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MODELLING AND SIMULATION OF DUAL CLUTCH

TRANSMISSIONS FOR DYNAMIC PERFORMANCE

1Andrei-Mircea Tamba

Scientific Coordinator: PhD. eng. Marius Bu

University POLITEHNICA of Bucharest, Romania

KEYWORDS: modeling, simulation, Simulink, dual clutch, transmission

ABSTRACT: Time to design and manufacture of the automobile industry must be as low as possible in the same time, it is necessary to be full field the requirements concerning. The

automobile performances such as fuel economy, emissions reductions, car comfort etc.

Computer modeling and simulation it is a very efficient way to solve those problems just in

designing phase.

This paper aims to present the main advantages of using DCT, to exemplify how to implement

this transmission in Simulink, as well as comparing and highlighting the benefits of using

simulation and modeling in computing, to data from vehicle manufactured.

1. INTRODUCTION

Most people know that cars are equipped with two types of transmissions: manuals, which

require that the driver change gears by pressing a pedal and moving a handle, and automatics,

which simplify changing gears and those, can be with continuous variation or planetary gears.

But having stringent requirements in the current automotive construction was tried to find a

solution to reduce emissions and fuel consumption, and have a contribution to the comfort as

automatic gearbox, but to keep high efficiency and low costs as manual gearbox. So there was

designed Dual Clutch Transmission (DCT).

The DCT is basically composed from two classic gearboxes, each branch having assigned a

clutch, an input shaft and an output shaft, see Figure 1.

Figure 1 Functional schema of DCT

The major advantage of this transmission is that the power flow will always pass through a

transmission line, while the other arm with disengaged clutch will preselect the next gear, so

that the phenomenon known as shift shock will not be met. Each gear has a similar coupling element as manual gearbox, but the control is made automatic. The Transmission Control

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Unit (TCU) controls hydraulic mechanism or electric actuators which engage or disengaged

clutch and gears, depending of operation conditions. Logical coupling feature is implemented

in software, which combined with hardware (command structure) can offer outstanding

performance and capacity to operate in a wide range of operating conditions.

It was used Simulink (Matlab) for modeling and simulation because this environment has the

following advantages: is most common modeling and simulation environment for academic

and industrial, allows creation of personalized components and libraries, dispose of a large

number of standard libraries and components, Matlab Application (under which you can use

Simulink) provides tools for post-processing the simulation results, and more.

2. MODELS DEVELOPMENT

Figure 2 Structure schema of the model used in simulation

Models used to simulate the longitudinal dynamics of motor vehicles have a similar structure,

composed of four elements corresponding to the engine, transmission, and electronic control

unit. Figure 2 is shown the structure of a propulsion system models equipped with automatic

transmission and is shown in Figure 3 corresponding vehicle model selected for simulation.

Figure 3 Vehicle model equipped with DCT

The model has been structured into subsystems, making it intuitive and easy to use, the data

being loaded dynamically through a file which can be changed easily and making it possible

to adapt the model for other test parameters.

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2.1. ENGINE MODEL

Features: model used external characteristic of the motor (engine map based on torque and

load speed); it is suitable for traction; includes the moment of inertia of the crankshaft and of

the parts solidary whit it; provides lower and upper limits of speed of rotations.

Figure 4 Model of internal combustion engine

Engine model, Figure 4, is built on equations:

][Nmdt

dIMM mmmms

- static momentum of engine (1)

Where: ][NmM m - momentum at crankshaft; ][2kgmIm - momentum of inertia of crankshaft

and of the parts solidary with it; ][rad/s

dt

dm 2 - crankshaft angular acceleration.

From equation (1)

dtI

MM

m

msm

m - angular speed (2)

For the integration of angular acceleration it is used an integration block with saturation to set

idle rotation speed and to limiting engine speed. Torque is determined by interpolation,

depending on load and engine speed, a 2D interpolation table.

Models input values are: Mm momentum at crankshaft [Nm]; X engine load [-]. Models output values are: nm engine speed [rpm].

The parameters needed for the following engine model are: engine load vector; engine load

speed; minimum engine speed; maximum engine speed; engine initial speed, torque matrix (to

determine torque map), engines inertia momentum.

2.2. TRANSMISSION MODEL

The transmission is encapsulated in a subsystem, and includes the knots (one in connection

with the engine, one in connection with the vehicle), clutches and two line of DCT, Figure 5.

Since power can flow through the two branches of the transmission, they resorted to the use

of knots to "guide" engine speed to clutches, and to "collect" the momentum at the end of the

two branches of the transmission and transmits on a single shaft to the wheels of the vehicle.

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Figure 5 Transmission model

2.2.1 Clutch model

Features: it is considered gears change in power flow. Models input values are: c clutch control [-]; nm engine speed [rpm]; nt input shaft speed [rpm]. Models output values are: Mt momentum at transmission shaft [Nm]; Mrm resistant momentum [Nm].

Figure 6 Clutch model

Models input order: 0 clutch disengage; 1 clutch engage; time for engagement.

2.2.2 Gearbox model

The gearbox has two branches which can be crossed by the power flow; the gears have been

split apart in groups by even and uneven gears. The branches are similar, Figure 7a, milieu

existing in several parameters, namely: selecting transmission ratio.

Figure 7 a) Model of a gearbox branch; b) DCT main transmission

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Another feature of this gearbox: main transmission ratio is different depending on the selected

gear, Figure 7b.

- wheel momentum, where - gearbox momentum; - gearbox

ratio; - main transmission ratio; transmission efficiency.

transmission shaft speed [rpm]

Models input values are: i control gear [-]; Mt gearbox transmission [Nm]; nr wheel speed [rpm]. Models output values are: Mr wheel torque [Nm]; nt transmission output shaft speed [rpm].

Parameters for the gearbox: gearbox control; gear ratios; main transmissions ratios;

transmission efficiency.

2.2.3. Transmission knots model

In divider knot, Figure 8a, momentum bifurcates on gearbox branches, and the engine speed

is sent to transmissions clutch.

Figure 8 Transmission knots model a) divider; b) adder

The input values of the dividing knot model are: Mm1,2 engine resistant momentum [Nm]; nm engine speed [rpm]. The output values of the dividing knot model are: Mm engine resistant momentum [Nm]; nm1,2 engine speed transmitted to branch 1/2 of the gearbox [rpm].

In adder knot, Figure 8b, momentums are added together from the two branches and the

resulted momentum is transmitted to the vehicle wheels.

The input values of the adder knot model are: Mm1,2 momentum from output of branch 1/2 of gearbox [Nm]; nr vehicle wheel speed [rpm]. The output values of the adder knot model are: Mr momentum at the transmission output to the vehicle wheels [Nm]; nr1,2 vehicle wheel speed transmitted to branch 1/2 of gearbox [rpm].

2.3 VEHICLE MODEL

Features: are considered all the resistance; model allows only go forward; take account of the

limits of grip, Figure 9.

][ NRRRR apri - total resistance;

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][)cos()( NGVfR par - rolling resistance;

][)( 303

2

02010VfVfVffVf - rolling resistance coefficient;

][NgmGaa - vehicle weight;

][,

NVAk

Ra

31

2 - air resistance;

][max NgmF xma - maximum traction force limited grip.

Input values: Mr wheel torque [Nm]. Output values: a vehicle acceleration [m/s2]; V

vehicle speed [km/h]; x displacement [m]; nr wheel speed [rpm].

Figure 9 Vehicle model

Models parameter: vehicle weight; rolling resistance coefficients; air resistance coefficient; rolling radius; cross-section area; adhesion coefficient; drive axle load distribution; influence

coefficient of the rotating mass; gravitational acceleration.

2.4. PARAMETER USED FOR SIMULATION

Table 1 Parameters used for simulation

Parameters Value [measuring unit] Vehicle

Weight 1316 kg

Rolling radius 0,3 m Air resistance coefficient 0,32

Maximum cross-sectional area 2,22 m2

Coefficient f0 0,0161 Coefficient f1 -1.0002*10-5 h/km

Coefficient f2 2,9152*10-7 h2/km2 Drive axle load coefficient 1

Coefficient of adhesion 0,8

Coefficient of influence of the rotating mass 1,02 Gearbox

Main transmission ratio TP1/TP2 4,059 / 3,136

Main transmission efficiency 0,92 Gear ratio 1 / 2 / 3 / 4 / 5 / 6 3,462 / 2,05 / 1,3 / 0,902 / 0,914 / 0,756

Engine

Type MAC Maxim torque 342 Nm

Maxim engine speed 5000 min-1

Idle engine speed 700 min-1 Inertia momentum of engine 0,15 kgm2

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Table 2 Engine speed caracteristic Engine load [%]

0,05 0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8 0,9 1

Eng

ine

spee

d [

rpm

]

750 10 20,5 45 75 100 120 120 120 120 120 120

1000 20 30 60 90 120 140 170 170 170 170 170

1592 0 21,6 46,2 77 120 149 195 243 263 295,8 295,8

1792 0 19,4 36 75 115 145 190 236 275 311 334,5

1993 0 10 31,2 70 110 140 189 232 270 310,6 338,8

2292 0 0 22 61 105 134 185 226 266 305 341,7

2490 0 0 20 59 100 128 180 224 259 301 339,7

2686 0 0 18,8 50 98 125 179 223,8 257 300 331,4

2986 0 0 9,6 45 90 120 170 222 255 295 323,3

3482 0 0 0 30 80 109 160 210 248 286 308,4

3980 0 0 0 19 64 97 148 192 236 263 286,9

4179 0 0 0 16 58 91 145 185 223,8 254 275,3

4377 0 0 0 14 50 88 138,5 178 214,5 243 251,3

4577 0 0 0 9,5 42 80 132 175 209,5 223,8 223,8

5000 0 0 0 0 21,5 70 113 149 153 153 153

3. RESULTS

Figure 10 Graphic of vehicle acceleration

After analyzing the simulation results are observed variation in the acceleration of gear

change times, so first gear acceleration reaches an approximate value of 7.6m/s2, further

decreasing with increasing speed, Figure 10.

Figure 11 Graphic of vehicle speed

After the simulation we can observe the speed variation curve during the change of all six

gears. As we can see, the moments of gear change are highlighted on the graphics Figure 10

and 11. 100km/h speed is reached on the fourth gear, on 7.84s. The sixth gear is switched at

about 140km/h, the maximum speed for the vehicle being 207.5km/h.

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Figure 12 Graphic of distance

After the simulation we observed that the vehicle travels a distance of 400m in 15.07s and

distance of 1000m in 28.09s, Figure 12.

Table 3 Comparative results

Model 2003 Volkswagen Golf 2.0 TDI DSG Results of simulation

0-100 km/h [s] 9,3 7,84

0-400m [s] 16,7 15,07 0-1000m [s] 30,5 28,09

Vmax [km/h] 203 207,5

Sources of errors are caused by the method of calculating the coefficient of rolling resistance,

coefficient of adhesion, of choice longitudinally, as well as ignoring the change of the

efficiency in the selected gear.

4. CONCLUSIONS

Considering and automobile simulation model, it can be obtained very similar values to those

obtained from tests in which the vehicle has undergone.

This simulation results let us know a lot of information: velocity variation, distance in time,

concerning automobile performance without financial investment or purchasing a real vehicle.

Dynamic performances can be clearly distinguished, as well as other cars in the simulation

data.

5. REFERENCES

1. ***, Matlab, Simulink - Using Simulink and Stateflow in Automotive Applications, The Math Works Inc., 1998

2. Andreescu, C., Course notes "Vehicle dynamics", Faculty of Transports, PUB 2008 3. Mustafa, R. , and others - Modeling and Analysis of the Electro-hydraulic and

Driveline Control of a Dual Clutch Transmission, FISITA, 2010

4. Oprean, M. Transmisii automate pentru automobile, Editura Printech, Bucharest, 1999