Belt drives
Updated April 2008
Purpose
To develop the knowledge and skills required to carry out the selection
of a wedge belt drive system.
Objectives
At the end of this section you should be able to:
- Describe the various types of belt
drive
-
Select a suitable wedge belt for a given power transmission
-
Select suitable pulleys and determine the speed of the driven shaft
-
Determine the centre distance between the pulleys and pitch length of
the belt
-
Determine the number of belts required
-
Determine the radial (overhung) load caused by a belt drive given the
ratio of the belt tensions
-
Finalise the design, including selection oftaper lock bushes (if used)
Belt drives are widely used for transmitting rotational mechanical
power from one rotating shaft to another. They are light, inexpensive,
quiet and capable of transmitting reasonably large amounts of power.
There are several manufacturers/distributors of belt drives in
Australia. The data in the manual was taken from the Fenner Catalogue.
Belt drive pulleys can be plain bushed or taper bushed for use with
taper-lock bushes. All the pulleys supplied by Fenner are of taper-lock
bush type. The advantage of the taper-lock bush is that no key is
required, it is easy to install and does not weaken the shaft (does not
cause as much stress concentration) as a keyed bush.
There are many types of belt drive but for the purposes of this module
you need only to be able to select the wedge belt type. These are a
type of vee belt that have largely superseded the older type of vee
belt. They have a deeper profile and are capable of transmitting more
torque and power than the older type.. The two types are
interchangeable on the pulleys, so even if a vee belt was originally in
place, it can be replaced by a wedge belt if necessary without changing
the pulleys.
The power that can be transmitted by a wedge belt drive depends upon a
number of factors, namely:
The angle of contact
The greater this is, the more torque and power can be transmitted. If
both pulleys are not of the same diameter, then the smaller pulley is
the one that determines the maximum torque and power that can be
transmitted. Not only does the smaller pulley have a shorter length of
contact, but it also has a smaller angle of
contact than the larger pulley, so it will always be the first to slip.
In cases where the pulleys are not the same diameter, the angle of
contact will
depend also upon the centre distance between the shafts. The greater
the centre distance, the greater the angle of contact. For this reason,
centre distances should not be below the recommended minimum value (sum
of the pulley pitch diameters) unless there are special circumstances.
The wedge angle of the belt (and groove).
Because you will be selecting a standard belt you are not able to
change this angle which is usually 34° or 38° depending upon the size
of the belt and the size of the pulleys.
The coefficient of friction.
You have little control over this because it is determined by the belt
material and the pulley material (and finish). In practice it is
important to keep oil and grease off the belt and pulleys because this
will reduce the friction (and could deteriorate the belt). Why would it
not be a good idea to use a rough surface on the pulley to increase the
coefficient of friction?
The pulley diameters.
The larger the diameters, the greater the torque and power. This is
simply because for a given belt tension force, the larger the pulley,
the larger the torque (torque = force x radius) and hence the greater
the power for a given speed. This is why it is not a good idea to
choose pulleys that are too small. On the other hand if the pulleys are
too large, the belt speed increases, centrifugal tension increases and
the drive takes up more space. So a reasonable compromise is needed
when choosing pulley pitch diameters.
Initial belt tensions.
The higher the initial tension in the belts, the greater the torque and
power that can be transmitted. At rest, when no power is being
transmitted, the belt tensions are equal on both sides of the pulleys.
As the pulleys rotate and transmit power, the belt tension rises in one
side (tight side) and reduces in the other (slack side). However, the
sum still stays the same. When the ratio of the belt tensions reaches a
certain limiting value, slipping will occur. Hence the greater the
initial tension in the belts, the greater the torque and power that can
be transmitted before slipping occurs.
However, it is not a good idea to have too much tension because this
will place high radial loads on the shaft and bearings and also will
reduce the belt life considerably. For this reason, initial belt
tensions should be set carefully. In their catalogue, Penner detail the
practical method for pre-setting the belt tensions. This method
requires a belt tension indicator (which is really just a force gauge)
that measures the force at the centre of the belt required to cause a
standard deflection (16 inn per m of span). There is a recommended
value for this force that should be adhered to when the belt drive is
initially installed.
As the belt wears, the initial tension needs to be re-set, so the
designer should allow for an adjustment method. Adjustment can be
provided by moving one shaft further away from the other or by means of
an adjustable jockey pulley. This pulley should be located on the
inside of the drive on the slack side as close as possible to the
larger pulley and should have a diameter at least equal to the smaller
pulley.
The size of the belt.
The larger the belt section, the greater the tension that can be
carried by the belt and the greater the torque and power. In the Data
Manual, four sizes of wedge belt are given, namely: SPZ, SPA, SPB, and
SPC. These are listed in increasing size, with the SPZ being the
smallest and the SPC being the largest.
The number of belts.
Belt drives with a single belt are the most common but belt drives are
often used with 2 to 6 belts in parallel on multi-grooved pulleys. In
the larger sizes up to 8 belts may be used. Clearly, the torque and
power increase in direct proportion to the number of belts.
Design and selection of belt drive systems
In your applied mechanics (or dynamics) you should have learnt how to
calculate the maximum torque and power that can be transmitted by a vee
or wedge belt drive, given the coefficient of friction, angle of
contact, groove angle and slack-side tension under load. For the
purpose of mechanical design you will now learn to use the
manufacturers catalogue in order to design and select a belt drive
system.
Note The calculation of torque and power based on mechanics principles
will usually overstate the amount of torque and power: This is because
this calculation does not consider the stresses in the belt and the
allowable stress that depends upon the belt material and method of
construction.
1. Types of Belt Drives: Read the Preamble on page 50 of the Data Manual.
Recognise the various types of belt drives available.
2. Minimum Diameter: Look at Table 1 on page 56. This gives you the
minimum pulley diameter for a given power and faster-shaft
speed.
3. Service Factors. Look at Table 3 on page 56. This gives you a
service factor which takes into account shock
loading and the hours per day of operation. You will encounter a
similar factor in the selection of many other mechanical power
transmission components. Note that in most cases, the drive is a
speed-reducing one. If the drive is speed-increasing one, then an
additional service factor should be applied (as shown in this table).
4. Power/Speed Graph: Look at the graph on page 57. This shows you where
each size of belt can be used according to the power and speed. You may
like to use coloured pencil or highlighter pen to shade the various
lines to make this graph easier to use.
5. Correction Factors: Given on page 58 and
the power ratings given on pages 59 to 64.
6. Pulley Dimensions: Given on pages 65 to
72. These are all for use with taper-lock
bushes. Taper-lock bush details are given on page 73.
7. Read the selection method given in pages 50 to 52.
It is not necessary that you work through this in detail at this stage
because it won't mean much to you until you try and work through a
problem on belt selection.
8. Study the Worked Example on page 54 in conjunction
with the selection method.
9. Work through Exercises 1 and 2 in this section.
Types of belt drives.
Belt drives can be broadly categorised into two groups,
positive(no-slip, toothed belts) and non-positive(slip, friction
belts). Traditionally belts
have
been of the non-positive (friction) type which include flat belts and
vee
belts.
In recent times toothed belts have become popular for use in
electro-mechanical systems such as video machines, turntables and
higher power applications such as servo drives and camshaft drives.
These are not
treated here.
Flat belt and Vee belt drives.
The following discussion on belt drives is limited to flat belts and
vee belts where power is transmitted by friction. These belt
drives
are subject to creep and even slip, depending on the load being
applied, and hence the drive ratio cannot be considered positive.
Flat belts with long centre distances were common in many industries in
the past. A central prime mover (eg. a steam engine) would
generate
power and belts would be used to transmit power to various machines.
These types of arrangement can still be found in some textile
industries. Today short centre drives are still in common use but
more
often vee belt drives are used.
Flat belts were commonly made from leather but today are usually made
from rubber (cotton fabric or cord impregnated and bound together by
vulcanised rubber). Leather belts are made from leather from the
butt
of the hide. Their ultimate tensile stress varies from 20 to 35
N/mm2.
Flat rubber belting is usually used as it is cheaper, has a higher
coefficient of friction, is more resistant to moisture and is stronger
than leather belting. Initial tensions in rubber belts vary from
about
2.5 to 4N per ply per mm width. Tensioning the belt results in
elongation so belts are made approximately 1 per cent shorter than the
theoretical tape line measurement. Belts can be purchased in
endless
form or made endless in the field by means of a vulcanised
splice.
Rubber belts will stretch about 2 per cent over their nominal life so
it is desirable to provide centre distance adjustment. Maximum
power
ratings are dependent on belt strength, angle of contact, small pulley
diameter, beltspeed in m/sec and service conditions.
Pulleys are generally made from cast iron or fabricated from steel. Flat belt pulleys
are generally crowned for self centring.
Vee belts
Vee belts are manufactured of rubber, fabric and cord. They provide a quiet, compact and resilient
form
of power transmission with minimum shock transmission between drive
shaft and driven shaft/s. The tapered cross sectional shape of a
vee
belt causes it to wedge firmly into a sheave groove so that the driving
action takes place through the sides of the groove rather than the
bottom. Vee belts operate most efficiently at speeds of about
20-25 m/sec. Design of vee belt drives is done using the selection
procedure shown below (or on pages 51 and 52 of the Belt_notes.pdf)
SELECTION PROCEDURE FOR VEE BELT
DRIVES
This selection procedure complies with BS3790.
1. Select service factor.
.
(a) The type of driven machine will determine the duty.
(b) Determine the type of driving machinery and operational hours per
day.
(c) Select service factor.
2. Calculate the Design power
rating.
Design power rating = Motor power Service
factor
3. Select the belt section.
(a) Mark the RPM of the faster shaft on the horizontal axis.
(b) Trace upwards along the vertical axis to the design power.
(c) At the point were they meet, note the recommended belt section or
sections if there is an overlap.
Notes: choose 'B' section belts in preference to 'A' section belts.
In the overlap between 'B' and 'C'
sections, 'C' section belts
are likely to be more desirable as fewer belts will be required.
4. Calculate the speed ratio (R). (Maximum ratio of about 6:1 in a single ratio)
5. Select pulley diameters.
(a) Determine recommended minimum motor pulley diameter from the table.
(b) Choose a combination of pulley diameters that gives required speed
ratio, keeping in mind (a).
(c) Record catalogue details of pulleys and bushes.
6. Calculate the belt length based on centre distance (C).
If the centre distance is not fixed then use:
To determine belt length use:
Choose a suitable belt and record belt actual belt length and
identification number.
7. Calculate the accurate centre
distance (CA) based on the belt selected.
8. Determine the basic power per
belt for 'A', 'B' and 'C' section belts respectively.
Each page has the basic power per belt table on the left hand side and
a table on the right hand side for calculating additional power which
depends on the belt speed ratio.
(a) Record basic (rated) power per belt from left hand table.
(b) Record approximate belt speed from left hand table
(c) Record additional power per belt from right hand table.
Power/belt = Basic power/belt + Additional
power/belt
9. Determine the Arc of contact
correction factor.
Refer Table 5
(a) Calculate (D-d)/C
(b) Record correction factor
(c) Record arc of contact ()
10. Determine the belt length
correction factor.
Refer Table 6 .
11. Calculate the number of
belts required.
Number
of
belts |
= |
Design power
rating (step 4)
-----------------------------------------
(Power/belt(step 8)arc factor(step 9)length factor(step 10)) |
12. Summarise results.
Gather the data that is required for a bill of materials/materials list.
(a) Pulley catalogue numbers and required dimensions.
(b) Taper lock bush catalogue numbers and required dimensions.
(c) check bore sizes against shaft sizes.
13. General arrangement drawing.
The centre distance CA has a negative tolerance to allow for initial
installation of belts over pulleys. CA has a positive tolerence
to
allow for take up as the belts are tensioned and for adjustment after
wear. At the centre of the span tensioning is satisfactory if the
belt
can be depressed 16mm/meter of centre distance. For installation
and
take up allowances see DESIGN DATA MANUAL.
WORKED EXAMPLE
Problem 1:
Design a vee belt drive to transmit power from an A.C. squirrel cage,
delta start, motor rotating at 1440 rev/min and rated at 11kW to a fan
rotating at 720 rev/min. Centres are to be near to, but not more
than,
750mm apart and the driven pulley is not to exceed 355mm outside
diameter. The drive is to run a minimum of 18 hours per day.
Data:
Motor: A.C. squirrel cage, delta
start; 11kW ; 1440RPM
Fan: 720RPM
Centre distance 750mm
Driven pulley 355mm O.D.
operating hours 18 hours per day
Solution:
1. Service factor (S.F.).
Medium duty, 18 hr/day
S.F = 1.3
2. Design power rating (D.P.R.).
3. Select vee belt section.
Can use either 'A' or 'B' section
choose 'B' section.
4. Calculate the speed ratio (R).
5. Select pulley diameters (d)&(D).
see - Recommended minimum standard
pulley diameters for electric motors.
Motor RPM=1440;Power=15kW
Minimum Diameter Motor pulley=118mm
Maximum O.D. driven pulley=355mm
Try D=315mm: d=D/R=315/2=157.5mm
Available combinations (D=315mm)
for d=150mm : R=2.1:1
for d=160mm : R=1.97:1
closest R=1.97, d=160mm, D=315mm
6. Calculate belt length (L).
Find L based on the centre distance (C) and the pulley pitch diameters
d and D.
Choose next smallest belt to this dimension to give centre distance
<750mm.
Select B2250,Cat No 240B0225 belt
(section 1711mm).
7. Accurate centre distance (CA).
8.
Determine the power per belt.
Power per belt |
= |
basic
power per belt for small pulley
+
Additional power per belt for speed ratio
|
by interpolation from tables
Power per belt |
= |
4.254
+
0.402
|
Power per belt = 4.656kW
9. Arc correction factor.
(D-d)/CA=(315-160)/748=0.2072
correction factor=0.97
10. Belt length correction factor.
for belt B2250
correction factor=0.98
11. Number of belts
Number
of
belts |
= |
step
4
--------------------
(step 8 * step 9 * step 10)
|
Number
of
belts |
= |
14.3
--------------------
(4.656 * 0.97 * 0.98)
|
Number of belts = 3.23 (round off
to 4 belts)
12. Summary of Results.
pulleys and bushes:
Motor pulley
|
Fan pulley
|
PCD=160mm |
PCD=315mm |
Cat No
013B0224 |
Cat No
013B0334 |
No of
grooves = 4 |
No of
grooves = 4 |
Taper lock
bush No 2517 |
Taper lock
bush No 3535 |
Maximum bore
60mm |
Maximum bore
90mm |
Pulley
type - 3 |
Pulley
type - 8 |
Outside
diameter = 169mm |
Outside
diameter = 324mm 355mm |
4 matched belts B2250, Catalogue number 240B0225.
Belt Assignment
Write
out your working fully.
Question 1. A 50 mm diameter
lineshaft (medium duty) is to rotate at 400 ± 10
rev/mm. Power is transmitted by a belt drive using a motor with frame
size B14-132M-4 and direct-on-line (DOL) start. The drive operates
for
10 hours per day. Centre distance between the motor and the shaft is to
be as close as possible to 600 mm.
(Motor Frame Sizes - Metric: Foot mounted / Flange mounted or refer to the imperial standard - Nema used in the US).
Determine:
(a) Wedge belt section required (use the largest
feasible)
(b) Pitch diameter of the pulleys at the motor and
lineshaft
(c) Speed of the lineshaft (to the nearest rev/mm) at
full load
(d) Wedge belt length
(e) Centre distance between the motor and the
lineshafi (to the nearest mm)
(f) Number of belts
(g) Catalogue number of the pulleys and taper bushes
at the motor and lineshaft.
Question 2. A conveyor is driven by a belt drive from a 3
phase 8 pole electric motor with star-delta start. At full load the
output power of the motor is 20 kW and the speed of the conveyor shaft
is to be 250 ± 10 rev/mm. Service can be described as heavy duty and
the conveyor will operate for 8 hours per day. The conveyor shaft is 60
mm in diameter and space restrictions limit the conveyor pulley to a
maximum diameter of 600 mm. The ratio of the belt tensions under load
is expected to be 8:1.
Determine:
(a) Motor type
(b) Wedge belt section required (use the largest
feasible)
(c) Pitch diameter of the pulleys at the motor and
compressor shaft (use the largest feasible)
(d) Speed of the conveyor (to the nearest rev/mm) at
full load
(e) Wedge belt length
(f) Centre distance between the motor and the
conveyor (to the nearest mm)
(g) Number of belts
(h) Catalogue number of the pulleys and taper bushes
at the motor and conveyor shafts
(i) Overhung load on the motor and conveyor shafts.