Formula Sheet: Belts, Ropes and Chains | Theory of Machines (TOM) - Mechanical Engineering PDF Download

 Page 1


Belts, Ropes and Chains
1. Velocity Ratio of Belt Drive
N
2
N
1
=
d
1
d
2
? VR =
Speed of driver
Speed of follower
=
Diameter of follower
Diameter of driver
If belt thickness t is included:
N
2
N
1
=
d
1
+t
d
2
+t
2. Types of Belt Drives
• Open belt drive — shafts rotate in the same direction.
• Crossed belt drive — shafts rotate in opposite directions.
• Compound belt drive — multiple pulleys on same shaft.
3. Length of Belt
Open Belt Drive:
L =p (R
1
+R
2
)+
(R
1
- R
2
)
2
C
+2C
Cross Belt Drive:
L =p (R
1
+R
2
)+
(R
1
+R
2
)
2
C
+2C
Where:
R
1
=
d
1
2
, R
2
=
d
2
2
, C = center distance
4. Tension Ratio (Capstan Equation)
T
1
T
2
=e
µ? Where:
• T
1
= Tension in the tight side
1
Page 2


Belts, Ropes and Chains
1. Velocity Ratio of Belt Drive
N
2
N
1
=
d
1
d
2
? VR =
Speed of driver
Speed of follower
=
Diameter of follower
Diameter of driver
If belt thickness t is included:
N
2
N
1
=
d
1
+t
d
2
+t
2. Types of Belt Drives
• Open belt drive — shafts rotate in the same direction.
• Crossed belt drive — shafts rotate in opposite directions.
• Compound belt drive — multiple pulleys on same shaft.
3. Length of Belt
Open Belt Drive:
L =p (R
1
+R
2
)+
(R
1
- R
2
)
2
C
+2C
Cross Belt Drive:
L =p (R
1
+R
2
)+
(R
1
+R
2
)
2
C
+2C
Where:
R
1
=
d
1
2
, R
2
=
d
2
2
, C = center distance
4. Tension Ratio (Capstan Equation)
T
1
T
2
=e
µ? Where:
• T
1
= Tension in the tight side
1
• T
2
= Tension in the slack side
• µ = Coefficient of friction
• ? = Angle of contact (in radians)
5. Power Transmitted
P = (T
1
- T
2
)v (Watts)
Where:
v =
pdN
60
6. Centrifugal Tension
T
c
=mv
2
(where m is mass per unit length)
Maximum tension in belt:
T
max
=T
1
+T
c
7. Condition for Maximum Power Transmission
T
c
=
T
max
3
, v =
r
T
max
3m
8. Chains
• Used for synchronous drives.
• No slip.
• Velocity ratio:
VR =
N
2
N
1
=
T
1
T
2
(where T = number of teeth)
9. Ropes
Used for large power transmission over long distances:
Similar equations as belts apply, with high µ and large cross-sectional area
2