Studying mathematical model of mine and quarry pneumatic lifting equipment in skip - guidance devices systems

Transcription

1 IOP onference Series: aterials Science an Engineering PAPER OPEN AESS Stuying mathematical moel of mine an quarry pneumatic lifting equipment in skip - guiance evices systems To cite this article: V Kitaeva et al 05 IOP onf. Ser.: ater. Sci. Eng View the article online for upates an enhancements. This content was ownloae from IP aress on 03//08 at :

2 RTEP04 IOP onf. Series: aterials Science an Engineering 8 (05) 03 oi:0.088/ x/8//03 Stuying mathematical moel of mine an quarry pneumatic lifting equipment in skip - guiance evices systems V Kitaeva, Yu ANikolaev, A V Taranov 3, A D ehtiev 4 National Research Tomsk Polytechnic University,Tomsk, Russia Professor of the Energetics Department in Karagana State Technical University, Karagana, Kazakhstan 3 Hea of Energetics Department in Karagana State Technical University, Karagana, Kazakhstan 4 Hea of The technology an communication systems Department in Karagana State Technical University, Karagana, Kazakhstan barton.kz@mail.ru Abstract. The article is evote to etermining the maximum loas acting on the guie roller evices of skips in the trunk of mine an quarry overpass lifting equipment necessary to evelop methos for calculating the guiing evices..introuction There are two basic ways of mining: open pit an unergroun in the mining inustry: open pit an unergroun. Unergroun mining less profitable, however, it is more environmentally frienly. In aition, this metho is essentially inevitable ue to the fact that the major mineral reserves are at greater epths an in the future will nee to solve the problems of evelopment of mineral eposits eep mines. The evelopment of the mining sector an the eepening of mining operations require a new type of transport, justifie an evelope in the works of Bogatyrev D, Kiselev V I, Kartaviy N G, Saginov A S, Nechyporenko S N, Piskunov O, Y.A. Nikolaev Yu A skip pneumatic lifting equipment esigne to reuce the cost of transportation of the rock mass..analysis of mine SPLI work The cycle of operation of pneumatic lifting equipment consists in the following (Figures an ). Skips 4, 5 are loae at the lower en of the mine from ispensers 5, 7 jet of rock mass falling from a height of more than ten meters in a skip an has a significant ynamic loas on the bottom an sies of the latter. After loaing the skip is inclue working boy (turbo blower) an compresse air begins to flow uner the bottom of the skip. When a certain overpressure skip is accelerate an begins to accelerate to the steay spee, etermines the performance blowers. The main part of the way to the top mark of the mine skips moves at a constant spee, an when approaching the upper stop evice 6, 9 is inhibite ue to ischarge of the compresse air to the atmosphere through the air valves 9 an 0. After entering the mine skip 4 in abutment evice 6 it is unloae through the sie walls into the hopper 7, an 5 of career skip installation, after fixing in the upper rotary evice 9, bens an unloae into the hopper 8. All the time of unloaing the skip 4 mine pneumatic lifting installation it is supporte by positive pressure in the cavity of the barrel 3. After unloaing the skip 5 last of career installation returns to its original position, stops are remove an skip 5 uner the action of gravity starts to fall own by squeezing uner a cushion of air. ontent from this work may be use uner the terms of the reative ommons Attribution 3.0 licence. Any further istribution of this work must maintain attribution to the author(s) an the title of the work, journal citation an DOI. Publishe uner licence by Lt

3 RTEP04 IOP onf. Series: aterials Science an Engineering 8 (05) 03 oi:0.088/ x/8//03 Figure. The structural layout of mine SPLI: working boy (turbo blower);, 9 air lock; 3 overpass with the guie an sealing evices; 4 skip; 5 ispenser; 6 the upper stop; 7 unloaing hopper; 8 the lower laning evice. Figure. The structural layout of SPLI open pit: working boy (turbo blower); air pipe; 3, 0 air lock; 4 overpass with the guie an sealing evices; 5 skip; 6 lower rotating part of the overpass; 7 ispenser; 8 unloaing hopper; 9 the upper rotating part of the overpass with a focus. The lowering spee of skips 4 an 5 an their laning on the lower laning gear 6, 8 is regulate by air locks an 3. The main an most crucial element of mine an career pneumatic lift systems are rails movement the skip evice performance epens on the reliability an urability of these plants.

4 RTEP04 IOP onf. Series: aterials Science an Engineering 8 (05) 03 oi:0.088/ x/8//03 However, the task of creating the guie evices of skips for mines an quarries pai insufficient attention has hinere the implementation of these machines in prouction. Therefore there is a nee to stuy an selection of the parameters guiing evices of skips of mine an career pneumatic lifting equipment. Large problem of etermining the parameters of guiing evices, one of the main elements of these systems, is not sufficiently evelope an nees to be resolve, as the reliable operation of skip pneumatic lift systems without solving this problem is impossible. To o this, you must evelop a methoology for calculating the guiing evices of mine an career pneumatic lifting equipment, as one of the main elements of these installations. In this regar, the choice of parameters an the esign proceure of guiing evices of skips of mine an career pneumatic lifting equipment, is an actual problem. Accoring to the kinematics of the pneumatic lifting equipment, the following basic operating moes guiing evices: - loaing the skip; - the skip entry in the guie evice with maximum acceleration; - motion of the skip in the guie evice with maximum acceleration; - the skip entry in the guie evice with a maximum spee; - uniform motion of the skip in guiing evices with a maximum spee; - unloaing the skip. Uner each moe guiance evices are subjecte to static an ynamic loas (Figures 3 an 4), representing ifferent kins of anger. Reaction of rollers epen on how far from the center axis of the vessel its mass is. Therefore, when esigning pneumatic lifting equipment is necessary to ensure such conitions that its center of mass is as close as possible to the axis of symmetry. But in reality, this conition is very ifficult to provie because of the uneven loaing. a) b) Figure 3. Scheme of loas guiing evices pneumatic lifting equipment when rolling the skip on rollers: а) the movement of the skip to guie evices with maximum acceleration; b) uniform motion of the skip in guiing evices with a maximum spee. 3

5 RTEP04 IOP onf. Series: aterials Science an Engineering 8 (05) 03 oi:0.088/ x/8//03 a) b) Figure 4. Scheme of loas guiing evices: а) the skip entry in the guie evice with maximum acceleration; b) the skip entry in the guie evice with a maximum spee. In aition, it is necessary to take into account the ynamic processes when ajusting the spee of the vessel an the conitions for its entry in the guie roller evices. The maximum values of reaction of rollers at a coal mine pneumatic lift installation epens only on the iameter (the skip-uty) an practically o not epen on the thickness of the wall of the skip. For ore mine pneumatic lifting installation with thicker walls the skip observe a significant reuction reaction of rollers by increasing the wall thickness of the skip. By increasing the iameter of the intensity of the reuction reaction the skip of rollers weakene. The maximum values of reaction of rollers an coal an ore of career pneumatic lift installation epen not only on the iameter (the skip loa capacity) an the wall thickness of the skip. By increasing the iameter of the intensity of the reuction reaction the skip of rollers weakene. The analysis of the results of a numerical calculation using license software shows that etermines the loa in etermining the esign parameters of the skip, as a rule, local external forces generate by reactions of rollers guiing evices [, ]. To solve the problem of etermining the ynamic interaction with the walls of the guie evices the skip (career overpass) evelope the esign scheme an a mathematical moel of the motion of skips of mine an career pneumatic lift systems (Figures 5 an 6). A system of ifferential equations of motion the skip in the guie evice. Unlike the previously known mathematical moels [3], the resistance in the guie evices are recore accoring to the eformation of the roller over time. The stuy parameters an guiing evices pneumatic mine lifting installation uring perios of unsteay motion the skip, as well as the regulation of its spee accomplishe using a mathematical moel, which is a system of seven ifferential equations that escribe the motion the skip along the axis of the shaft. This mathematical moel is base on the calculation scheme shown in Figure 5. 4

6 Figure 5. Design scheme of mine pneumatic lifting installation: а) general view; b) cross-section. At constant pressure vessels uner P = const system of ifferential equations goes to the following form (): ; ; ; ; ; ; ) ( t t t t t t t t t t t t R k F F S P P t z fr yy fr c a () where Z is current coorinate of movement the skip measure from the mark of the barrel bottom, m; М is the total mass of the payloa an the boy of the skip, kg; Р is current absolute air pressure in the cavity beneath the vessel barrel, Pa; а Р is the current value of the atmospheric pressure, Pа; RTEP04 IOP onf. Series: aterials Science an Engineering 8 (05) 03 oi:0.088/ x/8//03 5

7 RTEP04 IOP onf. Series: aterials Science an Engineering 8 (05) 03 oi:0.088/ x/8//03 S is sectional area of the skip, m; c F g is useful resistance force, N; F fr. yy is resistance k fr С force the skip in stem sealing evices, N; Ri i is reaction of rollers of guiing evices,n; R k is coefficient of rolling friction, N; is rigiity of guiing evices; fr R is raius of the roller of guie evice, m; 0,, 3, 4, 5, 6 is eformation of rollers of guiing evices; a is the isplacement of the center of mass of the laen the skip; α is the angle between the X axis an the irection of isplacement of the center of mass; β is viscous friction coefficient. Uner α = 0 an P = const (): 0 z ( P Pa ) S F F c t x x x t t fr. уу k fr С R 0 x () The resultant of the research esign scheme of mine pneumatic lifting installation an bears the highest possible operating forces is the basis for esign choice guiing evices, calculation of stresses acting in their elements by using the mathematical apparatus of the finite element program ANSYS et al., the selection structural materials an the isc rim roller, testing the strength an stability. The above mathematical moel an its numerical solution results allow proceures to evelop an algorithm for calculating the parameters guiing evices mine pneumatic lifting equipment. To solve the problem of etermining the ynamic interaction with the walls of the guie evices career skip evelope analytical moel an mathematical moel of motion skips career pneumatic lifting equipment. A system of ifferential equations of motion skip in the guie evice. Unlike the previously known mathematical moels resistance guiing evices recore in the roller strain epening on time. The stuy parameters an guiing evices career pneumatic lifting mechanism uring perios of unsteay motion skip, as well as the regulation of its spee accomplishe using a mathematical moel, which is a system of seven ifferential equations that escribe the motion skip along the career of an overpass. This mathematical moel is base on the calculation scheme shown in Figure 6. At constant pressure vessels uner P = const (3): n z k ( ) sin P Pa Sc F c Ffrуr i t R0 i ; ;... t t t t n n... ; n t t (3) c where is the angle of the career of an overpass to the horizon; n is the number of guiing evices are simultaneously in contact with loaer. The above mathematical moel an the results of its numerical solution allowe us to evelop an algorithm for calculating the parameters of proceures guiing evices career pneumatic lifting equipment. 6

8 RTEP04 IOP onf. Series: aterials Science an Engineering 8 (05) 03 oi:0.088/ x/8//03 Numerical stuy of the ynamics of motion skip pneumatic lifting equipment was carrie out by a licensing system atlab (atrix Laboratory), which is an interactive system for performing engineering an scientific calculations, an is focuse on work with arrays of ata [4,5]. The system makes it easy to exchange information with the wor processor icrosoft Wor, in particular to carry any text an images to the clipboar or rea text strings from the clipboar as executable instructions. The system atlab are special means of solving the auchy problem for x systems of orinary ifferential equations given in explicit F( t, x) t, an in the implicit x F( t, x) t. Here -matrix - the so-calle ODE solver (solver ODE), allows the user to select the metho, the initial conitions, etc. Figure 6. Open pit pneumatic lifting equipment scheme: а) general view; b) cross-section. To solve ODE systems in atlab various methos implemente. Their implementation calle ODE solvers. Solvers implement the following methos for solving systems of ifferential equations: - Oe 45 is one-step explicit Runge-Kutta 4th an 5th orer. This is a classic metho recommene for the initial sample solutions. In many cases, it gives goo results; - Oe 3 is one-step explicit Runge-Kutta n an 4th orer. In moerate rigiity of the system of ODE an low accuracy requirements, this metho can provie a gain in spee solutions; - Oe 33 is multi-step metho of Aams-oulton-Bashvorta variable orer. The aaptive metho that can provie high accuracy solutions; 7

9 RTEP04 IOP onf. Series: aterials Science an Engineering 8 (05) 03 oi:0.088/ x/8//03 - Oe 5s is multi-step metho of variable orer (from the first to the fifth, the efault is 5), using the formula of numerical ifferentiation. This aaptive metho, it shoul be applie, if the solver Oe 45 not provie solutions; - Oe 3 s is one-step metho, which uses a moifie Rosenbrock formula of orer. an provie a high computational spee with low accuracy; - Oe 3t is trapezium metho with interpolation. This metho gives goo results in solving problems escribing oscillators with nearly harmonic output signal; - Oe 3tb is implicit Runge-Kutta metho at the beginning of the solution an the metho using the inverse of ifferentiation formula of orer in the future. At low precision, this metho may be more efficient than Oe 5s. All solvers can solve systems of equations of the explicit form y = F(t, y). Solvers Oe 5s, Oe 3s, Oe 3t, Oe 3tb can solve the equations of implicit form y = F(t, y). All of these methos are incorporate in a means of solving ifferential equations Simulink. Solution of the mathematical moel in the application program atlab Simulink is shown in Figure 7. Figure 7. Solving mathematical moel of pneumatic lifting equipment in the application program atlab Simulink. 8

10 RTEP04 IOP onf. Series: aterials Science an Engineering 8 (05) 03 oi:0.088/ x/8//03 As escribe in the following functions for the solution of systems of ifferential equations, the following notation an rules: F is the name of the ODE-file, that is a function of t an y, which returns a column vector; tspan is the vector etermining the integration interval [t0 tfinal]. To obtain solutions at specific times t0, t,tfinal (arrange in orer of ecreasing or increasing), you must use tspan = [t0 t tfinal]; y0 is the vector of initial conitions; options is argument to create functions oeset; p, p is Arbitrary parameters passe to the function F; T, Y is solution matrix Y, where each line correspons to the time returne in the column vector T. We now turn to the escription of functions for solving systems of ifferential equations (we enote the concept solver one of the possible numerical methos for solving ODE: oe 45, oe 3, oe 3, oe 5s, oe 3s, oe 3t, oe 3tb): [T, Y] = solver ( F, tspan, y0) integrates the system of ifferential equations of the form y = F(t, y) the interval tspan with the initial conitions y0. F a string containing the name of the ODEfile. The function F (t, y) must return a column vector. Each row in the array of solutions Y correspons to the time returne in the column vector T. [T, Y] = solver ( F, tspan, y0, options ) gives a solution similar to that escribe above, but with the parameters etermine by the values of the argument options, create with oeset. ommonly use options inclue permissible value of the relative error RelTol (efault e 3) an the vector of allowable values of the absolute error AbsTol (all the components efault to e 6; [T, Y] = solver ( F, tspan, y0, options, p, p, ) provies a solution similar to that escribe above, by passing aitional parameters p, p Use options = [], if no options are specifie. ODE solver enables the prouction of solutions of systems of n equations. ODE system can be either homogeneous or heterogeneous. From the graphs, we can raw conclusions about the nature of ynamical fluctuations skip to the transverse axis of the shaft irection (Figure 8,9). Perioic fluctuations are ampe, where amping is exponentially amping factor for mechanical parameters of the ynamic system "skip - guiing evice" has ifferent meanings, which can be calculate from the equation. The experimental moel velocities an accelerations in the transverse irection are use to etermine the loas on the rollers an the guie evices powers are compare with the values obtaine from the mathematical moel. Reveale that the maximum ynamic loas on the guie evice by pneumatic skip lifting equipment as it moves are etermine epening on the weight of the loae skip, the shift of its center of mass, the angle of the overpass to the horizon an the coefficient of ynamic (3,4): R k V R i i o М g ko V М g n a l, (3) cos c, (4) Where V the velocity of the skip, m/s; k is stiffness coefficient overpass; o a is the isplacement of the center of mass of the laen skip; l is the istance between ajacent tiers of guiing evices; k k V is ynamic factor. c 9

11 RTEP04 IOP onf. Series: aterials Science an Engineering 8 (05) 03 oi:0.088/ x/8//03 Figure 8. Results of the solution of the mathematical moel of pneumatic lifting equipment in the application program atlab Simulink: а) epenence of the eformation roller from time to time; b) epenence of the acceleration skip from time to time; c) epenence on the time of travel Skip; ) epenence of the rate on the time skip. Figure 9. Walkthrough skip several tiers guiing evices: а) passage of two tiers; b) passage of fifteen tiers. 0

12 RTEP04 IOP onf. Series: aterials Science an Engineering 8 (05) 03 oi:0.088/ x/8//03 3.onclusions Develope an researche mathematical moel of the motion skip in systems of quarry pneumatic lifting equipment an mine have establishe patterns of interaction "skip - guiing evices". It was foun that the system of "skip - guiing evices" most loae at the time of entry unevenly loae skip stage vanes. Reveale that the maximum ynamic loas on the guie evice by pneumatic skip lifting equipment as it moves are etermine epening on the weight of the loae skip, the shift of its center of mass, the angle of the overpass to the horizon an the coefficient of ynamic. The aequacy of the emerging ynamic loas on the roller guie evice is confirme by experimental research moels skip pneumatic lifting equipment. References [] Zhautikov B. A. Analysis of efforts on housing skip open pit pneumatic lifting equipment Bulletin of the National Engineering Acaemy of the Republic of Kazakhstan P [] Nikolaev Yu A an Ruaya R P 98 A mathematical moel of pneumatic shaft skip lifting equipment Proceeings of the universities ining Journal 0 P. 88. [3] hen K, Dzhiblin P an Irving А ATLAB's mathematical research oscow: ir, 00 P. 346 [4] hernih I.V. SIULINK: creation environment engineering applications 003 Мoscow: DIALOG-IFI, 003 P. 496 [5] Porshnev S.V. Using Simulink package to escribe the ynamics of oscillating systems with several egrees of freeom Electronic scientific journal «Bulletin of Omsk State Peagogical University» 006 Р. 5