The Generalized Transmission Error of Parallel-Axis Gears

The traditional one-component transmission error of parallel-axis helical gears is generalized to a three-component transmission error which characterizes the composite displacement in the plane-of-contact resulting from arbitrary small deviations in the positions of both gears of a meshing pair from the positions of their rigid perfect involute counterparts. A set of linear algebraic equations is derived for the contribution to the three generalized transmission error components arising from elastic deformations of the teeth and gear bodies and deviations of the tooth running surfaces from equispaced perfect involute surfaces. It is shown how to combine this set of equations with the generalized transmission error definition and the equations of motion of a gear system to predict the dynamic response of gear elements in the system. For the case of negligible gearbody and bearing/bearing support inertial forces, an additional set of algebraic equations that includes the effects of bearing flexibility and misalignment is derived. Combining the solution of this set of equations with the above-mentioned generalized transmission error equations yields the three-component generalized static transmission error.