Lecture on Gears, Torque, and Gear Ratios

Introduction

• Biking and Gear Use
  • Start pedaling in low gear for easier movement.
  • Shift to higher gear as speed increases.
• Car Gear Shift
  • Begin in lowest gear, shift up with speed, down on hills.

Basics of Torque

• Definition:
  • Torque: Force causing rotation around a point.
• Example:
  • Small wrench vs. long wrench on a nut.
  • Formula: Torque = Length of wrench (m) x Force (Newtons).
  • Longer wrench increases torque.

Gear Mechanics

• Driver and Driven Gears
  • Driver gear connected to engine, drives the system.
  • Driven gear follows driver gear's rotation.
• Gear Ratios
  • 1:1 Ratio: Equal diameter gears, equal rotations.
  • 1:2 Ratio: Driven gear smaller, faster rotation.
  • 2:1 Ratio: Driven gear larger, slower rotation.

Changing Direction

• Reverse Gear
  • Driven gear rotates opposite to driver gear.
  • Insert idler gear to align output direction.

Gear Trains

• Simple vs. Compound Gear Train
  • Simple: Multiple gears side by side.
  • Compound: Gears on the same axis, saving space.

Calculating RPM and Torque

• Formulas:
  • Ratio = Teeth of output gear / Teeth of input gear.
  • RPM output = RPM input / Ratio.
  • Torque output = Ratio x Torque input.

Example Calculations

• Gear A and B
  • Gear A: 8 teeth, Gear B: 10 teeth.
  • Ratio: 1.25.
  • Gear A RPM: 150, Gear B RPM: 120.
  • Gear A Torque: 20 Nm, Gear B Torque: 25 Nm.
• Gear C and D
  • Gear C: 20 teeth.
  • Ratio from B to C: 2.
  • Gear C RPM: 60, Torque: 50 Nm.
  • Gear D: 8 teeth.
  • Ratio from C to D: 0.4.
  • Gear D RPM: 150, Torque: 20 Nm.

Compound Gear Train Example

• Gears A, B, C, D
  • Gear A: 8 teeth, Gear B: 10 teeth, Gear C: 20 teeth, Gear D: 8 teeth.
  • Complex calculations for speed and torque with shared shafts and compound arrangement.
  • Gear D rotates same direction as Gear A, faster but with less torque.

Conclusion

• Applications
  • Considerations for gearbox design, number of gears, required torque, and speed.
• Further Learning
  • Suggested resources for deeper exploration of mechanical and automotive engineering.

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