CAMS
A cam is a rotating machine element which gives reciprocating or oscillating motion to another
element known as follower. 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 cams are widely
used for operating the inlet and exhaust valves for internal combustion engines, automatic
attachment of machineries, paper cutting machines, feed mechanism of automatic lathes etc..
Made by :
Mouhyadin Mahmoud Ismael 5216
Ahmed Mohamed Attia 5456
Mahmoud Ayman 6528
Yahya Ismail Basiony 7181
Table of contents
Page
1
-Definitions
2
2-Terminology
3
3-Classification of cams and
followers
4-Uses
4
5-Force Analysis
9
6-Kinematic Analysis
8
12
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Definition
:
Cam : a rotating or sliding piece (such as an eccentric wheel or a cylinder with an
irregular shape) in a mechanical linkage used especially in transforming rotary
motion into linear motion or vice versa.
Cam follower : the peg or roller which follows the curvature of a cam and to which
the motion of the cam is thereby directly communicated
A cam and follower mechanism is a profiled shape mounted on a shaft, The
mechanism is developed by incorporating three members they are, a driver
member named Cam, a frame that supports cam and follower, the follower is
guided by the frame and lastly, the driven member named as a follower, When the
two links are connected either along a line or at a point, it is a higher pair.
Cam and follower are used to convert rotary motion into linear (reciprocating)
motion ,the cam is the driving component in the mechanism, making sure that the
follower follows the desired motion. The cam reciprocating, oscillating, or rotating
imparts reciprocating or oscillating motion to a second body, the follower, The
component which gives the desired motion in the mechanism.
The shape of the cam depends upon its own motion, the required motion of the
follower, and the shape of the contact face of the follower. The motion of the
follower is the output in the cam follower mechanism. The followers are designed
in such a way that, it always touches the cam during the cam operation.
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Terminology:
Some terms are used when describing the cam profile drawing.
Trace point: is a point on the follower, which describes the follower movement. For
roller follower, it is the center of the roller. So, the trace point is the roller center, which
means the movement of the follower will be described in terms of the motion of this
roller center.
If it is a flat face follower, then trace point we use is the point on the follower’s face which
is in contact with the cam surface when the follower is at one of the extreme positions,
we normally use that extreme position when the follower is closest to the cam center.
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Base circle: is the smallest circle that can be drawn with the cam center as the center
and touching the cam profile, this circle we call a base circle. So, the radius of the base
circle we call, Rb, is called base circle radius.
Pitch curve: to define the pitch curve, a kinematic inversion is applied. The system is
considered a four-link mechanism with fixed link, cam, follower, and roller.
A kinematic inversion is applied, holding the cam fixed, the locus of the center of the
roller will generate a curve parallel to the cam profile .
Working curve: The working surface of a cam in contact with the follower. For
the knife-edge follower of the plate cam, the pitch curve and the working
curves coincide. In a close or grooved cam there is an inner profile and an outer working
curve.
Pressure angle: Pressure angle is defined in every point in pitch curve.
It is the angle between direction of the follower movement and the normal to the pitch
curve. This angle is denoted by φ. Obviously, for the smooth movement of the follower,
the φmax should be less than the maximum value φ allowable. The φ will keep on
changing depending on the cam profile. If φ is too large a reciprocating follower will jam
in its bearings.
Pitch point: is the point on the pitch curve where the pressure angle is maximum
φmax.
Pitch circle: is the circle with center on cam center and passes through the pitch point.
Prime circle: is the smallest circle that can be drawn with the cam center as the center
and tangential to the pitch curve. This circle has a center at the cam-shaft axis and
tangential to the pitch curve. This circle is called the prime circle. If base circle radius is
Rb and Rr is roller radius, then the prime circle radius is:
𝑅𝑝 = 𝑅𝑏 + 𝑅𝑟
Lift or stroke is the maximum displacement or angle through which the follower
moves or rotates from its lowest position to the topmost position.
Classification of Cams and followers
Cams can be classified based on their physical shape. Disk or plate cam (Fig. 4.1a and
b): The disk (or plate) cam has an irregular contour to impart a specific motion to the
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follower. The follower moves in a plane perpendicular to the axis of rotation of the
camshaft and is held in contact with the cam by springs or gravity.
Fig. 4.1a and b
a) cylindrical cam (Fig. 4.2): The cylindrical cam has a groove cut along its cylindrical
surface. The roller follows the groove, and the follower moves in a plane parallel to the
axis of rotation of the cylinder.
Fig. 4.2
b) Translating cam (Fig. 4.3a and b). The translating cam is a contoured or grooved plate
sliding on a guiding surface(s). The follower may oscillate (Fig. 4.3a) or reciprocate (Fig.
4.3b). The contour or the shape of the groove is determined by the specified motion of
the follower
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Fig. 4.3a and b
Though the cams may be classified in many ways, yet the following two types are
important from the subject point of view:
a) cylindrical cam with reciprocating follower (b) Cylindrical cam with oscillating
follower.
Types of followers:
(i) Based on surface in contact. (Fig.6.4)
(a) Knife edge follower
(b) Roller follower
(c)Flat faced follower
(d) Spherical follower
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Fig. 6.4 Types of followers
(ii)Based on type of motion: (Fig.6.5)
(a) Oscillating follower
(b) Translating follower
(iii)
Based on line of motion:
(a) Radial follower: The lines of movement of in-line cam followers pass through the
centers of the camshafts (Fig. 6.4a, b, c, and d).
(b) Off-set follower: For this type, the lines of movement are offset from the centers of
the camshafts (Fig. 6.6a, b, c, and d).
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Fig.6.6 Off set followers
Uses :
The cam and follower mechanism represents an important role in achieving
uniform distribution of forces in a single machine element.
Spontaneous movement can be achieved by an engineer by attaching a cylindrical
roller to a machine element. The Cam and followers can be used in machine
elements with the size and shape of the nut. In addition, varieties of linear motions
can be found using this mechanism.
Apart from that, the cams and followers’ mechanism can absorb a high amount of
shock due to the greater thickness compared to other bearings which increase the
mechanical efficiency of the machine element.
Also, this mechanism is completely versatile in that it can be applied in a soda
machine or in aircraft applications. Furthermore, It is also used in conveyor belts.
However, flat followers are commonly used to operate the valves of an
engine while roller followers are used in oil and stationary engines.
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Applications of cams and followers :
•
Internal Combustion Engine to close and open the outlet valve and intake valve.
•
Automated Types of machinery, Cam and Follower are used in different parts which
are automated in motion.
•
In Hydraulic Systems, the main mechanism is Cam and Follower mechanism. In that
case, the mechanism is dependent on the fluid pressure.
•
In Printing Machinery, the mechanism of Cam and Follower helps the screen to be
printed. The push helps to take the position where the printing will be done and
the pull helps to print on that.
•
In Textile Types of machinery, the mechanism of Cam and Follower helps to stitch
clothes by a push and pull to move the Maku.
•
Screw pieces of machinery.
•
Gear-Cutting Machineries.
•
Wall-Clock.
•
They are used in the feed mechanism for Automatic Lathe Machine.
•
Paper cutting machines.
Force Analysis
There are many forces that are taken into consideration :
•
•
•
•
•
•
•
•
Working loads
Impact forces
Inertia forces
Vibratory forces
Frictional forces
Spring forces
Operating forces
torque
Working loads
Working loads, or applied loads, represent the useful work performed by a machine.
Working loads may be classified in these relative categories: gradually applied, suddenly
applied, and impact forces. Note that these three categories may not be directly related to
the speed of the cam. For example, a slow-speed cam mechanism, having a large flywheel,
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punching holes in tough sheet metal may have an impact load, while a high-speed system
pumping chemically processed air can have gradually applied loads. It is the responsibility
of the engineer to make an experienced judgment about the designed effect of the working
load on the system. Also, the application of working loads in a positive drive cam follower
may augment or reduce the other forces in a system. For example, if applied during the
initial cam stroke, they add to the inertia forces during the positive acceleration period.
During the negative acceleration period they tend to reduce the load by absorbing some
of the energy stored in the follower mechanism.
Impact forces
Impact is often called mechanical shock, referring to an extreme abruptly applied force. It
is a velocity shock transient force. Impact phenomena are especially important to the
designer since in all machines the highest forces and stresses arise because of impact. In
cam-follower systems the impact forcing functions are not precisely known. Thus, the
design for these forces requires an approximation of the idealized functions of velocity
changes on impact. As stated, practical design data for impact calculation are not directly
available, necessitating a larger design safety factor in considering its effects. Impact or
velocity shock factors have a load amplification factor of two to four times the static force
values. For more precise data on impact the designer could resort to experimental
measurement employing such powerful tools as strain gauges, high-speed photography,
and velocity and motion transducers. The sources of impact in cam-follower mechanisms
could be the result of: (a) backlash in a positive-drive cam and roller follower, (b) high-speed
systems which are nonlinearly elastic so that abrupt changes occur with results like impact,
and (c) the working load action as a cam-driven punching mechanism. To minimize impact,
the following is suggested, if possible: (a) minimize the velocity of impact, (b) minimize the
mass of impacting bodies, and (c) minimize sensitivity to local stress concentrations by
employing a ductile material with some capacity for plastic deformation.
Inertia forces
Inertia forces in most cam-follower systems are the most important of all the forces
analysed, especially at high speeds. Inertia forces are caused by the necessity of moving
the follower masses linearly or rotationally. The inertia force on a linearly moving follower
is where A = acceleration, in/sec2 w = equivalent follower weight, lb. The inertia force,
passing through the center of gravity of the body, has a direction opposite to that of the
acceleration. By D’Alembert’s principle, we may make a free-body diagram of all forces and
analyse the dynamic condition as a static problem. If the body has an unbalanced torque,
it will have an angular acceleration which will be resisted by a torque reaction. The direction
of this torque will be opposite to the direction of acceleration
VIBRATORY FORCES
Vibrations are generally caused by forces whose magnitudes, directions, and/or point of
application vary with time. These forces produce variations in elastic deformations. These
vibrations in turn produce stresses and forces that are superimposed on the inertia and
other forces in the follower systems. The magnitudes of the vibratory stresses and forces
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are influenced by the acceleration characteristics, as well as the rigidity and the damping
of the follower mechanism.
FRICTIONAL FORCES
Friction opposes the relative movement of contacting bodies in all machinery. It is a
surface phenomenon. In cam-follower systems, we have both sliding and rolling friction to
consider. The accurate way to include frictional resistance in a design is to measure it on
the actual machine or prototype. Handbooks list these resistances for some combinations
of materials, but the conditions under which the values are obtained seldom fit the specific
conditions. This is especially true in cam and follower action. Also, differences in friction
may be obtained under apparently similar conditions. Here are the three broad categories
of frictional action in cam-follower mechanisms: • Pure sliding that occurs between the cam
and flat-faced and spherical-faced followers • Rolling and some sliding in rolling-element
followers and cams • Linear ball-bearing guiding mechanisms that support translating
followers k k T I a .The friction force between two bodies is defined as the force at their
surface that resists their relative movement. The coefficient of friction (8.3) where F = the
friction force, lb Fn = normal reaction of one body on another, lb. To initiate the relative
motion, the static coefficient of friction is where Fs is the friction force between bodies not
sliding on each other. To maintain the motion the kinetic coefficient of friction is where Fk
is the friction force between bodies sliding on each other.
Spring forces
In cam-follower systems the follower must be always held in contact with the cam to
counteract the follower inertia. The follower inertia follows the acceleration curve with the
magnitude of the negative acceleration being of concern. The constraint of the follower
should be accomplished by utilizing a preloaded compression spring, usually a helical coil.
The spring force is directly proportional to the follower displacement. If the force is too
small it will allow the follower to jump off the cam. On the other hand, an excessive spring
force is reflected throughout the system during the total cycle of operation. This excessive
force will require a stronger design system and more wear of parts will result. Also, one of
the disadvantages of spring-loaded systems is that the spring force produces an additional
load on the system. spring force curve. The critical point is where the inertia and spring
forces are closest to each other. This point occurs in the vicinity of the maximum negative
acceleration. Jump will occur when the negative inertia force of the system exceeds the
available spring force. The spring force should exceed the total external load by 30 to 50
percent, depending on the mass and elasticity of the mechanism. Note, a small percent of
spring load is to include the spring strength loss that will occur over a period of use. Also,
in the design of a spring-loaded system the spring should be located at the farthest part of
the follower to eliminate all backlash and clearances. Surging, or coil flutter, at high speeds
is the common manifestation of spring performance. The surging of the spring is the result
of forced vibration waves advancing and reflecting throughout the length of the spring.
Thus, a complicated series of vibrations may be continually reinforcing and partially
cancelling each other during the action, further reducing the effective spring force
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operating forces
Let’s consider the operating forces of the complete cam mechanism system from the input
(usually an electrical motor) to the cam-follower working output. There are transient forces
that are more severe than the normal design (running) speed forces presented in latter
chapters. The following actions will be discussed: • start and stop • emergency stop •
interrupted drive Every cam-follower machine has specific needs to control these transient
operating forces. Generally, smaller machines with lower inertias require simple
equipment and heavy-mass machines need more elaborate controls of the actions. Usually
clutches or brakes are chosen. They engage or activate by mechanical, pneumatic,
hydraulic, electrical, or automatic means. The operating principle of the brake clutch is
positive contact (either jawed or toothed), friction contact, overrunning (by wedge relief),
overload safety by shear pins (to be replaced), and magnetic and fluid couplings. In normal
operation the machine must start, run at full speed, and stop. These steps produce positive
and negative inertia forces and inertia torques that influence the input transmission. The
clutch/brake system can have a no-load start, manually or automatically controlled, or have
gradual, smooth pickup of speed and load. It can also, when at full speed, have control of
variable torque load and be stopped by dynamic braking. In emergency operation, we have
overload protection and stopping of the machine. The clutch functions, reacting to
transient and infrequent overloads, to limit the speed and the torque, and for automatic
overload release, dynamic braking, and backstopping. Also, positive-drive shear pins may
be utilized to protect the system. These pins are designed to break and are replaced after
every failure. Interrupted drive operation carries a special design need for cam
mechanisms to be deliberately and rapidly started and stopped for functional reasons. A
case in point is a cam-driven indexing mechanism whose input is interrupted by an
electromagnetic clutch/brake unit, either to make the mechanism cycle on demand or to
produce an extended dwell period. The same system can also be applied when inching and
jogging is desired and indexing and load positioning.
kinematics :
Types of follower motion:
(a) Uniform velocity
(b) Uniform acceleration and deceleration ( parabolic motion )
(c) Simple harmonic motion
(d) Cycloidal motion
1.Uniform velocity:
The follower moves with uniform velocity during its rise and return stroke,
therefore the slope of the displacement curves must be constant. The acceleration
or retardation of the follower at the beginning and the end of each stroke is infinite.
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This is since the follower is required to start from rest and must gain a velocity
within no time. This is only possible if the acceleration or retardation at the
beginning and at the end of each stroke is infinite. These conditions are however,
impracticable. The acceleration of the follower is important in high-speed cams
because it affects inertia forces which results in vibration, noise, high stresses, and
wear.
All these factors are represented by symbol(Jerk =dA/dT), which means impact
characteristics that effects on cams by vibrations in the follower system . To have
the acceleration and retardation within the finite limits, it is necessary to modify
the condition which govern the motion of the follower. This may be done by
rounding off the sharp corners of the displacement diagram at the beginning and
at the end of each stroke, as shown in Fig. 5(a).
Figure 1
Figure 2
2. Uniform acceleration and deceleration (Parabolic Motion):
Constant acceleration is used for half of desired rise and followed by a motion of
constant retardation for the remainder of the rise.
parabolic motion results in a very low acceleration of the follower for a given stroke
and cam speed. The displacement diagram consists of two inverted parabolas with
an inflection point, at an angle (γ) called the inflection angle, Since the acceleration
and retardation are uniform, therefore the velocity varies directly with the time ,As
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shown in the next figures. There is rising and down with constant Acceleration and
Retardation ,so the cam rise ,then became constant “dwell” ,then Return
,then retard with constant acceleration.
3.Simple Harmonic Motion:
The velocity is zero at the beginning and at the end of the stroke and is gradually
changing in between.
The displacement, velocity, and acceleration diagrams when the follower moves
with simple harmonic motion are shown in The following Figures The displacement
diagram is drawn as follows:
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Consider the shown generation circle which a diameter Equal to the follower rise =
H. Point P is moving along the circumference with constant speed. The
displacement S is measured from the initial bottom point to the projection of point
P onto the vertical diameter as shown. φ is the generating circle angle (describes
the angular position of P).
Equation (5) can be written now as S = H/2 – H/2 cosαπ for αθ≤≤0.
Velocity v = ds/dt =θαπωαπsin2Hv for αθ≤≤0
Acceleration a = dv/dt =θαπαωπcos2Ha for αθ≤≤0.
4.Cycloid Motion:
The parabolic and the simple harmonic motions have certain acceleration at the
beginning and at the end of the motion. The inertia force of the follower is suddenly
applied which may cause serious shocks especially at high speeds. For this reason,
they are suitable only for low or moderate speeds. For high-speed cams the
optimum motion is when the acceleration is zero at the beginning and at the end
of the rise stroke.
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Cycloid and the eight-power polynomial curve are useful for high-speed cams. The
displacement, velocity, and acceleration diagrams when the follower moves with
cycloidal motion are shown in The Next Fig The cycloid is a curve traced by a point
on a circle when the circle rolls without slipping on a straight line. In case of cams,
this straight line is a stroke of the follower which is translating and the
circumference of the rolling circle is equal to the stroke (l) of the follower.
Therefore, the radius of the rolling circle is (l/2π).
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