Mobility of the Metrobus. Ways of Improvement

Home , M1 (Istanbul Metro), Metrobus (Istanbul)

The Archives of Automotive Engineering – Archiwum Motoryzacji Vol. 89, No. 3, 2020 61

MOBILITY OF THE METROBUS. WAYS OF IMPROVEMENT

OLEH Z. BUNDZA1, VOLODYMYR P. SAKHNO2, VIKTOR M. POLIAKOV3, DMYTRO M. YASHCHENKO4

Abstract

In this article it is offered the ways to improve the maneuverability of three-link metrobuses by choosing a rational layout scheme and design parameters of its trailer units. Considering that the movement of the metrobus is carried out on direct routes, that is, the maneuverability of the metrobus is appropriate to determine by the overall traffic lane (OTL) size. OTL equal to the difference of the radii of rotation of the points of the train, the farthest and closest to the center, that is, the difference of the overall radii of rotation - the outer (Rz = 12.5 m) and internal (Rv = 5.3 m). The methodology for calculating OTL is based on determining the angles of assembly of the road train links and the offset of the driven links trajectories relative to the trajectory of the master. Maneuverability indicators of the three-link metrobus are defined on elastic in the lateral direction wheels. Studies were performed for one-way rotation and ISO maneuvering with the obtained trajectories of links and the overall traffic lane of a metrobus with guided and unmanaged trailer links. Keywords: metrobus; mobility; trajectory; traffic lane; trailer

1. Introduction The metrobus or the new Bus Rapid Transport (BRT) bus system is the result of the development of the public transit bus network.

The BRT system has several distinct advantages [2, 12]: • high passenger capacity and efficient payment systems ensure low-cost travel; • high speed of movement allows the metrobus to carry a significant share of passenger traffic, which helps to reduce the number of cars on the city roads and, accordingly, to reduce exhaust emissions; • an expanded information system informs passengers of the route. The convenience, safety and organization of the road, which is inevitably improving, is far from being able to give passengers a high-speed bus system. In this system, passenger express buses move along specially designated lanes. They are separated from

1 National University of Water and Environmental Engineering, Department of building, roads, recovery, agricultural machines and equipment, 11 Soborna St., Rivne, 33028, Ukraine, e-mail: [email protected] 2 National Transport University, Department of Automobiles, 1 Mykhaila Omelianovycha-Pavlenka Str., 01010 Kyiv, Ukraine 3 National Transport University, Department of Automobiles, 1 Mykhaila Omelianovycha-Pavlenka Str., 01010 Kyiv, Ukraine 4 National Transport University, Department of Automobiles, 1 Mykhaila Omelianovycha-Pavlenka Str., 01010 Kyiv, Ukraine 62 The Archives of Automotive Engineering – Archiwum Motoryzacji Vol. 89, No. 3, 2020

the carriageway and equipped with closed passenger stations with level platforms and subways.

The rolling stock used in the BRT system is of two types: the first is a classic, two-deck metrobus with an engine running on both diesel and gas fuel; the second option is a new generation metrobus with a hybrid electric-gas engine. These two variants are inherent in articulated buses, 18 and 24 meters long [21].

2. Materials and methods Studies conducted by domestic and foreign scientists found that the creation of a modern automobile vehicle (AV) with improved energy efficiency may be based on a hybrid power plant, but the unresolved issue of rational distribution of power between the internal com- bustion engine and electric motors implementation [5, 7, 9].

In fact, a metrobus combines the benefits of a subway in a modern city with the relatively low cost of building such lines. Moreover, with the help of traffic intensity it is possible to adjust the passenger flow. In general, metrobus lines are suitable for areas that require transportation of (15000-18000) passengers per hour. However, there are many examples where they have generally replaced the metrobus in large metropolitan areas. For example, in Istanbul or Chinese Shanghai.

Another advantage of BRT systems is the speed of construction of such lines that can be used by existing highways in cities. Typically, such a line is built in (1-2) years, while the construction of the subway, tram lines can take (3-10) years.

The special development of the buses was with the advent of three-seater buses, Figure 1, which can carry up to 300 passengers against 180 passengers, in two-seater buses. Thus, having 3-lane buses that move at short intervals (up to 1 minute) the metrobus line can solve the transport problems of many Ukrainian cities, and in particular, completely elimi- nate the issue of transport connections of remote arrays, especially in Kyiv [1, 8, 14].

New developments in the field of creation of multi-link AVs and methods of optimization of their designs are focused on minimizing fuel, energy consumption, improving mobility and controlling. Many theoretical data on the optimization of complex mechanical systems and multi-objective optimization methods are given in [3, 6, 13]. In [4] the circuit solutions and features of construction of vehicles with a hybrid power plant, electrical systems and complexes of a hybrid car are considered. The analysis of structures and classification of multi-axle vehicles of traditional construction, the general regularities of their movement are considered in [17, 18, 20]. The Archives of Automotive Engineering – Archiwum Motoryzacji Vol. 89, No. 3, 2020 63

Fig. 1. The modern Volvo chassis metrobus

The reliability of theoretical recommendations for improving the construction of metrobuses is determined by the most adequate tracking of the main relationships between its elements, the physical consistency of the initial assumptions in the formulation of the problem and the correctness of the mathematical model adopted to determine energy performance and especially maneuverability. For this reason, the purpose of the work is to improve the maneuverability of the three-lane subway by choosing a rational layout scheme and design parameters of its hitch links.

3. Results The purpose of monitoring the rights of people with disabilities for accessibility to transport services is the creation of a basis for systematic analysis and synthesis of processes that develop in the system "transport - person" with emphasis on identifying the basic principles of its functioning, the nature of contradictions and the causes that lead to the problem in the logistics system transportation of people with disabilities. The results of the monitoring are the basis for establishing a list of measures to improve transport services.

Mobility of AV is estimated by nine indicators, six of which are kinematic and three dynamic. However, for a three-lane metrobus, two kinematic unit mobility values should be considered as the main ones [10, 11], namely: • the overall traffic lane (OTL) equal to the difference of the radii of rotation of the points of the train, the farthest and closest to the center, that is, the difference of the overall radii of rotation - the outer (Rz = 12.5 m) and internal (Rv = 5.3 m); • the ability to move backwards. The Archives of Automotive Engineering – Archiwum Motoryzacji Vol. 89, No. 3, 2020

reason, the purpose of the work is to improve the maneuverability of the three-lane subway by choosing a rational layout scheme and design parameters of its hitch links.

3. Results

The purpose of monitoring the rights of people with disabilities for accessibility to transport services is the creation of a basis for systematic analysis and synthesis of processes that develop in the system "transport - person" with emphasis on identifying the basic principles of its functioning, the nature of contradictions and the causes that lead to the problem in the logistics system transportation of people with disabilities. The results of the monitoring are the basis for establishing a list of measures to improve transport services. 64Mobility of AV is Theestimated Archives byof Automotive nine indicators, Engineering six –of Archiwum which areMotoryzacji kinematic Vol. 89, and No. three 3, 2020 dynamic. However, for a three-lane metrobus, two kinematic unit mobility values should be considered as the main ones [10, 11], namely: - the overall traffic lane (OTL) equal to the difference of the radii of rotation of the points of the Giventrain, that the the farthest movement and closest of tothe the metrobus center, that isis, carriedthe difference out on of thededicated overall radii lanes, of rotation the ability - the to moveouter in (R reversez = 12.5 mis) notand criticalinternal for(Rv =him, 5.3 thatm); is, the maneuverability of the metrobus is advisable- the abilityto determine to move bybackwards. the OTL size. WhenGiven thatdetermining the movement the of maneuverability the metrobus is carried of the out wheels on dedicated of vehicles lanes, the are ability taken to moveas rigid in reverse in the lateralis not critical direction for him and, that elastic is, the [19,maneuverability 22]. The methodology of the metrobus for is calculating advisable to OTLdetermine is based by the on OTL de- size. termining the angles of assembly of the road train links and the offset of the driven links trajectoriesWhen determining relative the maneuverabilityto the trajectory of the of wheelsthe master. of vehicles The are discrepancy taken as rigid in in the the lateralcalculation direction of maneuverabilityand elastic [19, 22 when]. The using methodology rigid or elasticfor calculating lateral wheelsOTL is forbased two-lane on determining highways the can angles reach of assembly of the road train links and the offset of the driven links trajectories relative to the trajectory of (13-15)%,the master. and The for discrepancy three-lane in highwaythe calculation trains of it maneuverability can be even greater.when using Therefore, rigid or elasticdetermining lateral thewheels mobility for two of-lane a three-row highways canmetrobus reach (13 will-15 )be%, carriedand for threeout on-lane models highway with trains elastic it can laterallybe even wheels.greater. Therefore, determining the mobility of a three-row metrobus will be carried out on models with elastic laterally wheels. In [15, 16], a system of equations is described describing the plane-parallel motion In [15, 16], a system of equations is described describing the plane-parallel motion of a three-lane trailer of a three-lanetrainset, which can trailer be applied trainset, to a metrowhichbus can as wellbe applied 1, in the to form: a metrobus as well 1, in the form:

m(u + vω) = Y1 cosθ1 +Y2 +YA−YBcosγ 1 + XBsin γ 1   Iω = aYA− b(Y2 cosθ1 + X 2 sinθ1) + c(YBcosγ 1) + M1 + M 2  I1ω1 = −YAλ cosθ + XAλ sinθ − M1 = 0  (1) I ω = d YB − b Y + c YC − M  2 2 1 1 3 1 3   I3ω3 = d2YС − b22 (Y4 cosθ3 + X 4 sinθ3 ) + M 2 − M 3 

Fig. 2. The scheme of rotation of a three-lane metrobus with a controlled second trailer The Archives of Automotive Engineering – Archiwum Motoryzacji Vol. 89, No. 3, 2020

The Archives of Automotive Engineering – Archiwum Motoryzacji Vol. 89, No. 3, 2020 65 Fig. 2. The scheme of rotation of a three-lane metrobus with a controlled second trailer

The reactions at the points of connection of the metrobus are recorded in the form [15]: The reactions at the points of connection of the metrobus are recorded in the form [15]:

XC = m3v3 − m3ω3u3 + X 4 cosθ3 −Y4 sinθ3  XC = m3v3 − m3ω3u3 + X 4 cosθ3 −Y4 sinθ3    YC = m3u3 + m3ω3v3 −Y4 cosθ3 − X 4 sinθ3 YC m3u3 m3 3v3 Y4 cos 3 X 4 sin 3  XB = m v − m ω u + m v cosϕ − m ω u + cosϕ X cosθ − cosϕY sinθ − XB = m2v2 − m2ω2u2 + m3v3 cosϕ2 − m3ω3u3 + cosϕ2 X 4 cosθ3 − cosϕY4 sinθ3 − 2 2 2 2 2 3 3 2 3 3 3 2 4 3 4 3  − sinϕ2m3u3 − sinϕ2m3ω3v3 + sinϕ2Y4 cosθ3 + sinϕ2 X 4 sinθ3  − sinϕ2m3u3 − sinϕ2m3ω3v3 + sinϕ2Y4 cosθ3 + sinϕ2 X 4 sinθ3   (2) YB = m2u2 + m2ω2v2 + sinϕ2m3v3 − sinϕ2m3ω3u3 + sinϕ2 X 4 cosθ3 − YB = m2u2 + m2ω2v2 + sinϕ2m3v3 − sinϕ2m3ω3u3 + sinϕ2 X 4 cosθ3 −  − sinϕ Y sinθ + cosϕ m u + cosϕ m ω v − cosϕ Y sinθ  − sinϕ2Y4 sinθ3 + cosϕ2m3u3 + cosϕ2m3ω3v3 − cosϕ2Y4 sinθ32  2 4 3 2 3 3 2 3 3 3 2 4 32  XA = −cosθm1v1 + cosθm1ω1u1 − cosθX1 + m1u1 sinθ + m1ω1u1 sinθ1 −Y1 sinθ  XA = −cosθm1v1 + cosθm1ω1u1 − cosθX1 + m1u1 sinθ + m1ω1u1 sinθ1 −Y1 sinθ   YA = −sinθm1v1 + sinθm1ω1u1 − sinθX1 − m1u1 cosθ − m1ω1v1 cosθ +Y1 cosθ  YA = −sinθm1v1 + sinθm1ω1u1 − sinθX1 − m1u1 cosθ − m1ω1v1 cosθ +Y1 cosθ 

The longitudinal forces on the wheels of the axles of the road train are defined as [15]: The longitudinal forces on the wheels of the axles of the road train are defined as [15]:

Хі=Zi×kf, (3) Хі=Zi×kf, (3)

The transverse forces on the wheels of the axles of the road train are defined as: The transverse forces on the wheels of the axles of the road train are defined as:

kіδі Y = kі і (4) Yі = 2 2 і 2 2 kі δі kі δі 1+ 2 1+ 2 (ϕі Zі ) (ϕі Zі ) In these equations the following notation is accepted: InIn thesethese equations equations the thefollowing following notation notation is accepted: is accepted: v – the longitudinal component of the speed of the center of mass of the bus; λ (lambda) – take-off of vv –– thethe longitudinallongitudinal component component of the of speedthe speed of the ofcenter the ofcenter mass ofof massthe bus; of λ the (lambda bus;) λ – (lambda) take-off of – the steering wheel of the bus; a; b – the distance from the center of mass of the bus to the attachment take-offthe steering of thewheel steering of the bus; wheel a; b of – thethe distancebus; a; bfrom – the the distance center of frommass theof the center bus to of the mass attachment of the points of the front (steered) axis and its rear axle; c – the distance from the center of mass of the bus to busthe front to the axle attachment of the first trailer; points с 2of – distancethe front from (steered) the center axis of massand itsof therear bus axle; to the c – point the ofdistance contact the front axle of the first trailer; с2 – distance from the center of mass of the bus to the point of contact fromwith thethe first center trailer; of d mass1 – the distanceof the bus from to the the center front of massaxle of thethe first first trailer trailer; (second – link) distance to the pointfrom with the first trailer; d1 – the distance from the center of mass of the first trailer (secondс2 link) to the point of contact with the bus; d2 – the distance from the center of mass of the second trailer (third link) to the theof contact center with of mass the bus; of d the2 – the bus distance to the frompoint the of center contact of mass with of the the first second trailer; trailer d 1(third – the link) distance to the frompoint ofthe engagement center of withmass the of first the trailer; first m,trailer J – mass (second and central link) momentto the point of inertia of contactof the bus; with the bus; d2 – the distance from the center of mass of the second trailer (third link) to the point of engagement with the first trailer; m, J – mass and central moment of inertia of the bus; v, u – longitudinal and transverse projections of the velocity vector of the center of mass on the axle associated with the tractor; ω (omega) – the angular velocity of the bus relative to the vertical axis; m1, J1 – mass and central moment of inertia of the steering wheel module of the bus; v1, u1 – longitudinal and transverse projections of the velocity vector of the center of mass of the control wheel module of the bus;

ω1 – the angular speed of the bus control wheel module; m2, J2 – mass and central moment of inertia of the first trailer; v2, u2 – longitudinal and transverse projections of the velocity vector of the center of mass of the first trailer;

ω2 – angular speed of the first trailer; m3, J3 – the mass and central moment of inertia of the control wheel module of the second trailer; v3, u3 – longitudinal and transverse projections of the velocity vector of the center of mass of the control wheel module of the second trailer; The Archives of Automotive Engineering – Archiwum Motoryzacji Vol. 89, No. 3, 2020

The Archives of Automotive Engineering – Archiwum Motoryzacji Vol. 89, No. 3, 2020 v, u – longitudinal and transverse projections of the velocity vector of the center of mass on the axle associated withThe the Archives tractor; of Automotive Engineering – Archiwum Motoryzacji Vol. 89, No. 3, 2020 v,ω (omega)u – longitudinal – the angular and transverse velocity of projections the bus relative of the to velocity the vertical vector axis; of the center of mass on the axle massociated 1, J1 – mass with andThe the central Archives tractor; moment of Automotive of inertia Engineerin of theg – steering Archiwum wheel Motoryzacji module Vol. of 89, the No. bus; 3, 2020 vω1, u1 – longitudinal and transverse projections of the velocity vector of the center of mass of the control v, (omega)u – longitudinal – the angular and transverse velocity of projections the bus relative of the to velocity the vertical vector axis; of the center of mass on the axle wheelm1, J1 –module mass and of the central bus; moment of inertia of the steering wheel module of the bus; associated with the tractor; vω11, u–1 the – longitudinal angular speed and of transverse the bus control projections wheel of module; the velocity vector of the center of mass of the control v, (omega)u – longitudinal – the angular and transverse velocity of projections the bus relative of the to velocity the vertical vector axis; of the center of mass on the axle wheelm2, J2 –module mass and of the central bus; moment of inertia of the first trailer; 66massociated1, J1 – mass with and the Thecentral tractor; Archives moment of Automotive of inertia Engineering of the –steering Archiwum wheel Motoryzacji mod uleVol. 89,of No.the 3, bus; 2020 vω21, –u 2the – longitudinal angular speed and of transversethe bus control projections wheel module;of the velocity vector of the center of mass of the first vω1 ,(omega) u1 – longitudinal – the angular and transversevelocity of projections the bus relative of the to velocity the vertical vector axis; of the center of mass of the control trailer;wheelm2, J2 –module mass and of the central bus; moment of inertia of the first trailer; m1, J1 – mass and central moment of inertia of the steering wheel module of the bus; vω212, –u 2theangular – longitudinal angular speed speed o fand the of transversethefirst bus trailer; control projections wheel module;of the velocity vector of the center of mass of the first v1, u1 – longitudinal and transverse projections of the velocity vector of the center of mass of the control trailer;m23, J23 – massthe mass and andcentral central moment moment of inertia of inertia of the of thefirst control trailer; wheel module of the second trailer; ωwheel3 – angular module speedof the bus; of the control wheel module of the second trailer; vω232, u–u3 2angular –– longitudinallongitudinal speed o andfand the transverse transversefirst trailer; projections projections of of the the velocity velocity vector vector of of the the center center of ofmass mass of theof the control first ω1 – the – angularmass andspeed central of the busmoment control of wheel inertia module; of the second trailer; mtrailer;wheelm43,, JJ34 –module the mass of theand second central trailer;moment of inertia of the control wheel module of the second trailer; m2, J2 – mass and central moment of inertia of the first trailer; ωv323, u–3 angular – – longitudinal longitudinal speed oof andf theand transverse controlfirst transverse trailer; wheel projections moduleprojections of of the the velocity ofsecond the velocity vectortrailer; of vectorthe center of ofthe mass center of the of control mass vv42, u24 – longitudinal and transverse projections of the velocity vector of the center of mass of the first wheelm4, J4 –module mass and of the central second moment trailer; of inertia of the second trailer; oftrailer;m3 the, J3 – second the mass trailer; and central moment of inertia of the control wheel module of the second trailer; ωv343, u–34 angular – longitudinal speed of and the transverse control wheel projections module of of the the velocity second vectortrailer; of the center of mass of thethe controlsecond ω 2– – acceleration angular speed inof thethe firstlongitudinal trailer; direction; Vwheeltrailer;m4, J4 –module mass and of the central second moment trailer; of inertia of the second trailer; m3, J3 – the mass and central moment of inertia of the control wheel module of the second trailer; Vωv4 3,– u– acceleration4 angular – longitudinal speed –in longitudinal theof and the longitudinal transverse control forces wheel projectionsdirection; moduleon wheels of of the the velocityof second axles vectortrailer; of a road of the train. center of mass of the second Xv31,, u X3 2–, longitudinalX3, X4 and transverse projections of the velocity vector of the center of mass of the control Xtrailer;m14,, XJ42 ,– X mass3, X4 and– longitudinal central moment forces of on inertia wheels of ofthe axles second of atrailer; road train. Мwheel –module the stabilizing of the second moments trailer; of the tires of the steering wheel module of the bus and VМv4 ,1,3– u acceleration 4 – – the longitudinal stabilizing in the and moments longitudinal transverse of the projectionsdirection; tires of the of steering the velocity wheel vector module of ofthe the center bus andof mass the second of the secondtrailer, ω3 – angular speed of the control wheel module of the second trailer; theXtrailer;described1, Xsecond2, X3, asX4 nonlinear trailer, – longitudinal described dependence forces as on nonlinear thewheels angle of ofdependence axles withdrawal, of a road on train. the angle of withdrawal, m4, J4 – mass and central moment of inertia of the second trailer; VМ 1,3– acceleration – the stabilizing 1in the moments longitudinal2 of the direction; tires3 of the steering wheel module of the bus and the second trailer, v4, uМ4 1–, 3longitudinal = σ 1 ×δ1,3 + andσ 2 ×transverseδ1,3 −σ 1 × projectionsδ1,3 of the velocity vector of the center of mass of the second(5) Xdescribed1, X2, X3, asX4 nonlinear – longitudinal dependence forces on thewheels angle of of axles withdrawal, of a road train. trailer;where: where:М1,3 – the stabilizing1 moments2 of the tires3 of the steering wheel module of the bus and the second trailer, М1,3 = σ ×δ + σ ×δ −σ ×δ (5) Vδ – accelerationσ σ σ1 1in,3 the 2longitudinal1,3 1 direction;1,3 described1,3, 1, 2 ,as 3nonlinear – – the the characteristics characteristics dependence of on the the of axis anglethe ofaxis of the withdrawal, of steering the steering wheel module wheel of module the bus of and the the bus second and δXtrailer;where1,31, X, 2σ,: 1 X ,σ3,2 X,σ43 – longitudinal forces on wheels of axles of a road train. 1 2 3 theМ1,3 М second –1 ,the3 = stabilizingσ trailer;×δ + σmoments×δ − ofσ the×δ tires of the steering wheel module of the bus and the second trailer,(5) Мδ1,32,3, –σ moments1,σ2,σ13 – theof1,3 viscous characteristics2 friction1,3 1 inof the 1the,3 steering axis of ofthe the steering bus and wheel the second module trailer, of the whic bush areand proportional the second described as nonlinear dependence on the angle of withdrawal, Мtrailer;towhere 2,3the – :angles moments of rotation of viscous of the driven friction wheels in the [15 steering]: of the bus and the second trailer, which 1 2 3 М2,3 – moments of viscous friction in the steering of the bus and the second trailer, which are proportional areδ1,3, М proportionalMσ112,,3,3σ ==2 ,σh113,3 ×–× δθthe11,3,3 to + characteristics σ the2 × δangles1,3 −σ 1 ×ofδ 1rotationthe,3 axis of of the the steering driven wheel wheels module [15]: of the bus and the second(6)(5) trailer;towhere the :angles of rotation of the driven wheels [15]:  М2,3 M– moments= h × θof viscous friction in the steering of the bus and the second trailer, whic h are proportional (6) δh1,31 і ,h σ3 –12,, 3σthe2,σ coefficients13,3 – the1,3 characteristics of viscous offriction the axis in the of steeringthe steering details wheel of the module bus and of trailer;the bus and the second to the angles of rotation of the driven wheels [15]: where:trailer;whereМ3,3 – :the moments of elasticity in the steering of the front and rear axles are proportional to the angles = ×θ (6) Мhof1 2іrotation,3 h M–3 moments–2, 3the hof coefficients1,3 the of 1driven, 3viscous ofwheels: frictionviscous in friction the steering in the of steering the bus details and the of second the bus trailer, and trailer; which are proportional h i h – the coefficients of viscous friction in the steering details of the bus and trailer; towhereМ1 3,3the –3 :anglesthe momentsM of3,3 rotation= χ of1,3 ×elasticity θof1,3 the driven in the wheels steering [15 of]: the front and rear axles are proportional to the angles(7) Мhof1 іrotation h 3– – the the of coefficientsmoments the driven of ofwheels: elasticityviscous friction in the in steering the steering of detailsthe front of the and bus rear and axles trailer; are proportional where3,3M 2χ,31,3= h–1 ,the3 ×θ coefficients1,3 of rigidity of the steering wheel of the bus and trailer. (6) M = χ ×θ (7) towhereTheМ 3,3the –integration :the angles moments3 ,3 ofof rotationthe of1,3 elasticityoriginal1,3 of theequation in the driven steering system wheels: of was the accomplishedfront and rear usingaxles areMaple proportional software. toIn the this angles case, of rotation of the driven wheels: heachwhere1 і h 3mode –χ the1,3 – coefficientswas the coefficientsmodeled of byviscous ofone rigidity or friction another of the in thelawsteering steering of rotation wheel details ofof the ofthe busthe steering busand andtrailer. wheel trailer; of the tractor. For M = χ ×θ o (7) ThecomputerМ3,3 –integration the simulationmoments3,3 of the of1 ,3of elasticityoriginal the1,3 most equation in typical the steering 90system metro of was thebus, accomplishedfront which and moved rear usingaxles in a straightareMaple proportional software.line before, toIn the this angleslaw case, of each mode was modeled by one or another law of rotation of the steering wheel of the tractor. For wherecontrolofwhere rotation χ χof1,3 a –of bus– the thethe drivencoefficients driven coefficients wheels wheels: of is rigidity givenof rigidity inof thethe of formsteering the [ 15steering wheel]: of wheel the bus of and the trailer. bus and trailer. computer1,3 simulation= χ of× theθ most typical 90o metrobus, which moved in a straight line before, the law(7) of The integration0M 3,3 offor the 1 ,30 original≤ 1t,3 ≤ t 0 equation system was accomplished using Maple software. In this case, Thecontroleach integrationmode of a wasbus drivenmodeled of the wheels originalby one is given orequation another in the formlawsystem of [15 rotation ]was: accomplishedof the steering wheelusing ofMaple the tractor. software. For where χ1,3 –β thet coefficientsfor t < t ≤ oft rigidity of the steering wheel of the bus and trailer. computer simulation of0 ≤the ≤most1 typical 90o metrobus, which moved in a straight line before, the law of In thisThe integration case,0 each offor the mode 0 originalt wast 0 equation modeled system by one was or accomplishedanother law ofusing rotation Maple of software. the steering In this wheel case, controlθ of= a βbust drivenfor t1 wheels≤ t ≤ t is2 given in the form [15]: (8) ofeach the mode tractor. βwast modeledForfor computert 0 < byt ≤ onet1 simulation or another lawof theof rotationmost typicalof the steering90o metrobus, wheel of thewhich tractor. moved For 0− βt for 0t ≤wheels t 2 -1 [0;[t0; tt01]] i– [ tturn3; tk]-in – thetime time interval, of movement tractor-driven of the steeringroad train wheels on a straight rotate evenly line according at speed toβ the= 0 .entrance05 s ; to the − βt for t 2 < t ≤ t 3 turnw[t1here; t 2and]: – theafter interval leaving of the the turn; time of the movement of the road train in a circle (may be absent); 0 for t > t -1 [0;[t0; tt01]] i– [ tturn3; tk]-in – thetime time interval, of2 movement tractor-driven of the steeringroad train wheels on a straight rotate evenly line according at speed toβ the= 0 .entrance05 s ; to the where:turn[t1; t 2and] – theafter interval leaving of the the turn; time of the movement of the road train in a circle (may be absent); where: -1 [t0; t1] – turn-in time interval, tractor-driven steering wheels rotate evenly at speed β = 0.05 s ; [[0;0; t00]] i i[ t[3t;3 ;tk ]t k–] the– the time time of movement of movement of the roadof the train road on atrain straight on linea straight according line to accordingthe entrance to to thethe entranceturn[t1; t 2and] – theafter to interval theleaving turn of the theand turn; time after of leavingthe movement the turn; of the road train in a circle (may be absent); -1 [t0; t1] – turn-in time interval, tractor-driven steering wheels rotate evenly at speed β = 0.05 s ; [t ; t ] – turn-in time interval, tractor-driven steering wheels rotate evenly at speed β = 0.05 s-1; [t01; t21] – the interval of the time of the movement of the road train in a circle (may be absent); [t1; t2] – the interval of the time of the movement of the road train in a circle (may be absent);

[t2; t3] – Interval of exit time of the road train from a turn (the driven wheels of the tractor- car evenly return to a neutral position). The Archives of Automotive Engineering – Archiwum Motoryzacji Vol. 89, No. 3, 2020 67

To study the behavior of the road train in such a turn were taken speeds of 5 m/s at the angle of rotation of the driven wheels of the tractor from θ = (3.0-35) grade. Scheme of the metrobus components is shown in Figure 3.

Fig. 3. Scheme of the metrobus components

The following initial data were accepted for the calculation: v = 5; λ (lambda) = –0.023, а = 3.68; b = 2.32; c = 8.71; d1 = 4.17; d2 = 4.17; с2 = (2-4); m = 18000; J = 38500; m1 = 400, J1 = 18.5; m2 = 9500; J2 = 31200; m3 = 400; J3 = 11.2; m4 = 9500; J4 = 31200; kf = 0; k1 = 160000; k2 = 320000; k3 = 180000; k4 = 180000; χ1 = 2600, χ3 = 2200; h1 = 30; h3 = 30; φ11 = 0.8; φ22 = 0.8; φ33 = 0.8; φ44 = 0.8; θ0 = 0; θ = θ0+kθ×n; kθ = 0.05; n = (1.2-10); θ3 = 0.2×θ; V = 0. Figure 4 shows the trajectories of motion of characteristic points of the links of the metrobus (midpoints of the axes Ві) when turning the metrobus on 90°: В1 – the trajectory of the specific point of the bus, В2 – the trajectory of the specific point of the first trailer, В3 – the trajectory of the characteristic second driven trailer, В4 – the trajectory of the characteristic point of the second unruled trailer.

Fig. 4. Trajectories of the links points of the road train 68 The Archives of Automotive Engineering – Archiwum Motoryzacji Vol. 89, No. 3, 2020

The calculations found that the parameter was changed c2 – distance from the rear axle of the bus to the point of contact with the first trailer from 1000 mm to 0 leads to a decrease in the radii of rotation on the circular trajectory of the last link, Figure 5. It also reduces the distance between the trajectories of the tractor and the links that follow it.

Fig. 5. Trajectories of the characteristic points of the first B2 trailer and the second managed trailer B3: a) where = 4 m; b) where = 2 m c2 c2

The influence of the location of the coupling point of the first trailer with the second is sim- ilar to the effect of the parameter c2 (Figure 6). The Archives of Automotive Engineering – Archiwum Motoryzacji Vol. 89, No. 3, 2020 69

Fig. 6. Trajectories of the characteristic points of the first trailer B2 and a second trailer B3: a) at = 4 m; b) at = 2.5 m d2 d2

In the circular motion of the metrobus, the angles of rotation of the driven wheels of the bus and the second trailer were set, as well as the speed of the road train and the trajectories of the center of mass of the bus were located [21], Figure 7 after which the overall traffic lane of the metrobus was constructed, Figure 8. 70 The Archives of Automotive Engineering – Archiwum Motoryzacji Vol. 89, No. 3, 2020

Fig. 7. The trajectories of the center of mass of the metrobus with a speed 5 m/s: a) second unruled trailer; b) second ruled trailer

Fig. 8. Overall traffic lane of the metrobus with a speed 5 m/s: a) second unruled trailer; b) second ruled trailer The Archives of Automotive Engineering – Archiwum Motoryzacji Vol. 89, No. 3, 2020 71

When performingThe Archives such oftactics Automotive as Engineerin'rearrangement’,g – Archiwum ISO Motoryzacji the steering Vol. 89, No. angle 3, 2020 of the steered wheels of the bus was set in the form [15]:

π ⋅ t 10  − t < 0 and t <  10 3 π 10  − t < and t < 7  3 3  π π ⋅ (t − 7) 41  − − t < −7 and t <  3 10 3 θ 0 =  (9) π 41 52 − − t < − and t <  3 3 3  52  π ⋅ (t − ) π 52 62 − + 3 − t < − and t <  3 10 3 3  0 otherwise The trajectories of the movement of the metrobus links when performing the ISO maneuver atThe speeds trajectories of 5 ofm/s the and movement 10 m/s of are the shown metrobus in Figureslinks when 9 andperforming 10. the ISO maneuver at speeds of 5 m/s and 10 m/s are shown in Figures 9 and 10.

а) b) Fig. 9. Trajectories of the movement of the metrobus links with unruled second trailer a) and a driven second trailer b) when performing an ISO maneuver and speed 5 m/s

Fig. 9. Trajectories of the movement of the metrobus links with unruled second trailer a) and a driven second trailer b) when performing an ISO maneuver and speed 5 m/s

а)

b) Fig. 10. Trajectories of the movement of the metrobus links with unruled second trailer a) and a driven second trailer b) when performing an ISO maneuver and speed 10 m/s

4. Conclusions The results of these studies proved that: Fig.- 10.promising Trajectories for ofbig the cities, movement in particular of the metrobus, for the citylinks of with Kyi unruledv is the second use of trailerthree- a)lane and buses a driven capable second of carrying up to 300trailer passengers b) when instead performing of 180 an in ISO two maneuver-lane buses. and speed With 10such m/s a capacity of three-lane buses operating at short intervals (up to one minute); the BRT system can be competitive with the metro line; - in the one-way rotation of the trajectories of the trailer links are shifted with respect to the trajectory of the bus to the center of rotation, thus increasing the overall traffic lane , and the offset of the trajectories and the overall traffic lane increased with the increasing of the base of trailers; 72 The Archives of Automotive Engineering – Archiwum Motoryzacji Vol. 89, No. 3, 2020

4. Conclusions The results of these studies proved that: • promising for big cities, in particular, for the city of Kyiv is the use of three-lane buses capable of carrying up to 300 passengers instead of 180 in two-lane buses. With such a capacity of three-lane buses operating at short intervals (up to one minute); the BRT system can be competitive with the metro line; • in the one-way rotation of the trajectories of the trailer links are shifted with respect to the trajectory of the bus to the center of rotation, thus increasing the overall traffic lane , and the offset of the trajectories and the overall traffic lane increased with the increasing of the base of trailers; • the standardized value of the overall traffic lane for the real design parameters of the three-lane metrobus, taking into account all its possible limitations (bus base, location of coupling points, trailer base, etc.) can provide a three-lane metrobus, both with unruled and driven second trailer. • at the same time, for controlled second trailer OTL is mixed by (12-15)% and it depends on the location of the coupling points of the trailers with the bus and with each other. • when performing an ISO maneuver at a 5 m/s highway speed, both the unruled and guided second trailer will fit into the normalized traffic corridor. However, a speed of 10 m/s, oscillations of the second guided trailer are already observed, and exceed the permissible ones, it can lead to loss movement stability of the metrobus.

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