Cam & Profile

Different types of cams are presented, how to draw profile that is also discussed.
For video: https://www.youtube.com/watch?v=86PV-37Frfg

1. Kinematic of machine(CE 101T) (Cam analysis) By: Poonam Savsani Department of Mechanical Engineering School of Technology 1

2. CAM - Definition A cam may be defined as a machine element having a curved outline or a curved groove, which, by its oscillation, rotation or reciprocating motion, gives a predetermined specified motion to another element called the follower . It is usually consists of a cam (the driver), the follower (the driven element), and the frame (the support for the cam and the follower).

3. PARTS OF CAM MECHANISM

4. KINEMATIC DIAGRAM FOR CAM MECHANISM

5. LEONARDO DA VINCI The first cam designs were found in Leonardo da Vinci’s sketches in his Codex Madrid I . Leonardo found cam mechanisms being very compact mechanical devices to transform rotary motion to linear motion.

6. Cam hammer Designed around 1497 by Leonardo da VinciThe hammer uses a cam to convert rotary motion to oscillating motion.

7. Examples for cam In IC engines to operate the inlet and exhaust valves

8. Classification of CAM Mechanism Based on modes of Input / Output motion Rotating cam – Translating follower Rotating cam – Oscillating follower Translating cam – Translating follower

9. Classification of followers According to the shape of follower Knife edge follower Roller follower Flat faced follower Spherical faced follower

10. According to the path of motion of follower Radial follower Offset follower

11. a) Radial follower When the motion of the follower is along an axis passing through the centre of the cam, it is known as radial followers. Above figures are examples of this type.

12. b) Offset follower When the motion of the follower is along an axis away from the axis of the cam centre, it is called off-set follower. Above figures are examples of this type.

13. According to movement Reciprocating follower oscillating follower

14. Classification of cams a) Radial or disc cam b) Cylindrical cam c) End cam

15. a) Radial or Disc cam In radial cams, the follower reciprocates or oscillates in a direction perpendicular to the cam axis.

16. b) Cylindrical cams In cylindrical cams, the follower reciprocates or oscillates in a direction parallel to the cams axis .

17. c) End cams It is also similar to cylindrical cams, but the follower makes contact at periphery of the cam as shown in fig

18. CAM Nomenclature Cam profile is the actual working surface contour of the cam. It is the surface in contact with the knife-edge, roller surface, or flat-faced follower .

19. CAM Nomenclature Base circle is the smallest circle drawn to the cam profile from the radial cam center. Obviously, the cam size is dependent on the established size of the base circle . Trace point is the point on the follower located at the knife-edge, roller center, or spherical-faced center . TRACE POINT

20. CAM Nomenclature Pitch curve : The path generated by the trace point as the follower is rotated about a stationery cam. Prime circle: The smallest circle from the cam center through the pitch curve

21. CAM Nomenclature Pressure angle: The angle between the direction of the follower movement and the normal to the pitch curve PRESSURE ANGLE Pitch point: Pitch point corresponds to the point of maximum pressure angle. PITCH POINT Pitch circle: A circle drawn from the cam center and passes through the pitch point is called Pitch circle Stroke: The greatest distance or angle through which the follower moves or rotates

22. Constraints on the Follower With external down ward force Without external down ward force

23. In all cam systems it is important that the follower is always in contact and following the motion of the cam. Gravity constraint The weight of the follower system is sufficient to maintain contact. Spring constraint The spring must be properly designed to maintain contact. Constraints on the Follower Positive mechanical constraint A groove maintains positive action.

24. Application of cam Camshaft of an Engine

25. Camshaft of an Engine incorporating a Rocker Arm

26. Oil pump working

27. ANALYSIS OF CAM FOLLOWER MOTION KINEMATICS OF CAM AND FOLLOWER

28. Rise - is when the follower is moving away from the cam centre. Dwell - is the period when the follower is stationary. Return - is when the follower moves back towards the cam centre. Stroke/Total follower travel/Throw (h) – is the greatest distance through which the follower moves. Kinematics Terminologies of Cam Mechanisms

29. Angle of return / descent Angle of dwell Angle of dwell Angle of rise / ascent / outstroke Angle of action

30. Displacement ( s ) – is the position of the follower from a specific zero or rest position in relation to time or the rotary angle of the cam. Velocity ( v ) – is the speed with which the cam moves the follower. Acceleration ( a ) – is the rate of change of the follower’s velocity.

31. Jerk ( j ) – is the rate of change of the follower’s acceleration. Angular velocity ( ω ) – is the speed of the cam or the ratio of the angular displacement by the cam to the time interval ∆ t . where θ is in radians

32. Follower Displacement Diagram A follower displacement diagram is a graph showing displacement of the follower plotted as a function of time. Since the cam usually rotates at constant angular velocity, the t -axis can be consider as the θ -axis . The follower displacement diagram determines the shape of the cam.

33. where: h is the stroke t is in seconds θ is in radians

34. Motion of the Follower Uniform motion ( constant velocity) Simple harmonic motion Uniform acceleration and retardation motion Cycloidal motion

35. a) Uniform motion (constant velocity) Displacement diagram Since the follower moves with uniform velocity during its rise and fall, the slope of the displacement curve must be constant as shown in fig RISE DWELL RETURN DWELL ANGLE OF ROTATION STROKE

36. ω

37. Generally, this design is not used for critical systems because the high acceleration at the two ends of the segment will result in large forces that will smooth out in the cam.

38. The shock effects inherent from the uniform velocity can be reduces by modifying the motion. The modification is to have the follower undergoing uniform acceleration at the start of the constant velocity interval and uniform deceleration at the end of the constant velocity interval, so that the velocity curve is continuous. Modified Uniform Velocity

39. In constructing the cam profile, we employ the principle of kinematic inversion, imagining the cam to be stationary and allowing the follower to rotate opposite to the direction of cam rotation. BASIC PRINCIPLE

40. 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, and 4. Dwell for the remaining 210° of cam rotation. The stroke of the follower is 40 mm and the minimum radius of the cam is 50 mm. The follower moves with uniform velocity during both the outstroke and return strokes. Draw the profile of the cam when cam rotates in clockwise direction. (a) the axis of the follower passes through the axis of the cam shaft, and (b) the axis of the follower is offset by 20 mm from the axis of the cam shaft. PLOT THE DISPLACEMENT DIAGRAM 40 mm 60° 30° 60° 210° A G H P 0 1 2 3 4 5 6 0’ 1’ 2’ 3’ 4’ 5’ 6’ B C D E F J K L M N

41. Profile of the cam when the axis of follower passes through the axis of cam shaft 60° 60° 30° 40 mm 60° 30° 60° A G H 0 1 2 3 4 5 6 0’ 1’ 2’ 3’ 4’ 5’ 6’ B C D E F J K L M N 1 0 2 3 4 5 6 0’ 1’ 2’ 3’ 4’ 5’ 6’ A B C D E F G H I J K L M N I 210°

42. the axis of the follower is offset by 20 mm from the axis of the cam shaft. 60° 60° 30° 40 mm 60° 30° 60° A G H 0 1 2 3 4 5 6 0’ 1’ 2’ 3’ 4’ 5’ 6’ B C D E F J K L M N 1 0 2 3 4 5 6 0’ 1’ 2’ 3’ 4’ 5’ 6’ I 210° A B C D E F G H I J K L M N OFFSET CIRCLE r=20 mm BASE CIRCLE r=50 mm

43. Simple Harmonic Motion Cams that produces simple harmonic motion to the follower are called eccentric cams . Eccentric cams are circular cams wherein the axis of rotation does not intersect the center of the circle. The displacement equation of simple harmonic motion can be written as :

44. SIMPLE HARMONIC MOTION

45. Time required for the out stroke of the follower in seconds, t O = θ O / ω Max velocity and acceleration during outstroke Max velocity and acceleration during returnstroke

46. 8 7 6 5 4 3 2 1 s ϴ o ϴ R 1 2 3 4 5 6 7 8 ϴ d

47. A cam, with a minimum radius of 25 mm, rotating clockwise 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 the valve through 50 mm during 120° rotation of the cam ; 2. To keep the valve fully raised through next 30°; 3. To lower the valve during next 60°; and 4. To keep the valve closed during rest of the revolution i.e. 150° ; 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 the line of stroke of the valve rod passes through the axis of the cam shaft, and the line of the stroke is offset 15 mm from the axis of the cam shaft. 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 r.p.m . Draw the displacement, the velocity and the acceleration diagrams for one complete revolution of the cam.

48. Profile of the cam when the line of stroke of the valve rod passes through the axis of the cam shaft 60 30 1 2 3 4 5 6 50 1 2 3 4 5 6 0’1’ 2’ 3’ 4’5 6’ 120 150 A B C D E F G H J K L M N P

49. 1 2 3 4 5 6 A B C D E F G H J K L M N P

50. Profile of the cam when the line of stroke of the valve rod is offset 15 mm from the axis of the cam shaft. 120° 30° 60° 1 2 3 4 5 6 0’ 1’ 2’ 3’ 4’ 5’ 6’ A B C D E F G H J K L M N P

51. angular velocity of the cam

52. Follower Moves with Uniform Acceleration and Retardation

53. Maximum Velocity during outstroke and return stroke. Maximum acceleration during outstroke and return stroke.

54. ϴ O ° ϴ D ° ϴ R ° ϴ D ° 0 1 2 3 4 5 6 0’ 1’ 2’ 3’ 4’ 5’ 6’ 0 1 2 3 4 5 6 0’ 1’ 2’ 3’ 4’ 5’ 6’ A G H N

55. A cycloidal curve is the path traced by a point on a circle as the circle rolls on a straight line. To create a cycloidal motion in cam design, involves superimposing cycloidal motion on constant velocity motion. No acceleration discontinuities, therefore it can be applied to high speeds. Cycloidal Motion

56. CYCLOIDAL MOTION

57. Displacement equation for the cycloid motion Maximum velocity during rise and return stroke

58. Maximum acceleration during rise and return stroke

59. Displacement dia for cycloid motion ϴ o A B S = 2 п r r = S/ 2 п 1 2 3 4 5 6 a' b' 0’ 1’ 2’ 3’ 4’ 5’ 6’ a b c d e

60. 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 simple harmonic motion. The follower dwells during next 30° of cam rotation. During next 120° of cam rotation, the follower moves inwards with simple harmonic motion. 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.

61. 120° 30° 120° 1 2 3 4 5 6 A B C D E F G H J K L M N P Min radius of cam=base circle radius = 25mm

62. 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 uniform acceleration and retardation . The follower dwells during next 30° of cam rotation. During next 120° of cam rotation, the follower moves inwards with uniform acceleration and retardation . 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.

63. 120° 30° 120° 1 2 3 4 5 6 A B C D E F G H J K L M N P

64. 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 simple hormonic motion . The follower dwells during next 30° of cam rotation. During next 120° of cam rotation, the follower moves inwards with uniform acceleration and retardation . 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.

65. 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 the first 120°rotation of the cam ; (b) Follower to return to its initial position during next 120° rotation of the cam ; (c) Follower to dwell during the next 120° of cam rotation. The distance between pivot centre and roller centre = 120 mm ; distance between pivot centre and cam axis = 130 mm ; minimum radius of cam = 40 mm ; radius of roller = 10 mm ; inward and outward strokes take place with simple harmonic motion. s

66. O A A1 120° 120° 120° 1 2 3 4 5 6 1’ 2’ 3’ 4’ 5’ 6’ 1 2 3 4 5 6 1’ 2’ 3’ 4’ 5’ 6’ B C D E F G H J K L M N