Load transmitting volume of tooth flank material decides the surface durability

We often experience that dedendum flank of gear tooth is severely damaged, but the mate-contacting addendum tooth flank is free from damage, especially in case of gears whose tooth number of pinion is small. The figure shows an example of this phenomenon to show the typical state of tooth flanks after gear endurance test, where both the mating driving and driven tooth flanks are shown with same magnification and by setting the PCD position coincided for easy understanding of correspondence of the tooth flank contact.  Big difference exists in wear state between addendum and dedendum, especially at the contact region near base circle, although the induced contact stress on both the tooth flanks and in the subsurface is symmetric and the magnitude is the same.

In fundamental research on steel fatigue carried out by metallurgists, the intended stress is given to the definite position of test specimen. The SN curve deals with such situation that the definite material position receives the intended repetitive stress history until it will be fatigue damaged.  When we consider the stressed situation of tooth flank material, the condition is considerably different from this. The stress condition at each local material over tooth flank is changing and different.  This is a fundamental difference between metallurgic fatigue investigation and gear tooth flank fatigue investigation.  The direct application of fundamental SN-curve data and its concept carried out by metallurgists to the surface fatigue problem of tooth flank is therefore not easy.  Gear academician has though not distinguished this difference of the stressed state.  All the methods today for the load carrying capability prediction of tooth flank directly adapts the contact stress value to the SN-curve concept according to the basic theory of steel fatigue, and simply believe, that the part of tooth flank at which the contact stress is high is liable to fail.

It is a matter of course, when the volume of the steel that transmit load is larger, the safety margin against failure increases. Gear engineers usually deal with the state of involute gear teeth meshing on the line of action or on the plane of action for convenience, where the sense of movement of contacting point on the actual material along tooth form at the power transmission is though lacking. The thought about durability and material volume that transmits load is neglected, when gear engineer deals with tooth flank durability, but the principle of safer big material volume is valid also to the fatigue phenomenon of tooth flank.  To escape from the contradictory that the damage state of dedendum and of addendum is different in spite of the same induced contact stress condition, a concept is proposed, that the volume of load transmitting tooth flank material decides the damage density that leads the progress of tooth flank damage.  This model for tooth flank durability explains the fact well,  that the dedendum tooth flank, especially near base circle is liable to fail and the mate-contacting addendum is free from damage.

For more information, see the lecture “Influence of stressed volume of tooth flank on the surface durability” at the VDI International Gear Conference held at TU Munich , Garching/Munich, on Sept.18 afternoon, 2019.

State of tooth flanks of driving and driven gear after endurance test


Prof.hc.Dr.-Ing. Aizoh KUBO RIAS, Kyoto  606-8202  Japan