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Chapter 20
Cams
12/25/2015
Mohammad Suliman Abuhiba, Ph.D., PE1
Introduction
A cam: a rotating machine element which gives
reciprocating or oscillating motion to another
element (follower)
Cam & follower have a line of contact and
constitute a higher pair.
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Mohammad Suliman Abuhiba, Ph.D., PE
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Introduction
Applications of Cams:
Inlet & exhaust valves of ICE
Automatic attachment of machineries
Paper cutting machines
Feed mechanism of automatic lathes
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Classification of Followers
1. According to the surface in contact
2. According to motion of follower
3. According to path of motion of follower
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Classification of Followers
1. According to surface in
contact
Knife edge follower
contacting end of follower =
sharp knife edge
Seldom used in practice
because small area of
contacting surface results in
excessive wear.
A considerable side thrust exists
between the follower & guide
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Mohammad Suliman Abuhiba, Ph.D., PE
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Classification of Followers
1. According to the surface
in contact
Roller follower
Rolling motion between
contacting surfaces
Rate of wear is greatly
reduced
Side thrust exists between
follower & guide
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Classification of Followers1. According to the surface in contact
Flat faced or mushroom follower
Side thrust between follower & guide is
much reduced
Only side thrust due to friction between
contact surfaces of follower & cam
Relative motion between these
surfaces is largely of sliding nature
Wear may be reduced by off-setting
axis of follower, Fig. 20.1 (f ) so that
when cam rotates, follower also rotates
about its own axis.
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Classification of Followers
1. According to the surface in
contact
Spherical faced follower
When a flat-faced follower is
used in automobile engines,
high surface stresses are
produced.
In order to minimize these
stresses, flat end of follower is
machined to a spherical shape
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Classification of Followers
2. According to motion of follower
Reciprocating or translating follower
Follower reciprocates in guides as cam
rotates uniformly.
Followers shown in Fig. 20.1 (a) to (d)
are all reciprocating or translating
followers.
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Mohammad Suliman Abuhiba, Ph.D., PE
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Classification of Followers
2. According to motion of
follower
Oscillating or rotating follower
Uniform rotary motion of cam
is converted into
predetermined oscillatory
motion of follower.
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Mohammad Suliman Abuhiba, Ph.D., PE
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Classification of Followers
3. According to path of motion of follower
Radial follower
Motion of follower is along an axis passing
through center of cam
Fig. 20.1 (a) to (e)
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Classification of Followers
3. According to path of
motion of follower
Off-set follower
Motion of follower is along an
axis away from axis of cam
center
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Classification of Cams
1. Radial or disc cam
2. Cylindrical cam
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Classification of Cams
1. Radial or disc cam
Follower reciprocates or oscillates in
a direction perpendicular to cam axis
Cams shown in Fig. 20.1 are all radial
cams
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Classification of Cams
2. Cylindrical cam
follower reciprocates or oscillates in a
direction parallel to cam axis.
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Terms Used in Radial Cams
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Terms Used in Radial Cams
Base circle
Smallest circle that can be drawn to cam profile
Trace point
A reference point on follower that is used to generate
the pitch curve
knife edge follower: knife edge represents trace point
and pitch curve corresponds to cam profile
Roller follower: center of roller represents trace point
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Terms Used in Radial Cams
Pressure angle
Angle between direction of follower motion & a
normal to pitch curve
If pressure angle is too large, a reciprocating
follower will jam in its bearings
Pitch point
A point on pitch curve having max pressure angle
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Terms Used in Radial Cams
Pitch circle
A circle drawn from the center of cam through the
pitch point
Pitch curve
Curve generated by trace point as the follower
moves relative to cam
knife edge follower: pitch curve & cam profile are
same
Roller follower: they are separated by radius of
roller
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Terms Used in Radial Cams
Prime circle
Smallest circle that can be drawn from center of
cam and tangent to pitch curve
Knife edge & flat face follower: prime circle &
base circle are identical
Roller follower: prime circle is larger than base
circle by radius of roller
Lift or stroke
max travel of follower from its lowest position to
topmost position
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Motion of the Follower
1. Uniform velocity
2. Simple harmonic motion
3. Uniform acceleration and retardation
4. Cycloidal motion
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Displacement, Velocity & Acceleration
Diagrams - Follower Moves with Uniform Velocity
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Fig. 20.4 Fig. 20.5
Example 20.1A cam is to give the following motion to a knife-edged
follower :
1. Outstroke during 60° of cam rotation
2. Dwell for the next 30° of cam rotation
3. Return stroke during next 60° of cam rotation
4. Dwell for the remaining 210° of cam rotation
The stroke of follower is 42 mm & min radius of cam is 50
mm. The follower moves with uniform velocity during both out
& return strokes. Draw the profile of cam when
a. Axis of follower passes through axis of cam shaft
b. Axis of follower is offset by 20 mm from axis of cam shaft
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Mohammad Suliman Abuhiba, Ph.D., PE
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Example 20.112/25/2015
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Example 20.112/25/2015
Mohammad Suliman Abuhiba, Ph.D., PE
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Example 20.112/25/2015
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Displacement, Velocity & Acceleration Diagrams
when Follower Moves with SHM
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S = Stroke of
follower
qO & qR = Angular
displacement of
cam during out &
return strokes of
follower
w = Angular
velocity of cam
Displacement, Velocity & Acceleration Diagrams
when Follower Moves with SHM
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Mohammad Suliman Abuhiba, Ph.D., PE
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Time required for out stroke of
follower in seconds,
P’ executes a SHM as P rotates
Motion of follower is similar to
that of P’
Peripheral speed of P’
Displacement, Velocity & Acceleration Diagrams
when Follower Moves with SHM
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Mohammad Suliman Abuhiba, Ph.D., PE
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Max velocity & Max acceleration of follower on out
stroke,
Max velocity & max acceleration of follower on
return stroke
Example 20.2A cam is to be designed for a knife edge follower with the
following data:
1. Cam lift = 40 mm during 90° of cam rotation with SHM
2. Dwell for next 30°
3. During the next 60° of cam rotation, the follower returns to
its original position with SHM
4. Dwell during remaining 180°
Draw the profile of the cam when
a. Line of stroke of follower passes through axis of cam shaft
b. Line of stroke is offset 20 mm from axis of the cam shaft.
The radius of base circle of the cam is 40 mm. Determine
the maximum velocity and acceleration of the follower during
its ascent and descent, if the cam rotates at 240 rpm.
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Mohammad Suliman Abuhiba, Ph.D., PE
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Example 20.3A cam, with a minimum radius of 25 mm, rotating cw at a
uniform speed is to be designed to give a roller follower, at
the end of a valve rod, motion described below :
1. To raise valve through 50mm during 120° rotation of
cam
2. To keep the valve fully raised through next 30°
3. To lower the valve during next 60°
4. To keep the valve closed during rest of the revolution
The diameter of the roller is 20 mm and the diameter of the
cam shaft is 25 mm. Draw the profile of the cam when
a. Line of stroke of valve rod passes through axis of cam
shaft
b. Line of stroke is offset 15 mm from axis of cam shaft.
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Example 20.3The displacement of the valve, while being raised and
lowered, is to take place with simple harmonic motion.
Determine the maximum acceleration of the valve rod when
the cam shaft rotates at 100 rpm.
Draw the displacement, the velocity and the acceleration
diagrams for one complete revolution of the cam.
12/25/2015
Mohammad Suliman Abuhiba, Ph.D., PE
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Example 20.4A cam drives a flat reciprocating follower in the
following manner:
During first 120° rotation of the cam, follower
moves outwards through a distance of 20 mm with
SHM. The follower dwells during next 30° of cam
rotation. During next 120° of cam rotation, the
follower moves inwards with SHM. The follower
dwells for the next 90° of cam rotation.The
minimum radius of the cam is 25 mm. Draw the
profile of the cam.
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Example 20.5Draw a cam profile to drive an oscillating roller follower to the
specifications given below:
a. Follower to move outwards through an angular
displacement of 20° during first 120° rotation of cam
b. Follower to return to its initial position during next 120°
rotation of cam
c. Follower to dwell during the next 120° of cam rotation.
The distance between pivot center and roller center = 120
mm ; distance between pivot center and cam axis = 130 mm
; minimum radius of cam = 40 mm ; radius of roller = 10 mm
; inward and outward strokes take place with SHM.
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Displacement, Velocity
& Acceleration
Diagrams
Follower Moves with
Uniform Acceleration &
Retardation
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Displacement, Velocity & Acceleration Diagrams
Follower Moves with Uniform Acceleration &
Retardation
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S = Stroke of follower
qO & qR = Angular displacement of cam during out
stroke & return stroke of follower
w = Angular velocity of cam
Time required for follower during outstroke, tO = qO/w
Time required for follower during return stroke,
tR=qR/w
Mean velocity of follower during outstroke = S/tO
Mean velocity of follower during return stroke = S/tR
Displacement, Velocity & Acceleration Diagrams
Follower Moves with Uniform Acceleration &
Retardation
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Mohammad Suliman Abuhiba, Ph.D., PE
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Max velocity of follower = twice mean velocity,
Max acceleration of follower during outstroke
Max acceleration of follower during return stroke
Example 20.6A cam, with a minimum radius of 50 mm, rotating cw at a
uniform speed, is required to give a knife edge follower the
motion as described below :
1. To move outwards through 40 mm during 100° rotation
of the cam
2. To dwell for next 80°
3. To return to its starting position during next 90°
4. To dwell for the rest period of a revolution i.e. 90°.
Draw the profile of the cam when
i. Line of stroke of follower passes through centre of cam
shaft
ii. Line of stroke of follower is off-set by 15 mm.
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Mohammad Suliman Abuhiba, Ph.D., PE
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Example 20.6The displacement of the follower is to take place with
uniform acceleration and uniform retardation. Determine the
maximum velocity and acceleration of the follower when the
cam shaft rotates at 900 rpm.
Draw the displacement, velocity and acceleration diagrams
for one complete revolution of the cam.
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Mohammad Suliman Abuhiba, Ph.D., PE
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Example 20.10It is required to set out the profile of a cam to give the
following motion to the reciprocating follower with a flat
mushroom contact face:
i. Follower to have a stroke of 20 mm during 120° of cam
rotation
ii. Follower to dwell for 30° of cam rotation
iii. Follower to return to its initial position during 120° of
cam rotation
iv. Follower to dwell for remaining 90° of cam rotation
The minimum radius of the cam is 25 mm. The out stroke of
the follower is performed with SHM and the return stroke
with equal uniform acceleration and retardation.
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Tangent Cam
with
Reciprocating
Roller Follower
Used for
operating inlet &
exhaust valves
of ICEs
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Mohammad Suliman Abuhiba, Ph.D.,
PE
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20.12. Tangent Cam with Reciprocating
Roller Follower
a = Semi-angle of action of cam or angle of
ascent
q = Angle turned by cam from beginning of the
roller displacement
f = Angle turned by cam for contact of roller with
the straight flank
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Tangent Cam with Reciprocating Roller
Follower
Roller has contact with straight flanks
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Tangent Cam with Reciprocating Roller
Follower
Roller has contact with straight flanks
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Tangent Cam with
Reciprocating Roller
Follower
Roller has contact with the
nose
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Tangent Cam with
Reciprocating Roller
Follower
Roller has contact with the
nose
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Tangent Cam with
Reciprocating Roller
Follower
Roller has contact with the
nose
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Example 20.13In a symmetrical tangent cam operating a roller
follower, the least radius of the cam is 30 mm and
roller radius is 17.5 mm. The angle of ascent is 75°
and the total lift is 17.5 mm. The speed of the cam
shaft is 600 rpm. Calculate:
1. The principal dimensions of the cam
2. the accelerations of the follower at the beginning
of the lift, where straight flank merges into the
circular nose and at the apex of the circular
nose. Assume that there is no dwell between
ascent and descent.
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Example 20.1312/25/2015
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Example 20.14A cam has straight working faces which are
tangential to a base circle of diameter 90 mm. The
follower is a roller of diameter 40 mm and the
center of roller moves along a straight line passing
through the center line of the cam shaft. The angle
between the tangential faces of the cam is 90° and
the faces are joined by a nose circle of 10 mm
radius. The speed of rotation of the cam is 120 rpm.
Find the acceleration of the roller center
1. when during the lift, the roller is just about to
leave the straight flank
2. when the roller is at the outer end of its lift.
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Example 20.1412/25/2015
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Circular Arc Cam with
Flat-faced Follower
r1 = Min radius of cam (radius
of base circle = OE
r2 = Radius of nose
R = Radius of circular flank =
PE
2a = Total angle of action of
cam = angle EOG
f = Angle of action of cam on
circular flank
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Circular Arc Cam with
Flat-faced Follower
Flat face of follower has
contact on the circular flank
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x = BA = BO − AO = CD − EO
Circular Arc Cam with
Flat-faced Follower
Flat face of follower has
contact on the circular flank
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Mohammad Suliman Abuhiba, Ph.D., PE
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Circular Arc Cam
with Flat-faced
Follower
Flat face of follower has
contact on the nose
Displacement of follower
when contact is at apex K of
the nose (a-q = 0)
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Circular Arc Cam
with Flat-faced
Follower
Flat face of follower has
contact on the nose
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Example 20.15A symmetrical circular cam operating a flat-faced
follower has the following particulars:
Minimum radius of the cam = 30 mm ; Total lift = 20
mm ; Angle of lift = 75° ; Nose radius = 5 mm ;
Speed = 600 rpm. Find:
1. the principal dimensions of the cam
2. the acceleration of the follower at the beginning
of the lift, at the end of contact with the circular
flank , at the beginning of contact with nose and
at the apex of the nose.
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Example 20.1512/25/2015
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Example 20.16A symmetrical cam with convex flanks operates a
flat-footed follower. The lift is 8 mm, base circle
radius 25 mm and the nose radius 12 mm. The total
angle of the cam action is 120°.
1. Find the radius of convex flanks
2. Draw the profile of the cam
3. Determine the maximum velocity and the
maximum acceleration when the cam shaft
rotates at 500 rpm.
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Example 20.1612/25/2015
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Evaluation Quiz
Quiz will be held on
Wednesday 09/12/2013
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