Met 305 tutorial_6_cams

MET 305 MECHANICS OF MACHINES TUTORIAL .5

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Cams1. IntroductionA cam is a rotating machine element, which gives reciprocating or oscillating motion to another element known as follower. The cam and the follower have a line contact and constitute a higher pair. The cams are usually rotated at uniform speed by a shaft, but the follower motion is predetermined and will be according to the shape of the cam The cam and follower is one of the simplest as well as one of the most important mechanisms found in machinery today. The cams are widely used for the inlet and exhaust valves of internal combustion engines, automatic attachment of machineries, paper cutting machines, spinning and weaving textile machineries, feed mechanism of automatic lathes etc.

2. Classification of FollowersThe followers may be classified as discussed below:2.1. According to the surface in contact. The followers, according to the surface in contact, are as follows:

(a) Knife edge follower. When the contacting end of the follower has a sharp knife-edge, it is knife-edge follower, as shown in Fig. (a). The sliding motion takes place between the surfaces (i.e. the knife-edge and the cam surface). This is seldom used in practice because the small area of contacting surface results in excessive wear. In knife-edge followers, a considerable side thrust exists between the follower and the guide. (b) Roller follower. When the contacting end of the follower is a roller, it is called a roller follower, as shown in Fig.(b). Since the rolling motion takes place between the contacting surfaces (i.e. the roller and the cam), therefore the rate of wear is greatly reduced. In roller followers also the side thrust exists between the follower and the guide. The roller followers are extensively used where more space is available such as in stationary gas and oil engines and aircraft engines.(c) Flat faced or mushroom follower. When the contacting end of the follower is a perfectly flat face, it is called a flat-faced follower, as shown in Fig.(c). It may be noted that the side thrust between the follower and the guide is much reduced in case of flat-faced followers. The only side thrust is due to friction between the contact surfaces of the follower and the cam. The relative motion between these surfaces is largely of sliding nature but wear may be reduced by off-setting the axis of the follower, as shown in Fig.(f) so that when the cam rotates, the follower also rotates about its own axis. The flat faced followers are generally used where space is limited such as in cams which operate the valves of automobile engines. Note : When the flat faced follower is circular, it is then called a mushroom follower.(d) Spherical faced follower. When the contacting end of the follower is of spherical shape, it is called a spherical faced follower, as shown in Fig.(d). It may be noted that when a flat-faced follower is used in automobile engines, high surface stresses are produced. In order to minimize these stresses, the flat end of the follower is machined to a spherical shape.


2.2.According to the motion of the follower. The followers, according to its motion, are of the following two types(a) Reciprocating or translating follower. When the follower reciprocates in guides as the cam rotates uniformly, it is known as reciprocating or translating follower. The followers as shown in Fig. 20.1 (a) to (d) are all reciprocating or translating followers.(b) Oscillating or rotating follower. When the uniform rotary motion of the cam is converted into predetermined oscillatory motion of the follower, it is called oscillating or rotating follower. The follower, as shown in Fig 20.1 (e), is an oscillating or rotating follower.

2.3. According to the path of motion of the follower. The followers, according to its path of motion, are of the following two types:


(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 follower. The followers, as shown in Fig. (a) to (e) are all radial followers.(b) Off-set 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. The follower, as shown in Fig. (f), is an off-set follower.Note : In all cases, the follower must be constrained to follow the cam. This may be done by springs, gravity

or hydraulic means. In some types of cams, the follower may ride in a groove. important in order to draw the cam profile.

3. Cam Terminology3.1. Base circle. It is the smallest circle that can be drawn to the cam profile.

3.2. Trace point. It is a reference point on the follower and is used to generate the pitch curve. In case of knife edge follower, the knife edge represents the trace point and the pitch curve corresponds to the cam profile. In a roller follower, the centre of the roller represents the trace point.

3.3. Pressure angle. It is the angle between the direction of the follower motion and a normal to the pitch curve. This angle is very important in designing a cam profile. If the pressure angle is too large, a reciprocating follower will jam in its bearings.

3.4. Pitch point. It is a point on the pitch curve having the maximum pressure angle.

3.5. Pitch circle. It is a circle drawn from the centre of the cam through the pitch points.

3.6. Pitch curve. It is the curve generated by the trace point as the follower moves relative to he cam. For a knife edge follower, the pitch curve and the cam profile are same whereas for a roller follower, they are separated by the radius of the roller.

3.7. Prime circle. It is the smallest circle that can be drawn from the centre of the cam and tangent to the pitch curve. For a knife edge and a flat face follower, the prime circle and the base circle are identical. For a roller follower, the prime circle is larger than the base circle by the radius f the roller.

3.8. Lift or stroke(throw, travel). It is the maximum travel of the follower from its lowest position to the topmost position.


4. Types of follower motions1. Uniform velocity

2. Simple harmonic motion


3. Uniform acceleration and retardation

4. Cycloidal Motion


5. Objective

a. To understand different types of followersb. To analyze various types of follower displacements c. To analyze and draw different types of cams for different types of followers and

motions

6. Procedure

1. Check the type of follower.2. Study the type of follower motion.3. Draw the displacement diagram.4. Construct the cam profile.

7. Problems

1. Draw the profile of a disc cam to give uniform motion (uniform velocity) during outstroke of 25 mm to a knife edge follower during the first half of the cam revolution. The return of the cam also takes place with uniform motion (uniform velocity) during the remaining half of the cam revolution. Minimum radius of the cam is 25 mm. Draw the shaft on which the cam is mounted showing the position of the key. Shaft diameter - 25 mm. The axis of the knife edge follower passes through the axis of the cam.


2. Draw the cam profile for cam with roller reciprocating follower. The axis of the follower passes through the axis of the cam and rotates anticlockwise. Particulars of the cam and the follower motion are the following:

Roller diameter = 5 mmMinimum radius of the cam = 20 mmTotal lift = 25 mm.

The cam has to lift the follower with simple harmonic motion during 180° of cam rotation, then allow the follower to drop suddenly halfway, and further return the follower with uniform velocity during the remaining 180° of cam rotation. Show the position of key on the shaft to which the cam is mounted. Determine the maximum velocity and maximum acceleration on the outstroke, if the cam rotates at a uniform speed of 100 r.p.m.

Answer


3.. Cam with 30 mm as minimum diameter is rotating clockwise at a uniform speed of 1200 r.p.m. clockwise and has to give the motion to the roller follower 10 mm diameter as defined below :

(i ) Follower to complete outward stroke of 25 mm during 120° of cam rotation with equal uniform acceleration and retardation.

(ii) Follower to dwell for 60° of cam rotation. (iii) Follower to return to its initial position during 90° of cam, rotation with equal uniform acceleration and retardation(iv) Follower to dwell for the remaining 90° of cam rotation.Layout the cam profile when:(a) the roller follower axis passes through the axis of the cam ;(b) the roller follower axis is offset to right by 5 mm.

Determine the uniform acceleration of the follower on the outstroke and the return stroke, and also the maximum velocity of the follower during outstroke and the return stroke.

Answer


4. Determine the profile of cam to give oscillatory motion to the follower, with uniform angular velocity about its pivot. One oscillation is completed in one revolution of the cam. The distance between the cam centre and the pivot of the follower is 50 mm. The base circle diameter is 40 mm. Angle of oscillation is 29°. The length of the oscillating lever = 50 mm with roller of 5 mm diameter at the end. The cam rotates anticlockwise.Answer


5. 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 (ii) follower to return to its initial position during 120° of cam rotation;(iv) Follower to dwell for remaining 90° of cam rotation. Cam rotates anticlockwise

Answer


6. It is required to set out the profile of a cam to give the following motion to the follower:(i) Follower to move outwards through 31.4 mm during 180° of cam rotation, with cycloidal motion;(ii) Follower to return with cycloidal motion during 180° of cam rotation.

Determine the maximum velocity and acceleration of the follower during the outstroke when the cam rotates at 2400 r.p.m. clockwise. The base circle of the cam is 30 mm diameter and the roller diameter of the follower is 10 mm. The axis of the roller is offset by 7.5 mm to the right.


10. Conclusion

This tutorial enables the student to construct any type of cam profile for any mechanism design.

Met 305 tutorial_6_cams

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