Jamming a Pulley: Assessing Stress on Shaft & Hole

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SUMMARY

The discussion focuses on the assessment of stress on a shaft and hole in a pulley system when a foreign object, such as a broom, is jammed into the pulley. It establishes that normal stresses occur at the hole where the jam occurs, while torsional stress affects the shaft due to the motor's continued torque application. Key factors influencing these stress magnitudes include the radius of the shaft, the distance of the holes from the pulley center, and the moment of inertia of the pulley and shaft. The moment of inertia is critical, as it is determined by mass distribution, total mass, geometry, and dimensions.

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  • Understanding of normal and torsional stress concepts
  • Knowledge of moment of inertia and its calculation
  • Familiarity with pulley systems and mechanical torque
  • Basic principles of mechanical engineering mechanics
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  • Research the calculation of moment of inertia for various shapes
  • Study the effects of torque on mechanical systems
  • Learn about stress analysis in mechanical components
  • Explore the design considerations for pulleys and shafts
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Mechanical engineers, design engineers, and students studying mechanics who are interested in understanding stress analysis in pulley systems and the implications of jamming mechanisms.

goonking
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A pulley-and-shaft is connected to a motor which applies torque to spin the pulley as shown below:
image392.jpg

Now imagine someone jams machine by sticking a broom into one of the holes of the pulley.
I would imagine there would be normal stresses at the hole (location of jam) and torsional stress on the shaft (from the motor attempting to continue turning), but magnitudes of these stresses would depend on factors like radius of the shaft, distance of holes from the center of the pulley, length of shaft, etc.

Are my assumptions reasonable?
 

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In order to jam the pulley, you need to apply a torsional stress on the pulley. In this case, you apply normal stress on the holes (which is torsional on the pulley) and torsional on the shaft, I agree.

I suppose the moment of inertia (of pulley and shaft) is the key in this case. The biggest torsional stress will be applied in the object with the biggest moment of inertia.
The moment of inertia depends on distribution of mass, the total mass, the geometry and the dimensions of the object.

The normal stress that is applied on the specific hole (in which you stick the broom) depends on the distance from the center of the pulley. When you apply this stress near the center, it must be bigger, because radius is smaller there.
 

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