Abstract: In the gear roll-forming process, extremely high stresses on the teeth of the rolling tools will appear when the rolling teeth are full filled with material. This will reduce the lifetime of the rolling tools. To understand the forming process and design the rolling tools as well as improve the lifetime of the rolling tools, it's necessary to model the tooth height estimation in the roll-forming of gear with axial infeed. The tooth profile equations are firstly derived based on the meshing theory. Considering its forming characteristics, the formula of envelope area evolution is obtained by the coordinate transformation method. The height estimation model of the formed teeth is then established with the assumption of volume conservation in the roll-forming process, and the equation for calculating the tooth depth on the correction section of rolling tools is also obtained. The roll-forming of spur gear with 46-teeth, module of 1.75 mm and pressure angle of 20° is taken as an example, and the proposed model and equation are verified by the finite element method and experiments. The compared results show that the maximum error between theoretical and experimental value is about 4.97%, and the rolling tools designed by the proposed tooth depth equation can ensure integrity of formed teeth, and avoid the forming of tip barreling and the folding defect which affect the performance of the formed teeth. Moreover, the root stress of rolling tools is reduced by 32.89%. This study will provide the theoretical foundation for calculating the tooth depth of rolling tools accurately.

Key words: gear roll-forming, meshing theory, tooth depth of rolling tools, tooth height estimation model, verification analysis