MODERNIZATION OF DRILLING RIGS USING DRIVING PLANETARY MACHINES WITH VARIABLE PARAMETERS Текст научной статьи по специальности «Физика»

© Turobkul R. Kholmuratov, Parviz S. Khujaev, 2022

UDK 621.01.531.8:004.942

2.5.21 Machines, aggregates and technological processes (engineering sciences)

MODERNIZATION OF DRILLING RIGS USING DRIVING PLANETARY MACHINES WITH VARIABLE PARAMETERS

Turobkul R. Kholmuratov, Parviz S. Khujaev

Tajik Technical University named after academician M. S. Osimi, Dushanbe, Republic of Tajikistan

МОДЕРНИЗАЦИЯ БУРОВЫХ УСТАНОВОК С ИСПОЛЬЗОВАНИЕМ ПРИВОДНЫХ ПЛАНЕТАРНЫХ МЕХАНИЗМОВ С ПЕРЕМЕННЫМИ ПАРАМЕТРАМИ

Т. Р. Холмуратов, П. С. Хужаев

Таджикский технический университет имени академика М. C. Осими, Душанбе, Республика Таджикистан

Abstract. Variable speed characteristics and variable gear ratios of the drive mechanisms of the working bodies of the drilling rig were obtained for a planetary mechanism with a double satellite and a rocker carrier. With the help of the obtained kinematic characteristics, the design and technological parameters of the planetary drive mechanisms of the technical means of drilling rigs will be established. Design and technological parameters will be tested with experimental studies depending on the variable speed characteristics of the planetary friction mechanism.

Key words: planetary mechanisms, boring machines, rotor, carrier, crank, rocker arm, slider, satellite, sun wheel

Аннотация. Для планетарного механизма с двойным сателлитом и водилом коромысла получены переменные скоростные характеристики и переменные передаточные числа механизмов привода рабочих органов буровой установки. С помощью полученных кинематических характеристик будут установлены конструктивные и технологические параметры планетарных механизмов привода технических средств буровых установок. Экспериментальными исследованиями в зависимости от изменяемой скоростной характеристики планетарного фрикционного механизма будут проверены конструктивные и технологические параметры.

Ключевые слова: планетарные механизмы, расточные станки, ротор, водило, кривошип, коромысло, ползунок, сателлит, солнечное колесо

Архитектура, строительство, транспорт DOI 10.31660/2782-232X-2022-4-93-100 93

2022. № 4 (102). С. 93-100

For citation: Holmuratov, T. R., & Khujaev, P. S. (2022). Modernization of drilling rigs using driving planetary machines with variable parameters. Architecture, Construction, Transport, 2022, (4(102)), pp. 93100. (In English). DOI 10.31660/2782-232X-2022-4-93-100.

Для цитирования: Холмуратов, Т. Р. Модернизация буровых установок с использованием приводных планетарных механизмов с переменными параметрами / Т. Р. Холмуратов, П. С. Хужаев. -DOI 10.31660/2782-232X-2022-4-93-100. - Текст : непосредственный // Архитектура, строительство, транспорт. - 2022. - № 4 (102). - С. 93-100.

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Introduction

Planetary mechanisms are finding ever more widespread use, both in transport and stationary machines. They allow transmissions to be made more compact and lighter, and have advantages in transmissions from high-speed engines to the working machine. They are widely used in lifting and transport engineering, automotive, tractor construction, in the forestry and woodworking industries, and epicyclical mechanisms are also

used as a drive for working bodies, as well as pile machines and concrete mixers - boring machines.

In this article, we will consider kinematic and dynamic studies of the proposed drive mechanisms. The planetary gear with a double satellite and rocker carrier allows obtaining variable speed characteristics and variable gear ratios for the drive mechanisms of technical means of drilling well oil and gas.

In rotary drilling (fig. 1), rock destruction occurs as a result of the simultaneous action of load and

Fig. 1. Scheme of rotary drilling of wells: 1 - bit, 2 - motor, 3 - spaces, 4 - horizons, 5 - drill pipes, 6 - sub, 7 - pipe (pipe string), 8 - winch, 9 - motors, 10 - switch, 11 - wire rope, 12 - crownblock (not shown), 13 - hook, 14 - flexible drill hose (sleeve), 15 - kelly, 16 - rotor, 17 - riser, 16 - tank system (not shown), 19 - high - pressure pipeline, 20 - pump, 21 - engine, 22 - receiving tanks of mud pumps

torque on the bit. Under the action of the load, the bit penetrates into the rock, and under the influence of the torque it cleaves it. During rotary drilling (fig. 1), the power from the motors (9) is transmitted through the winch (8) to the rotor (16) - a special rotary mechanism installed above the wellhead in the center of the rig. The rotor rotates the drill string and the bit (1) screwed to it. The drill string consists of a leading pipe (15) and 6 drill pipes (5) screwed to it using a special sub (6). Therefore, rotary drilling the bit deepening into the rock occurs when the rotating drill string moves along the borehole axis.

Expressing with respect to R, we have:

R = sjr2-p2 sin2 a + 2 pcosa. (3)

Substituting the value (2) into (3), we have:

R = ^r2- 2-a2 sirfy/ -acosy/ + l 2 -a2 sin2 у/ - a cosy/+n- cos a.

sma +

Object and methods of research

The object of research is the planetary mechanism. Rotor (16) (fig. 1) rotates according to the principle of a planetary mechanism around a central axis inside a fixed stator.

We take the radius of the crank 01 A1 = R1, the length of the carrier 02B = p, the wheel of the radius R, the radius OA = p-l, 02P = R (this is the line connecting the point of contact P with the point O2), the length of the guide AB = e, the radius of the satellite PB = r, and ty the angle between the radius of the carrier and the line O2P, the carrier and the leading link by and q> the angle between p and R (fig. 2). The angle of rotation of the composite carrier along ty will be [1, 2]:

y/ = <j>±a.

The skew angle is determined by the expression:

From the triangle O1O2A at O1O2 = a; O1A = R1 we

have:

Rf=a2+(p-l)2+2a(p-l)cosy/, (1)

where 7T-y/ = Z0102A is an obtuse angle.

Making transformations of expression (1), we have:

p = ^Rf-a2 sinyr - acosyr+/.

(2)

On the other hand, R is determined from the triangle O2BP on the basis of the cosine theorem:

r2 =R2 +p2-2pRcosa.

Ri , ^¡{p)2+[àp/dyf]2

ctga =

dp/dy/

Fig. 2. Diagram of friction mechanism with a composite carrier: 1 - crank, 2 - rocker, 3 - slider, 4 - guide, 5 - satellite, 6 - wheel

The variable gear ratio of the investigated mechanism is determined by the formula [3, 4]:

U

G>u

ua=-

(4)

7

fdpÏ [dt 2 [dy Idt

dp) dt J 2 + dt

V

(9)

Gear ratio between the satellites by the driving

link:

U

Ua .

CO,

(5)

(p-l)

where the relative speed of the composite carrier is:

acosif/

.dp . . p = -^- = y/asmy/

1-

y¡R *-a2 sin2i/s

(10)

The angular velocity of a composite carrier is determined by the angle of rotation y/:

aH =

dy/ ~dt'

The final gear ratio of the planetary friction mechanism with a composite telescopic rocker carrier (8) and (9), taking into account the formulas (2) and (10), will be written in the form of the gear ratio of the satellite link [7, 8]:

The angular velocities of the satellite are determined:

VR

(Oc ——, щ

(6)

asiny/

acosi/f

-Jr? -a2 sin2 у/ I\¡Rf -a2 sin2i//-acosy/+l~^

where oB, vA are the linear velocities of the center of the satellite and point A of the leading link, which is determined by the formulas [5, 6]:

If dp V ft1? V

(7)

^.teYJ^-o T.

A ]j{dt J I dt'_

Expressions (4) and (5) taking into account (6) and (7) have the forms:

asiny/ L acosif•/ ■Jr? -a2sin2у/ j +^Jr2 - a2 sin2 y/-acosy/+lJ

asiny/ j acosy/ Л k y¡Rf -a2sin2у/ j 2 +j\¡R2 - a2 sin2 y/-acosy/ J

where UCH, Ua accordingly, variable gear ratios

between the rocker carrier satellite and the driving

link satellite.

Based on expressions (10) taking into account / , da

(0H=(a1\1 + a J and p = —, where a we

obtain a generalized formula for determining the variable gear ratio of the investigated mechanism. Gear ratio satellite-rocker pair is:

Uch=-

(7 ± «')/>_

reo,

(8)

(1±J)

gear ratio satellite-lei

(11)

и

иа

-I 2

щ(1±а')р +[р]

(12)

г]Цщ(1±а'){Р-1)-] +(р)2

U

иа

{p)2+[dp/dy/]

[p-l]2+[dp/dy/]

2 '

Fig. 3. Calculation scheme for determining transfer functions: 1 - crank, 2 - rocker, 3 - slider, 4 - guide, 5 - spring

where =

dy/

If the carrier length and angle are constant, we obtain the Willis formula from (11) and (12). Taking into account the constancy of the "mismatch" angle, we have the following approximate formula for determining the gear ratio:

_yj(p)2 + [dp/dy/]2

" ch ~ _ '

The sum of the projections on the X-axis:

i=n

^X, -0, R, cosç?, -(p-l)cosy/-a-0.

i=1

The sum of the projections on the Y-axis:

i=n

Y/i =0, RjSinç), -(p-l)siny/-0.

i=l

From the expressions for zero sums of projections, we determine:

_ RjCOSç, -a _ RjSirxp, ' ' — — ; /

cosy/ smy/

(13)

or

(14)

The given basic kinematic dependences of the studied mechanisms make it possible to solve kinematic problems.

For dynamic analysis, consider the function of the transfer mechanism.

Results

We project the geometric parameters of the mechanism under study onto the coordinate axes OX and OY (fig. 3):

F(<p, ,y/) = Rfos^siny/ - asiny/ -- Rjsin^cosy/ = R^in^Çj -y/)- asinyr.

Then the total derivative has the form:

dF(<p1fyr) _ dF d<p, dF dy/ dt d(p, dt dy/ dt'

3F dF where 11' —- and n' =- are the transfer

дщ

function of the crank or n'-

ду/

R,cos((p,-y/) R,cos((p,-y/)-acosy/

Taking into account (14), the transfer function is equal to:

dF

n,= dy = d<h

d<h dF^ d*,

Then the angular velocity of the link, taking into account (13) and (14), is equal to:

0)2 = П'ц =

= щ [/?, cos( <h-y/)K R, cos( <fo-y/)~ acosy/)\

The transfer function of the link, taking into account (14), has the form [9, 10]:

dtf dfidy/ dy/2K > dy/

where second partial derivatives:

(15)

d2F

ду.r

дф, ду/ j = R1sin(<p]-y/)+asiny/.

/?, cos($ -y/^+acosy/

Then the angular acceleration of the link of the composite carrier has the form:

дф,2 дфду/ ду/ >

£2=П"щ2 =

dF'

dy/

CO2.

(16)

Equation (15), taking into account (14) and formulas (16), has the form:

n»=_I__

/?, cos($ -y/^-acosy/ •[/?, s/n($ -w)+2R1 s/n($ -y/)~\-

R, cos(</>, -y/)

Conclusions

A kinematic analysis of the models was carried out, on the basis of which dynamic dependencies between the design and technological parameters of the drive mechanisms of technological machines were established.

Analytical models of systems of nonlinear equations of motion of elements of planetary mechanisms in drilling rigs have been compiled. The transfer functions of the interaction of a pair of satellite-rocker and a pair of satellite-leading link, formulas for the angular velocities and accelerations of the rocker and the leading link were obtained.

Based on the experiments, the design and technological parameters of the drive planetary mechanisms of drilling rigs will be established depending on the variable kinematic characteristics obtained in the article.

References

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6. Usmankhadzhaev, Kh. Kh., Karimov, K. A., & Tiloev, S. (1982). Planetary friction mechanism with compound carrier. Tret'ya Vsesoyuznaya nauchnaya konferentsiya po inertsionno-impul'snym mekhanizmam, privodam i ustroystvam : tezisy dokladov, p. 123. (In Russian).

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8. Tiloev, S., Akhmadov, B. R., Saidamirov, S. M., Sharipov, F. B., & Kholmuratov, T. R. (2011). Dynamic model of a planetary mechanism with a double compound carrier. Materialy mezhdunarodnoy nauchno-prakticheskoy konferentsii "Obrazovanie i nauka v 21 veke". Sophia, pp. 7-9. (In Russian).

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Библиографический список

1. Холмуратов, Т. Р. Кинематическая модель соотношения планетарных механизмов с переменными передаточными / Т. Р. Холмуратов, И. Р. Муродзода, Ш. Зайниддин. - Текст : непосредственный // Вестник Таджикского национального университета. Серия естественных наук. - 2019. - № 1. -С. 94-100.

2. Холмуратов, Т. Р. Кинематические и динамические модели оптимизации конструктивно-технологических характеристик планетарного фрикционно-шатунного механизма с переменными параметрами : автореферат диссертации на соискание ученой степени кандидата технических наук / Т. Р. Холмуратов. - Душанбе, 2018. - 28 с. - Текст : непосредственный.

3. Малый патент № 201 Республики Таджикистан, МПК(2006) F 16 Н 21/00; 21/02; 21/26. Планетарный механизм : 21.07.2008 / Тилоев С., Саидов М. Х., Саидамиров С. М., Гиеев А. А., Ахмадов Б. Р., Тошов С. Д., Холмуротов Т. Р., Валиев С. З. - 7 с. - Текст : непосредственный.

4. Малый патент № 200 Республики Таджикистан, МПК(2006) F 16 Н 21/00; 21/02; 21/26. Эпициклический механизм (двухступенчатый) : 27.01.2008 / Тиллоев С., Саидов М. Х., Саидамиров С. М., Султон Х., Чалаев С., Тошов С. Д., Гиеев А. А., Ахмадов Б. Р., Шарипов Ф. Б., Холмуротов Т. Р. - 6 с. -Текст : непосредственный.

5. Фролов, К. В. Уменьшение амплитуды резонансных систем путем управляемого изменения параметров / К. В. Фролов. - Текст : непосредственный // Машиноведение. - 1965. - № 3. -С. 38-42.

6. Усманхаджаев, Х. Х. Планетарный фрикционный механизм с составным водилом / Х. Х. Усманхад-жаев, К. А. Каримов, С. Тилоев. - Текст : непосредственный // Третья Всесоюзная научная конференция по инерционно-импульсным механизмам, приводам и устройствам : тезисы докладов. -Челябинск, 1982. - С. 123.

7. Авторское свидетельство SU 1033797 А СССР, F 16 H 21/30. Эпициклический механизм : заявл. 11.03.1982 : опубл. 07.08.1983, бюл. № 29 / Х. Х. Усманходжаев, К. А. Каримов, С. Тилоев. - 3 с. -Текст : непосредственный.

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Information about the authors

Turobkul R. Holmuratov, Candidate in Engineering, Assistant Professor at the Department of Water Supply Systems, Heat and Gas Supply and Ventilation, Tajik Technical University named after Academician M. S. Osimi, e-mail: turob-2016@mail.ru Parviz S. Khujaev, Candidate in Engineering, Associate Professor at the Department of Water Supply Systems, Heat and Gas Supply andVentilation, Tajik Technical University named after Academician M. S. Osimi, e-mail: pkhujaev@gmail.com

Сведения об авторах

Холмуратов Туробкул Рахимович, канд. техн. наук, доцент кафедры систем водоснабжения, теплогазоснабжения и вентиляции, Таджикский технический университет имени академика М. C. Осими, e-mail: turob-2016@mail.ru

Хужаев Парвиз Сайдгуфронович, канд. техн. наук, доцент кафедры систем водоснабжения, теплогазоснабжения и вентиляции, Таджикский технический университет имени академика М. C. Осими, e-mail: pkhujaev@gmail.com