Unloaded transmission error and instantaneous gear ratio for non-circular gears with misalignments

Unloaded transmission error (UTE) determination is well established for gears with uniform motion. This established methodology is modified and applied to the case of non-circular gears. Reciprocity between two screws is introduced as part of this modification. One screw is a wrench defined by the tooth contact force and the other screw is a twist that defines the relative motion between the two gear elements. Associated with each meshing tooth set within a non-circular gear pair is a UTE curve. A maximum UTE value is introduced as the intersection between adjacent UTE curves. Cubic splines are used to interpolate these intersections and obtain a maximum UTE curve. Subsequently, generalized misalignments are presented to investigate the maximum UTE for misalignments. Absent from classical UTE analysis with misalignments is the instantaneous gear ratio. Developed is a procedure to obtain the instantaneous gear ratio for gears with misalignments. This procedure is valid for skew axis and non-circular gears. A parallel axis gear set is included to demonstrate the process. A special non-circular gear motion is constructed with part-uniform and part-varying motion. This hybrid motion facilitates a comparison between existing helical gears with uniform motion and spiral non-circular gears with varying motion.