Transmission Error Analysis of Involute Cylindrical Gears with Consideration of Gear Eccentricity

Derivation of Strict Analytical Solutions of Transmission Errors with Radial Eccentricity

Abstract

Exact analytical equations to analyze transmission error with radial eccentricity of an involute cylindrical gear pair are proposed. The equations include the amount and a phase angle of eccentricity of each gear in two dimensions and the relation between rotational angles is found an implicit function. The procedure to calculate concrete transmission error is shown shortly with those equations. Using best-fit procedure between measured and calculated transmission error of a gear pair whose number of teeth are relatively prime, it is verified that the equations have enough capability to predict actual transmission error with gear eccentricity. The best-fit procedure can be used as a kind of a high-pass filter to transmission error curve so as to analyze mesh frequency for example. The equations are also applied to predict transmission error of micro gear systems. For micro gears, manufacturing error and misalignment is rather larger than conventional sized gears. It is pointed out that this may lead larger transmission error than conventional one.