Increasing the Strength of Standard Involute Gear Teeth with Novel Circular Root Fillet Design

Abstract

In this study the idea of spur gear teeth with circular instead of the standard trochoidal root fillet is introduced and investigated numerically using BEM. The strength of these new teeth is studied in comparison with the standard design by discretizing the tooth boundary using isoparametric Boundary Elements. In order to facilitate the analysis the teeth are treated as non-dimensional assuming unitary loading normal to the profile at their Highest Point of Single Tooth Contact (HPSTC), so that non-dimensional stress vs. Contact ratio diagrams are plotted. The analysis demonstrates that the novel teeth exhibit higher bending strength (up to 70%) in certain cases without affecting the pitting resistance since the geometry of the load carrying involute is not changed. The circular fillet design is particularly suitable in gear with a small number of teeth (pinions) and these novels gears can replace their existing counterparts in any mechanism without any alterations. Finally the geometry of the generating tool (i.e. rack) is determined in order to be able to cut these teeth using a generating method (i.e. hobbing)

COMPARISON BETWEEN NIEMANN’S AND FINITE ELEMENT METHOD FOR THE ESTIMATION OF MAXIMUM ALLOWABLE STRESS OF MESHING SPUR GEAR TEETH AT HIGHEST POINT OF SINGLE TOOTH CONTACT

“…Instead, the applied method assumes that the maximum load during gear tooth meshing is applied to the Highest Point of Single Tooth Contact (HPSTC), (Spitas et al, 2005).…”

“…It can, thus, be assumed that the worst loading condition for a tooth of gear 1 does not occur when the load is applied to the highest addendum point (point B), because the total load is distributed at two pairs of gear teeth at this point, but at point Β΄ of contact path where only a single pair of gear teeth is meshing (Niemann, 1982;Spitas et al, 2005).…”

“…That is, during portion Α΄Β΄ of the contact path only a single tooth of each gear is loaded, whereas during portions ΑΑ΄ and ΒΒ΄ the load is distributed to two teeth of each gear. Thus, we can infer that the maximum gear tooth loading occurs at a point on part Α΄Β΄ of the contact path (Spitas et al, 2005).…”

A mathematical approach regarding a better geometry of the root fillet of symmetric and asymmetric gears with the main scope of increasing the fatigue strength of gear teeth and avoiding the occurrence of cracks

“…The starting point of this paper is the main theme of another paper 1 . The authors proposed a circular fillet root radius.…”

“…In this paper, there is presented that geometry influence upon tooth base fatigue depends on the planar curves contact. For example, in [1] and [2] there can be seen a circle that is in contact with the involute curve. It is said that that curve has an 1-degree contact with the root circle (more information regarding planar curves contact will be presented in the next sub-heading).…”