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Power Transmissions pp 487–506Cite as

The Numerical Calculus of Hobs Used to Cut W–N Gears

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Part of the book series: Mechanisms and Machine Science ((Mechan. Machine Science,volume 13))

Abstract

After a short introduction showing the evolution of Wildhaber–Novikov (W–N) gears, the evolution of the study of hob geometry is presented, with special focus on the author’s contribution in the field. Then a general method of study of the hob geometry is exposed. The calculus model takes into account the hob with non-zero rake angle, a wide range of re-sharpenings, a generation by relief grinding, which can easily be customized for the type of abrasive tool chosen, to obtain the profile of the abrasive tool and the hob profile for various re-sharpenings. The hob profile deviation is then evaluated in an axial plane. To reduce the cumulated profile error on re-sharpening, the setting parameters on relieving are modified. The algorithm is developed on matrix basis. In the next part of the paper the customizing of the general method is presented, for the case of hobs designed to cut gears with arc-of-circle profile (reference profile with two arcs of circle). This part includes numerical results presented in tables and diagrams, for hobs in the modulus range 4–20, three values of the rake angle (0˚, 3˚, 6˚), three values of the relief for each modulus and three values of the position angle of the generation rack (around the value of the angle of the basic helix) and five values of the re-sharpening angle (0˚, ± 3˚, ± 6˚). The calculi carried out have been the basis for the manufacturing and inspection of four sizes of hobs—for the moduli 4, 10, 14 and 20. Several details of the manufacturing of hobs for W–N gears are presented in the end of the paper.

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Abbreviations

mn :

Normal modulus

γ:

Hob rake angle

r:

Profile radius

KΔ; HΔ :

Relieving depth; arhimedic parameter

C; Г:

Curve; characteristic curve

П; Σ:

Plan, surface

S; index:

Reference system; tool

δ; Δ:

Deviation; cumulated error

Q:

Diametrical hob coefficient

U:

The parameter of the basic profile

p:

Linear parameter by which the profile describes the basic rack

μ:

The parameter of the generation of the surface of the abrasive tool relieving the hob

ν:

The parameter of the relative motion rack—worm

w:

The angular parameter of the hob rake surface

ʓ:

The position angle of the hob rake surface

ψ:

The setting parameters of the abrasive tool used for relieving

τ:

The angular parameter of the abrasive tool used for relieving

t:

The parameter of the hob rake surface

θ:

The position angle of the basic rack

Tab :

Square matrix representing the transfer from the reference system b to the reference system a

Xc :

Column matrix representing the vector radius of the current point from the system C, with the components xc, yc, zc

DXc(u) :

The derivative of the matrix Xc with respect to the parameter u

Nc :

Column matrix representing the normal vector attached to the current point C, with the components nxc, nyc, nzc

,:

The symbol for the dot product of two vectors. Ex.: A,B is the dot product of the vectors A and B (column matrix)

.:

The symbol of the vectorial product of two vectors. Ex.: A.B is the vectorial product of the vectors A and B (column matrix)

,.:

The symbol for the mixed product of three vectors. Ex.: A, (B.C) is the mixed product of the vectors A, B, C (column matrix)

  :

Matriceal product: no sign is applied. Ex.: AB is the product of the matrices A and B, which can be only done when A has as many columns as B has lines

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Authors and Affiliations

  1. S.C. Confind Campina, Campina, Romania

    Gheorghe Miloiu

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  1. Gheorghe Miloiu
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Correspondence to Gheorghe Miloiu .

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Editors and Affiliations

  1. , Machine Elements and Tribology, University Politehnica of Bucharest, Splaiul Independentei 313, Bucharest, 060042, Romania

    George Dobre

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Miloiu, G. (2013). The Numerical Calculus of Hobs Used to Cut W–N Gears. In: Dobre, G. (eds) Power Transmissions. Mechanisms and Machine Science, vol 13. Springer, Dordrecht. https://doi.org/10.1007/978-94-007-6558-0_39

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  • DOI: https://doi.org/10.1007/978-94-007-6558-0_39

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