RU2041034C1 - Method of cutting bevel gear wheels - Google Patents

Abstract

FIELD: mechanical engineering. SUBSTANCE: point of the innovation lies in making more precise "the numerical correction" ensuring the slope of the cutting edge of cutting tools. The edge shapes the right and left sides of the circular teeth of wheels forming a key pair. EFFECT: enhanced efficiency. 4 dwg

Description

 The invention relates to mechanical engineering and can be used in the treatment of bevel wheels with circular teeth.

An analogue is the method for processing bevel wheels of a gear cutting head with number cutters, the sharpening angles of which are determined by the formula
α _u = α ± Δα, (1) where α is the nominal angle of the profile of the cutter,
(-) refers to the outer edge of the cutting edge, (+) to the inner edge of the cutting edge. The closest analogue is presented in the book: Kedrinsky V.I. Writer K.N. Machines for processing conical wheels M. Mechanical Engineering, 1967, p. 421. Formula (8.13).

 The disadvantage of the closest analogue is the inaccurate geometry of the incisors, which does not ensure cutting of the qualitative shape of circular teeth.

 The aim of the invention is to increase the accuracy of machining of circular teeth of wheels on conventional gear cutting machines by changing the geometry of the cutting part of the cutters of the gear cutting head.

 The presented goal is achieved by calculating the sharpening angles of the cutting edges of the cutters for processing the concave and convex sides of a circular tooth.

 The essence of the invention consists in the correct determination of the angle of inclination of the cutting edge of the cutters of the forming side of the circular teeth, providing a nominal tooth profile.

Existing corners of the cutting edges of the cutting gear head are determined from geometrical calculations for the normal section of the profile of the tooth of the wheel when the circle line drawn by the nominal radius of the cutting head passes through the middle of the tooth cavity and is in the plane tangent to the generatrix of the wheel cavity cone. The deviation of the angle of the tooth profile is determined by the formula (1)
Δα = ± tgθ _f sinβ _n , where θ _{f is the} angle of the tooth leg,
β _{n the} angle of inclination of the circular tooth in the middle section of the tooth,
(+) (-) signs related to the convex and concave sides of a circular tooth.

 The calculated cutter angles according to the formula (1) do not provide the nominal tooth profile of the cut wheel, since the position of the variability of the deviation of the tooth profile of the cutter during the processing of the hypoid gear teeth is not taken into account.

где А радиус движения зуборезной головки (1)
A=

θ_f угол ножки зуба
R_m среднее конусное расстояние
r номинальный радиус зуборезной головки
φ₁ угол при вершине конуса колеса, образованный радиусом А движения оси зуборезной головки, номинальным радиусом зуборезной головки и средним конусным расстоянием колеса,
β_n угол наклона кругового зуба.The actual deviation of the profile of a circular tooth in the process of cutting a bevel wheel is variable and in general terms this position is presented in an article by R. N. Usubamatov "Correction of the pressure angle when cutting circular teeth of bevel wheels on a CNC machine". University News. Engineering, 1986, N 11, c. 115-119. The article presents the dependences of the alternating movement of a flat-top and cut wheel, which allows you to adjust the profile of a circular tooth according to the average section of the tooth. The actual deviation of the tooth profile is determined by the formula Δα = ± arctan [tgθ _f sin (φ-φ ₁ + β _n )] (2) where φ is the rolling angle of the tooth tooth
φ ₁ arccos

where A is the radius of movement of the gear cutting head (1)
A =

θ _f tooth leg angle
R _m mean cone distance
r nominal radius of gear cutting head
φ ₁ angle at the top of the wheel cone, formed by the radius A of the axis of motion of the gear cutting head, the nominal radius of the gear cutting head and the average conical distance of the wheel,
β _{n the} angle of inclination of the circular tooth.

The deviation of the tooth profile Δα at the initial and final moments of processing along the concave and convex sides of the teeth is calculated by the formula (2) for known angles of the beginning and end of cutting the sides of the teeth φ _n and φ _k, respectively.

For the concave and convex sides of the tooth, the beginning of φ _n and the end of φ _to cutting the tooth in the middle section are determined by the well-known formulas (RN Usubamatov. Processing of bevel wheels with circular teeth on CNC machines. Izvestiya VUZov. Mechanical Engineering, 1983, No. 8, p. 95-98).

The angles φ _n and φ _{k are} calculated by the formulas for the concave side φ = φ ₁ + + arccos (cos δ _a / cos δ _f ) φ _к = φ ₁ (3)
for the convex side φ _n = φ ₁
φ _k = φ ₁ -arccos (cos δ _a / cos δ _f ) (4)
δ _a , δ _{f the} angle of the cone of the protrusions and depressions of the teeth
Substituting the obtained calculated expressions of the angles φ _n and φ _k according to dependence (3, 4) in equation (2), we determine the deviation of the tooth profile angle Δα _n at the initial moment and Δα _k at the final moment of cutting of the circular tooth. Formula (2) shows that the actual deviation of the angle of the tooth profile Δα significantly differs from those recommended for profiling the sides of the incisors according to the formula (1). This discrepancy must be taken into account for processing more precise circular teeth of hypoid gears.

 In FIG. 1, 2 presents design schemes for determining the deviation of the tooth profile angle of the hypoid wheel and gear, respectively; in FIG. 3, 4 graphs of the deviation of the profile angle of the teeth of the wheel and gear during processing.

To determine the analytical dependences of the deviation of the sides of the tooth profiles of the hypoid gear, we use the prototype formula (2) to change the profile of the circular tooth of the bevel gear during cutting, which shows that the deviation of the tooth profile depends on the constant components θ _f , β _n and on the variable parameter φ _D , which is the angle lying in the plane of the tops of the teeth of the producing wheel, formed normally to the line of the circular tooth in the middle section in an arbitrary position of the axis of the cutting head and perpendicular to forming a cone of depressions.

For hypoid gears, the angles of the tooth leg of the wheel and gear are constant. The variables will be the angles φ _D and the angles of inclination of the tooth spiral, depending on the angle φ _D. To determine the deviation of the profiles of the circular teeth of the wheel and gear of the hypoid gear, we use the analytical methods of kinematic analysis. We represent the elements of the producing wheel and hypoid transmission in the form of a vector contour, the geometric sum of which is equal to the phase vector of the structural group.

+

+

=

+

+

+

=

где Е_к, Е_ш гипоидные смещения колеса и шестерни соответственно; А радиус движения оси зуборезной головки; r номинальный радиус зуборезной головки.In FIG. Figures 1 and 2 show the design schemes for changing the angle φ _{D of the} wheel and gear of the hypoid gear, the vector equations of which are respectively written in the following form:

+

+

=

+

+

+

=

where E _to , E _W hypoid displacement of the wheel and gear, respectively; A radius of movement of the axis of the gear cutting head; r is the nominal radius of the gear cutting head.

R _cr = R cos θ _{MK FK,} R _VS = R cos θ _{msh fsh}
R _mk ; R _{mш the} average conical distance of the wheel and gear, respectively; θ _fк , θ _{fш the} angles of the legs of the teeth of the wheel and gear, respectively.

sin φ_D-cos φ_D= (R $\genfrac{}{}{0ex}{}{\text{2}}{\text{в}}$ а²- b² r²)/2r
Представляя угол базового вектора в виде

tgΨ, производя тригонометрические преобразования, имеем
cos( φ_D+ Ψ)=(R² _вк-а²-b²-r²)cosΨ /2ra
После подстановок выражений а и b, и преобразований выражения угла φ_D представится так

cos arctg

(6)
Производя аналогичные выкладки по определению выражения угла φ_Dдля шестерни, имеем
-Е_ш+ Аsin φ -rcos φ_D=R_вшsin ε
D+Acos φ + rsin φ_D=R_вшcos ε (7)
Вводя обозначения уравнения (3) принимают вид:
c-r ˙cos φ_DR_вш ˙ cos ε
d+r ˙sin φ_DR_вш ˙sin ε
После представления угла базового вектора в виде

=tg τ алгебраических, тригонометрических преобразований и подстановок выражения угла φ_D будет иметь вид

c

×
(8)
D=R_mш cos θ_fш-L_ccos( μ-μ_o); где L_c

L_c расстояние от оси производящего инструментальные колеса до середины венца нарезаемого зубчатого колеса в плоскости касательной образующего конуса впадин.Projecting both sides of these vector equalities on the x and y axis, we arrive at the derivation of the equations for the wheel:
Е _к + Аsin φ-rcos φ _D = R _VK sin ε, (5) where φ is the angle of rotation of the generating wheel. We introduce the notation where Asin φ + Е _к = а, (Аcos φ = B), then equations (5)
take the form: ar cos φ _D = R _vcc sin ε
br sin φ _D = R _vk cos ε
Squaring both sides of each of these equalities into a square, adding term by term, and transforming, we obtain:

sin φ _D -cos φ _D = (R $\genfrac{}{}{0ex}{}{\text{2}}{\text{in}}$ a ² - b ² r ² ) / 2r
Representing the angle of the base vector as

tgΨ, making trigonometric transformations, we have
cos (φ _D + Ψ) = (R ² _vk-a ² -b ² -r ² ) cosΨ / 2ra
After substituting the expressions a and b, and transforming the expressions of the angle φ _D ,

cos arctg

(6)
Performing similar calculations by definition of the expression of the angle φ _D for the gear, we have
-E _W + Asin φ -rcos φ _D = R _W sin sin ε
D + Acos φ + rsin φ _D = R _int cos ε (7)
Introducing the notation of equation (3) take the form:
cr ˙cos φ _D R _sup ˙ cos ε
d + r ˙sin φ _D R _VSH ˙sin ε
After representing the angle of the base vector as

= tg τ of algebraic, trigonometric transformations and permutations of the expression for the angle φ _D will have the form

c

×
(8)
D = R _mш cos θ _fш -L _c cos (μ-μ _o ); where L _c

L _{c the} distance from the axis of the producing tool wheels to the middle of the rim of the cut gear in the plane of the tangent of the forming cone of the troughs.

μ- difference between gear and wheel angles
μ _o - angle of hypoid displacement.

Turning to the formulas for the deviation of the angle of inclination of the cutting edges of the gear heads in the process of cutting the teeth of the wheel and gear of the hypoid gear, by analogy with formula (2) we obtain
Δα _i = arctan [tgθ _fi sin φ _Di ] (9) where i = k, w are the indices of the wheel and gear; θ _{fi the} angle of the tooth leg; the expression of the angles φ _Di is represented by formulas (6), (8) for the wheel and gear, respectively.

In FIG. Figures 3 and 4 show graphs of the deviation of the profile angle of the circular tooth of the wheel and gear during processing at the running angles. The graphs are plotted with the initial data according to formulas (6) and (8)
for r 114.3 β _nk = 29.58 ^о
A = 110.6 θ _f = 4.916 E _k = 0 μ _o 0
R _k = 92.98 δ _f = 70.55 ^o δ _a = 76.31 ^o
φ _n = 114.45 φ _to 24.98 ^about μ = 18.71 ^about
for gear β _nш = 48.016 ^о
δ _f = 13.001 ^o δ _a = 18.466 θ _f = 0.8 ^o
φ _n = 110.65 ^o φ _k = 68.55 E _w = 29.4 R _w = 119.46
To obtain a more accurate tooth profile, it is necessary to compensate for the deviation of the tooth profile by sharpening the blades with undefined angles.

To obtain the nominal angle of the tooth profile of the wheel or gear on the required cone, the compensated deviation of the tooth profile Δα is calculated by the formulas (9), (6), (8). In formulas (6), (8), the parameter of the angular position φ _{D of the} axis of the cutting head is determined by the coordinate of the angle when the cutter blades begin to profile the tooth in the middle of the crown on the initial or required cone. The analytical dependence of the angle φ in this case is determined by the formulas of the boundary parameters of the cutting teeth of the hypoid gear presented in (2), where the parameters R _i , R _e are replaced by R _m , δ _a by δ θ _a by 0 where R _i , R _m , R _e , inner, middle and outer cone distance.

δ _{a the} angle of the cone of the protrusions of the teeth;
δ angle of the pitch cone;
θ _{a the} angle of the tooth head.

r

×
φ=arccos

± arctg

B=

F=cos δ_i /cos δ_f
D= R_mшcos θ_fш-L_c cos( μ-μ_o) для шестерни D= 0 для колеса, W развод резцов, δ_i угол делительного конуса, α номинальный угол профиля резцов, iк, ш, индексы колеса и шестерни соответственно, знаки (±) после α, перед W/2 относятся так: верхний знак для внутренней, нижний для внешней стороны резцов знаки перед вторым слагаемым в формуле (+) для вогнутой (-) для выпуклой стороны зуба остальные знаки (±) верхний для колеса, нижний для шестерни. Остальные параметры в соответствии с формулами (9), (6), (8).Summarizing the results, the formula for calculating the inclination angles of the cutting blades of the cutters of the gear cutting head for processing the wheels and gears of the hypoid gear will be presented in the form
α _u = α ± arctan (tgθ _fi sinφ _Di ) where

r

×
φ = arccos

± arctg

B =

F = cos δ _i / cos δ _f
D = R _mш cos θ _fш -L _c cos (μ-μ _o ) for gear D = 0 for a wheel, W cutter pitch, δ _i angle of pitch cone, α nominal profile angle of cutters, iк, ш, wheel and gear indices, respectively , the signs (±) after α, before W / 2 are as follows: the upper sign for the inside, the bottom for the outside of the incisors, the signs in front of the second term in the formula (+) for the concave (-) for the convex side of the tooth, the remaining signs (±) are the upper for wheels, lower for gears. The remaining parameters are in accordance with formulas (9), (6), (8).

 The presented dependences of the correction of the formula of the circular tooth of the wheel and gear of the hypoid gear by changing the geometry of the tilt angles of the cutting blades of the gear cutting head (9) when used for gear cutting processes can improve the accuracy of processing of hypoid gears.

cos arctg

-
φ=arccos

± arctg

B=

F=cos δ_i/cosδ_fi
i к, ш индексы колеса и шестерни
D_к=0
D_ш R_mш cos θ_fш-L_c cos ( μ-μ_o)
L_c=R_к cos θ_fк сos β_нк/сos(β_nк+μ_o)
μ=β_nш-β_nк
N_к=Е_кsin φ
N_к= D_шcos φ-E_шsin φ
R_вi=R_mi cos θ_fi
Знаки (±) перед R_mi, W, arctg, относятся верхний знак для вогнутой, нижний для выпуклой стороны круговых зубьев, остальные знаки (±) верхний для колеса, нижний для шестерни.PRI me R implementation. Calculation of the angles of the profiles of the cutters of the gear cutting head for cutting the teeth of the hypoid gear of the wheel and gear having the following parameters A = 110.6 β _nk = 29.58 ^о R _mk = 92.98 E _k = 0 r = 114.3 μ = 0 θ _fk = 4.916 ^о δ _к = 75.5 ^о δ _fк = 70.55 ^о α = 20 ^о
A gear for δ = 110.6 _fsh = ^about 13 _msh R E = 119.46 _m = 29,4 μ _o = 0 α = ²⁰ ° r = 114,3 β = 48.016 _{nsh fsh} ^of θ = ^about 0.8 δ _w = 13.8 ^o
The calculation of the angles of the profiles of the cutters of the gear head is made according to the formula
α _n = α ± Δα _i where (+) for internal,
(-) for the outside of the cutter,
Δα _i = arctan (tgθ _fi ˙sinφ _Di )

cos arctg

-
φ = arccos

± arctg

B =

F = cos δ _i / cosδ _fi
i k, w wheel and gear indices
D _to = 0
D _W R _mш cos θ _fш -L _c cos (μ-μ _o )
L _c = R _to cos θ _fк cos os β _nk / cos (β _nk + μ _o )
μ = β _nш -β _nк
N _k = E _k sin φ
N _k = D _w cos φ-E _w sin φ
R _bi = R _mi cos θ _fi
The signs (±) in front of R _mi , W, arctg, include the upper sign for the concave, lower for the convex side of the circular teeth, the rest of the signs (±) upper for the wheel, lower for the gear.

Based on the calculations performed for the given transmission parameters, the angles of the profiles of the cutters of the gear cutting heads for processing the wheels and gears of the hypoid gear will be:
for wheel
α _inner 20+ 0.619 = 20.619 ^about
α = _{the outer} 20-4,33 = ^about 15.67
for gear
α _inner 20+ 0,1002 = 20,1002 ^о
α = _externally ^about 20-0,645 = 19.355

Claims (1)

METHOD FOR CUTTING BEVELS OF GEAR WHEELS under conditions of rolling gear cutting head, the sharpening angles of the cutting elements of which are determined taking into account the "number correction", characterized in that in the manufacture of gears forming a hypoid gear, the "number correction" is determined by the formula
± Δα _i = arctan (tgQ _fi sin sin _Di ),
where Q _{f i the} angle of the tooth leg;
i wheel and gear indices;
signs (±) relate as follows: (+) for the inside, (-) for the outside of the cutter;
φ _{Di is the} angle formed by the normal to the line of the circular tooth in the middle of the ring gear at the point of intersection of the cutting blades of the cutters of the gear cutting head forming the initial cone at the point of the engagement pole and the normal to the generatrix of the trough cone.

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