internship report tu/emate.tue.nl/mate/pdfs/6346.pdftitle internship report tu/e author a.j.v.eck...

Development of a V-belt speedsensor for the CVT-CK2

A-J. van Eck

DCT 2005.64

Traineeship report

Coach: Ir. B. Bonsen

Supervisor: Prof. Dr. P.A. Veenhuizen

Technische Universiteit EindhovenDepartment Mechanical EngineeringAutomotive Engineering Science

Eindhoven, May 2005

Contents

Contents 2

1 Introduction 4

2 Problem Definition 62.1 Problem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62.2 Requirements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

2.2.1 Compact system . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62.2.2 Use with original belt . . . . . . . . . . . . . . . . . . . . . . . . . . . 72.2.3 Easily mountable and removable . . . . . . . . . . . . . . . . . . . . . 72.2.4 Follow displacements of the belt . . . . . . . . . . . . . . . . . . . . . 72.2.5 High accuracy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

3 Sensor choice 83.1 Sensor requirements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

3.1.1 Operation frequency . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83.1.2 Oil and temperature resistance . . . . . . . . . . . . . . . . . . . . . . 93.1.3 Sensor dimensions . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9

3.2 Different sensors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103.3 Functioning principle of the conductive sensor . . . . . . . . . . . . . . . . . 11

4 Development of sensor mounting system 134.1 Sensor placement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 134.2 Belt displacements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

4.2.1 X displacement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 144.2.2 Z displacement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 144.2.3 Rotation about Z-axis . . . . . . . . . . . . . . . . . . . . . . . . . . . 154.2.4 Rotation about Y -axis . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

4.3 Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 164.3.1 Translation in Z-direction . . . . . . . . . . . . . . . . . . . . . . . . . 164.3.2 Rotation about Z-axis . . . . . . . . . . . . . . . . . . . . . . . . . . . 184.3.3 Translation in X-direction . . . . . . . . . . . . . . . . . . . . . . . . 194.3.4 Sensor framework . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19

Development of a V-belt speed sensor for the CVT-CK2 2

Contents 3

4.3.5 Rotation about Y -axis . . . . . . . . . . . . . . . . . . . . . . . . . . . 214.3.6 Mounting sensor system to transmission-house . . . . . . . . . . . . 22

4.4 Materials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23

5 Conclusions 25

Bibliography 26

A Sensor specifications 27

B Belt displacement M-file 30

C Belt angle M-file 32

D 3-D views 34

E Exploded view 36

F How to build in 37

G Working plans 38

Development of a V-belt speed sensor for the CVT-CK2

Chapter 1

Introduction

The section Power Trains of the master track Automotive Engineering Science (AES) of thefaculty Mechanical Engineering does much research on the subject of continuous variabletransmissions, CVT’s. The greatest advantage of the application of these transmissions isthat the vehicle speed and the engine speed can be partly decoupled. This means that themotor can always be used in its most ideal working point. So performance and overall effi-ciency of the car can be improved.

The working principle of a CVT is based on a plain principle. This principle is initiallydeveloped by Hub van Doorne and is many years old. It was applied in the old Daf Vari-omatic, this was the first private car which was driven by a CVT-belt. The principle containsthree main parts, two pulleys and one V-belt. The V-belt runs through the two pulleys. Thebelt is driven by the primary pulley, the secondary pulley is driven by the belt. The pulleyscontain one fixed sheave and one movable sheave. The fixed sheave is a part of the shaft onwhich the pulley is mounted. The movable sheave can move in and outward over the shaft.When the sheave moves inwards the space between the movable and the fixed sheave be-comes smaller. The radius of the pulley will increase, because of the constant belt length therunning radius of the opposite pulley has to decrease. This means that de space between themovable and the fixed sheave has to increase; the movable sheave of the opposite pulley hasto move outwards. With the changing running radii the ratio of the transmission is chang-ing. This principle can be seen in figure 1.1. In the upper figure the belt is running on a largeradius on the left pulley and a small radius on the right pulley. When the left pulley movesoutwards you can see in the lower figure that the running radius of the left pulley decreases.

The running radii of the belt on the both pulleys determine the theoretical ratio of thetransmission. The running radius of a pulley is determined by the space between the fixedand the movable pulley sheave. This space can be measured with a special position sensor.The actual ratio of the transmission can be determined by measuring the speed of the in-going shaft and the outgoing shaft. The proportion of these speeds give the actual ratio ofthe transmission. When the theoretical ratio and the actual ratio do not correspond therewill be slip in the transmission. When slip occurs in the transmission there will be a higher


Chapter 1. Introduction 5

Figure 1.1: working principle of a CVT

power loss. This has a negative effect on the efficiency of the transmission. The slip can beprevented by using a higher clamp force on the movable pulley sheave. If the clamp forceis high enough no slip will occur. The disadvantage of a higher clamp force is also a higherpower loss. The most efficient situation can be realized when the clamp force is exactly highenough to prevent slip in the transmission. To determine this clamp force it is necessary toexactly know the slip in the transmission.

The slip in the transmission can be measured using the rotation speed and the radiusof the ingoing pulley. From these two data the theoretical belt speed can be calculated.When you can compare the theoretical belt speed with the actual belt speed the slip can bedetermined. So far there is still no suitable method at the TU/e to measure the actual beltspeed in a CK2. The goal of this internship is to develop and realize a measurement systemfor the belt speed. First the conditions where the systemmust satisfy to are determined. Thenext step is to choose a suitable sensor for the system. Finally the mounting system for thesensor has been developed.


Chapter 2

Problem Denition

2.1 Problem

A measurement system for the belt speed has to be developed. The section Power Trains ofthe master track Automotive Engineering Science has already a sensor to measure the beltspeed. This sensor has much disadvantages. The sensor can only be used with a specialadapted belt. It takes a lot of time and money to make these belts. The second disadvantageis the size of the sensor and its mounting system. The sensor is much too large to build in inan existing CVT. To make a new useful sensor first we look to the requirements of the newsystem.

2.2 Requirements

The sensor system has to fulfil to these requirements:

• compact system; possibly to build in in the existing transmission, the Jatco CK2

• possibility to use the original belt

• the system has to be easily mountable and removable

• the sensor has to follow the displacements of the belt

• high accuracy

In the following 5 paragraphs a short explanation on these requirements will be given. Somerequirements are discussed extensively in chapter 4.

2.2.1 Compact system

There is not much space in de CVT transmission. To fit the new sensor system into theoriginal transmission-box the system must be very compact. The exact available space in the


Chapter 2. Problem Denition 7

transmission depends on the place where the sensor system is placed. This exact place isdiscussed later in chapter 4.

2.2.2 Use with original belt

The sensor system must use the original belt without any adaptations. When the originalbelt is used the sensor system can easily build in in each random CVT transmission withoutadaptations. Secondly when the belt is worn out the belt can easily replaced by a new one.This is the greatest advantage of the use of a original belt. There are no additional costsbecause the system can be used in every existing transmission without adaptations.

2.2.3 Easily mountable and removable

The sensor system in used for optimization of the existing transmission. The sensor is onlyused to make a better control system for the clamp forces of the pulley. It is not necessaryto build in the sensor systems in passenger car for normal use. The transmissions that areavailable at the section Power Trains of the TU/e are used for different aims, so the sensoronly has to build in when measurings are done to the belt speed. So the sensor system mustbe easily mountable and removable.

2.2.4 Follow displacements of the belt

When the transmission ratio changes from low to over-drive the belt is also moving. Thesensor system must follow these displacements. If the sensor is placed on a fixed point, soit will not follow the belt displacements, the sensor can never give a accurate result. Thesensor can not measure the belt speed accurate when the belt angle with respect to thesensor changes. The exact displacements of the belt and the sensor system are discussed inchapter 4.

2.2.5 High accuracy

The belt speed is used to determine the slip of the belt in the transmission. When the slipis known a better control system for the clamp force can be made. The slip of the belt isdetermined using the belt speed, the running radius and the rotation speed of the pulley.The rotation speed of the pulley is measured using a sensor that gives 24 pulses for eachrotation. The belt speed must be measured at least this accurate. When counting all thelinks on the belt separately the measuring frequency is much higher than 24 pulses perrotation.


Chapter 3

Sensor choice

For the measuring of speed different sensors are available. All the sensors can be divided intwomain groups, sensors that make contact with the object which speed should bemeasuredand sensors that make no contact with the object. To prevent friction between the V-belt andthe sensor the choice has been made to use a sensor which make not direct contact with theV-belt. The sensors that are left can also divided in two groups, optical sensors and inductivesensors. These sensors can measure the speed of the V-belt using the links of which the V-belt is made. The V-belt exist of many loose links that held together by nine or twelve rings.Each link is 1.8mm thick. On the inside of the V-belt there is a space of 0.5mm betweenthe links, the sensor must be able to make make a distinction between the different links.The speed of the V-belt can be determined by counting all the links that will pass the sensorduring a specific time.

3.1 Sensor requirements

The sensor must meet the following conditions:

1. High operation frequency

2. Resistant against an oil/air mixture and high temperatures

3. Fit into the original CVT transmission

In the next paragraphs an explanation on these requirements will be given.

3.1.1 Operation frequency

First the operation frequency is discussed. The minimal and maximal link-pass frequencycan be found with the next formules [4]:

fmin =Vbelt(min)

d(3.1)


Chapter 3. Sensor choice 9

fmax =Vbelt(max)

d(3.2)

d is the thickness of one link. The belt speed Vbelt can be found with:

Vbelt = Rpri ×Npri (3.3)

The diameter Rpri is the diameter of the primary pulley. This diameter varies from 32mmup to 79mm. The rotational speed of the primary pulley Npri(rad/s) can be found with:

Npri =N

60× 2π (3.4)

The rotation speed of the pulley in this formula must be given in rounds per minute. Withthe following data this leads to:

min maxN(rpm) 500 6000Npri(rad/s) 52 628Rpri(m) 32× 10−3 79× 10−3

Vbelt(m/s) 1.67 49.6f(Hz) 930 27576

To obtain a good measuring it is necessary that the minimal operation frequency is atleast two times the link-pass frequency. If the sensor operates at a lower frequency it ispossible that the sensor will only measure the the gaps between the links or only the linksself. From these data the sensor speed can not be determined. In this case a measurefrequency of approximately 100KHz will give a good result.

3.1.2 Oil and temperature resistance

The sensor must be resistant against oil and high temperatures. Because the sensor is placesin the belt-box it comes in contact with oil. The oil temperature in the CVT can run up to130 degrees celsius. The greatest problem is the oil itself. Almost every sensor will react ifoil fly between the V-belt and the sensor. Sensors that react on oil are not applicable in thesystem. This means that optical sensors are not applicable on forehand.

3.1.3 Sensor dimensions

As a last the sensor must have small dimensions because the sensor must fit in the originaltransmission. The available space in the transmission is very small. The exact availablespace is discussed in chapter 4.



3.2 Dierent sensors

To choose the best sensor different sensors are evaluated. The sensors are evaluated on thebasis of the following qualities: dimensions, measure frequency, oil/temp resistance andprice.

sensor type dimensions High measure resistance pricefrequency against oil/temp.

RS 304-166 inductive 22mm× 6mm yes,up to 200MHz yes 10euroRS 171-2388 optical 10mm× 15mm yes no 46euroRS 235-5706 hall 30mm× 27mm no, 3Khz yes 27euro

The only sensor that meets all these requirements is a conductive sensor. For the restof the design of the V-belt speed sensor system a sensor of RS-components is used. Thechoice for this specific sensor has been made after consultation with VDT. VDT have beenalready busy with the development of a V-belt speed sensor and had good results with thissensor. One disadvantage of the inductive sensor is the required minimal surface speed. Ifthe surface speed, in this case the belt speed, is to low the sensor will give no output signal.So the belt speed can only measured accurate for speeds above 2.5m/s. For more details ofthe sensor see appendix A.



3.3 Functioning principle of the conductive sensor

The inductive sensor exist from a number of simple components. The most important com-ponents are the permanent magnet en the pole piece. Figure 3.1 shows a cross-section of theinductive sensor.

Figure 3.1: Cross-section of the inductive sensor

A permanent magnet inside the sensor projects a magnetic field to the area immediatelyin front of the sensor pole piece. Any ferromagnetic actuator moving through this area, orsuddenly leaving it, alters the reluctance state and produces a voltage output. The actuatorin this case is the belt with its links. Provided the actuator passes through the sensing areawith sufficient speed, the sensor generates an electrical signal of useful level. The amplitudeof the signal is proportional to the speed of the actuator. The signal will have a waveformthat agrees to the links and the air gaps between the links. At the output’s zero crossover thecenterline of the pole piece and that of the actuator are precisely aligned. The zero crossoveris a well defined point and can used as a reference, see figure 3.2. The output voltage of thesensor must be measured over a high resistance, for example 100kΩ.

Figure 3.2: actuator/sensor orientation to output zero crossing

By counting these points during a certain time the V-belt speed can be calculated. The signalmust possibly be filtered and can be converted to a block-signal for easier use.



Every inductive sensor has a optimum working point. In this point all the conditions areoptimal so the sensor give the best possible output and accuracy. For the used inductive sen-sor this optimum working point depends on the different distances and speed. The actuatorspeed is optimal when it is minimal 2.5m/s. The minimum belt speed it is reached whenthe transmission is running in low, then the belt speed is 1.7m/s. The maximum belt speedis reached in Over Drive, then the belt speed is 49.6m/s (see chapter 3.1.1). The actuatorspeed is in most cases equal or larger than the optimal minimal speed. The distances areshowed in figure 3.3.

Figure 3.3: optimum sensor/actuator relationship

The sensor operates in its optimum working point when:

A ≥ DB ≥ CC ≥ 3×DE - as close as possibleF ≥ D

In this case with the belt as a actuator the distances are: A = 1.3mm; B = 2mm; C =0.5mm; D = 0.4mm; E can be established as close as possible and F = 6mm. Only thethird condition is not met. So the sensor will not operate optimal, but because the otherconditions are met the sensor will operate almost optimal.


Chapter 4

Development of sensor mounting system

In this chapter the design of the total systemwill be discussed. In chapter 3 a sensor has beenchosen. The dimensions of this sensor are known. Now the best place in the transmissionhas to be determined. When the place has been determined the displacements of the beltmust be determined. The sensor must follow these displacements precisely.

4.1 Sensor placement

With the know sensor dimensions the best place to build in the sensor system is determined.The sensor measures the air gaps between the links of the belt. These air gaps occurs ontwo places on the belt. The first place is the outside of the belt in the contour of the pulley.When the belt is running over the pulleys there arise air gaps between the links. To measurethe speed on this place the sensor has to be placed on the outside of the belt. Because thelength of the sensor (22mm) there will not be enough space at this place. The other placewhere air gaps occurs is on the inside of the belt on the right piece. To use these air gaps thesensor must be placed on the inside of the belt between the two pulleys. Now there are onlytwo places left to mount the sensor system, but one of these places is eliminated because ofthe presence of an oil canal. The best place to mount the sensor system is exactly betweenthe two pulleys.

4.2 Belt displacements

The global place of the sensor is know. Now the displacements on this point can be deter-mined and the exact place can be determined. The best place is there where the belt hasminimal displacements. As a first a schematic reproduction of the CVT has been made witha coordinate system, see figure 4.1


Chapter 4. Development of sensor mounting system 14

Figure 4.1: schematic reproduction with coordinate system

4.2.1 X displacement

The displacement of the belt in the X-direction is calculated using a constant belt length.With a constant belt length and one know pulley running diameter the second pulley run-ning diameter can be calculated. The total belt length is given by [1] [3]:

L = R1 × αd + R2 × (2π − αd) + 2a× sinαd

2+ π × δ (4.1)

In this equation R is the diameter of a pulley; a is the distance between the two centersof the pulley; αd is the wrap angle of the belt. The wrap angle can be calculated with [3]:

cosαd

2=

(R2 −R1)

a(4.2)

With a matlab m-file (see appendix B) the position of the belt is plotted in figure 4.2In the figure you can see that there will be no displacement in the X-direction exact

between the two pulleys. But because the the slant form of the belt and the pulleys thebelt has a small displacement in the X-direction during shifting up and down. Also smallvibrations in the belt can occur, therefore the displacement in the X-direction can not beneglected. The exact displacement can not be calculated for this reason an estimate hasbeen made of a maximal displacement of 5mm.

4.2.2 Z displacement

The greatest displacement of the belt is in the Z-direction. During shifting up and down thebelt moves in this direction because of the displacements of the movable sheaves. From adetailed drawing of the CVT-ck2 a displacement of 8.75mm is found. In the design of thesystem a possible displacement in the Z-direction of 10mm is used.



−50 0 50 100 150 200

−100

−50

0

50

100

Figure 4.2: pulley diameters and belt

4.2.3 Rotation about Z-axis

The rotation about the Z-axis can also be calculated using equations 4.1 and 4.2. With theM-file from appendix B the wrap angle αd is calculated. The rotation of the belt is givenby [3]:

β =(180− αd)

2(4.3)

The belt angle versus the primary pulley diameter is plotted in figure 4.3. In figure 4.3 youcan see that the minimum angle is -16 degrees, the maximum angle is 16 degrees. The totalmaximum rotation in relation to the transmission house is 32 degrees.

4.2.4 Rotation about Y -axis

In theory there will be no rotation about the Y -axis. For safety the rotation freedom aboutthe Y -axis has not been fixed. So the sensor can follow optimal the belt if it will rotate in thisdirection. In the design an angle of maximal 5 degrees has been taken into account. Whenthe sensor can rotate free about the Y -axis it’s also much easier to mount the sensor in thetransmission house. Now it is not necessary to mount the slider mechanism exact parallelto the belt. A small deviation in the mounting system will give no problems.



Figure 4.3: Belt angel in relation to the transmission house

4.3 Design

All the displacements are known now. The mounting system of the sensor must be able tomake the displacements. First there is looked to the design of a construction that can followthe biggest displacements. That are the displacements in the Z-direction and the rotationabout the Z-axis. Later there is looked to the smaller displacements in the X-direction andthe rotation about the Y -axis. 3-D drawings of the total system can be found in appendix D.The complete working plans of all the components can be found in appendix G.

4.3.1 Translation in Z-direction

The displacement in the Z direction relative big. There are different manners to make sucha big translation possible [5]. A few options are discussed and the best design is chosen. Thefirst option is a very simple one rod mechanism. One side of the beam is fixed hinged tothe edge of the transmission. The sensor will be fixed hinged to the other side of the rod. Asimple schematic drawing is shown in figure 4.4.



Figure 4.4: One-rod mechanism Figure 4.5: four-rods mechanism

The advantage of this system is that it is very simple to make. The greatest disadvantagesare the big dimensions of this rod because of the great displacement it must make. In thetransmission there is no place for such a big rod. The second disadvantage is the displace-ment in the other directions. When the sensor moves in the Z-direction it will also movesin a direction perpendicular on this movement. So the movements in different directionshave been coupled. This coupling can be deleted by using a two or four rod system (see fig-ure 4.5). The disadvantages of this options are the big dimensions to realize such a system.Also the many joint points is a disadvantage. It is very difficult to make these joints withoutmargin.

The third option is to make a slider mechanism. A great advantage of such a system isthat it can be build very compact. For this application two different designs are made. Thebest one is chosen. In figure 4.6 and 4.7 you can see the different designs. In both designsthere are two vertical round slides, these two round slides prevent the mechanism to rotate.These two rounds can also be replaced by one slide with a different form, for example squareor triangular. So the system can be made with less components. The disadvantage of thisforms is that a considerable friction appears as soon as a force comes that is not in the samedirection of the movement freedom. When this friction becomes to high the total systemwill not be able to move anymore. The intention is that the measurement system wont haveany influences on the belt, so friction must be avoided. From the two options in figure 4.6and 4.7 the second one is chosen. Option 1 has different disadvantages. The constructionis build around the belt, so it is difficult to mount and remove the system. Furthermore theconstruction is very large because the sensor must be able to rotate and move freely with thebelt, so there must be enough space between the two slides. The block-system that shoveamong the two sliders should only move in the Z-direction, for this reason 5 freedom de-grees must be fixed. One slider will fix 4 degrees of freedom, the displacement in the X and



Y -direction and the rotation about these axis. Only the rotation about the X-axis should befixed. Therefore the second slide is add, to prevent these to fix also 4 degrees of freedom thehole in the block-system is not circular [5]. This can be seen in figure 4.8.

Figure 4.6: two slides, option 1 Figure 4.7: two slides, option 2

Figure 4.8: view from above of the block

4.3.2 Rotation about Z-axis

The wrap angle of the belt about the Z-axis is calculated in paragraph 4.2.3. The belt is inthe X-direction 15mm wide. The neutral point of the belt, where the belt moves minimal iscalculated in paragraph 4.2.1. The belt rotates about an fictitious line, see figure 4.9. Thisline lies 4mm from the lower part of the link. The turn point of the sensor framework mustmust lie on 1 line with this line. In the final design the rotation about the Z-axis is combined



Figure 4.9: side and front view of one link with rotation line

with the translation in the X-direction so the rotation point is always exact on the fictitiousrotation line. This is explained in the next paragraph. To create a rotation point exactly onthis line two rods are mounted on the slider block.

4.3.3 Translation in X-direction

The displacement of the belt in the X-direction is very small. For this translation thereare the same options as for the translation in the Z-direction, see paragraph 4.3.1. Becauseof the very small available space in the transmission box there is also chosen for a slidermechanism. The slider mechanism exist from two slots in the rods that are mounted onthe slider block. Two protrusion on the sensor framework slide in these two slots. Theprotrusions are circular so that the sensor framework can also rotate in the two slots aboutthe Z-axis. The design in this stadium is shown in figure 4.10.

4.3.4 Sensor framework

The sensor framework is a framework that is made around the belt. This framework fitsaround the belt with aminimal clearance so there is minimal friction between the frameworkand the belt. The framework follows all the displacements of the belt. On this frameworkthe sensor is placed. The framework exists from a block where the sensor is mounted onand two belt slides. The slides ensure that the belt is followed. The slides push the blockwith the sensor against the inside of the belt. The slides press against the iron rings of thebelt. There is chosen to press to these rings and not to the links because of the friction. Thesurface of the rings is very smooth and therefore there will be less friction. To ensure thatthe framework follows the belt and that the belt will not get stuck while the belt is runningthere is chosen for a so-called three points imposition [5]. The framework makes contactwith the belt on three points on each side of the framework. This is realized by making theblock with the sensor as small as possible and the slides as wide as possible. At both endsof the slides a small circular protrusion is made to create two points where the slides make



Figure 4.10: situation sketch rotation about z-axis and translation in x-direction

contact with the belt. The third contact with the belt is made on the inside of the belt withthe block with the sensor in it. In the figure below you can see the three contact point withthe belt (figure 4.11).

Figure 4.11: contact points between belt and sensor framework



4.3.5 Rotation about Y -axis

As last the rotation about the Y -axis has been added to the design. To make it possible forthe sensor framework to rotate about the Y -axis two attachments are added. The two attach-ments together are circular, see figure 4.12. On the attachments is a rectangular protrusionto prevent the attachments to rotate about the Z-axis. The protrusion slides in the rectangu-lar slot in the rod that is mounted on the slide block. Because the sensor framework mustbe able to rotate (see 4.3.3) a hole in the lower part of the attachment is made. The protru-sions on the sensor framework will fit in these holes, see figure 4.13. Now the whole sensorframework can rotate about the Y -axis and translate in the X-direction.

Figure 4.12: The two attachments that form a circle.



Figure 4.13: connection between attachment and belt slider

4.3.6 Mounting sensor system to transmission-house

The connection between the sensor system and the transmission-house is made by twoblocks. These blocks can be mounted to the transmission-house with two bolts. Exactbetween the two pulleys the transmission house makes a bow. The blocks have exact thesame shape as the transmission-house. By means of this form the two blocks will lie al-ways exact above each other. Because the transmission-house is not complete parallel to thebelt and perpendicular to the pulleys maybe some extra rings must be place between thetransmission-house and the upper block. A small deviation can be caught by the system it-self. The upper block has two longer protrusions because of the transmission-house consistout of two parts. The upper part, the cover of the transmission-house, must be removed toplace the sensor. Therefore nothing can be mounted to the cover. A short description howto build in the sensor system can be found in appendix F.



4.4 Materials

The design of the sensor mounting system is ready. Now the best materials must be chosen.The requirements for the total system are

1. strong

2. light weight

3. hardwearing

To create a light weight system the best material to use is aluminium. Aluminium has alow density and fabrication is easy. The disadvantages of aluminium are that its not verystrong an not so hardwearing, so for moving objects it is not useful. To see if aluminium issuitable for the rods of the system a simple calculation is done in Unigraphics. The rods areloaded in the Y -direction and the Z-direction. The results are shown in figure 4.14 and 4.15.In these figures you can see that the displacement in both directions with aluminium arealmost three times bigger than with steel. The displacements of the aluminium rod are toolarge for this application. So for the rods aluminium is not suitable. Therefore steel has beenchosen for the two rods.

For the block and the two round slides two different materials are chosen. Because of thesmall diameter of the round slides hardened steel has been chosen. This is very strong andthe surface is extremely smooth. For the block is chosen for bronze. The combination ofhardened steel and bronze gives a slider mechanism with a very low friction. These two ma-terials are also used in bearings. For the two attachments also bronze has been chosen. Thismaterial is easy to fabricate. It is also important to use different materials for the connectionswhich slide against each other. When two different materials are used the materials will not"eat" into each other. The sensor framework is also made of steel. Because the sensor frame-work rotates about the two attachments. These are made of bronze, so the sensor frameworkmust bemade of a different material. The sensor frameworkmust be hardwearing because itis continuously in contact with the running belt. If normal steel does not satisfy it is possibleto apply a surface hardening. This can easily be done afterwards. The oil in the transmissionensures the necessary lubrication for the moving components. If these lubrication is notenough for the system an extra oil canal must be made in the transmission-house. The twomounting blocks are made of aluminium. Aluminium is easy to edit, so the blocks can beadapted until these fit on the transmission-house.



(a) aluminium (b) steel

Figure 4.14: xation rod loaded in X-direction

(a) aluminium (b) steel

Figure 4.15: xation rod loaded in Z-direction


Chapter 5

Conclusions

The design of the measurement system is proposed. The system meets all demands madein chapter 2. A compact, easily mountable and removable and precise system has been de-signed to use with the original belt.

After the total design of the measurement system working plans of al the components hasbeen made, see appendix G. All components have been made by Toon van Gils. Of somecomponents the external form has been adapted so it was possible to make them with theavailable tools. These adaptations have however no influence on the functioning principleof the sensor-system.

The next step is to build in the system in the CVT-CK2. During assembly a few thingshave to be taken into account to make the system complete.

• To mount the two mounting blocks there must be made four holes in transmissionhouse. If these holes are entirely through the transmission house then hese holesmust be closed with a sealing to prevent oil leakage out of the transmission.

• The sensor has two standard wires, they still have to be checked for resistance againstoil and high temperatures.

• The wires must come out of the transmission house. The best place must be deter-mined.

After the installation of the system the sensor signal must be made suitable for furtherprocessing to read out the speed of the belt. If the signal is made suitable the totale system isready to use. Test must expel if the whole system works. After the test there can be checkedif new adaptations must be made to material, form or sensor signal. If the system is nothardwearing the steel components can be hardened. The developed system is cheap, easy touse and easy to make.


Bibliography

[1] Fundamentals of Machine ElementsBernard J. Hamrock, Bo Jacobson, Steven R. Schmid.McGraw-Hill International Editions(1999)ISBN 0-07-116374-3

[2] Technisch tekenen volgens Nederlandse normen, 7th editionL.A. de Bruijn, F.J. SiersEducative Partners Nederland BV (1996)ISBN 90-401-0825-0

[3] Gedeelte Mechanische Overbrengingen, january 2000H.J. Lammers, J.G.H. Schrouff, A.M. KlunderUniversity Eindhoven, faculty mechanical engineering

[4] Polytechnisch zakboekje, 48th editionP.H.H. Leijendeckers, J.B. Fortuin, F. van Herwijnen, H. LeegwaterKoninklijke PBNA BV.ISBN 90-6288-266-0

[5] Constructie Principes 1, March 2000P.C.J.N. Rosielle, E.A.G. RekerUniversity Eindhoven, faculty mechanical engineering


Appendix A

Sensor specications


Appendix A. Sensor specications 28


Appendix A. Sensor specications 29


Appendix B

Belt displacement M-le

clear; format long e;

syms R1 a b L

L=7.041935119883963e+002;

b=168;

for Rp=32:24:80

R21 = b*cos(a/2) + R1;

R22 = -(R1.*a + 2.*b.*sin(a./2) -L)./(2.*pi-a);

maxit=100000000;

tol=1e-5;

a=0;

k=0;

conv = 0;

while (~conv)

k = k+1;

error=b*cos(a/2) + Rp--(Rp.*a + 2.*b.*sin(a./2) -L)./(2.*pi-a);

a=a+0.0001;

conv = (error<tol) | (k==maxit);

end;

Rs=b*cos(a/2) +Rp;

xp=-sin(1/2*(pi-a))*Rp;

yp=cos(1/2*(pi-a))*Rp;

xs=-sin(1/2*(pi-a))*Rs;

ys=cos(1/2*(pi-a))*Rs;

axis equal

xpp=-Rp:0.1:Rp;


Appendix B. Belt displacement M-le 31

ypp=sqrt(Rp.^2- xpp.^2);

plot(xpp,ypp,'r')

hold on

plot(xpp,-ypp,'r')

grid

hold on

xsp=-Rs:0.1:Rs;

ysp=sqrt(Rs.^2 -xsp.^2);

plot((xsp+168),ysp,'r')

plot((xsp+168),-ysp,'r')

grid

x=[xp,xs+168];

y=[yp,ys];

plot(x,y,'r')

plot(x,-y,'r')

hold on

grid

title('Belt displacement Z-direction')

ylabel('Pulley radius')

end


Appendix C

Belt angle M-le

clear; format long e;

syms R1 a b L

L=7.041935119883963e+002;

b=168;

Rs=[];

Rp=[];

A=[];

R21 = b*cos(a/2) + R1;

R22 = -(R1.*a + 2.*b.*sin(a./2) -L)./(2.*pi-a);

for R1=34:2:80;

maxit=100000000;

tol=1e-10;

a=0;

k=0;

conv = 0;

while (~conv)

k = k+1;

error=b*cos(a/2) + R1--(R1.*a + 2.*b.*sin(a./2) -L)./(2.*pi-a);

a=a+0.00001;

conv = (error<tol) | (k==maxit);

end;

ag= (a/(2*pi))*360;

A=[A,ag];

R2=b*cos(a/2) +R1;

Rs=[Rs,R2];

Rp=[Rp,R1];

end


Appendix C. Belt angle M-le 33

%plot pulley diameter versus belt angle

figure(2)

plot(Rs,((180-A)/2))

grid

title('Primary pulley diameter versus belt angle')

Xlabel('primary pulley diameter (mm)')

Ylabel('belt angle (degrees)')


Appendix D

3-D views

Figure D.1: isometric view


Appendix D. 3-D views 35

Figure D.2: left side view Figure D.3: top view

Figure D.4: front view Figure D.5: back view


Appendix E

Exploded view

Figure E.1: exploded view


Appendix F

How to build in

This chapter will give a short explanation how to build in the sensor system in the CVT-CK2.

• First unscrew the cover of the CVT. To lift the cover also three bolts from the shaftbearing must be unscrewed. Now the cover can be lifted.

• Place the two mounting blocks to the transmission house using four bolts.

• Fit the sensor framework around the belt. This is easiest if the belt is moved out thetransmission.

• Screw the bottom rod to the slider block.

• Place the slider block between the two mounting blocks and put the two round slidesthrough the mounting blocks. (If the belt is removed it must be placed back now.)

• Place 1 attachment on the lower rod. Next the sensor framework can be placed on theattachment.

• Place the second attachment on the upside of the sensor framework.

• Place the second rod and screw it to the slider block.

• Place the cover back on the transmission-house.


Appendix G

Working plans


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