DETERMINING THE MAGNITUDE OF TRACTION FORCE ON THE AXES OF DRIVE WHEELS OF SELF-PROPELLED MACHINES

Transcription

1 Easten-Euopean Jounal of Entepise Technologies IN /7 ( 88 ) Volkov V P omuvannia optymalnoho tempeatunoho stanu tanspotnoho dvyhuna za akhunok kompleksnoho kombinovanoho pohivu [Text] / V P Volkov I V Hytsuk // Vestnyk KhNADU 2015 Issue 69 P Mohamed E Development and analysis of a vaiable position themostat fo smat cooling system of a light duty diesel vehicles and engine emissions assessment duing NEDC [Text] / E Mohamed // Applied Themal Engineeing 2016 Vol 99 P doi: /japplthemaleng Che idik N A Recent advancement of nanofluids in engine cooling system [Text] / N A Che idik M N A iti Mohd Yazid R Mamat // Renewable and ustainable Enegy Reviews 2017 Vol 75 P doi: /jse Xu Z Compaison of in-cylinde combustion and heat-wok convesion pocesses of vehicle engine unde tansient and steadystate conditions [Text] / Z Xu J u J Liu Z Yuan J hu L Tan // Enegy Convesion and Management 2017 Vol 132 P doi: /jenconman Gabiel-Buenaventua A Enegy ecovey systems fo etofitting in intenal combustion engine vehicles: A eview of techniques [Text] / A Gabiel-Buenaventua B Azzopadi // Renewable and ustainable Enegy Reviews 2015 Vol 41 P doi: /jse Наведено принципи утворення тягової сили тракторів та автомобілів Точка прикладання тягової сила знаходиться на осі приводного колеса Причому величина тягової сили приблизно у два рази перевищує реактивну силу що передається від дороги на приводне колесо Визначення принципів утворення тягової сили дозволяє інтенсифікувати дослідження технічних та енергетичних засобів загалом та обґрунтувати принципи зменшення негативного впливу рушіїв на родючий шар ґрунту зокрема Ключові слова: тягова сила приводне колесо самохідні машини енергетичний засіб трансмісія Приведены принципы образования тяговой силы тракторов и автомобилей Точка приложения тяговой силы находится на оси ведущего колеса Причем величина тяговой силы примерно в два раза превышает реактивную силу что передается от дороги на приводное колесо Определение принципов образования тяговой силы позволяет интенсифицировать исследования технических и энергетических средств в общем и обосновать принципы уменьшения негативного влияния движителей на плодородный слой почвы в частности Ключевые слова: тяговая сила приводное колесо самоходные машины энергетическое средство трансмиссия UDC DOI: / DETERMINING THE MAGNITUDE O TRACTION ORCE ON THE AXE O DRIVE HEEL O EL-PROPELLED MACHINE G Golub Docto of Technical ciences Pofesso Head of Depatment Depatment of tactos cas and bioenegosistem* gagolub@uknet V Chuba PhD Associate Pofesso Depatment of tanspot technologies and means in AIC* vvchuba@uknet *National Univesity of Life and Envionmental ciences of Ukaine Heoiv Oboony st 15 Kyiv Ukaine Kukhaets Docto of Technical ciences Associate Pofesso Head of Depatment Depatment of mechanical engineeing and agoecosystems Zhytomy National Agoecological Univesity tayi blvd 7 Zhytomy Ukaine kikhaets@gmailcom 1 Intoduction A clea undestanding of the application pocesses that ae means fo the pupose of thei futhe impovement It also concens the issues of fomalization of the pocess of ceating taction foce on the dive wheel of tactos and vehicles This is especially impotant fo the agicultual machine-tacto units that cause a numbe of poblems elated to the inteaction between unning systems and the suface of fetile laye of soil olving the poblems aimed at binging down negative impact of engines on the fetile laye of soil is a elevant task today 2 Liteatue eview and poblem statement The occuence of taction foce on the dive wheel is often explained by the fact that at the point of contact between the wheel and oad suface the toque (ig 1 3) causes tangent foce O The counteaction of oad to this tangent foce 50 G Golub Kukhaets V Chuba 2017

2 Applied mechanics is expessed by a eactive foce tansfeed fom the oad to the dive wheel This foce is diected in the diection of motion of the vehicle and it is called the taction foce ТС Taction foce fom the wheels is tansfeed to the dive axle and futhe on the fame focing the vehicle to move [1] This explanation of the oigin of taction foce gives ise to consideable doubts since the foces of eaction chaacteize only the stess that is ceated by a dive wheel while inteacting with the oad Reaction foces ae not the activ ones Taction foce fom the oad suface by no means can be passed on to the fame of a vehicle and it cannot set it in motion Thee is anothe explanation The toque fom the vehicle engine is passed on to the diving wheels It then causes fiction foce at the point of contact between the wheel and the oad (a foce of oad counteaction to the otation of dive wheel) This foce is also called tangent o tangential eaction The fiction foce as the sum of tangential eactions of the dive wheels is equal to the taction foce which is tansfeed to the fame of the vehicle Taction foce sets the vehicle into a fowad motion Thus the taction foce is epesented as the sum of stesses in a hoizontal diection which aise as a esult of soil counteaction to the otation of the wheel [2] uch explanation is also false because fiction foce is the passive foce and it cannot move a vehicle ig 1 Diagam of foces and inteaction between the wheels and the oad duing ascending motion of a bus ig 2 Diagam of foces and inteaction between the wheels and the oad duing hoizontal motion of a feight vehicle ig 3 Diagam of foces and inteaction between the wheels and the oad duing ascending motion of a ca One moe vaiant of a false explanation which is in pinciple simila to the pevious ones is as follows The toque of the engine applied though the mechanisms of tansmission to the dive wheels of a vehicle causes otation of the wheels In the place of contact between the wheel and the oad the toque gives ise to the tangent foce O while the tangent eaction Т is ceated by the oad and it is equal by magnitude to the tansitional foce but diected in the opposite diection Total tangent eaction of the dive wheels is tansmitted to the ea axle and causes the motion of the whole vehicle which is why it is called the taction foce [3] Anothe explanation fo physical essence of the occuence of taction foce on the dive wheels is given in [4] It is agued by analogy to the descibed above that the foce on the adius of a wheel which acts fom the toque is called the tangent foce of the wheel thust This foce applied to the wheel due to the fiction and adhesion in contact with suppoting suface is balanced by the esultant eaction of soil equal to it by magnitude but oppositely diected Given this the diving foce is the foce applied in the cente of the wheel and diected in the diection of motion of the machine In ode to explain how the foce got thee the foce of soil eaction is called an extenal foce while the tangent foce intenal And since the intenal foce cannot lead to displacement then the machine has to move unde the action of the extenal foce the eaction of soil allibility of this explanation is pedetemined by the abitay choice of teminology and by the absence of clea explanation of the physical essence of the pocess of fomation of the taction foce of the dive wheel Pape [5] pesented a toque on the dive wheel as a pai of foces One of the foces is applied in the cente of the wheel This is a mistake as the toque does not ceate a foce applied in the cente of the wheel By analogy the foce passing though the cente of otation does not ceate otational moment Examining a diagam of foces and moments acting on the tacto aticle [6] also states that the foce that pushes the tacto occus in the contact spot between the dive wheel and the gound It should be noted that the autho pesents the diagam of foces and moments acting on the tacto which lacks a vecto of the taction foce since powe analysis does not make it possible to apply taction foce to the axis of the wheel In pape [7] authos exploe optimal methods of contol ove taction foce depending on the diving toque and conside diving foce as the diffeence between the hoizontal soil eaction and intenal olling esistance of the wheel (defomation of the tie) The eaction of soil and the intenal olling esistance ae caused by the action of the diving toque It is stessed that the foce of motion esistance of a vehicle is applied to the axis of wheel otation which is cetainly tue Diving foce which has to compensate fo the foce of motion esistance should also be applied to the axis of wheel otation and diected in the opposite diection Howeve the authos do not give the explanation fo the tansfomation of toque of the dive wheel into a diving foce Aticles [8 9] give expessions fo detemining the taction effot of tacto which is deived as the diffeence between hoizontal action of the gound foce on the wheel and esistance foce to the motion of the wheel Physical essence of the occuence of taction foce is also missing Autho of [10] examines distibution of toque and taction effot on the dive wheel of a wheeled tacto He detemines diving foce as the diffeence between the hoizontal component of soil eaction on the wheel otation and the esistance foce to the wheel olling Numeically the foce is equal to the sum of toque applied to wheel and the otational moment of wheel inetia divided by the dynamic adius of wheel otation Taction foce of a tacto is detemined by authos of pape [11] based on the balance of foces applied to the dive wheel Diving toque applied to the wheel is divided into otational moment of wheel inetia and the diving toque 51

3 Easten-Euopean Jounal of Entepise Technologies IN /7 ( 88 ) 2017 Diving toque of the wheel ceates taction foce of the wheel foces to ovecome the esistance to wheel olling It should be noted that the wheel taction foce and the olling esistance foce ae located in the point of contact between the wheel and the gound and diected in such a way that they counteact to the diving toque of the wheel hen examining motion of the dive wheel with active tead taction foce is epesented as the sum of hoizontal effots opeating on the wheel im and the tead In this case diection and the point of taction foce application is not specified [12] Taction foce is also detemined as the diffeence between hoizontal action of the taction foce applied to the wheel axis and the wheel motion esistance foce applied in the point of contact between the wheel and the gound [13] Hoizontal esultant foce of soil esistance is also consideed as a taction effot that leads to the fowad motion uch foce is consideed as a function of soil and wheel paametes located in the place of contact between the wheel and the gound pointed in the diection of motion [14] All of the above explanations of physical essence of the occuence of taction foces on the dive wheels ae the most common and mostly false It should be noted that a lot of espectable monogaphs and textbooks epesent taction foce as the atio of toque on the dive wheel to its adius Moeove they conside taction foce to be the eaction of oad on the wheel otational foce In many monogaphs and scientific aticles authos geneally avoided the need to intoduce a vecto of taction foce They ealize that taction foce is applied on the axis of the wheel but cannot explain how the foce got thee Most authos consideing gound esistance in the point of inteaction between the wheel and the gound to be the diving taction foce tansfe this esistance to the axis of the wheel Howeve such a tansfe is not substantiated That is why a well-easoned fomalization is equied of the phenomenon of the fomation of taction foce on the axis of the dive wheel in self-popelled tanspotation vehicles and tactos 3 Reseach goal and objectives The goal of pesent eseach is to substantiate the fomation of taction foce on the dive wheel axis of self-popelled tanspotation vehicles tactos etc and detemining the magnitude of taction effot To accomplish the goal the following tasks have been set: to establish the mechanism of fomation of taction foce on the dive wheel axis; to eceive an expession fo detemining the magnitude of taction effot of tactos and to compae it with expeimental data 4 Mateials and methods fo examining inteaction between the dive wheel and the suface To conduct eseach into inteaction between the dive wheel and the suface we employed mathematical modelling based on the laws of mechanics In ode to check the dependences deived we modeled a change in the taction foce on the hook depending on a change in the tansmission gea atio of a tacto hen pefoming theoetical calculations we accepted values of tacto pefomance indicatos in line with the paametes obtained when conducting expeimental studies on a change in the taction foce of tacto MTZ-80 (Belaus) In the couse of eseach we conducted seveal expeiments in the elevant geas unde nominal modes of engine opeation at maximal fuel feed uel consumption engine otation indicatos of skidding and taction foce on the hook wee egisteed (Table 1) [15] Gea Basic taction indicatos of tacto MTZ-80 uel consumption kg/hous Engine otations pm peed km/hous kidding el units Table 1 Taction foce on the hook N (educing) (educing) Duing studies weight of the tacto was 3808 kg wheel olling fiction coefficient 08 adius of the wheel dive olling 0725 m aea of the tacto fontal suface 45 m 2 and the fontal tacto dag coefficient of dag 075 N с 2 /m 4 Coefficient of tansmission efficiency was accepted accoding to studies [16] at the level of 096 Low heat geneating capacity of the diesel fuel was accepted at the level of 425 MJ/kg Effective efficiency coefficient of the engine fo the espective modes was obtained based on a egulatoy chaacteistic of the D-240 engine opeation of tacto MTZ-80 [15] tubble of wheat seved as agicultual backgound when conducting the studies 5 Results of examining inteaction between the dive wheel and the suface hen the dive wheel contacts the suface thee will occu a bake moment due to the foces of suface eaction which counteacts to the wheel otation (ig 4) The magnitude of the bake moment in this case is: M = R (1) B R DT whee М B is the bake moment on the dive wheel due to the occuence of suface eaction foce which counteacts to the wheel otation N m; R R is the suface eaction foce that counteacts to the wheel otation N; DT is the adius of the dive wheel taking into account defomation of the tye m Duing fomation of the instantenous cente of otation the foce with which the wheel acts on suface compensates fo the foce of suface eaction that is R R = In this case the foce that compensates fo the foce of suface eaction in ecalculation fo the shaft of the wheel is deived fom atio: = (2) DT 52

4 Applied mechanics and it will equal to: o DT = (3) d M ТA = D = 2D = 2 = (6) whee is the foce on the wheel which compensates fo the foce of suface eaction N; is the foce that compensates fo the foce of suface eaction in ecalculation fo the shaft of the wheel N; is the adius of the dive shaft m Because the diving toque on the shaft of the wheel can be epesented by a pai of foces and D and identical by magnitude and pointed in the opposite diections (ig 5) and the magnitude of toque can be detemined as the sum of the poduct of foces magnitudes by the shaft adius it is possible to wite: M = + = ( + ) (4) D D whee M is the toque on the dive shaft N m; whee D = is the diving foce in the point of intesection of the line that passes though the cente of shaft otation and the instantaneous otation cente of the wheel and the cicle poduced by the shaft diamete N whee ТA is the taction foce on the otation axis of the dive shaft is the shaft is positioned on the suppoting suface N Because DT D = = (7) then taction foce on the shaft axis consideing (6) will have a value: TA DT = 2 (8) ith egad to the equality of moments of the taction foce elative to the foce action shoulde in paticula adius of the shaft and taction foce elative to the foce action shoulde in paticula adius of the defomed wheel it is possible to wite (ig 6): = (9) TA TA DT whee TA is the taction foce on the otation axis of the dive shaft when the wheel is positioned on the suppoting suface N In this case taction foce on the shaft axis in ecalculation fo the wheel will have a value: ig 4 Calculation diagam of the foce that compensates fo the foce of suface eaction in ecalculation fo the wheel shaft DT TA = TA = 2 = 2 DT DT (10) ince a pai of foces does not have the esultant foce that is the action of a pai of foces on the body cannot be mechanically equivalent to the action of any one foce then espectively a pai of foces cannot be balanced by one foce Duing gip in the point of contact between the shaft and the suface thee occus a compensation of one foce of the shaft toque by the foce of gip with the suface that is = R R In this case an instantenous cente of otation is ceated in the point of contact oce РВ ceates a toque elative to the instantaneous cente of otation which is numeically equal to the moment on the engine shaft: M = D d (5) ig 5 Calculation diagam of taction foce on the shaft without a dive wheel Thus if the wheel is emoved while the shaft is mounted on the suppoting suface then taction foce on the shaft axis would equal to: = 2 = d TA D D ig 6 Geneal diagam fo the calculation of taction foce of the dive wheel That is adius of the wheel does not affect the calculation of taction foce on the wheel axis and the taction foce itself is equal to the doubled foce which compensates fo the foce of suface eaction in the inteaction between the wheel and the suface that is: = =2 (11) TA R whee TA is the taction foce on the otation axis of the dive shaft N; R is the esistance foce which is diected opposite to the taction foce N The pesence of esistance foces to the woking tools inetia foces (at acceleation and deceleation) foces to 53

5 Easten-Euopean Jounal of Entepise Technologies IN /7 ( 88 ) 2017 ovecome the ascent as well as the olling foces leads to the existence of esistance foces R on the dive wheels axes wheels which ae diected against the motion and which need to be ovecome at displacement: = + + = mgf cosα+ R R AR M + k v + f m g + kab +θabv (12) 2 / 2 AR M whee R is the foce to ovecome the fiction of olling N; AR is the ai esistance foce N; M is the foce of taction esistance of the woking machine N; m is the mass of a tacto o a vehicle kg; g is the acceleation of the Eath s gavity foce m/s 2 ; f is the olling fiction coefficient el units; a is the inclination angle of the suface ad; k AR is the coefficient of ai esistance N s 2 /m 4 ; is the aea of fontal dag of a tacto o a vehicle m 2 / ; v is the motion speed m/s; f is the total fiction coefficient of the woking machine el units; m M is the mass of the woking machine kg; k is the specific soil defomation esistance N/m 2 ; a is the width of the pocessed laye m; b is the depth of the pocessed laye m; θ is the speed coefficient of the woking machine N s 2 /m 4 Ovecoming esistance foces is ensued by the taction foce TA applied to the axis of the dive shaft which is pointed in the diection of motion of the wheel The total magnitude of the pai of foces on the dive wheel equies a toque on the shaft of the dive wheel of magnitude: M = 2 + M = + M (13) DT B TA DT B whee М В is the bake moment on the dive wheel due to the losses on fiction defomation of soil and wheels and othe bake moments that occu on the wheel N m It is possible to detemine fom the given expession the maximal taction foce on the dive wheel (at two dive wheels): М 2 М = (14) МАХ В TAМАХ DT 1 TAMAX = ( MMAX 2 MB ) (15) DT 1 N EMAX = 2 M η w TAMAX TR B DT D (16) whee М МАХ is the maximal toque on the dive shafts n m; ТAМАХ is the maximal taction foce on the dive wheels N; N EМАХ is the maximal engine powe ; w D is the angula velocity of the dive shaft of a wheel 1/s; h TR is the tansmission efficiency el units Thus the maximal taction foce that occus on the dive wheels is diectly popotional to the engine powe and deceases in popotion to the gowth of bake toque on the dive wheels due to the losses on fiction defomation of soil and wheels and othe bake moments that occu on wheels The lagest poblems in detemining the maximal taction foce aise in detemining a bake moment on the dive wheel due to the losses on soil and wheels defomation This powe losses can be taken into account though the intoduction of skid coefficient then the total taction foce will have a value: 1 d N = η TR (17) w EMAX TAMAX DK D whee d is the skid coefficient el units It is moe appopiate to expess the given fomula not though the shaft otations of the dive wheel but via engine otations because it is possible to contol this magnitude: 1 d itr = q Q ηη w ТAМАХ МАХ Е TR DT E (18) whee q МАХ is the maximal fuel supply kg/s; Q is the lowe heat geneating fuel capacity kj/kg; w E is the angula velocity of the engine cankshaft 1/s; і TR is the tansmission gea atio el units; h Е is the effective engine efficiency el units It is advisable to take also into account the dependence of effective engine efficiency on the engine cankshaft angula velocity: 2 η Е =α E +β E +γ w w (19) whee α β γ ae the coefficients of appoximation It is advisable to also take into account the dependence of fuel supply on the engine otations: q MAX l ρ k w = 2π PL PL PL E (20) whee PL is the aea of the plunge pai m 2 ; l PL is the active un of the plunge m; ρ is the fuel density kg/m 3 ; k PL is the coefficient of fuel supply by the plunge of fuel pump; i is the numbe of fuel spays pe one engine otation ev -1 The diving foce of machine-tacto unit is the enegy of fuel which an intenal combustion engine of enegy means convets into otations and toque that ae tansmitted to the dive wheels The toque of the engine is spent on the dive of the woking machine though the powe take-off shaft and the ceation of taction foce The taction foce of the machine-tacto unit dive wheels can be detemined fom the following expession [17]: 1 d PLlPLρkPL HMQ M = Q i η η 2π η w η T E TR TR DT M M TRPTO TRPTO (21) whee i TRPTO is the gea atio of tansmission fom the engine to powe take-off shaft units; η TRPTO is the efficiency coefficient of tansmission of the powe take-off shaft el units; Н M is the pessue geneated by the fan of the woking machine Pa; Q M is the volumetic ai consumption by the fan of the woking machine m 3 /s; h M is the efficiency coefficient of the fan of the woking machine el units; w M is the angula speed of otating pats of the woking machine ad/s It follows fom expession (21) that the taction foce on the hook which can be achieved by a mobile enegy means fo example tacto will take the fom: 1 d PLlPLρEkPL НMQM = Q η 2π η w i η ТH Е DT M M TRPTO TRPTO 2 itr TR fmt g kar v (22) η whee k AR is the coefficient of ai esistance N s 2 /m 4 ; is the aea of machine-tacto unit fontal dag m 2 54

6 Applied mechanics ig 7 shows chats of expeimental and estimated data on a change in the taction foce of enegy means depending on the tansmission gea atio Expeimental dependence of change in the taction effot is constucted accoding to the conducted studies on the tacto MTZ-80 pefomance [15] Theoetical dependence is calculated using expession (22) based on the values of elevant paametes which wee epoted in aticle [15] when caying out expeimental eseach into a change in the taction esistance of tacto MTZ-80 and which ae outlined in chapte "Mateials and methods fo examining inteaction between the dive wheel and the suface" of the pesent pape ig 7 Dependence of taction foce of enegy means on the tansmission gea atio The detemination index of values of expeimental and theoetical dependences of a change in the taction foce on the change of tansmission gea atio calculated accoding to pocedue [18] is η 2 =0986 (Table 2) Because detemination index is 0986 it is possible to ague about the adequacy of the deived theoetical dependence (22) to model a change in the the taction foce at a change in the tansmission gea atio 6 Discussion of esults of examining inteaction between the dive wheel and the suface As a esult of the eseach conducted we substantiated pinciples of the occuence of taction foce on the axis of the dive wheel of tactos and vehicles Detemining the pinciples of fomation of taction foce makes it possible to intensify studying engineeing and enegy means in geneal and to substantiate the pinciples of educing negative impact of the engines in paticula on the fetile soil laye Impoving effectiveness of scientific eseach will contibute to the impovement of technical and enegy means uch studies ae elevant fo agicultual machine-tacto units This is linked to the fact that the wok of agicultual machine-tacto units is associated with poblems concening the inteaction between unning systems and the suface of fetile laye of soil Pesent aticle questioned the position on that the total tangent soil eaction unde the action of the dive wheels on it is the taction foce which is tansfeed to the ea axle and thus sets the whole vehicle o tacto into motion Regading the motion of wheeled enegy means and vehicles then the diving foce fo them is the fuel enegy Intenal combustion engine of enegy means convets fuel enegy into otations and toque which ae tansfeed though tansmission to the dive wheels In the machine-tacto units the toque of the engine is also spent on the dive of the woking machine though the powe take-off shaft and ceation of the foce of taction The point of application of taction foce is on the axis of the dive wheel Moeove the magnitude of taction foce is about two times geate than the eactive foce tansfeed fom the oad to the dive wheel In this case the suface eaction is tansmitted fom the oad to the dive wheel and counteacts to the wheel otation Calculation of detemination index of expeimental and theoetical values of taction foce dependences on the tansmission gea atio Table 2 Gea atio of Expeimental value tansmission el units of taction foce N Estimated value of taction foce N The squae of deviation of expeimental values fom the geneal aithmetic mean The squae of deviation of expeimental data fom theoetical Detemination index um of values

7 Easten-Euopean Jounal of Entepise Technologies IN /7 ( 88 ) 2017 uthe studies ae planned fo detemining a degee of compaction of the soil medium unde the wheels of agicultual machine-tacto units The eseach is also equied to claify the natue of skidding This will help establish enegy losses at wheels olling taking into account inte-defomation between the wheel and the suface of the olling 7 Conclusions 1 e substantiated and fomalized ceation of taction foce in the fom of expession fo the calculation of the taction foce on the axis of the dive wheel Taction foce is about two times lage than the eactive foce tansfeed fom the oad to the dive wheel The maximal taction foce that occus on the dive wheels is diectly popotional to the engine powe and deceases in popotion to the gowth of the bake toque on the dive wheels due to fiction losses the defomation of soil and wheels and othe baking moments that occu on wheels 2 The diving foce of tactos and vehicles is fuel enegy which is conveted by intenal combustion engine of an enegy means into otations and toque which ae tansfeed using the tansmission to the dive wheels In the machine-tacto units toque of the engine is also spent on the dive of the woking machine though the powe take-off shaft and ceation of the foce of taction The adequacy of the deived theoetical dependence of taction foce on the hook which can be attained by a mobile enegy means is confimed on the basis of compaison of expeimental and calculated data on a change in the taction foce of an enegy means Detemination index of the values of expeimental and theoetical dependences of taction foce at a change in the tansmission gea atio is η 2 =0986 indicating the possibility to apply the theoetical dependence eceived fo simulating the taction foce of enegy means Refeences 1 Iani R A A dynamic teamechanic model fo small lightweight vehicles with igid wheels and gouses opeating in sandy soil [Text] / R A Iani R J Baue A akentin // Jounal of Teamechanics 2011 Vol 48 Issue 4 P doi: / jjtea Li Y Attitude-based dynamic and kinematic models fo wheels of mobile obot on defomable slope [Text] / Y Li L Ding G Liu // Robotics and Autonomous ystems 2016 Vol 75 P doi: /jobot Baskiy I B Konstukciya osnovy teoii i aschet taktoov [Text] / I B Baskiy D Byuhovec V V Ivanov et al Moscow: Vysshaya shkola p 4 Didenko M K Ekspluatatsiya mashyno-taktonoho paku [Text] / M K Didenko Kyiv: Vyshcha shkola p 5 vishchevskiy B Ehkspluataciya mashinno-taktonogo paka [Text]: ucheb / B vishchevskiy Moscow: el hozgiz p 6 Kut kov G M Taktoa i avtomobili Teoiya i tekhnologicheskie svoystva [Text] / G M Kut kov Moscow: Kolos p 7 Osinenko P V A method of optimal taction contol fo fam tactos with feedback of dive toque [Text] / P V Osinenko M Geissle T Helitzius // Biosystems Engineeing 2015 Vol 129 P doi: /jbiosystemseng Nguyen V N Expeimental analysis of vetical soil eaction and soil stess distibution unde off-oad ties [Text] / V N Nguyen T Matsuo Inaba T Koumoto // Jounal of Teamechanics 2008 Vol 45 Issue 1-2 P doi: / jjtea avaedi Y Pediction of tactive esponse fo flexible wheels with application to planetay oves [Text] / Y avaedi A Pechev M chainghausen L Richte // Jounal of Teamechanics 2011 Vol 48 Issue 3 P doi: / jjtea Zebowski J Taction efficiency of a wheeled tacto in constuction opeations [Text] / J Zebowski // Automation in Constuction 2010 Vol 18 Issue 2 P doi: /jautcon Kolato B A simulation model of 2D tacto pefomance [Text] / B Kolato I Bialobzewski // Computes and Electonics in Agicultue 2011 Vol 76 Issue 2 P doi: /jcompag Yang Y Dawba pull of a wheel with an actively actuated lug on sandy teain [Text] / Y Yang Y un Ma // Jounal of Teamechanics 2014 Vol 56 P doi: /jjtea Ghotbi B Mobility evaluation of wheeled obots on soft teain: Effect of intenal foce distibution [Text] / B Ghotbi Gonzalez J Kovecses J Angeles // Mechanism and Machine Theoy 2016 Vol 100 P doi: / jmechmachtheoy Ding L Expeimental study and analysis on diving wheels pefomance fo planetay exploation oves moving in defomable soil [Text] / L Ding H Gao Z Deng K Nagatani K Yoshida // Jounal of Teamechanics 2011 Vol 48 Issue 1 P doi: /jjtea Antonov A P Tyagovye haakteistiki sel skohozyaystvennyh taktoov [Text] / A P Antonov N M Antyshev A P Bannik N Mazepov B I Peysahovich Moscow: Rossel hozizdat p 16 Habadin V Rezul taty opedeleniya mekhanicheskogo KPD tansmissii pi tyagovyh ispytaniyah taktoov v pocesse toganiya s mesta pod naguzkoy [Text] / V Habadin A V hishkin // Vesnik IGKHA 2013 Issue 52 P Holub H A Vyznachennia tiahovoi syly enehozasobiv py oboti na dyzelnomu biopalyvi [Text] / H A Holub V V Chuba // Mekhanizatsiya ta elektyfikatsiya silskoho hospodastva 2013 Vol 2 Issue 98 P Dospekhov B A Metodika polevogo opyta (s osnovami statisticheskoy obabotki ezul tatov issledovaniy) [Text]/ B A Dospekhov Moscow: Agopomizdat p 56