This project deals with the design and fabrication of wave motion of cam. The apparatus consists of 18 cams which are made in contact with 18 respective flat face equal length followers. The face angles for consecutive cams are 45 degrees. Thus the followers move in a sinusoidal wave. The graph is plotted between the face angle and the follower displacement. The design is almost same to the cam shaft in the automobile engine. This concept is basically applied in the automobile engines, vessel engines etc. This principle can be used in reciprocating machine parts moving in the wave motion.
A cam is a mechanical component of a machine that is used to transmit motion to another component, called the follower, through a prescribed motion program by direct contact.
A cam mechanism consists of three elements: the cam, the follower (or follower system), and the frame. The follower is in direct contact with the cam. The cam may be of various shapes. The follower system includes all of the elements to which motion is imparted by the cam. This may be connected directly to the follower, or connected through linkages and gearing. The frame of the machine supports the bearing surfaces for the cam and for the follower.
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Uses of Cam
The cam mechanism is a versatile one. It can be designed to produce almost unlimited types of motioning the follower. It is used to transform a rotary motion into a translating or oscillating motion. On certain occasions, it is also used to transform one translating or oscillating motion into a different translating or oscillating motion.
Cams are used in a wide variety of automatic machines and instruments. Typical examples of their usage include textile machineries, computers, printing presses, food processing machines, internal combustion engines, and countless other automatic machines, control systems and devices. The cam mechanism is indeed a very important component in modern mechanization.
Classification of Cams
Cams can be conveniently classified into two main groups:
Cams that impart motion to the follower in a plane in line with the axis of rotation of the cam (as does a cylindrical cam).
Cams that impart motion to the follower in a plane at 90 degrees to the axis of rotation, as with face or edge cams. Most cams fall into this category.
The cam, as a means of producing a given type of motion, is simple and reasonable to design, provided the simple principles are understood. Another advantage is that, generally, a cam can easily be changed or modified to allow a change of motion, without interfering with the remainder of the mechanism.
A circular cam is often called an eccentric cam because the axis of rotation of the cam is offset from the geometric center of the circular disc.
A concentric disc attached to a rotating shaft would have its axis of rotation coinciding with its geometric center.
It must be appreciated that this type of cam, where the follower is in contact with the edge of the cam disc, is only capable of imparting positive motion to its follower in one direction, that is, during the rise portion of the cam movement. During the fall portion of the cam movement the follower must be maintained in contact with the cam either by the mass of the follower and its mechanism or, more usually, by a spring. Both methods have their advantages.
A groove can be milled in the face of cam discs. As the cam rotates, a follower located in the groove has its motion guided by the groove. This type of cam is called a box cam.
Cylindrical cams are used when motion has to be transmitted parallel to the axis of rotation of the cam. The cylindrical or barrel cam consists of a rotating cylinder with a helical (screw shaped) groove in its curved surface. A follower with a tapered roller end is located in the groove. As the cylinder turns, the follower moves in a straight line parallel to the axis of the rotation barrel cam. This type of cam is often used to guide thread on sewing machines, looms and fabric making machines.
PROFILE SHAPES OF SOME CAMS
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The most common kind of cam is the plate cam. It consists of a narrow plate or disc, which is fixed to a rotating shaft. The plate is shaped so that the follower will produce a pre-determined form of motion. Most cams are designed to have a smooth curved shape so that the motion transmitted to the follower is smooth and without sudden jerks.
These type cams are often used for controlling valves. For example, they are used on motor car camshafts to operate the engine valves. A follower controlled by a pear-shaped cam remains motionless for about half a revolution of the cam. During the time that the follower is stationary, the cam is in a dwell period. During the other half revolution of the cam, the follower rises and then falls. As the pear-shaped cam is symmetrical, the rise motion is the same as the fall motion.
These cams are sometimes called eccentric cams. The cam profile is a circle. The center of rotation of the cam is often from the geometric center of the circle. The circular cam produces a smooth form of motion called a simple harmonic motion. These cams are often used to produce motion in pumps. Circular cams are often used to operate steam engine valves. As the cam is symmetrical, the rise and fall motions are the same.
HEART SHAPED CAMS
This cam causes the follower to move with a uniform velocity. Heart-shaped cams are essential when the follower motion needs to be uniform or steady as, for example, in the mechanism that winds thread evenly on the bobbin of a sewing machine. A heart-shaped cam can be used for winding wire evenly on the former of a solenoid.
UNIFORM ACCELERATION AND RETARDATION CAMS:
A cam shaped as shown controls the motion of the follower so that it moves with uniform acceleration and retardation. The follower gains and looses velocity at a constant rate. Uniform acceleration and retardation cams are used to controls the motion of linkages in complex machinery.
There are three types of cam followers, and since the type of follower influences the profile of the cam it is worthwhile considering the advantages and disadvantages of each type. The three types are the knife-edge, the roller follower and the flatfoot or mushroom follower.
The knife edge follower
This is the simplest type, is not often used due to the rapid rate of wear. When it is adopted, it is usually for reciprocating motion, running in slides and there is considerable side thrust, this being a component of the thrust from the cam.
The roller follower
This eliminates the problem of rapid wear since the sliding effect is largely replaced by a roller action. Some sliding will still take place due to the varying peripheral speed of the cam profile, due to the changing radius of the point of contact. Note also that the radial position of the contact between the cam and the roller, relative to the follower center, will change according to whether a rise or fall motion is taken place: this fact has to be considered when constructing the cam profile. Again, with the roller follower, considerable side thrusts are present, a disadvantage when dealing with reciprocating motions. This side thrust will be increased when using small rollers.
The flat foot or mushroom follower
This has the advantage that the only side thrust present is that due to the friction between the follower and the cam. The problem of wear is not so great as with the knife-edge follower, since the point of contact between the cam and follower will move across the face of the follower according to the change of shape of the cam. A trick to lessen further the effect of wear is to design the follower to be capable of axial rotation and arrange the axis of the follower to lie to one side of the cam. Thus the contact with the cam will tend to cause rotation of the follower. The cam profile, to work with a flatfoot follower, must be convex at all parts, in order to prevent the corners of the follower digging into the cam profile. The minimum cam radius should be as small as possible to minimize sliding velocity and friction.
Three types of cam followers
CAM DESIGN CONSIDERATIONS
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All three types of cam followers can be mounted in the following ways:
1) In-line with the cam center line,
2) Offset from the cam center line, or
3) Mounted on a swinging radial arm.
All cam followers wear at different rates depending on the follower shape, size, type etc. the next section shows how to reduce wear in a flat-foot follower.
Overcoming resistance to cam motion
When using a spring anchored to a fixed point, the force exerted by the spring will vary during the camshaft revolution, reaching a maximum when the follower is at the full diameter of the cam and the spring at its maximum extension. The camshaft drive has to overcome this increasing resistance to rotation. During the fall portion of the cam motion, the spring loading (which is decreasing) is tending to push the cam round, assisting rotation. These conditions give rise to unbalanced torque (turning moments) requirements from the camshaft driving motor. Using a double-arm cam lever with two followers, one on each arm and each running on its cam, can eliminate this fluctuating load. The cams must be designed to match each other, the second cam rising when the first cam falls, but care must be taken to provide a small amount of clearance: when one cam is driving, the other follower must be slightly clear of its cam. This is to ensure that the followers do not lock when passing over peaks. This difficulty can be eliminated if two separate arms, with followers on two mating cams, are used, the arms being spring-loaded together. This will give an almost constant spring length during the camshaft revolution.
When the cam turns through one motion cycle, the follower executes a series of events consisting of rises, dwells, and returns. Rise is the motion of the follower away from the cam center; dwell is the motion during which the follower is at rest; and return is the motion of the follower toward the cam center. When a designer is developing a cam profile to produce a certain motion, the information available to him/her would certainly include the amount of movement required by the follower (the displacement).
The time available in which this movement is to be carried out, and the angular speed of the camshaft (assumed to be constant, as it usually is). He/she would also be aware of the type of motion and its characteristics most likely to be suitable for his particular purpose. It has already been seen that, to appreciate the forces acting on the cam and its follower, it is necessary to know the accelerations imparted to the follower. From the time available and the r.p.m. of the camshaft, it is possible to calculate the number of degrees of camshaft rotation available to carry out the motion. In order to have a complete picture of this information it is advisable to construct a displacement-time, velocity-time, and acceleration-time graph for the motion. From these figures it is possible to gauge the disadvantages likely to occur in practice.
The features that should be appreciated in any design are:
· Low acceleration and deceleration values at the beginning and end of the strokes, to lesson the spring loading necessary to maintain contact between cam and follower.
· No abrupt changes in acceleration.
· Low masses to be moved.
These features are more critical as the speed of the cam is increased and several standard types of motion are used. Three types of motion will be considered next.
Design requirements in the part of the machine under consideration will dictate the type of movement required in the cam follower. This is then translated into the profile of a cam, which will give the follower the required motion. When designing this profile the movement of the follower is usually considered in four separate sections: the period when the follower is at the bottom of its movement, called the bottom dwell; the movement required during the rise or lift of the follower; the period when the follower remains at the top of its movement, called the top dwell; and the movement required when the follower returns to the bottom position. There are three different types of follower motion in standard use, which is shown below.
Uniform (constant) velocity
Since the velocity is constant, the displacement diagram will be a straight line with constant slope and the velocity diagram rectangular with zero acceleration. However, to achieve this velocity immediately at the commencement of the motion, and maintain it until the very end of the stroke, would require infinitely high accelerations and declarations for infinitely short periods of time at the beginning and end of the stroke. This of course is impossible. To reduce these peak accelerations and declarations and to make the motion possible the conditions are modified to include a short period of uniform acceleration and deceleration at the beginning and end of the motion. This means that the follower moves with uniform velocity for most of the stroke, parabolic or circular arcs being introduced at the beginning and end of the displacement diagram. Despite these modifications it can be seen that, considering the conditions previously laid down, the high accelerations, particularly those at the end of the outgoing stroke and the beginning of the fall stroke, require heavy springing to ensure continuous contact between edge cam and follower.
Simple harmonic motion
The displacement diagram is a sine curve and if a cam is produced from this curve only (i.e. devoid of top and bottom dwell) it will have lobes of circular form. Consideration shows that this type of cam will give the smoothest change of motion in the follower. An eccentric cam transmits simple harmonic motion to the follower. Examples of simple harmonic motion from everyday life are the up and down motion of a cork bobbing on the waves on a pond, and the oscillating motion of a pendulum weight as it swings from side to side, as shown below.
Another example of simple harmonic motion is the projection (or shadow) of uniform circular motion onto a straight line. If we view from above, a toy train engine going around a circular track, we will see circular motion. But if we look at the shadow of the train cast by a lamp edge-on to the track, the engines shadow appears to oscillate back and forth. The shadow is said to be moving in simple harmonic motion which is shown below.
Simple harmonic motion follower performance graph
Uniform acceleration and retardation.
This displacement curve is parabolic. It gives a uniform rate of acceleration from the start to the midpoint and a similar uniform rate of retardation from the midpoint to the end of the movement.
DRAWING CAM PROFILES
Uniform velocity with a knife-edge follower
In-line knife edge follower,
50 mm minimum diameter,
40 mm lift (rise) with uniform velocity,
0 degrees to 90 degrees bottom dwell, 90 degrees to 180 degrees rise,
180 degrees to 270 degrees top dwell, 270 degrees to 360 fall,
Simple harmonic motion with a roller follower
In-line roller follower, diameter 12 mm,
minimum cam diameter 50 mm,
total rise 42 mm, both rise and fall have simple harmonic motion,
0 to 90 degrees bottom dwell,
90 to 180 degrees rise with simple harmonic motion,
180 to 270 degrees top dwell,
270 to 360 degrees fall with simple harmonic motion,
because this is a symmetrical cam it can rotate in either direction.
Uniform acceleration and retardation with an incline flat face follower
In-line flat face follower,
minimum cam diameter 50 mm,
rise 36 mm through 180 degrees and a similar fall, both having U.A.R.,
this produces a symmetrical cam giving the required follower motion with either direction of rotation.
Uniform acceleration and retardation and uniform velocity, with a knife-edge follower
In-line knife edge follower,
minimum cam diameter 50 mm,
rise 42 mm through 180 degrees with uniform acceleration and retardation,
fall 42 mm through 180 degrees with uniform velocity,
Uniform velocity with offset roller follower
minimum cam diameter 50 mm,
bottom dwell 0 to 60 degrees, rise 60 to 150 degrees, top dwell 150 to 210 degrees, fall 210 to 300 degrees 300 to 360 degrees bottom dwell,
total lift 36 mm, uniform velocity, clockwise rotation, roller follower diameter 12 mm,
offset 20 mm to the right of the cam centerline.
Uniform velocity with a radial arm roller follower
roller follower diameter 16 mm, mounted on a radial arm to the dimensions given,
full lift of roller 0 to 180 degrees, top dwell 180 to 270 degrees, fall 270 to 360 degrees, uniform velocity,
Design of the Apparatus
Type of the cam used : Circular disc cam
Diameter of the cam : 44.45mm
Diameter of the Hole : 5 mm
Number of cams used : 18
Off-set of the hole : 10mm
Type of the follower used : Flat-face follower
Length of the rod : 152.4 mm
Number of followers used : 18
Diameter of the follower : 3mm
Spindle length : 30.48mm
Thickness of the spindle : 5mm
Distance between the followers : 5mm
Face angle between the cams : 45o
Maximum displacement of follower : 22mm
Lift of the follower : 23mm
From the graph plotted:
Amplitude = 9mm
One cycle = 360o
Displacement of bent measurement rods:
The difference in the displacement of the bent measuring rods is as follows
Maximum distance between consecutive rods: 95mm
Minimum distance between consecutive rods : 55mm
Thus the apparatus can be used also for the longitudinal wave motion.
COST OF ESTIMATION
COST IN RUPEES
18 X 60 = 720
Flat face follower
18 X 20 = 360