The theoretical basics of forming the face toothings in flat wheels of spiroid gears by means of a single cutting edge tool, using NC machine tools, have been presented in the paper. Based on kinematics - geometrical formulas, there is described a geometrical model of creating the tooth spaces, as well as a geometrical model of determination of the modification depth along the tooth line. Equations of the tooth line have been calculated, as well as mathematical formulas enabling the determination of the modification depth, assuming the correct matching of the worm with the flat worm wheel of the spiroid gear. Based on geometrical models and mathematical formulas algorithms have been elaborated in order to determine the envelope condition and modification depth of the tooth line. Then, on the basis of the algorithms computer programs have been elaborated that are going to be used to design the flat spiroid gears, as well as to calculate their geometrical dimensions. It has also been possible to illustrate the modification depth along the tooth line. The simulation results have been illustrated by the gear example. Finally two methods are presented of machining the face toothings in spiroid gears with a single edge-cutting tool: accurate and approximate ones. Based on the algorithms and programs a comparative simulation of both methods has been elaborated.

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