CVT slip simulation

Citation for published version (APA):Mansvelders, R. E. (2004). CVT slip simulation. (DCT rapporten; Vol. 2004.092). Technische UniversiteitEindhoven.

Document status and date:Published: 01/01/2004

Document Version:Publisher’s PDF, also known as Version of Record (includes final page, issue and volume numbers)

Please check the document version of this publication:

• A submitted manuscript is the version of the article upon submission and before peer-review. There can beimportant differences between the submitted version and the official published version of record. Peopleinterested in the research are advised to contact the author for the final version of the publication, or visit theDOI to the publisher's website.• The final author version and the galley proof are versions of the publication after peer review.• The final published version features the final layout of the paper including the volume, issue and pagenumbers.Link to publication

General rightsCopyright and moral rights for the publications made accessible in the public portal are retained by the authors and/or other copyright ownersand it is a condition of accessing publications that users recognise and abide by the legal requirements associated with these rights.

• Users may download and print one copy of any publication from the public portal for the purpose of private study or research. • You may not further distribute the material or use it for any profit-making activity or commercial gain • You may freely distribute the URL identifying the publication in the public portal.

If the publication is distributed under the terms of Article 25fa of the Dutch Copyright Act, indicated by the “Taverne” license above, pleasefollow below link for the End User Agreement:www.tue.nl/taverne

Take down policyIf you believe that this document breaches copyright please contact us at:openaccess@tue.nlproviding details and we will investigate your claim.

Download date: 02. May. 2022

CVT Slip Simulation

R. E. Mansvelders

DCT 2004.92

Traineeship report

Supervisor: dr. P.A. Veenhuizen

Technische Universiteit Eindhoven Department Mechanical Engineering Dynamics and Control Technology Group

Eindhoven, July 25, 2004

Contents

1 Introduction 2

2 Introduction of the slip-simulation 3

3 Friction CVT 5 3.1 Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . , . . . . . . . . . 5 3.2 How friction works in a CvT . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 3.3 Friction and Clamping Force . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 3.4 Separation of Clamping force . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 3.5 Determining Friction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

4 Model implementation, Model 1 11 4.1 Model 1: One block . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 4.2 Model 1: One block dynamics . . . . . . . . . . . . . . . . . . . . . . . . . . . 12

5 Model implementation, Model 2 14 5.1 Model 2: Three blocks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 5.2 Model 2: Three blocks dynamics . . . . . . . . . . . . . . . . . . . . . . . . . 14

6 Slip Control 19

7 Integration of a Virtual Reality model 2 1

8 Simulation and results Matlab/Simulink model 23 8.1 Macro Slip. . . . . . . . . . . . . . . . . . . . . . . . . . . . . - . . . . . . . . 23 8.2 Increasing slip speed vs needed forces . . . . . . . . . . . . . . . . . . . . . . 25

9 Simulation and results Virtual Reality model 2 7

10 Conclusions and recommendations 29

11 Appendix A: Design in Matlab/Simulink 3 1

12 Appendix Ei: Design of Virtuai Reaiity modei 34

Chapter 1

Introduction

There's been proven that a Continuously Variable Transmission (CVT) has the same effi- ciency as a manual transmission. To capture the market the CVT has to be improve and be better than a manual transmission. Therefore the aim of today's research is to get a better robustness and improve of the efficiency. To get maximal robustness, current control strategies prevent macro slip at all times between the push belt an the pulleys of the CVT. This has to be done to prevent harmful wear in the CVT. Lately there's be done experiments [I], [2] in the macro slip region. There's been dis- covered that running for a short time period in the macro slip region, there's was no harmful wear. In the macro slip region the push belt will slip more than normally allowed. To create this more slip, the pulley clamping forces has to be decreased. This decrease in clamping forces, results in a decrease in the needed power for the clamping forces, which results in a better efficiency and an improving in fuel consumption.

Aim of this research The aim of this research is to make a slip-simulation to get a better understanding how the slip and the forces between an infinitesimal small part of the push belt and pulley reacts. Therefor the friction in this part will be explained and some assumptions are made to de- termine the friction for the simulation. Next, model implementations are made to make the slip-simulation and understand the needed dynamical equations. Thereafter a slip control is designed to create slip between the infinitesimal small part of the push belt and pulley. With an increasing slip, the forces in this infinitesimal part will be simulated and the needed forces on this part will be viewed. After a MatlabISimulink implementation, the results have to show that increasing the slip- speed, results in a reduction of the needed forces. The visualization of this problem will be made through an integrated Virtual Reality model in the Matlab/Simulink model.

Chapter 2

Introduction of the slip-simulation

The meaning of the slip-simulation is to obtain a slip-speed (V& [m/s]) of the push belt on the pulley. To simplify this problem the simulation is based on an infinitesimal part of the push belt, see figure 2.1 and 2.2. In this infinitesimal part the pulley is simulated as a belt over two axes. The push belt is simulated as a block on top of this belt over the two axes.

Figure 2.1: Infinitesimal part for the simulation, model 1

Figure 2.2: Infinitesimal part for the simulation, model 2

In the first model the belt is simulated as one block on top of the belt, like a pull belt, see

3

figure 2.1. This model is to get a feeling for the needed dynamical equations. In the second model there's a push belt added and simulated as three blocks, one fixed with a spring to a rigid wall and between the blocks a spring is added, on top of the belt, see figure 2.2 In both models the pulley is simulated as a belt with the same speed as the pulley VPuIl,, [m/s], massinertia J [kgm2] and an input torque T [Nm]. The friction between block(s) and belt will create a slip. Important is that the friction in these problems wi!! he cdculated in t,angellt,lal and axial direction (respectively in the models x- and y-direction). To create a slip in both directions, a slip control is build. The control compares the slip with a setpoint and create the needed control forces. These control forces are important to create the slip, see chapter 6: Slip Control.

Chapter 3

Friction CVT

3.1 Introduction

Between the pulley and the push-belt of the CVT, there's friction. This friction causes slip, which is necessary to get a torqw distribut,icn through the push-belt. Came the torque dls- tribution is one of the mean activities of the CVT, the understanding of friction is important. In other researches generally the dynamical behavior of friction is only researched in tangen- tial direction (in the simulation x-direction). But in reality the friction works in axial (in the simulation y-direction) and tangential direction. Out recent experimental studies, it's discovered to get more efficiency of the CVT to lower the current maximal clamping force in a short time period, without obtain directly wear in the macro slip region. Cause the clamping force and slip are directly influenced by friction, the understanding and the dynamical behavior of friction is necessary and will be explained in this chapter.

3.2 How friction works in a CVT

Friction is the reaction force between two surfaces in contact. This force is the result of many different mechanisms, like contact geometry, material properties of the surfaces, displacement, relative velocity and presence of lubrication [3]. For the sir~plicity of the simdation there7s dry (no) Iubrication, so the friction can be mod- eled as elastic en plastic material deformation of the surfaces in contact. Assuming plastic deformation, till it can carry the normal load FN, the contact area is:

Within H the hardness of the weakest material of the surfaces in contact. Each contact in tangential deformation is first elastic until the applied shear pressure exceeds the shear strength rY, when it becomes plastic. In sliding the friction f ~ r c e caases fricticx p:

with:

Ft = T ~ A

In dry-rolling contact, friction is the result of a non-symmetric pressure distribution in the contact. The pressure distribution is caused by elastic hysteresis in either of the bodies, or local sliding in the contact. For rolling friction Ff the friction coefficient, between 0.2 < p < 1.4, is proportional to the normal load, also called Coulomb friction:

Ff = PFN (3.4)

From experimental results, the maximal friction coefficient is equal to 0.09 [-I.

3.3 Friction and Clamping Force

Since torque is transmitted by friction in a variator, the friction coefficient in axial (y-) direction, py can be defined [4].

Figure 3.1: Infinitesimal small part of the push belt with length Rdp

Looking at the infinitesimal part of the push belt with length Rdp as shown in figure 3.1. The pulling force F of the part causes dF,:

1 dF, = 2 F sin -dp = F d p

2 (3.5) The conical form of the variator causes normal forces dN:

dN, = dN cos P (3-7)

The axial component of this force, N,, is equal to the clamping force F,,. Aker substitution:

To get the clamping force Fa,, the function has to be integrated to the wrapped part, y, of the pulley. Also the pulling force F is depending on the formula of Eytelwein:

PCP F(p) = Fl = Fz exp - sin ,B

with cp = a, the creep angle on the pulley. The torque in the push belt is equal to:

Next step is to integrate over the infinitesimal part:

with yl,2 = ac + Y J . After substitution and integrating the follow equations obtained:

with:

0 yz =7r+26

0 b = arcsin - i """l) For the simulation:

k = i = l Rz

The overclamping angle 6 = 0

So after substitution, the clamping force Fax is equal to:

3.4 Separation of Clamping force

In reality the clamping force has two main functions:

Keep belt tension optimal to transmit torque

Change pulley ratio for shifting

Tnese two functions can be create threw the pressure acting on the primary and secondary pulley. The first function needs an optimal secondary pressure. The second function, shifting, can be done by changing the prirnazy pressure. For the simulation the two functions of the clamping force are separated, respectively:

Normal force, or clamping force F,

Horizontal force, or shifting force Fh

The two functions are separated to create slip in tangential and axial direction (in the sim- ulation respectively x- and y-direction). The separation is necessary to build a slip control, which creates the slip in both directions, with the forces F, and Fh. This will be explained in chapter 4, 5 and 6.

Still the total friction ptot and the friction in x- and y-direction, px and py, has to be de- termined. The total friction is always opposite of the total slip-speed. After calculating the total slip-speed through the dynamic equations, discussed later, the total friction can be de- termined. Therefore a so called "Friction Slip-speed graphic" is needed, see figure 3.2. From this graphic the next equations can be determined.

Figure 3.2: Friction Slip-speed graphic The maximum total p is 0.1, so R,Mu in the graphic is max 0.1

The total friction between push belt and block is equal to:

h o t = + p$

and the total siip-speed of the block is equal to:

For the friction between push belt and block in x-direction means:

Vslip,x I-Cx = - I Ptot l (3.17)

lVslip,totl

For the friction between push belt and block in y-direction:

From experimental results the behaviour of friction coefficient versus slip-speed can be seen in figure 3.3 [2]. It can be seen that the maximum friction coefficient (0.09 [-I) is reached fast. With increasing slip-speed, the friction coefficient will have a few loss.

Figure 3.3: Representation of friction coefficient versus slip-speed s,

For the simulation p,,, = 0.1. In the simulation the total friction coefficient will be determined through a so called "look-up table" in Simulink, see figure 3.4. The maximum friction coefficient is equal to 0.1 [-I, input is the total slip-speed, V&J,~ and the output is the totale friction coefficient ptot. Cause the total slip-speed cannot be negative, the look-up table is plotted only for positive values. The maximum friction force occurs at a small displacement from the starting point, after 0.6

[mlsl.

Figure 3.4: Look-up table

Chapter 4

Model implementation, Model 1

4.1 Model 1: One block

In this model, figure 4.1, the belt will be simulated as one block fixed on top of the belt as described in the chapter 2: I~troductior, ef the slip-simdation. This mode! is to get a feeling and understanding in the relevant dynamical equations. Setpoints will be give in to create a slip in x-direction and y-direction (the shift-direction). These setpoints will in Matlab/Simulink be respectively coupled to horizontal (Fh), shift force, and vertical force (F,), clamping force. See chapter 6: Slip Control, for the needed control strategie. These forces will control the slip in both directions, see figure 4.2.

Figure 4.1: Model 1: One biock

Figure 4.2: Forces on block

4.2 Model 1: One block dynamics

For this modei the dynamic equations can be determined: Dynamic equation in x-direction

with:

Dynamic equation in y-direction

with:

Slip-speed The slip-speed in x-direction of the block is defined as:

within

VPUae, is the speed of the pulley and Vblock,x is the speed of the block in x-direction. Cause the block is fixed, the total Vblock = 0. SO the V,liP, is equal to VPUlley which can be calculated through the input variables of the pull-belt, see table 4.1.

Cause the friction force acts in negative direction on the pu:Lbe!t, actioii-reactian, the torcpe difference is equal to:

AT = T - FW,,r (4.8)

same as:

AT = T - pxFnr

Table 4.1: Input variables

Vpulley, Vslip,x can now be calculated, see eq4.2

V p u ~ l e y = Vslip,x (4.11)

The slip-speed in y-direction of the block follows from the dynamic equation in y-direction:

Chapter 5

Model implementation, Model 2

5.1 Model 2: Three blocks

This model is based on a push belt. The push belt is modeled as three blocks, one fixed through a h e a i r spring to a rigid wall and between the blocks a lineair spring is added, with spring stiffness k. The model and the relevant dynamical model are visualized in the figures 5.1 and 5.2.

Figure 5.1: 3 Blok Model

5.2 Model 2: Three blocks dynamics

D ynamical equations in x-direction From figure 5.2 and 5.3, it's easy to get the dynamic equations in x-direction separately on

Figure 5.2: 3 Block Dynamic Modei

Figure 5.3: 3 Block Dynamic Model

the blocks with each mass m: Dynamic equation on mass 1:

with:

Substitution of equation 5.2, 5.3 and 5.4 in equation 5.1 gives:

Dynamic equation on mass 2:

Substitution of eqmtion 5.7, 5.8 and 5.9 ir, eq-~atior, 5.6 gives:

Dynamic equation on mass 3:

m33% = FWx,3 - Fk,32

with:

Fwx,3 = ~x,3Fn

Fk,2l = k(x2 - 21)

Substitution of equation 5.12, 5.13 and 5.14 in equation 5.11 gives:

D ynamical equations in y-direction Dynamic equation on mass 1:

with:

Dynamic equation on mass 2:

m27j; = Fh - Fwy,2

with:

F w y , ~ = Py,2Fn

Dynamic equation on mass 3:

m3G = Fh - Fwy,3

with:

Slip-speed The slip-speed on a block is defined as:

The total slip-speed can be calculated through equation 3.16. For the determination of VPulle, equation 5.28.

Through action-reaction, the friction force on each block will work in opposite way on the push-belt. Therefor the total torque difference, AT, is equal to:

same as:

Calculation within Matlab/Simulink The goal of this problem is to calculate for each blok separately the p,, py and the V&,, Vslip,,. The calculation has be done by an iterative process with initial conditions, cause each block is dependent of the other blocks. By the use of Matlab/Simulink this iterative problem can be solved and simulated.

Design in Matlab/Simulink For calculation of px, p, and VSlip,,, for each block separately, it's needed that each block has his own simulation part in the Sirnulink-model. In the first block the speed of the push belt is calculated through:

Last equation can substituted in equation 5.27. After integration and calculation of VPune,, the VSlip, of mass 1 can be compute with equa- ticn 5.25. Within T/block, calculated through integration of the dynamic equation of mass

1;

The needed displacement of block 1 can be compute through:

Cause there's no velocity in y-direction, Vslip,y can be computed out of the dynamic equation in y-direction:

Now the slip-speed in x- and y-direction are computed. The total friction, friction in x- and y-direction can be determined with the look-up table, figure 3.4, and the equations 3.17, 3.18 and 3.15. The use of MatlabISimulink is necessary cause the input variables follows also kom the sec- ond and third block. For the design in MatlabISimulink the three blocks are separate. Each block has to calculate, the relevant dynamical equations and the external variables like the control forces, Fn and Fh, the slip-speeds and the friction coefficients. The design in Simulink can be viewed in appendix A.

In the second and third block the same equations are used as described above. Only the input is Vpulley as calculated above, so there's no need for compute this with equation 5.27 anymore. Vslip of the blocks can be computed through the dynamic equations of each block. Output of second and third block are the friction moments, Tw,2 and Tw,3 in x-direction. These are necessary for computing Vpulley in the first block. In tabel 5.1 the inputs and outputs are given for each block for in the Matlab/Simulink model.

Outputs

Fn1, F h l , Klip,xl, Vslip,yl, Vszip,l B ~ O C ~ 1

Block 2

Inputs

T, r, J, m

Block 3

D ynamical equation

Twz,21 Twx,~ , Vblock,l

r, Ill

Block 2 Dynamical equation

Table 5.1: Input-Outputs for each biotk in the Matiab/Simuiink model

/Jd, Pyl, PI, Twz,l, Vpulley - Fn2, Fh2, Klip,x2, vslip,y2, Klip,2

Vpulley Vblock,~

r, nl

Vpulley, Vblock,~

Illputs

r, m, k

Block 3

PXZ, Py2, P2, Twz,~ Fn3, Fh3, vslzp,z3 , Vslzp,y3, %lzp,3

Pz3, Py3, P3, l7wz,3

Outputs

xblock,l

Twz,2, xblock,l, xblock,3 r, m, k

Vblock,2

xblock,3 Twx,3, xblock,2 Vblock,~

Chapter 6

Slip Control

To create a slip between the belt and the pulley, the needed forces has to be controlled. As discussed before, the control forces in the simulation are the shift force (Fh) and the clamping force (F,). These control the slip in x- and y-direction. In figures 6.1 and 6.2 the visualization of the control in both direction are shown.

Figure 6.1: Slip control in x-direction

The slip control is based on a simple gain(P)-control. First the slip is compared with a reference (input setpoint, see figure 6.3). The setpoint for the slip in x-direction will be keep constant, for a constant pulley speed. The setpoint for the slip in y-direction will increase and decrease in a iixed time period. This has to be done, to similate a shifting movement of a CVT. Then the difference, between setpoint and slip, is multiplied with a gain, which results in the needed control forces. With the relevant dynamic equations and the look-up table, the

Figure 6.2: Slip control in y-direction

friction coefficients (pi), friction torques (TWj) and pulley-speed (V,,s,,) can be determined.

Figure 6.3: Setpoints for the slip control

Chapter 7

Integration of a Virtual Reality model

The visualization of this problem can be made through an integrated Virtual Reality (VR) 151 model in the Matlab/Simulink model, see also appendix B. Therefore a mode! is build that visualize the three-block model in x-direction. This VR-model is a real-time model, which means running the MatlablSimulink model specific variables can be changed. For this VR-model the input torque, T, can be varied. This will results in a larger friction moment, T,, on each block, visualized with the thickness of the lower arrows on each block. Also the connected springs will vary in size. The setpoints in slip-speed can be changed. Increasing the slip-speed in x-direction, results in a reduction of the needed clamping forces. Therefor the normal force on each block, equal to the clamping force, is visualized in the VR-model. Larger clamping force will be visualized with the thickness of the upper arrows on each block. See figure 7.1 - 7.4 for the VR-model with different torque inputs.

Figure 7.1: Vhtiial Reality Mode!, T = 10 [Nm]

Figure 7.2: Virtual Reality Model, T = 30 [Nm]

Figure 7.3: Virtual Reality Model, T = 50 [Nm]

Figure 7.4: Virtual Reality Model, T = 90 [Nm]

Chapter 8

Simulation and results Mat lab/Simulink model

The next assumptions of theoretical and experimental research have to be seen from the slip simulations.

0 Macro Slip

0 Increasing slip speed in x-direction results in decreasing of the needed forces

The first assumption can be viewed by the torque on each infinitesimal small part of the push belt compared with the input torque. Macro slip will occur if the applied (input) torque will be larger than the maximum transmittable torque (Ttrans = Twzl + Twx2 i Twx3). The second assumption can be viewed by a graph of the needed clamping force vs slip speed in x-direction. Also with a increase slip speed in x-direction, the shift force and the needed power will be plotted.

8.1 Macro Slip

The MatlablSimulink model creates outputs for each block. The outputs can be viewed in figure 8.1. Macro slip can be viewed between 14.95 and 15 seconds, see figure 8.2. The macro slip occurs in this time period, cause the total slip speed Vslip,tot is in this period larger than 0.6 [m/s]. The setpoints gives in this time period a Klip,z = 0.356 [m/s] and &lip,y = 0.485 [m/s], which results in Vslip,tot > 0.6 [m/s]. From the look-up table, figure 3.4, the total maximum friction coefficient is reached, and the control in the model cause an increase of the clamping forces Fn in this time period. These increase in clamping force, results that the input torque is equal to the transmittable torque at macro slip, cause the control is of a closed-loop design.

Figure

Time

0 5 i O 15 20

%me Time

8.1: Simulink Simulation Results Block 1, setpoints Vx = 0.1 and Vy,max =

Time

> ' ...... .......

5 10 $5 2l 14.9 14.8 $5

..... .... ---- I= ..... ..& .......................... ..... : ..... .... ....

Ii. - A - - -. . -

..... ..... ...

1496 1498 15 14.96 1498 15 15.m 15.04 14 95 14 96 14.97 14.98 14.93 15 Time Time Tim.

Figure 8.2: Simulink Simulation Results Block 1, setpoints Vx = 0.3 and Vy,max = 0.5 [m/s]

8.2 Increasing slip speed vs needed forces

Increasing the slip speed in x-direction can be done by increasing the setpoint Vx. Without a shift-speed, Vslip,y = 0 [m/s], increasing the slip-speed in x-direction Vslip,, results that the needed clamping force will decrease as expected, see figure 8.3. In this figure can be seen that after a slip-speed of 0.6 [m/s], the clamping force will be constant and the maximum friction coefficient is reached, see figure 8.4.

Setpoint Vy,max = 0 [mls]

0.5 1 1.5 2 Setpoint Slipspeed x-direction [mls]

Figure 8.3: Clamping forces F, [N] vs slip speed x-direction Vslip,, [m/s]

Setpoint Vy,max = 0 [mls] 0.1

0.09

0.08

-i- 0.07 - 2 0.06

"'""0 0.5 1 1.5 2 Setpoint Slipspeed x-direction [mls]

Figure 8.4: Friction coefficient p, [-] vs slip speed x-direction [m/s]

The control is in such design, that at macro slip, the input torque is equal to the transmit- table torque. Which means when higher (macro-slip) slip-speed in x-direction is reached, the decrease in clamping force is less and will be constant.

Next, the effect of increasing the slip speed in x-direction on the needed shift force is de- termined. Therefor a shift speed is created, threw a maximum setpoint of 1 [m/s] for the slip speed in y-direction, Vslip,y. Cause shifting is not all the time, Vslip,y is increased till the maximum in a given time period, see figure 6.3. The result of shift force Fh vs slip speed in

x-direction Vslip,z can be seen in figure 8.5.

Setpoint Vy,max = 1 [mls]

"0 0.5 1 1.5 2 Setpoint Slipspeed x-direction [mls]

90

80

70

60

B so- - u_'- 40

30

20

10-

Figure 8.5: Shift forces Fh [N] vs slip speed =direction %lip,% [rn/s]

-

-

-

-

-

-

-

With this result the needed power to shift, Pshift, can be calculated with equation 8.1:

Pshift = py ' FIZ ' Vslip,y (8.1)

Cause there's no displacement in y-direction, py - F, is equal to the shift force Fh and the slip in y-direction equal to the shift-speed. This results in equation 8.2:

Pshi f t = py . FIZ . V~l ip ,~ Fh ' Khi f t (8.2)

Now the needed shift power (Pshift = PowerSlipyi) vs increasing slip speed in x-direction can be plotted, see figure 8.6.

Setpoint Vy,max = 1 [mls]

Setpoint Slipspeed x-direct~on [mls]

Figure 8.6: Power distribution [W] vs slip speed x-direction Vslip,% [rn/s]

From figure 8.6 can be concluded increasing the slip speed in x-direction has a decrease in needed Pshift, which results in a decrease in fuel consumption.

Chapter 9

Simulation and results Virtual Reality model

The Virtual Reality (VR) model shows the friction torque T, and clamping force Fn on each block. 1,s described ir, chapter 7, the input t o r q ~ e T acd the se tpo i~ t Vx or V&,, can be changed. Increasing T results in a larger T, and larger Fn. Cause Vsli,,, is controlled to be constant with increasing T, the friction coefficient /I, will increase till the maximum of 0.1 [-I and the clamping force will increase. The VR-model has to show increasing T with a different Vslip,, results in a different clamping force for each simulation. Therefor 2 simulations have be made. First with I/slip,, equal to 0.1 [m/s], second with Kli,,, equal to 1.0 [m/s]. In these simulations the input torque is changed to shown the difference in clamping force, see figures 9.1, 9.2 and 9.3.

Figure 9.1: Visualization clamping forces. Left-side: I/slip,z = 0.1 [m/s], Right-side: VSliP,, =

1.0 [m/s] and input torque T = 10 [Nm]

See table 9.1 for the inputs, outputs and the size difference what is shown in figures 9.1, 9.2 and 9.3.

From table 9.1 can be concluded that increasing Vsli,;, results in a decrease in needed clamping force. However there's no linearity in value of clamping force with increasing input torque. From the figures and table can be seen at high input torque, the clamping force is a t both VSli,,,, almost equal. The reason is for low input torque T and Kli,,, < 0.6 [m/s] the slip

Figure 9.2: Visualization clamping forces. Left-side: V,lip,x = 0.1 [m/s], Right-side: Vslip,x =

1.0 [m/s] and input torque T = 70 [Nm]

Figure 9.3: Visualization clamping forces. Left-side: VSlip, = 0.1 [m/s], Right-side: Vslip,z = 1.0 [m/s] and input torque T = 145 [Nm]

Table 9.1: Inputs-outputs of the VR simulations

control needs a higher clamping force than at high V,l+,x > 0.6 [m/s], cause the friction coefficient is below 0.1 [-I. For high input torque T and V,lip,x < 0.6 [m/s] the controlled VSlip,, has a small increase which results directly in larger friction coefficient. Cause this friction coefficient reach almost the maximal value of 0.1 [-I at high input torque, the needed clamping force is almost the same for both Vslip,x.

Setpoint Vx [m/s] Input torque [Nm]

Clamping force F, [N]

Setpoint Vx [m/s] Input torque [Nm]

Clamping force F, [N]

Size difference 1-1

70 3274

70 2343

1.40

0.1 10

1000

1.0 10

340

2.94

145 4914

145 4846

1.01

Chapter 10

Conclusions and recommendations

The slip-simulation is successfully build in a MatlabISimulink model and visualized with an intergraded Virtual Reality model. Therefor a slip model implementation, dynamic equations, determination of friction and slip control have been made. The assumption increasing slip speed in x-direction, &p,z, results in decreasing of the needed forces. Increase in Vslip,z results in a decrease in needed clamping force and a reduction in needed shifting force. These both reductions will result in decrease of needed power and so in reduction of fuel consumption. From the Virtual Reality model the reduction in needed clamping force can be viewed.

Recommendations The slip-simulation is very simplistic, therefor some improvements can be made to create a more realistic push-belt slip-simulation:

Real push-belt simulation

The infinitesimal part between the push belt and pulley is based on 3 blocks. A more realistic push belt can be made to simulate all segments of the push belt.

Ratio difference during shift

During shifting not all segments has slip with the pulley. During shifting there's a ratio difference, so only the segments on the wrapped angle has slip.

e Material influence

Friction between push belt and segments

In this simulation there's only friction between push belt and pulley. In reality there's also friction between segments and belt in the van Doorne push belt.

Bibliography

[I] M.v. Drogen, M.v.d. Laan, "Determination of Variator Robustness under Macro Slip Conditions for a Push Belt CVT", SAE International, 2004, 2004-01-0480.

[2] P.A. Veenhuizen, B. Bonsen, T.W.G.L. KLaassen, K.G.0.v.d. Meerakker, H. Nijmei- jer, F.E. Veldpaus, "Simulated behavior of a vehicle with V-belt type geared neutral transmission with variator slip control".

[3] H. Olsson, K.J. Astrm, C. Canudas de Wit, M. Gfvert, P. Lischinsky, "Friction Models and Friction Compensation", 1997-11-28 16:52.

[4] J.v. Rooij, "Clamping Force Theory", March 18, 2002.

[5] "Vitual Reality Toolbox, User's Guide", The Mathworks, July 2002.

Chapter 11

Appendix A: Design in

Figure 11.1: Sirnulink Design of block 1

Figure 11.2: Sirnulink Design of block 2 and 3

. in1 om1

From3 . in?

In3

G*.S

B id , I

Figure 11.3: Complete MatlabISimulink model

.

. constann

From4

B 1 o e 2

In1 Dull

in2

Got07

Chapter 12

Appendix B: Design of Virtual Reality model

First to get each block a displacement, the calculated displacements has to convert to relative displacements, see figure 12.1.

Figure 12.1: Simulink Design of block 2 and 3

Next all variables of the VR model needs an input, see figure 12.2.

Figure 12.2: Sirnulink Design of block 2 and 3