RU2111094C1 - Method of gear cutting of hypoide gearing wheels - Google Patents

Abstract

FIELD: machine engineering, cutting gear wheel and pinion of hypoide gearing. SUBSTANCE: method comprises steps of working gear wheel and pinion by means of gear cutting head with cutters whose sharpening angles are selected while taking into account "number correction" depending upon rotation angles of gear cutting head at shaping. rotation angles are selected according to given formula. EFFECT: enhanced efficiency. 5 dwg

Description

 The invention relates to mechanical engineering and can be used in the treatment of wheels and gears of a hypoid gear.

где
γ_i,φ - углы поворота элементов гипоидной передачи и производящего колеса зуборезной головки соответственно, α - номинальный угол профиля зуба.An analogue is the method of cutting gears forming a hypoid gear, presented by Russian patent N 2043187. The analogue shows the variable rolling movements when cutting the wheel and gear, allowing you to cut the exact profiles of circular teeth in the middle section. Variable rolling movement can be implemented on gear-cutting machines with a rolling modifier or on machines with programmed control. The rolling movement of the cut and producing wheels is represented by the formula (I):

Where
γ _i , φ are the rotation angles of the elements of the hypoid gear and the producing wheel of the gear cutting head, respectively, α is the nominal angle of the tooth profile.

где
i = к, ш - индексы колеса и шестерни;
θ_fi - угол ножки зуба;
A - радиус движения резцовой головки;
E_i - гипоидное смещение;
D_к = 0 - для колеса;
D_ш= R_mшcosθ_fш-L_ccos(μ-μ₀) для шестерни;
L_c - расстояние от оси производящего инструментального колеса до середины венца нарезаемого зубчатого колеса в плоскости касательной образующей конуса впадин;
μ₀ - угол гипоидного смещения;
μ = β_nш-β_nк - разность углов наклона круговых зубьев гипоидных колеса и шестерни;
N_к = E_кsin φ_n - для колеса;
N_ш = Dcos φ_n -E_шsin φ_n
R_Bi = R_micos θ_fi
R_mi - среднее конусное расстояние;
φ_n - расчетный угол положения зуборезной головки;
r_mi - средний радиус начальной окружности;
r - номинальный радиус зуборезной головки.The deviation of the tooth profile is determined by the formula:

Where
i = k, w - wheel and gear indices;
θ _fi is the angle of the tooth leg;
A is the radius of movement of the cutting head;
E _i - hypoid displacement;
D _to = 0 - for the wheel;
D _W = R _mш cosθ _fш -L _c cos (μ-μ ₀ ) for the gear;
L _c is the distance from the axis of the producing tool wheel to the middle of the rim of the cut gear in the plane of the tangent generatrix of the cone of the troughs;
μ ₀ is the angle of hypoid displacement;
μ = β _nш -β _nк - the difference between the angles of inclination of the circular teeth of the hypoid wheel and gear;
N _to = E _to sin φ _n - for the wheel;
N _w = Dcos φ _n -E _w sin φ _n
R _Bi = R _mi cos θ _fi
R _mi is the average conical distance;
φ _n is the calculated position angle of the gear cutting head;
r _mi is the average radius of the initial circle;
r is the nominal radius of the gear cutting head.

The signs (± Δα _i ) - (+) for the concave, (-) for the convex sides of the tooth, the remaining signs (±) are the top for the wheel, the bottom for the gear.

 The disadvantage of the analogue is the need to use a special mechanism that corrects the process of processing teeth on the machines according to the required law, or the use of machine tools with program control, which is not always feasible.

 The prototype adopted the method of cutting bevel gears according to Russian patent N 2041034. According to this method, the cutting of the wheels and gears of the hypoid gear is carried out by gear-cutting heads with cutters having a “numerical correction”, determined by the formula (2).

 The disadvantage of the prototype is the inaccurate geometry of the cutters of the gear cutting head. The proposed formula for calculating the "numerical correction" is presented by the position of the formation of the tooth profile in the area from cutting the tool into the workpiece to the intersection of the cutter of the cone of the tooth cavities. This position is not correct, because actually the profiling of the tooth sides occurs on the site of the line of engagement of the pair producing-cut wheel (machine engagement) (see "Applied Mechanics" edited by V. M. Osetskogo. M .: Mechanical Engineering, 1977, p. 273, fig. 182). In other areas, the incisors cut through the tooth cavity without forming a tooth involute. In this case, it is necessary to select only the areas of formation of the involute of the tooth and determine the dependence of the deviation of the tooth profile on the site of the line of engagement.

 The objective of the invention is to improve the accuracy of machining of circular teeth of wheels on conventional gear cutting machines by changing the "number correction" of the cutting part of the cutters of the gear cutting head. The task is achieved by calculating the "numerical corrections" to 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 "numerical correction" of the incisors of the forming side of the circular teeth, providing a normal tooth profile.

 In FIG. 1 shows an engagement line; in FIG. 2 is a diagram for calculating the rotation angles of a gear cutting head of the beginning and end of tooth profiling of a hypoid gear wheel; in FIG. 3 is a diagram for calculating rotation angles of a producing wheel of a beginning and an end of a tooth profiling of a gear of a hypoid gear; in FIG. 4 - deviation of the tooth profile of the hypoid gear wheel at the turning angles of the producing wheel; in FIG. 5 - deviation of the tooth profile of the gear of the hypoid gear at the turning angles of the producing wheel.

For the concave, convex and concave sides of the tooth of the wheel, the angles of the start φ _nni and the end φ _{kni of the} tooth profiling in the middle section are determined according to the diagrams of FIG. 2.

The engagement line "a-c" of FIG. 1 allows us to determine the segments ac = kv, according to which the dependences of the angles of rotation of the producing wheel of the gear cutting head are determined on the section of tooth profiling ac = h _ai / tg α, where h _ai is the height of the tooth head. The angles of the beginning and end of rotation of the producing wheel for profiling the tooth are determined according to the diagrams of FIG. 2 and FIG. 3.

γ₁ - определяется по схеме:

ac=

cb, принимая

ac = отрезку ac, что вполне допустимо, т. к. при обработке с коррекцией добавляют углы гарантированной обработки, компенсирующие принятое допущение. Учитывая, что
γ₂= ac/R_mcosθ_fк, ac = h_a/tgα
тогда

На фиг. 4 построены графики наклонения профиля зуба колеса на угле формирования профиля зуба по линии зацепления по вогнутой и выпуклой сторонам кругового зуба. Отклонение профиля зуба имеет место по всей высоте зуба. Для получения более точного профиля зуба необходимо изменить геометрию режущих кромок резцов зуборезной головки.For the wheel (Fig. 2):

γ ₁ - is determined by the scheme:

ac =

cb taking

ac = segment ac, which is quite acceptable, because when processing with correction, the angles of guaranteed processing are added to compensate for the assumption. Given that
γ ₂ = ac / R _m cosθ _fк , ac = h _a / tgα
then

In FIG. 4, graphs of inclination of the tooth tooth profile at the angle of formation of the tooth profile along the line of engagement along the concave and convex sides of the circular tooth are plotted. Deviation of the tooth profile takes place along the entire height of the tooth. To obtain a more accurate tooth profile, it is necessary to change the geometry of the cutting edges of the cutter head cutters.

The compensated deviation of the profile of the teeth of the incisors in this case should be calculated by the formula (1) provided that the cutting edges pass the point of the gearing pole “P” of the pair “cutting wheel-gear head” on the initial cone along the concave and convex side of the circular tooth. The angular coordinate φ _{n of the} position of the axis of the cutting head is determined according to the scheme of FIG. 2.

Подставляя выражение и производя преобразования, получим

Данные выражения позволяют рассчитать отклонение профиля зуба колеса после подстановки в формулу (2).

Substituting the expression and performing the transformations, we obtain

These expressions allow you to calculate the deviation of the tooth profile of the wheel after substitution in the formula (2).

 Based on the obtained dependences, the deviations of the wheel tooth profile were calculated at the formation angles along the engagement line along the convex and concave sides of the circular tooth and at the engagement point "P" on the initial cone (Fig. 4).

For the concave side of the circular tooth of the wheel: Δα _vogn = 2,304 ^o with φ _n = 70,142 ^o
For the convex side of the circular tooth of the wheel: Δα _issue = 1,670 ^o C when φ _n = 65,445 ^o
The angles of the beginning and end of rotation of the gear cutting head for profiling the gear tooth are determined according to the scheme of FIG. 3.

Подставляя выражение и производя преобразования, получим:

Данное выражение позволяет рассчитать отклонения профиля зуба шестерни после подстановки в формулу (2).

Substituting the expression and performing the transformations, we obtain:

This expression allows you to calculate the deviation of the gear tooth profile after substitution in the formula (2).

Based on the obtained dependences, the deviations of the gear tooth profile were calculated at the formation angles along the engagement line along the concave and convex sides of the circular tooth and at the point of the “P” engagement pole on the initial cone (Fig. 5). For the concave side of the gear Δα _vogn = 0.607 ^o at φ _n = 87.03 ^o for the convex side Δα _vol = 0.602 ^o at φ _n = 85.50 ^o
Based on the calculations performed for the specified 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 a wheel α _int = 20 + 1.67 ^o = 21.67 ^o ; α _ext = 20 - 2,304 ^o = 17,696 ^o;
for gear α _inner = 20 + 0.602 ^o = 20.602 ^o ; α _ext = 20 - 6,607 ^o = 19,393 ^o.

Claims (1)

A method of cutting gears of a hypoid gear, in which the gear and the wheel are processed using a gear cutting head, the sharpening angles of the cutters of which are selected taking into account the "number correction", characterized in that the processing is carried out by a gear cutting head, in which the sharpening angles of the cutters when taking into account the "number correction" determined depending on the rotation angles φ _p gear cutting head during profiling, which are selected by the formula

where A is the radius of movement of the gear cutting head;
E ₁ - hypoid displacement;
R _{m i} is the average conical distance;
r is the nominal radius of the gear cutting head;
θ _{fi the} angle of the tooth leg;
i - indices of the wheels and gears of the hypoid gear;
W is the divorce rate of the incisors;
h _f is the height of the tooth leg;
α nominal angle of the tooth profile;

L _c is the distance from the axis of the producing wheel to the middle of the rim of the cut gear in the plane of the tangent generatrix of the cone of the troughs;
μ is the angle of hypoid displacement;
μ _o - the difference between the angles of inclination of the circular teeth of the wheel and gear,
the signs (±) relate as follows: (+) - for the wheel, (-) - for the gear.

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