12/25/2015. Chapter 20. Cams. Mohammad Suliman Abuhiba, Ph.D., PE

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1 Chapter 20 Cams 1

2 2 Introduction A cam: a rotating machine element which gives reciprocating or oscillating motion to another element (follower) Cam & follower have a line constitute a higher pair. of contact and

3 3 Introduction Applications of Cams: Inlet & exhaust valves of ICE Automatic attachment of machineries Paper cutting machines Feed mechanism of automatic lathes

4 4 Classification of Followers 1. According to the surface in contact 2. According to motion of follower 3. According to path of motion of follower

5 5 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

6 6 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

7 7 Classification of Followers 1. 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 (f ) so that when cam rotates, follower also rotates about its own axis.

8 8 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

9 9 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 (a) to (d) are all reciprocating or translating followers.

10 10 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.

11 11 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 (a) to (e)

12 12 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

13 13 Classification of Cams 1. Radial or disc cam 2. Cylindrical cam

14 14 Classification of Cams 1. Radial or disc cam Follower reciprocates or oscillates in a direction perpendicular to cam axis Cams shown in Fig are all radial cams

15 15 Classification of Cams 2. Cylindrical cam follower reciprocates or oscillates in a direction parallel to cam axis.

16 16 Terms Used in Radial Cams

17 17 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

18 18 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

19 19 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

20 20 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

21 21 Motion of the Follower 1. Uniform velocity 2. Simple harmonic motion 3. Uniform acceleration and retardation 4. Cycloidal motion

22 22 Displacement, Velocity & Acceleration Diagrams - Follower Moves with Uniform Velocity Fig Fig. 20.5

23 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 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 23

24 Example

25 Example

26 Example

27 Displacement, Velocity & Acceleration Diagrams when Follower Moves with SHM 27 S = Stroke of follower q O & q R = Angular displacement of cam during out & return strokes of follower w = Angular velocity of cam

28 28 Displacement, Velocity & Acceleration Diagrams when Follower Moves with SHM 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

29 Displacement, Velocity & Acceleration Diagrams when Follower Moves with SHM Max velocity & Max acceleration of follower on out stroke, 29 Max velocity & max acceleration of follower on return stroke

30 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 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. 30

31 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 To lower the valve during next 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. 31

32 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. 32

33 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. 33

34 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. 34

35 35 Displacement, Velocity & Acceleration Diagrams Follower Moves with Uniform Acceleration & Retardation

36 36 Displacement, Velocity & Acceleration Diagrams Follower Moves with Uniform Acceleration & Retardation S = Stroke of follower q O & q R = Angular displacement of cam during out stroke & return stroke of follower w = Angular velocity of cam Time required for follower during outstroke, t O = q O /w Time required for follower during return stroke, t R =q R /w Mean velocity of follower during outstroke = S/t O Mean velocity of follower during return stroke = S/t R

37 37 Displacement, Velocity & Acceleration Diagrams Follower Moves with Uniform Acceleration & Retardation Max velocity of follower = twice mean velocity, Max acceleration of follower during outstroke Max acceleration of follower during return stroke

38 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 To return to its starting position during next 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. 38

39 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. 39

40 Example 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. iii. iv. Follower to dwell for 30 of cam rotation Follower to return to its initial position during 120 of cam rotation 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. 40

41 41 Tangent Cam with Reciprocating Roller Follower Used for operating inlet & exhaust valves of ICEs Mohammad Suliman Abuhiba, Ph.D., PE

42 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

43 43 Tangent Cam with Reciprocating Roller Follower Roller has contact with straight flanks

44 44 Tangent Cam with Reciprocating Roller Follower Roller has contact with straight flanks

45 45 Tangent Cam with Reciprocating Roller Follower Roller has contact with the nose

46 46 Tangent Cam with Reciprocating Roller Follower Roller has contact with the nose

47 47 Tangent Cam with Reciprocating Roller Follower Roller has contact with the nose

48 Example 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. 48

49 Example

50 Example 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. 50

51 Example

52 52 Circular Arc Cam with Flat-faced Follower r 1 = Min radius of cam (radius of base circle = OE r 2 = 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

53 53 Circular Arc Cam with Flat-faced Follower Flat face of follower has contact on the circular flank x = BA = BO AO = CD EO

54 54 Circular Arc Cam with Flat-faced Follower Flat face of follower has contact on the circular flank

55 Circular Arc Cam with Flat-faced Follower Flat face of follower has contact on the nose 55 Displacement of follower when contact is at apex K of the nose (a-q = 0)

56 Circular Arc Cam with Flat-faced Follower Flat face of follower has contact on the nose 56

57 Example 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. 57

58 Example

59 Example 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 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. 59

60 Example

61 61 Evaluation Quiz Quiz will be held on Wednesday 09/12/2013

Instantaneous Centre Method

Instantaneous Centre Method The combined motion of rotation and translation of the link AB may be assumed to be a motion of pure rotation about some centre I, known as the instantaneous centre of rotation.