week 5 dynamics of machinerykisi.deu.edu.tr/hasan.ozturk/makina dinamigi/makina... ·...

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WEEK 5 Dynamics of Machinery

• References • Theory of Machines and Mechanisms, J.J.

Uicker, G.R.Pennock ve J.E. Shigley, 2003

Prof.Dr.Hasan ÖZTÜRK

A cam is a rotating machine element which gives reciprocating or oscillating motion to another element known as follower. The cam and the follower have a line contact and constitute a higher pair. 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 cam and follower is one of the simplest as well as one of the most important mechanisms found in modern machinery today. The cams are widely used for operating the inlet and exhaust valves of internal combustion engines, automatic attachment of machineries, paper cutting machines, spinning and weaving textile machineries, feed mechanism of automatic lathes etc.

CAMS

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retaining spring

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ANALYSIS OF AN ECCENTRIC CAM

(a) Eccentric plate cam and flat-face follower; (b) free-body diagram of the follower; (c) free-body diagram of the cam.

An eccentric is the name given to a circular plate cam with the cam-shaft mounted off center. The distance e between the renter of the disk and the center of the shaft is called the eccentricity.

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230 ( ) .= ⇒ − + −∑

yF F k y m yδ P:preload

, , y y ymy

F23 is the critical condition. It must always have positive value. When F23=0, the contact is lost and hence cam and follower are no longer touching each other. It means that follower is no more following the profile of the cam. It is free and floating in the air.

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0M =∑

which can be written, through a trigonometric identity, as:

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Plot of displacement, velocity, acceleration, and contact force for an eccentric cam system;

Jump (float) may occur (F23=0)

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Graph of Torque Components and Total Cam-Shaft Torque

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Displacement diagram and derivatives for full-rise parabolic motion.

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Displacement diagram and derivatives for full-rise parabolic motion.

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Harmonic Motion:

Parabolic Motion:

Rise Return

1 cos2Ly πθ

β

= −

1 cos2Ly πθ

β

= +

sin2

Ly π πθωβ β

=

sin

2Ly π πθωβ β

= −

2

22 cos

2Ly π πθωβ β

=

22

2 cos2

Ly π πθωβ β

= −

Rise Return the first part of the

parabolic rise the second part of the

parabolic rise the first part of the

parabolic return the second part of the

parabolic return 2

2y L θβ

=

2

2 4y L L Lθ θβ β

= − + −

2

2y L Lθβ

= − +

2

2 4 2y L L Lθ θβ β

= − +

2

4Ly ωθβ

= 2

4 4L Ly θ ωβ β

= − +

2

4Ly ωθβ

= − 2

4 4L Ly θ ωβ β

= −

22

4Ly ωβ

= 22

4Ly ωβ

= − 22

4Ly ωβ

= − 22

4Ly ωβ

=

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EXAMPLE:Parabolic Motion

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The cam-contact force can be written as:

Note that jump will first occur at θ=ωt=600 because this is the first position where F approaches zero.

RISE RETURN the first part of the

parabolic rise the second part of the

parabolic rise the first part of the

parabolic return the second part of the

parabolic return 2

2y L θβ

=

2

2 4y L L Lθ θβ β

= − + −

2

2y L Lθβ

= − +

2

2 4 2y L L Lθ θβ β

= − +

2

4Ly ωθβ

= 2

4 4L Ly θ ωβ β

= − +

2

4Ly ωθβ

= − 2

4 4L Ly θ ωβ β

= −

22

4Ly ωβ

= 22

4Ly ωβ

= − 22

4Ly ωβ

= − 22

4Ly ωβ

=

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