7。Conclusion

The investigations carried out in relation to the undercutting of teeth of involute gears by a rack-cutter, result in the following conclusions:

1。The undercutting of teeth is done by the rectilinear profile of the rack-cutter (traditional case — type I), as well as by the rack-cutter fillet, on which the teeth crests of the tool's cutting teeth are cut (the non-traditional case — type II)。

2。The undercutting of teeth, caused by the rack-cutter fillet is found in two variants, defined in the present work as “undercutting

— type IIa” and “undercutting — type IIb”。

3。In the presence of the undercutting — type IIа the tooth thickness in their bottom is decreased without cutting their involute profile, and in the presence of undercutting — type IIb a part of the involute profile is additionally cut。

4。If the teeth of a gear, cut by a rack-cutter, are undercut of type IIb, they are also undercut of type IIa。

5。The condition for non-undercutting — type II is defined uniquely by two independent parameters: the number z of the teeth cut and the profile angle α of the rack-cutter。

6。In order to avoid the undercutting of the involute teeth (type I, IIa and IIb), it is necessary to satisfy the traditional boundary condition (2) as well as the boundary condition  (19)。

7。The proposed indices of undercutting δr, δt, λr and λt allow the extent of teeth undercutting in radial and tangential direction to be expressed by the respective quantitative value。

References

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