Fedoriachenko, S.

Mesheryakov, L.

Ziborov, K.

Зиборов, К.А.

Зіборов, К.А.

Мещеряков, Л.

Федоряченко, С.

English

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Гірнича електромеханіка  80 УДК 622.625  K. Ziborov, PhD, associated professor, S. Fedoriachenko, PhD, associated professor, L. Mesheryakov, PhD, professor (Ukraine, Dnepropetrovsk, National Mining University)   CALCULATION ALGORITHM OF TRACTIVE PROPERTIES AND SAFETY FACTOR  OF MINE SECTIONAL LOCOMOTIVE   Introduction. During the rock mass and coal transportation by the mining rail transport along the mining shafts, the rail’s functions are not only carrying static loads, but to transmit the dynamical stress and bogie mass to the rail track structure as well. The interaction area between wheel and rail facilitates transmitting braking and tractive forces. In order to increase the productivity of the mining rolling stock, an adhesion weight of the mod-ern mining locomotives increases either and now achieves 10-28 tons. This mass allows hauling heavier mining tub with significantly increased static loads on the rail track on the steeper slopes. Due to the fact, that existing mining rail tracks have been designed for much lower locomotives’ weight, increased axial loading on the rail track elements rocketed up to 1,5-2,5 times and for mining tub 7 times more.  However, increased adhesive weight did not solve the problem insufficient friction properties of rolling stock that caused unreasonable energy loss, reduction of its exploitation characteristics. Exploitation indexes of railway transport show, that to overcome friction up to 30 % of all consuming energy is necessary, and loss of material of friction pair amounts 15 % of producing metal [1.]. Each of mining drifts has its own climate environment, rail track profile and plan, bending radii, track in-cline, admissible haulage speed and braking distance etc. All these factors dependence on both economic and exploitation indexes, and on transport system reliability in general. Thus, study of the rail, wheel and their inter-action surface as a standalone system elements, wheel-rail interaction control, allow optimizing their work dur-ing difficult motion regime.    Modern design methods [2], which base on the scientific simulation and research approaches, facilitate def-inition of the location and character of arising dynamical loading and prevent their growth during forming within the mining vehicle chassis.  This prevents the following dynamical load transfer on the bolster structure. Thus, the structure selection and selection of mining machines parameters, which bases on the detailed analysis of running processes, might be an essential part of energy-mechanical system and its scheme development during development [2]. The purpose of the paper is to develop guidelines for mining rolling stock development (structural schemes, construction parameters) in order to achieve rational motion regimes with high exploitation characteristics and low energy consumption.  As it is known, the frictional surfaces move across the interaction area with tangential velocities V1 and V2. The bodies have the components of angular rotation velocity relatively to the base tangent to the surface. Differ-ent relations of the wheel set line speed V1 and speed of rotational motion V2 is characterized by the sliding ve-locity V . After each wheel’s turn on the interaction area resilient and plastic deformations arise. As a result, the fric-tion elements wheel-rail start negotiate through the finite size area. Taking into account existing rail track imper-fections and imperfections of contact area, let assume nominal and real contact areas. All force interactions of frictional pair wheel-rail are carrying within the real contact area. Therefore, the tangent reaction xyQ   is formed with elementary forces xyiQ , which act on each i-th point of the real contact area (fig. 1). Thus, during analytical research we need  to proceed from the elementary contacting area of the interacting bodies. These forces are directed opposite to the sliding velocity of i-th point iV  in the contact area. In gen-eral, the forces' vectors are inclined with an angle i  to their total force. xyQ  (fig. 2). The total force, in the case when    doesn’t independent on iV  direction, acts in the direction opposite to the wheel’s slipping velocity, and their scalar product VQxy  defines the power of dissipative forces in the contact area.  Figure 1 - Real contact areas of interacting bodies Гірнича електромеханіка  81 Thus: ikizixy QQ  cos1,                (1) where k  – amount of the  contact points in the slip-ping area;  – coefficient of friction limit. During mining locomotive motion along the min-ing drifts, the wheel contacts rolls both on the inner and outer rails, which have different curvature and gage width.  This fact induces the lateral displacement of the contact area though its width.  The worn wheel tread profile represents the total envelope profile of all rails that are contacting with tread [3]. The tread areas, which contact with rails most often, expose to inten-sive sliding, high contact stress and significant wear in comparison to other tread areas. Mine drifts with big amount of straight track segments lead to wear concentra-tion on the rolling area at the center of the wheel tread. In this case the wear of the flange is minimal. Otherwise, motion on the curvilinear rail track segments (most often case for coalmines) causes significant flange wear. As a result of frictional interaction of the wheel and rail, a clearance between contact surfaces forms. Uncon-trollable growth of the clearances provokes additional dynamical forces, acting on the bogie and track, that reduce the exploitation characteristics of the machine. However, there is possible to revise the machine design and additional kinematical movability either to reduce the duration of nonstationary motion regime. This is essential for mining conditions, which is marked by lots of un-favorable factors [4]. To provide the smooth wear of coupled kinematical members a coupling with local movability can be applied [4]. For example, locomotive of the module scheme, that includes a few sections. It allows for development of the ve-hicle with different trailing weight, energy supply system and necessary exploitation indexes. The distinguish feature of such locomotives is kinematical coupling between bogie and tractive section (Figure 3).  Such connection provides necessary relative movability and transmits vertical loading from frame to bogie, horizon-tal lateral forces – centrifugal force, reaction of overrunning rail, which has geometrical imperfections in all surfaces. Movability around the vertical axis is necessary for tractive bogie turn and in order to avoid odd couplings, because the pin does not carry the chassis weight; around lateral axis – for correct weight distribution between locomotive axles and reduction influence on the rail track; longitudinal movability is absent because the tractive effort transmits in this direc-tion. In order to define relations between kinematical and dynamical characteristics of mine rollingstock we need to provide the analysis of rail and wheel interaction, and to evaluate locomotives tractive and safety properties. The obtained data allows for assessment of the safety index, which is used to describe by safety coefficient [5]:  1tg1tgyzQQSF  (2)  where  – angle of wheel flange;   – friction coefficient; zQ  – normal rail reaction under ongoing wheel, N; yQ  – guiding force on the ongoing wheel, N. Local and regular rail imperfections lead to additional growth of guiding force yQ  that can cause the de-railment at some certain critical value (Figure 4, а). Reduction of guiding force can improve stability and predict derailment (Figure 4, b).   Figure 2 – Calculation scheme of forces and slipping velocities in the i-th point of contact area   a)  b) Figure 3 - (a) pin joint locomotive; (b) locomotive joint   Гірнича електромеханіка  82   a)      b) Figure 4 - The scheme of forces distribution during motion in the bending (a) and  on the straight segment (b).  The most complex motion regime is driving through curvilinear rail track with wheel flange climbing by both rear and front axles. This induces the rotation of tractive bogie in relation to mass center (Figure 5). Simultaneously, the middle section rotates around pin joint. At axial displacement of the wheels, a reaction force arises at the point of flange contact, which acts flatwise to motion direction. A sudden growth of these forces appears while wheel misa-lignment. To reduce reactive forces an additional local movability of kinematical pair coupling is necessary.   Figure 5 - General scheme of tractive bogie rotation in relation to mass center during wheel climbing (1- tractive bogie; 2 – middle section; 3 – pin joint)  The usage of mathematical simulation facilitates the designing and dynamical interconnection of mine roll-ing stock. The study of mining vehicle dynamics is provided via developed system of differential equations. As mentioned above, the characteristics of contact surfaces, and the pressing force define friction properties at the contact point. When the position of the wheel set in the rail track cannot be achieved through the friction forces, there is a two-point contact appears and lat-eral forces on the flange, which protects the wheel set from derailment (Figure 4 а, b). At the same time, an additional resistance force arises. However, the forces on the flange are connected with frictional components, which may lead to force reduction in the contact area. Thereby it facilitates the wheel climbing on the rail, especially on curved track sec-tions of small radius. To enhance the stability and safety, reduce load on the vehicle’s chassis and the track and to reduce motion resistance become possible while the usage of a new kinematical design where the kinematical pairs will have an additional local movability. Thus, it will reduce the number of redundant links with shortage of the unnecessary weight. To determine the appropriate value of mobility, providing the nec-essary performance, we can use modern means of computer simulation interoperability of mine transport and track. Taking into account the denoted above approach of wheel and rail interaction evaluation, the motor torque, reduced to the wheel set with rigid connection between the wheels, as a function of absolute motion velocity V  and relative velocity of the boundary layers iV   of the frictional pair wheel-rail, defines as Nixyiдв RQM1. The value xyiQ  for each wheel calculates according to [4].  Figure 6 - Safety factor relation to track curvature subject to structural scheme. V=4 m/s - - - -   sectional locomotive; ––––  conventional locomotive  Гірнича електромеханіка  83 Each point of the grip characteristics is corresponded by its distinguish en-ergy state of interaction process of the pair wheel-rail. Thus, alteration of the grip accompanies by a change of the state. At a constant locomotive speed V  altera-tion of the tangent component xyQ  takes place during increase of the boundary layer displacement of frictional pair material iV , which leads to energy loss in the contact area and unstable state of the eletromechanical system The relation between torque and angular velocity of the electric motor DC series excitation, which is the most popular in mine locomotives, has the follow-ing form [6, 7]:   FEдвFECMCCRMCCUC30230 .  ,                                 (3)  where CU  – voltage; 2R  – winding resistance; .двM – engine torque; MC – en-gine constant; EC  – EMF constant; FC – DC and magnetic flux constant. Expression (2) converted into the angular velocity of rotation of the wheel set with applied torque, can be written in a simpler form:  1.0 CMUCдвC  ,            (4)  where 0С  and 1С  – constants of the motor. Considering, that VRV    or   RVV /  , the expression (3) rearranges in the form:     21122202120.RCVVURCCUCM CCдв. (5)  The critical velocity can be determined by equating the limit values for traction grip and power to each other. The maximum permissible torque, at which there will be no grip disruption, will be defined from the expression of .двM  after substitution the relative velocity V  [4]. Using the relation between torque and angular velocity of tractive motor, we can determine the voltage CU as a function of the speed V for these conditions and formulate requirements for tractive motor control algorithm. (Figure 7). Conclusions. While constant locomotive speed V variation of the tangential component Qx occurs when the increment speed of the boundary layers of friction pair materials δV leads to energy loss in the contact area and the unstable state of the electromechanical system. To increase stability and safety, reduce the load on the vehicle and chassis, as well as on the rail track, additional movability of the kinematic connection of its members can be used. Basing on the thrust forces equations subject to adhesion and permissible power for definite condi-tions we can determine the values of engine voltage Uc as a function of the locomotive speed.  References  1. Исаев И.П. Проблемы сцепления локомотивов / И.П. Исаев, Ю. Лужнов. – М. : Машиностроение, 1985. – 238. 2. Зиборов К.А. Application of computer simulation while designing mechanical systems of mining rolling stock / К.А. Зиборов, В.В. Процив, С.А. Федоряченко // Научный Вестник НГУ – Д. : НГУ, 2013. – №6. – С. 55 - 59.  3. Зиборов К.А. . The frictional work in pair wheel-rail in case of different structural scheme of mining rolling stock / К.А. Зиборов, С.А. Федоряченко // Progressive technologies of coal, coalbed methane and ores mining – Netherlands : CRC Press, 2014. – С. 517 - 521.  4. Зиборов К.А. Характеристики фрикционной пары "колесо—рельс" шахтного локомотива при кинематических и силовых несовершенствах / К.А. Зиборов – М. : Горная электромеханика и оборудование, 2014. – №3 (100). – С. 26 - 32. 5. Гарг В.К., Динамика подвижного состава : пер. с англ. / В.К. Гарг, Р.В. Дуккипати ; под. ред. Н.А. Панькина. – М.: Транспорт, 1988. – 391 с. 6. Шахтарь П.С. Рудничные локомотивы / П.С. Шахтарь // М.: Недра, 1982. – 296 с. 7. Волотковский С.А. Рудничная электровозная тяга / С.А. Волотковский. М.: Недра, 1981.  Рекомендовано до друку: д-ром техн. наук, проф. Самусею В.І.   Figure 7 – Control algorithm 

Calculation algorithm of tractive properties and safety factor of mine sectional locomotive

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Calculation algorithm of tractive properties and safety factor of mine sectional locomotive

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