The generalized transmission error of spiral bevel gears

The traditional definition of the transmission error of parallel-axis gear pairs is reviewed and shown to be unsuitable for characterizing the deviation from conjugate action of bevel gear pairs for vibration excitation characterization purposes. This situation is rectified by generalizing the concept of the transmission error of parallel-axis gears to a three-component transmission error for spiral bevel gears of nominal spherical involute design. A general relationship is derived which expresses the contributions to the three-component transmission error from each gear of a meshing spiral bevel pair as a linear transformation of the six coordinates that describe the deviation of the shaft centerline position of each gear of the pair from the position of its rigid perfect involute counterpart.