Upload
mangyan
View
27
Download
0
Tags:
Embed Size (px)
Citation preview
Dr. Hanafy M. Omar
1
Chapter 5: Cams
CAM - Definition A cam is a machine element used to drive another element,
called a follower, through a specified motion by direct contact.
Cam-and-follower mechanism are simple and inexpensive , have few moving parts, and occupy very little space.
Furthermore, follower motion having almost any desired characteristics are not difficult to design.
For these reasons, cam mechanisms are used extensively in modern machines.
Cam
Follower
Examples for cam
In IC engines to operate the inlet and exhaust valves
Classification of CAM Mechanism
Based on the basic shapes
(a)plate cam,
(b) wedge cam
(c) barrel cam
(d) face cam.
Classification of CAM Mechanism
Based on modes of Input / Output motion
Rotating cam Translating follower
Rotating cam Oscillating follower
Translating cam Translating follower
Rotating cam Translating follower
Rotating cam oscillating follower
Translating cam Translating follower
Classification of followers
According to the shape of follower
Knife edge follower
Roller follower
Flat faced follower
Spherical faced follower
Knife edge follower
Roller follower
Flat faced follower
Spherical faced follower
According to the path of motion of follower
a) Radial follower
b) Offset follower
When the motion of the follower is along an axis passing through the centre of the cam, it is known as radial followers.
The above figures are examples of this type.
Radial follower
Offset 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. Above figures are examples of this type.
CAM Nomenclature Cam profile: The outer surface of the disc cam.
Base circle : The circle with the shortest radius from the cam center to any part of the cam profile.
Trace point: It is a point on the follower, and its motion describes the movement of the follower. It is used to generate the pitch curve.
CAM Nomenclature Pitch curve : The path generated by the trace point as the follower is
rotated about a stationery cam. Prime circle: The smallest circle from the cam center through the
pitch curve Stroke: The greatest distance or angle through which the follower
moves or rotates
Motion of the Follower As the cam rotates the follower moves upward and downward.
The upward movement of follower is called rise (Outstroke)
The downward movement is called fall (Returnstroke).
When the follower is not moving upward and downward even
when the cam rotates, it is called dwell.
Displacement diagram for a cam Displacement is the distance that a follower moves during
one complete revolution (or cycle) of the cam while the follower is in contact with the cam.
It is the plot of linear displacement, y() of follower versus angular displacement () of the cam for one full rotation of the cam.
y=y()
Types of follower motion 1. Uniform motion ( constant velocity)
2. Simple harmonic motion
3. Uniform acceleration and retardation motion
4. Cycloidal motion
Uniform motion (constant velocity)
Since the follower moves with uniform velocity during its rise and fall, the slope of the displacement curve must be constant as shown in figure
This motion is not useful for the full lift because of the sharp corners produced at the boundaries wit the other segment of the displacement curve.
To solve this problem, the modified displacement curve is used
Displacement diagram
Modified Uniform motion (constant velocity)
The sharp corners are eliminated in the modified uniform motion displacement diagram
Displacement diagram
Cam Profile Design It is required to determine the exact
shape of a cam surface required to deliver a specified follower motion.
We assume here that the required motion has been completely determined graphically as well as analytically.
Let us address the case of plate cams.
Basic Principle In constructing the cam profile, we employ the principle of
kinematic inversion, imagining the cam to be stationary and allowing the follower to rotate opposite to the direction of cam rotation.
Taking the cams with knife-edge follower for example, the locus generated by the trace point as the follower moves relative to the cam is identical to cam surface. By this way cam surface can be figured out.
Graphical Layout of Cam Profiles
For the case of reciprocating knife-edge follower
As shown in left figure, the displacement diagram of the follower is given, y=y (). Construct the plate cam profile.
Graphical Layout of Cam Profiles (the case of reciprocating knife-edge follower) Step1: divide the displacement-diagram abscissa into a number of segments.
Step2: divide the prime circle into corresponding segments.
Step3: transfer distances, by means of dividers, from the displacement diagram directly onto the cam layout to locate the corresponding positions of the trace point.
Graphical Layout of Cam Profiles (the case of reciprocating knife-edge follower)
Step4: draw a smooth curve through these points. The curve is just the required cam profile.
Graphical Layout of Cam Profiles (the case of reciprocating knife-edge follower)
Graphical Layout of Cam Profiles (the case of reciprocating offset roller follower)
As shown in left figure, the displacement diagram of the follower is given, y=y ().
Construct the plate cam profile.
Graphical Layout of Cam Profiles (the case of reciprocating offset roller follower) Step1: construct the prime
circle with radius r0.
Step2: construct the offset circle with radius equal to the amount of offset e.
Graphical Layout of Cam Profiles (the case of reciprocating offset roller follower)
Step3: divide the displacement-diagram abscissa into a number of segments.
Step4: divide the offset circle into corresponding segments and assign station numbers to the boundaries of these segments.
Step5: construct lines tangent to the offset circle from these station, dividing the prime circle into corresponding segments.
Graphical Layout of Cam Profiles (the case of reciprocating offset roller follower)
Step6: transfer distances, by means of dividers, from the displacement diagram directly onto the cam layout to locate the corresponding positions of the trace point, always measuring outward from the prime circle.
Graphical Layout of Cam Profiles (the case of reciprocating offset roller follower)
Step7: draw a smooth curve through these points. The curve is just the required cam
profile.
Step8: draw the roller in its proper position at each station and then construct the cam profile as a smooth curve tangent to all these roller positions.
Graphical Layout of Cam Profiles (the case of reciprocating offset roller follower)
Graphical Layout of Cam Profiles (the case of reciprocating flat-face follower)
As shown in left figure, the displacement diagram of the follower is given, y=y ().
Construct the plate cam profile.
Graphical Layout of Cam Profiles (the case of reciprocating flat-face follower)
Step1: divide the displacement-diagram abscissa into a number of segments.
Step2: divide the prime circle into corresponding segments.
Step3: transfer distances from the displacement diagram directly onto the cam layout.
Step4: construct a line representing the flat face of the follower in each position.
Graphical Layout of Cam Profiles (the case of reciprocating flat-face follower)
Step5: construct a smooth curve tangent to all the follower positions. This curve is the required cam profile.
Low Speed Cams This cams are sometimes composed of a combination of curves, such as
straight lines are circular arcs, which can be produced easily by
machine tools (easy to manufacture), as shown in following two cams.
In these cams, the acceleration changes abruptly at each of the tangency
points because of the instantaneous change in the radius of curvature of
the cam profile.
Graphical Layout of Cam Profiles (the case of reciprocating flat-face follower)
High Speed Cams Although cams with discontinuous acceleration
characteristics have sometimes been accepted to save cost in low speed applications
However, for high speed applications (to increase the productivity), such cams exhibit major problems like high noise and wear
To overcome these problems, It is extremely important that not only the displacement and the velocity curve but also the acceleration curve be made continuous for the entire motion cycle.
2
2 )(,
)(),(
d
yd
d
dyy
must be continuous
Note 2
22
2
2
,
d
yd
dt
yd
d
dy
dt
dy
Parabolic Motion If the rotation angle of the cam is , the displacement
diagram equation for a parabolic motion of rise L is given by
First Half Rise: second Half 2
2
Ly
2
121
Ly
After differentiation we found that
First Half
L
d
yd
L
d
dy
4
4
2
2
Second Half
L
d
yd
Ld
dy
4
14
1
2
2
There is a discontinuity in the velocity and acceleration
Parabolic Motion
Displacement diagram and derivatives for full-rise parabolic motion
Simple Harmonic Motion
Displacement diagram and derivatives for full-return simple harmonic motion
Displacement diagram and derivatives for full-rise simple harmonic motion
The velocity and acceleration are continuous
cos1
2
Ly
cos1
2
Ly
Rise Return