A case study was performed to examine the viability of the material characterization procedures using worm gear tests and assess how variable failure modes can be analyzed using a selected gear pair geometry. In the presented case, a worm gear with a gear ratio of i=21 and module m=2 mm. Here, the worm wheel was produced using a specific type of polyamide (PA) compound in pair with a steel worm. The goal of the study was to characterize the fatigue and wear performance of the tested worm wheel material paired with the selected steel in both dry and grease-lubricated conditions.

Thermal Failure Initial tests were executed in dry running conditions with temperature control, at an output load on the wheel of 50 Nm and 100 rpm speed. Even at such moderate load conditions, the generated heat losses (combined with thermally induced wear) were exceedingly high, leading to imminent thermal failure (Figure 11). Based on these results, it was concluded that continuous running tests could only be executed in lubricated conditions and possibly at a lower running speed for thermal failure to be avoided and other failure mechanisms to develop.

Fatigue Characterization Tests in grease-lubricated conditions were subsequently carried out at an output speed of 60 rpm. A suitable grease for the used material pair can decrease the coefficient of friction to such a degree that thermal overload can be avoided and a quasi-steady thermal state at a selected temperature can be achieved. Combined with suitable active temperature control, which on the used rig is achieved by integrating a thermal spot sensor yielding the reference sample temperature, conditioned air inflow and an active PID-based control algorithm, it was possible to retain the worm wheel temperature at room level, i.e., 23 ± 4°C even at higher output torques. For accurate temperature measurements, it is important to account for any influence of the used lubricant on the surface emissivity. For the grease used, the emissivity was found to be very close to the emissivity of the polymer, i.e., approximately ε = 0.95. The results from the fatigue characterization testing presented in the form of an S-N curve as typically used in design and rating models as the one defined in the VDI 2736: Part 3 guideline, are shown in Figure 12 (plotted for 50 percent failure probability in line with Ref. 17). The observed failure mode throughout the range of testing loads was, rather surprisingly, root fatigue, where the location of fatigue crack nucleation was at the root below the active tooth flank (Figure 13). Since the worm wheel was composed of two polymers (i.e., it was a two-component injection-molded part), there could have been an influence of the transition between the two materials at the gear rim on the root fatigue failure. Due to this material configuration, the rim thickness of the first (gearing) material was reduced, which could have hastened the root crack nucleation at the root diameter.

The exhibited failure mode falls outside of the assumptions laid out for the fatigue model described in the VDI guideline for worm wheels, where fracture at the flank as a function of shear stresses is predicted (see the section “Tooth Root Load Carrying Capacity”). The obtained results underline the necessity for a thorough revision and expansion of current state-of-the-art guidelines to account for and model other types of failure modes, which can indeed occur in certain material/lubrication/load configurations. Wear Characterization While wear rate prediction models are not presented in the VDI guideline for worm gears (even though such a model is defined for cylindrical gears), wear can, notwithstanding, be an important damage mode that can itself lead to failure or contribute to other failure modes like tooth fracture. In general, the same two categories of wear characterization methods could be used, i.e., the gravimetric (weight-loss) or geometric (tooth thickness reduction) types of methods. While wear can be described in terms of weight loss, due to a lack of suitable conversion models for evaluating the wear rate based on these measurements, currently, the thickness reduction method is preferred. An additional benefit of using the latter is that it enables measurements in any type of lubrication regime, while the gravimetric method is only valid for dry running conditions. Still, the thickness reduction method poses several challenges, mostly in terms of reducing measurement uncertainty, which can result from: Location of measurement variation in the lead direction Angular deviations of the measurement tool relative to the tooth Variations in the diameter or height of measurement (in general measurements should be done at the reference circle diameter) Other operator-related errors The noted sources of error can influence the measurements noticeably. It is therefore important to ensure repeatable measurement conditions and avoid any other external influences and decrease the measurement uncertainty to the highest degree possible. To achieve consistent results, the measurements should be executed on an appropriate bench with positioning tables, while the measurement tool should be suitably calibrated and with high enough resolution to allow for micron-level accuracy. In our example, a Mitutoyo GMA-25MX micrometer was used for the task. Figure 15 shows results obtained from three tests executed at 60 Nm in grease lubricated running conditions.

Thermal Measurements In lifetime gear tests carried out for root/flank fatigue or wear characterization, temperature is a key parameter that must be accounted for, since the mechanical properties and durability of polymers are highly dependent on it. These types of lifetime tests should, in most cases, be carried out at controlled temperatures to distinguish between the influence of the specified load and temperature on the service life of the gear pair. Temperature control (i.e., the retention of a gear sample at a selected temperature) can only be imposed if a suitable thermal measurement system is integrated into the test rig. To obtain consistent measurements, the sensors must be calibrated, the measured material emissivity correctly accounted for and the measurement position precisely specified. Per VDI (Ref. 17), the measurement location is defined to be at one quarter of the wheel’s face width, on the active (i.e., meshing) flank side where the temperature is the highest (Figure 16a). IR thermal sensors, i.e., spot sensors or thermal cameras, are commonly used to measure the temperature as described. Figure 16b shows measurements obtained using an Optris Xi 80 thermal camera on a PA worm wheel run at 60 Nm in grease lubricated conditions without any active temperature control (i.e., the temperature is allowed to increase organically due to generated frictional/hysteresis heat losses). In this case, the camera was positioned almost perpendicularly to the wheel. An additional thermal sensor was positioned fully in line with the VDI specifications to measure the temperature on the active flank side. The difference in measured temperatures between both sensors is shown in Figure 17. The variation between VDI-specified measurement method and the thermal camera measurement was, in this case, a substantial 11 percent. The results underscore the importance of defining and adhering to measurement setup specifications to obtain compliant and comparable results in the type of tests described.