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Belt Tracking Project

Qasim Khan

A thesis submitted in partial fulfilment

Of the requirements of the degree of

BACHELOR OF APPLIED SCIENCE

Supervisor: J.K. Spelt

ii

ABSTRACT

Belt tracking is a major problem in the conveyor industry. To prevent the belt from running off

pulleys, designers at SIEMENS incorporate belt tracking mechanisms such as crown pulleys and

belt tensioners into their conveyors. However, they have little understanding of how crown

pulleys function when used with belt tensioners and whether it can solve all of their tracking

problems. This report attempts to resolve the issues faced by SIEMENS and propose an efficient

solution to belt tracking. It was found through analytical and experimental work that belt wrap

angle, free belt length, and crown taper angle are the most influential parameters that affect the

performance of a crown pulley. In addition, to improve belt tracking, tapered crown pulleys

should be installed on conveyors instead of trapezoidal crown pulleys currently used by

SIEMENS. Next, research has shown that the crown pulleys become inefficient even for slight

pulley misalignments (i.e. with belt tensioners). Hence, the conventional method for tracking

with tensioners can also be applied to crown pulleys. Finally, one can make modifications to the

crown conveyor systems based on the aforementioned results, but it is best to install an automatic

belt tracker that can effectively keep a belt centred on the conveyor in all circumstances.

iii

ACKNOWLEDGEMENTS

A special thanks to the engineering department at SIEMENS Canada who funded as well as

shared their experiences during the course of the project. Also, without the expert advice of

Professor Spelt, I would not have been able to finish this project.

iv

TABLE OF CONTENTS

INTRODUCTION ....................................................................................................................................................... 1

1.2—METHODS OF BELT TRACKING ............................................................................................................. 2 1.3—MOTIVATION .............................................................................................................................................. 5 1.4—OBJECTIVE .................................................................................................................................................. 6

IMPORTANT PARAMETERS OF CROWN PULLEYS ....................................................................................... 7

2.1—PRELIMINARY ANALYSIS OF CROWN PULLEY MECHANICS ...................................................... 7 2.2—RELEVANT CROWN PULLEY PARAMETERS ................................................................................... 11

2.2.1—Goran Gerbert Results .......................................................................................................................... 11 2.2.2—V-Ribbed Belt Backside Pulley Mistracking......................................................................................... 16

OPTIMAL CROWN PULLEY COMBINATIONS ............................................................................................... 21

3.1—APPROACH TO FIND OPTIMAL COMBINATION ............................................................................. 21 3.2—CONVEYOR SYSTEM MODEL ............................................................................................................... 24 3.3—EXPERIMENTAL RESULTS/DISCUSSION & CONCLUSIONS ......................................................... 26

LIMITATIONS OF CROWN PULLEYS ............................................................................................................... 30

4.1—BELT TRACKING EXPERIMENT .......................................................................................................... 30 4.2—USE OF BELT TENSIONER ...................................................................................................................... 33

SOLUTION FOR CROWN PULLEY SYSTEMS ................................................................................................. 39

5.1—IMPROVEMENTS TO CURRENT CROWN PULLEY SYSTEM ......................................................... 40 5.1.1—CROWN PULLEYS ............................................................................................................................... 40 5.1.2—FREE BELT LENGTH ........................................................................................................................ 40 5.1.3—BELT TENSIONER .............................................................................................................................. 41

5.2—AUTOMATIC BELT TRACKING ............................................................................................................ 44 5.2.1—PT Max Belt Tracker by Flexco ............................................................................................................ 45 5.2.2—Tilt Belt Tracker .................................................................................................................................... 48

FIGURES & TABLES .............................................................................................................................................. 53

6.1—SECTION 1: INTRODUCTION .......................................................................................................................... 53 6.2—SECTION 2: IMPORTANT PARAMETERS OF CROWN PULLEYS ..................................................................... 53 6.3—SECTION 3: OPTIMAL CROWN PULLEY COMBINATION ............................................................................... 54 6.4—SECTION 4: LIMITATIONS OF CROWN PULLEYS .......................................................................................... 55 6.5—SECTION 5: PROPOSE A SOLUTION ............................................................................................................... 57

REFERENCES .......................................................................................................................................................... 59

APPENDIX A ............................................................................................................................................................. 61

APPENDIX B ............................................................................................................................................................. 62

APPENDIX C ............................................................................................................................................................. 67

APPENDIX D ............................................................................................................................................................. 68

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LIST OF SYMBOLS

Ω = Rotational speed of the pulley.

dm = mass of the element dy by dy.

Φ = Taper angle of crown pulley.

r = Radius of pulley.

T = Tension in the belt due to the distance between pulleys.

Fc = Centripetal force due to the velocity of the element.

Fct = Force that brings up the belt.

Ff = Frictional force.

μ = Coefficient of friction .

F = Belt tension along tangent t

.

Q = Transverse force along generatrix g

.

N = Contact force along normal n

.

B = Belt width.

M = Bending moment around normal.

vc = Velocity of belt along the tapered side.

S = Flexural rigidity.

FN = Normal force.

Crr = Coefficient of rolling friction.

vi

LIST OF FIGURES

Page Number

Figure 1.1.1 1

Figure 1.2.1 2

Figure 1.2.2 2

Figure 1.2.3 3

Figure 1.2.4 4

Figure 1.2.5 5

Figure 2.1.1 7

Figure 2.1.2 7

Figure 2.1.3 8

Figure 2.1.4 8

Figure 2.2.1 12

Figure 2.2.2 12

Figure 2.2.3 13

Figure 2.2.4 15

Figure 2.2.5 15

Figure 2.2.6 17

Figure 2.2.7 17

Figure 2.2.8 19

Figure 3.1.1 22

Figure 3.1.2 24

Figure 3.2.1 26

Figure 3.3.1 27

Figure 3.3.2 28

Figure 3.3.3 28

Figure 4.1.1 31

Figure 4.2.1 35

Figure 4.2.2 38

Figure 5.1.1 41

Figure 5.1.2 42

Figure 5.1.3 43

Figure 5.2.1 45

Figure 5.2.2 47

Figure 5.2.3 47

Figure 5.2.4 49

Figure 5.2.5 52

Figure 6.2.1 53

Figure 6.2.2 53

Figure 6.3.1 54

Figure 6.3.2 54

Figure 6.4.1 55

Figure 6.4.2 55

Figure 6.4.3 56

Figure 6.4.4 56

Figure 6.5.1 57

Figure 6.5.2 57

Figure 6.5.3 58

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INTRODUCTION

1.1—BACKGROUND One of the main objectives of a conveyor designer is to devise ways to ensure that the belt stays

aligned on a conveyor and that “people be able to walk away from the system and not worry

about its operation for reasonable periods of time.”[9] Belt tracking, more commonly known as

belt training, refers to the procedure/method that keeps a belt running straight on a conveyor

system. If no method of tracking is employed, the belt is likely to drift to one side of a conveyor

and ultimately slip off the pulleys. A typical representation of a misaligned belt is depicted in

Figure 1.1.1 which results in material spillage, increase in belt wear, as well as an increase in

power consumption of the conveyor. In the extreme misalignment case, a worker may need to

shut down the conveyor to realign the belt which would add to the conveyor downtime.

The challenge in keeping a belt centered lies

in the unpredictable movement of the belt

under various external conditions (i.e. pulley

misalignment, uneven weight distribution of

the deposited material, idler misalignment

etc). In addition, the improper alignment of the supporting structure which holds the conveyor

sections also contributes to the lateral movement of the belt [9]. Therefore, one of the easiest

ways to keep the belt tracking properly as proposed by CEMA (Conveyor Equipment

Manufacturers Association) is to carefully align conveyor components using the procedures

outlined in CEMA’s “Belt Conveyors for Bulk Materials”. This guide book is considered to be a

reliable source for conveyor safety dimensional and application standards.

Figure 1.1.1: Belt misalignment. [1]

2

Discussions with experienced personnel from companies such as SIEMENS and Continental

Conveyors have shown that it is not always possible to perfectly align the components of a

conveyor. People in the labour make careless mistakes when taking measurements, tightening

bolts to a specified torque value, etc. Also, there are transient conditions [1] such as uneven

distribution of material on the belt that may cause belts to misalign despite all efforts to ensure

proper installation and maintenance. As a result, other methods have been devised to help the

belt track correctly even if the root problems persist.

1.2—METHODS OF BELT TRACKING A common remedy to the belt tracking problem is to employ guide rollers (See Figure 1.2.1).

The rollers are positioned at regular intervals along the conveyor and exert a force on the belt

when it begins to drift to one side. The force restricts the drifting motion of the belt and prevents

it from running off the conveyor.

Another method is to use belt training idlers (See Figure1.2.2). A training idler has the carrying

roll frame mounted on a central pivot approximately perpendicular to the conveyor belt. Means

Figure 1.2.1: Guide rollers assist in belt tracking. [2]

Figure 1.2.2: Belt Training idlers.

[2]

3

are provided to cause the carrying rolls to become skewed with respect to the center line of the

conveyor. As the belt traverses the skewed rolls, they urge the displaced belt to return to the

conveyor center line and, in doing so, the rolls are urged to return to proper alignment as well

[2].

The third common practice in the industry, and is

also the focus of this thesis, is to use crown

pulleys (See Figure 1.2.3) in conveyor systems so

that belt tracks by itself to the center with minimal

human interference. The main characteristic of

these pulleys is the tapered end which is usually

1/8” per foot of pulley diameter. The physics and

the parameters that govern the behaviour of crown pulleys in tracking belts will be discussed

later in this report.

Figure 1.2.4 shows a typical conveyor system with belt wrapping around the drive and the driven

pulley at each end. Usually there are rollers between the two end pulleys (not in the conveyor of

Figure 1.2.4). The drive pulley shaft is coupled with a gear box and a motor. As the drive pulley

rotates, the tail pulley also rotates due to the friction generated by belt tension between the pulley

and the belt. A belt tensioner is attached to the pillow block bearing of the tail pulley on both

sides of the conveyor.

Figure 1.2.3: Two types of crown pulleys with shaft

going through them. Tapered Crown pulley has

tapered sides on both ends. A Trapezoidal Crown

pulley has a flat surface at the top along with tapered

ends. [3]

4

Another common way of centering a belt is to install belt tensioners. A belt tensioner is used by

humans to adjust the tension in the belt in such a way that a belt, when it begins to wander off the

pulleys, is brought back to the center. Typically, the following procedure is followed (refer to

Figure 1.2.5) to track the belt when the drive and tail pulleys are both flat face drum pulleys

(without tapered ends) and with crown pulleys (pulleys with tapered ends):

1) Tail Section: if the belt drifts in direction A on the tail pulley, the belt tensioner on side X

should move (reduce its stroke) in direction C in order to decrease tension on that side.

2) Tail Section: if the belt drifts in direction B of the tail pulley, the belt tensioner should on

side Y should move in direction D in order decrease tension on that side.

3) Head Section: if the belt drifts in direction A of the drive pulley (head pulley), the belt

tensioner on side Y should move in direction C.

Figure 1.2.4: Typical belt conveyor built at SIEMENS

[4].

5

4) Head Section: if the belt drifts in direction B of the drive pulley (head pulley), the belt

tensioner on side X should move in direction D.

All of the aforementioned methods of belt tracking, but not limited to, adjust the tension in the

belt in such a way that the belt realigns itself. However, each method has its own pros and cons

which must be carefully evaluated during the conveyor design phase. Often, conveyor designers

prefer a method that requires no human interference and belt tracking is done automatically such

as the case for crown pulleys.

1.3—MOTIVATION My experience at SIEMENS has shown that there is not a great deal of understanding of how a

crown pulley functions and what its limitations are when used in conjunction with a belt

tensioner. SIEMENS has recently incorporated crown pulleys in their conveyor systems without

much knowledge of the tracking potential that these special pulleys possess. Their reason for

X

Y

X

Y

Figure 1.2.5: Belt tensioner use in centering belt. [5]

6

using them, as pointed out by the management, has less to do with belt tracking and more to do

with remaining square with its competitors who adopted crown pulley systems many years ago.

However, they now want to get a better understanding of these systems and have assigned this

project to myself.

Engineers at SIEMENS claim that the belt movement on crown pulleys becomes unpredictable

for particular belt configurations and is ineffective for others. So they are unsure of whether it is

feasible to incur the extra cost of buying crown pulleys while they could use flat face drum

pulleys (no tapered sides) instead at a cheaper price. Therefore, the goal of this project is to

resolve some of these belt tracking issues associated with crown pulleys so that belt tracking is

made easier and efficient.

1.4—OBJECTIVE The objective of this thesis paper is two fold. First, research and experiments will be conducted

to understand the important parameters of crown pulleys that aid in belt tracking. Second, a

solution will be proposed to the crown pulley system based on the results from the first part so

that belt tracking is made simple and efficient with minimal human interference.

7

IMPORTANT PARAMETERS OF CROWN PULLEYS

In this section of the report, a simple preliminary analysis is shown which explains the

mechanism of a crown pulley. Then some literature on belt tracking is presented which examines

rigorously how different factors such as taper angle, entry span, tension, type of belt, etc

contribute to the effectiveness of the crown pulley in belt tracking.

2.1—PRELIMINARY ANALYSIS OF CROWN PULLEY MECHANICS There is a general consensus in the literature as well as in numerous engineering forums that the

belt, when it is off centered on a crown pulley, will move up the crown towards the larger

diameter (Figure 2.1.1). It is important to know which parameters (i.e. taper angle, friction, belt

tension, etc) contribute to this behaviour.

The phenomenon of a belt moving up a crown is similar to a car driving around a curved banked

(Figure 2.1.2). The analysis shown next gives more details on what kinds of forces are generated

on the belt.

Figure 2.1.1: Belt moves up the crown

and towards the center because greater

force is exerted on side A.

Figure 2.1.2: Car traveling around a banked curve.

The velocity of the car generates a centripetal force

according to the equation. Fr = v2/curvature radius

[7].

8

Please note that this analysis is highly simplified and yet it provides reasonable estimates about

the relevant parameters of crown pulleys as confirmed by other detailed literature (see section

2.2 for comparison).

ASSUMPTIONS

There is no belt slippage.

Moment due to uneven distribution of tension along the tapered side of the crown pulley

is not accounted for.

Flexural rigidity (S) of the belt is not accounted for which will add to the resistance of

belt movement. It is defined as EI and is a measure of the resistance of a beam to

bending.

Variation of tension along the curvature of the pulley is neglected.

ANALYSIS

Consider the belt configuration on two trapezoidal crown pulleys shown in Figure 2.1.3.

The small element “dy” by “dy” on the belt is shown again in Figure 2.1.4 with resulting forces

as the pulleys rotate.

Figure 2.1.3: Two perfectly aligned

crown pulleys with an off centered

belt. Figure 2.1.4: Forces acting on small

belt element as the pulleys rotate.

9

The symbols are defined as follows:

Ω = Rotational speed of the pulley

dm = mass of the element dy by dy

Φ = taper angle

r = radius which changes as belt moves up.

T = Tension in the belt due to the distance

between pulleys.

Fc = Centripetal force due to the velocity of

the element.

Fct = Force that brings up the belt.

CALCULATION

r

vdmFc

2

)(

Where v = ωr

So, ))(( 2rdmFc

sin

)90cos(

cct

cct

FF

FF

Plug in Fc expression into the equation for Fct to get,

sin))(( 2rdmFct

Let us consider the frictional force along the tapered side which prevents the motion of the belt.

)( CNf FTF

Where, Ff = frictional force

μ = Coefficient of friction

FCN = Fc cosΦ = cos))(( 2rdm

Hence, ])cos)[(( 2rdmTFf

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Finally, the net force that is bringing up the belt is obtained by a simple force balance along the

tapered side of the crown pulley.

Net Force = FNET = Fct – Ff

FNET = sin))(( 2rdm - ])cos)[(( 2rdmT

FNET = Trdm )cos)(sin)(( 2 (Eq 2.1.1)

DISCUSSION

The calculations shown above for the given belt configuration takes into account the main forces

that act on a belt element positioned on the tapered side of the pulley. Equation 2.1.1 summarizes

some of the important parameters that are involved in bringing the belt back to the center and

moving it up the crown. These are: the rotational speed of the pulley, radius of the crown pulley,

taper angle theta, friction coefficient between the pulley and belt, and tension in the belt.

It is important to note that the direction of the belt tension “T” will vary in different belt

configurations and it may actually help the belt move up by increasing the value of FNET. The

following general conclusions can be drawn based on equation 2.1.1:

1. Higher rotational speed of the pulley results in higher value of FNET. Hence, the belt

moves to the center quickly.

2. There is an optimal taper angle at which FNET is maximized. Hence, the belt moves

to the center quickly. The designer has to be careful not to select a very large value

for taper angle because it might damage the belt due to higher tensions [9].

3. An increase in friction factor slows down the belt movement. The traction between

the pulley and the belt, as suggested by CEMA, should be just enough so that belt

does not slip. For all other friction factors, the power consumption to drive the

11

conveyor would increase so the designer must carefully evaluate the benefits versus

the cost incurred due to an increase in friction factor.

4. An increase in tension in the belt slows down the movement of the belt along the

tapered side. An increase in tension may arise due to a number of reasons such as

overloading, misalignment of conveyor components, etc.

As mentioned earlier, the analysis above is primitive and does not account for many other

relevant factors some of which are embedded in the assumptions made. However, the

implications of equation 2.1.1 are verified in the next section and by the experiments in section 3

of this report. A comprehensive analysis of the movement of belt on crown pulleys is presented

by Goran Gerbert in his article “Flat Belt Axial Motion on Conical Pulleys.”[8]

Some of the

highlights of his research are discussed next.

2.2—RELEVANT CROWN PULLEY PARAMETERS

2.2.1—Goran Gerbert Results

Professor Gerbert of Chalmers University of Technology presented his research on the

movement of flat belt on conical pulleys at the Power Transmission and Gearing conference in

1996. The objective of this section is to summarize his findings and the approach he has taken to

reach his conclusions. For complete details of his analytical results, it is recommended that the

reader refer to his paper “Flat Belt Axial Motion on Conical Pulleys.”[8]

OBJECTIVE

The objective was to theoretically derive an expression which will estimate the velocity of the

belt moving along the tapered side of a pulley. This particular expression would contain all of the

12

relevant parameters that govern the movement of the belt on the crown pulley. The results of the

equations were verified by a series of experiments and general conclusions about the movement

of belt on crown pulleys were given.

APPROACH

Figure 2.2.1 is a representation of a belt wound around a cone. The equilibrium of a belt element

located on the tapered side or generatrix of the pulley is shown in figure 2.2.2. Although the belt

element accounts for all of the acting forces, the solution to obtain the velocity of the belt along

the generatrix will simplify the model by eliminating some frictional forces.

The parameters defined in figure 2.2.2 are as follows:

F = belt tension along tangent t

Q = transverse force along generatrix g

N = Contact force along normal n

Itμ dN = friction force along tangent (- t

)

Igμ dN = friction force along generatrix (- g

)

Inμ dN = friction torque opposite speed .

B = belt width

M = bending moment around normal ( n

)

Figure 2.2.1: Flat belt wound around a cone. Here, Y is

the cone angle, ω is the rotational speed, ψ is a small angle

along the tapered side, θ defines the orientation of a belt

element. [8]

Figure 2.2.2: Force equilibrium on a small belt

element. Note, the friction along the tangential and

generatrix (tapered side) are accounted for. [8]

13

In, Ig, and It reduce the coefficient of friction to account for simultaneous sliding and rotation. In

the next steps, not shown here, an equilibrium balance of the element yields a set of equations. In

addition, deflection, friction, and velocity analyses of the small belt element each generate a set

of independent equations. The velocity analysis has the important parameter vc which is the

velocity of the belt element moving up the tapered side (generatrix) of a pulley. It is worth noting

that because the bending deflection of the belt is important in determining vc, flexural rigidity of

the belt “S” is taken into account.

A general situation of the belt running on two pulleys is depicted in Figure 2.2.3. With the

independent equations determined for a belt element, the objective now is to combine the

contacting parts of the belt (E and X) with the two free strands of the belt. The free strand of the

belt has a length A as defined in the diagram below.

The equilibrium and deflection analysis of the belt strand gives the equations (Eq 23, 24, 25 in

the Goran’s paper) that define completely the movement of the belt along the generatrix (i.e. the

belt’s generatrix velocity vc). Hence, using the equations of the belt element defined for E and X

Figure 2.2.3: General case of a belt running on two crown pulleys. E and X are the entrance and exit points of

the belt, respectively. W is the distance along the generatrix between E and X. A is the length of the free belt

strand. [8]

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and the belt strand equations, the solution for vc as a function of belt width (B), length of free

strand (A), pulley taper angle (Y), coefficient of friction (μ), longitudinal strain stiffness (c), and

flexural rigidity (S) is defined as follows:

SMALL BELT TENSIONS

(sliding present) ]}

2)([

)(48

)2

({

2

**

*

*

** BAA

AFv c (Eq 2.2.1)

LARGE BELT TENSIONS (no

sliding along generatrix) **

**

1

)( FA

YAv c

(Eq 2.2.2)

NOTE: Please refer to [8] for details of the simplified friction model used in obtaining the above

solutions.

The non-dimensional parameters used in equations 2.2.1 and 2.2.2 are defined as follows:

R

vv c

c* , R

AA* ,

R

BB* ,

S

FRF

2

*

NUMERICAL RESULTS

The generatrix velocity v*c as a function of belt tension F* is shown in Figure 2.2.4 below in

which μ and taper angle Y are parameters. Also shown in Figure 2.2.5 is a plot of analytical

results of v*c versus belt width B* and free belt length A*. The following general conclusion can

be made about the generatrix (velocity of belt along the tapered side) velocity v*c based on these

graphs:

Has a maximum for low tension (F* < 0.1 for practical taper angles Y<1o).

Decreases with tension in practical applications (F* > 0.1).

Is not very much dependent on belt width and friction.

Increases almost linearly with taper angles.

Increases almost linearly with length of belt strand.

15

Figure 2.2.4: Generatrix velocity R

vv c

c* versus belt tension. Parameters examined are taper angle Y and

coefficient of friction μ. [8]

Figure 2.2.5: Generatrix velocity R

vv c

c* versus belt tension. Parameters examined are belt width

R

BB* and free belt length

R

AA* [8]

16

EXPERIMENTS

Experiments were performed using three kinds of belts (rubber, v-belt, and tape). Two equal

sized crown pulleys were used. The pulleys were rotated slowly under the belt tension and the

axial displacement of the belt on the pulleys was measured using a calliper. The plot of the

theoretical results versus experimental results for the generatrix velocity is shown in Figure

6.2.2. The analytical results match remarkably well with the empirical data from the

experiments.

SUMMARY

Axial motion of a flat belt running on two conical pulleys has been investigated both

theoretically and experimentally. From the results, it is apparent that the flexural rigidity S of the

belt perpendicular to the axis of rotation is the main property influencing the axial motion of the

belt. Bending deflection and bending moment are caused by friction between belt and pulley [8].

In addition, the general conclusions concerning the generatrix velocity of the belt v*C were given

in the numerical results section of 2.2.1.

2.2.2—V-Ribbed Belt Backside Pulley Mistracking

This section presents the experimental results obtained by Russell Gross and Richard Meckstroth

from Dayco Products and Ford Motor Co, respectively. The results pertain to the effects of

backside pulleys (usually flat without a crown) of an accessory drive system of an engine which

can generate significant v-belt misalignment. Test were conducted to determine the v-belt

alignment sensitivities of the system variables such as belt tension, belt wrap, belt span length,

belt backside surface, backside pulley crown.

17

The issues addressed by Gross and Meckstroth are similar to the ones faced by a crown pulley

conveyor system that SIEMENS manufactures. Although, the data itself is not very useful to a

conveyor design which uses a flat belt instead of a v-belt, at least it will highlight the important

trends that relate to crown pulleys and confirm some of the general conclusions derived in earlier

sections of the report.

A typical representation of a v-bet running on a grooved pulley is shown in Figure 2.2.6. In an

accessory drive system of an engine (Figure 2.2.7), a v-belt runs over groove pulleys and wraps

around a backside pulley (flat faced) which directs it to another grooved pulley.

Figure 2.2.6: Pulley definitions [11]

What is of concern to the designers of accessory drive system is the lateral movement of the v-

belt on the backside pulley due to misalignments of other grooved pulleys. The lateral movement

will produce engine noise called “belt chirp” which is audible inside the cabin of the vehicle

Figure 2.2.7: An accessory drive

system of an engine. Pulley 1 and 2 are

grooved while pulley 3 is flat faced.

[12]

18

[11]. Hence, to minimize this belt movement, a crown is added to the backside pulleys. The next

section discusses the advantages of a crowned backside pulley.

BACKSIDE PULLEY CROWN EXPERIMENT & RESULTS

The test fixture for the experiments include two grooved pulleys and a crowned backside pulley.

The fixture is designed such that tension in the belt can be adjusted as well as misalignment in

the grooved pulleys with respect to other pulleys can be induced. The details of the test fixture

are not as important as the method to obtain data for the effectiveness of crown pulleys.

To obtain the data, deliberate alignment error setup by the entrance grooved pulley was 1.0 mm

with respect to the exit grooved pulley. As this forced misalignment of the v-belt occurs, the

aligning tendency of the crown on the backside pulley versus controlled variables (i.e. tension,

crown taper angle, belt wrap angle, entry span length, etc) can be measured. The belt wrap angle

defines how much the belt wraps around a pulley (Figure 6.2.1). For a conveyor system shown in

Figure 1.2.4, the belt wrap angle is is 180o for the drive and driven pulleys. The entry span length

is the same as the free belt length (A) as defined in section 2.1 of the report and is the distance

between the grooved pulley and the backside pulley. The graph in Figure 2.2.8 shows the effect

of crown in minimizing the 1.0 mm misalignment.

From the graph we can see that two types of belts (rubber and fabric back), two tensions (577 N

and 289 N), and two wrap angles (180o and 96

o) were tested for flat backside pulleys and

crowned backside pulleys. The following general conclusions can be drawn from the

experimental results:

19

A crown reduces the induced misalignment of 1 mm.

The greater the entry span length, the more effective is the crown.

A high belt wrap angle around the crown pulley increases the efficiency of the crown.

Variation in tension in the belt has negligible effect on the effectiveness of the crown in

comparison to the belt wrap angle and entry span length.

A fabric back belt is more effective than a rubber back belt.

Figure 2.2.8: The effect of crown versus different entrance lengths with different control

variables.

Some of these conclusions verify the results obtained by Goran Gerbert while others give more

insight into the parameters that govern the movement of belt on a crown pulley. One of these is

the entry span length. Fenner Dunlop, a conveyor belting company in the United States, claims

that the “effectiveness of the crown is increased to a length of approximately 10 feet.

20

Lengthening the unsupported span beyond 10 feet (approx 3 meters) does not seem to increase

the effectiveness of the crown.” [9]

CONCLUSION

Gross and Meckstroth conclude that the most influential of parameters that effect the

effectiveness of a crown pulley are the entrance belt length and the belt wrap angle. Hence, these

must be taken into consideration when designing conveyor systems with flat belts. It is important

to note that the effect of these two parameters will be more pronounced for a flat belt than a v-

belt because the flexural rigidity of a v-belt is higher (cannot bend as much due to the moments

created by aligning forces).

21

OPTIMAL CROWN PULLEY COMBINATIONS

Thus far in the report, all of the relevant parameters that govern the behaviour of belt on crown

pulleys have been investigated. Now it is necessary to also address the issues of how different

combinations of crown pulleys have an effect on belt tracking. As mentioned in the introduction

of the report, there are two types of crown pulleys that are manufactured in the industry: tapered

and trapezoidal (Figure 1.2.3). SIEMENS currently uses trapezoidal drive and driven pulleys for

their conveyors. However, they are unsure of which combination of pulleys should be installed

on a conveyor system to yield optimal tracking results. The optimal tracking results are

characterized by how quickly a belt tracks to the center given all of the components of a

conveyor are perfectly aligned and the only tracking forces are generated by the crown pulleys.

Obviously, there will be cost savings associated with buying different kinds of pulleys and the

benefits that result from improved tracking. This section will present the results obtained from

conducting experiments of various combinations of pulleys and hope to clarify the issues at

hand.

3.1—APPROACH TO FIND OPTIMAL COMBINATION A small conveyor model was built to represent the conveyor system at SIEMENS. In addition,

scaled conveyor pulleys (tapered, trapezoidal, flat face drum) were manufactured in accordance

with CEMA standards. The model was built to allow for testing of different combinations of

pulleys and under varying belt tensions as will be explained in section 3.2. Most importantly, it is

designed such that experimental results can be reproduced.

22

The experiments will show how fast the

belt moves to the center or runs off the

pulley while all other conveyor

components are aligned. The two

common configurations of belt on

conveyor pulleys that are encountered in

the industry are shown in Figure 3.1.1.

Types of pulleys that were used in the

experiments (the only ones that are

manufactured in the industry) are as

follows:

Trapezoidal Crown Pulley denoted by C1.

Tapered Crown Pulley denoted by C2.

Drum Pulley denoted by D.

Combinations of drive-driven (i.e. C1-D where C1 is drive and D is driven) pulleys tested in the

experiment are the following:

C1-D

C1-C1

C2-D

C2-C2

C1-C2

D-D

The list above constitutes all of the possible combinations of pulleys that SIEMENS could

employ on their conveyor systems and hence the reason why they were tested. The experimental

Figure 3.1.1: Common belt configurations. In A, belt is off

centered to the left. In B, belt is oriented diagonally. L and

R are tensioners on left and right side, respectively.

A B

R L R L

23

results show how a particular crown pulley’s belt centering capability could be reduced or

enhanced in the presence of another type of a pulley.

Two belt configurations (Figure 3.1.1) were tested during the experiment. For each

configuration, two belt tensions were set. For each belt tension, two belt speeds (S1 and S2) were

established. Please refer to the data sheets in appendix B to see how various parameters were

grouped together during the testing. It is worth noting that it would have been sufficient to

conduct the experiments at one tension and one belt speed in order to determine the best pulley

combination. However, as will be shown in section 3.3, varying the tension and the belt speed

will provide further confirmation to some of the general conclusions drawn about crown pulleys

in section 2.

During the experiments, measurements were taken to determine how long it takes for the belt to

reach the center; hence, quantifying the effectiveness of crown pulleys. The belt recovery speed

(speed along tapered side of pulley) is obtained by taking the ratio of the distance the belt

traverses along the taper by the time the belt takes to reach the center (Figure 3.1.2). Please note

that there is a difference between the belt recovery speed and belt speed. In addition, belt

tensions were changed by using two rubber belts each with different unstretched lengths (Figure

6.3.1). Hence, the belt that has a smaller unstretched length would generate a higher belt tension

when it runs on the conveyor pulleys (refer to appendix D for belt tension calculations). The belt

speed S1 and S2 are set by adjusting the hand drill on two speed settings and then counting how

many revolutions (1 revolution = 60 cm) the belt traverses in some fixed amount of time. S1 was

found to be 6 cm/s and S2 was found to be 10 cm/s.

24

3.2—CONVEYOR SYSTEM MODEL A simplified small scale model (8.0:1.4) of a typical conveyor built at SIEMENS is built. An

actual conveyor has the following components that were included in the scale model:

20.0 cm Pulley diameters (crowned and drum conveyor pulleys)

76.2 cm wide rubber belt

Belt tensioner

The scale model has been manufactured out of hard wood (see Figure 3.2.1). The end pulleys are

made from 3.7 cm wooden dowel in accordance with current industry standards given by ANSI

and CEMA [2]

(a taper angle of approximately 1o). The rollers between the end pulleys are not

included in the model because it is assumed that they have minimal effect in the movement of

the belt and are perfectly aligned.

Figure 3.1.2: The belt recovery speed is calculated by

measuring the time it takes for point A on the belt to

travel distance Y. Once the belt is centered, there will

be equal distance Y on both sides of belt.

25

A 1.3 cm through hole is drilled in the pulley in order to insert the shaft (see appendix A for

pulley pictures). The shafts are force fitted into pulleys so that there is no relative motion

between the shaft and pulley and rotation occurs due to shaft turning alone. The widths of

pulleys are 16.5 cm while the rubber band width is approximately 13.7 cm. The maximum length

of the conveyor is 30.5 cm. Finally, the conveyor outer frame (to hold the shaft, pulley, and belt)

was manufactured using a CNC machine so that shaft holes would perfectly align. This would

ensure that the pulleys are not misaligned during the experiment. The shaft holes of the outer

frame contain ball bearings which securely hold the shaft during experiments. This significantly

improves the accuracy of the results as well as repeatability of the experiments.

The drive pulley will be driven by a hand drill that has a chuck big enough to hold the pulley

shaft (See appendix A for picture). The speed of the hand drill can easily be adjusted. The torque

from the belt wrap is considered negligible and does not have an effect on the rotational speed of

the shaft at a particular speed setting of the hand drill.

It is worth noting that the belt type (represented by a rubber band), tension, and coefficient of

friction will not be scaled from an actual conveyor built at SIEMENS. However, the

experimental data will reasonably show which crown pulley combination is the most effective.

26

Figure 3.2.1: Conveyor Scale Model. Note that bearings have been removed in the bottom picture

3.3—EXPERIMENTAL RESULTS/DISCUSSION & CONCLUSIONS In all the pulley combinations with different belt configurations, the belt always comes to the

center of the pulley and does not wander off. Therefore, crowning a pulley certainly helps in belt

tracking. The optimal pulley combination would have the fastest belt recovery speed for both

belt configurations. The results are presented next.

RESULTS & DISCUSSION

For the first case, when the belt speed is kept constant at S1 for belt configuration A, that data

shows that pulley combination C2-C2 has the fastest belt recovery speed (see Figure 3.3.1). In

27

addition we find that as the tension in the belt increases, the belt recovery speed decreases for all

pulley combinations. This trend is in close agreement with results from section 2.

At S1 and Config A

0.00

1.00

2.00

3.00

4.00

5.00

6.00

7.00

C1-D C1-C1 C2-D C2-C2 C1-C2

Pulley Combination

Be

lt R

ec

ov

ery

Sp

ee

d (

mm

/s)

T1

T2

Next, at belt speed S1 and belt configuration B, the belt recovery speed is the fastest for pulley

combination C2-D (see Figure 3.3.2). Also, not so surprisingly, as the tension increases in this

configuration (T1’ > T2’), the belt recovery speed rises. This was pointed out in section 2.1 and

the reason is that the forces in the belt help it move towards the center because of the diagonal

configuration of the belt.

From Figure 3.3.2, it is seen that the belt recovery speeds are significantly larger than the speeds

for configuration A. Again, the reason for this is the diagonal configuration of the belt. The

graph also has one other important feature. It can be observed that the D-D combination results

in the slowest belt recovery speed than any other combination of pulleys. This makes sense

because the flat faced drum pulley (D) only uses the tension in the diagonal belt to track the belt

while the crown pulley uses both the tension and the pulling effect of the crown to bring the belt

Figure 3.3.1: Belt recovery speed at S1 and Config A for each pulley combination. Also,

T1>T2

28

to the center. Hence, it is certainly advantageous to use crown pulleys when there is an absence

of any external source generating uneven tension in the belt such as a belt tensioner (the effect of

belt tensioner will be examined in a later section).

At S1 and Config B

0.00

5.00

10.00

15.00

20.00

25.00

30.00

35.00

40.00

45.00

C1-D C1-C1 C2-D C2-C2 C1-C2 D-D

Pulley Combination

Belt

Reco

very

Sp

eed

(m

m/s

)

T1'

T2'

Finally, to see the effect of

changing the belt speed S on the

belt recovery speed, please see

the graph in Figure 3.3.3 which

plots the recovery speed of the

belt at speed S1 and S2 for

tension T1.

Figure 3.3.2: Belt recovery speed at S1 and Config B for each pulley

combination. T1’>T2’

Figure 3.3.3: Belt recovery speed at T1 and A for each pulley combination.

S2 > S1.

At T1 and Config A (Trend true for B as well)

0.00

1.00

2.00

3.00

4.00

5.00

6.00

7.00

C1-D C1-C1 C2-D C2-C2 C1-C2

Pulley Combinations

Be

lt R

ec

ov

ery

Sp

ee

d

(mm

/s)

S1

S2

29

The graph shows that as the belt speed is increased from S1 to S2 (a higher rotational speed

setting on the hand drill), the belt recovery speed is also increased. This trend holds true for all

belt configurations. The result confirms Gerbert’s equation for v*c (belt recovery speed or

generatrix speed) which predicts that v*c decreases as the rotational velocity of the pulley

increases

CONCLUSIONS

From the graphs, it is certain that tapered crown pulleys (C2) are better than trapezoidal crown

pulleys (C1) in belt tracking. This is true because for both configurations A and B, C2-D

combination yields a higher belt recovery speed than C1-D combination.

The best pulley combination for belt configuration A is of C2-C2 and for configuration B is C2-

D. So, at first look, it is not easy to decide which one to choose. However, it would be correct to

say that C2-C2 should be considered the best pulley combination for all belt configurations

because it has the second fastest belt recovery speed for configuration B while C2-D does not for

belt configuration A. Therefore, two tapered crown pulleys should be employed to achieve

optimal belt tracking performance.

30

LIMITATIONS OF CROWN PULLEYS

So far in the report, it has been shown that crown pulley conveyor systems are capable of

improving belt tracking. However, experience has shown that if the lateral forces on the belt are

high, the crown pulley cannot help the belt center. These forces could be generated by uneven

distribution of material or due to misalignment of conveyor components. Obviously, it is not

possible to control all of the factors that might limit the functionality of a crown pulley. Hence

the reason SIEMENS has installed belt tensioners (Figure 1.2.4) on their conveyor systems for

greater belt tracking potential.

The purpose of this section of the report is to highlight the sensitivity of a crown due to the

misalignment of conveyor pulleys. Also, experimental results will be presented that give insight

into the behaviour of belt tracking on crown pulleys when belt tensioners are used.

4.1—BELT TRACKING EXPERIMENT “Belt Tracking Experiment” [13] paper, which was published by SAE in 1990, explains the

impact of crown pulley misalignment in automotive drive systems (similar to the one discussed

in section 2.2.2). The pulley misalignments are defined using the concept of toe and camber as

illustrated in Figure 4.1.1 below. The toe and camber, set for the test idler (crown pulley), angles

contribute to v-belt mistracking and results in lateral movement of belt on the pulley. A positive

toe and camber are defined as the angle that would cause belt motion in the positive direction.

[13] The test plan to quantify the effect of toe, camber, and crown is explained next.

31

(a)

(b)

Figure 4.1.1: (a) Toe and Camber Sign Conventions [13]. (b) is the test fixture used in experiments. Pulley

#2 belt wrap angle is less than 180o but can be adjusted to this angle.

32

TEST PLAN

A full factorial Design of Experiment was conducted to investigate the effect of toe, camber, and

pulley crown. The desired combination of toe, camber and crown was set on the test fixture

(Figure 4.1.1 b) and the position of the belt in motion was recorded as it rode over the backside

pulley (test idler #2). Belt tension was maintained at 534 N for all of the tests [13].

In order to quantify the effects of the pulley crown, an experiment was first conducted with flat

faced pulley (pulley #2 without crown) at some toe and camber. A second experiment for the

same toe and camber angles was conducted but this time with crowned pulley (pulley #2 is

crowned).

TEST RESULTS

The results for 1800 belt wrap angle (see graph in figure 6.4.1) show great sensitivity to belt

mistracking due to toe and camber angles and not much to the pulley crown. The results indicate

that toe and camber effects can add linearly to produce large belt mistracking if they both have

the same signs (sign convention in figure 4.1.1 a). In addition, the data shows that if toe and

camber have opposite signs, they can reduce the cumulative mistracking effect [13]. The pulley

crown helped neutralize the effect of toe and camber by small amounts but could not prevent

mistracking even for minute toe/camber angles. On average, every degree of camber caused over

two degrees of belt misalignment and a degree of toe caused about a degree of belt misalignment

[13].

33

The test results for smaller belt wrap angles (5 0) indicate that the sensitivity to toe and camber

decreases with decreasing belt wrap. In addition, figure 6.4.2 shows that camber induced belt

misalignment increases faster than toe induced belt misalignment at larger wrap angles.

CONCLUSION

The test pulley crown had very small impact in preventing the v-belt from mistracking due to the

induced toe and camber. In addition, based on statistical analysis of the data, belt misalignment

sensitivity to toe and camber increases proportional to the square of belt wrap angle [13].

The general conclusions reached based on v-belt experiments will also hold true for flat belts

running on crown pulleys in a conveyor system (at 1800 belt wrap angle) because the inherent

nature of belt tracking is the same. However, if one needs to obtain empirical data for flat belts

running on two crown pulleys, it is recommended to build a test fixture similar to the one used in

these experiments and refer to the original SAE paper for more details. It is true that two crown

pulleys together in a conveyor system would have a greater effect in preventing lateral belt

movement but there is no guarantee that this would suffice if toe and camber angles are big.

REFERENCE MATERIAL

For more information on camber effects on belt tracking, please refer to reference [16]

4.2—USE OF BELT TENSIONER

A brief description about belt tensioners was given in section 1 of the report. Belt tensioners

exploit the concept of toe angle, as discussed in the previous section, to bring the belt back to the

center if it mistracks. The underlying principle is that a belt moves from the side that has high

34

tension to the side that has low tension. This phenomenon is analogous to water moving from

high pressure to low pressure, or heat flowing from hotter body to colder body, etc.

A belt tensioner is employed once the crown pulleys cannot prevent the belt lateral movement. A

worker usually spots the belt movement and follows the procedure as outlined in section 1.2 to

center the belt. The procedure is best suited for pulleys that are not crowned and SIEMENS

wants to know what would happen if the same procedure is used for crowned pulleys. Based

solely on intuition and research that was presented in section 4.1, it would be safe to assume that

crown pulley effects become miniscule in comparison to the toe effect (i.e. belt tensioner).

Hence, the induced toe created by the tensioner should generate enough force that may aid in belt

tracking if the proper procedure is followed.

The effect of belt tensioner on belt tracking will be analyzed for different combinations of

pulleys in different belt configurations by conducting experiments on the conveyor model.

APPROACH/METHODOLOGY

In this experiment, the focus is on observing how the belt moves laterally when a belt tensioner

is used on the tail (driven) pulley. There is no requirement on belt tension except for the fact that

it should be large enough to prevent any belt slippage. The belt which was used for these

experiments had an unstretched length of 25 cm and a spring constant equal to 227 N/m.

Similarly, there is no need to use a hand drill to rotate the shaft because neither belt speed nor

belt recovery speed is of any use. Therefore, the shaft can be rotated with hands at a moderate

pace (1 rev/sec).

35

The objective is to test each of the two common belt configurations (shown in Figure 3.1.1) with

the right and the left belt tensioner (on the tail pulley) extended as shown in Figure 4.2.1. In each

case, the belt tensioner stroke is the same (2.5 cm) so that the toe angle generated on the tail

pulley remains the same.

BR AR

BL AL

Figure 4.2.1: BR and BL will test the effect of tensioner in belt configuration B.

AR and AL will test the effect of tensioner in belt configuration A.

36

The four tensioner cases shown in Figure 4.2.1 were tested for each pulley combinations

mentioned in section 3.1 (i.e. C1-C1, C2-C1, C1-C2, C2-C2, C1-D, C2-D, and D-D). All of these

combinations were tested because SIEMENS is unsure of which combination of pulleys should

they install on their conveyor systems that would give the best results with a belt tensioner. As

for the D-D combination, it is used to quantify how much the crown pulley can hinder the belt’s

lateral movement given the forces generated by the toe angle from the belt tensioner. Finally,

during the experiments, belt revolutions are counted until the belt runs off the pulley.

RESULTS & DISCUSSION

In all the experiments, the belt always runs off the tail (driven) pulley and moves to the side it

touches first. For instance, for case BL and AL in Figure 4.2.1, the belt moves to the left side.

The opposite is true for case AR and BR for which the belt moves to the right side. Another

important feature that was observable was that the belt, before running off the pulleys, oriented

itself perpendicular to the drive pulley. So even though the initial belt configuration for BR and

AL is diagonal, the tensions in the belt adjust it such that the belt becomes perpendicular to the

drive pulley as it is running off the pulleys. It is clear that the crown pulley cannot prevent the

belt’s lateral movement due to the induced tail pulley misalignment as hypothesized earlier.

The graph in Figure 4.2.2 shows how many revolutions it takes for the belt to run off the pulley

for different belt tensioner cases (BR, AL, BL) and different combinations of pulleys. The AR

case is not included because the belt runs off the pulley in less than 0.2 revolutions for all pulley

combinations. As a result, the belt tensioner case AR should never be used when centering the

belt using a tensioner. It is observed from the graph that C2-C2 combination takes the highest

37

number of belt revolutions (the longest time) to run off the pulley for each of the belt tensioner

case than any other pulley combination. Hence, if it is desired to center the belt quickly using a

belt tensioner, C2-C2 combination should be avoided. Next, it is seen that the tensioner case BR

takes significantly less belt revolutions to run off the pulley than the other two cases. This is true

because the high diagonal belt tension forces the belt to quickly align perpendicular to the drive

pulley while at the same time, it is moving to the left due to the pulley angle created by the

tensioner.

Finally, it is important to note that crown pulleys counter the forces generated by the belt

tensioner toe angle but they cannot prevent the belt from running off the pulleys. This is seen in

the graph of figure 4.2.2 by comparing the stacked column of D-D (two flat faced pulleys) with

the rest of crown pulley combinations. Clearly, D-D takes the least number of belt revolutions

(shortest time) for all three tensioner cases to run off the pulley. Therefore, if both the drive and

tail (driven) pulleys are crowned, the belt movement in the lateral direction will be very slow if a

tensioner is used.

CONCLUSION

A belt tensioner can definitely help center the belt if crown pulleys are unable to do so. The

procedure outlined in section 1.2 is very much applicable to a conveyor system with crown

pulleys or flat faced pulleys. The difference is that it may take longer for the crown pulley

conveyor systems to center the belt than a flat faced pulley conveyor system. If a belt is oriented

like in configuration B (Figure 3.1.1) and a belt tensioner is used because the crown pulley

cannot track the belt, one may find that the belt is moving in an unusual manner. This happens

38

because the belt first tries to align perpendicular to the drive pulley while at the same time it is

moving towards the low tension side. The procedure to tackle this problem will be presented in

section 5 of the report.

Belt Run-off Revolutions v.s. Pulley

combinations for Three Belt Tensioner Cases

0

5

10

15

20

25

C2-C2 C1-C2 C2-C1 C1-C1 C1-D C2-D D-D

Pulley Combination

Be

lt R

ev

olu

tio

ns

to

Ru

n

off

Pu

lle

y

BR AL BL

Figure 4.2.2: Graph shows how many revolutions it takes for the belt to run off the pulley for different belt

tensioner cases (BR, AL, BL) and different combinations of pulleys.

39

SOLUTION FOR CROWN PULLEY SYSTEMS

In the previous sections of the report, a thorough analysis of crown pulley conveyor systems was

presented. The goal of this section is to propose a solution to the crown pulley system so that belt

tracking is made easier and efficient.

Rich Gilman, a technical services manager at Flexco USA, claims in his article “How to track

mistracking belts” [14] that there are two approaches to fixing belt tracking problems: one could

either “eliminate the cause” or “treat the symptom.” The cause of belt mistracking has been

discussed in earlier sections and can be summarized as follows:

Misaligned pulleys and idlers (rollers) are not perpendicular to the structure of the

conveyor.

Pulley faces are not clean because material build-up can have the effect of making pulley

diameter inconsistent across the pulley face [14].

Belt splices, if any, are not square with the centerline of the belt. Belt splices are usually

mechanical or vulcanized (chemically bonded) which replace or fix any damaged part of

a conveyor belt with a new belt.

Uneven deposit of material onto the conveyor [9].

CEMA has outlined, in detail, methods to eliminate the above mentioned flaws and should

strictly be followed especially when installing new conveyor systems. However, in real life, there

will always be some tracking problems due to unknown factors. In such cases, eliminating the

true cause of the problem might result in substantial effort, downtime, and expense. Therefore, it

40

would be faster, cheaper, and easier to treat the “symptoms” of mistracking instead of the

“cause”. This section will discuss ways to treat the symptoms of belt mistracking in light of the

research that has been presented thus far in the report.

5.1—IMPROVEMENTS TO CURRENT CROWN PULLEY SYSTEM

5.1.1—CROWN PULLEYS

Research has shown that increasing the taper angle of the crown pulley can center a belt quickly

in comparison to other factors such as friction (produced by the pulley lagging). For instance, if

the taper angle and friction are doubled, the belt recovery speed for larger taper angle would be

twice as fast while for greater friction it would be approximately 1.2 times as fast (see Figure

2.2.4). Hence, taper angle on crown pulleys should be maximized within reasonable values

acceptable for belt life and should be at least the industry standard if not more.

Next, experiments in section 3 have shown that tapered crown pulleys generate stronger belt

tracking forces than trapezoidal or flat faced pulleys. Hence, these should be incorporated into

the conveyor system. Again, the cost of belt wear produced by trapezoidal and tapered crown

pulleys should be weighed against the benefit of belt tracking provided by the two types of

pulleys. If belt mistracking is frequent and leads to dire consequences, then it would be advisable

to use tapered crown pulleys at the expense of higher maintenance costs.

5.1.2—FREE BELT LENGTH

The concept of free belt length (entry span length) has a great impact on the efficiency of crown

pulleys. The conveyor shown in Figure 5.1.1 is different than the one built at SIEMENS, but it

41

does have common components such as the return idler 10 and other idlers such as 13, 14, 15 and

1. Research has shown that for the tail crown pulley to have maximum efficiency, the distance

between idler 10 and pulley 11 (as the belt approaches 11) should be around 3 meters [9]

Lengthening the free belt length beyond 3 meters will not further increase the efficiency but

decreasing would reduce the effectiveness. Snub pulleys can reduce effectiveness by 50% or

more [9]. Same proposition holds for a drive pulley 16 in Figure 5.1.1. If the distance between

roller 15 and pulley 16 is small, the drive pulley should not be crowned because the high tension

at the crown edge of the drive pulley would cause belt wear.

Figure 5.1.1: A conveyor model. [9]

5.1.3—BELT TENSIONER

When a belt tensioner (attached to the tail pulley) is used to track a belt, it is recommended to

follow the following procedure if confronted with belt configurations similar to A or B as shown

in Figure 3.1.1:

Belt Configuration A: To prevent the belt from running off the pulley on the left side,

worker should increase the RIGHT belt tensioner stroke length until the belt starts

42

moving to the right. The increase in length is towards the drive pulley. When the belt is

centered, the induced toe angle by the tensioner stroke should be eliminated in order to

realign the tail pulley perpendicular to the belt.

Belt Configuration B: In this belt configuration, one can be faced with three scenarios:

1) The belt on the drive pulley is moving to the left and is about to run off the pulley

(Figure 5.1.2). In such a case, the right tensioner stroke should be extended towards

the drive pulley. The belt will behave similar to case BL as shown in Figure 4.2.1.

During the process, the belt would orient itself such that it is perpendicular to the

drive pulley, and at the same time, it would first drift towards the center and then to

the right. It is worth noting that the belt will not run off the pulleys until it has

achieved this perpendicular configuration similar to A. Once the belt is in

configuration A, or is close to it, the “R” tensioner should be restored to its original

stroke and the procedure for belt configuration A should be followed to center the belt

using the tensioner.

Figure 5.1.2: Belt configuration B with two belt tensioners L and R

43

2) In the second scenario, the belt is running to the right on the tail pulley as shown in

Figure 5.1.3. Therefore, the “L” tensioner should be extended towards the drive

pulley. The situation would be similar to case BR shown in Figure 4.2.1. The belt

would orient itself to run perpendicular to the drive pulley and would be off centered

similar to belt configuration A. Once the belt is in configuration A, or is close to it,

the “L” tensioner should be restored to its original stroke and the procedure for belt

configuration A should be followed to center the belt using the tensioner.

Figure 5.1.3: Belt configuration B with two belt tensioners L and R

3) The worse scenario is when the belt is running off the drive and the tail pulley and is

close to the edge. In such a case, there are no set rules to follow when using a belt

tensioner. Ideally, it would be easiest to shutdown the conveyor and realign the belt

manually. However, if the belt is not too close to the edge, then the worker should spot on

which side (tail or drive) the belt is running off quicker. Based on this decision, one

should follow the procedures 1 or 2 for the side on which the belt is running off fast. The

44

belt will initially move towards the center but will probably not orient itself perpendicular

to the drive pulley (depends on how influential the external factors are which are causing

the belt misalignment). If it does then the procedure for belt configuration A should be

followed to center the belt. If it does not, then the belt tensioner stroke should be restored

to its original length and step 3 should be repeated again.

5.2—AUTOMATIC BELT TRACKING Crown pulleys have their limitations in belt tracking. Therefore, some other method such as a

belt tensioner has to be employed to center the belt if excessive external forces are acting on it. A

belt tensioner may not be the most effective solution to belt tracking if the frequency of

mistracking is high. A worker would always have to keep an eye on the conveyor and follow a

detailed procedure to realign the belt whenever it mistracks. Hence, it is common to install an

automatic belt tracker on a conveyor system, between the drive and tail crown pulleys, which

detects belt movement and takes the necessary steps to bring the belt back to the center.

There are two types of automatic trackers in the industry: the pivoting kind and the tilting kind.

The pivoting kind uses the principle of toe angle while the tilting kind uses the concept of

camber angle as discussed in section 4.1. Figure 5.2.1 shows the tilting belt tracker. The

mistracking belt pushes against the sensing guide rollers which activate the control cylinders.

The cylinders push on the belt and create uneven tension which forces the belt to move to the

center.

45

Figure 5.2.1: Tilting automatic belt tracker. [20]

An automatic tracker is usually powered pneumatically, hydraulically, or electromechanically.

However, there are also mechanically driven trackers that do not require an input of energy.

SIEMENS is quite interested in these types and wants to know which ones are available in the

industry. The sections that will follow will discuss some designs available for mechanical

automatic belt trackers and how they aid in belt tracking.

5.2.1—PT Max Belt Tracker by Flexco

Research on various suppliers of belt trackers (i.e. Sandvik, Eckles-Bilt, MATO Industries etc)

has shown that mechanically driven trackers are usually the pivoting kind. However, the PT Max

Belt Tracker from Flexco uses both the pivoting and tilting action to center the belt. It was shown

in section 4.1 that the cumulative effect of the two actions (toe and camber) could greatly effect

the movement of belt on a conveyor pulley. Figure 5.2.2 shows a picture of the PT Max belt

tracker for the top side belt. Please note that Flexco has not explained how their tracker works

46

because of its patented design. So the information given next on the functionality of this tracker

is solely based on research presented in this paper and some details revealed by the engineering

department at Flexco. Although PT Max is a good design and could be installed onto a conveyor,

the hope is to understand its function so a better design could be developed.

HOW PT MAX WORKS

In Figure 5.2.2, if the belt travel is in the negative x-direction and starts to drift in the positive y-

direction, the belt will engage with sensing guide rollers 2. When this happens, a moment is

created about the z-axis in the clockwise direction due to the offset distance L. This moment

causes the rollers to turn in the same direction as the guide rollers. The resulting configuration is

shown in 5.2.3. The induced toe angle by the rollers causes the belt to move to the right and

begins to push against sensing rollers 1. As the belt traverses to the right, the rollers realign

perpendicular to the belt travel. At the same time, the tracker would tilt slightly about the x-axis

in clockwise direction because of the offset distance D of sensing roller 1. This induces a toe

angle which further helps the belt track to the center. The tilting effect is highly dependent on

how fast the belt is drifting and the distance D (greater the better).

47

Figure 5.2.2: PT Max Belt Tracker. The central pivot allows it to pivot around the z-axis and tilt about the x-axis

[17].

Figure 5.2.3: The pivoting acting on PT Max. The belt is initially drifting in the positive y direction.

48

THINGS TO CONSIDER—NEXT STEPS

The following things should be investigated before installing this automatic belt tracker:

Cost of the automatic belt tracker.

Belt wear that is induced.

The weight of the tracker is enormous and needs a lifting crane to install [17].

Maintenance issues.

5.2.2—Tilt Belt Tracker

From market research and the v-belt experimental results presented in section 4, it is certain that

camber effects have a significant impact on belt tracking. Hence the reason why there are many

companies selling pivoting trackers. The mechanics and factors that govern the movement of flat

belt on a pivoting roller, with belt wrap angles smaller than 20 0) have not been investigated in

this report and should be considered a future research topic.

The toe effects (i.e. used by tilt trackers), on the other hand, simply use the principle of applying

a force on the side of the belt that is drifting outwards in order to increase the tension on that

side. This causes the belt to drift in the opposite direction towards the center (just like a belt

tensioner). This section will present a mechanism design of an automatic belt tracker which uses

the principles of a tilt tracker similar to the one that SIEMENS is planning to install but is not

manually operated. The hope is that with slight modifications to the design presented in this

report, SIEMENS will transform its manual tilt belt tracker to an automatic tilt tracker at almost

no additional cost and within the same available space. Further modifications could also take into

account the principles of camber effects (after doing the necessary research).

49

HOW TILT TRACKER WORKS

The tilt tracker is shown in Figure 5.2.5. This automatic tracker works by using the force of the

mistracking belt to create uneven weight distribution about a pivot point. This creates a moment

about the pivot point which causes the roller to tilt. The principle is best illustrated with the free

body diagrams in Figure 5.2.4.

Initially, the forces are balanced and there is no moment generated about pin O. However, if F is

displaced by a small distance dL as shown in Figure 5.2.4 b, moment will generate about O and

would equal:

))((2

)()(

dLFM

dLLFdLLFM

o

o

Figure 5.2.4: Free Body Diagram (FBD) of the tilt tracker mechanism.

50

Now consider the force Fb shown in Figure 5.2.4 (c) that acts to counter the moment M0. Fb is

calculated as follows:

)(

))((2

)())((2

dLL

dLFF

dLLFdLFM

b

bo

Eq 5.2.1

It is this force Fb that the tilt tracker applies on a mistracking belt to center it. The mechanism

shown in Figure 5.2.5 is designed to move some weight (F) by small distance (dL) in order to

generate force Fb on the belt. The objective is to maximize Fb within the reasonable limits of a

belt’s life so that the belt tracks quickly to the center.

DETAILS OF MECHANISM

The holding rod of the mechanism is fixed to the conveyor stringer (Figure 6.5.1). The pivoting

rod rotates about the pivot pin when the mistracking belt pushes against the sensing guide rollers.

These rollers push the steel wheel by a small distance (wheel does not have much space to move)

which in turn moves the mass plates. The mass plates (represented with F in Eq 5.2.1) always

remain parallel to the ground. Once the mass plates on either side of the tracker are displaced

from equilibrium position, the pivoting rod will rotate and apply force Fb on the belt. The belt

will start drifting to the opposite side from the high tension side to low tension side. In the

process, it will push on the other sensor guide roller which will bring the two steel wheels back

to the equilibrium position. Note that the sensor rollers will also pivot with the pivoting rod.

IMPORTANT FEATURES

Some features of the mechanism are critical for proper functioning. First, the pair of sensor guide

rollers on each side of the tracker should be equally spaced in order to eliminate any moment on

51

the steel wheel (created about the y-axis). Also, the distance between the pair sensor rollers on

each side of the tracker should be minimized so that the drifting belt has contact with both of

them.

Next, it is desirable to minimize the pivot angle of the pivoting rod when the steel wheel

displaces the mass plates because the sensor rollers also pivot with it. If they tilt too much, the

belt may not make adequate contact to exert pressure to move the steel wheels. Hence, the

control of the pivoting rod is accomplished by limiting the space of the steel wheel to move in

the x-direction. Less movement of the wheel results in a reduced value for “dL” in equation

5.2.1. So in order to maximize the force on the belt “Fb”, mass plates “F” should be increased.

It is obvious that F cannot increase indefinitely because a belt may not be able to push this mass

on the wheel. The rolling friction (assuming no slippage) generated between the steel wheel and

the steel container is give by ))(( CrrFF Nf , where FN is the normal force and Crr is the

coefficient of rolling friction. FN in this case is equal to F and Crr is obtained from experiments

and equals 0.001 [18] for steel. So, the friction force (Ff) generated due the mass plates should be

provided by the mistracking belt in order to move the steel wheels. To get an idea of how much

force a drifting belt can exert, some experiments must be conducted. For instance, a belt with

varying drift speeds can push against a load cell which would output a force value.

Finally, the steel wheel moving space must remain clean (i.e. no material build-up) at all times.

A possible solution is to completely enclose the wheel so material cannot enter.

52

Figure 5.2.5: The tilt tracker with important components labelled.

CONCLUION

The attempt of this section was to provide SIEMENS with a mechanism that can effectively and

automatically track a belt. The tilt tracker mechanism proposed in this section resembles closely

with the manual tracker that SIEMENS currently uses (not included here due to patent issues).

Hence, with slight modification to the mechanism and a detailed machine design analysis (stress,

deflections, fatigue, etc) the tracker could perform its intended function very efficiently.

53

FIGURES & TABLES

6.1—Section 1: Introduction

6.2—Section 2: Important Parameters of Crown Pulleys

Figure 6.2.1: Definition of belt wrap angle around a pulley [15].

Figure 6.2.2: Comparison between theory and experiments. Experimental and theoretical data was obtained for μ =

0.4, B/R = 0.6, and A/R = 9. The solid line shows the theoretical curve while the empirical data points closely follow

the solid line curve [8].

54

6.3—Section 3: Optimal Crown Pulley Combination

Figure 6.3.1: Two belts are used to vary tension during experiments. Left one has an unstretched length of 27 cm.

Right one has an unstretched length of 25 cm.

(A) (B)

Figure 6.3.2: (A) represents belt configuration A. (B) represents belt configuration B.

55

6.4—Section 4: Limitations of Crown Pulleys

Figure 6.4.1: Belt misalignment (in mm) at 0.2 mm Crown and 180o belt wrap angle. [13]

Figure 6.4.2: Toe and Camber induced belt misalignment sensitivity to belt wrap angle [13]

56

Figure 6.4.3: Belt misalignment (in mm) at 0.2 mm Crown and 5o belt wrap angle. [13]

Figure 6.4.4: Belt tensioner case AL. The tail pulley is misaligned to mimic a belt tensioner.

57

6.5—Section 5: Propose a Solution

Figure 6.5.1: Tilt tracker attached to conveyor structure (stringer)

Figure 6.5.2: Tilt tracker front view.

58

Figure 6.5.3: Tilt tracker top view.

59

REFERENCES

[1] “Teletrak Conveyor Components.” 2008. [online]. Available:

http://www.kaveri.in/products_conveyor_belttracking.asp. [Accessed : Jan 5, 2009]

[2] Conveyor Equipment Manufacturer’s Assocaition, Belt Conveyors for Bulk Materials.

New York 2005.

[3] “Teletrak Conveyor Components.” July 2001. [online]. Available:

http://www.bryantpro.com/prodlit.asp. [Accessed : Jan 31, 2009]

[4] Catalog WT 02-2007, Continuous Weighing and Process Protection, SIEMENS AG,

Germany.

[5] “Belt Tracking Hi Life Models.” Oct. 19, 2001 [online]. Available:

http://www.hiroller.com/PDF/Ex_BeltTrackingHiLife.pdf, [Accessed: Dec 21, 2008]

[6] Butler Jutice. “Pulleys.” 2005 [online] Available:

http://www.butlerjustice.com/pulleys.html, [Accessed: Dec 20, 2008]

[7] John D. Cutnell and Kenneth W. Johnson. Physics 7Ed. New York: Wiley, 2007.

[8] Gerbert, Goran. “Flat belt axial motion on conical pulleys,”American Society of

Mechanical Engineers, Design Engineering Division (Publication) DE, v 88, 1996, p 443-

452

[9] “Belt Tracking.” Oct. 2003. [online]. Available:

http://www.fennerdunlopamericas.com/pdf/TrackingFDA0105.pdf, [Accessed: Oct 10,

2008]

[11] Russell Gross, and Richard Meckstroth, “V-Ribbed Belt Backside Pulley Belt

Mistracking” SAE Paper 980836.

[12] Sam Memmolo. “Technology Corner.” 2009 [online]. Available:

http://www.shadetreemechanic.com/images/cummins%20turbo%20diesel%20drive%20s

ys%204.jpg, [Accessed: Feb 15, 2009]

[13] R.Ahoor, and R.J. Meckstroth, “Belt Tracking Experiment” SAE Paper 901770.

[14] HOW TO CORRECT MISTRACKING BELTS.

Coal Age; Jul2005, Vol. 110 Issue 7, p52-53, 2p, 3 color

[15] “Design.” [online]. Available: http://www.rubberfix.com.au/images/wrap_angle_1.gif.

[Accessed: March 2, 2009]

60

[16] Barfoot, G.J.: Quantifying the Effect of Idler Misalignment on Belt Conveyor Tracking;

bulk solids handling Vol. 15 (1995) No.1, pp. 33-35.

[17] “PT Max.” Internet: http://www.flexco.com/products/pt_max_belt_positioner, [2008]

[18] Wikipedia. “Rolling Resistance.” March 23 2009 [online]. Availble:

http://en.wikipedia.org/wiki/Rolling_resistance, [Accessed: Mar 5, 2009]

[19] Catalog PS-454 ENG7.2008, Sandvik-Active Steel Belt Tracking Control, Sandvik

Process Systems, Germany.

61

APPENDIX A

Starting from left: Two trapezoidal crown pulleys, two tapered crown pulleys, one flat faced pulley.

Hand Drill attached to the shaft of drive pulley with a 0.5” chuck

Chuck holding the

drive pulley shaft

62

APPENDIX B

Pulley

Combination

Belt

Configuration

Distance travelled by

belt along the pulley to

center (cm).[Distance Y

shown in Fig 3.1.2]

Belt Tension

(Stretch of the belt).

T1 > T2 and

T1'>T2'

Speed

Variation

Average

(mm/s)

0.87 0.74 0.80 0.80

1.33 1.11 1.23 1.22

0.78 0.67 0.73 0.73

1.17 1.13 1.14 1.15

23.50 22.90 23.20 23.20

33.30 32.10 33.00 32.80

22.20 22.60 22.10 22.30

30.10 29.60 30.20 29.97

20.10 20.30 19.70 20.03

28.50 28.40 28.50 28.47

17.40 17.80 16.50 17.23

26.90 26.00 28.10 27.00

Observation (Speed to reach

center) mm/s

T2

S1

S2

T1

S1

S2

S1

S2

T2'

S1

S2

EXPERIMENTAL DATA SHEET

C1-D

T1'

S1

S2

T2'

S1

S2

B

T1'

2.00

2.00

B Two Flat Pulley 2.00

A

63

Pulley

Combination

Belt

Configuration

Distance travelled by

Belt along the pulley

to center

(cm).[Distance Y

shown in Fig 3.1.2]

Belt Tension (Stretch

of the belt). T1 > T2

and T1'>T2'

Speed

Variation

Average

(mm/s)

3.08 3.00 2.98 3.02

4.34 4.40 4.32 4.35

2.10 2.26 2.13 2.16

2.97 3.10 2.89 2.99

22.20 21.80 21.70 21.90

40.00 40.80 40.00 40.27

15.70 15.80 15.90 15.80

30.60 30.30 30.20 30.37

20.10 20.30 19.70 20.03

28.50 28.40 28.50 28.47

17.40 17.80 16.50 17.23

26.90 26.00 28.10 27.00

EXPERIMENTAL DATA SHEET

Observation (Speed to reach

center) mm/s

C1-C1

A 2.00

T2

S1

S2

T1

S1

S2

B 2.00

T1'

S1

S2

T2'

S1

S2

B Two Flat Pulley 2.00

T1'

S1

S2

T2'

S1

S2

64

Pulley

Combination

Belt

Configuration

Distance travelled by belt

along the pulley to center

(cm).[Distance Y shown in

Fig 3.1.2]

Belt Tension

(Stretch of the belt).

T1 > T2 and

T1'>T2'

Speed

Variation

Average

(mm/s)

3.45 3.30 3.39 3.38

7.14 7.20 7.20 7.18

2.60 2.65 2.70 2.65

5.30 5.40 5.27 5.32

42.30 41.70 42.10 42.03

50.00 48.60 48.70 49.10

33.30 34.50 34.10 33.97

41.50 41.80 41.20 41.50

20.10 20.30 19.70 20.03

28.50 28.40 28.50 28.47

17.40 17.80 16.50 17.23

26.90 26.00 28.10 27.00

EXPERIMENTAL DATA SHEET

Observation (Speed to reach

center) mm/s

C2-D

A 2.00

T2

S1

S2

T1

S1

S2

B 2.00

T1'

S1

S2

T2'

S1

S2

B Two Flat Pulley 2.00

T1'

S1

S2

T2'

S1

S2

65

Pulley

Combination

Belt

Configuration

Distance travelled by

belt along the pulley to

center (cm).[Distance

Y shown in Fig 3.1.2]

Belt Tension (Stretch

of the belt). T1 > T2

and T1'>T2'

Speed

Variation

Average

(mm/s)

6.14 6.10 6.15 6.13

7.14 7.20 7.20 7.18

4.96 5.10 5.00 5.02

6.20 6.24 6.20 6.21

31.25 32.00 32.10 31.78

38.20 37.80 37.00 37.67

25.80 25.90 26.30 26.00

30.20 30.30 30.00 30.17

20.10 20.30 19.70 20.03

28.50 28.40 28.50 28.47

17.40 17.80 16.50 17.23

26.90 26.00 28.10 27.00

EXPERIMENTAL DATA SHEET

Observation (Speed to reach

center) mm/s

C2-C2

A 2.00

T2

S1

S2

T1

S1

S2

B 2.00

T1'

S1

S2

T2'

S1

S2

B Two Flat Pulley 2.00

T1'

S1

S2

T2'

S1

S2

66

Pulley

Combination

Belt

Configuration

Distance travelled by

Belt along the pulley to

center (cm).[Distance Y

shown in Fig 3.1.2]

Belt Tension

(Stretch of the belt).

T1 > T2 and

T1'>T2'

Speed

Variation

Average

(mm/s)

4.23 4.40 4.30 4.31

6.94 7.14 7.09 7.06

3.35 3.20 3.30 3.28

4.46 4.32 4.45 4.41

22.40 22.50 22.30 22.40

33.30 33.80 32.90 33.33

18.30 18.60 18.10 18.33

29.70 29.80 29.80 29.77

20.10 20.30 19.70 20.03

28.50 28.40 28.50 28.47

17.40 17.80 16.50 17.23

26.90 26.00 28.10 27.00

EXPERIMENTAL DATA SHEET

Observation (Speed to reach

center) mm/s

C1-C2

A 2.00

T2

S1

S2

T1

S1

S2

B 2.00

T1'

S1

S2

T2'

S1

S2

B Two Flat Pulley 2.00

T1'

S1

S2

T2'

S1

S2

67

APPENDIX C

68

APPENDIX D

The procedure below shows the how the spring constant for conveyor model belt was obtained.

Any elastic material obeys the Hooke’s Law which is defined as F = kx.

For the rubber belt, a mass of 0.5 kg was attached and the deflection of the rubber was measured

with a ruler. Then the spring constant (k) is determined by the ratio of the force and the

deflection. The table below shows the different values that were obtained from the test:

Force (F) Deflection (x) Spring Constant (k)

9.81 N 2.1 cm 233 N/m

9.81 N 2.2 cm 222 N/m

9.81 N 2.15 cm 228 N/m

AVERAGE 227 N/m

Hence, the spring constant of the belt is 227 N/m.

Belt tensions in the initial configurations for the experiments conducted in section 3 are

calculated as follows:

Unstretched

Length

(cm) A B

Stretched Length

(cm)

Tension

(N)

Stretched Length

(cm)

Tension

(N)

Belt 1 27 30 6.8 30 8.1

Belt 2 25 30 11.4 30 12.7

NOTE: A and B are the two belt configurations tested during the experiments. For

configuration B (Figure 3.1.1), the stretch in the belt is determined by measuring the

diagonal distance.

69