problems for practice

PROBLEMS FOR PRACTICE

On Knife-Edge Followers

1. Draw the profile of a cam operating a knife-edged follower from the following data: (a) Follower to move outward through 40 mm during 60° of cam rotation;

(b) Follower to dwell for the next 45°;

(c) Follower to return its original position during next 90°;

(d) Follower to dwell for the rest of the cam rotation.

The displacement of the follower is to take place with simple harmonic motion during both the outward and return strokes. The least radius of the cam is 50 mm. The line of stroke of follower passes through the axis of the camshaft. If the cam rotates at 300 rpm, determine the maximum velocity and acceleration of the follower during the outward stroke and the return stroke.

[A.U., Nov/Dec 2009]

[Hint: Example 3.3]

[Ans. 1.885 m/s; 1.256 m/s; 177.66 m/s²; 78.96 m/s²]

2. A cam with a minimum radius of 25 mm and rotating in the clockwise direction, is to be designed for a knife-edge follower with the following data:

-  ascent of the follower through 35 mm during 60° of cam rotation;

- dwell for next 40° of the cam rotation;

- descent of the follower during the next 90° of cam rotation;

- dwell during the rest of the cam rotation.

The ascent and descent of the cam are with simple harmonic motion and the line of stroke of the follower is offset 10 mm from the axis of the camshaft.

(1) Draw the displacement diagram.

(ii) Draw the profile of the cam.

(iii) What is the maximum velocity and acceleration of the follower during the ascent and the descent if cam rotates at 150 rpm?

[Ans. 0.825 m/s; 38.82 m/s²; 0.55 m/s; 17.27 m/s²]

3. A cam, with a minimum radius of 50 mm, rotating clockwise at a uniform speed, is required to give motion as detailed below to, a knife-edge follower:

(i) To move outwards through 40 mm during 100° rotation of cam

(ii) To dwell for next 80°,

(iii) To return to its starting position during next 90o.

(iv) To dwell for the rest period of revolution.

Draw the profile of the cam when the line of stroke of the follower passes through the centre of the camshaft. 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 camshaft rotates at 900 rpm. Draw the displacement, velocity and acceleration diagrams for one complete revolution of the cam.

[A.U., Nov/Dec 2011]

 [Hint: Refer Example 3.5]

[Ans. 4.32 m/s; -4.8 m/s; ± 466.76 m/s²; 575.88 m/s²]

4. Use the following data in drawing the profile of a cam in which a knife-edged follower is raised with uniform acceleration and deceleration and is lowered with SHM.

Least radius of cam 60 mm; Lift of follower = 45 mm; Angle of ascent = 60°; Angle of dwell between ascent and descent = 40°; Angle of descent = 75°

If the cam rotates at 180 rpm, determine the maximum velocity and acceleration during ascent and descent.

[Ans. 1.6 m/s; 1.02 m/s; 58.3 m/s²; 46.25 m/s²]

5. Draw the profile of disc cam to give uniform acceleration and retardation outstroke of 25 mm to a knife-edge follower during first half of revolution. Return of cam also takes place with uniform motion during remaining half of cam revolution. Assume minimum radius of cam as 25 mm.

6. Draw the cam profile for the following data: Base circle radius of cam = 50 mm; Lift = 40 mm; Angle of ascent with cycloidal = 60°; Angle of dwell = 90°; Angle of descent with uniform velocity = 90°; Speed of cam = 300 rpm; Follower offset = 10 mm; Type of follower = knife edge.

7. Draw. the cam profile and indicate the data for the following requirements: The lift of the follower is 40 mm, ascent angle is 120°, dwell angle is 90° and descent angle is 75°. During the ascent, the motion of the follower is cycloidal motion and during descent the motion is uniform acceleration and retardation motion. The base circle radius of the cam is 25 mm and there is no offset in the line of camshaft and the knife-edge follower.

[Hint: Refer Example 3.6]

[A.U., Nov/Dec 2006]

On Roller Followers

8. A cam with a minimum radius of 25 mm, rotating clockwise at a uniform speed is to be designed for a roller follower at the end of valve rod. The valve rod is raised through 50 mm during 120° rotation. The angle of dwell is 30°. The valve is lowered through next 60°. The valve is closed during the rest of revolution. The diameter of roller is 30 mm and the diameter of camshaft is 25 mm. Draw (i) displacement diagram, and (ii) cam profile. The line of stroke is offset 15 mm from the axis of the camshaft. The displacement takes place with SHM.

9. A cam rotating clockwise at a uniform speed of 200 rpm is required to move a roller follower with a uniform and equal acceleration and retardation on both the outward and return strokes. The angle of ascent, the angle of dwell (between ascent and descent) and the angle of descent is 120°, 60° and 90° respectively. The follower dwells for the rest of cam rotation. The least radius of the cam is 50 mm, the lift of the follower is 25 mm and the diameter of the roller is 10 mm. Draw the cam profile and find the maximum velocity and acceleration of the follower during the outstroke.

[Hint: Refer Example 3.11]

[A.U., Nov/Dec 2013]

[Ans. 0.5 m/s; 10 m/s²]

10. Draw the profile at a cam to raise a valve with harmonic motion through 40 mm in 1/4th of revolution, keep it fully raised through 1/10th revolution and to lower it with harmonic motion in 1/6th revolution. The valve remains closed during the rest of the revolution. The diameter of the roller is 20 mm and minimum radius of the cam to be 30 mm. The diameter of the camshaft is 30 mm. The axis of the valve rod passes through the axis of the camshaft. Assume the camshaft to rotate with a uniform velocity.

[Hint: Refer Example 3.8]

[A.U., Nov/Dec 2011]

11. Draw the cam profile for the following data: Base circle radius of cam = 50 mm; Lift = 40 mm; Angle of ascent with SHM = 90°; Angle of dwell = 90°; Angle of descent with uniform acceleration and deceleration 90°; Speed of cam = 360 rpm; Type of follower Roller follower (with roller radius = 10 mm).

12. A cam with a minimum radius of 25 mm, rotating in clockwise direction with a uniform speed of 100 rpm is to be designed to give the motion for a roller follower as follows: To raise through 50 mm during 120° rotation of cam with SHM. Fully raised through next 30°. To lower during next 60° with UARM Dwell for the remaining period. Draw the profile of the cam when the line of stroke of the follower is offset by 15 mm from the axis of the camshaft.

13. Layout the profile of a cam so that

1. Follower is moved outwards through 30 mm during 180° of cam rotation with cycloidal motion.

2. Follower dwells for 20° of the cam rotation.

3. Follower returns with uniform velocity during the remaining 160° of the cam rotation.

The base circle diameter of the cam is 28 mm and the roller diameter 8 mm. The axis of the follower is offset by 6 mm to the left. What will be the maximum velocity and acceleration of the follower during the outstroke if the cam rotates at 1500 rpm counter clockwise.

[Ans. 3 m/s; 471.2 m/s²]