = 103nm/mmkCU = 110nm/mm

Time (s)

Fill

pres

sure

(bar

)

(c)

0 0.80.60.40.20.0

4

3

2

1

Fill

pres

sure

(bar

)

Time (s)

x0CU = 6.5mmx0CU = 6mmx0CU = 6mm

x0CU = 5.5mmx0CU = 5mm

(d)

4

3

2

1

00.80.60.40.20.0

Time (s)

ks = 0.00346

ks = 0.00276

ks = 0.00276

ks = 0.00226

ks = 0.00186

Fill

pres

sure

(bar

)

(e)

00.80.60.40.20.0

4

3

2

1

Time (s)

kseal = 0.0021

kseal = 0.0018

kseal = 0.0018

kseal = 0.0015kseal = 0.0012

Fill

pres

sure

(bar

)

(f)

Figure 9: Oil fill results for various clutch parameters.


Once the shift valve suddenly opens wide, a large amountof ATF oil flows to the piston cylinder, which increases theflow and reduces the main line pressure (Figure 10(a)). So themain line pressure and the systemflow can be used to evaluatethe effects of fast fill pressure. Because the variation in mainline pressure also affects other clutch pressures, it should notbe reduced excessively.

The real fill pressure at the stable fill stage increases withthe fast fill time (Figure 10(b)). The reason is that the filledvolume and the maximal clutch piston speed increase at thefast fill stage. Subsequently, the clutch piston eliminates thegap and reaches the kiss point rapidly. So if a long fast fill timeis required, overfill may occur and the shift quality may beaffected.

The clutch fill is affected by the fast fill timeII, the fast fillpressureFP, the stable fill timeIII, and the stable fill pressureFTP combined. FTP affects the transferred torque afterengagement, which has priority over clutch fill control. SoFTP is treated as the input for optimizing other parameters.

The fast fill time II affects clutch fill significantly(Figure 9(b)), while the stable fill time III affects it slightly.The difference of the control effect of III for differenttransmissions could be compensated by adjusting the fast filltime II. So the preferred strategy is to adjust II while IIIis usually set to be a constant, which is determined by thevelocity and displacement requirements of the clutch piston.The stable fill time III is formulated as

III = [FTPCU seal CU (0.75 + 0CU)]

2CU. (15)

In order to avoid bad shifting performance, the percent-age of the clutch fill time in the whole shift time is limitedstrictly, such as within 47% used in this paper. So the fast filltime II is constrained by

II II max

= 0.47shift

[FTPCU seal CU (0.75 + 0CU)]

2CU.

(16)

Meanwhile, the fast fill pressure FP should be applicablefor different conditions such as different temperatures ofATF fluid and main line pressures. Here the fast fill timeII is again limited as II = 0.7II max. According to thecontrol requirement, the gap between clutch plates should beeliminated with the clutch fill time, which is formulated as

FP () + FTP () = 0.7II max

CU (FP)

+

III

0.7II max

CU (FTP) = .

(17)

In order to engage clutches smoothly, the energy of theclutch piston in the end should be smaller than the extrusion

energy

of ATF fluid between clutch plates; otherwise thereis an impact. So the clutch fill pressures are constrained by

0 FP FP CU FP + FTP FTP CU FTP

1

2CU

2

seal ,(18)

where FP and FTP are equivalent factors of the target pressureand real pressure at fast fill phase and stable fill phase,respectively.

In order to avoid that the main line pressure decreasesbelow the safe level in fast fill phase, a safety fluid flow of ATFfluid is required. So the maximum velocity of the piston isusually limited by

CU (FP) CUmax pump, (19)

where pump is the flow of pump; is the safety factor forflow loss.

So the fast fill pressure can be controlled as

FP = FP min (FP max 1, FP max 2) + (1 FP) FP min.(20)

Oversized FP would cause unstable clutch fill process; herean optimal value2/3 is tested to be effective.

3.3.3. Stable Fill Pressure. The stable fill pressure mainlyaffects the final stage of clutch engagement. At this stage,because of increased spring resistance, the piston deceleratesuntil the gap is eliminated. The simulation results for variousstable fill pressures are shown in Figure 11. During period in Figure 11, a reduced amount of ATF fluid is fed intothe piston chamber because of a sudden current reduction.However, the piston continues to move rapidly, causing thefill pressure to decrease according to (12). During period in Figure 11, when the piston speed decreases to a certainlevel, namely, CU > CUCU, the fill pressure increases tothe target level gradually. In an ideal situation, the clutchpressure should be onlyKP and the piston speed should equalzero when the fill is nearly completed. However, numerousfactors affect fill pressure; consequently, realizing the idealsituation is nearly impossible. Nevertheless, the robustness ofthe clutch fill control can be improved by reducing the fastfill pressure and increasing the stable fill pressure. Clearly,reducing the fast fill pressure reduces the maximal pistonspeed; increasing the stable fill pressure ensures that the fillpressure reaches the kiss-point pressure before the fill processis completed. An appropriate stable fill pressure FTP valuecan be calculated by

FTP = KP +10

2

(1)2

. (21)

4. Automatic Test Method for DeterminingInitial Clutch Fill Parameters

Because of distinct inconsistencies in the mass productionof transmissions and in the open-loop control characteristics


0 10 20 30 40 50 600

1

2

3

4

5

6

0

0

2

4

6

8

10 20 30 40 50 60

Pum

p flo

w (L

/min

) Li

ne p

ress

ure (

bar)

Pisto

n sp

eed

(mm

/s)

Clut

ch p

ress

ure (

bar)

0 10 20 30 40 50 6011

12

13

14

15

16

0 10 20 30 40 50 6019

19.5

20

20.5

21

21.5

Time (s)

Time (s)Time (s)

Time (s)

2

Q1Q2

Q3Q4

PCV,P1PCV,P2

PCV,P3PCV,P4

PCU1PCU2

PCU3PCU4

xCU1xCU2

xCU3xCU4

(A) (B)

(C) (D)

(a) Fast fill pressure

0 0.2 0.4 0.6 10

1

2

3

4

0.8

Real pressure

Command pressure

Time (s)

Fill

pres

sure

(bar

)

(b) Fast fill time

Figure 10: Pressure response at various target pressures and fast fill times.


of clutch fill pressure, obtaining the initial fill parameters iscrucial to improving shift quality. The direct method is tocalculate fill parameters based on obtained clutch pressuresignals by sensors from the transmission end-of-line (EOL)test according to previos equations.

In the EOL test, because the allowed testing time is short,only one key control parameter can be tested while theother control parameters remain unchanged. By analyzingthe effects of the aforementioned parameters on fill pressure,the fast fill time can be adjusted to alter the characteristicparameters, thus enabling the clutch pressure to reach thekiss-point pressure KP within the preset time. The clutchfill testing scheme is formulated as shown in Figure 12.During testing, the fast fill time gradually increases andwhether the fill requirement is satisfied can be determinedby observing three conditions denoted as 1, 2, and 3,respectively, in Figure 12. 2 is defined from start2 to end2.1 is defined from start1 to end1. The condition 1 requiresthat, immediately after the fast fill stage ends, the pressure isboth below KP and within the range of 1 to 1, ensuringthat the piston moves smoothly. The condition 2 requiresthat, after the fill stage ends, the clutch pressure is exceedingKP, ensuring that the piston reaches the final engaged pointwithin the preset time.The condition3 requires that, duringthe fast fill stage, themaximal fill pressure cannot exceed

3

.The ranges for1,2, and3 are related to themass toleranceranges of the transmission components.

In the fill phase, the clutch pressure within the range of1 and 2 is associated with the fast fill time. This pressurecan be increased by increasing the fast fill time; therefore, theoptimal fast fill time can be obtained by applying the learningrules of the EOL test shown in Table 1. Figure 13 shows theautomatically measured EOL results. Beginning from 120ms,the fast fill time increases in increments of 10ms. As the fastfill time increases, the pressure at 1 and 2 increases untilit reaches the required level at 170ms. Moreover, during eachfast fill stage, the main line pressure of the system decreasessuddenly and causes flow deficiency when a large amount ofATF fluid instantly enters the piston cylinder.

5. Effects of Overfill and Underfill onShift Quality

Shift quality optimization is applied to ensure that the torquefrom the offgoing clutch is transferred smoothly to theoncoming clutch without flares or tie-up.

5.1. Effects of Underfill. Because numerous factors affectclutch fill and an open-loop is used for pressure control,the piston cannot be ensured to reach the kiss point exactlywhen the clutch fill phase ends. Figure 14 shows how underfillinfluences clutch shifting processes. When clutch fill is com-pleted, the clutch pressure does not reach the kiss point at thebeginning of the torque exchange stage. However, because ofunderfill, the pressure of the oncoming clutch cannot remainequal to the target pressure at the initial stage of torqueexchange, causing the engine load to decrease and, thus,engine flare to occur. If engine flare continues for a long time

4

3

2

1

00.80.60.40.20.0

0

2

4Commandpressure

Piston speed

A B

Time (s)

Fill

pres

sure

(bar

)

Pisto

n sp

eed

(mm

/s)

Pmin 2

4

PFTP = PKPPFTP = PKP + 10 kT2P

Figure 11: Fill results at various stable fill pressures.

G1G2

Time (s)

Fill

pres

sure

(bar

)

UpDownG3

Tend2Tstart2

Tstart1

Tend1

PFP

PFTPPKP

Ppre

PL1 PH1PH2

PH3

Figure 12: Fill end-of-line test method based on the pressurefeedback.

Table 1: Learning rules of the fill end-of-line test.

1 2 3 Fill learning rule <

1

< KP < 3 Up1

1

< KP < 3 Up >

1

< 3

Down1

1

> 2

< 3

Down1

1

KP 2 < 3 CorrectOther conditions Fail

at a high rotational speed, the clutch friction plates generate ahigh amount of heat. Therefore, underfill would shorten thelife of clutches. Moreover, engine flare aggravates the slippingof clutches and causes the line pressure to increase based onthe PI (proportional-integral) control of the offgoing clutch.Although clutch slipping can be reduced, it causes fluctuationin the rotational speed (Figure 14).

5.2. Effects of Overfill. Overfillmeans that a certain amount oftorque is transferred by clutches during the clutch fill phase.Overfill occurs when the fill pressure is too high. Figure 15shows the pressure response of the clutch when overfilloccurs. At the fill stage, after the fast fill period ends, thepressure is still higher than FTP; consequently, the oncoming


0 2 4 6 8 10 12 140

1

2

3

4

0

5

10

15

20

Clut

ch p

ress

ure (

bar)

Time (s)

Line

pre

ssur

e (ba

r)

Ok120ms 130ms 140ms 150ms 160ms

170ms

PFTP

PKP

Figure 13: Automatically measured fill results.

12

10

8

6

4

2

05251.651.250.850.450

3000

2800

2600

2400

2200

Inpu

t spe

ed (r

pm)

Clut

ch p

ress

ure (

bar)

Target input speed

Current input speed

Offgoingclutch

Oncomingclutch

Time (s)

Line

pre

ssur

e (ba

r)

20

10

0

Figure 14: Effects of underfill.

clutch can transfer a small amount of torque. This inevitablycauses a sudden increase in engine load, causing the rotationspeed of the transmission input shaft to decrease rapidly,resulting in negative slip of the offgoing clutch. Typicallythe pressure is reduced through PI control to compensatefor the negative slip. Negative slip that still exists before thetorque phase considerably affects the torque exchange phasebecause, at this moment, the slow decrease in the torque ofthe offgoing clutch and the rapid increase in the torque of theoncoming clutch cause a substantial shift impact. If a smallamount of positive slip exists before the torque phase begins,then a buffer zones is used for the torque exchange control;thus, the shift impact can be avoided. In conclusion, overfillcauses transmission shift impact to occur.

6. Fuzzy-Adaption-Based Correction Method

Since certain components, especially those in constantmotion such as the clutch return spring and the seal ring,exhibit performance decay after being used for a long time,the characteristics of these components change as the work-ing time increases.TheEOL test data represent only the initial

2600

2400

2200

2000

1800

Time (s)

Offgoingclutch

Oncomingclutch

Line pressure

Target input speed

Current input speedInpu

t spe

ed (r

pm)

Clut

ch p

ress

ure (

bar)

Line

pre

ssur

e (ba

r)

12

10

8

6

4

2

02.01.61.20.80.40.0

Figure 15: Effects of overfill.

characteristics of transmissions. Therefore, achieving clutchfill control by using the adaption method is the prerequisitefor ensuring shift quality throughout the entire life cycle of atransmission. Figure 16 shows the proposed adaption controlstrategy for the clutch fill process. The current clutch slip isused to evaluate the current shift quality during the shiftingprocess and to optimize the fill control parameters. Becausethe fill control affects only the shift quality at the fill andtorque exchange stages, the fill control parameters II andFTP can be optimized by monitoring the clutch slip based on1 and2, shown in Figure 16.

According to the input speed

, the output speed

, andthe ratio of current gear, the clutch slip

can be calculatedby

=

=

. (22)

Both the fast fill timeII and stable fill pressureFTP affectclutch fill results. The stable fill pressure FTP exerts a moreevident influence on the speed adjustment required for theclutch to reach the kiss-point pressure thanII does but easilyleads to excessively high pressure and so affects shift quality.The fast fill time II determines the movement speed of thepiston after the fast fill stage.The correction coefficients of thecontrol parameters FTP and II can be obtained by using anempirical fuzzy adaption control method, which is describedin Figure 17. The input variable of fuzzy adaptive control isthe clutch slip

. The clutch slip is processed fuzzily andthen fuzzy subsets 1 and 2 are obtained, respectively. Thecorrection factors

and

for fast fill pressure and filltime are then calculated. First, the current clutch slip domainin region 1 is defined as 1 = {

1

, 2

, 3

, 20 rpm} andthe fuzzy subset of which is {NB, NM, NS, ZO}. The currentclutch slip domain in region 2 is defined as 2 = {

4

, 5

,20 rpm, 40 rpm,

6

, 7

, 8

}, the fuzzy subset of which is {NB,NS, ZO, PS, PM, PB}. Based on the following observations,the fuzzy control rules shown in Tables 2 and 3 are used.


Time (s)

Clut

ch p

ress

ure (

bar)

Inpu

t spe

ed (r

pm)

nint

no

nc

k1

k2

k3

k4k5

k6

k7

k8

Tfill TtqW1 W2

TIIPFTP

Figure 16: Adaption control strategy for the clutch fill process.

Table 2: Empirical fuzzy control rules for fast fill time.

2

NB NS ZO PS PM PB1

NB NB NB NB NB NB NBNM NB NB NM NS NS NSNS NM NS NS ZO ZO PSZO ZO ZO ZO PS PM PB

Table 3: Empirical fuzzy control rules for stable fill pressure.

2

NB NS ZO PS PM PB1

NB NM NM NM NM NS NSNM NM NM NS NS NS NSNS NM NS NS ZO ZO PSZO NS NS ZO PS PS PM

(1) The control priority level for adjusting fill controlparameters is higher when negative slip occurs in1and2 than when positive slip occurs.

(2) In 1 and 2, the fill control parameters are notadjusted within the slip range of 20 to 40 rpm.

(3) The priority for adjusting fast fill time II is higherthan that for adjusting the stable fill pressure FTP.

(4) When a negative slip occurs in2, only the stable fillpressure FTP must be adjusted.

Based on the rules shown in Tables 2 and 3, the correctioncoefficients for fast fill timeII and stable fill pressureFTP canbe obtained using

II () = II ( 1) + 20 ,

FTP () = FTP ( 1) + 0.2 .(23)

Figures 18 and 19 show the adaption result for the fastfill time II and stable fill pressure FTP of clutch 4 duringthe 200,000 km transmission durability test. The fill controlparameters should be corrected when the transmission isbeing used to enable the fast fill time and stable fill pressureto meet the shift quality requirements. Figure 18 shows that ahigh main line pressure results in a short fast fill time anda high clutch torque coefficient results in a low stable fillpressure. In Figure 19, the horizontal axis is the clutch torquecoefficient, namely, the ratio coefficient of the clutch torqueto the input shaft torque of the transmission, which is relatedto the mechanical structure of the transmission. The clutchtorque coefficient varies when using different gears. The testresults indicate that the transmission characteristics changeas the mileage increases especially the first 8,000 km.

7. Conclusions

(1) A mathematical model of an electrohydraulic clutchshift control system in an automatic transmission waspresented.

(2) By analyzing the effects of key model parameters onclutch filling process, four special dynamic character-istic parameters were chosen for optimal clutch fillcontrol.

(3) An automatic method was proposed for testing initialclutch fill parameters.

(4) In order to prevent the underfill or overfill in clutchfill phase, a fuzzy adaption control method was pro-posed. 200,000 km road vehicle test results verifiedthat this method can effectively prevent the clutchshift quality from declining through the natural decayof the performance of components during the lifecycle of the transmission.

Nomenclature

SV,CV,CU, SP: Solenoid valve, shift control valve,clutch, and return spring, respectively

sub1,sub2 (optional): Mass of the spool sub2 of the part sub1,and only one subscript is used if there isonly one spool

sub1,sub2: Fluid flow at port sub2 of the part sub1

leaksub1: Leakage of the part sub1

sub1,sub2: Pressure at port sub2 of the part sub1sub1,sub2 (optional): Electromagnetic force exerted on the

spool sub2 in the part sub1, and onlyone subscript is used if there is only onespool

sub1,sub2 (optional): Spring force exerted on the spool sub2in the part sub1, and only one subscriptis used if there is only one spool

sub1sub2: Force exerted on the mass sub1 fromthe mass sub2

sub1: Stiffness of the return spring of the partsub1

sub1: Stamping coefficient of the part sub1


Torque phasefuzzy processing

Clutch slipcalculation

Clutch controlstate

Timer

Fill phasefuzzy processing

Fill controlparametercorrection

Transmission system Fill pressurecalculation

Timer

P2C conversion

Empirical fuzzy logic

I

niTfill

ns

ns

ic

KT

KP

PP PFTP(n)

TII(n)

F1

F2

Ttq

Figure 17: Fill fuzzy adaptive control system diagram.

5 10 15 200

50

100

150

200

250

300

Fast

fill t

ime (

ms)

Line pressure (bar)

0km2000 km4000 km8000 km

12000 km16000 km20000 km

Figure 18: Adapted fast fill time during the entire life cycle of thetransmission.

0.2 0.6 1 1.4 1.81.2

1.4

1.6

1.8

2

Stab

le fi

ll pr

essu

re (b

ar)

Clutch torque factor

0km2000 km4000 km8000 km

12000 km16000 km20000 km

Figure 19: Adapted stable fill pressure during the entire life cycle ofthe transmission.

sub1,sub2 (optional): Displacement of the mass sub2 of thepart sub1

0sub1,sub2 (optional): Preload of the mass sub2 of the part sub1sub1,sub2 (optional): Velocity of themass sub2 of the part sub1sub1,sub2 (optional): Acceleration of the mass sub2 of the part

sub1sub1,sub2 (optional): Sectional area of the chamber sub2 of the

part sub10sub1,sub2 (optional): Initial volume in the chamber sub2 of the

part sub1 sub1,sub2: Opening area of the port sub2 of the part

sub1sub1: Voltage applied in the coil of the part

sub1 sub1: Inductance in the part sub1sub1: Electric resistance of the part sub1sub1: Electric current in the coil of the part

sub1Vsub1: Back EMF coefficient of the part sub1sub1: Magnetic force coefficient of the part

sub1sub1: Bulk modulus of the part sub1Cdsub1: Unitless discharge coefficient of the part

sub1: Density of the automatic transmission

fluid (ATF)seal: Sealing force of the clutch piston

: Static frictional resistance coefficient ofthe clutch piston

stick: Static viscous friction of the clutch pistonpre: Prefill pressure of the clutch pistonFP: Fast fill pressure of the clutch pistonFTP: Stable fill pressure of the clutch pistonKP: Kiss-point pressure when the clutch

starts to transfer torqueAPP: Cylinder force exerted on clutch plates2

: Torque-pressure characteristiccoefficient of the clutch

: Relative torque coefficient of the inputshaft in the current gear

I: Prefill time of the clutch pistonII: Fast fill time of the clutch pistonIII: Stable fill time of the clutch piston


shift: Required shift time: Temperature of ATF fluidvar1: Weight factors of the variable var1

: Vertical height from port of the shiftvalue to the center of clutch pistonchamber

: Maximum stroke of the clutch pistonper: Stroke of the clutch piston in clutch fill

phase per: Damping coefficient of O-type seal ring.

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper.

Acknowledgment

The authors would like to acknowledge financial support ofthe National Science Foundation of China (51105017) and theNational Science and Technology Support Program of China(2011BAG09B00).

References

[1] Z. Zhao, H. Chen, and Y. Yang, Fuzzy determination of targetshifting time and torque control of shifting phase for dry dualclutch transmission, Mathematical Problems in Engineering,vol. 2014, Article ID 347490, 19 pages, 2014.

[2] B. Luo, S. Liu, and Y. Mo, Automatic clutch control strategyresearch based on multi-mode control, in Proceedings of theInternational Conference on Systems and Informatics (ICSAI 12),pp. 9094, May 2012.

[3] C. Lazar, C.-F. Caruntu, and A.-E. Balau, Modelling andpredictive control of an electro-hydraulic actuated wet clutchfor automatic transmission, in Proceedings of the IEEE Interna-tional Symposium on Industrial Electronics (ISIE 10), pp. 256261, July 2010.

[4] C. J. Lee, F. Samie, andC.-K.Kao, Control of selectable one-wayclutch inGMsix-speed automatic transmissions, inProceedingsof the ASME Dynamic Systems and Control Conference (DSCC09), vol. 2, pp. 605609, January 2009.

[5] Z. Sun and K. Hebbale, Challenges and opportunities in auto-motive transmission control, in Proceedings of the AmericanControl Conference, pp. 32843289, June 2005.

[6] X. Song,M.A.M. Zulkefli, Z. Sun, andH.-C.Miao, Automotivetransmission clutch fill control using a customized dynamicprogramming method, Journal of Dynamic Systems, Measure-ment and Control, Transactions of the ASME, vol. 133, no. 5,Article ID 054503, 2011.

[7] Q. Liu, H. Bo, and B. Qin, Analysis of the transient electromag-netic field of direct action solenoid valve, in Proceedings of the20th International Conference on Nuclear Engineering and theASME Power Conference, vol. 1, pp. 475479, ASME, July 2012.

[8] S. Iqbal, F. Al-Bender, B. Pluymers, and W. Desmet, Mathe-matical model and experimental evaluation of drag torque indisengaged wet clutches, ISRN Tribology, vol. 2013, Article ID206539, 16 pages, 2013.

[9] X. Song, M. A. M. Zulkefli, and Z. Sun, Automotive transmis-sion clutch fill optimal control: an experimental investigation,

in Proceedings of the American Control Conference, pp. 27482753, Marriott Waterfront, Baltimore, Md, USA, July 2010.

[10] P.-L. Chen, X.-L. Yu, and L. Liu, Simulation and experimentalstudy of electro-pneumatic valve used in air-powered engine,Journal of Zhejiang University: Science A, vol. 10, no. 3, pp. 377383, 2009.

[11] X.-Y. Song, Z.-X. Sun, X.-J. Yang, and G.-M. Zhu, Modelling,control, and hardware-in-the-loop simulation of an automatedmanual transmission, Proceedings of the Institution of Mechani-cal Engineers, D: Journal of Automobile Engineering, vol. 224, no.2, pp. 143160, 2010.

[12] D. Karnopp, Computer simulation of stick-slip friction inmechanical dynamic systems, Journal of Dynamic Systems,Measurement and Control, Transactions of the ASME, vol. 107,no. 1, pp. 100103, 1985.

[13] L. Glielmo, L. Iannelli, V. Vacca, and F. Vasca, Gearshift controlfor automatedmanual transmissions, IEEE/ASMETransactionson Mechatronics, vol. 11, no. 1, pp. 1726, 2006.

Submit your manuscripts athttp://www.hindawi.com

Hindawi Publishing Corporationhttp://www.hindawi.com Volume 2014

MathematicsJournal of


Mathematical Problems in Engineering

Hindawi Publishing Corporationhttp://www.hindawi.com

Differential EquationsInternational Journal of

Volume 2014

Applied MathematicsJournal of


Probability and StatisticsHindawi Publishing Corporationhttp://www.hindawi.com Volume 2014

Journal of


Mathematical PhysicsAdvances in

Complex AnalysisJournal of


OptimizationJournal of


CombinatoricsHindawi Publishing Corporationhttp://www.hindawi.com Volume 2014

International Journal of


Operations ResearchAdvances in

Journal of


Function Spaces

Abstract and Applied AnalysisHindawi Publishing Corporationhttp://www.hindawi.com Volume 2014

International Journal of Mathematics and Mathematical Sciences


The Scientific World JournalHindawi Publishing Corporation http://www.hindawi.com Volume 2014


Algebra

Discrete Dynamics in Nature and Society



Decision SciencesAdvances in

Discrete MathematicsJournal of

Hindawi Publishing Corporationhttp://www.hindawi.com

Volume 2014 Hindawi Publishing Corporationhttp://www.hindawi.com Volume 2014

Stochastic AnalysisInternational Journal of

dynamic analysis and control of the clutch filling process in clutch-to-clutch transmissions

Documents