How to Calculate Spur Gears

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Spur gears are a simple assembly consisting of a cylinder with teeth projecting outward, and are used to provide standard rotary motion from one parallel shaft to another. Spur gears provide a constant speed that can be increased or decreased by the number of teeth on the gear assembly. Mechanical engineers use several design variables to size and design gears for specific applications, load and speed requirements. Variables that are either directly or indirectly related to the number of teeth in the gear assembly include the diametral pitch (P), pitch diameter (PD), outside diameter (OD) and number of teeth (N).

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  • Calculate the diametral pitch (P) using the formula P = N/PD. Diametral pitch is the primary gauge engineers use to optimize gear size and speed of rotation to fit a given application and/or pull a specific load.

  • Calculate pitch diameter (PD) using the formula PD = N/P. Pitch diameter is a support variable to the diametric pitch. For example, diametric pitch can be viewed as the number of teeth of a gear per inch of its pitch diameter.

  • Calculate outside diameter (OD) using the formula OD = (N + 2)/P. You calculate the outside diameter of a gear to help control the pulling strength of the gear. The larger the diameter, the more pull it will have.

  • Calculate the number of teeth (N) using the formula N = PD x P. You calculate the number of gear teeth to help control speed of gear rotation.

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