The need for development of new approach to modelling lift and head electric drives of quarry digger in the process of digging has been justified. The differences of the mathematical model suggested from the traditional approach are shown. The disadvantages of existing control systems in digger electric drives are revealed, the method of their removing is proposed

Semykina, I. Yu.

Zavyalov, V. М.

Electronic archive of Tomsk Polytechnic University

REFERENCES1. Zhuravlev A.N., Ryltsev I.K. Order assembly of drill cutter chisel bearings // The Bulletin of the Samara centre of science of the Russian academy of sciences. – 2005. – V. 7. – P. 442–449.2. Zhuravlyov A.N. Order assembly of tworow roller bearings // Assembly in mechanical engineering, instrument making. – 2004. –№ 10. – P. 14–17.3. Zhuravlev A.N. Influence of the structural factor of the ordered assembly on dynamic parameters of roller bearings // Heavy mechanical engineering. – 2006. – № 2. – P. 25–27.4. Bogomolov R.M., Morozov L.V. Selective computer assembly ofdrill cutter chisels // Assembly in mechanical engineering, instrument making. – 2003. – № 6. – P. 34–38.Received on 30.12.2006Mathematics and mechanics. Physics37The important link in technological chain of openpitmining for minerals is rock excavation. At the same time,recently there has been a decrease in the basic technicaland economic parameters of quarry equipment utilization, including quarry diggers. It can be partially explained by insufficient reliability of operated machines. Search of ways to further increase technological level of career diggers demands mathematical model developmentadequately describing their basic working processes.In order to describe dynamic processes taking placeduring work of quarry diggers, kinematic schemes of itsdrives are represented in the form of multimass mechanical systems. At the same time, the approach accordingto which full design schemes of drives are simplified upto twomass [1, 2] is rather widespread. Parameters ofsuch design schemes are thought to be constant. However, in actuality, design scheme parameters of digger drives is changed during the work. Thus, application of thestandard approach leads to mistakes at loading calculation of specific joints in quarry diggers and complicatesresearches addressed to increase their reliability.The most complex operation made by quarry diggeris the process of digging, from the point of view of external loadings occurrence. In this connection, descriptionof quarry digger work exactly in this mode is rather actual problem.During digging two electric drives take part simultaneously: lift and head, therefore at creating of thedescribed mathematical model it is necessary to consider both kinematic features of electric drives and theirmutual connection. Thus the greatest role will be played by change in parameters of electric drives, caused bychange in geometrical position of ladle and lever.The simplified design scheme of interconnected electric drives of lift and head is shown in Figure 1. On thisscheme the following designations are accepted: Jн is the total reduced inertia moment of the first mass of head drive,including inertia moment of engine rotor, reducer and head drum; сп is the reduced rope rigidity of head mechanism;Jп is the total reduced inertia moment of the first mass of liftdrive, including inertia moment of engine rotor, reducer liftdrum; сп the is total reduced rope rigidity of lift mechanism;mр, mк, mп are the masses of lever, ladle and rock respectively; Мн is the electromagnetic moment of head engine, reduced to speed of head drum; Мп is the electromagnetic moment of lift engine, reduced to speed of lift drum; ωн, ωп arethe angular speeds of the first weight of head and lift driverespectively; Fсн, Мсп is the force and resistance moment ofhead and lift drive respectively; vк is the linear speed of ladle head; ωк is the angular speed of ladle and lever.Fig. 1. Design scheme of lift and head electric drives in a quarry diggerIt is necessary to consider the design of ladle suspensionand lever mounting for definition of digger parameters deUDC 621.879.322.017.3:004.942MATHEMATICAL MODEL OF MECHANICAL PARTS INTERCONNECTED ELECTRIC DRIVES OF HEAD AND LIFT IN ROCK DIGGERV.M. Zavyalov, I.Yu. SemykinaKuzbass State Technical University, KemerovoEmail: Zaval@hotbox.ruThe need for development of new approach to modelling lift and head electric drives of quarry digger in the process of digging has been justified. The differences of the mathematical model suggested from the traditional approach are shown. The disadvantages of existing control systems in digger electric drives are revealed, the method of their removing is proposed.pending on their spatial position. Thus we shall believe thatladle is the material point, lever is the core with all the weightuniformly distributed on its axis. The constructive schemeused at model synthesis of interconnected electric drives ofdigger lift and head is shown in Figure 2. Here the followingdesignations are taken: α is the arrow inclination angle relative to horizon; β is the inclination angle of elevating roperelative to lever; rн is the pressure of head drum; rп is the radius of lift drum; lр is the full length of lever; dст is the lengthof an arrow from the saddle bearing up to the head block; Gкпis the ladle weight with rock; Gр is the lever weight; Р01 is thetangential force of resistance to cutting; Р02 is the normalforce of resistance to cutting; ϕн, ϕп are the angular positionsof head drum and lift drum respectively; sк is the value of lever rundown; ϕк is the lever angular position.Fig. 2. Schematic image of digger drives designTo obtain the equation of interconnected electric drivesmotion we shall take Lagrange’s equation of the second sort:where L=Wк–Wп is the Lagrange’s function; Wк is the kinetic energy; Wп is the potential energy; qi is the generalizedcoordinate; Qi is the generalized force. Solution of Lagrange’s equation for mechanical subsystem of interconnectedlift and head electric drives with selection of ϕн, ϕп, sк and ϕк,as generalized coordinates will be a system of equations:(1)where designations are as follows: F12н is the resilient force in a head rope; F12п is the resilient force in lift rope. Asit is possible to see, analyzing (1), besides resilient forces at work in head and lift electric drives of quarry digger there are forces of reaction in connections, and forces caused by change of drive parameters which createadditional forse, not considered at use of the traditionalapproach. Thus, the offered mathematical model reflects dynamic processes taking place in the mechanicalpart of head and lift drives more precisely.Resilient force in a head rope F12н is defined by thedependence:where s0 is the initial value of lever rundown. For definition F12п it is necessary to consider in details possibleconditions of a lift rope. With the change in ladle coordinates, leading to length reduction of the АВ piece(Fig. 2), lift rope sagging occurs in a real digger. Thus, alift rope can be only in stretched or in normal condition.In this connection the dependence of resilient force in alift rope on coordinates of lift and head drives is nonlinear and can be described as:where L0 is the initial value of rope length in the pieceАВ. Current value of which is defined as:It is necessary to consider when using this model(1), that weight of rock increases during the excavationprocess. Rock weight change mп can be described by thedependence assuming, that ladle is fully filled at its raising to the maximal angle of elevation ϕmax. In this case:where Vк is the ladle volume; ρп is the rock volumetric mass.Besides rock mass, rigidity of resilient connectionsalso changes during digging. This parameter depends onplenty of factors, most essential of which is ropelengthening. As the general length of head rope remainsconstant, the change of its rigidity will be insignificantwhereas rigidity of lift rope changes in wider limits. Total rigidity of lift rope will be defined as [3]:where Е is the rope resiliency module; F is the total area of all wires in a rope; LВС is the length of a lift ropefrom the elevating drum up to the head block (Fig. 2).During considered mathematical model operation itis necessary to consider changing character of electricdrives loading. Magnitude of loading is influenced byspatial arrangement of ladle and lever, soil heterogeneity, coordination inconstancy of lift and head motions,casual changes in face height and turning angle of digger during work [4]. We shall believe that forces of resistance to cutting Р01, Р02 have casual character, ladleweight with rock Gкп has determined character, and leverweight Gp is constant.Head drive loading consists of composed resistanceforces directed towards ladle lever. Considering direction of forces shown in Fig. 2 the equation of this loading has the view:,ïAB BCEFc =L +L0 maxmax 0max( ) ,  at ;,  at ,ê nï ê êï ê n êVmm Vρϕ ϕ ϕ ϕϕ ϕρ ϕ ϕ⎧ = − <⎪ −⎨⎪ = ≥⎩2 2 2 cos( ).AB ê ñò ê ñò êL s d s d α ϕ= + − −12 0 012 0( ( )),  at ;0,  at ,ï ï ï ï AB AB ï ïï AB ï ïF ñ r L L L L rF L L rϕ ϕϕ= − − > −⎧⎨ = ≤ −⎩12 0( ( )),í í í í êF ñ r s sϕ= − −12 122 212 122122 2; ;( ) cos2;sin 2 2( )2( )2 12í í í í ï ï ï ïí ïp ní ð ê ê ê n ê ê ñí ï êêð ê np nn cn p ê ê ê ê n ê ê ê ê êêp pp ê p ê nd M r F d M r Fdt J dt Jl mF m s m m s F F vdtdvdt m m ml mF M m v s m m v s sdtddt l lm s m m mω ωω ω ββ ω ω ωω− −= =⎛ ⎞+ − + + − − −⎜ ⎟⎝ ⎠= + +⎛ ⎞− − − − + −⎜ ⎟⎝ ⎠= ⎛ ⎞− + + +⎜ ⎟⎝ ⎠2;; ; ; ,êí n ê êí n ê êsd d ds dvdt dt dt dtϕ ϕ ϕω ω ω⎧⎪⎪⎪⎪⎪⎪⎪⎨⎪⎪⎪⎪⎪⎪⎪ = = = =⎩,ii id L L Qdt q q⎛ ⎞∂ ∂− =⎜ ⎟∂ ∂⎝ ⎠Bulletin of the Томsк Pоlytеchnic University. 2007. V. 310. № 338(2)Lift drive loading is defined as the moment of forcecomposed of resistance forces, directed perpendicularto ladle lever. The equation of this loading has the view:(3)For final description of interconnected lift and headelectric drives loading we shall show likelihood characterof resistance forces to cutting Р01, Р02. As a rule, duringcalculations it is accepted that Р02=0,1Р01 [5]. It is possible to write resistance to cutting for tangential force as: (4)where P–01(t) is the mathematical expectation of resistanceforce to cutting; Pн01(t) is the lowfrequency casual component characterizing variation of chip thickness; P в01(t) isthe highfrequency casual component characterizing variation of rock resistance to excavation process. Each of theserandom variables is described by corresponding correlationfunction. Thus, the equations (2)–(4) completely defineloading of lift and head electric drives in a quarry digger.The analysis of interconnected lift and head driveswork was made by the method of computer modeling bymeans of the program written in Delphi 7 environment.Parameters of quarry digger EKG8I with electric drive,built by the system TVGD, were used during modeling. Condition when the ladle lever is located verticallyand the ladle stays on the ground was accepted as initialposition. Modeling was conducted in two modes: in amode of soil excavation at presence of sharpchangingcomponent loading and increasing rock mass, and in amode of loaded ladle lowering with constant rock mass.The results of modeling are presented in Fig. 3–6.Fig. 3. Current of anchor circuit in the lift drive Comparing transitional processes of anchor circuitcurrent in the lift drive, obtained by means of modeling(Fig. 3) with similar transitional processes of a real diggerpresented in [1] it is possible to reveal their similarity whichconfirms adequacy of the developed mathematical model.According to [2], regulators of control systems indigger drives are adjusted to technical optimum proceeding from parameters of electric part and engine moment of inertia. However presence of resilient connection or parameters change in drives are not considered.Hence, in digger real operating conditions proceedingin it processes will differ from technical optimum. Analyzing schedules of ladle position, shown in Fig. 4, it ispossible to draw a conclusion that fluctuations causedby rope resilience occur at excavation operation and atloaded ladle movements in space. In Fig. 5 and 6 it is visible that elastic fluctuations, both in the head and inthe lift rope have frequency nearby 2...3 Hz and amplitude of about tens of кN, which represents double excess of nominal loads. Presence of such fluctuations essentially increases fatigue wear process and, hence, reduces functioning reliability of rope and digger itself.Fig. 4. Ladle position in spaceFig. 5. Resilience force in the head drive Fig. 6. Resilience force in the lift drivesoil extractionloaded ladlelowerings, m ϕ, rad01 01 01 01( ) ( ) ( ) ( ),í âP t P t P t P t= + +01 cos cos .2pñn ê p ê ê êï ê êlM P s G s G sϕ ϕ⎛ ⎞= + − +⎜ ⎟⎝ ⎠02 ( )sin .ñí êï ð êF =P + G +G ϕMathematics and mechanics. Physics39From the aforesaid it is possible to draw a conclusion that application of subordinate regulation systemsfor digger electric drives can not provide demandednonfailure operation of its work. Replacement of subordinate regulation systems by more perfect systemsthat would take into account dynamic processes is necessary in order to increase reliability of quarry diggers.It is necessary to use mathematical model of interconnected head and lift drives in diggers to synthesize suchcontrol systems.Bulletin of the Томsк Pоlytеchnic University. 2007. V. 310. № 340REFERENCES1. Volkov D.P., Kaminskaya D.A. Dynamics of electromechanical systems in diggers. – Moscow: Mashinostroenie, 1971. – 384 p.2. Nosyrev M.B., Karyakin A.L. Calculation and modeling of SAUmain electric drives in singleladle diggers. – Sverdlovsk: Publishinghouse SGI, 1987. – 88 p.3. Stepanov A.G. Machine dynamics. – Ekaterinburg: UrO RAS,1999. – 392 p.4. Gaydukevich V.I., Titov V.S. Random loading of power electric drives. – Moscow: Energoatomizdat, 1983. – 160 p.5. Poderni R.Yu. Mountain machines and complexes for open works.In 2 v. – V. 1. – Moscow: Publishing house MSGU, 2001. – 422 p.Received on 27.12.2006According to the modern ideas about the process,loose material (LM) production occurs in the form ofstochastic shifts of substance blocks of arbitrary, constantly changing shape with low substance concentration on the boundaries between them [1–3]. Arcs formed at periodic formation and crushing of block structure may take any profiles, however, their average shapeshould be rather smooth. The process may be presentedmore simplified in the form of the system of periodically appearing and destructing arcs situated in the wholematerial volume. In this case lower arcs crushing precedes the crushing of upper ones and so the parameters ofLM production are determined in general by the conditions of arc formation over the discharge outlet [1–5].In connection with the examined mechanism of outflowprocess the supposition about the fact that substancemotion in flared section of outlet zone occurs under theinfluence of stress field appearing due to discharge outlet opening is seemed to be physically based [2, 3, 6, 7].The subject of the given investigation is a hydraulicor mass (in foreign terminology «mass flow») flow shapeof loose material. Such shape is typical for well loosesubstance (as a rule for those having low humidity andcontent of fines) and at its presence the area of still material occurs only in the low part of the container (zones CEM and NFD in Fig. 1). According to the proposeddesign diagram it is accepted that in the upper cylindrical area ABCD the rate and volume density of the material are constant and undergo changes only in flared section CMND of outflow zone. The validity of such supposition is confirmed by numerous experimental data ofvarious authors.To close the combined equation of motion and continuity of steady axissymmetric outflow of compressible LM in spherical coordinates the stress tensor constituents are presented according to the hypothesis ofP.I. Lukyanov [2] about stress redistribution in LM layer at discharge outlet opening, widely used at present byvarious authors. Expression (1) [7] describing the forcesinfluence on substance layer having the shape of a spatial cone the special case of which is the ratio of BussineskFrelich is used in the given paper [2]:(1)Here Δσr is the radial stress in material array; ν is thecoefficient of distribution ability; q is the vertical stressfunctioning on the level of discharge outlet plane; β isthe slop angle of container walls to the vertical.Taking into consideration the results of numerousinvestigations both theoretical and experimental havingshowed that loose material motion near the dischargeoutlet is close by the shape to the radial one [2–4, 6],the system may be considerably simplified. Along the lines with constant value of angle θ for the case of radialmotion we obtain the following combined equation:2cos .2(1 cos )rq ννν θσ β−∇ = −UDC 622.831.3:622.33ON IMPROVEMENT OF MATHEMATICAL MODEL OF LOOSE MATERIAL PRODUCTIONYu.E. ProshuninNovokuznetsk branch of Tomsk Polytechnic UniversityEmail: nftpu@inbox.ruOn the bases of studying the history of formation of stress fields and densities in fixed layer of cohesive compressed loose material, formation of secondary stress field, appearing in the substance layer under the external action, and determining the conditions of massivedestruction the mathematical description of loose material production has been proposed.

Mathematical model of mechanical parts interconnected electric drives of head and lift in rock digger

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