Gears heat up during operation. An exemplary temperature measurement conducted by a thermographic camera is shown in Figure 3. Friction between the meshing teeth and hysteretic effects are the main reasons for the temperature increase in plastic gears. The rate of heat generation and the resulting temperature rise depend on several factors, e.g., torque, rotational speed, coefficient of friction, lubrication, thermal conductivity, convection, gear geometry, etc. To ensure the reliable operation of a plastic gear, its operating temperature needs to be lower than the material’s permissible temperature for a continuous load.

The first rating point for plastic gears is the prediction of the operating temperature to ensure no thermal overload (Figure 1c) occurs under the specified operating conditions. The VDI 2736 guideline employs a slightly supplemented Hachmann-Strickle model (Ref. 23), which was presented in the 1960s. The Hachmann-Strickle model was later supplemented by Erhard and Weiss (Ref. 24).

Evidently, the equations are almost the same, as there is difference only in one factor, the kj, where the guideline provides different values for the root region and the flank region. In the proposed equation the most important factor is the coefficient of friction, which is dependent on several parameters, e.g., material combination, temperature, load, lubrication, sliding/rolling ratio, siding speed, etc. The VDI model is analytic and easy to use, while the accuracy of results is limited. Several scientific studies, e.g., Fernandes (Ref. 25), Casanova (Ref. 26), Černe (Ref. 27), were presented recently which dealt with this topic and each one proposed different, advanced, numerically based temperature calculation procedures. Root Stress Control To avoid root fatigue fracture, which is a fatal failure, the root stress σF in a gear needs to be lower than the material’s fatigue strength limit σFlim for the required operating lifespan . To account for unexpected effects some additional safety SF is usually also included.

The guideline further simplifies the equation by assuming that for plastic gears, if the condition b/m≤12 is met, the root load factor can be defined as KF=KA∙KV∙KFβ∙KFα≈1….1.25. While Equation 4 is simple to use and familiar to any gear design engineer, the major drawback is that it does not account for the load-induced contact ratio increase, hence overestimating the actual root stress values. A more accurate root stress calculation can be achieved by employing numerical manners, e.g., by FEM simulation. FEM-based methods are, however, labor and cost-intensive. Assuming the root stress for the gear design under evaluation is calculated, it needs to be compared to a fatigue limit σFlim which is a material property and needs to be characterized by extensive gear testing on a dedicated test bench. For plastic materials, the σFlim is temperature dependent; therefore, several S-N curves generated at different gear temperatures are required .