RU2040376C1 - Hobbing cutter - Google Patents

Abstract

FIELD: mechanical engineering. SUBSTANCE: hobbing cutter has a housing whereon cutting teeth 2 are mounted over the screw line. The teeth are shaped using the auxiliary performing rack and have straight side cutting edges and flat front surface turned relatively the cutter axis. Cutting teeth 2 of the hobbing cutter are made using of auxiliary performing rack with concave profile of teeth. The angle by which the cutting edges are turned in the plane of side of the rack tooth profile and angle by which the front plane is turned are defined by relationships presented in the invention description. EFFECT: improved design. 8 dwg

Description

 The invention relates to mechanical engineering and can be used for cutting gears with an involute profile of modified teeth.

 The purpose of the invention is to simplify the possibility of cutting cylindrical gears with a profile modification of the teeth of the involute profile.

 In FIG. 1 schematically shows a worm cutter; in FIG. 2 position of the front surface of the worm cutter relative to the main cylinder; in FIG. 3 curvature indicatrix of the initial tool surface of the worm cutter; in FIG. 4-8 diagrams of the location of the vectors needed to derive the calculated dependencies.

, (1) а угол поворота передней плоскости Ψ установлен равным
Ψ arcsin

, (2) где φ угол разворота режущих кромок;
R_и радиус вогнутого зуба производящей рейки;
R_2и второй главный радиус кривизны вспомогательной производящей рейки;
Ψ угол разворота передней плоскости
А₁ sin ζ cos α_и;
А₂ cos α_и cos ζ ctg α_п sin α_и;
А₃ sin ζ cos α_и + sin ζ ctg α_п' sin α_и;
ζ угол наклона к оси фрезы плоского прямобочного немодифицированного сечения вспомогательной производящей рейки червячной фрезы;
α_п угол профиля плоского прямобочного немодифицированного сечения вспомогательной производящей рейки червячной фрезы;
α_п' угол профиля зуба червячной фрезы в передней плоскости.The worm mill contains a housing 1. On the housing along a helical line are cutting teeth 2 with straight lateral cutting edges 3. The cutting teeth are made with a flat front surface 4. The front surface of the teeth is deployed relative to the axis of the cutter. The cutting edges 3 are deployed in the flat lateral side of the profile of the auxiliary producing rail of the cutter at an angle φ equal to
φ arcsin

, (1) and the angle of rotation of the front plane Ψ is set equal to
Ψ arcsin

, (2) where φ is the angle of rotation of the cutting edges;
R _{and the} radius of the concave tooth of the producing rail;
R _{2 and the} second main radius of curvature of the auxiliary producing rail;
Ψ angle of rotation of the front plane
A ₁ sin ζ cos α _and ;
A ₂ cos α _and cos ζ ctg α _n sin α _and ;
A ₃ sin ζ cos α _and + sin ζ ctg α _p 'sin α _and ;
ζ the angle of inclination to the cutter axis of a flat straight-side unmodified cross-section of the auxiliary producing rail of the worm cutter;
α _{p the} angle of the profile of a flat straight side unmodified section of the auxiliary producing rails of the worm cutter;
α _p 'the angle of the tooth profile of the worm cutter in the front plane.

,

и

, направленными из начала пространственной системы координат под углами:
α_и угол профиля вспомогательной производящей рейки на исходной поверхности червячной фрезы (по ГОСТ 9324-80 этот угол установлен равным α_и 20^о);
ζ угол наклона передней плоскости к оси червячной фрезы;
α_п угол профиля зуба червячной фрезы в передней плоскости.To calculate the angle Ψ, it is convenient to use transformations with vectors

,

and

directed from the beginning of the spatial coordinate system at angles:
α _and the profile angle of the auxiliary producing rail on the initial surface of the worm cutter (according to GOST 9324-80, this angle is set equal to α _and 20 ^about );
ζ the angle of inclination of the front plane to the axis of the worm cutter;
α _{p the} angle of the tooth profile of the worm cutter in the front plane.

выбран равным по модулю 1 и направлен под углом α_и к оси Y. Вектор

выбран таким, чтобы его проекция на плоскость XZ равнялась 1, и направлен под углом ζ к оси Z. Вектор

выбран таким, чтобы его проекция на плоскость XZ равнялась 1, и направлен под углом Ψ к оси Z.Vector

chosen equal modulo 1 and directed at an angle α _and to the Y axis. Vector

chosen so that its projection onto the XZ plane is equal to 1, and is directed at an angle ζ to the Z axis. Vector

chosen so that its projection onto the XZ plane is 1, and is directed at an angle углом to the Z axis.

^=-

^cosαи⁺

^sinαи; (3)
пр.

=1,

-

sin ζ

ctgα_п+

cos ζ; (4)
пр.

=1,

-

sin Ψ

ctg

+

cos Ψ. (5)
Из этого на основании свойства смешанного (векторно-скалярного) произведения трех векторов имеем

(6)
Раскрыв определитель (6), после преобразований приходим к квадратному уравнению
A₁sin² Ψ + A₂sin Ψ A₃ 0, (7) где А₁ sin ζ cos α_и; (8)
A₂ cos α_и cos ζ ctg α_п sin α_и; (9)
A₃ sin ζ cos α_и + sin ζ ctg α_п' sin α_и. (10)
Действительный корень уравнения (7) равен
sin Ψ

(11) откуда
Ψarcsin

(12)
Червячная фреза работает следующим образом.Based on this, we can write

^{= -}

^cosα and ⁺

^sinα and; (3)
etc.

= 1,

-

sin ζ

ctgα _n +

cos ζ; (4)
etc.

= 1,

-

sin Ψ

ctg

+

cos Ψ. (5)
From this, based on the property of a mixed (vector-scalar) product of three vectors, we have

(6)
Having opened the determinant (6), after the transformations we arrive at the quadratic equation
A ₁ sin ² Ψ + A ₂ sin Ψ A ₃ 0, (7) where A ₁ sin ζ cos α _and ; (8)
A ₂ cos α _and cos ζ ctg α _n sin α _and ; (nine)
A ₃ sin ζ cos α _and + sin ζ ctg α _n 'sin α _and . (10)
The real root of equation (7) is
sin Ψ

(11) where
Ψarcsin

(12)
A worm mill works as follows.

 The workpiece gear impart rotation around its axis. A worm cutter rotating around its axis is informed of a lateral feed before cutting into the workpiece. To implement the process of cutting the teeth of the worm mill give a longitudinal feed along the axis of rotation of the workpiece.

 The worm cutter can be used in the manufacture of cylindrical gears with profile modification of the teeth (with flanked teeth). This simplifies the technology of cutting modified teeth.

Claims (1)

Worm milling cutter for cutting cylindrical gears with an involute tooth profile, on the housing of which, cutting teeth are profiled on the basis of an auxiliary producing rail with straight lateral cutting edges and with a flat front surface deployed relative to the axis of the cutter, characterized in that the worm cutting teeth milling cutters are made on the basis of an auxiliary producing rail with a concave tooth profile, in the plane of the side of which the cutting edges are rotated at an angle of redelyaemy formula

while the angle of rotation of the front surface is selected by the formula

where φ is the angle of rotation of the cutting edges;
R _{u the} radius of the concave tooth of the producing rail;
R _{2 . u the} second main radius of curvature of the auxiliary producing rail;
j is the angle of the front plane;
A ₁ = sinζ cosα _and ;
A ₂ = cosα _and cosζ-ctgα _n sinα _n ;

ζ the angle of inclination to the cutter axis of a flat straight-side unmodified cross-section of the auxiliary producing rail of the worm cutter;
a _{p is the} angle of the profile of a flat straight-side unmodified section of the auxiliary producing rail of the worm cutter;

the angle of the tooth profile of the worm cutter in the front plane.

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