Научная статья на тему 'OF EVOLVENT GEAR WHEELS OF GEOMETRIC PARAMETERS'

OF EVOLVENT GEAR WHEELS OF GEOMETRIC PARAMETERS Текст научной статьи по специальности «Естественные и точные науки»

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Ключевые слова
involute / product / teeth / parameters / calculation / theoretical / evolvente / эвольвента / изделие / зубья / параметры / расчет / теоретическая / эвольвента.

Аннотация научной статьи по естественным и точным наукам, автор научной работы — Sherzod Baxtiyorovich Qurbanov

The line of communication is divided into theoretical and practical. The theoretical contact line is the section through the points of contact of the contact line drawn on the main circles. Since the tooth involute gear is limited by the head circumferences, the side surface contact of the tooth passes along the practical meshing line, which is the point where the head circumferences intersect the theoretical line. In gears, the contact point moves from one point to another along the practical engagement line based on the direction of rotation of the wheel, that is, the teeth come into contact at the first point, and come out of contact at the second point.

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Линия общения делится на теоретическую и практическую. Теоретическая контактная линия представляет собой сечение через точки соприкосновения контактной линии, проведенной на основных окружностях. Поскольку эвольвентное зубчатое колесо ограничено окружностями головки, контакт боковой поверхности зуба проходит по практической линии зацепления, которая является точкой пересечения окружностей головки с теоретической линией. В зубчатых передачах точка контакта перемещается из одной точки в другую по линии практического зацепления исходя из направления вращения колеса, то есть зубья входят в контакт в первой точке, а выходят из контакта во второй точке.

Текст научной работы на тему «OF EVOLVENT GEAR WHEELS OF GEOMETRIC PARAMETERS»

SCIENTIFIC PROGRESS VOLUME 4 I ISSUE 1 I 2023 _ISSN: 2181-1601

Scientific Journal Impact Factor (SJIF 2022=5.016) Passport: http://sjifactor.com/passport.php?id=22257

OF EVOLVENT GEAR WHEELS OF GEOMETRIC PARAMETERS

Sherzod Baxtiyorovich Qurbanov

Karshi engineering-economic institute, PhD, associate professor

ABSTRACT

The line of communication is divided into theoretical and practical. The theoretical contact line is the section through the points of contact of the contact line drawn on the main circles. Since the tooth involute gear is limited by the head circumferences, the side surface contact of the tooth passes along the practical meshing line, which is the point where the head circumferences intersect the theoretical line. In gears, the contact point moves from one point to another along the practical engagement line based on the direction of rotation of the wheel, that is, the teeth come into contact at the first point, and come out of contact at the second point.

Keywords: involute, product, teeth, parameters, calculation, theoretical, evolvente

АННОТАЦИЯ

Линия общения делится на теоретическую и практическую. Теоретическая контактная линия представляет собой сечение через точки соприкосновения контактной линии, проведенной на основных окружностях. Поскольку эвольвентное зубчатое колесо ограничено окружностями головки, контакт боковой поверхности зуба проходит по практической линии зацепления, которая является точкой пересечения окружностей головки с теоретической линией. В зубчатых передачах точка контакта перемещается из одной точки в другую по линии практического зацепления исходя из направления вращения колеса, то есть зубья входят в контакт в первой точке, а выходят из контакта во второй точке.

Ключевые слова: эвольвента, изделие, зубья, параметры, расчет, теоретическая, эвольвента.

Gear couplings with zero involute are widely used in mechanical engineering and aircraft engineering. Such couplings consist of two zero gears (as opposed to positive and negative) that are in contact, or are called meshing gears [1].

The construction of the involute can be described as follows. A thread is wound around the drum in a clockwise direction. We release this thread while maintaining its tension. At the end of the process of unwinding the thread from the spool, it forms a curve, which is called an involute. Another way is possible: when moving a straight line in a circle without sliding, a point draws an involute curve[1].

SCIENTIFIC PROGRESS VOLUME 4 I ISSUE 1 I 2023 _ISSN: 2181-1601

Scientific Journal Impact Factor (SJIF 2022=5.016) Passport: http://sjifactor.com/passport.php?id=22257

A straight line is called a training line, and a circle is called a base circle. Therefore, it can be said that an involute is formed when the preparation line is moved in the main circle.

Its property is derived from the formation of an involute, which is used in the process of grinding gears.

1. The normal to the involute is the product of the base circle.

2. The center of curvature of the involute lies on the main circle

3. The radius of curvature of the involute at a specific point is equal to the length of the arc wrapped around the base circle [2].

When the thread is released from the drum counterclockwise, it creates a right involute, which projects the right tooth of the future wheel. If the thread is wound counterclockwise, then loosened clockwise, a left involute is created, the left side of the tooth is projected.

The contact point of an involute gear wheel is a higher kinematic pair. From this point it is possible to transfer the general normal to the involute property based on the involute and the spur gear involute, which is the product of the base circles of spur gears.

The angle between the product and the perpendicular to the central line is called the angle of inclination. For standard zero gears, this angle is equal to the profile angle of the given contour. The distance between the center of rotation of the gear wheel is called the distance between the axles.

In the process of working gears, the contact point takes a different position, but in any case, it is a collision with the main circle based on the properties of the normal involute transferred to the side surface of the tooth. In the meshing process, the contact point moves along the general product transferred to the main circle, so this product is the meshing line of the involute transmission. Thus, the engagement line of an involute transmission is a drift line drawn under the angle of engagement with the central line

[3].

The line of communication is divided into theoretical and practical. The theoretical contact line is the section through the points of contact of the contact line drawn on the main circles. Since the tooth involute gear is limited by the head circumferences, the side surface contact of the tooth passes along the practical meshing line, which is the point where the head circumferences intersect the theoretical line. In gears, the contact point moves from one point to another along the practical engagement line based on the direction of rotation of the wheel, that is, the teeth come into contact at the first point, and come out of contact at the second point. In involute gear wheels, the theoretical engagement is considered frictionless, that is, there is no side friction

SCIENTIFIC PROGRESS

VOLUME 4 I ISSUE 1 I 2023 ISSN: 2181-1601

Scientific Journal Impact Factor (SJIF 2022=5.016) Passport: http://sjifactor.com/passport.php?id=222ff7

between the teeth; however, in real gears there will be side damage, and its value will depend on the level of accuracy of the wheel preparation [4].

The main parameters of gear wheels are: coupling module m, number of teeth z and rack-like tool, angle of inclination of the surface of the teeth a. The remaining parameters are generated by the main parameters (m, z, a). The number of teeth z, the diameter of the circumference of the legs of the teeth df and the diameter of the circumference teeth da can be measured directly from the wheel itself. The remaining parameters are found by calculation [5].

If the number of teeth z is even, da and df can be measured directly from the wheel itself (Fig.1, a), if the number of teeth z is odd, da and df can be measured directly from the wheel cannot be measured directly. In this case, as shown in (Fig.1, b), dtesh

,h1 and h2 are first measured, and then

da dtesh + 2h1 df=dtesh+2h2

(1) (2)

formulalar da va df dimensions are calculated.

da

da

/. h _ d mem

A V df 1

a)

b)

Figure 1. Evolvente with even (a) and odd (b) number of teeth

gear wheels

Based on the characteristics of the involute curve (the normal transferred to an arbitrary point of the involute surface is an attempt to the main circle that created this involute) it is possible to find the modulus of adhesion [6].

So, if we include several teeth between the teeth of the barbell circle (section AB in Fig. 2), then AB will be an attempt at the main circle with a diameter that forms a normal involute. If we measure l1 covering "n" teeth and measure l2 covering "n+1" teeth, then

SCIENTIFIC PROGRESS VOLUME 4 I ISSUE 1 I 2023 _ISSN: 2181-1601

Scientific Journal Impact Factor (SJIF 2022=5.016) Passport: http://sjifactor.com/passport.php?id=222ff7

PB=l2-li=nmcosa (3)

from this

P

m =-B— (4)

n- cosa

where a=20° is the inclination angle of the tooth of the rack-shaped tool, this value is equal to cos20°=0.9397 according to GOST [7].

Figure 2. A circle forming an evolvente

The value of m modulus found using the formula (4) may differ from the standard modulus due to measurement inaccuracies. Therefore, the value of the calculated module is compared with the GOST-1597 values of the modules, and the value of the module specified in this GOST (closer to the value of the calculated module) is selected [7].

The teeth of the gear being measured can also be corrected (corrected), in which case the relative displacement of the rack-like tool is determined as follows:

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X =

f

v

nSa n —----z • inv a

P 2

\

J

2 • tg a

(5)

from this

inv a=inv 20°=0,014904 tga=tg20°=0,364

PB=l2 - li - pitch of the teeth measured along the arc of the main circle;

SB=l2-PBn - tooth thickness obtained along the main circular arc.

The standard engagement angle of the rack-like tool that creates gears made in the following decades is a=20°, but sometimes corrected (correction) gears with a^20° are also found [8].

In order to find out whether the bevel angle of the teeth of the rack-like tool that forms gears is different from a=20° or 20°, it is enough to compare the diametric df of the gear legs with the previously measured value and the value found by the following formula:

df=m(z+2X-2,5) (6)

If df^db then a^20° bo'ladi.

When determining the main parameters of gear wheels, it is necessary to calculate or measure the following values:

- the number of teeth of gear wheels is assumed to be z;

- diameters da and df of gears are measured;

- according to the table, the number of teeth measured with a barbell circle "n" is found, and the sizes l1 and l2 are calculated by the barbell circle as Pb, SB;

- gear module m is found according to formula 4 and rounded according to GOST-1597;

- the pitch of the p teeth along the arc of the circle that divides the diameters of the dividing d and main db circles;

- the relative displacement of the reciprocating tool is determined according to formula 5;

- the value of df is determined according to formula 6 and compared with the measured value of d [9].

From the above observations, there is an uninterrupted sequence of two-pair engagements in the engagement process, that is, two pairs of teeth are engaged part of the time, and one pair is part of the time. As a result, in a two-pair coupling, all loads

SCIENTIFIC PROGRESS VOLUME 4 I ISSUE 1 I 2023 _ISSN: 2181-1601

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transmitted through the gear are divided between two pairs of teeth, and in a single-pair coupling, all loads fall on one pair of teeth. Thus, the transmission is smooth compared to the kinematic ratio, depending on the compensation result, the gear is discontinuous when working under load, in particular, the noise generated by the gear is the result of this discontinuity. In order to increase smoothness and reduce noise, bevel gears are used, in which the coverage coefficient can be greater than that of straight gears.

REFERENCES

1. Artobolevsky I.I. Mechanism of theory. M.: Nauka, 1988.

2. Frolov K.V. and b. Mechanism and machine theory. T.: Teacher, 1990.

3. Ismailov I.I., Qurbanov Sh.B., Irgashev D.B. Design of gears used in gear reducers // SCIENCE AND INNOVATION international scientific journal volume 1 issue 5 uif-2022: 8.2 | issn: 2181-3337, 106-113 b. https://doi.org/10.5281/zenodo.7017958

4. Usmonkhodzhaev Kh.Kh. Mechanism and machine theory. Tashkent, "Teacher", 1981.

5. Ismailov I.I., Qurbanov Sh.B., Irgashev D.B. The role and importance of gear reducers in mechanical engineering // SCIENCE AND INNOVATION international scientific journal volume 1 issue 5 uif-2022: 8.2 | issn: 2181-3337, 117-121 b. https://doi.org/10.5281/zenodo.7017971

6. Joraev A., Mavlyaviev M., Abdukarimov T., Mirashchmedov D. Mechanism and machine theory. Tashkent, Gafur Ghulam publishing house, 2004, p. 3-18.

7. Rustamoxhaev R. A collection of problems and examples from the theory of mechanisms and machines. Tashkent. "Teacher", 1987

8. Yoldoshbekov S.A., Muhamedzhanov B.K. Mechanism and machine theory. Tashkent. "Voris publishing house" LLC, 2006. 200 p.

9. http://www.ziyonet.uz/

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