Session 11

Lecture notes Design of Transmission System

Design of Pulleys and Sprockets

The pulleys are used to transmit power from one shaft

to another by means of flat

belts, V-belts or ropes. Since the velocity ratio is the inverse ratio of the diameters of driving and
driven pulleys, therefore the pulley diameters should be carefully selected in order to have a
desired velocity ratio. The pulleys must be in perfect alignment in order to allow the belt to
travel in a line normal to the pulley faces.
Types of Pulleys for Flat Belts
Following are the various types of pulleys for flat belts :
1.
2.
3.
4.
5.

Cast iron pulleys,

Steel pulleys,
Wooden pulleys,
Paper pulleys, and
Fast and loose pulleys

The cast iron pulleys may be solid as shown in Fig. 11.1 or split type as shown in Fig.
11.2

Fig. 11.1.Solid cast iron pulleys

Prepared byMr.M.Subramanian ASP, & Mr. B.Charles, AP, Department of Mechanical Engineering
Adithya Institute of Technology

Session 11
Lecture notes Design of Transmission System

Fig. 11.2.Split cast iron pulley.

The following procedure may be adopted for the design of cast iron pulleys.
1. Dimensions of pulley
(i) The diameter of the pulley (D) may be obtained either from velocity ratio consideration or
centrifugal stress consideration. We know that the centrifugal stress induced in the rim of the
pulley,
t = v 2
Where = Density of the rim material = 7200 kg/m3 for cast iron
V = Velocity of the rim = DN / 60,
D being the diameter of pulley and N is speed of the pulley.
The following are the diameter of pulleys in mm for flat and V-belts.
20, 22, 25, 28, 32, 36, 40, 45, 50, 56, 63, 71, 80, 90, 100, 112, 125, 140, 160, 180,
200, 224,250, 280, 315, 355, 400, 450, 500, 560, 630, 710, 800, 900, 1000, 1120, 1250,
1400, 1600, 1800,2000, 2240, 2500, 2800, 3150, 3550, 4000, 5000, 5400.

The first six sizes (20 to 36 mm) are used for V-belts only.

Prepared byMr.M.Subramanian ASP, & Mr. B.Charles, AP, Department of Mechanical Engineering
Adithya Institute of Technology

Session 11
Lecture notes Design of Transmission System
(ii) If the width of the belt is known, then width of the pulley or face of the pulley (B) is
taken25% greater than the width of belt.
B = 1.25 b ; where b = Width of belt.
According to Indian Standards, IS : 2122 (Part I) 1973 (Reaffirmed 1990), the width of
pulleyis fixed as given in the following table :

Table 1.1 Standard width of pulley [PSG Design data book Page No: 7.54]

Belt width in mm

Width of pulley to be greater than

belt width by (mm)

Upto 125

13

125-250

25

250 375

38

475 500

50

The following are the width of flat cast iron and mild steel pulleys in mm :
16, 20, 25, 32, 40, 50, 63, 71, 80, 90, 100, 112, 125, 140, 160, 180, 200, 224, 250,
315, 355,400, 450, 560, 630.
(iii) The thickness of the pulley rim (t) .
For cast iron
t=D/300+ 3 mm for single belt

[PSG Design data book Page No: 7.57]

t = D/200+ 6 mm for double belt. [PSG Design data book Page No: 7.57]
Where D= the diameter of the pulley(mm).

Prepared byMr.M.Subramanian ASP, & Mr. B.Charles, AP, Department of Mechanical Engineering
Adithya Institute of Technology

Session 11
Lecture notes Design of Transmission System
The thickness of rim for all sizes of steel pulleys usually 5mm for D is 40 to 2000mm
2. Dimensions of arms
(i) The number of arms may be taken as
*4 arms for pulley diameter upto 450mm [PSG Design data book Page No: 7.56]

*6 arms for diameter over the 450 mm. [PSG Design data book Page No: 7.56]

(ii) The cross-section of the arms is usually elliptical with major axis (a1) equal to twice
theminor axis (b1). The cross-section of the arm is obtained by considering the arm as cantilever
i.e.fixed at the hub end and carrying a concentrated load at the rim end. The length of the
cantilever istaken equal to the radius of the pulley. It is further assumed that at any given time,
the power istransmitted from the hub to the rim or vice versa, through only half the total
number of arms.

Let

Fig. 11.3.Cast iron pulley with two rows of arms.

T = Torque transmitted,
R = Radius of pulley, and
n = Number of arms,

Tangential load per arm,

Maximum bending moment on the arm at the hub end,

Prepared byMr.M.Subramanian ASP, & Mr. B.Charles, AP, Department of Mechanical Engineering
Adithya Institute of Technology

Session 11
Lecture notes Design of Transmission System

And section modulus,

Now using the relation,

bor t= M/ Z, the cross-section of the arms is obtained.
(iii) The arms are tapered from hub to rim. The taper is usually 1/48 to 1/32.
(iv)When the width of the pulley exceeds the diameter of the pulley, then two rows of arms are
provided, as shown in Fig. 11.3. This is done to avoid heavy arms in one row.

3. Dimensions of hub
(i) The diameter of the hub (d 1) in terms of shaft diameter (d) may be fixed by the
followingRelation:
d1 = 1.5 d + 25 mm
The diameter of the hub should not be greater than 2 d.
(ii) The length of the hub, the minimum length of the hub is (2/3) B but it should not be more
than width of the pulley (B).

Design of Sprockets
Terms Used in Chain Drive
The following terms are frequently used in chain drive.
1. Pitch of chain. It is the distance between the hinge centre of a link and the
corresponding hinge centre of the adjacent link, as shown in Fig. 11.4. It is usually
denoted by p. Fig. 11.4.Terms used in chain drive.

Prepared byMr.M.Subramanian ASP, & Mr. B.Charles, AP, Department of Mechanical Engineering
Adithya Institute of Technology

Session 11
Lecture notes Design of Transmission System
2. Pitch circle diameter of chain sprocket. It is the diameter of the circle on which
the hinge centres of the chain lie, when the chain is wrapped round a sprocket as shown
in Fig. 11.4. The points A, B, C, and D are the hinge centres of the chain and the circle
drawn through these centres is called pitch circle and its diameter (D) is known as pitch
circle diameter.

Figure 11.4
Principal Dimensions of Tooth Profile
The standard profiles for the teeth of a sprocket are shown in Fig. 11.5. According to
Indian Standards (IS: 2403 1991), the principal dimensions of the tooth profile are as
follows:

Prepared byMr.M.Subramanian ASP, & Mr. B.Charles, AP, Department of Mechanical Engineering
Adithya Institute of Technology

Session 11
Lecture notes Design of Transmission System

Figure 11.4

Prepared byMr.M.Subramanian ASP, & Mr. B.Charles, AP, Department of Mechanical Engineering
Adithya Institute of Technology

Session 11
Lecture notes Design of Transmission System

Prepared byMr.M.Subramanian ASP, & Mr. B.Charles, AP, Department of Mechanical Engineering
Adithya Institute of Technology

Session 11
Lecture notes Design of Transmission System

Two Marks
1. When do you prefer a chain drive to a belt or rope drive? [May 2008]
Chain drives are preferred for velocity ratio less than 10, chain velocities upto 25m/s, and
for power ratings up to 125kW.
2. What are the different types of chains?
a) Link(or welded load) chains,
b) Transmission (or roller) chains, and
c) Silent (or inverted tooth) chains
d)
3. What ate the applications of link(or hoisting) chains?
a) Link (or hoisting) chains are widely used

Prepared byMr.M.Subramanian ASP, & Mr. B.Charles, AP, Department of Mechanical Engineering
Adithya Institute of Technology

Session 11
Lecture notes Design of Transmission System
b) In low capacity machines such as hoists, winches and hand operated cranes as the
main lifting appliances, and
c) As slings for suspending the load from hook or other device.

Problem :-An overhung pulley transmits 35 kW at 240 r.p.m. The belt drive is vertical and
the angle of wrap may be taken as 180. The distance of the pulley centre line from the nearest
bearing is 350 mm. = 0.25. Determine:
1. Diameter of the pulley;
2. Width of the belt assuming thickness of 10 mm;
3. Diameter of the shaft;
4. Dimensions of the key for securing the pulley on to the shaft; and
5. Size of the arms six in number.
The section of the arm may be taken as elliptical, the major axis being twice the minor axis.
The following stresses may be taken for design purposes:
Shaft Tension and compression 80 MPa
Key Shear 50 MPa
Belt:Tension 2.5 MPa
Pulley rim:Tension 4.5 MPa
Pulley arms:Tension 15 MPa

1. Diameter of the pulley

To find the diameter in equation
t = v 2
Where = Density of the rim material = 7200 kg/m3 for cast iron
V = Velocity of the rim = DN / 60,
D being the diameter of pulley and N is speed of the pulley.
2. Width of the belt
*We know that the power transmitted (P) = (T1 T2) v

Prepared byMr.M.Subramanian ASP, & Mr. B.Charles, AP, Department of Mechanical Engineering
Adithya Institute of Technology

Session 11
Lecture notes Design of Transmission System
*Relation between tight side to slack side 2.3log (T1/T2) =
*Cross-sectional area of the belt, = b t
*Mass of the belt per metre length, m = Area length density
*Centrifugal tension,TC = m.v2
*Maximum tension in the belt,T = .b.t
*Tension in the tight side of the belt (T1)= T TC
*To select the standard width of the belt (b) in PSG data book page No 7.52
3. Diameter of the shaft
We know that the torque transmitted by the shaft,
T= (P x 60)/ (2N)
Bending moment on the shaft due to the tensions of the belt,
M = (T1 + T2 + 2TC ) L
Equivalent twisting moment

T e= T 2+ M 2

Te=(/16) x s x d3
4. Dimensions of the key
To select the key size in PSG data book page No 5.16 based on shaft diameter (d)

5.

To find the length of shaft based on

Mt = (WLA/2) s
PSG data book page No 7.106
Mt= (WLA/2) b
PSG data book page No 7.106
Size of arms PSG data book page No 7.106
a) Number of arms - 4 for diameter up to 450mm & 6 for diameter over to 450mm
b) Cross section arm : elliptical
c) (1) thickness of arm,
b, near boss = 2.94

=2.94

aD
4n

for single belt

aD
2n

for double belt

Prepared byMr.M.Subramanian ASP, & Mr. B.Charles, AP, Department of Mechanical Engineering
Adithya Institute of Technology

Session 11
Lecture notes Design of Transmission System
Where a, width of pulley
D, diameter of pulley
N number of arms in the pulley
(2) Thickness of arm,b near rim = (2/3) x breadth of boss(or taper 4 mm per
100mm)
d) Radius of the cross section of arms r = (3/4) b
e) Minimum length of bore l = (2/3)a (it may be more for loose pulley, but in no case
it exceeds a)
Quiz
1. The crowning on a 300 mm width of pulley face should be
(a) 9 mm
(b) 12 mm
(c) 15 mm
(d) 18 mm
2. The steel pulleys are ............ in weight than cast iron pulleys of the same capacity.
(a) Heavier
(b) lighter
3. For a steel pulley of 500 mm, the recommended number of spokes are
(a) 2
(b) 4
(c) 6
(d) 8
4. The thickness of rim for all sizes of steel pulleys should be
(a) 5 mm
(b) 10 mm
(c) 15 mm
(d) 20 mm
5. The width of the pulley should be
(a) Equal to the width of belt
(b) less than the width of belt
(c) greater than the width of belt
Application

Elevator

Prepared byMr.M.Subramanian ASP, & Mr. B.Charles, AP, Department of Mechanical Engineering
Adithya Institute of Technology