Friction Belt Drive Problems
Friction Belt Drive Problems
Friction Belt Drive Problems
1. Figure Q1 illustrates an open flat belt drive. Identify all the links and kinematic
pairs in the drive.
O1 O2
Fig. Q1
In the flat-belt drive of Fig. Q1, the angle of wrap on the smaller pulley is 1600, the
speed ratio is 5 to 1, and the nominal diameter of the smaller pulley is 100 mm.
Calculate the centre distance and the length of the belt.
Suppose that the belt is linearly elastic and that, after assembly, it retains a constant
length whether it transmits power or not. If the mass per unit length of the
assembled belt is 0.2 kg/m, the limiting coefficient of friction between the belt and
either pulley is 0.25, and the linear speed of the belt is limited to 20 m/s, determine
the initial tension for maximum power transmission without slip, and the
corresponding transmitted power.
2. Name the three most common mechanisms for the transmission of mechanical
power between two parallel shafts.
A flat belt drive has a centre distance of 1.55 m. The smaller pulley, which is the
driver, has an effective diameter of 0.2 m, and is driven at 1000 rpm. The angle of
wrap on the smaller pulley is 150 degrees. Neglecting the mass of the belt and
assuming the free lengths of the belt to be straight,
Determine the linear belt speed and the angular velocity ratio of the drive,
assuming there is no slip between the belt and either pulley
Determine the tensions in the free lengths of the belt and the direction and
magnitude of the total load on the bearings of the driving shaft.
3. The belt in an open V-belt drive is 2230 mm long, and operates on sheaves whose
pitch diameters are 300 mm and 400 mm, respectively. The length of the belt may
be estimated by use of the following equation:
( D2 D1 ) 2
L = 2C + 1.57( D1 + D2 ) +
4C
4. In an open flat-belt drive, the belt has a unit mass of 0.2 kg/m. When the drive is
operated such that maximum power is transmitted, with just no slip between belt and
either pulley, the tensions in the tight and slack sides of the belt are 450 N and 260
N, respectively. Given that the two pulleys are made of the same material, that the
belt is linearly elastic and retains a constant overall length under all operating
conditions, that the smaller pulley diameter is 150 mm, that the larger pulley
diameter is 420 mm, and that the centre distance is 480 mm, determine:
The linear speed of the belt
The power transmitted
The limiting coefficient of friction
The approximate length of the belt
5. Explain why a belt drive can provide some overload protection to driven machines
and contrast this phenomenon with the case of a chain drive.
The smaller sheave in a V-belt drive has a pitch diameter of 200 mm and a V-groove
of 400 included angle. The angle of wrap on this sheave is 1500. If the maximum
running belt tension is to be 1000 N, and the coefficient of friction is 0.25, determine
the number of belts that will be required in order to transmit 40 kW at 1200 rpm.
You may neglect the mass of the belts.
Pulley 1
Pulley 2
O1 O2
Fig. Q6
What are the values of the torques on the two shafts? What is the accurate length of
the belt? What is the combined reaction on the bearing supporting the shaft whose
axis is at O1.
7. Compare the V-belt drive, the chain drive and the gear drive in the contexts of:
Power transmission capacity
Speed of operation
Compactness
Noise levels
A V-belt drive has a groove angle of 380. The linear speed of the belt is to be 10.5
m/s and the smaller pulley, which is to be the driver, is to be driven at 1 000 rpm. If
the speed ratio is to be 5:1, the angle of wrap on the smaller pulley is to be 1500 and
the coefficient of static friction between the belt and the pulleys is 0.27, determine:
(i) The centre distance of the drive
(ii) The length of the belt
(iii) The power transmitted by the drive, if the tension in the slack side of the belt is
to be 285 N. You may neglect the mass of the belt.
4.0 Resources
BUDYNAS, RICHARD G. and J. KEITH NISBETT. Shigleys Mechanical
Engineering Design, 8th Edition, Chapter 17 Flexible Mechanical Elements.
McGraw-Hill International, 2008.
DIMAROGONAS, ANDREW D. Machine Design. A CAD Approach, Chapter
10 Design of Dry Friction Elements. Wiley Interscience, 2001.
WILSON, CHARLES E. Computer Integrated Machine Design, Chapter 10
Belt Drives. Prentice Hall International, 1997.
BURR, ARTHUR H. and JOHN B. CHEATHAM. Mechanical Analysis and
Design, Second Edition, Chapter 3 Friction Theory and Applications. Prentice
Hall, 1995.
SPOTTS, M. F. Design of Machine Elements, 6th Edition, Chapter 6 Belts,
Clutches, Brakes, and Chains. Prentice Hall, 1991.
JUVINALL, ROBERT C. Fundamentals of Machine Component Design,
Chapter 19 Miscellaneous Power Transmission Components. John Wiley and
Sons, 1983.
BLACK, PAUL H. and O. EUGENE ADAMS Jr. Machine Design, 3rd Edition,
Chapter 14 Belt Drives and Hoists. McGraw-Hill International, 1981.
http://school.mech.uwa.edu.au/~dwright/DANotes/V-belts/intro/intro.html#top
Many standard texts on engineering mechanics include chapters on friction, which
may deal with belt friction and clutch theory.
Many standard texts on the theory of machines include chapters dealing with belt
drive theory.
Other Internet Resources.