Research Article Fully Equipped Dynamic Model of a Bus

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Research Article Fully Equipped Dynamic Model of a Bus I. Kowarska, 1 J. Korta, 1 K. Kuczek, 2 and T. Uhl 1 1 Department of Robotics and Mechatronics, AGH University of Science and Technology, Aleja Mickiewicza 30, 30-059 Krakow, Poland 2 EC Engineering Sp. z o.o., Ulica Opolska 100, 31-323 Krakow, Poland Correspondence should be addressed to T. Uhl; [email protected] Received 26 June 2013; Accepted 5 February 2014; Published 15 July 2014 Academic Editor: Nuno Maia Copyright © 2014 I. Kowarska et al. is is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Nowadays, the time to market a new vehicle is crucial for every company as it is easier to meet the customers’ needs and expectations. However, designing a new vehicle is a long process which needs to take into account different performances. e most difficult is to predict a dynamic behavior of a vehicle especially when such a big vehicles as urban buses are considered. erefore, there is a necessity to use a virtual model to investigate different performances. However, there is a lack of urban bus models that can fully reflect a dynamic behavior of the bus. is paper presents a fully equipped urban bus model which can be used to study a dynamic behavior of such vehicles. e model is based on innovative technique called cosimulation, which connects different modeling techniques (3D and 1D). Such a technique allows performing different analyses that require small deformations and large translations and rotations in shorter time and automatic way. e work has been carried out in a project EUREKA CHASING. 1. Introduction In nowadays vehicle industry, time to market is a crucial parameter. It is caused by an increasing number of customers’ needs and expectations to be met. However, vehicle design is a long process, during which engineers need to take into account many guidelines and fulfill all the requirements connected to safety and comfort of the occupants. Predicting the structural dynamic behavior is one of the most difficult tasks, especially when such big vehicles as urban buses are considered. Due to their size and complexity, experimental derivation of comprehensive dynamic performances can be very difficult and economically unjustified. However, as vehicle dynamics is a very important performance, it cannot be neglected in vehicle analyses. erefore, there is an opportunity to take advantage of numerical modeling and simulations, to investigate structural performances under different operational conditions. However, despite that fact, there is a lack of engineering literature describing urban bus virtual prototyping projects. Such a literature would have been of help in understanding how to create models that allow accurately predicting the dynamic behavior of the bus. Standard vehicle design process provides short concept design phase and very long prototype testing stage. However, following van der Auweraer and Leuridan [1, 2], modern product development is oſten based on virtual prototyping according to the rule “Design Right First Time” [3]. It is caused by the need for decreasing production costs and time to market of new vehicle and improving the product quality at the same time. e main objective for the engineering design of pas- senger vehicles is to develop models that perfectly reflect the behavior of a real construction. Typically, to obtain trustworthy structural dynamic response, modal analysis of a real structure has to be performed [4, 5]. Modal analysis is carried out to extract structural resonance frequencies and spatial description of vibration patterns, called normal modes frequencies and shapes, respectively. Classical modal analysis is based on a controlled excitation of a system vibration and measurement of a structure response. is can be easily simulated with a standard finite element approach. However, due to the necessity of input forces measurements, classical formulation has a limited use for a lot of large structures like an urban bus, and it is more convenient to use a method based on operational excitation, called operational modal analysis [6]. erefore, during the simulations, engineers try Hindawi Publishing Corporation Shock and Vibration Volume 2014, Article ID 201952, 9 pages http://dx.doi.org/10.1155/2014/201952

Transcript of Research Article Fully Equipped Dynamic Model of a Bus

Research ArticleFully Equipped Dynamic Model of a Bus

I. Kowarska,1 J. Korta,1 K. Kuczek,2 and T. Uhl1

1 Department of Robotics and Mechatronics, AGH University of Science and Technology, Aleja Mickiewicza 30,30-059 Krakow, Poland

2 EC Engineering Sp. z o.o., Ulica Opolska 100, 31-323 Krakow, Poland

Correspondence should be addressed to T. Uhl; [email protected]

Received 26 June 2013; Accepted 5 February 2014; Published 15 July 2014

Academic Editor: Nuno Maia

Copyright © 2014 I. Kowarska et al. This is an open access article distributed under the Creative Commons Attribution License,which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Nowadays, the time tomarket a new vehicle is crucial for every company as it is easier tomeet the customers’ needs and expectations.However, designing a new vehicle is a long process which needs to take into account different performances. The most difficult isto predict a dynamic behavior of a vehicle especially when such a big vehicles as urban buses are considered. Therefore, there isa necessity to use a virtual model to investigate different performances. However, there is a lack of urban bus models that canfully reflect a dynamic behavior of the bus. This paper presents a fully equipped urban bus model which can be used to studya dynamic behavior of such vehicles. The model is based on innovative technique called cosimulation, which connects differentmodeling techniques (3D and 1D). Such a technique allows performing different analyses that require small deformations and largetranslations and rotations in shorter time and automatic way. The work has been carried out in a project EUREKA CHASING.

1. Introduction

In nowadays vehicle industry, time to market is a crucialparameter. It is caused by an increasing number of customers’needs and expectations to be met. However, vehicle designis a long process, during which engineers need to take intoaccount many guidelines and fulfill all the requirementsconnected to safety and comfort of the occupants. Predictingthe structural dynamic behavior is one of the most difficulttasks, especially when such big vehicles as urban buses areconsidered. Due to their size and complexity, experimentalderivation of comprehensive dynamic performances canbe very difficult and economically unjustified. However,as vehicle dynamics is a very important performance, itcannot be neglected in vehicle analyses. Therefore, there isan opportunity to take advantage of numerical modeling andsimulations, to investigate structural performances underdifferent operational conditions. However, despite that fact,there is a lack of engineering literature describing urbanbus virtual prototyping projects. Such a literature wouldhave been of help in understanding how to create modelsthat allow accurately predicting the dynamic behavior of thebus. Standard vehicle design process provides short concept

design phase and very long prototype testing stage. However,following van der Auweraer and Leuridan [1, 2], modernproduct development is often based on virtual prototypingaccording to the rule “Design Right First Time” [3]. It iscaused by the need for decreasing production costs and timeto market of new vehicle and improving the product qualityat the same time.

The main objective for the engineering design of pas-senger vehicles is to develop models that perfectly reflectthe behavior of a real construction. Typically, to obtaintrustworthy structural dynamic response, modal analysis ofa real structure has to be performed [4, 5]. Modal analysisis carried out to extract structural resonance frequencies andspatial description of vibration patterns, called normalmodesfrequencies and shapes, respectively. Classical modal analysisis based on a controlled excitation of a system vibrationand measurement of a structure response. This can be easilysimulated with a standard finite element approach. However,due to the necessity of input forces measurements, classicalformulation has a limited use for a lot of large structures likean urban bus, and it is more convenient to use a methodbased on operational excitation, called operational modalanalysis [6]. Therefore, during the simulations, engineers try

Hindawi Publishing CorporationShock and VibrationVolume 2014, Article ID 201952, 9 pageshttp://dx.doi.org/10.1155/2014/201952

2 Shock and Vibration

to recreate vehicle operating conditions to obtain the mostaccurate results.

Virtual test rides can be modeled with multibody tech-niques. Multibody models are used to model the dynamicbehavior of a vehicle, which may undergo large translationaland rotational displacements. For this reason, those modelscan be used to simulate vehicles rides. Unfortunately, manyproblems connected to dynamics cannot be solved by usingrigid body approximation of the structure. The necessity formore reliable models describing the complex behavior ofmechanical systems undergoing large motions with smallelastic deformations forced the development of many power-ful analysis techniques. One of the most popular is couplingof rigid multibody systems and flexible components (mostlyfinite elementmodels), supplemented by auxiliary 1D systems[7].

For this reason, the authors decided to build a hybridurban bus model that was composed of a rigid-flexible struc-tural multibody model, equipped with on-board intelligentsystems that have an influence on riding conditions and,consequently, on the results of dynamic analyses.

The developedmodel can be used to evaluate a structure’sbehavior during virtual test rides, which can be carried out ontest lanes providing desired dynamic excitations and forcingdifferent maneuvers.

In this paper, an introduction to rigid-flexible bodycoupling is provided in the beginning. The subsequent partsdescribe the link between 3D spatial model and block 1Dmodeling of the on-board systems and themodel itself. Such alink is called cosimulation and is an innovative technique thatallows performing simulations from different engineeringdomains (from vehicle dynamics to NVH analysis) in shortertime and in automatic way.The paper describes hybrid urbanbus modeling process with underlined base model partslike suspension, structure, and on-board systems. Simulationresults are then correlated with experimental data showingcorrectness of the technique. Those chapters are then fol-lowed by the discussion and conclusions.

2. Coupled Rigid-Flexible Multibody Model

Due to the fact that the full model has been developed withLMS Virtual.Lab software, rigid and flexible equations ofmotion are provided based on [8].

Multibody modeling technique has been developed tosimulate industrial and technological applications that aremade of interconnected components which exhibit relativemovement. These components are represented by sets ofbodies linked together by joints and coupling elements likesprings, dampers conjugated with constraints, and externalforce components. The system has to be prepared in orderto allow motion in the desired direction to ensure requiredoperating conditions (Figure 1).

Rigid multibody systems are considered to have a fixedframe of reference in which motion of the chosen points isobserved.

To describe rigid multibodymotion as a function of time,generation of equations of motion is needed. However, for

Body 1 Body 2

Body 3

Joint

Force ele

ment

Figure 1: Multibody system.

large systems, it is a nontrivial task. For this reason, a lotof formalisms have been developed. Numerical formalismsespecially play a significant role as they are used in computermultibody codes which becomesmore andmore popular andsophisticated [9].

The most popular formalism is one based on Newton-Euler equations rewritten in thematrix form and used in LMSVirtual.Lab [8]:

[𝑀 Φ𝑇𝑞Φ

𝑞0 ] ⋅ [ 𝑞1] = [𝑄𝑔] , (1)

where𝑀represents amultibodymassmatrix,Φ𝑞is a Jacobian

matrix of the vector of constrains relative to the generalizedcoordinates 𝑞, and 𝑄 is a vector of applied forces while 𝑔 isthe constraint acceleration gamma term and 𝜆 is the vector ofLagrange multipliers of the constraints. Equation (1) is thensolved inside Virtual.Lab with special integration codes.

Unfortunately, many dynamic problems cannot be solvedusing only rigid body formulations. In case of small deforma-tions, especially, to calculate structural dynamics, the linearfinite element modeling (FEM) method is employed. Forthis reason coupling between multibody systems and finiteelement models has become an issue. Finite element modelsrepresent linear elastic deformation and can be integratedwith nonlinear, large rotations and translations (multibodymodels). Different solutions for flexible multibody systemscan be found in [10].

In Virtual.Lab formulation, the coupled flexible-rigidmultibody models require a finite element analysis. Theflexibility is represented with a set of flexible body modeswhich is a combination of normalmodes (to represent naturalvibration) and static ones (to represent loading and couplingbetween bodies).

Shock and Vibration 3

+ +

M M

Figure 2: Example of 1D model (block-diagram).

Equation of motion with applied flexibility leads to

[[[[[[

𝑀𝑟𝑀𝑟𝑓Φ𝑇𝑞𝑟

𝑀𝑓𝑟

𝑀𝑓Φ𝑇𝑞𝑓

Φ𝑞𝑟

Φ𝑞𝑓

0

]]]]]]⋅ [[𝑞𝑟��𝜆]]= [[𝑄𝑟𝑄𝑓𝑔]]. (2)

Mass matrix𝑀 is divided into 𝑟-rigid part and 𝑓-flexiblepart; the same applies for Jacobian matrixΦ of the constraintequations. Apart from rigid generalized coordinates 𝑞, a vec-tor of modal coordinates 𝑢 appeared; 𝜆 represents Lagrangemultiplier. On the right-hand side, vector of applied forces 𝑄divided into 𝑄

𝑟forces applied on a rigid body and 𝑄

𝑓forces

applied on a flexible body (including body stiffness matrix)and general constrain force 𝑔 are shown.

Thementioned set of flexible bodymodes can be obtainedin a large number of methods [8]. One of them is the Craig-Bampton dynamic reduction [11]. This method combinesnormal modes with static-constraint modes (𝑞, 𝑢

𝑏) by Craig-

Bampton transformation matrix ΦCB which contains a fixedbase modeshape Φ

𝐿and a rigid body vector Φ

𝑅:

𝑢 = ΦCB ⋅ {𝑢𝑏𝑞 } = [ 𝐼 0Φ𝑅Φ𝐿

] ⋅ {𝑢𝑏𝑞 } . (3)

Modern coupling techniques are still under investigation.

3. 1D System Simulation

The one-dimensional modeling is a mathematical approachin representation of components. In contrast to 3D CAEmodeling, this approach gives the capability to simulatethe behavior of systems before detailed CAD geometry isavailable. Model components are described using validatedanalytical models that represent the systems behavior. Thistechnique of modeling is also referred to as a block modelingor a multiport modeling technique [12]. 1D models arephysical models of real systems that are described withmathematical models (systems equation of motion).

One-dimensional models are created by linking individ-ual physical elements together, creating a block diagram offull system (Figure 2). In such a system, the signal flowsbetween individual components. Due to different mathemat-ical representations of individual elements, the input signalis transformed in a predefined manner, to form an output.Those 1D models can be treated separately (solving theirequations of motion) or can be linked with 3D models bycosimulationmethod linking the two solvers (1D and 3D) thatcan run separately by embedding one set of equations into theother, using only one single solver.

This solution is widely used among automotive engineersespecially to simulate electronic systems inside a vehicle [13].

Forc

e (N

)

Velocity (m/s)

Damper characteristicLogarithmic (damper characteristic)

Rebound

Compression

Figure 3: Typical damper characteristic and its logarithmic approx-imation.

One platform that provides a possibility to build 1Dmodels is LMS Imagine.Lab AMESim that is used in thiswork.

4. Hybrid Urban Bus Model

4.1. Coupled Bus Multibody Model. The urban bus modeldeveloped at AGHUST has been based on a real city bus con-struction. Individual components have been modeled usingCAD geometry and characteristics and additional informa-tion provided by themanufacturer.Themodel contains about70 individual parts and about 90 kinematic joins.Thenumberof general coordinates (including modal coordinates) is lessthan 500.

In case of structural dynamics behavior, the suspensionis used only as a filter between the track and the bussuperstructure. Because of a high rigidity of the suspensionstructural elements and the frequency band of interest, theirdeformations were neglected. For this reason, all suspensionelements, excluding tires, have been prepared as rigid bodies.Only coupling elements (dampers and bushings) have beendescribed with original characteristics to incorporate properstiffness and damping characteristics to the model. To obtainaccurate damping elements characteristics for the front andthe rear suspension, a logarithmic approximation has beenperformed according to the following (Figure 3):

𝐹 = 𝑐 ⋅ ln (V) . (4)

𝐹 represents a rebound/compression damper force, 𝑐 is aconstant (depends on damper type), and V is a car bodyvibration velocity relative to the wheels.

4 Shock and Vibration

To connect bus suspension elements, based on suppliertechnical data, bushing elements are used. Those elementsprovide an interface between two parts, damping the energytransmitted through the bushing. Bus suspension bushingsare made of rubber separating the faces of two metal objectswhile allowing a certain amount of movement.

To provide good simulation results, bus suspension bush-ings have been modelled inside Virtual.Lab Motion softwareas special connector element called bushing. This elementallows providing real bushing characteristics to the virtualmodel as an excel file.

Such connectors minimize vibrations through the chassisof the vehicle in virtual simulations like in the real vehicle.

Another important element that provides tractionbetween the vehicle and the road and absorbs shock is thetire. Based on available information about tire characteristicsfrom the bus manufacturer, those components have beenmodeled using a Virtual.Lab special tire module calledComplex Tire, which permits inputting tire parameterslike diameter, stiffness, damping, and so forth, in termsof providing real ride conditions. Parameters values havebeen taken from supplier data and adjusted to the valuesthat provide good correlation between real experiment andsimulation.

Unfortunately, because of missing measurement of realbushing and tires, no correlation directly for those elementshas been done.

Urban buses are often equipped with a pneumatic sus-pension where standard steal springs are replaced with aircushions, filled with pressurized air. The main advantages ofusing air springs over the standard steel-spring suspensionsin an urban bus are

(i) high comfort expressed by small deflections andlower natural frequencies,

(ii) possibility of controlling the operation conditions, bymodifying the internal pressure value,

(iii) kneeling function—in case of buses this functioneases getting on and off the vehicle on stops [14].

Air springs have beenmodeled as combined damping andstiffness forces elements controlled by ECAS (electronicallycontrolled air suspension) system. Such a configuration pro-vided a possibility of applying real air spring characteristicsto the model.

Due to the fact that the scope of the investigationswas to measure bus driver’s comfort by means of structurevibration level, the bus superstructure has been modeled as adeformable element. Nastran finite element coding was usedto create a FEmodel based onCAD geometry. To simplify themodel, some of the elements like engine or gear have beensubstituted with concentrated mass elements. Figure 4(a)presents an urban bus suspension multibody model andFigure 4(b) presents a coupled flexible-rigid urban busmodel.

4.2. Bus On-Board Systems. To ensure the most realisticsimulation conditions and obtain the most accurate responseof the analyzed urban bus, electronic auxiliary systems havealso been taken into consideration. Nowadays, vehicles are

equipped with electronic devices which improve ride qualityand safety. For a regular urban bus, the most importantare ABS/ASR and EBD (i.e., anti-lock braking system/anti-slip regulation and electronic breaking force distribution)to maintain safety during breaking maneuvers and ECAS(i.e., electronically controlled air suspension) system whichcontrols the work of a pneumatic suspension [15]. To assurea realistic prediction of the behavior of the bus in operatingconditions, the abovementioned systems have been appliedto the coupled multibody model.

As it was mentioned before, bus structure and suspensionhave been modeled with 3D models (multibody and FEmodels), which is necessary to simulate its dynamic behavior.In case of on-board systems, it is not necessary to create 3Dmodels of electronic devices as the most important thing issignal flow from the bus to the electronic units and vice versa.For this reason, on-board systems have been modeled with1D block diagrammethod in Imagine.Lab AMESim software.To integrate 3D bus model and 1D electronic devices, acosimulation between Virtual.Lab and AMESim has beenused to exchange information between 3D and 1D models.

Such a cosimulation technique allows reducing simula-tion time, increasing the realism of the virtual bus.

A brake assist (ABS/ASR and EBD) block diagram,coupled with other parts of the model, is shown in Figure 5.In this circuit, predefined ABS/ASR and EBD elementshave been used. The characteristic parameters have beenelaborated according to the data provided by the systemsmanufacturers. The principles of the breaking maneuver,used for the simulation of themodel equippedwith electronicelements, are similar to realistic driver behavior. Multibodysolver sends a signal toAMESim,which contains informationabout bus actual travelling velocity and angular velocities ofeach wheel. Based on those, breaking torque for each wheelis evaluated and resent to the leading model. Figure 6 showsthat, with break assistant system, the angular velocity of thewheels is a nonzero value, while, without it, axes are blockedin slippage.This underlines the importance of this system forthe passenger’s safety.

The second system applied to a coupledmultibodymodelwas ECAS. Figure 7 presents the ECAS numerical model.This circuit has been fully developed at AGHUST.The inves-tigated system has been equipped with 6 air cushions, twoconnected to the front axle and four supporting the rear one.This asymmetry is due to the unequalmass distribution—thatis, engine, gearbox, and auxiliary systems are located at theback of the vehicle.

The ECAS system has beenmodeled using the inputs pro-vided by the bus manufacturer. By virtue of submitted data,there was a need for approximation of the received numbers.The derivation of the mathematical models describing thedynamical behavior of the air spring can be found in [16–20]. In general, if isothermal process is assumed inside the airspring, its static stiffness can be described by the following[18]:

𝑘𝑠= 𝑑𝐹𝑑𝑥 = 𝑃

𝐴2𝑒𝑉 + (𝑃 − 𝑃

𝑎) 𝑑𝐴𝑒𝑑𝑥 , (5)

Shock and Vibration 5

(a) (b)

Figure 4: (a) Multibody bus suspension system; (b) rigid-flexible multibody bus model.

Driver’ s breaking

EBD

ABS/ASR

Coupled urban bus model

Runstats

Breaking torque

Wheels angular velocity

Bus velocity

k k k

k

k

k

k

k

k

k k k k

k

k

Figure 5: ABS/ASR/EBD signal circuit.

0 1 3 4 5 6 72

1500

1000

500

Time (s)

Whe

els a

ngul

ar v

eloc

ity (d

eg/s

)

Bus without ABS/ESR and EBD Bus with ABS/ESR and EBD

Figure 6: Virtual breaking performance on a slippery road. Com-parison of angular velocity of the left wheel: with and without breakassist.

where 𝐹 is an applied force, 𝑥 is an air sprig deflection(difference between nominal and compressed air springheight), 𝑃 is the absolute pressure inside the air spring, 𝑃

𝑎is

the atmospheric pressure,𝑉 denotes internal bellows volume,and𝐴

𝑒is an effective area of an air spring (i.e., supported load

value divided by 𝑃).Based on a manufacturer’s technical data, a regression

model approximating the static response of each air springwas developed. To fit a curve on the obtained measurementpoints, linear robust least squaresmethodhas been employed.Standard least squaresmethod tends tominimize the squareddistance between the regression curve and the provided datapoints; thus, it is sensitive to outliers. To omit that problem,algorithm described by (6) [17] was implemented whichassigns a weighting factor to every measurement point. Thevalue is inversely proportional to the distance of themeasured

6 Shock and Vibration

Multibody model interference blockAir spring

forceAir spring deflection Compressed air source

Central valve

Air spring valve

Switch

SwitchBump stop force

Inflated air spring force

Figure 7: One-quarter of an ECAS model.

×104

5

4

5

3

5

2

5

18

76

54

3

Forc

e (N

)

Pressure (bar) 200 220240 260

280 300320 340

360 380400

Air spring deflection (mm)

Normal work air spring characteristic

(a)

8

7

6

5

4

3

2

Forc

e (N

)

170 180 190 200 210

Air spring deflection (mm)

Bum stop air spring characteristic

(b)

Figure 8: Measurement data approximation: the inflated air spring (a) and the bump stop (b) characteristics.

points from the fitted polynomial curve; thus, the influenceof the outliers can be minimized. Furthermore, points whichare further than would be expected are ignored during theregression process. Consider

𝑆 = 𝑛∑𝑖=1

𝑤𝑖(𝑦𝑖− 𝑦𝑖)2, (6)

where 𝑤𝑖is the weighting factor for the squared distance

between measured 𝑦𝑖and fitted 𝑦

𝑖values. Measuring equip-

ment inaccuracies are supposed to be invariant in time;hence, the variance of the acquired data should be constant.If this assumption is violated, it is highly probable that inputdata set contains some elements of poor quality. The weights𝑤𝑖are then applied to transform the variances to a constant

value. Results of approximation are visible in Figure 8.Because of a strong nonlinearity of the abovementionedcharacteristic and for simplification, the characteristic wassplit into two separate regions: force generated by an inflatedair spring and force generated by a bump stop, after reachinga critical deflection. The latter is expressed only as a functionof bump stop material stiffness.

Consistent with a measured air spring deflection(received from a multibody model) and desired pressure,corresponding force value is sent back to the base structure.If the deflection falls below the specified value, the signal isswitched to the bump stop characteristics. If, on the otherhand, operational height is within the allowable tolerances,compressed air flow is cut off and the air spring is working asan inflated cushion.

Based on [18], the authors have introduced also anappropriate damping coefficient to the analyzed bus modelto simulate not only air spring stiffness but also its dampingbehavior.

Coupling between flexible and rigid bodies and linkwith on-board systems block diagrams ensures real rideconditions. Because of a juncture between different modelingtechniques, such a structure is called a hybrid model.

5. Simulations

The hybrid model described in a previous chapter has beendeveloped to perform structural dynamics analyses underoperational conditions.

Shock and Vibration 7

0 10 20 30 40 50Frequency (Hz)

10x

Experimental dataNumerical data

Am

plitu

de (m

m/s2)

(a) Frequency response—point A

0 10 20 30 40 50Frequency (Hz)

10x

Experimental dataNumerical data

Am

plitu

de (m

m/s2)

(b) Frequency response—point B

0 10 20 30 40 50Frequency (Hz)

10x

Experimental dataNumerical data

Am

plitu

de (m

m/s2)

(c) Frequency response—point C

0 10 20 30 40 50Frequency (Hz)

10x

Experimental dataNumerical data

Am

plitu

de (m

m/s2)

(d) Frequency response—point D

Figure 9: Comparison between numerical and experimental vibration acceleration as a function of frequency: (a) point A; (b) point B; (c)point C; (d) point D.

In order to examine a usefulness of the developed modelfor the structural measurements, virtual test has been per-formed and compared with the real test ride on a test track,which was combined from two different surfaces on its leftand right side. To obtain the needed data, the conditions ofthe analysis were set the same as in the case of experiment;that is, the traveling speed was set to 30 km/h. During theexperiment, the driver was obliged to keep the velocityconstant, but, because of many factors (e.g., speedometerinaccuracy, irregular pavement conditions, etc.), thiswas onlya rough value. Nevertheless, as can be seen in Figure 9, theresults of numerical computations are in great correlation

with the data obtained experimentally. The peaks at 11 Hzand their harmonics are the consequence of the form of thetest track surface, which was covered by regularly distributedcurbstones, and the vehicle’s speed. Other peaks are causedby structural dynamic response.

Several measurement points located near the suspensionmountings (points A (Figure 9(a)) and B (Figure 9(b)))and near the driver seat (points C (Figure 9(c)) and D(Figure 9(d))) were chosen to collect the experimental dataduring the tests.The obtained results were compared with theoutput from the numerical computations, which is shown inthe examples in Figure 9.

8 Shock and Vibration

Figure 10: Hybrid urban bus model-stress Von Mises’s measure-ment.

The differences are results of imprecise mapping of theroad due to its complicated shape. Inaccuracies can alsoresult from differences in placing the accelerometers on realand virtual structures, which affects the output data strongly.Another reason of the numerical and experimental datavariations can arise from the tire modelling technique. Asmentioned before, the tires have been modelled with thespecialized Virtual.Lab module, including proper featureslike stiffness and damping. However, due to the complexity oftire dynamic characteristics and the difficulties in modellingthe contact between the track and thewheels, those importantparameters can be only roughly approximated.

However, the developed model is precise enough to beused for different measurements. For instance, the describedmodel can be used for stress and strain evaluation; hence,the weakest regions can be pointed out. Figure 10 showsan example of a stress distribution map. Such analyses areextremely useful because they can reveal structural defectsin the very first phase and, hence, the problem can be solvedbefore the first prototype is released.

6. Conclusions

Urban buses have not yet been investigated thoroughly whichopens the way to many improvements that can be obtainedcheaply, by means of numerical methods. The presentedhybrid urban bus model is a link between different modelingtechniques which takes advantage of them in order tosolve complex structural dynamics problems. Utilization ofcoupled flexible-rigid multibody model instead of dynamicloads on finite element model only gives more reliablerepresentation of reality. Buses work on the streets and theirsstructures are extorted with road irregularities. Applyingsuch load conditions to a pure FE model is not a trivialtask. However, with the proposed model, it can be achievedusing an arbitrary track model and a contact connectionwith tires. Hybrid urban bus model has been developed,linking FE structure model (to make stress calculation onit possible), rigid suspension multibody model (for vehicledynamics simulations with large translations and rotations),and 1D modeling techniques of on-board electronic devices

(where time-consuming 3Dmodeling is not necessary). Sucha model is useful for analyses of structure behavior underreal, operational loads and optimizing in terms of vehicleparameters.

Such a model has been simulated in terms of operationalconditions from real bus test on test truck. Results ofsimulation and real experiments have been compared. Thecomparison presented good correlation between data, whichmeans that model can be used for virtual prototyping ofurban buses.

The proposed multibody hybrid model can be usedinstead of FE representation, ensuring more precise results;due to application of realistic operating conditions, the usageof commercial software ensures the availability of themethod.

The elaborated modeling technique can be also used inthe optimization problems, combining both structural andvehicle dynamics, which is planned for the future.

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper.

Acknowledgments

This work is a part of international project EUREKA E! 4907done at AGH University of Science and Technology fromPoland with consortium from Belgium LMS Internationaland Poland including EC Engineering and Solaris Bus &Coach. The authors would like to gratefully acknowledgethe support from the Polish National Centre of Researchand Development. The authors kindly acknowledge also theother researchers at LMS International, EC Engineering,and SOLARIS Bus & Coach, who have contributed to theCHASING R&D activities and results reported in this paper.

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