One-Sided Contact Loss in Axially Floating Herringbone Gears: A Saturation-Oscillator Theory

Axial floating of one member is used to equalise the load sharing of herringbone gears. Common treatments prescribe or linearise the floating displacement, assuming both helices stay in contact. A torsional–axial model with a slice-based mesh model is excited by the pitch-deviation difference of the helices. Condensing the faster torsional mode gives a saturation oscillator: the restoring force saturates when one helix loses contact, and mesh damping acts only while both are loaded. Closed-form criteria for contact loss, describing-function responses, and a regime map are derived; the full model verifies the dynamic response, and static contact finite element analysis the force–deflection relation and the saturating restoring force. In the cases examined, peak single-helix loads reach 2.3–3.0 times the nominal share for a single harmonic, and more under multi-order excitation at light load; the displacement-excitation approach predicts equal sharing, the linear floating model tensile forces. On rigid bearings, separated and contacting responses coexist below the axial resonance. For an industrial ISO grade 5 pair, contact loss is predicted at light load and high speed with or without compensated lead slope modification. The oil films of its journal bearings, acting through shaft tilt, dissipate the differential motion and raise the threshold far above the rigid-bearing value.