How Do You Calculate Operator Force and Torque in a Multi-Gear System?

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SUMMARY

This discussion focuses on calculating operator force and torque in a multi-gear system designed for a gearbox with four spur gears: A (30t, 3in), B (60t and 10t gears), C (60t and 30t gears), and D (20t, 2in). The operator needs to determine the force applied to the input shaft, which is the 30t gear, while considering the motor's 5ft-lb of torsional inertia. The conversation highlights the importance of using the correct units for mass moment of inertia, specifically slug-ft² in USC units, to ensure accurate calculations.

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  • Understanding of gear ratios and their impact on torque transmission
  • Familiarity with the concepts of torque and force in mechanical systems
  • Knowledge of mass moment of inertia and its units in mechanical engineering
  • Basic principles of spur gear design and operation
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  • Calculate gear ratios for the multi-gear system to determine torque multiplication
  • Learn about the relationship between force, torque, and radius in rotating systems
  • Study the principles of calculating mass moment of inertia for different shapes
  • Explore the application of the formula T = F × r for torque calculations in gear systems
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Mechanical engineers, students in mechanical design courses, and anyone involved in gearbox design and analysis will benefit from this discussion.

fishinhrox12
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I am designing a gearbox to take a human input with a crank 12 in. long attached to a shaft that drives the first gear which goes through a gearbox and eventually turns a motor shaft in case of electrical failure. This is for a class concept design. The motor has 5ft-lb of torsional inertia and I need to calculate the operator force.
the gear box is set up with 4 spur gears, A,B,C, and D.
A is a 30t gear, 3in diameter
B is a gear with a big tooth and smaller gear attached to the top of it so that they both spin in the same direction at the same speed(see attached picture).
B will have a 60t large gear attached to a 10t small gear with respective diameters, 6 and 1 inches.
C is the same idea, the large is a 60t 6in. gear and the smaller is 30t, 3in.
D will be a single spur gear with 20t, 2in.

How do I calculate the torque or force that the operator must apply to the input shaft(the 30t gear, top left)
 

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What is 5ft-lb of torsional inertia about? The units do not make sense. Mass moment of inertia should be in slug-ft^2 if you are working in USC units with feet for length.
 

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