To evaluate the strength of the tooth root, the FKM guideline is an appropriate tool.  Currently, however, the FKM guideline is valid only for steel and aluminum alloys. To include other  met- als, experiments on specimens including complete worm gears and finite element analyses  were performed. For the method to be accurate, the strength limits must be known. Therefore,  fatigue tests were performed on actual components using a hydraulic fatigue tester (Fig. 1). These  results formed the basis for the comparison of the various methods.


A simulation was required to compute the local stresses and to determine the parameters  mentioned in the previous section. To evaluate the local stresses, the point at which the maximum  occurs must be identified. This point is located on the tension side at the end face of the tooth (Fig.  2). The stresses obtained at this point were used to estimate the strength according to the FKM  guideline. 

Using the parameters from actual worm gear sets, virtual models were created with CAD  software. Next, with FEA soft- ware, meshes were generated and boundary conditions were  defined for the model (Fig. 3). The stresses at the tooth root caused by applied forces were  analyzed with the FEA software.


Calculation process.  

The calculation process was obtained from the FKM guideline. To evaluate the worm wheel  according to the FKM Guideline, both the static strength and the fatigue strength must be  calculated; the procedures are shown in Figure 4.


Both values are based on the determination of a degree of utilization. The utilization is  determined by comparing the stress limit σAK with the working stress. The bearable stress  σAK is evaluated on the basis of the tensile strength, the geometrical parameters and the  material properties. The local stresses were determined from the finite element analysis, and  the material properties were investigated through laboratory tests.

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