belt tracking
Post on 16-Apr-2015
58 Views
Preview:
DESCRIPTION
TRANSCRIPT
- i -
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
v
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
- 1 -
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
10
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]
14
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
top related