8.2 Gear Terminology and Calculations Explained

Key Concepts

• Pitch Circle
• Module
• Diametral Pitch
• Circular Pitch
• Backlash
• Gear Ratio
• Center Distance
• Velocity Ratio

Pitch Circle

The pitch circle is an imaginary circle on which two meshing gears appear to roll without slipping. It is the reference circle for gear dimensions and is used to calculate various gear parameters.

Example: In a pair of meshing gears, the pitch circle diameters of the two gears are used to determine the center distance between their shafts.

Module

The module is a measure of gear tooth size and is defined as the ratio of the pitch circle diameter to the number of teeth. It is typically expressed in millimeters.

Example: If a gear has a pitch circle diameter of 100 mm and 20 teeth, the module is calculated as 100 mm / 20 = 5 mm.

Diametral Pitch

Diametral pitch is the number of teeth per inch of the pitch circle diameter. It is the reciprocal of the module and is commonly used in imperial units.

Example: If a gear has 24 teeth and a pitch circle diameter of 2 inches, the diametral pitch is calculated as 24 teeth / 2 inches = 12 teeth per inch.

Circular Pitch

Circular pitch is the distance between corresponding points on adjacent teeth measured along the pitch circle. It is equal to the pitch circle circumference divided by the number of teeth.

Example: If a gear has a pitch circle circumference of 125.66 mm and 20 teeth, the circular pitch is calculated as 125.66 mm / 20 = 6.283 mm.

Backlash

Backlash is the amount of clearance between the non-driving side of a gear tooth and the adjacent tooth on the meshing gear. It is necessary to allow for manufacturing tolerances and thermal expansion.

Example: In a gear train, if the backlash is too large, it can cause play and affect the precision of the motion, while too little backlash can lead to binding.

Gear Ratio

The gear ratio is the ratio of the number of teeth on the driven gear to the number of teeth on the driving gear. It determines the speed and torque relationship between the gears.

Example: If a driving gear with 10 teeth meshes with a driven gear with 30 teeth, the gear ratio is 30 / 10 = 3:1, meaning the driven gear rotates three times for every one rotation of the driving gear.

Center Distance

Center distance is the distance between the centers of two meshing gears. It is calculated as the sum of the pitch circle radii of the two gears.

Example: If two gears have pitch circle diameters of 50 mm and 100 mm, the center distance is (50 mm / 2) + (100 mm / 2) = 25 mm + 50 mm = 75 mm.

Velocity Ratio

Velocity ratio is the ratio of the rotational speed of the driving gear to the rotational speed of the driven gear. It is the inverse of the gear ratio.

Example: If a driving gear rotates at 600 rpm and the gear ratio is 3:1, the velocity ratio is 1 / 3, meaning the driven gear rotates at 600 rpm / 3 = 200 rpm.

Examples and Analogies

Think of the pitch circle as the imaginary track on which two gears roll together, like two cyclists riding side by side on a track.

The module is like the size of the steps you take while walking. The larger the module, the bigger the steps (teeth) on the gear.

Diametral pitch is like the number of steps you take per mile. The more steps (teeth) per inch, the finer the gear teeth.

Circular pitch is like the distance between the toes of your shoes. The larger the distance, the bigger the gap between gear teeth.

Backlash is like the space between your fingers when you clap. Too much space and the clap is weak, too little and it's too tight.

Gear ratio is like the number of times you can lift a weight compared to your friend. If you can lift it three times for every one of your friend's lifts, the gear ratio is 3:1.

Center distance is like the distance between two people holding hands. The longer the arms, the greater the distance between their centers.

Velocity ratio is like the speed at which you can run compared to your friend. If you run three times faster, the velocity ratio is 3:1.