cam third.ppt

7/30/2019 Cam Third.ppt

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Choosing the Prime Circle

Start with something about 3 times max lift h.

Compute f for all values ofq.

Iterate to an acceptable condition.

Maximum pressure angle for a translating roller

follower should be f < = 30 degrees.

Eccentricitye can be introduced to correctasymmetry in max and min f if desired.


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Type of Motion Constraints

Critical Extreme Position (CEP)

End points of motion are critical

Path between endpoints is not critical

Critical Path Motion (CPM)

The path between endpoints is critical

Displacements, velocities, etc. may be specified

Endpoints usually also critical


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Types of Cam Motion Programs

No-Dwell or Rise-Fall (RF)

Single-Dwell or Rise-Fall-Dwell (RFD)

Double-Dwell (RDFD)

Multi-Rise-Multi-Dwell-Multi-Fall

Different Motion Programs Needed for Each


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A Cam Timing Diagram


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Constant Velocity

Constant velocity: Displacement of the follower isproportional to the cam displacement and the slopeof the displacement curve is constant

q thhs

h

dt

dsv Constant

0dt

dvf

q: Cam rotation angle (instantaneous) f : Cam rotation angle for the max follower displacementh: total displacement s:follower displacement v: follower velocity

Though acceleration is zero, during rise or fall of the follower, it is infinite at thebeginning and end of motion as there are abrupt changes in velocity at these points.

This results in infinite inertia forces and this is not suitable for the practical point ofview


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The Fundamental Lawof Cam Design

The cam-follower function must have continuous

velocity and acceleration across the entire interval,

thus making the jerk finite.


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Harmonic functions are differentiable

however single harmonic functions are notbeing used in camCam function over the entire interval ispiecewise function made up of severalsegments, some of which may be dwellportions or other functions.

A dwelll will always have zero velocity andzero acceleration

Simple Harmonic

Motion

Thus we must match the dwellszero values at the ends of thosederivatives of any segments thatadjoin them

SHM functions when used withdwells does not satisfy thefundamental law of cam design

SHM displacement function willsatisfy the fundamental law is the

non-quick return RF( i.e 180 riseand fall n 180 with no dwells)


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q: Cam rotation angle (instantaneous)

f : Cam rotation angle for the max follower displacement

: Angle on the harmonic circle

his total displacement sis follower displacement

At any instant, follower displacement

cos22

hhs

cos12

hs

q

For the rise of the follower displacement, the cam is rotated through an angle f whereas a point on th

harmonic semicircle traverses an angle .Thus a cam rotation is proportional to the angle turned by the point on the harmonic semicircle

Simple Harmonic Motion(SHM)

This expression is also valid for more than 90. In that case co sbecomes negative so that sis again positive and more than h/2


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Simple Harmonic Motion (SHM)

There is an abrupt change ofacceleration from zero to max at thebeginning of the follower motion andalso from max to zeroThese abrupt changes result in infinite

jerk, vibration and noise


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Acceleration in the first half of the follower motion whereas it is deceleration during the laterhalf. Displacement curve is found to be parabolic

The magnitude of the acceleration and deceleration

is the same and constant in the two halves

Divide each half of the cam displacement intervalinto n equal divisions

Divide half the follower rise into n2 equal divisionsProject 12 displacement interval to the first ordinate

of the cam displacement, 22 to the second ordinate,

32 to the third and so on.

The second half of the curve is similar to the first

half

Constant Acceleration and Deceleration


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The equation for the linear motion with constantacceleration f(during the first half of the followermotion) is found as follows

where v0 is the initial velocity at the start of themotion(rise or fall) and is zero in this case

As f is constant during the acceleration period,considering the follower at the midway

The velocity is linear during the period and is givenby


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A cyloidal is the locus of a point on a circle rolling on a straight line

Divide the cam displacement interval into n equal parts( n even)

Draw the diagonal of the diagram and extend it below

Draw a circle with the centre anywhere on the lower portion of the diagonal such that its

circumference is equal to the follower displacement. i.e .2r= h or r = h/2

Divide the circle into n equal parts and number them as shown in the diagram

Project the circle points to its vertical diameter and then in a direction parallel to the diagonal of

the diagram to the corresponding ordinates

Cycloidal


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Mathematically a cycloidal is expressed as


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Choosing Cam Functions

They must obey the fundamental law

Lower peak acceleration is better:F = ma

Lower peak velocity lowers KE = 0.5 mv2

Smoother jerk means lower vibrations

Magnitude of jerk is poorly controlled inmanufacturing


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Direction of cam rotation: ClockwiseFollower: Knife edgeLifts: SHMLowers: Uniform velocity

A cam profile is constructed on the principle ofkinematic inversion. i.e. considering the cam to be

stationary and the follower to be rotating about itsin the opposite direction of the cam rotation

Draw the prime circle of the cam with radius

Divide the prime circle into segments from

the vertical position indicating angles of

ascent, dwell and descend in the opposite

direction of the cam rotation

Divide each segment of ascent and descent

into the same number of angular parts in

the displacement diagram

On the radial line produces, mark distances

equal to the lift of the follower beyond the

circumference of the prime circle

cam third.ppt

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