Generalized model of undercutting of involute spur gears generated by rack-cutters

In this work a generalized approach for defining the phenomenon undercutting of involute teeth is proposed, where besides the traditional boundary case, called undercutting — type I, additionally two more boundary cases, defined as undercutting of type IIa and type IIb are described. According to this approach, the traditional undercutting — type I is caused by the rectilinear profile of the rack-cutter and the non-traditional undercutting — type IIa and type IIb is caused by the rack-cutter fillet. The parametric equations of the so-called boundary fillets of the types IIa and IIb defining the area of existence of the rack-cutter fillet are drawn. Explicitly, an additional boundary condition for avoiding the undercutting of type IIa and type IIb is drawn. The maximum value of the radius of the rack-cutter fillet, at which there is no undercutting, is specified. Two types of quantitative indices for the estimation of the extent of undercutting of the teeth in a radial and tangential direction are defined.