3D TEHL simulation of bevel gears - new approaches in gear engineering

Bevel gear pairs are used to transmit rotational movements and torques between shafts at an angle to each other and are characterized by a high load capacity and smooth operation. Typical applications are axle drives of vehicles or multi-stage industrial gears. Bevel gears are often designed with straight or spiral toothing. If there is an axis misalignment between the shafts at an angle to each other, this is referred to as a hypoid gear pairing.

Engineering challenges

Due to increasing power densities as well as the pursuit of further increasing efficiencies and lifetimes, continuous optimization of bevel gears is necessary. This requires knowledge of the friction effective in tooth flank contact. The friction can be influenced by changing the operating conditions, the lubricant, the materials including coatings or the surface macro and micro geometry. The optimization of bevel gear pairs can be done by tests and/or by thermo-elastohydrodynamic simulations (TEHD simulations). TEHD simulations allow a closer look into the tooth flank contact and thus contribute to a better understanding of the processes taking place there. Furthermore, meaningful TEHD simulations shorten product development cycles and reduce development costs.

Software for higher Efficiency

For the calculation of elastohydrodynamic lubricant film formation in bevel gear pairs, analytical calculation equations with numerous simplifications or two-dimensional models are frequently used. Tribo Technologies GmbH offers with the 3D TEHD software Tribo-X the simulation module "Bevel Gears", which allows the calculation of bevel gear pairs according to the latest state of the art. The simulation module was developed in cooperation with the Chair of Machine Elements and Tribology at the Otto von Guericke University Magdeburg and allows the transient, three-dimensional calculation of stress, friction and temperature distribution in the lubrication gap and in the tooth flanks along the entire length of action of straight, skew and spiral bevel gears as well as hypoid gears. Real tooth flank geometries in tooth height and width direction including gearing corrections, mixed friction, the influence of tooth flank roughness on the gap flow (microhydrodynamics) and the solid contact, tooth flank coatings, pressure and temperature dependent lubricant properties as well as non-Newtonian flow behavior of the lubricant are considered. The consideration of non-Newtonian flow behavior of the lubricant is essential for a reliable friction calculation. The simulation module also allows the calculation of wear of the tooth flanks (profile form deviation). The calculation results can also be used as input data for models to calculate the pitting life or the scuffing load capacity.

Calculation example

Using the example of a spiral-toothed bevel gear pair with octoidal toothing, the potential provided by TEHD simulations becomes evident. A bevel gear pair subjected to identical loads at 40 or 80 °C is compared. By taking into account mixed friction, it is possible to calculate the solid contact load ratio, which gives an indication of the share of the load borne by solid contacts. This reveals serious differences. While the gearing at 40 °C largely runs in the mild mixed friction regime, a hydrodynamic lubricating film build-up at 80 °C almost no longer takes place, which leads to severe solid contacts. Nevertheless, the mild mixed friction due to high fluid friction leads to a larger temperature increase in the contact. In the first half of the line of action, the frictional power at 40 °C is higher than the frictional power at 80 °C. In the second half of the line of action, this is vice-versa. The reason for this is the different levels of friction between fluid friction and boundary friction. Overall, the average power loss for one meshing cycle at 40 °C is 65.4 W, and 63.8 W at 80 °C. The local distribution shows the lubricating gap, pressure and temperature at 40 °C in the standardized meshing position 0.6. The lubricating gap contour follows the classic shape with a constriction at the contact outlet. The pressure distribution is determined by the contact geometry. The temperature distribution indicates that an increase in temperature caused by compression and backflow already occurs in front of the contact.

The calculation model as well as these and other results will be presented and discussed at the International Conference on Gears 2019.


From left to right:
Dipl.-Ing. Ronny Beilicke, Project Engineer, Tribo Technologies GmbH

Dr.-Ing. Lars Bobach, Research assistant, Chair of Machine Elements and Tribology, Otto von Guericke University Magdeburg

Prof. Dr.-Ing. habil. Dirk Bartel, Head of chair, Chair of Machine Elements and Tribology, Otto von Guericke University Magdeburg