Angle of twist of a gear relative to another

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SUMMARY

The discussion focuses on calculating the angle of twist of gear A relative to gear D, specifically addressing the need to consider two moments caused by an applied torque of 85Nm. The equation for the angle of twist incorporates contributions from both shaft sections AB and CD, emphasizing that omitting the factor of 2 leads to an incorrect calculation of the twist. The correct formula includes the moments from both sections to accurately determine the relative twist between the gears.

PREREQUISITES
  • Understanding of torsional mechanics and torque calculations
  • Familiarity with the properties of hollow shafts
  • Knowledge of material properties, specifically Young's modulus
  • Basic proficiency in using equations for angle of twist in mechanical systems
NEXT STEPS
  • Study the derivation of the angle of twist formula for hollow shafts
  • Learn about the effects of torque on multiple connected shafts
  • Explore the application of Young's modulus in torsional calculations
  • Investigate practical examples of gear systems and their angular displacements
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Mechanical engineering students, professionals involved in gear design, and anyone studying torsional mechanics in mechanical systems.

fonseh
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Homework Statement


why we need to consider 2 moment caused by the 85Nm in this question ? The question ask for the determine the angle of twist of gear A relative to D .

Homework Equations

The Attempt at a Solution


Why shouldn't the angle of twist = (85)(0.4) / ( (0.5pi)( 0.015^4- 0.01^4)(75)(10^9) ) + (85)(0.25) / (0.5pi)(0.02^4)(75)(10^9) only ?
 

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I'm not quite sure I understand your question but the factor of 2 you removed is there to account for the fact there are two identical shaft sections, AB and CD.
Without that 2 you're ignoring one of the hollow sections and your answer is the twist of A relative to C (or B relative to D).
 

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