SRI LANKA INSTITUTE OF
INFORMATION TECHNOLOGY
Department of Mechanical Engineering
Module Name
Module Code
Lecturer
Date
Session
: Mechanical Design I
: ME 2050
: Harshana Senavirathna
: 27/07/2020
: 04
Friction
Clutches
By: Harshana Senavirathna
B.Sc. Eng (Hons)UOM, M.Sc (UOP) AMIESL, AMIMECHE(UK), MIEEE
Dept. of Mechanical Engineering,
Sri Lanka Institute of Information Technology
1
Clutches
A clutch enables two co- axial shafts
to be engaged or disengaged while
at rest or in relative motion.
Clutch types
2
Clutch classification
Friction Clutches
• In friction clutches, slipping will occur until
the two shafts are brought to the same
speed
• This feature permits gradual engagement of
the driven shaft such as in a car drive .
3
Type of Friction clutches
Disc clutch
Drum clutch
Conical clutch
Automotive-type disk clutch
4
Friction
Static Friction
Friction
Dynamic Friction
5
Friction
Comparison
Wear
• Wear between two rubbing surfaces
depends on;
• Pressure between the surfaces
• Speed at which they rub
6
Simple disc clutch
Clutch disengaged
Simple disc clutch
F
7
Uniform pressure
Assuming the pressure p is uniform throughout the
disc;
Normal force acting on the ring element is,
𝑑𝐹 = 2𝜋rpdr
𝐹=
2𝜋𝑝𝑟𝑑𝑟
𝐹 = 𝜋p 𝑟
− 𝑟
Uniform pressure
Torque dT acting on the ring element is;
𝑑𝑇 = 2𝜋𝜇𝑝𝑟 dr
𝑇 = ∫ 2𝜋𝜇𝑝𝑟 dr
𝑇=
2𝜋𝜇𝑝 𝑟 − 𝑟
3
𝑇=
2𝜇𝐹 𝑟 − 𝑟
3 𝑟 −𝑟
Substituting F,
8
Uniform Wear
• In the case of uniform wear, it is assumed that the
surface of the disc wear uniformly.
• Wear is function of pressure p and the sliding
velocity. In the case of uniform wear;
𝑝𝑣 = 𝑐 (C is a constant)
𝑃𝑟𝜔 = 𝑐
For a given 𝜔 ,
𝑝𝑟 = ⁄ = 𝑝
𝑟
Substituting for clamp force F
Uniform wear cont.:
𝑟 dr
𝐹 = ∫ 2𝜋𝑝
𝐹 = 2𝜋𝑝
𝑟 𝑟 −𝑟
Total Torque,
𝑇=
2𝜋𝑟𝜇𝑝. 𝑟dr
𝑟 . rdr
𝑇 = ∫ 2𝜋𝜇𝑝
𝑇 = 𝜋𝜇𝑝
𝑟 𝑟
−𝑟
Substituting F,
𝑇 = 𝐹𝜇
𝑟 +𝑟
2
9
Conical Clutch
Conical Clutch
1. Cones : female cone (green), male cone(blue)
2. Shaft: male cone is sliding on splines
3. Friction material: usually on female cone, here on male cone
4. Spring: brings the male cone back after using the clutch control
5. Clutch control: separating both cones by pressing
6. Rotating direction: both direction of the axis are possible
10
• A Conical clutch transmits rotation from one shaft to
another through friction forces
• The cone has a half angle of 𝛽 and the two halves are
forced together with a force R
Geometry
11
Uniform Pressure Theory
• The force between the two surfaces pressing
together develops a uniform pressure in between
the two surfaces (i.e. p Nm-2)
• Let the normal pressure acting on the surfaces is R’
and
• The normal force acting on the elementary area is
dR’
From (1)
Uniform Pressure Theory
12
When the clutch slips, the frictional force can be
given as;
• The torque generated due to the frictional
force,
13
The total torque can be taken by integrating throughout the
surface,
• As R’ is the total normal force acting on the surface,
the axial force can be given as,
14
Uniform Wear Theory
• Uniform wear theory assumes the wear is
uniform everywhere and it is directly
proportional to velocity × pressure
• Considering the same elementary area,
• If the velocity at any point is “v”
• Angular velocity “𝝎”
15
From equation (4),
16
Substituting in the equation,
Friction Clutches
Design
17
Clutch configuration
Service factors
18
Friction materials and its properties
Typical values for dynamic friction coefficients, permissible
contact pressures and temperature limits
Basic requirement for clutch design
1. The necessary actuation force should not be excessive.
2. The coefficient of friction should be constant.
3. The energy converted to heat must be dissipated.
4. Wear must be limited to provide reasonable clutch life.
19
Other considerations in clutch design
Design Problem
Energy loss in slipping of the clutch
The contact surfaces in a cone clutch have an effective diameter of 80 mm. The
semi-angle of the cone is 15o and Coefficient of friction is 0.3. Find the torque
required to produce slipping of the clutch, if the axial force applied is 200 N.
The clutch is employed to connect an electric motor, running uniformly at 900
r.p.m. with a flywheel which is initially stationary. The flywheel has a mass of 14
kg and its radius of gyration is 160 mm. Calculate the time required for the
flywheel to attain full-speed and also the energy lost in slipping of the clutch.
20
References
1) Meriam J.L and Kraige L.G Engineering Mechanics:
Statics, John Wiley and Sons Inc.. SI Version
2) Kiusalaas, J., Pytel, A. (2012) Mechanics of
Materials, 2nd ed., Cenagage Learning.
3) Juvinall R C & Marshek K M, Fundamentals of
Machine Component Deisgn. John Wiley & Sons Inc.
4) Hearn E.J, (2000), Mechanics of Materials, McGrawHill, UK
5) Nash.W, Potter M.C, (2011), Strength of Materials,
McGraw-Hill, UK
6) Johnston R, De Wolf J,(2000) Statics and Mechanics
of Materials, McGraw-Hill , UK
21