Engineering Expert Witness Blog

      Last time we introduced a way to convert individual gear speeds in relation to one another within a gear train by employing a conversion tool known as the gear ratio.    Today we’ll introduce the gear ratio formulas, of which there are two types.

      The first formula for determining gear ratio is based on knowing the driving gear revolutions per minute (RPM), notated as n_Driving, and the driven gear RPM, n_Driven.     Given that knowledge we can calculate the gear ratio, R, that exists between them by the formula:

R = n_Driving ÷ n_Driven             (1)

      The other way to determine gear ratio, R, is by knowing the number of teeth on both the driving gear, N_Driving, and the driven gear, N_Driven.    That’s right, it all boils down to simply counting the number of teeth on each gear.  In this instance the gear ratio is calculated by the following formula:

R = N_Driven ÷ N_Driving             (2)

      Equations (1) and (2) may look virtually identical, but they’re not.    In mechanical engineering calculations, lower case n is typically used to denote the RPM of rotating objects such as shafts, wheels, pulleys, and gears.    Upper case N is typically used to denote the number of teeth on a gear.

      Next time we’ll see how to manipulate these two equations so as to arrive at a particular gear ratio.

_______________________________________