The present paper describes modern methodology of the bevel gear design with a particular focus on issues concerning the theoretical basis and the preparation of the numerical simulation of the machining. The assumptions used in developing the mathematical model of cutting teeth are given and an example of the teeth flank surfaces of a gear and a pinion resulting from the virtual processing is shown. The correctness of the mathematical model of cutting teeth was verified by comparing the resulting based on the model grid points, the side of the tooth surface, resulting from the simulation cutting teeth in CAD. A high convergence of the two surface geometry was demonstrated, which allows for the use of the analysis for each of the models independently.
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