BELTS
BELTS - are flexible transmission elements which transmits power between shaft by means of
pulleys on the shaft.
ADVANTAGES OF BELT DRIVES DISADVANTAGES OF BELT DRIVES
They are simple and economical, Velocity ratio is not constant due to slipping
Don’t require parallel shafts, Heat buildup occurs
Absorbs good amount of shaft and vibration Speed is usually limited to 35 m/s
Long distant power transmission, Power transmission is limited to 370 kW
Lubrication-free and less maintenance cost Use of idler pulley is necessary
TYPES OF BELTS
FLAT BELT – is the simplest type, often made from leather of
rubber coated fabric. Mostly used in factories and workshops where a
moderate amount of power is to be transmitted, from one pulley to
another when the two pulleys are not more than 8 meters apart.
ADVANTAGES OF FLAT BELT DISADVANTAGES OF FLAT BELT
Can be used with high speed drives The tension must be kept high so as
Can be used in dusty and abrasive environment to keep it slow by two percent
Allows long distance between shafts This high tension results in high
Offer long life, high efficiency, low cost, and low maintenance bearing loads and belt stress
Noise
V-BELT – is mostly used in the factories and workshops, where a
great amount of power is to be transmitted, from one pulley to
another, when the two pulleys are very near to each other.
CIRCULAR BELT – is mostly used
in the factories and workshops, where a great amount of power is
to be transmitted, from one pulley to another, when the two pulleys
are more than 8 metres apart.
TOOTHED BELT – is a power
transmission belt with evenly spaced
teeth on the bottom side which mesh with grooves cut on the periphery
of the pulley to produce a positive, no slip, constant speed drive
MEMD-513: Machine Design 2 1
Types of Belt Drives Types of Belt Joints
Open Belt Drive
Crossed Or Twist Belt Drive
Quarter Turn Belt Drive
Belt Drive With Idler Pulley Cemented Joint
Compound Belt Drive Laced Joint
Stepped or cone pulley Drive Hinged Joint
Fast and Loose Pulley Drive Creep Of Belt
Friction causes the belt to grip the driving sheave,
increasing the tension in one side called the tight
side of the drive.
The opposite side of the belt is still under tension at
a smaller value. This side is called the slack side or
loose side.
The phenomenon called creep exists because the
driving pulley receive a longer (stretched) belt than it
delivers and the driven pulley receives a shorter
belt than it delivers, giving relative motion between
the belt and pulley.
Important Elements for Belt Drives
Types of Belt Drives based on
Strength of Leather Belt
Peripheral Speed
The strength of leather depends upon the method
Light Drives are used to transmit small powers of tanning
at belt speed up to about 10 m/s such as in
agricultural machines and small machine The breaking strength of oak-tanned belting varies
from 3 to more than 6 ksi.
tools.
Mineral tanned leather is stronger with breaking
Medium Drives are used to transmit medium strength of 7 to 12 ksi.
powers at belt speeds over 10 m/s but up to
22 m/s such as in machine tools, cars, etc. Belt Speeds
Heavy Drives are used to transmit large The tension in the belt due to centrifugal force
increases rapidly above about 2,500 fpm.
powers at belt speed above 22 m/s such as in
compressors, generators and main drives.
MEMD-513: Machine Design 2 2
Experience suggests that the most economical FLAT BELT FORMULAS
designs are obtained for a belt speed of 4,000 to
4,500 fpm. OPEN BELT FORMULAS
For leather, speeds of 7,000 to 8,000 fpm are in
use.
Flat fabric belts operate up to 20,000 fpm and
more.
On high-speed centrifugal blowers, it has been
observed that the arc of contact θ is reduced from Length of Belt
180° at rest to 110 ° in motion, one of the side 2
π ( D2−D1 )
effects of speed. L= ( D1 + D2 ) +2 C+
2 4C
Initial Tension
Angle of Wrap Or Contact
In order to transmit power, the belt must have
some initial tension (tension at rest).
θ1=180−2 sin−1 ( D 2C−D )
2 1
θ2 +θ1=360
As suggested by Taylor*, the recommended initial D −D
tension of belt should be 71 lb/in. of width. θ2=180+ 2sin−1 ( 2C )
2 1
Tension pulley is used to maintain initial tension CROSS BELT FORMULAS
and also greatly increases the arc of contact on the
nearest pulley, preferably the smaller one.
Rubber Belt
Rubber belts are made in layers (say 3 to 12),
which are called plies, of canvas duck
impregnated with rubber which is later vulcanized.
Length of Belt
According to the Goodrich Company, the
2
permissible net belt pull is 13.75 lb/ply per inch of π ( D2 + D1 )
width, which gives a simple means for quick L= ( D1 + D2 ) +2 C+
2 4C
estimation. Angle of Wrap Or Contact
Flat Belt for nonparallel Shaft
The Law of belting states that the center line of
θ1=θ 2=180+2 sin−1
ARC OF CONTACT
( D 2−D
2
C )
1
the belt as it approaches the pulley must lie in a
plane perpendicular to the axis of that pulley, or s1=r 1 θ2 s2=r 2 θ2
must lie in the plane of the pulley, otherwise the
belt will run off the pulley.
Where,
If two intersecting shafts are to be belt connected, D1 – diameter of the driving pulley
two (2) guide pulleys must be used, one on the D2 – diameter of the driven pulley
approaching side and one on the receding side of r1 – radius of the driving pulley
the belt.
r2 – radius of the driven pulley
Two shafts at right angles to each other may be C – center distance
connected by the quarter turn arrangement. This θ1 – angle of contact of the driving pulley
drive satisfies the law of belting for only one
direction of rotation. If rotation is to be reversed, a
θ2 – angle of contact of the driven pulley
guide pulley may be located to direct the belt
properly.
MEMD-513: Machine Design 2 3
BELT TENSION RATIO BELT SPEED
F 1−F c fθ NO SLIP MENTIONED
=e
F 2−F c v=π D1 N 1=π D2 N 2
WITH SLIP MENTIONED
CENTRIFUGAL FORCE v1 =π D1 N 1 ( 1−%slip )
2
ρb t v
F c=
g v 2=π D 2 N 2 ( 1+%slip )
Slip (or slippage) occurs when the frictional force
NET BELT PULL/ EFFECTIVE BELT between the belt and pulley is not sufficient in which the
belt moves forward slightly on the driving pulley and
PULL/ NET BELT TENSION
causes the driven pulley to rotate at a lower speed.
e fθ −1 Slippage occurs first on the pulley whose angle of wrap
F 1−F2= ( F1−F c ) ( e fθ ) is smaller (driver pulley). When not of the same material,
compare the tension ratios (𝑒𝑓𝜃) of the big and small
pulleys. Slippage occurs first on the pulley whose
ρ v2 efθ −1
(
F 1−F2=bt S d−
g )( e fθ ) tension ratio is lower.
DESIGN STRESS INSTALLATION OF IDLER PULLEY
For old transmission capacity
F1
Sd = e fθ −1
bt ( F 1−F 2) O=( F 1−F c ) ( e fθ )
SU
Sd = X Joint Factor For new transmission capacity
FS '
e f θ −1
Basic assumptions if the following are not given in
( F 1−F 2) N =( F1 −Fc ) f θ
e ( '
)
the problem Hence;
'
e f θ −1
LEATHER BELT
Sd =400 X Joint Factor , psi
( F1−F 2 ) NEW (ef θ
= fθ
'
)
=( 1+%increase )
( F 1−F2 )OLD e −1
RUBBER BELT
( e fθ )
Sd =350 X Joint Factor , psi
Where,
JOINT FACTOR ρ – mass density of belt
For leather: ρ = 0.035 lb/in3
Cemented Joint: JF = 1 For rubber: ρ = 0.0435 lb/in3
Wire Laced By Machine: JF = 0.88 f – coefficient of friction
For leather on iron or steel: f = 0.3
Metal Hooks: JF = 0.35 For leather on paper pulley: f = 0.5
b – width of the belt
POWER TRANSMITTED t – thickness of the belt
P=( F 1−F 2 ) v g – gravitational constant
F1 – angle of contact of the driving pulley
F2 – angle of contact of the driven pulley
MEMD-513: Machine Design 2 4
Sample Problems 3. An electric motor running at 1200 rpm drives a
punch press shaft at 200 rpm by means of a 130 mm
1. In an open belt drive, the center distance between two wide and 8 mm thick belt. When the clutch is
pulleys is 300 mm. If the pulley diameters are 20 mm engaged, the belt slips. To correct this
and 100 mm respectively, determine the: condition, an idler pulley was installed to increase
(a) belt length the angle of contact but the same belt and pulley
(b) angle of contact of the driver and driven pulley were used. The original contact angle of the 200
mm motor pulley is 160°. The original tension
2. In a cross belt drive, the center distance of two pulleys ratio is 2.4 and the net tension is 12 N/mm of the belt
is 3 meters and the pulley diameters are 150 mm width. An increase in transmission capacity of 20%
and 250 mm., determine the: will prevent slippage. Determine the:
(a) belt length (a) coefficient of friction
(b) angle of contact of the driver and driven pulley (b) net belt tension
(c) forces on tight side and slack side
3. A ¼ in belt transmit 30 hp while running on a 2-ft (d) expected new load on slack side and tight side,
pulley rotating at 600 rpm. The allowable belt stress total load and new angle of contact after the
is 500 psi; the angle of contact is 150 deg. Compute increase in capacity.
the belt width required, assuming the coefficient of
friction is 0.40 and the specific weight of belt material
Is 0.035 Ib/in3.
4. Two pulleys which are 24 inches in diameter and
which run at 370 rpm are connected by a leather belt
3/8 inch thick. If the belt transmits 30 Hp and the
distance between shafts is 10 ft.
(a) Compute the width of the belt required
considering the allowable design stress of 400 psi,
the coefficient of friction is 0.45 with contact angle of
180 deg.
. (b) What is the approximate length of the belt
required?
Sample Problems
1. Compute the centrifugal force: for a leather belt with
the following given: w = 100 mm, thickness = 6.4
mm, V = 18.3 m/s Note: the density of leather belt is
approximately 0.035 lb/in3 or 974 kg/m3.
2. An open belt drive connects a 450 mm driving pulley
to another driven pulley 1000 mm in diameter. The
belt is 300 mm wide and 10 mm thick. The
coefficient of friction of the belt drive is 0.30 and the
mass is 2.8 kg/m of the belt length. The center
distance between shafts is 4 m. The maximum
allowable tensile stress on the belt is 1500 kPa and
the speed of driving pulley is 900 rpm. Determine the
following:
(a) density of the belt
(b) angle of contact of the driver and driven pulley
(c) power transmitted in hp and kW
(d) loads on tight side and slack side
MEMD-513: Machine Design 2 5
