Machine Elements - Cam Design

Cam

A rotating mechanism of irregular shape, as on a wheel on a machine: used to change the direction of the motion of another part moving against it, as rotary into reciprocating or variable motion.

-In-line Knife Edge Follower
-Radial Roller Follower
-Offset Roller Follower
-Oscillating Roller Follower
-Flat-Faced Follower
-Oscillating Flat-Faced Follower

Common types of Disk Cam

CAM FOLLOWER

A part with a sliding contact with the cam. Two (2) types and most common used are Reciprocating and Oscillating follower.

Reciprocating and Oscillating Follower

Two types and most common used cam follower.

-DISK CAM
-CYLINDRICAL CAM

COMMON CLASSIFICATION OF CAM ACCORDING TO SHAPE

DISK CAM

Cam profile curve is worked in a flat plate

CYLINDRICAL CAM

Cam profile curve is worked around a blank cylinder.

-IN-LINE/RADIAL FOLLOWER
-OFFSET FOLLOWER
-OSCILLATING FOLLOWER

CLASSIFICATION ACCORDING TO TYPES OF FOLLOWER

-SIMPLE MOTION
-PARABOLIC MOTION
-HARMONIC MOTION
-CYCLOIDAL MOTION

CLASSIFICATION BASED ON THE TYPE OF MOTION

IN-LINE/RADIAL FOLLOWER

The follower is considered to be ______ or _____ when its centerline passes through the center of cam rotation. Seldom used in actual practice since it produces high contact stresses.

OFFSET FOLLOWER

The centerline of the follower has an offset distance with respect to the center of cam rotation.

OSCILLATING FOLLOWER

Special type cam mechanism with a follower oscillating at a certain center having a defined distance with respect to center of cam rotation

SIMPLE MOTION

The cam profile is generated in reference with the predefined motion of the follower.

PARABOLIC MOTION

Analytically, the cam profile is generated by following the motion curve of an equation of a Parabola.

HARMONIC MOTION

Cam profile is generated by following the motion curve of a harmonic motion

CYCLOIDAL MOTION

Cam profile is generated by following the motion curve of a cycloid.

BASE CIRCLE

The smallest circle tangent to the cam surface about the center of cam rotation.

CAM PROFILE

The actual contacting surface of a disk type cam. Its curvature is generated using either one of the following considerations: (1) Assumption of the required motion for the follower then design the cam profile to give this motion and, (2) Assumption of the shape of the cam then determine what characteristics of displacement, velocity and acceleration this contour will give.

Dilemma (Cam Profile)

After the cam is designed, some contour will be difficult to manufacture.

Solution (Cam Profile)

Follow the second method by making the cam symmetrical and by using shape for the cam contours that can be generated through machining and other metal working process.

Result (Cam Profile)

Manufacturing of cams for automotive application that must be produced cheaply and accurately has been solved.

STROKE

The distance measured between two extreme position of the follower

TRACE POINT

Is a point on the follower that corresponds to the contact point of fictitious knife edge follower.

PITCH CURVE

Is the path of trace point relative to the cam profile.

PRESSURE ANGLE

The angle between the direction of motion of the trace point and the common normal (line of action) to the contacting surfaces.

PRESSURE ANGLE

It is a measure of the instantaneous force
transmission properties of the mechanism.

larger - more power

The ______ is the pressure angle, ______ is required to operate the cam mechanism.

Line of action

the axis where the force from rotating cam profile is ACTUALLY transmitted on the follower.

Graphical Method and Analytical Method

two distinct methods of how Cam contours or cam profiles are generated

DISK CAM WITH OFFSET ROLLER FOLLOWER

The development of this type of cam has been integrated to minimize the pressure angle of the contacting surface, thus, reducing the power requirement during outward rotation (lifting motion) although there is a large pressure angle in the return motion.

DISK CAM WITH OFFSET ROLLER FOLLOWER

the follower axis has an offset distance from the vertical axis passing through the cam rotation.

DISK CAM WITH OFFSET ROLLER FOLLOWER

The method of construction will be almost the same in an exception that roller follower is being offset with the specified distance from the reference axis given.

DISK CAM WITH FLAT-FACED FOLLOWER

The principal construction of this type of cam are the same as in the radial roller follower with the exception that the cam profile is drawn tangent to the various position of the flat face follower.

DISK CAM WITH FLAT-FACED FOLLOWER

In this case, there is no need to distinguish between radial and offset followers because they are kinematically equivalent. That is any follower shaft parallel to the one shown will produce the same output motion.

DISK CAM WITH FLAT-FACED FOLLOWER

One important factor of the design of this type of cam is the determination of the minimum length of follower face to ensure a smooth contact of the mating surfaces during the operation. This minimum length can be defined graphically by measuring the maximum parallel distance between the axis passing through the center of cam rotation and the normal axis to the point of contact corresponding to the angle of cam rotation.

length of the follower face equation

length of the follower face equation for offset follower, for symmetrical construction

DISK CAM WITH OSCILLATING ROLLER FOLLOWER

In this type of cam, an oscillating follower move at a certain degree as the cam rotates and touches the mating surface of the follower.

DISK CAM WITH OSCILLATING ROLLER FOLLOWER

The principal construction of this type of cam is the same as in the reciprocating roller follower, only, various condition shall be established first before doing the layout of the cam contour.

Conditions for layouting cam contour in DISK CAM WITH OSCILLATING ROLLER FOLLOWER

1. Distance between the center of cam rotation and center of oscillation of the follower,
2. Position of center of oscillation relative to the center of cam rotation and,
3. Radius of oscillation of the follower.

DISK CAM WITH OSCILLATING FLAT-FACED FOLLOWER

Graphically, the construction method in generating the cam contour of this type of cam is a combination of knowledge in a reciprocating and oscillating follower.

DISK CAM WITH OSCILLATING FLAT-FACED FOLLOWER

The concept of finding the minimum length as in the reciprocating flat face follower is also applied in this type of cam.

DISK CAM WITH OSCILLATING FLAT-FACED FOLLOWER

The construction is almost similar with the oscillating roller follower in an exception that cam contour is drawn normal to a flat surface.

select the motion with which the follower will move

before a cam contour can be determined, it is necessary to ____________ in accordance with the requirements of the system.

slow speed

If operation is to be at _______, the motion may be any one of several common motions, for example, parabolic (constant acceleration and deceleration), parabolic with constant velocity, simple harmonic, or cycloidal.

PARABOLIC MOTION

has the lowest theoretical acceleration for a given rise and cam speed for the motions listed, and for this reason it has been used for many cam profiles. However, in slow-speed work, this has little significance.

PARABOLIC MOTION

may or may not have equal intervals of acceleration and deceleration, depending on requirements.

PARABOLIC MOTION

may also be modified to include an interval of constant velocity between the acceleration and deceleration; this is often spoken of as modified constant velocity

S = ½ At^2

analytically, the parabolic motion can be constructed using the displacement formula as _____

inflection point

In plotting the displacement-time graph, it is necessary to determine the ____ ____ if the motion is parabolic or a modification thereof.

inflection point

The ______ for parabolic motion will be at the midpoint of the displacement scale and of the time scale if the intervals are equal. The slope of this point of inflection can be used as a guide in constructing the section of the displacement having a constant velocity.

HARMONIC MOTION

has the advantage that, with a radial roller follower, the maximum pressure angle will be smaller than with parabolic motion with equal time intervals or with cycloidal motion.

HARMONIC MOTION

This will allow the follower to be less rigidly supported and more overhung in its construction. Less power will also be needed to operate the cam.

S = r(1-cos(θ)) ; where ‘r’ is the radius of the construction circle (r = S/2) and ‘θ’ being the angle of cam rotation

analytically, the harmonic motion can be constructed using the displacement formula

Dwell

defined as the interval of cam rotation (in degrees) where the follower has no considerable motion or the cam is at rest position.

where ‘S’ is the total displacement of the follower, ‘s’ is the specific lift with respect to cam rotation, ‘θ’ being the angle of cam rotation and ‘β’ is the total angle in consideration.

analytically, the type of cycloidal motion presented below (other types will be presented in the preceding topics) can be constructed using the displacement formula:

r = S/2π

radius of the construction circle in cycloidal motion

different types of motion curve

________ produce dynamic effect that tends to separate the cam with the follower and produces significant level of machine vibration that should be avoided

cams operating at higher speeds

For __________, the selection of the motion of the cam follower must be based not only on the displacement but also on the forces acting in the system as a result of motion selected.

jerk

The rate of change of acceleration is determined by the third derivative of the displacement and has been given the name "___"

jerk

is an indication of the Impact characteristic or the loading; it may be said that
impact has _____ equal to infinity.

Lack of rigidity and backlash in the system

____________ also tends to increase the effect of impact loading.

parabolic motion

In ________ where the jerk is infinite, this impact occurs twice during the cycle and has the effect of a sharp blow on the system, which may set up undesirable vibrations as well as cause structural damage.

Kloomok and Muffley

As a means of avoiding infinite jerk. and its deleterious effect on the cam train, a system of cam design has been developed by _________ that utilizes three analytic functions: (a) cycloid (and half-cycloid), (b) harmonic (and half-harmonic), and (c) eighth-power polynomial.

(a) cycloid (and half-cycloid)
(b) harmonic (and half-harmonic)
(c) eighth-power polynomial.

three analytic functions developed by Kloomok and Muffley in a system of cam design

matching accelerations.

Infinite jerk is avoided at the ends by ________.

no discontinuities can appear in the displacement time curve

velocities, in curve fitting, will also match because ______.

Cycloid

provides zero acceleration at both ends of the action. Therefore, it can be coupled to a dwell at each end.

two cycloids should not be coupled together

Because the pressure angle is relatively high and the acceleration returns to zero unnecessarily, _______________.

Harmonic

provides the lowest peak acceleration and pressure angle among the three curves.

Harmonic

preferred when the acceleration at both start and finish can be matched to the end acceleration of the adjacent profiles.

Half-harmonic

Because acceleration at the midpoint is zero, the _______ can often be used where a constant-velocity rise follows an acceleration.

eighth-power polynomial

________ has a nonsymmetrical acceleration curve and provides a peak acceleration and pressure angle intermediate between the harmonic and the cycloid.