Wear simulation of worm gears for lifetime prediction

The determination of the load capacity of worm gears in terms of wear with experiments is time-consuming and expensive. An efficient method to analyze wear for various operating conditions is given by simulation models. They describe the tribology in the tooth contact with mathematical equations based on empirical or physical relationships.

Transmission with worm gears allows high gear ratios in a single stage and a smooth operation. Due to a tooth contact with substantial sliding and mixed friction conditions, worm gears are often subjected to abrasive wear. In the design of worm gears a precise prediction of wear is therefore crucial to determine the load capacity or to reduce the wear intensity by optimizing the gear geometry. This phase is often accompanied by time-consuming physical gearbox tests for validation. An efficient alternative for physical gearbox tests is given by methods of numerical simulation.

At the Institute of Machine Elements, Gears & Transmissions at the TU Kaiserslautern a simulation tool for abrasive wear in worm gears was developed. The tribological simulation tool includes a locally resolved calculation of friction and wear in the lubricated tooth contact.

Modelling of friction and wear

After an initial analysis of the geometry of the gears, the meshing area is determined by means of a tooth contact analysis and discretized in contact points of multiple mesh positions. For each contact point the lubricant film height is calculated by using approximate equations for the elasto-hydrodynamic contact. Here, tooth friction is divided into fluid friction and boundary friction. Whereas fluid friction is a result of shearing of the fluid, boundary friction occurs from the direct contact of surface asperities. Whether fluid or boundary friction predominates at one point depends on the film height and the micro geometry of the contacting surfaces.

As wear correlates with boundary friction and the sliding distance in contact, wear is calculated based on frictional energy by using the energetic model of Fleischer [1]. According to this energetic concept, frictional energy is not completely dissipated as heat energy, but irreversible stored in the material as grid defects caused by mechanical deformations. Energy is accumulated until a critical level is reached, which results in fracture of material and wear.

The simulation model is supplemented with experimental data at various stages of the calculation to receive valid results. For example, measured surface data of worm and worm wheel tooth flank is used to determine the relationship between the lubricant gap height and the proportion of load applied on the metallic surface. Furthermore, the model parameter of the energetic wear model is determined for the tooth contact in worm gears from measured wear data of experimental wear tests.

Procedure of wear simulation and applications

The simulation is designed as an iterative procedure. Wear and friction are first determined for the manufactured state of the gears. To consider the effect of wear in the simulation, the macro geometry of the worm wheel tooth is modified locally after each calculation step according to the calculated wear. Thus, the simulation tool allows a transient analysis of friction and wear.

Figure 1: Accumulated wear height on the worm wheel tooth flank from an exemplary wear simulation of the running-in phase

In general, wear in worm gears can be divided in two different phases. Within an initial phase (running-in), the surface as well as the size of the contact pattern adapt to the operating conditions. Both phases could be analyzed with the simulation tool. Figure 1 shows exemplary results for the accumulated wear of a simulation during the running-in phase.

The following steady wear phase is characterized with constant wear and takes up most of the lifetime of the gears. Depending on the wear intensity of the worm gear under the designated operating conditions, wear can be a limiting factor for the lifetime of the gears. The maximum wear can be defined by various criterions as degradation of the lubricant by wear particles or the minimum thickness of the tooth to avoid tooth breakage. In this context, the simulation tool allows to determine the wear rate for steady operation of a specific worm gear box. By comparing the wear rate with the tolerated wear, the lifetime of the worm gear box could be estimated.

More details on the energetic wear simulation of worm gears will be presented at the International Conference on Gears 2021.


Dipl.-Ing. Kevin Daubach has been working since 2017 as a research assistant at the Institute of Machine Elements, Gears & Transmissions at the TU Kaiserslautern in the field of wear in worm gears.

Jun. Prof. Dr.-Ing. Manuel Oehler did his doctorate on the optimization of the efficiency of worm gears. Since 2019, he has been Junior Professor for Mechanical Drive Technology at the Institute of Machine Elements, Gears & Transmissions at the TU Kaiserslautern.

Prof. Dr.-Ing. Bernd Sauer is Head of the Institute of Machine Elements, Gears & Transmissions at the TU Kaiserslautern.

[1]        Fleischer, G.; Gröger, H.; Thum, H.: Verschleiß und Zuverlässigkeit. VEB Verlag Technik, Berlin (1980).