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Experimental and Analytical Ride Comfort Evaluation of a Railway Coach
K. V. GangadharanMechanical Engineering Department, National Institute of Technology Karnataka, Surathkal,Srinivasnagar 575025, India. Email: [email protected] or [email protected]
C.Sujatha*Machine Dynamics Lab., Applied Mechanics Department, Indian Institute of TechnologyMadras, Chennai, 600 036, India. Email: [email protected] or [email protected]
V. RamamurtiMachine Dynamics Lab., Applied Mechanics Department, Indian Institute of Technology
Madras, Chennai, 600 036, India. Email: [email protected](* Corresponding author)
ABSTRACT
The dynamic performance of a railroad vehicle as related to safety is evaluated in terms of specific performanceindices like ride quality. The ride quality is interpreted as the capability of the railroad vehicle suspension tomaintain the motion within the range of human comfort and or within the range necessary to ensure that there isno damage to the cargo it carries. The recent trend in dynamic analysis is to make use of finite element (FE)models, which are closer to the real systems than conventional rigid body models. Experimental and analyticalevaluation of Sperling’s ride index and ISO 2631 ride comfort analysis of a suburban railroad vehicle using anelaborate finite element model is presented in this paper. The track power spectral densities (PSDs) were used asinputs to the system and the response predictions were carried out using random vibration theory. Measurementswere also made at different parts on the coach and bogie of an electrical multiple unit trailer (AC/EMU/T) runningon a broad gauge (1676 mm) suburban track to obtain the dynamic response under normal operating conditions.A comparison of predicted ride index and measured ride index has been presented. A through parametric studyhas brought out possible design modifications for better ride index and ride comfort.
KEY WORDS
Railroad vehicle, ride index, ride comfort, dynamic response, finite element modeling, track irregularities, powerspectral density
NOTATION
a peak acceleration Sp(f) force power spectral density α(if) receptanceB acceleration weighting factor Sx(f) displacement power spectral density φ rollf frequency (Hz) Wz Sperling’s ride index θ pitch[K] stiffness matrix {x} displacement vector[M] mass matrix z bounce
1 INTRODUCTIONThe dynamic performance of a railroad vehicle as related to safety is evaluated in terms of specific performanceindices. The quantitative measure of ride quality is one of such performance indices. Ride quality is interpreted asthe capability of the railroad vehicle suspension to maintain the motion within the range of human comfort and orwithin the range necessary to ensure that there is no damage to the cargo it carries. The ride quality of a vehicledepends on displacement, acceleration, rate of change of acceleration and other factors like noise, dust, humidityand temperature. EERI report B 153/RP21 [1] gives a detailed comparison of different methods used forevaluation of ride index. There are two approaches generally used to evaluate the ride quality of a vehicle: theride index method and the fatigue time method. The Sperling’s ride index (Wz) is the ride index used by IndianRailways to evaluate ride quality and ride comfort. Ride comfort implies that the vehicle is being assessedaccording to the effect of the mechanical vibrations on the human body, whereas ride quality implies that thevehicle itself is being judged. According to International Standards Organisation (ISO), the influence of vibrationon the human body is expressed by the fatigue time T. ISO 2631 (1985) [2] defines three levels of fatigue time T:fatigue − decreased proficiency, exposure limits and reduced comfort boundary.
Safety, ride comfort and economy are the major factors behind any successful transportation business.Elmaraghy [3] presented a computer program developed in FORTRAN, to find the ride quality of a rail vehicleconsidering analytical track PSDs as input. Lyon [4] described the experimental methods used for dynamicmeasurement in rail vehicle research and emphasised the importance of response measurement along the lengthof the coach for accurate ride quality calculation. Sujatha et al. [5] conducted experimental and analytical studieson a typical Indian bus to evaluate whole body vibration exposure of the occupants and the driver. Finite element(FE) models were used for the analytical studies. Suzuki [6] presented a review of various ride comfort evaluationmethods and relevant research carried out in Japan. Hariharan [7] estimated the ride index of a high power dieselmultiple unit rail coach of Indian Railways. He used the multi−body simulation package, ADAMS/Rail for ride indexestimation.
This paper presents the ride index evaluation and comparison of reduced comfort boundary curves withanalytically and experimentally determined dynamic response of the Electrical Multiple Unit/Trailer (EMU/T) coachand also presents a parametric study to evaluate possible design changes to improve ride comfort of a suburbanrailroad vehicle.
2 MATHEMATICAL MODELS OF VEHICLE /TRACK SYSTEM
Sub structure
Car body
Bogie
Primary suspension
Wheel and axle
Track
Figure 1 A railway vehicle component description
Secondary suspension
An EMU/T coach running on broad gauge (1676 mm) suburban Indian track has been modelled. The vehicleconsists of a car body, two bogies per car, four wheels and two axles for each bogie (Figure 1). The vehicle hastwo tier suspension bogies. The car body is connected to the bogies through the secondary suspension, whichhas four sets of coil springs and two dampers in the vertical direction. Wheels and axles are connected to thebogies through the primary suspension system. Four coil springs, two on either side of the wheel constitute theprimary suspension. These springs are vertically guided using dashpots fixed in the centre of the coil springs. Twoapproaches used for modelling the track vehicle system are those using the finite element model and the rigidbody model.
2.1 Finite element modelsThree different FE models were generated with increasing levels of sophistication. The simplest is the modelwhere the underframe alone was modelled by lumping the superstructure mass and inertia. The next level wasachieved by adding the superstructure framework on to the underframe model, neglecting the sheet metalcovering the framework. The last and most elaborate FE model is the one where the superstructure frameworkand the sheet metal panels were also modelled. Details of the model developed and relevant dynamic parametershave been presented by the one of the authors in an earlier work [8]. A brief explanation of the FE model usedhas been presented in this paper.
In the FE model, the rail has been treated as a beam on elastic foundations (BEF), ie. the track has beenconsidered as an Euler Bernoulli beam resting on Winkler’s foundation with vertical translation and rotation aboutlateral axis being present. The primary and secondary suspensions were modelled as springs with verticaldegrees of freedom (dof) in the case of the vertical model and as springs with vertical and lateral dof in the caseof the combined vertical and lateral model. The axle, bogie frame and underframe with sole bar, cross bearer andsuperstructure framework were modelled with 3D beam elements with all the six dof present. All sheet metalpanels were modelled using triangular plate elements. The model has 576 nodes, 866 beam elements and 768triangular plate elements. It has 3080 active dof and a bandwidth of 216. Mass and stiffness matrices wereassembled in banded form to save core and labour. The problem size is 3080 × 216 for the vertical and lateralcombined model (Figure 2)
Z
X
Z
Y
Y
X
Figure 2 FE model of vehicle / track system – UFBP model.
2.2 Rigid body modelA rigid body model for vertical dynamics studies was developed, consisting of seven rigid bodies ie. car body, twobogies, four wheels and axles and stiffness of primary and secondary suspensions. Degrees of freedomconsidered are the bounce (z), pitch (θ) and roll (φ) of the car body and bogie. Besides, the wheel and axle'sbounce and roll are also taken into account adding up to 17 degrees of freedom (Figure 3). The equations ofmotion were written for all the masses and moments of inertia and are rearranged in matrix form [9]
[ ]{ } [ ]{ } { }0xKxM =+&& (1)
zc
zb1
zw1
θc
θb1
φw1
φb1
φc
Figure 3 Seventeen dof vertical rigid body model of vehicle / track system
3 SPERLING’S RIDE INDEX (Wz)The ride index Wz was introduced by Sperling, in order to evaluate ride quality and ride comfort of a railroadvehicle [10]. The vehicle itself is judged by the ride quality and ride comfort implies that the vehicle is assessedaccording to the effect of mechanical vibration on the occupant.
Ride quality, ( ) 10/13896.0 faWz = (2)
Ride comfort, ( )[ ] 10/13 )(896.0 fFfaWz = (3)
where a is the peak acceleration in cm/s2, f the frequency in Hz and F(f) the frequency dependent weighting factorthat expresses human vibration sensitivity. F(f) is different for vertical and horizontal vibration components. Table1 gives the ride index evaluation scale. Equations (2) and (3) were rewritten without changing their contents, tosuit the use of electronic instrumentation directly to evaluate the ride index.
( ) 10/133BaWz =
( ) 67.6/122BaWz = (4)
where a is the amplitude of acceleration in cm/s2 and B the acceleration weighting factor (Figure 4). Thefrequency weighting factors are defined for ride quality and ride comfort in different directions as follows.
The weighting function B for vehicle ride quality is
( ) ( ) ( )[ ]( ) ( )[ ]( )
2/1
22322
2222
55.3100444.0547.1252.0135.30645.0056.0114.1
+−+−
+−=
ffffffB (5)
The weighting factor B for ride comfort in the horizontal direction is given by
( )( ) ( )
2/1
2322
222
0368.0563.1277.0125.0911.1737.0
−+−
+=
fffffBw (6)
The weighting factor B for ride comfort in the vertical direction is given by
( )( ) ( )
2/1
2322
222
0368.0563.1277.0125.0911.1588.0
−+−
+=
fffffBs (7)
Hence
sw BB 25.1= (8)
0 5 10 15 20 25 300.0
0.2
0.4
0.6
0.8
1.0 Ride comfort horizontal Ride comfort vertical Ride quality
Wei
ghtin
g fa
ctor
B
Frequency Hz
Figure 4 Sperling’s ride index − frequency weighting curves
The vehicle body vibration is not at a single frequency, but encompasses a whole spectrum of frequencies inwhich the natural frequencies of the vehicle are very much pronounced. In such cases, the ride index calculationhas to be done for the entire spectrum. The Wz ride factor is determined for each individual frequency fromEquation (4) and the total Wz factor is calculated as
( ) 10/110103
102
101 ntotal WzWzWzWzWz ++++= Λ (9)
or
( ) 67.6/167.667.63
67.62
67.61 ntotal WzWzWzWzWz ++++= Λ (10)
The vibration spectrum of the vehicle is not discrete, but a continuous function of frequency. The total Wz rideindex can be obtained for a continuous spectrum by integration over the given range of frequencies.
∫10/1
332
1
=
f
fdfBaWz (11)
where f1 and f2 are the lower and upper end of the range of frequencies considered.
Table 1 Ride evaluation scales − ride quality and ride comfort [10]
Ride index Wz Ride quality1 Very good2 Good3 Satisfactory4 Acceptable for running
4.5 Not acceptable for running5 Dangerous
Ride Index Wz Ride comfort1 Just noticeable2 Clearly noticeable
2.5 More pronounced but not unpleasant3 Strong, irregular, but still tolerable
3.25 Very irregular3.5 Extremely irregular, unpleasant, annoying;
prolonged exposure intolerable4 Extremely unpleasant ; prolonged exposure
harmful
3.1 Ride Index − Analytical ResponseThe ride index (both ride comfort and ride quality) was calculated from the predicted dynamic response. A railroadvehicle can be treated as a system with eight random loadings, i.e. random input disturbances due to the trackirregularities at each of the eight rail wheel contact points. If the input from the left rail is completely correlated
with that of the right rail, then the system can be simplified to a case of four random loadings. For a single randomloading to a system, the response is given by the following equation.
)()()( 2 fSiffS px α= (12)
Equation (12) gives the simple relationship between the spectral densities of excitation and response. Here Sx(f)is the output displacement power spectral density, Sp(f) is the input force power spectral density and α(if) is theratio of displacement at any point to a unit sinusoidal force as the input. This equation can be extended for fourrandom loadings. The dynamic response of different points on the coach floor was predicted using the FE modelwith the track irregularity PSD as input. Track PSDs of the Indian rail tracks were obtained from Iyengar andJaiswal [11], the origin of which can be traced to Research and Design Standards Organisation (RDSO),Government of India, Ministry of Railways. The track PSDs used for the present work have been shown in Figure5 as spatial PSDs.
The dynamic response at four points on the central line of the coach as indicated in Figure 6 has beendetermined. Table 2 shows the ride index (vertical direction) at four different points on the coach. The table showsboth ride comfort and ride quality at different speeds. As shown in Figure. 7, the response at different points onthe coach varies at different speeds. This variation is reflected in the ride index also. In all the cases, the extremeend of the coach has higher vibration and hence higher ride index. The pattern of variation of vertical accelerationresponse along the length of the coach is not same at all speeds. This is seen from the variation of ride index atdifferent points too. For the coach analysed, upto 60 kmph, ride comfort value is less than 2, i.e. in the ‘justnoticeable’ to ‘clearly noticeable’ region. From 75 kmph to 150 kmph, ride comfort is in the range of ‘morepronounced but not unpleasant’ to ‘strong, irregular, but still tolerable’ region. Similarly, ride quality upto 60 kmphvaries from ‘good’ to ‘satisfactory’ and 75 kmph to 150 kmph, it is in the range of ‘satisfactory’ to ‘acceptable forrunning’. It is to be stressed that the coach used for the analysis is a suburban coach which runs at an averagespeed of 45 kmph. From the lateral acceleration response, ride index in the lateral direction was calculated andtabulated in Table 3. The lateral acceleration levels were higher than the vertical acceleration and at speedsabove 75 kmph, the vehicle showed acceleration levels and ride indices higher than the acceptable limits. Thelateral rms acceleration does not vary along the length of the coach and hence same ride indices were found atdifferent locations on the coach floor.
0.01 0.1 1
10-1
100
101
102
103Track vertical profile PSD
Ver
tical
pro
file m
m 2 /
(c/m
)
Frequency c/m0.01 0.1 1
10-2
10-1
100
101
102
103
104Track alignment PSD
Alig
nmen
t mm
2 / (c
/m)
Frequency c/m
0.01 0.1 110-2
10-1
100
101
102
103
104Track Cross level PSD
Cros
s lev
el m
m 2 /
(c/m
)
Frequency c/m0.01 0.1 1
10-2
10-1
100
101
102
103
104Track gauge PSD
Gau
ge m
m 2 /
(c/m
)
Frequency c/m
Figure 5 Geometrical track irregularity PSDs in spatial domain (mm2/(cycle/m) vs cycle/meter)
1 3 5 7
2 4 6 8
Longitudinal
Late
ral
Figure 6 Measurement points on the floor of the coach (Top view of the floor)
0 4000 8000 12000 16000 20000
0.00
0.02
0.04
0.06
0.08
0.10
150120
9075
6045
3015
Vertical rms acceleration along solebar length
Speed
kmph
Distance along solebar mmV
ertic
al rm
s acc
eler
atio
n g
Figure 7 The vertical rms acceleration response along solebar length
Table 2 Ride index predicted (vertical direction) at different speedsRide quality
(at locations 2, 4, 6 and 8 on floor)Ride comfort
(at locations 2, 4, 6 and 8 on floor)Speedkmph 2 4 6 8 2 4 6 8
15 1.26 1.22 1.30 1.36 1.43 1.36 1.46 1.5630 1.90 1.38 2.03 1.47 2.31 1.51 2.46 1.6645 1.84 1.56 1.96 1.64 2.20 1.64 2.37 1.8260 1.84 1.81 1.84 1.87 2.01 1.91 1.94 2.0275 2.15 2.10 2.24 2.22 2.38 2.23 2.51 2.3790 2.56 2.51 2.72 2.72 2.83 2.70 3.03 2.92
120 2.80 2.78 2.94 3.20 3.03 2.99 3.17 3.24150 2.73 2.65 2.79 2.84 3.07 2.96 3.14 3.18
Table 3 Ride index predicted (lateral direction) at different speedsRide quality
(at locations 2, 4, 6 and 8 on floor)Ride comfort
(at locations 2, 4, 6 and 8 on floor)Speedkmph 2 4 6 8 2 4 6 8
15 2.26 2.26 2.26 2.26 2.58 2.58 2.58 2.5930 2.31 2.31 2.31 2.31 2.65 2.65 2.65 2.6545 2.06 2.06 2.06 2.06 2.40 2.40 2.40 2.4060 2.02 2.02 2.02 2.02 2.29 2.29 2.29 2.2975 2.81 2.81 2.81 2.81 3.22 3.22 3.22 3.22
3.2 Ride Index − Measured ResponseThe ride comfort and the ride quality were calculated from the measured acceleration responses at differentpoints on the coach. The measurements were carried out at different stretches of suburban track at about 45kmph speed as explained in [12]. Table 4 shows the comparison of the ride index calculated from the analyticalresponse and the measured response in the vertical direction and Table 5 shows the comparison of lateral rideindices. The ride index obtained from measured response has the same pattern of variation as the analytical rideindex with 10 to 30 % higher magnitudes. The measured dynamic response also has the same level of highervalues; this can be attributed to incomplete inputs used for analytical prediction, system parameter variation andpossible small speed variations during measurement. Along with the track irregularities, irregularities on wheelslike wheel flats might have been present in the normal running condition. The coaches used for measurementwere the same as the one modelled, but a difference in system properties due to extensive use might have beenpresent. The track PSD used for analysis was measured on a continuously welded main line track [11], whereasthe response measurements were carried out on suburban tracks with short welded rails. It has been found thatthere are variations in the response amplitude for different stretches of the track. Tables 4 and 5 give two sets ofride indices calculated from the dynamic response measured on different stretches of the track.
The FE model was used to predict the ride index of the railroad vehicle at different locations of the coach floor.There exist considerable variation of the ride indices calculated from one end of the coach to the middle of thecoach (Table 2). The measured response and corresponding ride indices verified these analytical findings. A rigidbody model cannot predict the variation in the ride index along the length of the coach. This emphasises the needfor using an FE model for ride index analysis. The measured ride indices show that the ride comfort at 45 kmph isin the range of ‘clearly noticeable’ to ‘more pronounced but not unpleasant’. It has been found that the end of thecoach has higher vibration levels than the rest of it. The analytical studies show that the car cg can have higher orlower amplitude of vertical acceleration response compared to other points on the coach depending on thelocation in the coach and speed (Figure 7). This has been clearly brought out in the analytical ride indices shownin Table 2.
Table 4 Comparison of analytical and experimental ride indices at 45 kmph− vertical
Analytical Experimental*Locationon thecoach Ride quality Ride comfort Ride quality Ride comfort
2 1.84 2.20 2.582.59
2.822.84
4 1.56 1.64 2.012.02
2.212.26
6 1.96 2.37 2.362.16
2.712.23
8 1.64 1.82 2.192.02
2.442.26
Table 5 Comparison of analytical and experimental ride indices at 45 kmph−lateralAnalytical Experimental*Location
on thecoach
Ride quality Ride comfort Ride quality Ride comfort
2 2.06 2.40 3.093.07
3.343.32
4 2.06 2.40 3.123.10
3.373.36
6 2.06 2.40 3.00.3.15
3.113.38
8 2.06 2.40 3.013.06
3.143.21
* Two sets of values for two similar stretches of track indicated
4 COMFORT GUIDELINES − ISO 2631The evaluation of ride comfort involves assessment of human sensitivity to vibration, which depends not only onthe physiological and biomechanical response of the human body, but also on a number of psychological andenvironmental factors. The human reaction to vibration is a function of the amplitude and frequency ofacceleration applied to the body, the direction (vertical and horizontal) and character of the motion (linear orrotation). Extensive research has been conducted on human sensitivity to vibration and its results have beenreviewed in literature [13]. The International Standards Organisation [2] has specified numerical values for limitsof exposure to vibrations transmitted from a solid surface to the human body in the frequency range of 1 − 80 Hz.These limits cover human sensitivity to vertical and lateral vibration to periodic vibration exposure time rangingfrom 1 minute to 24 hours.
Figure 8 shows the predicted vertical rms acceleration response of car cg in one−third octave bands at differentspeeds, superimposed over ISO curves for 1 hour and 8 hour ‘reduced comfort boundaries’. It can be seen fromthe figure that upto 90 kmph, the response acceleration levels are below the 1 hour curve. The frequency range ofthe analytical response increases with speed as the input temporal track PSD has larger frequency componentsat higher speeds. Predicted vertical acceleration response of four different points on the coach floor has beenplotted along with ISO curves in Figure 9. The rms acceleration values in one−third octave bands of the measuredacceleration response in the vertical direction, of four different points on the coach floor were calculated andplotted along with ISO curves in Figures 10
2 5 12.5 31.50.001
0.010
0.100
2 5 12.5 31.50.001
0.010
0.100
2 5 12.5 31.50.001
0.010
0.100
2 5 12.5 31.50.001
0.010
0.100
2 5 12.5 31.50.001
0.010
0.100
2 5 12.5 31.50.001
0.010
0.100
ISO 1 HrISO 8 Hr30 kmph
Frequency Hz
ISO 1 HrISO 8 Hr90 kmph
Rms a
ccel
erat
ion
g
Rms a
ccel
erat
ion
g
Frequency Hz
ISO 1 HrISO 8 Hr120 kmph
Rms a
ccel
erat
ion
g
Frequency Hz
ISO 1 HrISO 8 Hr45 kmph
Rms a
ccel
erat
ion
gRm
s acc
eler
atio
n g
Frequency Hz
ISO 1 HrISO 8 Hr60 kmph
Rms a
ccel
erat
ion
g
Frequency Hz
ISO 1 HrISO 8 Hr150 kmph
Frequency Hz
Figure. 8 Analytical vertical response (1/3 octave rms acceleration) and ISO curves for reduced comfort boundaryfor 1 hour and 8 hours at various speed.
2 5 12.5 31.51E-3
0.01
0.1
2 5 12.5 31.51E-3
0.01
0.1
2 5 12.5 31.51E-3
0.01
0.1
2 5 12.5 31.51E-3
0.01
0.1
ISO 1 hrISO 8 hr45 kmph
Rms a
ccel
erat
ion
g
Verrtical rms acceleration at point 2
Rms a
ccel
erat
ion
g
Frequency Hz
ISO 1 hrISO 8 hr45 kmph
Rms a
ccel
erat
ion
gRm
s acc
eler
atio
n g
Frequency Hz
Verrtical rms acceleration at point 4
ISO 1 hrISO 8 hr45 kmph
Frequency Hz
Verrtical rms acceleration at point 6ISO 1 hrISO 8 hr45 kmph
Frequency Hz
Verrtical rms acceleration at point 8
Figure. 9 Analytical vertical response (1/3 octave rms acceleration) of different points on a coach floor and ISOcurves for reduced comfort boundary for 1 hour and 8 hours
2 5 12.5 31.51E-3
0.01
0.1
2 5 12.5 31.51E-3
0.01
0.1
2 5 12.5 31.51E-3
0.01
0.1
2 5 12.5 31.51E-3
0.01
0.1
ISO 1 hrISO 8 hr45 kmph
Rms a
ccel
erat
ion
g
Verrtical rms acceleration at point 2
Rms a
ccel
erat
ion
g
Frequency Hz
ISO 1 hrISO 8 hr45 kmph
Rms a
ccel
erat
ion
gRm
s acc
eler
atio
n g
Frequency Hz
Verrtical rms acceleration at point 4
ISO 1 hrISO 8 hr45 kmph
Frequency Hz
Verrtical rms acceleration at point 6ISO 1 hrISO 8 hr45 kmph
Frequency Hz
Verrtical rms acceleration at point 8
Figure. 10 Measured vertical response (1/3 octave rms acceleration) of different points on a coach floor and ISOcurves for reduced comfort boundary for 1 hour and 8 hours
5 PARAMETRIC STUDYA parametric study was undertaken to find the influence of different suspension parameters on the dynamicresponse or ride index. This study was carried out using the 17 dof vertical rigid body model and track PSD asinputs. The parameters considered for the analysis were primary stiffness, primary damping, secondary stiffness,secondary damping and car mass (tare − gross).
These parameters were varied by ± 25% of their present values in steps of 5%, except for the car mass, whichwas varied from tare mass to gross mass, in order to find the influence of loading on ride index. The vehiclespeeds considered for the analysis were 15 to 150 kmph in steps of 15 kmph. The performance indicesconsidered for the study were RMS acceleration at car cg and bogie cg, RMS displacement at car cg and bogiecg and ride index at car cg
The results of the parametric study have been plotted in terms of performance index versus vehicle parameter.Figures 11 and 12 show the variation of different performance indices as a function of primary stiffness andsecondary stiffness respectively. Remaining parameters and its influence have been summarised in the nextsection (graphs are not presented)
1800 2000 2200 2400 2600 28000.00
0.05
0.10
0.15
0.20
0.25Boige cg
Car cg
Primary stiffness N/mm
Rms acceleration at bogie cg vs. primary stiffnessRM
S ac
cele
ratio
n g
1800 2000 2200 2400 2600 28000.00
0.05
0.10
0.15
0.20Car cg kmph
15 30 45 60 75 90 105 120 135 150
Rms acceleration at car cg vs. primary stiffness
RMS
acce
lera
tion
g
Primary stiffness N/mm
1800 2000 2200 2400 2600 2800
20
30
40
50Boige cg
Primary stiffness N/mm
RMS
disp
lace
men
t mm
Rms displacement at car cg vs. primary stiffness Rms displacement at bogie cg vs. primary stiffness
1800 2000 2200 2400 2600 280012
14
16
18
Primary stiffness N/mm
kmph 15 30 45 60 75 90 105 120 135 150RM
S di
spla
cem
ent m
m
Figure. 11 The influence of primary stiffness
2400 2600 2800 3000 3200 3400 3600 3800 40000.00
0.05
0.10
0.15
0.20
0.25Bogie cg
Rms acceleration at bogie cg vs. secondary stiffness
RMS
acce
lera
tion
g
2400 2600 2800 3000 3200 3400 3600 3800 40000.00
0.05
0.10
0.15
0.20 Car cg
Secondary stiffness N/mmSecondary stiffness N/mm
Secondary stiffness N/mm
kmph 15 30 45 60 75 90 105 120 135 150
Rms acceleration at car cg vs. secondary stiffnessRM
S ac
cele
ratio
n g
Secondary stiffness N/mm
2400 2600 2800 3000 3200 3400 3600 3800 4000
20
30
40
50
60Bogie cg
RMS
disp
lace
men
t mm
Rms displacement at car cg vs. secondary stiffness Rms displacement at bogie cg vs. secondary stiffness
2400 2600 2800 3000 3200 3400 3600 3800 400012
14
16
18Car cg
kmph 15 30 45 60 75 90 105 120 135 150RM
S di
spla
cem
ent m
m
Figure. 12 The influence of secondary stiffness
5.1 Observations from the Parametric Study
The increase in the primary suspension stiffness reduces the rms acceleration levels at the car cg and bogie cgmarginally upto a speed of 105 kmph. It has been found that increasing the primary stiffness reduces thedisplacement response at the car cg and the bogie cg considerably at all the speeds. The influence of secondarystiffness has been found to be just the opposite of that of the primary stiffness. A reduction of the secondarystiffness value from the present value reduces the acceleration and the displacement response at the car cg andthe bogie cg at all the speeds. The variation of the primary damping is seen to have little influence on theresponse at the car cg or at the bogie cg. At speeds above 90 kmph, increase in the primary damping is shown toproduce marginal reduction in the response amplitudes at the car cg and bogie cg. The secondary damping hasgreat influence at speeds higher than 75 kmph. An increase in the secondary damping reduces the responseamplitude at speeds greater than 75 kmph, whereas upto 75 kmph speed, the secondary damping has littleinfluence. The car mass variation from tare mass condition to gross mass condition has influence at higherspeeds. The car mass variation has practically no influence at speeds below 60 kmph. An increase in car massreduces the response amplitude at higher speeds. It has also been observed that all the parameters exceptprimary and secondary stiffness and secondary damping have very limited influence at low speeds.
From the parametric study, it has been found that the increase in primary stiffness, the reduction of secondarystiffness and the increase in secondary damping will improve the performance of the railroad vehicle, in terms ofride index and dynamic response.
6 SUMMARY AND CONCLUSIONSThe Sperling’s ride indices were determined for a railroad vehicle both experimentally and analytically using thetrack PSD as input. The Sperling’s ride quality and the ride comfort were predicted analytically at different speeds.Using ISO 2631 guidelines, reduced comfort boundaries for 1 hour and 8 hours have been superimposed over thepredicted response and measured response.
An extensive parametric study has been carried out with emphasis on better ride index and reduced dynamicresponse. The parametric study has brought out possible design changes required in different parameters todeliver better ride index. It should be noticed that the parametric study was carried out to suggest designmodifications to improve ride index, but other dynamic behaviour like stability, curve negotiation capability etc.were to be considered when implementing the design modifications.
REFERENCE1. EERI B 153/RP 21 Application of ISO standard 2631 to railway vehicles. Utrecht, 1993
2. ISO 2631 (1985) Evaluation of human exposure to whole body vibration. International StandardsOrganisation.
3. Elmaraghy, W. H (1987) Ride quality and dynamics of rail vehicle models for microcomputers. VehicleSystem Dynamics,16, 193 − 211.
4. Lyon, D. (1987) Dynamic measurements in the research and development of rail vehicles. Vehicle SystemDynamics,16, 149 − 165.
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