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TOM2

Unit IV

Cam and Follower

Q1) Classify cams in detail.

Ans.

Cams are classified according to

According to shape

Wedge and flat cams

A wedge cam has a wedge W which, in general, has a translational motion.

The follower F can either translate or oscillate.

A spring is, usually, used to maintain the contact between the cam and the follower.

In the figure the cam is stationary, and the follower constraint or guide G causes the relative motion of the cam and the follower.

2. Radial or disc cams

Cam in which the follower moves radially from the center of rotation of the cam is known as a radial or a disc cam.

Radial cams are very popular due to their simplicity and compactness.

3. Spiral cams

Spiral cam is a face cam in which a groove is cut in the form of a spiral as shown in the figure.

The spiral groove consists of teeth which mesh with a pin gear follower.

The velocity of the follower is proportional to the radial distance of the groove from the axis of the cam.

The use of such cam is limited as the cam has to reverse the direction to reset the position of the follower.

It finds its use in computers.

4. Cylindrical cams

In a cylindrical cam, a cylinder that has a circumferential contour cut in the surface rotates about its axis.

The follower motion can be of two types as follows:

In the first type, a groove is cut on the surface of the cam and roller follower has a constraint oscillating motion.

Another type is an end cam in which the end of the cylinder is the working surface.

Spring-loaded follower translates along or parallels to the axis of the rotating cylinder.

Cylindrical cams are also known as barrel or drum cams.

5. Conjugate cams:-

Conjugate cam is a double-disc cam, the two discs being keyed together and are in constant touch with the two rollers of a follower.

Thus, the follower has a positive constraint.

Such type of cam is preferred when the requirements are low wear, low noise, better control of the following, high speed, high dynamic loads, etc.

6. Globoid cams

Globoid cams have two types of surfaces, convex or concave.

A circumferential contour is cut on the surface of rotation of the cam to impart motion to the follower which has an oscillatory motion.

The application of such camps is limited to moderate speed and where the angle of the oscillation of the follower is large.

7. Spherical cams

A spherical cam, the follower oscillates about an axis perpendicular to the axis of rotation of the cam.

The follower oscillates about an axis parallel to the axis of rotation of the cam.

A spherical cam is in the form of a spherical surface which transmits motion to the follower.

b. According to follower movement

The motions of the followers are distinguished from each other by the dwells they have.

Rise return rise ( R-R-R)

In this, there is an alternate rise and return of the following with no periods of dwells.

Its use is very limited in the industry.

The follower has a linear or angular displacement.

2. Dwell rise return dwell (D-R-R-D)

In such type of CAM, there is a rise and return of the follower after a dwell.

This type is used more frequently than the R-R-R type of cam.

3. Dwell rise dwell return dwell (D-R-D-R-D)

It is the most widely used type of CAM.

The dwelling of the cam is followed by the rise and dwell and subsequently by return and dwell as shown in the figure.

In case the return of the follower is by a fall, the motion may be known as well as Dwell-Rise-Dwell.

Q2) Classify follower details.

Ans.

The followers may be classified as discussed below:

According to the surface in contact. The followers according to the surface in contact, are as follows:

Knife edge follower:

When the contacting end of the follower has a sharp knife-edge, it is called a knife-edge follower, as shown in the figure.

The sliding motion takes place between the contacting surfaces.

It is rarely used in practice because of 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.

2. Roller follower:

When the contact and of the following is a roller, it is called a roller follower, as shown in the figure.

Since the rolling motion takes place between the contacting surfaces, therefore the rate of ware 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.

3. Flat-faced or mushroom follower:-

When the contact and of the following is a perfectly flat face, it is called a flat-faced follower, as shown in the figure.

It may be noted that the side thrust between the follower and the guide is much reduced in the case of flat-faced followers.

The only side thrust is due to friction between the contact surfaces of the follower and the camp.

The flat-faced followers are generally used where space is limited such as in cams that operate the valves of automobile engines.

4. Spherical faced follower:-

When the contacting end of the follower is spherical, it is called a spherical faced follower, as shown in the figure.

It may be noted that when a flat-faced follower is used in automobile engines, high surface stresses are produced.

To minimize the stresses, the flat end of the follower is the machine to a spherical shape.

b. According to the motion of the follower the followers, according to its motion are of the following two types

Reciprocating for translating follower

When the follower reciprocates in guides as the cam rotates uniformly, it is known as a reciprocating or translating follower.

The followers as shown in the figure a to f are all reciprocating or translating followers.

2. Oscillating or rotating follower

When the uniform rotary motion of the cam is converted into a predetermined oscillatory motion of the follower, it is called oscillating for rotating follower.

The follower, as shown in the figure is an oscillating or rotating follower.

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

Radial follower:-

When the motion of the follower is along an axis passing through the center of the cam, it is known as a radical follower.

The followers, as shown in the figure a to e are all radial followers.

2. Offset follower:-

When the motion of the follower is along an axis away from the axis of the cam center, it is called offset follower.

The follower, as shown in figure (f) is an off-set follower.

Q3) Explain the procedure of drawing velocity & acceleration diagrams for uniform velocity motion.

Ans.

The displacement, velocity, and acceleration diagrams when a knife-edge follower moves with uniform velocity as shown in figure a, b and c respectively.

The abscissa represents the time that may represent the angular displacement of the cam in degrees.

The ordinate represents the displacement or velocity or acceleration of the follower.

Since the follower moves with uniform velocity during its rise and return stroke, therefore the slope of the displacement curves must be constant.

In other words,

must be straight lines.

The follower remains at rest during part of the cam rotation.

The periods during which the follower remains at rest are known as dwell periods, as shown by lines

in figure a.

From figure c we see that the acceleration or retardation of the follower at the beginning and the end of each stroke is infinite.

This is because the follower is required to start from rest and has to gain a velocity within no time.

This is only possible if the acceleration or retardation at the beginning and the end of each stroke is infinite. These conditions are however impracticable.

To have the acceleration and retardation within the finite limits, it is necessary to modify the conditions which govern the motion of the followers.

This may be done by rounding off the sharp corners of the displacement diagram at the beginning and the end of each stroke, as shown in figure a.

By doing so the velocity of the follower increases gradually to its maximum value at the beginning of each stroke and decreases gradually to zero at the end of each stroke as shown in figure b.

The modified displacement, velocity, and acceleration diagrams are shown in the figure.

The round corners of the displacement diagram are usually parabolic curve because the parabolic motion results in a very low acceleration of the follower for a given stroke and cam speed.

Q4) Explain the procedure of drawing velocity & acceleration diagrams for SHM motion.

Ans.

The displacement velocity and acceleration diagrams when the follower moves with simple harmonic motion are shown in the figure a b and c respectively.

The displacement diagram is drawn as follows:

Draw semicircle on the follower stroke as diameter.

Divide the semicircle into any number of even equal parts.

Divide the angular displacement of the cam during our stroke and return stroke into the same number of equal parts.

The displacement diagram is obtained by projecting the points as shown in figure a.

The velocity and acceleration diagrams are shown in figure b and c respectively.

Since the follower moves with a simple harmonic motion, therefore velocity diagram consists of a sine curve and the acceleration diagram is a cosine curve.

We see from the figure that the velocity of the follower is zero at the beginning and the end of its stroke and increases gradually to a maximum at mid-stroke.

On the other hand, the acceleration of the follower is maximum at the beginning and the ends of the stroke and diminishes to zero at mid-stroke.

Let h =stroke of the follower,

=angular displacement of the cam during out stroke and return stroke of the follower respectively, in radian, and

= Angular velocity of the cam in radian/s

Maximum velocity of the follower on the outstroke

Maximum acceleration of the follower on the outstroke.

Similarly, the maximum velocity of the follower on the return stroke.

And the maximum acceleration of the follower on the return stroke.

Q5) Explain the procedure of drawing velocity & acceleration diagrams for uniform acceleration uniform deacceleration motion.

Ans.

The displacement, velocity, and acceleration diagrams when the follower moves with uniform acceleration and retardation are shown in the figure a b and c respectively.

The displacement diagram consists of a parabolic curve and may be drawn as discussed below:

Divide the angular displacement of the cam during outstroke into an even number of equal parts and draw vertical lines through these points as shown in figure a.

Divide the stroke of the follower into the same number of equal even parts.

Join Aa to intersect the vertical line through point 1 at B. Similarly, obtained other points C, D, etc. As shown in figure a. Now join these points to obtain the parabolic curve for the outstroke of the follower.

Similarly as discussed above, the displacement diagram for the follower during return stroke may be drawn.

Since the acceleration and retardation are uniforms, therefore the velocity varies directly with the time. The velocity diagram is shown in figure b.

Let h=stroke of the follower.

=angular displacement of the cam during out stroke and return stroke of the follower respectively, and

= Angular velocity of the cam.

Maximum velocity of the follower during outstroke,

Similarly, the maximum velocity of the following during return stroke,

We see from the acceleration diagram, as shown in figure c, that during the first half of the outstroke there is uniform acceleration and during the second half of the outstroke there is uniform retardation.

Thus, the maximum velocity of the follower is reached after the time

(during out stroke) and

(during return stroke).

Maximum acceleration of the follower of during out stroke,

Similarly, maximum acceleration of the following during return stroke,

Q6) Explain the procedure of drawing velocity & acceleration diagrams for cycloidal motion.

Ans.

The displacement, velocity, and acceleration diagrams when the follower moves with cycloidal motion are shown in the figure a b and c respectively.

We know that cycloidal is a curve traced by a point on a circle when the circle rolls without slipping on a straight line.

In the case of the cam, the straight line is a stroke of the follower, which is translating, and the circumference of the rolling circle is equal to the stroke of the follower. Therefore, the radius of the rolling circle is S/2π.

The displacement diagram is drawn as discussed below:

Draw a circle of radius S/2π with A as the center.

Divide the circle into any number of equal even parts. Project these points horizontally on the vertical centerline of the circle. These points are shown by a' and b' in the figure a

Divide the angular displacement of the cam during outstroke into the same number of equal even parts as the circle is divided. Draw vertical lines through these points.

Join AB which intersects the vertical line through 3' at c.

From a' draw a line parallel to AB intersecting the vertical lines through 1’ and 2’ at a and b respectively.

5. Similarly, from b’ draw a line parallel to AB intersecting the vertical lines through 4’ to 5’ at d & e respectively.

6. Joinpoint A a b c d e B by a smooth curve. This is the required cycloidal curve for the following during outstroke.

Let = angle through which the cam rotates in time t seconds, and

= Angular velocity of the cam.

The velocity is maximum when

Maximum velocity of the following during outstroke,

Similarly, the maximum velocity of the following during return stroke,

Maximum acceleration of the following due to out stroke,

Similarly, maximum acceleration of the following during return stroke,

The velocity and acceleration diagrams are shown in the figure b and c respectively

Q7) Explain the different processes of controlling the cam profile.

Ans.

Pressure angle

is defined as the angle between the line of stroke of follower and common normal drawn at the contact point as shown.

As the cam rotates, force is transmitted along the common normal.

This force

can be resolved

Along the direction of follower motion

Perpendicular to the direction of follower motion

which may cause Jamming of follower in its guides & failure of follower assembly.

Also, it is observed that if we select a smaller value of

to avoid the above problems,

Size of CAM increases.

Therefore, manufacturing cost increases

The inertia of CAM increases therefore it cannot be used for quick starting and stopping the application.

As a matter of compromise, the pressure angle for the cam is selected as 30°

The pressure angle can be reduced by increasing the prime circle radius.

The cam size is determined by considering two factors: the pressure angle and the minimum radius of the curvature.

The pressure angle for oscillating and translating roller follower radial cams are shown below.

For flat faced followers is the pressure is zero at all times.

In force close cams, the pressure angle is important during the rise portion where the cam is driving the following, in return motion it is the spring force that lowers the follower; hence the pressure angle is not that critical.

Using eccentricity, for the same cam size can reduce the pressure angle during the rise while there is some increase of pressure angle during the return, or for the same pressure angle, a smaller cam size can be used.

In practice for roller followers, it is common to determine the cam size using the maximum pressure angle criteria and then check that the cam curvature is satisfactory.

In the case of a flat-faced follower, the cam curvature is the determining criteria for the cam size.

Q8) Explain undercutting with a neat sketch.

Ans.

Sometimes, the prime circle of a cam can be proportioned to provide a satisfactory pressure angle; still, the follower may not be completing the desired motion.

This can happen if the curvature of the pitch curve is too sharp.

The figure a show the pitch Circle of a cam.

In figure b, a roller follower is shown generating this curve.

In figure c, a larger roller is shown trying to generate this curve.

It can easily be observed that the cam curve loops over itself to realize the profile of the pitch curve.

As it is impossible to produce such a cam profile, the result is that the camp will be undercut and become a pointed cam.

Now when the roller follower will be made to move over this cam, it will not be producing the desired motion.

It may be observed that the camp will be pointed if the radius of the roller is equal to the radius of the curvature of the pitch curve.

Thus, to have a minimum radius of curvature of the cam profile, the radius of curvature of the prime circle must always be greater than that of the radius of the roller.

Q9) Explain the jump phenomenon with a neat sketch.

Ans.

In a cam-follower system, the contact between the cam surface and follower is maintained through retaining spring.

Beyond the particular speed of CAM rotation, the follower may lose contact with the cam, because of inertia force acting on the follower.

The phenomenon is called a jump phenomenon.

When the follower re-establishes contact with the cam, it may do so with severe impact loads that can damage the surface of the cam, and hammering noise can be heard at this jump Speed.

During the follower jump, transient vibrations are set up in the follower and these occur only with high speed, highly flexible cam-follower system.

With the jump, the cam and follower separate owing to excessively unbalanced forces exceeding the spring force during the period of negative acceleration.

This is undesirable since the fundamental function of the cam follower system; the constraint and control of follower motion are not maintained.

Also, the life of the cam flank surface reduces due to the hammering action of the follower on cam, and hammering noise is generated which further results in vibrations of the system.

The jump phenomenon will be avoided by limiting the speed of CAM or by increasing stiffness of the retaining spring.

The figure shows an eccentric cam follower, which is analyzed for jump phenomenon.

Lift of follower = y =

Differentiating equation with respect to time t we get

The velocity of follower =

Differentiating equation with respect to time t, we get

Acceleration of follower=

Where cam angle turned from the lowest position

Now consider the arrangement as shown in the figure

Let m=mass of follower

e=eccentricity

k = stiffness of spring

F = contact force between cam and follower

= total spring force

P = preload in spring

=Angular speed of cam

Then, from the free body diagram, we have

Inertia force = External forces

This contact force between cam and follower is maximum when

and minimum when

0 It is also dependent upon the square of CAM velocity.

When this contact force between cam and follower becomes negative, the follower would lose contact with the surface resulting in the jump.

This would happen if the speed is increased beyond a particular critical speed

(at

Where =jump speed

Therefore, to avoid jump

Or to avoid jump

Q10) What do you mean by advanced cams? State its applications.

Ans.

In any class of machinery where automatic control and accurate timing are important, the cam is an indispensable part of the mechanism.

Cam follower mechanism finds application in a wide variety of devices and machines, such as printing presses, shoe machinery, textile machinery, automobile engines, and pumping devices.

The cam follower mechanism is versatile and almost any arbitrarily specified motion can be achieved. The use of algebraic polynomials to specify the following motion is a new choice for cam profiles.

In which the differential equations of motion are solved using polynomial follower motion equations.

This class of motion function is highly versatile, especially in high-speed automobiles.

A 2-3 polynomial cam profile is cubic and follower acceleration is discontinuous at the endpoints making it unsuitable at higher speeds.

3-4-5 polynomial cam profile has 6 polynomial coefficient and a degree of 5, provides added control over follower acceleration at the endpoints

A 3-4-5 polynomial cam profile has an extended control as it provides a zero acceleration at the endpoints and no control over the follower jerks at

Q11) Explain 2-3 polynomial cams.

Ans.

The 2-3 Polynomial D-R-D Cam

In this type of cam curves, four boundary conditions are used to hence displacement equation is given by,

……1

Boundary condition is

Differentiating the above equation w.r.t to get the velocity of the follower

Initially put boundary conditions in equation (1),

Now put the boundary conditions in equation (2)

Put in equation (3)

……. 5

Solving equation (4) and (5) we get

The figure shows the plot of displacement, velocity, acceleration, and jerk curves.

From Fig it is clear that acceleration is finite at all points for the complete stroke and jerk is constant throughout the stroke. But it is infinite at the start and end of each stroke which causes high inertia forces at these points.

Q12) Explain 3-4-5 polynomial cams.

Ans.

The 3-4-5 Polynomial D-R-D Cam

In this type of cam curves, six boundary conditions are used hence displacement equation is given by,

……. 1