Expt No: 07

To verify cam-jump phenomenonAim: Verification Cam Jump PhenomenonApparatus : Experimental set with eccentric cam and flat face follower, spanner,tachometer and motor drive.

Theory:INTRODUCTION:- A Cam is a mechanical member for transmitting a desired motion to a follower by direct contact. The driver is called as the ‘Cam’ & the driven member is called as the ‘Follower’. The cam may remain stationary, translate, oscillate or rotate whereas the follower may translate or oscillate. Cam Mechanism is a case of a higher pair with line contact. In its simplest form, a cam mechanism consists of three links with higher pairing between two links.CLASSIFICATION OF CAMS: Cams can be basically classified in three ways-1.According to the follower motion.2. According to the shape of the cam.3. According to the manner of constraint of the follower.1. According to the follower motion:-I) Dwell-Rise-Dwell Cams (D-R-D):-

II) Dwell-Rise-Return-Dwell Cams (D-R-R-D):-

The dwelling of the cam is followed by rise & another dwell period. Then the fall or return of the cam & further dwell period.

The dwelling of the cam is followed by rise & another dwell period. Then the fall or return of the cam & further dwell period.

This type has the rise & return preceded & followed by dwells

III) Rise-Return-Rise Cams (R-R-R):-

.

2. According to the shape of the cam:-I) Wedge Cam (Flat Cam):-

II) Radial Cam (Disc Cam):-

This type has only the rise-return-rise contour & it has no dwells. It has very limited use in machinery

A wedge cam has a wedge which in general has a translational motion. The follower may either translate or oscillate. The follower is held in contact by a spring.

Instead of using a wedge, a flat plate with groove can also be used & hence also called as flat cam. The follower is held in contact by a positive drive groove & roller.

III) Cylindrical Cam (Barrel):-

3. According to the manner of constraint of the follower:-I) Pre-loaded Spring Cam :-

In radial or disc cam, the position of the follower is determined from the cam axis. The follower reciprocates or oscillates in a plane at right angles to the axis of the cam. This cam is very much popular due to its simplicity & compactness.

In cylindrical cam, a cylinder which has a circumferential contour, cutting into a surface of rotation. The follower reciprocates or oscillates in a plane parallel to the axis of the cam. In case of cylindrical cams, cylindrical roller followers are usually used.

A preload compression spring (usually a helical coiled type) is used for the purpose of keeping the contact between the cam & the follower.

A positive drive cam does not need any external force to maintain contact between the follower & the profile of cam.

e.g. Yoke Cam, Conjugate Cam, Wedge Cam.

II) Positive Drive Cam:- .

III) Gravity Cam:-

CLASSIFICATION OF FOLLOWERS:-Followers can be classified as follows-1.According to the Shape of the Follower.2. According to the Movement of the Follower.3. According to the Location of Line of Movement.

1. According to the Shape of the Follower:-

I) Knife - Edge Follower:-

A positive drive cam does not need any external force to maintain contact between the follower & the profile of cam.

e.g. Yoke Cam, Conjugate Cam, Wedge Cam.

In gravity cam, the rise of a cam is achieved by the rising surface of a cam & the return due to the force of gravity or due to the weight of the follower. This cam gives uncertain behavior & hence not preferred.

II) Roller Follower: -

III) Flat Faced Follower (Mushroom Follower):-

2. According to the Movement of the Follower:-

I) Reciprocating Follower:-

.

II) Oscillating Follower:-

In this, a sharp knife edge is in contact with cam. It is the simplest in construction, but it of very little practical use due to the fact that extreme wear of the cam surface & the contact surface will take place.

In this type of follower, the rate of wear is greatly reduced. The roller action at low speed is pure rolling, but as the speed increases, sliding occurs. The roller follower jams the cam in case of steep rise.

In this case, the contacting end of the follower is a perfectly flat face. The relative motion between the contact surfaces is largely of sliding nature. High surface stresses can be reduced by using a spherical faced follower also known as ‘Mushroom Follower’

In this type, the cam rotates & the follower reciprocates or translates in the guides

In this type, the cam rotates & the follower oscillates about a suitable pivot on the frame

3. According to the Location of Line of Movement:-I) Radial Follower (In-Line Follower):-

II) Offset Follower:-

TERMINOLOGY & DEFINITIONS:-

In this case, the line of action of the movement of follower passes through the center of rotation of the cam.

In this type of follower, the line of action of the movement of the follower is offset from the center of rotation of the cam.

1) Cam Profile:-It is the actual working surface contour of the cam, which is in contact with the knife edge, roller or flat faced follower.2) Base Circle:-It is the smallest circle drawn tangent to the cam profile, from the center of rotation of the radial cam.3) Trace Point:-It is the point on the follower to trace the cam profile.It is located at the knife edge of a knife edge follower, at the roller center of a roller follower or mushroom follower, but at the point of contact for the flat faced follower.4) Pitch Curve:-It is the path of the trace point which is obtained by assuming that the cam is fixed & the trace point of the follower rotates around the cam.5) Prime Circle:-It is the smallest circle drawn tangent to the pitch curve from the cam center.6) Pressure Angle:-It is the angle at any point between the normal to the pitch curve & the instantaneous direction of the follower motion. It represents the steepness of the cam profile. A high value of maximum pressure angle is not desirable as it might jam the follower in the guides.7) Pitch Point:-It is the point on the cam pitch curve having the maximum pressure angle.8) Pitch Circle:-It is the circle passing through the pitch point & having its center at the cam axis.9) Lift:-It is the maximum travel of the follower from its lowest position to the topmost position.

Cam jump phenomenon:“In cam-follower system the follower is kept pressed against the cam surface by means of spring. Due to inertia of the follower, beyond a particular speed during part of the cam rotation the follower may lose contact with the cam. The phenomenon is known as ‘cam jump’ which is a type of vibration.”-This is transient and occurs at high speeds. Highly flexible cam-follower systems can become excessively unbalanced because of cam jump due to force exceeding spring force.-Beyond a particular speed the follower loses contact with cam surface and when follower again comes in contact with cam surface, it may do serve contact with

cam surface.

Fig. Cam and follower response curve-During jump the follower is losing the contact with the cam surface and when follower again comes in contact with the cam surface, it may damage cam surface due to severe contact, it may damage cam surface due to severe contact also hammering noise may produce.-Jump phenomenon can be avoided by increasing stiffness of the returning spring or by limiting the speed of cam or increasing the amount of preload on spring.

Analysis for jump in eccentric cam:

Consider an eccentric cam with flat face follower as shown in figure, Let, y=distance covered by follower at cam rotation θ y=Velocity of followerÿ=Acceleration of followerm= mass of the follower. e = eccentricity.F= contact force between cam and followerFs= total spring force=P+kyω= angular speed of cam. r=Radius of circular disc cam δi =Intial compression of the spring.k=stiffness of springP=Preloaded in spring=mg+k δi

m ÿ =Inertia forcefrom fig,Lift of follower ,y=OS2-OS1

=A2Q+QY-OS1

=R+e cos(180-θ)-(R-e) =R-e cosθ-R+e

Differentiating above equation,

Velocity of follower , y=e(0+sin θ) dθdt

=e ω sin θAcceleration of follower ,ÿ= e ω2 cos θ

From FBD,Inertia force = External force

-mÿ = Fs– F

∴ F = mÿ + Fs

But,Fs= P + ky

= P + k[e (1- cosθ)] = P + ke (1- cosωt)

∴ F= m (e ω2cos ωt)+ P + ke (1- cosωt) =mω2(e cos ωt) + P + ke – ke cosωt

F = [mω2-k]e cos ωt)+ (P + ke)

Thus contact force is max when θ =0o, min when θ =180o, contact force also depends on square of cam velocity.

This velocity when it becomes less than zero, the follower would loose control with cam resulting in a jump. This would happen at critical speeds.

F = 0 =(mωj2 – k)e cos180- (P + ke), where ωj=jump speed

=(mωj2 – k)(-e) + (P + ke),

∴ (mωj2 – k) e = P + ke

∴ωj2 = (P + 2ke)/ (me)

∴ω j= 2√ (P+2k e )me

to avoid jump,ω j< 2√ (P+2k e )me

or P>(mω2-2k)e

Experimental setup:The setup is a motorized unit consisting of camshaft driven by DC motor. The shaft runs in double ball bearing. At the free end of the cam shaft the cam can be easily moved as the follower is properly guided in gun metal bushes. Any type of follower can be used to suit the cam under test.

A spring is used to provide controlling force to the follower system. Weight of the follower rod can be adjusted as per requirement. Arrangement for regulation of speed is provided.

Procedure:

1. Eccentric cam and roller follower were taken for trial.2. Motion is started by rotating the motor and speed is increased gradually.3. Speed at which audible noise is heard is noted.

Observations:Cam diameter =Eccentricity =Follower mass =Spring stiffness =Initial spring compression =Observation table:

Sr.No.

Deflection(mm)

Theoretical speed(Nth) rpm

Practical Speed (Npr)rpm

1.2.3.4.5

Calculations:

ω j=❑√ (P+2k e )me

where,

m= mass of the follower. e = eccentricity.k=stiffness of spring P=Preloaded in spring=mg+k δi

Sample calculations for observation no. are as shown below,

Conclusion:

1. It is not advisable to operate cam above jumping speed as it creates a thudding noise.2. Practical & analytical N differs due to inertia of follower nut and springs.