3.3 Gears, Wheels, & Belts

Gears, Wheels, and Belts in Fire Service Machinery

Gears, wheels, and belts are mechanical components designed to transmit rotational motion, adjust speed, and multiply torque. On the NTN FireTEAM exam, you will encounter diagrams of gear trains, wheel-and-axle setups, and belt-driven pulleys. To answer these questions successfully, you must understand gear ratio math, rotational direction rules, the trade-off between speed and torque, and how force is transmitted through shafts and belts.

Gear Mechanics and Gear Ratios

A gear is a wheel with teeth along its perimeter that mesh with another toothed wheel. When gears mesh, they transmit rotational force from a driver gear (the gear supplying the input force, such as a motor shaft) to a driven gear (the output gear connected to the load).

The relationship between two meshing gears is defined by the Gear Ratio:

$\text{Gear Ratio} = \frac{\text{Number of Teeth on Driven Gear}}{\text{Number of Teeth on Driver Gear}} = \frac{N_{\text{driven}}}{N_{\text{driver}}}$

Alternatively, the gear ratio can be calculated using the diameters of the gears:

$\text{Gear Ratio} = \frac{\text{Diameter of Driven Gear}}{\text{Diameter of Driver Gear}}$

Speed vs. Torque Trade-off

Gears allow you to trade rotational speed for rotational force (torque). The total work output must equal the work input (excluding friction). Therefore:

• Increasing Torque (Speed Reduction): If a small driver gear turns a large driven gear, the gear ratio is greater than 1. The driven gear rotates slower than the driver gear, but it outputs more torque.
• Increasing Speed (Torque Reduction): If a large driver gear turns a small driven gear, the gear ratio is less than 1. The driven gear rotates faster than the driver gear, but it outputs less torque.

Example Calculations

1. Case A: Large Driven Gear. A driver gear with 10 teeth meshes with a driven gear with 40 teeth.
   • $\text{Gear Ratio} = \frac{40}{10} = 4$.
   • This is a 4:1 gear ratio. For every 4 rotations of the driver gear, the driven gear completes 1 rotation. The output speed is reduced to $\frac{1}{4}$ of the input speed, but the output torque is multiplied by 4.
2. Case B: Small Driven Gear. A driver gear with 30 teeth meshes with a driven gear with 10 teeth.
   • $\text{Gear Ratio} = \frac{10}{30} = \frac{1}{3}$.
   • This is a 1:3 gear ratio. For every 1 rotation of the driver gear, the driven gear completes 3 rotations. The output speed is tripled, but the output torque is reduced to $\frac{1}{3}$ of the input torque.

Rotational Direction in Gear Trains

Understanding how gears affect the direction of rotation is a common question type on the FireTEAM test.

• Two Meshing Gears: When two gears mesh directly, they rotate in opposite directions. If the driver gear turns clockwise (CW), the driven gear must turn counter-clockwise (CCW).
• Gear Trains (Three or More Gears): In a line of three gears (Gear A meshes with B, B meshes with C):
  • If Gear A turns CW, Gear B turns CCW.
  • Since Gear B turns CCW, Gear C must turn CW.
  • This leads to the general rule: In a series of meshing spur gears, every odd-numbered gear in the train rotates in the same direction as the first gear, while every even-numbered gear rotates in the opposite direction.
• Idler Gears: Gear B in the example above is called an idler gear. It does not change the gear ratio between Gear A and Gear C, but it serves to make the driven gear (C) rotate in the same direction as the driver gear (A).

Spur Gears vs. Bevel Gears

• Spur Gears: Have teeth cut parallel to the axis of rotation and transmit power between parallel shafts. They are the most common type of gear.
• Bevel Gears: Have teeth cut on a cone-shaped surface. They are used to transmit rotational force between shafts that intersect, typically at a 90-degree angle.
• Fire Service Application: Manual gate valves on fire engines use bevel gears. When a firefighter turns a vertical handwheel, a bevel gear meshes with another bevel gear at a 90-degree angle to turn a horizontal stem inside the valve casing, opening or closing the valve.

Wheel-and-Axle Mechanics

A wheel-and-axle consists of a large wheel attached to a smaller shaft (the axle) that rotate together.

• Mechanical Advantage: The mechanical advantage of a wheel-and-axle is the ratio of their radii: $\text{MA} = \frac{\text{Radius of the Wheel}}{\text{Radius of the Axle}} = \frac{R_{\text{wheel}}}{r_{\text{axle}}}$
• Force Multiplication: If you apply force to the outer edge of the wheel (large radius), you multiply the torque on the axle (small radius). A larger wheel requires less force to turn the axle.
• Fireground Application:
  • Hose Reels: Booster hoses are stored on large reels. The reel has a large diameter handwheel or handle. To roll up the heavy wet hose, the firefighter turns the outer rim of the wheel, providing a mechanical advantage to wind the hose onto the axle.
  • Fire Hydrant and Valve Wheels: Gate valves on fire trucks and water supply networks are operated by large handwheels. Under high water pressure, the gate inside the valve experiences massive resistance. A large handwheel provides the mechanical advantage needed for a firefighter to overcome this resistance and turn the small stem to operate the valve.

Belt-Driven Pulleys

Belt drives consist of two or more pulleys connected by a continuous flexible belt. They are used to transmit rotational force over longer distances than gears.

• Grip and Friction: Belt drives rely on friction rather than teeth to transmit power. They can slip if overloaded, which acts as a safety release but reduces efficiency.
• Speed and Torque: The speed and torque relationships are identical to gears, using the pulley diameters: $\text{Pulley Ratio} = \frac{\text{Diameter of Driven Pulley}}{\text{Diameter of Driver Pulley}}$
• Rotational Direction:
  • Open Belt: If the belt is open (runs straight between pulleys), both pulleys rotate in the same direction (both CW or both CCW).
  • Crossed Belt: If the belt is crossed (forms a figure-8), the pulleys rotate in opposite directions (one CW, the other CCW).
• Fire Service Application: Small gasoline engines on portable pumps and ventilation saws sometimes use belt drives to spin the pump impeller or circular saw blade.