Optimization design of shearer drum height adjusting mechanism based on particle swarm optimization algorithm Текст научной статьи по специальности «Строительство и архитектура»

_ISSN 2782-4004 (print) ISSN 2782-6341 (online)

MECHANICAL ENGINEERING

Original article Ей№ QCPJUN

DOI: 10.21285/1814-3520-2024-1-31-39

Optimization design of shearer drum height adjusting mechanism based on particle swarm optimization algorithm

Degen Li111, Wenbo Jia2, Chunping Ren3

1-3Heilongjiang University of Science and Technology, Heilongjiang, Harbin, China

Abstract. The underground working environment of the shearer is complex and the working conditions are relatively poor. It is necessary to continuously adjust the height of the rocker arm during the operation, improve the operation efficiency, and improve the ability of the shearer to adapt to the more complex coal seam working environment. In order to optimize the structure of the shearer adjustment mechanism, the strength and strength of the adjustment mechanism are improved by increasing the size and angle of the adjustment mechanism and reducing the size and angle. Therefore, an optimized particle group design method is proposed to optimize the drum adjustment mechanism of the shearer. Seven parameters such as large lever, small lever and maximum swing angle are selected as design variables. Under the condition of limiting mining height and rocker length, an optimization model with rolling angle and cylinder stress as objective functions is established. The working characteristics of each part of the coal machine height adjustment mechanism are analyzed. The particle swarm optimization algorithm is used to optimize the key parameters, and the optimization results are verified to ensure their accuracy. The optimization results are compared with the original parameters. The results show that compared with the pre-optimization, the cylinder stroke is shortened by 17.9%, the cylinder length is shortened by 8.94%, the rolling angle is reduced by 2.83%, the cylinder tension is reduced by 12.1%, and the rocker bending moment is increased by 6.83 %, which meets the original design goal. Therefore, the research provides a reference for the optimal design of the coal machine height adjustment system.

Keywords: shearer, adjustment mechanism, rolling angle, rocker length, optimization, particle swarm, optimal design

Funding: This work was supported by The National Natural Science Foundation of China (Project no. 51974111).

For citation: Li Degen, Jia Wenbo, Ren Chunping. Optimization design of shearer drum height adjusting mechanism based on particle swarm optimization algorithm. iPolytech Journal. 2024;28(1):31-39. https://doi.org/10.21285/1814-3520-2024-1-31-39. EDN: QCPJUN.

МАШИНОСТРОЕНИЕ

Научная статья УДК 622.23.05

Оптимизационная конструкция механизма регулировки высоты барабана машины для добычи угля на основе

алгоритма роя частиц

Дэгэнь Ли11-, Вэньбо Цзя2, Чуньпин Жэнь3

1-3Хэйлунцзянский научно-технический университет, г. Харбин, КНР

Резюме. Цель - оптимизация конструкции механизма регулировки высоты барабана угледобывающей машины путем изменения размера и угла механизма регулировки для повышения надежности работы механизма в тяжелых эксплуатационных условиях. В работе использован метод оптимизации роя частиц. В качестве опорных параметров были выбраны значения длины большого рычага, длины малого рычага и максимального угла поворота коромысла. При условии ограничения рабочей высоты и длины коромысла установлена многоцелевая оптимизационная модель с углом качания и напряжением цилиндра барабана в качестве целевых функций и переведена в одноцелевую функцию (при помощи линейных весовых коэффициентов). Граничные условия оптимизации получены на основе анализа рабочих характеристик каждой части механизма регулировки рабочей высоты угледобывающей машины - угол качания, ход цилиндра, нагрузка на цилиндр и коромысло, ограничение по высоте и длине коромысла и рычагов. Алгоритм оптимизации роя частиц использован для оптимизации ключевых размерных и угловых параметров коромысла. Результаты оптимизации проверены для оценки их точности. Установлено, что по сравнению с исходными параметрами удалось достичь следующих изменений оптимизируемых величин: ход цилиндра сократился на 17,9%, длина цилиндра сократилась на 8,94%, угол качания уменьшился на 2,83%, напряжение цилиндра уменьшилось на 12,1%, на 6,83% увеличился изгибающий момент коромысла. Таким образом, предложены рекомендации по оптимизации конструкции системы регулировки высоты коромысла угледобывающей машины, способствующие повышению надежности ее работы в сложных условиях.

iPolytech Journal

2024. Т. 28. № 1. 31-39

2024;28(1):31-39

© Li Degen, Jia Wenbo, Ren Chunping, 2024 https://ipolytech.elpub.ru -

2024;28(1):31-39

ISSN 2782-6341 (online)

Ключевые слова: угледобывающая машина, механизм регулировки, угол прокрутки, длина коромысла, оптимизация, рой частиц, оптимизационная конструкция

Финансирование. Работа была выполнена при поддержке Национального фонда естественных наук Китая (проект No. 51974111).

Для цитирования: Ли Дэгэнь, Цзя Вэньбо, Жэнь Чуньпин. Оптимизационная конструкция механизма регулировки высоты барабана машины для добычи угля на основе алгоритма роя частиц // iPolytech Journal. 2024. Т. 28. № 1. С. 31-39. (In Eng.). https://doi.org/10.21285/1814-3520-2024-1-31-39. EDN: QCPJUN.

INTRODUCTION

The working efficiency and stability of coal mining machine determines the mining rate of coal which is as one of the key parameters of coal mining [1]. During the working process of the coal miner, the swing of the rocker arm mainly relies on the height adjustment mechanism for control, therefore, the height adjustment mechanism is an important part of the coal miner and affects the working efficiency and reliability of the coal miner [2]. The key components of the height adjustment system are easily damaged due to excessive forces due to the complex working environment and changing loads. This is why it is so important to optimise the size of the key components of the raising mechanism.

Liu Chunsheng et al. [3] used the interior point penalty function method to optimise the height adjusting mechanism of the coal mining machine and obtained the optimal solution for the key components of the height adjusting mechanism of the coal mining machine. Zhao Lijuan et al. [4] used similar theory to optimise the design of the coal mining machine height adjustment mechanism and obtained the optimal solution for the key components of the coal mining machine height adjustment mechanism. Wang Yadong et al. [5] verified the accuracy of the control strategy for adaptive height adjustment of the coal mining machine by simulating the drum through idealised signals and combining the virtual prototype with algorithms. Li Fuqing et al. [6] used Matlab/Simulink to dynamically analyse the height-adjustment mechanism. Ji Cheng [7] established a mechanical model of the height adjustment system of the coal mining machine and concluded that the hydraulic cylinder damping was negatively correlated with the vibration of the cut-off section. Drawing on the aforementioned research results, the author applied the particle swarm algorithm to optimise the key components of the height adjusting mechanism and used a coal mining machine as a design example to verify the accuracy of the optimised design results.

MATHEMATICAL MODEL OF THE HEIGHT ADJUSTING MECHANISM

The control of the roller coal mining machine height adjustment mechanism mainly relies on the hydraulic cylinder, the hydraulic cylinder is an important part of the coal mining machine, owing to the harsh working environment of the coal mining machine, and the small space of the body, the structure is more compact, the size of the cylinder requirements are also more strict. Damage to the cylinder is mainly comes in the form of cylinder head breaking off or piston rod breakage; repairing the damage will not only reduce efficiency, but also increase costs, so the design of the height adjustment mechanism must ensure the minimum load on the hydraulic cylinder to effectively improve the reliability of the machine.

When determining the design load of the height adjustment cylinder, it is important to select the correct working conditions for the calculation. The working condition of the coal miner down-hole is to adjust the height while hauling, with the front drum rotating counterclockwise and the drum adjusting downwards at its highest position to calculate the design load of the heightening cylinder. The structure and dimensions of the coal miner's height adjustment mechanism is shown in Fig. 1. When the drum is adjusted upwards, the push cylinder moves forward, pushing the bottom end of the lower trunnion plate forward, the top end of the lower trunnion plate upwards, the rocker arm moves upwards together with the lower trunnion plate, and the drum is raised together with the rocker arm; when the drum is adjusted downwards, the push cylinder contracts, driving the bottom end of the lower trunnion plate downwards, and the top end of the lower trunnion plate. When the drum is lowered, the push cylinder contracts and moves the bottom end of the lower trunnion plate down, the top of the lower trunnion plate is lowered and the rocker arm is lowered and the drum moves down.

а b

Fig. 1. Structure (а) and dimensions (b) of the height adjustment mechanism Рис. 1. Конструкция (а) и размеры (b) механизма регулировки высоты

DETERMINATION OF THE OBJECTIVE FUNCTION, PENDULUM ANGLE

In the diagram, Li is the vertical distance between the full extension point A of the cylinder and the swing center 0, L2 is the length from the swing centre 0 of the rocker arm to the end of the body, L3 is the vertical distance from the swing centre 0 to the rear stranding point 0i of the cylinder, La is the straight line distance from 0 to the point 0i, L5 is the horizontal distance fro m t he swing centre 0 to the re arst randing po int 0i of the colindet, La \e the lengte o^0e roekenarm, Hi is the maximum upprrswin\ height of thedrum, H2isthe maximum lower swing height of the drum, 0i is the maximum upper swing angle of the drum, 02 is the maximum lower swing angle of the drum, p and Y are the installation position angles, A and B are the positions of the piston rod and the stranding point of the small rocker arm when the cylinder is fully deep out and retracted [8-10].

The expansion and contraction of the push cylinder drives the movement of the rocker arm. In the process of coal mining, the height of the drum needs to be adjusted continuously, and the rocker arm swings continuously. In order to improve the efficiency, the angle of swing should be reduced to make the adjustment more rapid, i.e. the angle of swing of the cylinder up and down A^ is minimum. In other words:

^ = (KCOi - KAOi )2 + (KCC{ - KBOif; (1)

L4rio y-R rmap + y + fa +$2)

Kac =-;

e4cory- R ppriP + y + fr +$2)'

RhioaP + y) - L4rloy

=

KBO, -

■•CO,

R - L4 sin у L4 cosy

Rectifying equation (1) yields that the objective function is expressed as follows:

Y =

R - L4 sin y L4 cos y

(2)

L4siny- R sin(ß + y + ^ + ф2) L4 cos y - R cos(ß + y + ф + ф2 )

R - L4 sin y R sin(ß + y) - L4 sin y L4 cos y L4 cos y- R cos(ß + y)

CYLINDER STROKE

The swinging arm needs to be driven by the expansion and contraction of the cylinder, the stroke of the cylinder should be reduced, i.e. the minimum cylinder stroke in order to improve efficiency,

Smax = S + + S2 + + S4 + S5 = S + SZ .

Eq: Sz- Axial dimensions required for the construction of the cylinder, which can be considered as a constant, mm.

The requirement that the cylinder stroke s be minimal is equivalent to smax =^/r2 + l\ -2RL4corp is minimal, so that the objective function

5 =

^R2 + L4 - 2RL4 cosß .

(3)

1 L4 cos y- R cos(^ + y)

OBJECTIVE FUNCTION OF THE FORCES ON THE CYLINDER

In order to protect the key components of the raising system, it is necessary to minimise the load on the system, i.e. to minimise the force on the cylinders.

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к-M

M,

R sin a

G

F y sin ф + ( Fz - Gx cos ф

L ■

Sinf =

La sin(^j + ф2 + ß)

Jr2 + L24 - IRL, cos(^j +ф2 + ß) ■

Y =

0.55Г . . 1.91x10'N„nK sin^j + (- Hl

G,

1.5

nD„

^ - Gj -^^ф

RL4 sin(^1 + ф+ ß) ■у/r2 + L, - 2RL4 cos(^1 +фг+Р)

(4)

ROCKER ARM FORCES

The rocker arm is an important part of the coal mining machine, connecting the machine body to the drum. It is necessary to minimise the force on the rocker arm to protect the rocker arm during work.

F, =

G

F sin Ф1 +(F - G1 - y)cos Ф1

L6 . (5)

In summary, there are four sub-objective functions, which belong to the multi-objective optimization problem. It is generally converted into a single objective function for optimization in order to make the optimization objective function simple. In this paper, the linear weighting coefficient method is used to convert the multi-objective function into a single objective function for optimization, from the formulae (2), (3), (4), (5) can be obtained from the optimal objective function, that is

F(x)min = + W2s + W3F3 + w4F4 . (6)

Where wi, w2, W3, W4 and are weighted factors indicating the magnitude of the influence of each sub-goal on the overall goal. General requirements W1+W2+W3+g4=). C6onsid€ir the level of impact, Fetch wi = 0.3, w2 = 0.3, W3 = 0.3,

W4= 0.1.

BINDING CONDITIONS, MINING HEIGHT CONSTRAINTS

There is a limit to the height at which the coal miner drum can swing up and down [11, 12], and the range of heights at which the drum can swing up and down, H and H2, can be obtained, as shown in Fig. 2. There are L6sm^H, L6sin^2 =sh2. The constraints are

g(1) = L6 sin Ф1 - H^0 ■ g (2) = L6si^2 - H2^0.

(7)

(8)

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COAL THROWING CONSTRAINTS

During the working process of the coal miner, the cut-off teeth on the drum cut off the coal and the falling coal blocks are thrown down to the scraper conveyor with the movement of the drum blades to the coal outlet, the rocker mechanism of the coal miner is shown in Fig. 2.

Fig. 2. Rocker arm mechanism model Рис. 2. Модель коромысла

To keep the coal from falling on the body, as shown in Fig. 2, there is

L7 = L6 cosф -1 Dy cos

ф + arcsin( d )

In Eq, Ly is horizontal distance from E to point O, mm;

Dy is blade diameter, mm; H is rocker width, mm. Binding conditions are

1 2

g(3) = L6cosфl -- Dy cos

ф + arcsin( d )

(9)

- L2 ^0.

CONSTRAINTS ON THE LENGTH OF THE ROCKERARM

The gearing system inside the rocker arm is shown in Fig. 3. In order to extend the length of the rocker arm, a number of idler pulleys are installed in the rocker arm, generally the number of idler pulleys is no=2~5.Zo is the number of teeth of the idler pulley. Z2>Z1 (Transmission ratio requirements), m is the modulus, maximum length of rocker arm is Lmax= [4z0 + (Z + z2)/2]m . Thus with l ^l, i.e.

g(4) = Lmax - L6^0 .

(10)

g(8) = ¿5max "L4cos^0; (14)

g(9) = 4m. -L4sinr^0; (15)

g (10) = L4 sin Y-L3min ^0. (16)

SMALL ROCKER CONDITIONS

Rmax^R^Rmin,

i.e.

g (11) = Rmax - R^0; (17)

g(12) = R - Rmrn^0. (18)

THRUST OF THE CYLINDER

After determining the maximum working pressure of the cylinder p and the inner diameter of the cylinder D1 and the diameter of the piston rod d, it is required that the hydraulic pressure generated by the cylinder should be greater than orequalto theload force [13-15], i.e.

Fig. 3. Rocker arm transmission system Рис. 3. Система передачи коромысла

CYLINDER STROKE

As seen in Fig. 1, the stroke size of the cylinder depends on the maximum swing angle, i.e.

s SAO1 SBO1

or

= 2 + L4 - 2RL4 cos(^ + ф2 + p) -,Jr2 + L - 2RL4 cos p ;

n

M

; 2R sin

Ф1+Ф2 2

j(D -d2)pk^-

4 R sin Л

In the formula, k is residual factor, ki=0.8,

then

The size of the cylinder stroke should meet

n

}BO1-

>

s + s + s + s + s + s = s + s

g (13) = - ( D2-d2) pk1-

Mx

5

R sin X

■^0. 19)

well organized

g(5) = 2^/ R2 + L4 - 2 RL4 cos p- (11)

R2 + L24 -2RL4 cos($ +02 + p) -sz^0.

NON-INTERFERENCE CONDITIONS AT POINTS A AND B

The perpendicular distance from A and B to point O cannot be too small, then there is

R sinGtf + r)^^; R siniP + Y + fa +^L6min,

i.e.

g(6) = R sin(^ + r) - L4min^0; (12) g(7) = RsmiP+Y + b + £)-L6min^0. (13)

CYLINDER REAR STRAND POINT CONDITIONS

The rear pivot point should be higher than the height of the transported coal seam, then there is

¿5^4 COsr , L3mx^L4 sin^Amn , i.e.

PARTICLE SWARM ALGORITHMS

The particle swarm algorithm (PSO) is a swarm optimisation algorithm [16-18] for solving nonlinear functions that iteratively searches for the optimal solution to an objective by simulating the flight foraging behaviour of a population of birds. without the selection, crossover and mutation operations required by genetic algorithms, the PSO algorithm is characterised by fast computational speed and easy parameter adjustment, and is widely used in the field of optimization4 [19, 20].

Suppose that the population of the particle algorithm consists of N particles moving in an D-dimensional search space. Then the position of the / particle, i.e. x={.xn,xl2,-,xj, the velocity v.=(vn,v.2,---,vw) of the / particle, the optimal position p^ = (pn,p2,...,pwf of the particle, and the population optimal position P#«=(Pgl,Pg2,-,PgDy of the population.

The iterative equations for position and velocity are expressed as follows; xkd+1 = Xkd + v'j1, c = wvd+- xd)+c^p* - Xd) where v

4Кантович Л.И., Мерзляков В.Г. Горные машины и оборудование для подземных горных работ: учеб. пособие. М.: Изд-во МГГУ, 2014. 408 с.

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is the velocity component of the particle in the cf-dimensional direction after k iterations; xd is the position component of particle i in the cf-dimensional direction after k iterations; Pbert is the position of the optimal fitness value reached by particle i after k searches; Pgbert is the optimal position reached by all particles after k searches, w is the inertia factor, k is the number of iterative searches, ri, /2 represent the random number of the interval at [0,1]. Ci and C2 are the acceleration factors, which represent the cognitive and social factors respectively. The flow chart of the particle swarm optimisation algorithm is shown in Fig. 4.

Start

Initialize each parameter

Calculation of individual particle adaptation values

Find individual and group optima

Update the velocity and position of individual particles

N Satisfaction of termination >

conditions

I End 1

J

Fig. 4. Particle swarm optimization process Рис. 4. Процесс оптимизации роя частиц

Table 1. Variable optimization results

Таблица 1. Результаты оптимизации переменных

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EXAMPLE OF AN OPTIMISED DESIGN

Parameter setting of the particle swarm algorithm Set the population parameters as follows: population dimension d=7, number of individuals in the population n = 1000 number of iterations m=200, learning factor Ci=C2=0.5, inertia weights w = 0.44.

CALCULATION EXAMPLES

MG300/700-WD coal mining machine as an example of calculation, raw data: h1 = 3187,

H2 = 267, Dy = 1200, D = 1400, h = 500, Lmax = 2267,L2 = 628, Lmx = 320, A = 832^ L^ = im L3m„=460, = 360, Rmlo = 420, Rmx = 600, NH = 300, n = 42, T = 5.9x 1, G1 = 25440, G2 = 24890, P = 23, D = 180, d = 140, w1 = 0.3, w2 = 0.3,

w3= 0.3, w4 = 0.1, z1 = 22, z2 = 40, n = 7. From equation (5), this objective function has seven variables that do not interfere with each other, i.e. ^ /u 0^ 02^ Y, replacing these

7 variables with x.

Initial values of design variables,

X = [l6, l^fa, R, P,yf = [2313,1753,57°,15°,476,35°,16°f,

the optimised results are shown in Table 1.

The changes in each objective function after optimisation are shown in Table 2.

As can be seen from Table 2, through optimisation, the cylinder stroke and length have been reduced by 17.9% and 8.94% respectively compared to before optimisation, improving the safety of the cylinder, the swing angle of the rocker arm has been reduced by 2.83% compared to before optimisation, which can make the coal miner more suitable for the narrow space downhole, the cylinder pressure has been reduced by 12.1% compared to before optimisation, improving the reliability of the cylinder, and the bending moment of the rocker arm has been increased by 6.83% compared to before optimisation, improving the strength of the

Design volume L6/mm L4/mm 01/(°) 02/(°) R/mm ß/(°) Y/(°)

Original 2313 2754 37.8 16.0 504 38.0 14.0

Optimisation 2480 2684 36.5 15.8 550 40.6 12.7

Д1/% 7.22 -2.45 -3.44 -1.38 9.13 6.84 -9.29

Table 2. Objective function optimization results Таблица 2. Результаты оптимизации целевой функции

Design volume Cylinder stroke, s/mm Cylinder length SBO1/mm Swing angle 0mJ( ° ) Cylinder pull F3/N Rocker momen F4/N

Original 1017.5 1850.0 53.80 485324 7.352*108

Optimisation 835.4 1684.6 52.28 426589 7.854*108

Д2/% -17.9 -8.94 -2.83 -12.10 6.83

rocker arm. The bending moment of the rocker arm has increased by 6.83% compared to that before optimisation, improving the strength of the rocker arm.

CONCLUSION

A particle swarm optimisation algorithm is applied to optimise the key dimensions of the key components of the height raising mechanism by constructing an optimisation model for the height raising system of the coal mining machine. The particle swarm optimization

algorithm was applied to the optimal design of the height-adjusting mechanism of the coal mining machine, and the optimization results were obtained with seven key parameters as the optimization objects. The result is that the cylinder stroke is shortened by 17.9%, the cylinder length is reduced by 8.94%, the swing angle is reduced by 2.83%, the cylinder tension is reduced by 12.1% and the rocker bending moment is increased by 6.83%, which has a better effect on the improvement of efficiency and the protection of the machine.

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2024;28(1):31-39

ISSN 2782-6341 (online)

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INFORMATION ABOUT THE AUTHORS

ИНФОРМАЦИЯ ОБ АВТОРАХ

Degen Li,

Heilongjiang University of Science and Technology, PuYuan Road, SongBei District, Harbin, Heilongjiang 150022, China H [email protected]

Ли Дэгэнь,

Хэйлунцзянский университет науки и технологий 150022, ул. Пуюань, р-н Сунбэй, г. Харбин, г Хэйлунцзян, Китай И [email protected]

Wenbo Jia,

Heilongjiang University of Science and Technology, PuYuan Road, SongBei District, Harbin, Heilongjiang 150022, China [email protected]

Цзя Вэньбо,

Хэйлунцзянский университет науки и технологии 150022, ул. Пуюань, р-н Сунбэй, г. Харбин, г. Хэйлунцзян, Китай [email protected]

Chunping Ren,

Heilongjiang University of Science and Technology, PuYuan Road, SongBei District, Harbin, Heilongjiang 150022, China [email protected]

Жэнь Чуньпин,

Хэйлунцзянский университет науки и технологий, 150022, ул. Пуюань, р-н Сунбэй, г. Харбин, г. Хэйлунцзян, Китай [email protected]

Contribution of the authors

The authors contributed equally to this article.

Conflict of interests

The authors declare no conflict of interests.

The final manuscript has been read and approved by all the co-authors.

Information about the article

The article was submitted 09.11.2023; approved after reviewing 23.12.2023; accepted for publication 28.12.2023.

Вклад авторов

Все авторы сделали эквивалентный вклад в подготовку публикации.

Конфликт интересов

Авторы заявляют об отсутствии конфликта интересов.

Все авторы прочитали и одобрили окончательный вариант рукописи.

Информация о статье

Статья поступила в редакцию 09.11.2023 г.; одобрена после рецензирования 23.12.2023 г; принята к публикации 28.12.2023 г.