Abstract
An approximate formula of gear transmission error with radial eccentricity is derived explicitly from exact solutions. Derived formula consists of two sinusoidal functions and an offset term. It is very simple and easy to examine the relation among transmission error, gear specifications and the parameters of eccentricity. If the sum of the parameters of amount of eccentricity is the same, the peak-to-valley value of transmission error is also the same in the case of a gear pair, which has the number of teeth relatively prime. The fact is also true under the different initial phase angles of eccentricity. The maximum residual between exact solutions and approximate one is only about 1.0 urad or less. It can be found that the derived approximate formula is enough to analyze the transmission error with radial eccentricity for gear pairs of the conventional size.
