Concave modifications of tooth surfaces of beveloid gears with crossed axes

Abstract

The mathematical models of the beveloid gear surfaces with different scenarios of combinations of profile concave modification and lead crowning are derived. Four schemes of modifications were proposed for beveloid gears with crossed axes. Tooth contact analysis is developed to study the influences of different schemes of concave modifications on the mesh behaviors including film thickness, transmission errors, contact ratio, root stresses, and contact patterns. Comparison of the contact characteristics of a beveloid gear drive with and without concave modifications is conducted. The results show that all the concave modification schemes can increase the area of contact patterns and decrease the maximum value of contact stresses, while the minimum film thickness can be increased. For the scheme i.e. the pinion with profile crowning modification and gear with profile concave modification, the contact ratio increases firstly then decreases to a relative lower value. Also, the root stresses are increased obviously. For the scheme for pinion without modification and gear with lead concave modification and the scheme for both pinion and gear with lead concave modification, the transmission errors are decreased slightly. The scheme for the pinion with combined crowning modification and gear with combined concave modification shows the largest improvement for the mesh behaviors in terms of the transmission errors and contact patterns where an almost contact condition can be found for the crossed beveloid gear pair.

A Review on Micropitting Studies of Steel Gears

“…It is deserved to be mentioned that the effects of gear modification techniques on the gear contact characteristics have also been investigated by the author's team [42]. Liu et al [43] proposed a mathematical concave modification model for the beveloid gear tooth surfaces with crossed axes. The loaded tooth contact analysis (LTCA) and the theoretical tooth contact analysis (TCA) were performed to the analytical contact patterns.…”

“…The minimum film thickness with different modification quantities of Case 4 (Reprinted with permission from[43]. Copyright 2018 SAGE).Coatings 2018, 8, x FOR PEER REVIEW 6 of 28…”

Herleitung einer analytischen Optimierungsmethode für Beveloidräder durch lokale Anpassung der Verzahnungsdaten

“…Brecher et al [4] Liu et al [11,12] überlagern die mathematisch bestimmten Flankengeometrien der Beveloidräder mit Zahnflankenmodifikationen, die quadratisch in Richtung der Zahnbrei-te und -höhe ausgeführt werden können. Die Modifikationen sind dabei konkav, was eine Verringerung der Zahndicke in der Zahnbreitenmitte bedeutet.…”

Effects of cutter modification on the meshing characteristics of intersected beveloid gear and involute cylindrical gear

“…At present, a lot of research on tooth modifications and meshing characteristics has been done. The concave modification of the beveloid gear tooth surface was proposed by Liu et al [2] . Zhou et al derived the equations of the gear face of the tooth with modifications [3] .…”