Bulletin of the Transilvania University of BraşovCIBv 2015 • Vol. 8 (57) Special Issue No. 1 - 2015

THE VERTICAL VIBRATIONS STUDY OFMOTOR BOGIES FOR RAILWAY

VEHICLES

V. ŞTEFAN1 I. SEBEŞAN2 C. PLEŞCAN3 L. BLAGA4

M. CARABINEANU5 G. A. BADEA6 G. DUMITRU7

Abstract: A vehicle passing over irregularities or discontinuities tread(joints, wear undulating spaces merge two coupons welded rail, etc.) inducesmechanical vibrations that are transmitted tread and vehicle acceleratingphenomenon of wear. The dynamic forces occurring with these vibrations byadding them to the static values affect road safety if they exceed certainlimits, so it is important to know them. A well-balanced primary suspensionmakes bogie accelerations received from track to be smoothed largely.

Key words: wear undulating, vertical acceleration, bogie, gallop.

1 Railway Territorial State Inspectorate of Braşov - ASFR.2 Rolling Stok Department, Politechnica University of Bucharest.3 Civil Engineering Department, Transilvania University of Braşov.4 Politechnica University of Bucharest & ASFR.5 Politechnica University of Bucharest & Romanian National Railway Safety Authority - ASFR (NSA).6 Politechnica University of Bucharest - ASFR.7 Control Traffic Safety Department, National Railway Safety Agency - ASFR.

1. Introduction

The running track is a mechanicalsystem whose elements deform elasticallyunder time varying external requests,which take arise interaction with movingvehicles [1]. These elements (rail,sleepers, fastenings, ballast, substructure,etc) resiliently deform [6] and movingrelative to each other during movement ofvehicles [7], inducing oscillations in thewheel-rail contact that transmit bothvehicle structure and track [10]. Thepriming vibration in the wheel-rail systemoccurs mainly at passing vehicles overdisruptions to the running rail track andshowing various defects railhead (rust,wear, wave, etc.) [9].

This paper will study the verticaldynamic overloads that occur in the bogiewhen travelling on a way to wear waveamplitudes and accelerations are primedusing deterministic methods.

2. The Study Bogie Vibrations Bob

The railway bogie is considered a motorvehicle whose equivalent mechanicalmodel is shown in Figure 1. havingsuspended bogie mass denoted by m+ andpass over the path defective levelling withspeed v. Assuming that defectslongitudinal level of the two threads aresymmetrical about the center line of thetrack and considering that η it is a functionharmonic form ,

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corresponding equivalent mechanicalmodel shown in Figure 1, the equations ofmotion for the bob will be given in theform (1), the disturbance to the bouncinghas the expression (2).

(1)

Fig. 1. Model equivalent to studymechanical vibrations of the bogie

jumping movement

Given that the present rail vehicles andelastic symmetry plans mass vertical -transverse and vertical - longitudinal studyof kick on forced vibration can be usedadequately reduced model of Figure 2.

Fig. 2. Model equivalent to study mechanicalvibrations of the bogie jumping movement

Correspondingly reduced modelequation of motion bob, is given in theform (3).

(3)

In Figure 2, the notation used is thereduced mass of the bogie to kick on:

, reduced stiffness of the bogieto the jumped movement: ,low damping coefficient for the bogiejumping motion: and that themovement in the vertical direction of thereduced mass of the bogie: q.

Due to the interaction with the wheels ofthe railway vehicle tread wear [10] andforms of wear with some periodic gait [2].The wavelengths range between 30÷300mm and amplitude to 0,015 mm. If wedenote by the undulations depth on astretch of rail length L equation profilethese irregularities [5] can be described bythe relation (4).

and (4)

and (5)

Since the system excitation sinusoidaland vertical movement of the system willbe sinusoidal in the complex form of thesemovements can be written as shown inequation (5), where is the amplitudeof the disturbance that produces bouncing,its pulsation, is the amplitude ofvertical displacement of the sprung massof the bogie α - is the phase shift betweenthe excitation and the moving q [4].

(6)After the derivation and replaced them

expressions in (3), we obtain the equation(6). Considering the bogie an objectoriented transfer function attached toequation (6) is given by the ratio between

V. ŞTEFAN et al.: The Vertical Vibrations Study of a Motor Bogies for Railway Vehicles 289

the output function and the input

function , resulting the relationship (7).

(7)

If the equation (7) the followingsymbols are namely pulsation of the own

bogie , disagreementbetween excitation and pulsation own

bogie , to the amortization of the

bogie ,obtaining expression of the transferfunction module (8), which allows thetransition from q to ω.

(8)

Accordingly, the phase differencebetween the disturbance η and the answerq of the vibrant system will be in the form(9).

(9)

The same way that we obtained relation(8), determine response relationship foracceleration factor , whose expressionwill be given in the form (10).

(10)

In order to determine the amplitude ofthe disturbing movement η0s a two-axlebogie, it should be noted that the pulses η1,

and η2 which acts on the two axles are outof phase [4]. If the bogie wheelbase is 2a+,the movement velocity is v, for anharmonic amplitude η0k and pulsation ωwe have the expression (11). Substitutingthe relations (11) in (2) follows therelationship (12) amplitude disturbance ηthe movement of the jumping.

and

(11)

(12)

Corresponding relation (12), amplitudeperturbation depends on the jumpedmovement considered harmonic amplituderatio between the product and cosine pulsetime fault semi-wheelbase the bogie andthe speed at which it passes over defect.

2.1. The Study of Bogies VibrationGallop

Gallop movements of the bogies due tothe excitation received from the wheel-track system, may overlap with theflexural vibration of the vehicle box, andif the oscillation frequencies of the twomotions are similar in certain conditionscan lead to the movement of the resonance[4]. To avoid these situations, we havedetermined the main parameters thatinfluence the movement of the vehicle andset conditions that gave resonance occurs.

Under the assumption that the bogie issymmetrical (both geometrically and interms of the distribution of masses,stiffness and depreciation) against planslongitudinal and transverse pass verticallythrough the centre of mass of the bogie,we have a decoupling of movementsaltation vertical movement of the bogieframe and its gallop [2].

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Considering further that defectslongitudinal level of the two-wire path aresymmetrical with respect to the centralaxis of the track, and that η is a functionharmonic form , reducedaccordingly equivalent mechanical modelshown in Figure 3 equations of motionwill be played gallop form (13).

(13)

Substituting in (13) the moment ofinertia Iy suspended parts of the bogie inrelation to the y axis, corresponding to theradius of gyration determined by therelationship (14) can be written as (14).

(14)

From equation (14) and to study thevibrations that forced gallop reducedmodel can be used in Figure 4, where theidentification, we will track thedisturbance that produces motion gallop

[5]: , the reduced mass of thebogie for movement gallop:

, reduced stiffness of the

bogie: , the low damping

coefficient for the bogie: , thedisplacement in the vertical direction ofthe reduced mass of the bogie movementgallop: q= .

With these notations, equation (14) canbe written as (15) and (16) using thefollowing notations for pulsation ownbogie for movement gallop:

, t he difference between thepulsating excitement that produces its ownmotion gallop and pulsation bogie [2]:

and that the degree of dampingof the bogie for movement gallop:

.

Fig. 3. The variation the vibration accelerationjumping movement qs (ω), excitation depending

on the defect path

Fig. 4. The variation the vibration accelerationjumping motion qs (ω) and vibrationacceleration gallop qg (ω), excitation

depending on the defect path

The gallop bogie movement issinusoidal, can be written in complex form

(17) where It is the amplitude of thedisturbance that produces gallop, pulsationof this movement, represents theamplitude of vertical displacement of thesprung mass of the bogie α - the phase

V. ŞTEFAN et al.: The Vertical Vibrations Study of a Motor Bogies for Railway Vehicles 291

shift between the excitation andmoving displacement q.

and (15)

(16)

(17)

After the derivation expressions (17)and replaced them in equation (16) givesthe response factor (18) of the gallopmovement. The module of the transferfunction, which allows switching from qto ω, is determined by the relation (19).

(18)

(19)Accordingly, the phase difference

between the disturbance ηg and the answerq of the system will be played rousingform (20). The same way that we obtainedrelation (19), determining factor moduleresponse time acceleration gallop [5], thiswill be the expression (21).

and

(20)

(21)

The amplitude η0g of the disturbance thatproduces gallop, is determined taking into

account the pulsations η1 and η2 the twoaxles are out of phase, the vehiclewheelbase 2a+ the forward speed v, for anharmonic amplitude η0k and pulsation ω,can be written as (22). After replacing thedisturbance in relation to gallop apparentrelationship (23).

(22)

(23)

As in the case of the jumpingmovement, perturbation amplitudegalloping movement depends amplitudesharmonic sense considered and pulsationratio of product defect with semi-wheelbase date the bogie and the speedwith which it passes over defect [2].

3. The Determination of PartiesSuspended Bogie Accelerations,Vibrations Jumping Products andGallop

The amplitude the acceleration producedby the parties suspended bogie of thebouncing motion with viscous dampingcan be determined from equation (10), thereplacement of variable can play in form(24).

(24)

The amplitude the acceleration producedby the parties suspended bogie bouncingmotion with viscous damping can bedetermined from equation (10),replacement variables that can play intoshape (25).

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(25)Likewise the results in the relation of the

amplitude of acceleration of the bogiesuspension parts produced by themovement of galloping shown in equation(23) or replace the amplitude of thecorresponding relationship given byequation (23) we obtain the final shape(22) amplitude. From relations (24) and(25) that the vertical accelerations of thebogie jumped and the gallop depend onthe elastic parameters of the suspensiondamping and especially the amortization.The moving at high speed bogies of avehicle over track defects at thewavelengths small and large amplitudescan produce accelerations unacceptablesystem [8].

3.1. Practical Application

It is considered elastic system consistsof a rail bogie motor vehicle, havingprimary suspension and amortization oneach of the two axles, horny similar pathwears uneven vertical wave [5]. The studyintends to system parameters in Table. 1to determine accelerations arising from afaulty level crossing whose profile isknown equation.

The graph accelerations due to the bogievibration jumping recorded travelling atspeed 27.77 m/s over an area ofundulating wear of the rail, (Figure 5)shows that up to a value of the pulsationexcited about 45 rad/s, there are nosignificant values [3].

Fig. 5. The variation the vibration accelerationjumping motion qs (ω) versus excitation path

and velocity the defect

Fig. 6. The variation the vibration accelerationjumping movement qs (ω) versus excitation

path and velocity the defect

V. ŞTEFAN et al.: The Vertical Vibrations Study of a Motor Bogies for Railway Vehicles 293

The elastic parameters of the bogie system Table 1

Around bogie jump oscillation its ownfrequency is recorded maximumaccelerations then reverses and dangerousincrease with increasing speed and / ordecreasing wavelength defect.

Comparing graphics acceleration due toboth vibration and vibration gallopjumping the bogie recorded travelling atspeed 27.77 m/s over an area ofundulating wear of the rail (Figure 6)shows that there is a value and of the pulsegalloping excited about 45 rad/s, to whichthe accelerations are not as significant.

The gallop frequency is determinedaround the bogie is recorded maximumaccelerations then reverses and a similarpattern to those of the jumped movement[2]. The movement of railcar thought overthis defect can be done safely up to speed44.44 m/s, this being the maximumallowed speed bus traffic on railway linesfrom our country. Furthermore, in thegraph 3D of Figure 5 and Figure 6 theremay be same.

4. Conclusions

The comfort criterion variable verticalloading vehicles is essential, dampingcoefficients corresponding to the two floorsof the suspension being adopted in themajority of cases this criterion.

The study vibrations and the bogie gallopjumping are revealed the dependencevertical accelerations of two importantparameters and elastic degree of dampingsuspension axles and pulsation excitationreceived from track.

The speed circulation greater than 40 m/son track with undulating who wear largeamplitudes and small wavelengths, canproduce unwanted acceleration in the bogieframe, which transmit the box and whichaffects both comfort and road safety.

Acknowledgements

The work has been funded by theSectorial Operational ProgrammeHuman Resources Development 2007-

Parameters Name Symbols Values Unit ofmeasure

unsparing mass of the axle 1600 Kg

vertical stiffness of the primary suspension 3.164x106 N/m

vertical suspension damping coefficient primary 7.8 x103 Ns/m

pulsation suspended bogie own mass to jumping motion 68.46 rad/s

frequency of the sprung mass of the bogie to jumping motion 10.9 Hzsuspended mass of a bogie 2700 Kgreduced mass of the bogie to jumping motion mrs 1600 Kgradius of turn of the bogie relative to the axis y 1.4 mlow bogie mass gallop mrg 2646 Kgsemi-wheelbase the bogie a+ 1 mpulsation own bogie for movement sprung mass gallop 48.9 rad/s

frequency of the sprung mass of the bogie to gallop 7.78 Hzforward speed of the vehicle v 27.77 m/samplitude undulations h1 15x10-6 mthe wavelength of the defect Λ 2 mthe degree of damping of the suspension jumping motion primary Ds 0.084 -the degree of damping of the suspension gallop primary Dg 0.06 -

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2013 of the Ministry of European Fundsthrough the Financial AgreementPOSDRU / 159 / 1.5 / S / 132395.

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