RU2128303C1 - Modified involute gear train - Google Patents

Abstract

FIELD: mechanical engineering; reduction gears and transmissions for driving various machines and items of equipment. SUBSTANCE: gear (wheel) of modified involute gear train has curvilinear modification of profiles of tooth points in form of arc of circle. Modified sections of tooth points of gear (wheel) are engageable with respective sections of profile at tooth root of gear (wheel) in and section of gear train. Center of top circle of modified sections is made coincident pitch point. Radius ρ_t of top circle is determined from the following relationship: ρ_t= x_k1/cosα_t, where x_k1 is abscissa of point K1 of intersection of circle r_a2 of points of involute sections K1B of wheel teeth profile with top-line of action 1-1 and α_t is profile angle. Engagement factor is no less than 1.1 for spur gear train and more than 1.0 for helical gear train. EFFECT: increased load-carrying capacity and enhanced kinematic accuracy of drive. 2 dwg

Description

 The present invention relates to mechanical engineering and can be used in gearboxes and transmissions to drive various machines and equipment, for example, in main gearboxes of rolling mills and main gears of ore and coal grinding mills.

The well-known involute transmission (see J.I. Dicker. "Involute meshing." - M., 1935), which has the following disadvantages:
- due to uneven wear of the active surfaces of the teeth (the gearing is purely rolling, therefore there is practically no wear here, and the tooth tip and root have maximum slip, therefore the teeth wear out significantly here), gear ratio pulsation, reduction in kinematic transmission accuracy, dynamic loads occur , which ultimately leads to failure of the contact or bending strength of the teeth.

 Modified involute gear is also widely known, the design of which is determined by the recommendations of the current GOST 13755-81 "Involute spur gears".

 According to the recommendations of GOST 13755-81, only the head of the gear teeth and the wheel undergoes modification, when the line of modification is straight, and the coefficients of height and depth of modification are 0.45 and 0.008 from the transmission module, respectively.

 Therefore, the modified sections of the tooth profiles are disengaged, are non-conjugate, and the conjugate sections of the profiles (involute) in terms of tooth height are 1.1 modules instead of two transmission modules, unmodified according to GOST 13755-81.

 In this regard, such a modified gear transmission requires careful long running-in, since 45% of the active surface of the gear teeth is disengaged.

 However, despite this drawback, tooth modification even in such a primitive way is useful, as it facilitates the transition of the involute surface to a more stable form and contributes to a smoother transmission after the necessary careful and long running-in.

Also known is an involute gear transmission with a curved modification of the profiles of the teeth of the wheels (AS 945524 F 16 H 1/06), which differs in that the modified section (again only on the heads of the teeth) of the profile is described by a curve with a radius (0.3 - 0, 8) m _n , while the length of the modified section of the profile is selected from the condition
h = C • H,
where C is a coefficient taking into account the environment and material of gears;
H is the average hardness of the transmission wheels in units of the Vickers scale.

 Transmission by A.S. 945524 on the technical nature and the achieved effect is closest to the proposed transmission, therefore, adopted as a prototype.

Transmission by A.S. 945524, the prototype, has all the same disadvantages as the involute transmission, modified according to the recommendations of GOST 13755-81:
- the modified portion of the head of the gear tooth is disengaged from the tooth tooth leg, and the modified portion of the gear of the gear tooth head is disengaged from the gear tooth leg, therefore, only the middle part of the tooth with the involute profile remains engaged, therefore, the transmission load capacity is significantly reduced and transmission requires careful and long running-in;
- the modification curve is assigned valantaristically; it is not the stable profile that remains after running-in gears. Moreover, the modification curve for A.S. 945524 cannot have a mating surface on the corresponding tooth segment of the wheel (gear), since the requirements of the main gearing theorem, Willis theorem are not satisfied (see F.L. Litvin. “Theory of gears.” - M., 1960, p. . 18-20), along which the normal to each contact point must pass through the same point - the pole of engagement;
- gear modified by a.s. 945524, has a mechanical overlap coefficient of 1-1.1, which means that the load from the gear to the wheel is transmitted by one pair of teeth, one gear tooth and one tooth of the wheel, so the load capacity of such a transmission is significantly limited.

 Due to these shortcomings, the prototype has a low load capacity and a resource of smooth operation.

 The purpose and objectives of the invention are to increase the load capacity and resource kinematic accuracy (smooth operation) of the transmission.

где

абсцисса точки пересечения окружности вершин эвольвентных участков профилей зубьев колеса с линией зацепления;
α_t - торцевой делительный угол профиля зуба колеса.The technical result, due to which the goal and task are solved, is to ensure the conjugation of the modified sections of the tooth profiles immediately after its manufacture, to significantly increase the stability of the initial geometry of the active surfaces of the teeth and to ensure two-pair gear engagement in all relative positions of the gear and wheel. This technical result is achieved in that the modified sections of the profile of the heads of the teeth of the wheel (gear) are made paired with the corresponding sections of the profile on the leg of the teeth of the gear (wheel) in the end section of the transmission. In this case, the center of the profile circle of the modified sections is aligned with the engagement pole, and the radius of the circle is determined by the dependence

Where

the abscissa of the point of intersection of the circumference of the vertices of the involute sections of the profiles of the teeth of the wheel with the line of engagement;
α _t - end pitch angle of the tooth profile of the wheel.

 Moreover, the magnitude of the part of the overlap coefficient, determined by the involute section of the profiles, is made not less than 1.1 for spur gears and more than 1.0 for helical gears.

The features that distinguish the proposed transfer from the prototype are new and significant, as they give it new qualities:
1. The mechanical overlap coefficient of the proposed gear in all phases of the gearing is equal to two instead of 1.1 (1.0) (see GOST 13755-81), therefore, in all phases of the gearing there is a two-pair gearing, which positively affects the load capacity of the gear .

 2. The modified sections of the tooth profiles of the proposed gear are conjugated with a linear contact, since the normal at any point of contact, being the radius of the profile arc of a circle, passes through the same point - the pole of engagement, and the prototype modified sections are disengaged.

 3. The proposed transmission has increased stability of the initial geometry, since in the peripheral areas of the involute profile, where the maximum wear of the teeth occurs, the slip is replaced by clean rolling, which naturally increases the resource of smooth operation and transmission efficiency.

 The proposed transmission is illustrated by drawings: in FIG. 1 shows a gearing pattern for gear teeth and wheels in the transmission end section, and FIG. 2 shows a design diagram for determining the coordinates of the input and output contact points of involute sections of tooth profiles.

координаты точек K₁ и K₂;

радиусы точек K₁ и K₂;
YO₂X - система координат.In FIG. 1 and 2, the following notation is accepted:
1 - gear;
2 - wheel;
ρ _t is the radius of curvature of the arc convex-concave sections of the tooth profile;
k1 B and KB '- involute sections of the tooth profile;
AK1, BC and aK, B'C 'arc sections of the tooth profile;
r ₁ , r ₂ - dividing radii of the gear and wheel;
α _t is the angle of the tooth profile in the end section;
P is the gearing pole;
ll - engagement line;
C is the radial clearance;
K ₁ (K ₂ ) - input (output) point of contact of the involute section of the profile;
r $\genfrac{}{}{0ex}{}{\text{uh}}{\text{a1}}$ and (r $\genfrac{}{}{0ex}{}{\text{uh}}{\text{a2}}$ ) - the radius of the vertices of the involute section of the profile of the tooth gear (wheel);
a _w is the center distance;
O ₁ , O ₂ - the axis of rotation of the gears and wheels;

the coordinates of the points K ₁ and K ₂ ;

the radii of the points K ₁ and K ₂ ;
YO ₂ X - coordinate system.

 The proposed transmission contains a gear 1 (Fig. 1) and a wheel 2 with a curved modification of the profiles of the tooth heads and the form of an arc of a circle.

 The modified sections AK1, aK of the profile of the heads of the teeth of the wheel 2 (b 'c' of the gear 1) are made paired with the corresponding sections AK1, A'K 'of the profile on the leg of the teeth of the gears 1 (B'C' of the wheel) in the end section of the gear.

 Moreover, the center P of the profile circle of the modified sections AK1, aK, A'K ', BC, B'C', b'c 'is aligned with the gearing pole P.

где

абсцисса точки K₁ пересечения окружности вершин эвольвентных участков K1B профилей зубьев колеса 2 с линией l-l;
α_t - торцевой делительный угол профиля зуба.The radius ρ _{t of the} profile circle is determined by the dependence

Where

the abscissa of the point K _{1 of the} intersection of the circumference of the vertices of the involute sections K1B of the tooth profiles of the wheel 2 with the line ll;
α _t - end dividing angle of the tooth profile.

 Moreover, the magnitude of the part of the mechanical overlap coefficient determined by the involute sections K1B and K1d of the profiles is made not less than 1.1 for spur gears and more than 1.0 for helical gears.

 An example of a specific implementation of the proposed transmission for the main gearbox of the 5th mill stand 2000 of the Novolipetsk Metallurgical Plant instead of the basic involute transmission.

Initial data:
m = 30 mm - the module is normal;
Z ₁ = 38, Z ₂ = 112 - the number of gear teeth and wheels;
a = 2600 mm - center distance;
α = 20 ^o is the angle of the profile;
X ₁ = X ₂ = 0 is the displacement coefficient of the original circuit;
β = 30 ^o 04 '24''= 30.073348 ^o - the angle of inclination of the teeth.

 We determine the geometric parameters of the modified involute gear transmission.

Угол зацепления в торцовом сечении передачи

Основные диаметры шестерни и колеса

Принимаем высоту модифицированного участка профиля на головке зуба колеса (шестерни), равной h' = 5 мм, поэтому высота эвольвентного участка профиля на головке зуба составит
h $\genfrac{}{}{0ex}{}{\text{э}}{\text{a}}$ = m-h′ = 25 мм.Gear pitch and wheel pitch diameters

Gearing angle at the transmission end section

Main gear and wheel diameters

We take the height of the modified section of the profile on the head of the tooth of the wheel (gear) equal to h '= 5 mm, so the height of the involute section of the profile on the head of the tooth will be
h $\genfrac{}{}{0ex}{}{\text{uh}}{\text{a}}$ = mh ′ = 25 mm.

где

d $\genfrac{}{}{0ex}{}{\text{э}}{\text{a1}}$ = d₁+2h $\genfrac{}{}{0ex}{}{\text{э}}{\text{a}}$ = 1367,333;
α_a1 = 27,366954^o,

d $\genfrac{}{}{0ex}{}{\text{э}}{\text{a2}}$ = d₂+2h $\genfrac{}{}{0ex}{}{\text{э}}{\text{a}}$ = 3932,666;
α_a2 = 24,485126^o..Determine the coefficient of mechanical overlap of the remaining involute active surface of the gear teeth

Where

d $\genfrac{}{}{0ex}{}{\text{uh}}{\text{a1}}$ = d ₁ + 2h $\genfrac{}{}{0ex}{}{\text{uh}}{\text{a}}$ = 1367.333;
α _a1 = 27.366954 ^o ,

d $\genfrac{}{}{0ex}{}{\text{uh}}{\text{a2}}$ = d ₂ + 2h $\genfrac{}{}{0ex}{}{\text{uh}}{\text{a}}$ = 3932.666;
α _a2 = 24.485126 ^o ..

We consider ξ _α sufficient, since for oblique gears it must be at least one in accordance with GOST 16532-70.

 For further calculations, it is necessary to know the coordinates of the beginning and end of the working section of the engagement line of unmodified, involute sections of the active surfaces of the gear teeth.

 In this regard, we determine the coordinates of the point K1 (Fig. 2) - the beginning of the engagement.

В результате решения этих уравнений имеем

.To do this, we solve the equation of the circle r $\genfrac{}{}{0ex}{}{\text{uh}}{\text{a2}}$ = 1966.333 and the equation of the line ll

As a result of solving these equations, we have

.

 We determine the coordinates of the point K2 (Fig. 2) - the end of the meshing.

В результате решения этих уравнений имеем

.To do this, we solve the equation of the circle r $\genfrac{}{}{0ex}{}{\text{uh}}{\text{a1}}$ = 683.6665 and the equation of the line ll

As a result of solving these equations, we have

.

 To verify the correctness of the calculations, we determine the coefficient of mechanical overlap as the length of the working section of the engagement line divided by the main step.

.The distance between K ₁ and K ₂ is

.

.The main step is

.

.The coefficient of mechanical overlap is

.

Therefore, ξ _α defined in different ways coincided, therefore, the calculations are correct.

 We determine the height of the active involute section of the profile on the tooth tooth leg.

(фиг. 2)

.To do this, we determine first

(Fig. 2)

.

.The height of the active involute section of the profile on the tooth tooth leg is

.

.We also determine the height of the active section of the profile on the leg of the tooth of the wheel

.

.Determine the radius of curvature of the modified section of the profile for the point K ₁ at the entrance to the mesh

.

радиус кривизны модифицированного участка профиля для точки K2

.Due to the fact that the input section K1P of the line ll and the output section PK2 are not equal to each other, since the gear ratio is rarely equal to unity, we define

radius of curvature of the modified section of the profile for point K2

.

.For technological reasons, it is advisable to use only one value of ρ _t , namely

.

приведет к тому, что контактная линия в виде дуги окружности с радиусом

впереди идущей пары зубьев сместилась параллельно оси зубчатого колеса и будет одновременно с такой же контактной линией сзади идущей пары зубьев перемещаться с постоянной равномерной скоростью параллельно осям передачи от входного к выходному торцу передачи.As for the modified portion at the exit from the engagement, the increase

will lead to the contact line in the form of an arc of a circle with a radius

in front of a walking pair of teeth it has shifted parallel to the axis of the gear and will simultaneously with the same contact line behind a walking pair of teeth move at a constant uniform speed parallel to the transmission axes from the input to the output end of the transmission.

где

В стандартной, в том числе и в базовой передачах, активная поверхность зуба распространяется не на всю его высоту.Determine the magnitude of the displacement of the contact line at the output modified section of the tooth profile with respect to the contact line at the input section of the tooth

Where

In standard, including basic gears, the active surface of the tooth does not extend to its entire height.

The tooth root has a section of the profile that is not active, that is, it does not participate in the transfer of load from the gear to the wheel, since the input K ₁ and output K ₂ points of the engagement line are located not at the center axis, but at some distance from it at one and the other side.

 This section of the profile is a "dead" zone, which in the proposed modified engagement is turned into an active section of the tooth profile.

 To determine the height of the "dead" zone in a standard, base gear, we first determine the height of the active section of the tooth leg profile in the base gear (prototype).

Координаты точки k $\genfrac{}{}{0ex}{}{\text{б}}{\text{2}}$ базовой передачи составляют

.For this, we solve together the equation of the circle r _a1 = 688.666 and the equation of the line ll

K point coordinates $\genfrac{}{}{0ex}{}{\text{b}}{\text{2}}$ base gear make up

.

для базовой передачи

.Determine

for basic gear

.

Следовательно, в базовой передаче высота "мертвой" зоны профиля зуба колеса составляет

.The height of the involute section of the profile on the tooth leg of the wheel of the base gear is

Therefore, in the base gear, the height of the "dead" zone of the profile of the tooth of the wheel is

.

Determine the diameters of the tops of the gear teeth and wheels of the modified gear
d _a1 = d ₁ + 2m + 2 • 5 = 1387.333;
d _a2 = d ₂ + 2m + 2 • 5 = 3952.666.

 In this specific example of the proposed transmission, the diameter of the tips of the teeth is increased in comparison with the standard gear by 10 mm, although the height dimensions of the teeth can be accepted as standard, as in the prototype.

 To increase the height of the teeth in this particular case seems possible, since here we are dealing with the transfer of a large module - 30 mm.

 So, the total height of the convex-concave sections on one tooth is 20 mm: 10 mm at the head and 10 mm at the tooth leg.

у колеса

Определяем диаметры впадин зубьев шестерни и колеса модифицированной передачи

d₁ - (2m+2•5+2•5) = 1237,333;

d₂ - (2m+2•5+2•5) = 3802,666.The height of the active involute section of the profile on the tooth heads is 25 mm, and on the tooth legs
gear

at the wheel

Determine the diameters of the cavities of the gear teeth and wheels of the modified gear

d ₁ - (2m + 2 • 5 + 2 • 5) = 1237.333;

d ₂ - (2m + 2 • 5 + 2 • 5) = 3802.666.

 The radial clearance value is taken equal to 5 mm.

.The tooth height of the modified gear is

.

 The manufacture of the proposed transmission is performed as follows: a gear blank (wheels) is mounted on the table of a hobbing machine; the well-known technology sets up the kinematics of the machine for cutting gear teeth (wheels) with the parameters specified in the example of a specific implementation of the proposed transmission.

 A worm cutter with an initial contour corresponding to the end section of the proposed transmission is installed on the machine support, and gear teeth (wheels) are cut by the rolling method.

 In the process of operation, the proposed transmission has contact on convex-concave sections in the form of an arc of a circle on the gear leg and the tooth head of the wheel of one pair of teeth and at the gear head and the tooth leg of the wheel of the second pair of teeth, while on the involute sections of the active surfaces of the teeth there is also a linear contact.

The proof that the convex-concave sections are in contact along a line representing an arc of a circle is that any normal drawn to this arc passes through the mesh pole, since the origin of the radius ρ _t is the mesh pole P according to the invention, i.e. Willis's theorem, which is the main linking theorem, is satisfied.

 When the gears and wheels rotate, the arc contact lines move at a constant speed without sliding from one end of the transmission to the other.

 At the same time, the contact line of the involute sections of the profiles continuously moves from point K1 to point K2 (Fig. 2).

 Therefore, in the proposed transmission, at least two pairs of teeth are simultaneously engaged due to additional convex-concave sections, and in some phases of engagement, three pairs of teeth are also engaged, since the involute sections of the tooth profiles according to the invention have an overlap coefficient of more than unity .

 Due to this, and also due to the fact that the thickness of the tooth at its root in the proposed gear is greater than that of the known gears, the flexural strength of the teeth of the proposed gear is significantly greater than the flexural strength of the teeth of the prototype.

 This is because the moment of resistance to bending load increases in proportion to the increase in tooth thickness in the second degree (for the case of the proposed transmission with an increased tooth height), and the bending moment increases in proportion to the increase in tooth height in the first degree. As a result, the stresses from the bending of the teeth of the proposed transmission are significantly reduced.

 Due to the fact that the convex-concave sections interact with each other during clean rolling, without sliding, increased stability of the initial geometry of the active surfaces of the teeth of the proposed transmission is ensured, since the friction coefficient during rolling is an order of magnitude smaller than when sliding.

 Therefore, the resource of kinematic accuracy, smoothness of the transmission is significantly increased.

 The proposed transmission has practically no source of internal dynamics acquired by the known transmission structures during their operation due to uneven wear of the active surfaces of the teeth.

 The extension of the arc sections to the sections with the maximum gliding of the involute section both from the head side and from the tooth leg side reduces friction power losses, since the slip is replaced by pure rolling, therefore, the proposed transmission has a higher efficiency.

 Thus, the goal has been achieved due to the fact that the proposed design of the gear transmission ensures the conjugation of modified sections of tooth profiles, increasing the stability of the initial geometry of the active surfaces of the teeth and provides at least simultaneous two-pair gearing of the gear teeth and wheels in all phases of gearing of gear teeth and wheels.

 The expected economic effect of the use of gear transmission consists of the effect of increasing the load capacity, increasing the kinematic accuracy resource (smooth operation of the transmission) and increasing the transmission efficiency.

Claims (1)

A modified involute gear transmission containing a gear and a wheel with a curved modification of the tooth head profiles in the form of an arc of a circle, characterized in that the modified sections of the profile of the heads of the teeth of the wheel (gear) are made conjugate with the corresponding sections of the profile on the tooth tooth gear (wheel) in the end section transmission, while the center of the circular arc of the modified sections is aligned with the gearing pole, and the radius of the profile circle is determined by the dependence

Where

the abscissa of the point of intersection of the circumference of the vertices of the involute sections of the profiles of the teeth of the wheel with the line of engagement;
α _t - end dividing angle of the tooth profile,
the magnitude of the part of the coefficient of frontal overlap, determined by the involute sections of the profiles, is made not less than 1.1 for spur gears and more than 1.0 for helical gears.

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