New Methods for the Calculation of the Load Capacity of Bevel and Hypoid Gears


Pitting and tooth root breakage are still the two most frequent failure types occurring in practical applications of bevel gears. There are several national and international standards for the calculation of the load carrying capacity of these gears such as DIN 3991, AGMA 2003 and ISO 10300. But up to now these standards do not cover bevel gears with offset (hypoid gears). For that reason a research project was carried out at FZG (Gear Research Centre, Munich, Germany) to analyze the influence of the hypoid offset on the load capacity of bevel gears by systematic theoretical and experimental investigations.
The results of the tooth root tests showed, as expected, an increasing load capacity with higher offsets. In contrast, the pitting tests showed an increasing, but after reaching a maximum, a decreasing load capacity with higher offsets. This can be explained by two interfering phenomena: On the one side higher offsets lead to decreasing pinion loads and thus decreasing contact stresses; on the other side the permissible stresses are decreasing due to the higher sliding velocities.
Regarding these test results a new standard capable calculation method was developed on the basis of ISO 10300. First the bevel gear geometry is transformed into a virtual cylindrical gear. Systematic theoretical investigations and comparisons with tooth contact analysis methods have shown that the new virtual cylindrical gears have representative mesh conditions compared to the bevel gears. This includes the size and shape of the contact area as well as the load distribution between the mating teeth. Particularly with regard to hypoids it is necessary to consider the unbalanced mesh conditions between drive and coast side flank, what can be described by the limit pressure angle. Several influence factors were adjusted considering geometry, material properties and operating conditions of the gear set. For the tooth root safety factor the influence factors were adapted to the specific conditions of hypoid gears. For the calculation of the pitting safety factor two new influence factors were introduced to consider the hypoid specific sliding conditions on the gear flanks. The recalculation of the pitting and tooth root tests showed a very good correlation of calculated with real load capacity of the test gears.
Meanwhile the newly developed calculation method is widely-used in the gear manufacturing industry. For that reason it is currently introduced into the revision of ISO 10300 as method B1 beside method B2 based on the AGMA calculation method for bevel and hypoid gears.
ISBN: 1-978-61481-009-4 Pages: 20
Authors: B. R. Höhn, K. Stahl, and C. Wirth

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