chapter 20 - islamic university of gazasite.iugaza.edu.ps/mhaiba/files/2013/09/ch-20-cams1.pdf20.1....

Chapter 20

Cams

1/2/2015

Dr. Mohammad Suliman Abuhiba, PE 1

20.1. Introduction

A cam is a rotating machine element which gives

reciprocating or oscillating motion to another

element known as follower.

Cam and follower have a line of contact and

constitute a higher pair.

1/2/2015

Dr. Mohammad Suliman Abuhiba, PE

2

20.1. Introduction

Applications of Cams:

Inlet and exhaust valves of internal

combustion engines

Automatic attachment of machineries

Paper cutting machines

Feed mechanism of automatic lathes

1/2/2015


3

20.2. Classification of Followers

1. According to the surface in contact

a. Knife edge follower

b. Roller follower

c. Flat faced or mushroom follower

d. Spherical faced follower

2. According to motion of follower

a. Reciprocating or translating follower

b. Oscillating or rotating follower

3. According to path of motion of follower

a. Radial follower

b. Off-set follower

1/2/2015


4


1. According to surface in

contact

a. Knife edge follower

contacting end of follower =

sharp knife edge

Seldom used in practice

because the small area of

contacting surface results in

excessive wear.

A considerable side thrust exists

between the follower and guide

1/2/2015


5


1. According to the surface

in contact

b. Roller follower

Rolling motion between

contacting surfaces

Rate of wear is greatly

reduced

Side thrust exists between

follower and guide

1/2/2015


6

20.2. Classification of Followers 1. According to the surface in contact

c. Flat faced or mushroom follower

Side thrust between follower & guide is

much reduced

The only side thrust is due to friction

between the contact surfaces of follower &

cam

Relative motion between these surfaces is

largely of sliding nature

Wear may be reduced by off-setting the axis

of follower, Fig. 20.1 (f ) so that when cam

rotates, follower also rotates about its own

axis.

1/2/2015


7


1. According to the surface in

contact

d. 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

1/2/2015


8


2. According to motion of follower

a. 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.

1/2/2015


9


2. According to motion of

follower

b. Oscillating or rotating

follower

Uniform rotary motion of cam

is converted into

predetermined oscillatory

motion of follower.

1/2/2015


10


3. According to path of motion of follower

a. Radial follower

When motion of follower is along an axis

passing through center of cam

Fig. 20.1 (a) to (e)

1/2/2015


11


3. According to path of

motion of follower

b. Off-set follower

Motion of follower is along an

axis away from axis of cam

center

1/2/2015


12

20.3. Classification of Cams

1. Radial or disc cam

2. Cylindrical cam

1/2/2015


13


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

1/2/2015


14


2. Cylindrical cam

follower reciprocates or oscillates in a

direction parallel to cam axis.

1/2/2015


15

20.4. Terms Used

in Radial Cams

1/2/2015


16

20.4. 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 the trace

point and the pitch curve corresponds to cam profile

Roller follower: center of roller represents trace point

1/2/2015


17


Pressure angle

Angle between direction of follower motion and a

normal to the pitch curve

If the pressure angle is too large, a reciprocating

follower will jam in its bearings

Pitch point

A point on the pitch curve having maximum

pressure angle

1/2/2015


18


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

1/2/2015


19


Prime circle

Smallest circle that can be drawn from the center

of the cam and tangent to the pitch curve

Knife edge & flat face follower: prime circle and

base circle are identical

Roller follower: prime circle is larger than base

circle by radius of roller

Lift or stroke

maximum travel of follower from its lowest

position to topmost position

1/2/2015


20

20.5. Motion of the Follower

1. Uniform velocity

2. Simple harmonic motion

3. Uniform acceleration and retardation

4. Cycloidal motion

1/2/2015


21

Displacement, Velocity & Acceleration

Diagrams - Follower Moves with Uniform Velocity

1/2/2015


22

Fig. 20.4

Fig. 20.5

20.7. Displacement, Velocity & Acceleration

Diagrams when Follower Moves with SHM

1/2/2015


23

S = Stroke of

follower

qO & qR = Angular

displacement of

cam during out &

return strokes of

follower

w = Angular

velocity of cam



1/2/2015


24

Time required for the out stroke

of the follower in seconds,

P’ executes a SHM as P rotates

Motion of follower is similar to

that of P

Peripheral speed of P’



1/2/2015


25

Max velocity & Max acceleration of follower on

outstroke,

Max velocity & max acceleration of follower on

return stroke

Displacement, Velocity

& Acceleration

Diagrams

Follower Moves with

Uniform Acceleration &

Retardation

1/2/2015


26

Displacement, Velocity & Acceleration Diagrams

Follower Moves with Uniform Acceleration &

Retardation

1/2/2015


27

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

1/2/2015


28

Max velocity of follower = twice mean velocity,

Max acceleration of follower during outstroke

Max acceleration of follower during return stroke

Example 20.1 A 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 42mm and minimum radius of cam

is 50 mm. The follower moves with uniform velocity during

both the out and return strokes. Draw the profile of cam

when

a. Axis of follower passes through the axis of cam shaft

b. Axis of follower is offset by 20 mm from axis of cam shaft

1/2/2015


29

Example 20.1 1/2/2015


30

Example 20.1 1/2/2015


31

Example 20.1 1/2/2015


32

Example 20.2 A 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.

1/2/2015


33

Example 20.3 A 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.

1/2/2015


34

Example 20.3 The 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.

1/2/2015


35

Example 20.4 A 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.

1/2/2015


36

Example 20.5 Draw 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.

1/2/2015


37

Example 20.6 A 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.

1/2/2015


38

Example 20.6 The 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.

1/2/2015


39

Example 20.10 It 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.

1/2/2015


40

20.12. Tangent

Cam with

Reciprocating

Roller Follower

Such cams are

used for operating

inlet & exhaust

valves of internal

combustion

engines

1/2/2015


41

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

1/2/2015


42


Roller Follower

Roller has contact with straight flanks

1/2/2015


43


Roller Follower

Roller has contact with straight flanks

1/2/2015


44

20.12. Tangent Cam

with Reciprocating

Roller Follower

Roller has contact with the

nose

1/2/2015


45

20.12. Tangent Cam

with Reciprocating

Roller Follower


nose

1/2/2015


46

20.12. Tangent Cam

with Reciprocating

Roller Follower


nose

1/2/2015


47

Example 20.13 In 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.

1/2/2015


48

Example 20.13 1/2/2015


49

Example 20.14 A 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.

1/2/2015


50

Example 20.14 1/2/2015


51

20.13. 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

1/2/2015


52

20.13. Circular Arc

Cam with Flat-faced

Follower

Flat face of follower has

contact on the circular flank

1/2/2015


53

x = BA = BO − AO = CD − EO

20.13. Circular Arc

Cam with Flat-faced

Follower


contact on the circular flank

1/2/2015


54

20.13. Circular Arc

Cam with Flat-

faced Follower


contact on the nose

Displacement of follower

when contact is at apex K of

the nose (a-q = 0)

1/2/2015


55

20.13. Circular Arc

Cam with Flat-

faced Follower


contact on the nose

1/2/2015


56

Example 20.15 A 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.

1/2/2015


57

Example 20.15 1/2/2015


58

Example 20.16 A 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.

1/2/2015


59

Example 20.16 1/2/2015


60

Evaluation Quiz

Quiz will be held on

Wednesday 09/12/2013

1/2/2015


61

chapter 20 - islamic university of gazasite.iugaza.edu.ps/mhaiba/files/2013/09/ch-20-cams1.pdf20.1....

Documents