Road Profile Data 4m5b1
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Road Roughness Measurements using PSD Approach K Ramji, Associate Member A Gupta, Non-member V H Saran, Member Prof V K Goel, Fellow Prof V Kumar, Fellow The interest of the highway engineer is focused on road roughness in the frequency range of interest, which corresponds to a wave number range appropriate for the prevailing traffic speed. The effect of road roughness on the design and operation of road vehicles has been a subject of intensive research since 1960. In the literature considerable effort has been spent on the investigation of vehicle vibration excited by surface irregularity. Road profile measurement is an important step preceding vehicle development. The present paper deals with the measurement and analysis technique to evaluate road roughness in the form of power spectral density (PSD). A profile measuring trailer unit has been designed and developed. Measurements of road roughness have been taken on five types of Indian roads and one mosaic floor (for academic interest only) using an on-line system, and results are represented by power spectral density and compared with the standard results given by the International Standard Organization (ISO) to classify the type of road. Keywords: Road roughness; Power spectral density; Road profilometer; Bituminous road; Portland cement concrete road
NOTATION Ak (n)
: FFT component
C
: capacitance
fcc
: cut off frequency
fs
: maximum frequency of measured signals
K
: number of segments
N, Csp
: constants
P ( fn )
: power spectrum estimate
R
: resistance
Sqr ( η)
: power spectral density of road surface profile
T
: sampling interval, s
Z0
: vertical undulations of the road surface
Z&1 − Z& 0
: relative velocity of trailer frame and the roadfollowing wheel
Z&&1
: frame vertical absolute acceleration
K Ramji is with Mechanical Engineering Department, College of Engineering, Visakhapatnam 530 003; A Gupta and Prof V Kumar are with Electrical Engineering Department and V H Saran and Prof V K Goel are with Mechanical and Industrial Engineering Department all at IIT Roorkee, Roorkee 247 667. This paper (modified) was received on June 8, 2004. Written discussion on this paper will be received till January 31, 2005.
Vol 85, November 2004
INTRODUCTION With the growing awareness for better highways for an ever increasing traffic loading and concern for aging highway systems, the Government of India has established the National Highway Authority (NHA). The major function of the NHA will be the planning of new routes, preparing maintenance schedules and acceptance or replacement of newly constructed highways. Naturally, appropriate management systems are needed to make objective assessment of highway quality. Generally, highway engineers using a response type single wheel trailer unit, eg, Dipstick or Merlin devices, specify road roughness as the total vertical distance measured by the measuring wheel per kilometer of distance travelled (mm/km). Such specification of road roughness by highway engineers is convenient for the construction and maintenance of roads, but is not useful for providing input to the vehicle model, for evaluation of ride index and enger comfort. These devices do not yield data to obtain the power spectral density (PSD) of the road surface roughness, which is essential for evaluation of vehicle ride behaviour. The purpose of the present work was to measure the road profile in PSD form, which can be used as input to the vehicle model. Vehicle designers also use road roughness data to investigate its effect on vehicle braking and steering behaviour, as the normal tyre forces are affected by road roughness. According to International Standard Organization (ISO)26311, the ride comfort is specified in of root mean square (RMS) acceleration over a frequency range. The pavement surface profile of interest to the highway engineer covers a wavelength range2 of about 0.01 mm to 100 m. This range is too wide to be measured in of a single scale, but can be described and measured in four scales: micro-texture, macro-texture, mega-texture and road roughness. The road roughness usually covers a wavelength from 0.1 m to 100 m. 193
Since, road profiles are random in nature, these are better described by statistical techniques. One such statistical characterization that has been found useful in describing the road roughness is power spectral density. Road surface irregularities are statistically classified by frequency and amplitude distribution by Macaulay3, ie, one can perform a frequency analysis to make an estimate of the amplitudes for various wavelengths present. One method of analyzing random data by Bendat and Piersol4 and Stearns5 is in of its power spectral density (PSD), which is a measure of its mean squared value distribution within a frequency band. It is therefore necessary to measure the road profile and then compute the power spectral density from these data as it will help in the analysis of ride behaviour of vehicles. Wambold6, using a quarter car model to represent the vehicle and using ISO 26317 as the model of subjective response, predicted that car engers should be most sensitive to pavement disturbances within the special frequency range of approximately 0.23 cycles/m to 0.66 cycles/m. On the other hand, Janoff8 presented results that indicated that the car engers respond most strongly to pavement disturbances at spatial frequencies in the range of approximately 0.36 cycles/m to 2.3 cycles/m. These values, translated to temporal frequencies at a travel speed of 80 km/h, give corresponding ranges of approximately 5 Hz to 15 Hz and 8 Hz to 50 Hz, respectively. Hayhoe, et al 9 explained the reason for anomalies in the relationship between the ride quality and the profile characteristics. They found that the profiles contain a large number of pulses — like disturbances and these pulses contribute a significant portion of the energy in the profiles at high frequencies. They argued that the presence of pulses in pavement profiles could be a significant factor in subjective response to road roughness. The ISO10 and Wong11 have proposed a road roughness classification (A-H) based on the power spectral density. Various types of road roughness measuring devices and different kinds of surface roughness along with their measurement criteria have been discussed by Hegmon2, ISO10, Wong11 and Van Deusen12. Road elevation profiles can be measured either by performing close interval rod and level surveys described by Wambold, et al 13, or by using high-speed profilometers discussed by Spangler and Kelly14; Hudson15; Darlington and Milliman16. An inertial profilometer concept implemented at General Motors Research (GMR) laboratories in the 1960 and later developed in 1966, has been widely used for highway evaluation and application by Spangler and Kelly14; Hudson15; Darlington and Milliman16. In the present scenario, the laser based road profile measuring systems given by Prem17; Mimuro and Maemura18; Mimuro, et al 19 are being used to measure vertical undulations of roads in most of the developed countries. On surveying the literature, very few publications discuss the measurement of road undulations for Indian roads. Karuppaiah, et al 20, Tamboli and Joshi21 have made an attempt to measure road roughness for Indian roads in of power spectral 194
density. The PSD of the actual road vertical undulations/ excitations have been represented in the form of an exponential form given by Tamboli and Joshi21 for urban Indian roads and non-urban highways. Several research works12,20-23 have addressed the effect of road roughness on vehicle behaviour and have also described mathematical modelling of power spectral density of road surface profiles. The present paper deals with the development of a profile measuring trailer unit. Measurements of road roughness have been taken on five types of Indian roads and one mosaic floor (for academic interest only) using a PC (personal computer) — based on line data recording system. The results have been presented in the form of a power law equation, which could be used as a road input in vehicle models for evaluation of ride behaviour. ROAD PROFILOMETER A prototype road surface profilometer with three-wheels shown in Figure 1 has been designed and developed by the authors at IIT, Roorkee. The front wheel is a caster wheel while the rear wheels are the driving wheels. The road-following wheel is a solid rubber wheel (another wheel), which maintains with the road surface by a spring and dashpot unit. The specifications and dimension of the trailer frame, solid rubber wheel (road following wheel), caster and other rear wheels are given below: l l
l
The trailer frame is made of angle iron 35 mm × 35 mm size and 6 mm thickness for sufficient rigidity. The road following wheel has a metal rim with a solid rubber tyre of 120 mm dia. The small diameter wheel with large radial stiffness facilitates measurements of low and middle frequency road surface irregularities with good accuracy. The three wheels including the caster wheel of the trailer unit are 3.50 × 10, 4 PR pneumatic tyres, each of 372.5 mm dia.
The trailer unit is instrumented with a transducer to measure relative velocity ( Z&1 − Z& 0 ) between the trailer frame and the road surface (road-following wheel). The accelerometer, mounted on the frame just above the road-following wheel, measures the vertical acceleration ( Z&&1 ) of the frame, the integration of the signal gives the frame vertical velocity ( Z&1 ) . The velocity signal is then added to the relative velocity signal of the frame and the road-following wheel, the resulting signal is integrated to yield the road undulations (vertical displacement, Z0 ) profile. The measurement approach followed in this paper, ie, the single integration of relative velocity between the wheel and frame, rather than merely double integrating the acceleration of the solid rubber wheel, ensures wide acceptability in the measurement of road roughness. The roadfollowing wheel is a solid rubber tyre of 120 mm dia moulded on metal rim. It acts as a mechanical filter, which transmits low and middle frequency road surface undulations but attenuates high frequency (low wavelength) road surface values. IE (I) Journal—CV
Velocity and acceleration transducers Computer for data recording
Trailer
Optocoupler unit
Road profiling wheel Figure 1 Experimental test set-up for measurement of road roughness
( Z&&1 )
( Z&1 − Z& 0 )
The schematic operations of data acquisition are shown in Figure 2. The data (analog signals) obtained from the transducers are stored in digital form on microcomputer mounted on the trolley for data processing later on. In this system, the transducer signals, ie, acceleration and relative velocity are sampled and converted to digital values for use in profile computation. The sampling and computation of the road profile are performed as a function of distance instead of time, which makes the measurements independent of trailer speed and easier to handle. For this purpose an optocoupler, which gives pulses at regular interval of distance travelled, has been mounted on the rear axle, of the trailer. TRANSDUCERS AND DATA PROCESSING
Z&1 − Z& 0
Z&1
–
+
Figure 2 Schematic operation of road profilometer
Vol 85, November 2004
The acceleration of the trailer frame is measured using a strain gauge type accelerometer, suitable for measuring low frequency vibrations of low magnitude, ie, from 0 g to 5 g. Transducers of this type are used in applications requiring small size, small mass and measurement of low frequency (0 Hz - 200 Hz). An internal signal conditioner conditions the signal of the sensing element to a -friendly voltage. The strain gauge type accelerometer pickup was manufactured by Bruel and Kajer and has been already calibrated to International standards. However, before beginning of the experiment, the accelerometer was checked by holding it in hand in horizontal position and rotating it by 90 ° (upside down position), to yield a signal of 1 g on an oscilloscope. At present sensitivity of 1.39 V/g was used. More details of acceleration transducer are given below. Rated output, µ V/g : 553 Strain, µ
:
110.6 195
Frequency response, Hz
:
0–240
Non-linearity
:
1% of rated output
Input resistance, Ω
:
122.8
Output resistance, Ω
:
122.8
Safe temperature, ° C
:
0–50
Safe excitation, V
:
5
The relative velocity pick-up is a cable-activated transducer of 5V/m/s sensitivity, that produces a voltage proportional to the relative velocity between the trailer frame and the roadfollowing wheel. A product of ASM (Automatic Sensorik Messtechnik) of , the unit is precalibrated to International Standards. Internal signal conditioner conditions the signal of the sensing element to -friendly voltage, current or digital pulse. More details of velocity transducer are: Model
:
WGS5-500-10V-T5-L10-HG
Function designation
:
Position and relative velocity transducer
Range
:
0 V-10 V dc signal conditioner
Sensitivity
:
5 V/m/s
Linearity
:
0.1% of measured value
Maximum acceleration
:
60 g
Max velocity
:
10 m/s
Sensor component
:
Tachogenerator
Accuracy
:
0.1 %
It has been described earlier that the vertical undulations (profile) of the road surface are recorded as a function of distance travelled by the trailer unit, which is measured by a single perforated disc mounted on the rear axle of the trailer unit along with an optocoupler. The optocoupler consists of a gallium arsenide infrared emitting diode and a silicon phototransistor mounted in closed proximity. The two are optically coupled but electrically insulated from each other. Whenever an infrared ray from the diode es through the perforation in the disc, a pulse is generated. The three pneumatic tyres (3.50 × 10, 4 PR) of the trailer including the caster wheel are each of 372.5 mm φ . Therefore, the linear distance covered in one wheel rotation is 1170 mm. The optocoupler unit has a perforated disc with 10 equidistant holes on its circumference. Therefore, the distance travelled by the trailer unit between two adjacent holes, which corresponds to two consecutive pulses is 117 mm (or 0.117m), which is also evident from the raw data of bituminous newly laid road given in Table 1. With a 10-hole disc, the distance travelled between two consecutive pulses is 0.117 m. The signals from the two transducers, ie, relative velocity pickup and acceleration pickup are taken to ADC card (8112 HG) using shielded cable, to prevent noise from external electric and 196
magnetic fields being picked up. A 12-bit ADC card (ACL-8112) featuring eight differential inputs, 16 digital inputs/outputs and one timer has been used for data acquisition from transducers. The signals obtained from the transducers are properly filtered using hardware filter before being taken to ADC card, (Figure 2). The hardware filter was a low third order ‘RC’ filter with cut off frequency given by
f cc =
1 2π RC
(1)
The values of C and R were taken as 0.47 µF and 17 kΩ , respectively, which gave the cut off frequency as 20 Hz. Filtered acceleration signal is integrated using a software integrator based on trapezoidal rule. The integrated acceleration signal is again filtered using a band filter. In the absence of filtering, any offset present can cause numerical overflow. Filtered velocity pick-up data are subtracted from integrated acceleration data and signal is again integrated to get the roughness profile. This roughness data (vertical undulations) is used to obtain power spectral density. The scheme of operations is shown in Figure 2. The sampling and computation of the road profile are performed as a function of distance instead of time, which makes the measurements independent of trailer speed and easier to handle. For this purpose an optocoupler, which gives pulses at regular interval of distance travelled, has been mounted on the rear axle of the trailer. In any experimental test program proper care needs to be taken in order to ensure the accuracy and reliability of the test data. Signals obtained from the transducers through ADC card are processed to obtain useful information. The first requirement is to sample the transducer signals and filtering the signals to remove any electrical noise. The accelerometer signals are integrated by software employing the trapezoidal rule to obtain velocity signals. The road surface profile of wavelength of 100 mm or more are normally encountered on typical highways and are of interest to vehicle dynamicist. The profile data was acquired by normally towing the trailer unit at a speed of nearly 1 m/s. Thus, the maximum frequency of measured signals fs was about 10 Hz. Therefore, the minimum sampling frequency, known as the Nyquist rate should be 2 fs or 20 Hz in order to prevent aliasing. Sampling at points which are too far apart will lead to confusion between the low and high frequency components in the original data and is called aliasing. Before choosing the sampling frequency one more important factor, ie, the lowest frequency of interest must be considered, which was chosen as 0.1 Hz. The fast Fourier transform (FFT) is efficient and fast method for computing the discrete Fourier transform (DFT). Computation of DFT required M2 complex operations (addition and multiplication) and hundred of hours of machine time prior to 1965. In 1965, a method for computing the DFT was given by Cooley and Tukey24 that requires approximately Mlog2M operations where M is power of 2. This method of computing Fourier Transform which requires a number of IE (I) Journal—CV
Table 1
Vertical undulations for newly layed road
Distance travelled, m
Vertical undulations, mm/m SEC1 SEC2
Distance travelled, m
Vertical undulations, mm/m SEC1 SEC2
Distance Vertical undulations, travelled, mm/m m SEC1 SEC2
Distance travelled, m
Vertical undulations, mm/m SEC1 SEC2
0.000
–0.423
0.402
5.850
–0.245
3.149
11.700
–2.766
–0.188
17.550
–0.117
0.502
0.117
0.090
0.553
5.967
–1.768
4.341
11.817
–2.440
–0.124
17.667
1.109
1.045
0.234
0.157
–0.388
6.084
–4.348
3.992
11.934
–3.081
–0.562
17.784
0.509
1.289
0.351
0.535
–0.677
6.201
–3.830
4.634
12.051
–2.466
1.102
17.901
–0.626
1.626
0.468
1.789
0.382
6.318
–4.864
3.164
12.168
–1.812
1.917
18.018
0.298
1.296
0.585
1.361
–0.540
6.435
–5.854
2.883
12.285
–1.978
1.083
18.135
0.029
1.186
0.702
1.643
–1.759
6.552
–5.033
2.654
12.402
–1.364
–0.066
18.252
0.546
1.055
0.819
2.444
–1.325
6.669
–5.932
1.406
12.519
–1.061
–0.725
18.369
–0.108
3.199
0.936
1.487
–1.056
6.786
–5.028
2.084
12.636
–2.302
–2.093
18.486
–2.005
3.344
1.053
0.739
–2.557
6.903
–3.600
1.751
12.753
–2.474
–5.441
18.603
–0.244
1.074
1.170
1.919
–1.516
7.020
–4.861
3.295
12.870
–3.875
–6.683
18.720
–1.434
1.901
1.287
0.697
–0.454
7.137
–3.759
2.552
12.987
–1.265
–6.503
18.837
–1.099
0.718
1.404
1.684
–0.887
7.254
–2.492
2.357
13.104
–1.381
–2.050
18.954
0.891
1.343
1.521
1.934
0.155
7.371
–2.290
–0.358
13.221
–1.564
4.335
19.071
0.434
2.352
1.638
0.406
1.694
7.488
–0.748
–1.335
13.338
–0.769
5.148
19.188
1.121
1.246
1.755
1.256
0.772
7.605
–0.325
–1.913
13.455
–2.547
5.120
19.305
1.279
1.039
1.872
2.099
–0.936
7.722
–1.475
–2.451
13.572
–2.537
3.049
19.422
2.348
2.249
1.989
0.650
–0.198
7.839
–3.435
–0.997
13.689
–2.020
0.324
19.539
3.429
2.258
2.106
1.149
–1.116
7.956
–4.675
–0.524
13.806
–3.778
1.992
19.656
1.978
–0.062
2.223
2.247
–1.772
8.073
–4.002
–1.768
13.923
–3.365
1.583
19.773
2.880
–0.246
2.340
2.318
–0.879
8.190
–3.274
–2.109
14.040
–3.220
0.090
19.890
4.053
0.588
2.457
2.344
–0.327
8.307
–3.021
–0.728
14.157
–5.322
0.253
20.007
4.493
0.590
2.574
4.001
–0.503
8.424
–4.009
–2.157
14.274
–4.221
1.983
20.124
5.836
1.423
2.691
2.929
–0.918
8.541
–3.351
–2.807
14.391
2.545
1.964
20.241
–2.290
1.388
2.808
2.695
0.986
8.658
–5.645
–2.435
14.508
–4.165
2.454
20.358
–5.859
2.048
2.925
3.799
0.250
8.775
–4.374
–2.576
14.625
–4.286
4.026
20.475
—
1.937
3.042
3.718
0.184
8.892
0.776
–2.632
14.742
–3.798
5.574
20.592
—
2.835
3.159
3.081
1.121
9.009
0.856
–3.331
14.859
–2.276
5.303
20.709
—
0.302
3.276
3.240
0.418
9.126
1.721
–2.494
14.976
–2.720
5.548
20.826
—
–0.063
3.393
0.019
–0.672
9.243
1.056
–3.000
15.093
–1.404
4.259
20.943
—
–2.559
3.510
0.153
0.133
9.360
1.681
–3.272
15.210
–1.855
6.397
21.060
—
–2.599
3.627
1.881
–0.139
9.477
–1.151
–2.523
15.327
0.922
6.572
21.177
—
–1.697
3.744
2.640
–0.458
9.594
–1.277
–2.396
15.444
–0.244
3.741
21.294
—
–1.605
3.861
2.040
0.272
9.711
–0.148
–4.642
15.561
–0.232
3.292
21.411
—
0.327
3.978
0.853
0.510
9.828
–1.015
–4.646
15.678
0.531
3.547
21.528
—
0.921
4.095
0.498
–0.528
9.945
–0.850
–2.878
15.795
–0.656
1.739
21.645
—
0.668
4.212
0.954
0.533
10.062
–0.13
–4.387
15.912
–0.818
1.931
21.762
—
2.062
4.329
–0.969
2.612
10.179
–0.633
–3.931
16.029
1.349
2.555
21.879
—
0.915 Table 1 Cond
Vol 85, November 2004
197
Table 1
Vertical undulations for newly layed road (Cond)
Distance travelled, m
Vertical undulations, mm/m SEC1 SEC2
Distance travelled, m
Vertical undulations, mm/m SEC1 SEC2
Distance travelled, m
Vertical undulations, mm/m SEC1 SEC2
Distance travelled, m
Vertical undulations, mm/m SEC1 SEC2
4.446
0.264
3.182
10.296
0.833
–0.333
16.146
0.853
2.336
21.996
—
0.065
4.563
1.376
4.113
10.413
1.630
–0.616
16.263
1.051
2.207
22.113
—
0.144
4.680
–2.286
1.653
10.530
2.146
0.641
16.380
1.596
2.886
22.230
—
0.036
4.797
–3.480
1.510
10.647
–3.186
–0.773
16.497
–0.386
2.958
22.347
—
–1.187
4.914
–4.799
0.552
10.764
–7.994
0.933
16.614
–0.079
2.322
22.464
—
–1.548
5.031
–4.202
–0.037
10.881
–1.373
–1.049
16.731
–0.868
2.175
22.581
—
–1.284
5.148
–3.030
–0.540
10.998
3.429
0.816
16.848
–0.993
1.688
22.698
—
–1.400
5.265
–0.944
1.466
11.115
–2.638
–0.458
16.965
–0.298
1.514
22.815
—
–2.778
5.382
–0.456
2.437
11.232
–1.742
–1.824
17.082
–1.629
1.345
22.932
—
–2.839
5.499
–0.702
2.768
11.349
–1.273
–0.444
17.199
–1.022
1.582
—
—
—
5.616
–0.381
3.451
11.466
–13.093
–0.419
17.316
–0.533
1.635
—
—
—
5.733
–1.986
3.300
11.583
–8.608
–0.950
17.433
–0.020
1.810
—
—
—
The signals obtained from the transducers are properly filtered and long wavelength components are attenuated before the data is processed to evaluate road roughness profile. Along with the software filter a low , third order hardware filter with cut off frequency of 20 Hz has also been used. A filter based on the window method of finite impulse response (FIR) has been designed, using the Fourier series method given by Britton26. The Fourier series method of FIR filter design is based upon the fact that frequency response of a digital filter is periodic and is therefore representable as a Fourier series. A desired target frequency response is selected and expanded as a Fourier series, which is truncated to a finite number of that are used in Fourier coefficients. The resulting filter has a frequency response that approximates the original desired target response. 198
The signal so obtained after filtering, were further processed, to bring it to a useful form. The accelerometer signal is to be integrated to obtain the velocity and displacement signals. 0.30 0.25
Series 1
0.20 Magnitude
The signals obtained from transducers are properly filtered and long wavelength components are attenuated before the data is processed to evaluate road roughness profile. Two types of filters, hardware filters and software filters are used for filtering the signals. Software filters are used to remove noise present in transducer signals. Signals from velocity pick-up are filtered using a low filter (0 Hz-10 Hz), while the signals from acceleration pick-up are filtered using a band filter (0.3 Hz10 Hz).
Finite impulse response and magnitude response of band filters and low filters are shown in Figures 3(a) and 3(b) and Figures 4(a) and 4(b), respectively.
0.15 0.10 0.05 0 –0.05 0
50
100
150
200
250
300
–0.10 –0.15
Time, s
Figure 3(a)
Finite impulse response of a band filter (0.3 Hz-9 Hz)
1.2 1.0
Series 1
0.8 Magnitude
operations equal to Mlog2M become known as Fast Fourier Transform. The FFT developed by Cooley and Tukey24 in 1965 is significantly less computationally intensive method for evaluating the DFT and thus particularly attractive for real time spectral analysis using digital signal processing (DSP) technology. The FFT algorithm used for computing DFT has been taken from Samuel and David25. The FFT algorithm requires the number of samples to be an integral power of 2. Since, 29 is equal to 512, with proper adjustment of the delay, a sampling rate of 61 Hz was chosen which gives a resolution of 0.12 Hz in power spectral density, which is acceptable.
0.6 0.4 0.2 0 –0.2
0
10
20
30
Frequency, Hz Figure 3(b) Magnitude response of band filter (0.3 Hz-9 Hz)
IE (I) Journal—CV
0.35
Series 1
0.30 0.25 Magnitude
0.20 0.15
K segments of length L. For each segment of length L, a modified periodogram is calculated. That is, a window W ( j ), j = 0, 1, . . . . . . . . . . , L – 1 is selected and the sequences X1 ( j ) W ( j ), ... ... ..., Xk( j ) W( j ) are formed. The finite Fourier Transforms A1 (n), A2 (n) ... ... ... ... ... , Ak (n) of these sequences is taken. Here
0.10
Ak ( n) =
0.05 0 –0.05 0
50
100
–0.10
150
200
250
300
Figure 4(a) Finite impulse response of a low filter (0 Hz-9 Hz)
Series1
Magnitude
0.8 0.6 0.4 0.2 0 –0.2
0
5
10
15
20
25
30
35
Frequency, Hz
Figure 4(b) Magnitude response of low filter (0 Hz-9 Hz)
Numerical integration is resorted to when the analytical evaluation of integration is either difficult or impossible and when the function to the integration is available at discrete points. However, when it is possible to obtain closed form solution by analytical integration, it must be preferred for its exactness. Consider the integral
I=
z
b a
f(t ) d t
(2)
where f (t) is continuous function of t over a ≤ t ≤ b , and the integral may be evaluated using equal or unequal intervals. In the present work, the integral has been performed based on the Trapezoidal rule employing equal intervals, which is chosen because of its simplicity and reduced errors at high sampling rate. This particular integration technique has poor response characteristics near the Nyquist frequency but presents no difficulty in this application, as the frequencies contained in the signal, are typically less than 10 Hz, well below the Nyquist frequency. The signal corresponding to road surface undulation is obtained which is further processed for power spectral density. Welch27 gave a method for estimation of power spectra by using FFT algorithm. It involves sectioning the record, taking modified periodograms of these sections, and averaging these modified periodograms. The data sample X ( j ) is divided into Vol 85, November 2004
− 2 πijn / L ∑ Xk ( j ) W ( j ) e
j=0
(3)
L K ∑ Ak ( n) UK k = 1
2
(4)
where
1.2 1.0
L −1
The spectral estimate is the average of these periodograms, ie, P ( fn ) =
Time, s
1 L
U =
1 L −1 2 ∑ W ( j) . L j=0
EVALUATION OF ROAD ROUGHNESS Profile data for Indian roads have until recently been unavailable and it is of interest to examine some of their characteristics. Recently Karuppaiah, et al 20 and Tamboli and Joshi21 have published limited information on profile data of Indian roads but no comparisons were made with data available for international roads. Tamboli and Joshi21 have represented the Indian road profile data in an exponential form, which may be computationally more convenient to handle. It has been found in the literature11,12 that the relationship between the power spectral density Sqr ( η) and the spatial frequency ( η) for different ground profiles is usually represented in power law, which generally approximates as S qr ( η ) = C sp η− N
(5)
where η is spatial frequency in cycles/m; Sqr ( η) , power spectral density of road surface profile in m2/cycle/m. N is a dimensionless constant whereas Csp is an empirical constant whose dimensions vary with the value of N. RESULTS AND DISCUSSION In the present work, the road tests were conducted on five different roads and one mosaic floor using the road profilometer designed and developed in Vehicle Dynamics Laboratory (VDL), IIT, Roorkee. Using power series analysis, best-fit curves were obtained for each road profile yielding different values of Csp and N, which are given in Table 2. Five different types of road surfaces consist of four bituminous roads from serial number 1 to 4, one Portland cement concrete (PCC) road at serial 5 and one mosaic floor (similar to very smooth surface) at serial number 6 are evaluated in this study. The tests were performed at slow speeds by pushing the trailer unit on these road surfaces and the mosaic floor with test lengths varying from 21 m to 60 m. The measured data was recorded by a microcomputer, mounted directly on the road profilometer, which computed the power spectral density values. 199
S No
Description of road surface
1
Newly layed
Institute road data C sp N
International road data C sp N
2.2 × 10 − 07
2.7 × 10 − 07
2.0
2.1
surface road (Runway road type of NACA-TN-3305) 2
Smooth road
1.0 × 10 − 06
2.4
2.4 × 10 − 06
2.1
(Smooth runway type of NACA-TN-3484) 3
Rough road
4.9 × 10 − 06
2.2
4.4 × 10 − 06
2.1
3.5 × 10 − 07
2.1
4.8 × 10 − 07
2.1
5.5 × 10 − 07
1.7
6.4 × 10 − 07
1.9
(Highway with gravel) 4
Smooth highway road
5
PCC Road (Runway road type of NASA-TND-510)
6
Mosaic floor
2.2 × 10 − 07
2.2
—
—
Several test runs were carried out along the width of a given road surface like section 1 (SEC 1) and section 2 (SEC 2) and average values of PSD have been reported here. Figure 5 and Figure 6 show vertical undulations and power spectral density values, respectively for a typical institute bituminous road. This was a newly constructed road surface and is similar to air port runway road (NACA-TN-3305)12. The amplitude level Figure 5, indicates the roughness level; higher amplitudes would mean rougher roads. The wave number (or spatial frequency) in Figures 5 and 6 corresponds 0.1 cycles/m to 10 cycles/m or to a wavelength (inversely proportional to spatial frequency) of 10 m
Undulations, mm
10
Sec 1 Sec 2
5 0
0
5
10
15
20
25
–5
Measured road distance position, m
Figure 5 Vertical undulations against measured road distance of bituminous newly layed road
200
1.00E+00 1.00E–01
Spatial frequency, cycles/m 0.1
1.00E–02 1.00E–03
1
Sec 1 Sec 2
10 y=2.17E-07x –2.07E+00 y=2.28E-07x –1.98E+00
1.00E–04 1.00E–05 1.00E–06 1.00E–07 1.00E–08 1.00E–09
Figure 6 PSD as a function of spatial frequency for bituminous newly layed road
at the origin to about 0.1 m towards right. The PSD data for different road surfaces are reported in Table 2, which indicates drop in amplitude with wave number. The rate at which amplitudes decrease with wave number is characterized by the value of N, the larger the value of N, the more steep the decrease in amplitudes. Therefore, measurements were taken on mosaic floors and values of Csp and N are found to be 2.2 × 10 − 7 and 2.2, respectively. The roughness values were found to be nearly the same as that for runway road type NACA-TN-330512. As per ISO specifications, such surfaces could be treated as a good surface. SUMMARY AND CONCLUSIONS Measurements of the actual road roughness profiles, using indigenously designed and developed road profilometer, is presented for five different institute roads and one mosaic floor. The road roughness is represented in of power spectral density as a function of spatial frequency and compared with the data of international roads. Based on ISO surface roughness classification, the roads in IIT, Roorkee could be classified between average, good and very good roads. PSD data for Indian roads will provide additional input for highway engineers in India to develop better management systems for objective assessment of highway quality and an essential input for vehicle designers for achieving better vehicle ride behaviour. It is hoped that this study will stimulate further research on effect of road roughness on the vibration behaviour of Indian vehicles and rider sensitivity to vibrations. ACKNOWLEDGEMENT The research work reported here was carried out under a research scheme financially ed by the Department of Science and Technology, Government of India, New Delhi. The financial is gratefully acknowledged. REFERENCES
–10 –15
Power spectral density, m2/cycles/m
Table 2 C sp and N values for power spectral density functions for various roads
1. ‘ISO 2631 Mechanical Vibration and Shock Evaluation of Human Exposure to Whole Body Vibrations — PART I.’ General Requirements, 1997. 2. R R Hegmon. ‘Some Results from Ongoing Research on Road Roughness.’ Vehicle, Tyre, Pavement Interface ASTM STP 1164, 1992, pp 14-31.
IE (I) Journal—CV
3. M A Macaulay. ‘Measurement of Road Surfaces, Advances in Automobile Engineering — Part I.’ G H Tidbury, (ed), Pergamon Press, Oxford, England, 1963.
Profilometer.’ Highway Research Record, vol 214, Washington, DC, 1968, pp 50-67.
4. J S Bendat and A G Piersol. ‘Random Data: Analysis and Measurement Procedures.’ Wiley-Interscience, New York, 1971.
17. H A Prem. ‘Laser Based Highway-speed Road Profile Measuring System.’ Proceedings of the Tenth IAVSD Symposium on The Dynamics of Vehicle on Roads and Tracks, Prague, 1987, pp 300-304.
5. S D Stearns. ‘Digital Signal Analysis.’ Hayden Book Company INC, Rochelle Park, New Jersey, 1975.
18. T Mimuro and T Maemura. ‘Road Profile Measuring System using Laser Displacement Sensors.’ JSAE Review, vol 11, no 4, 1990.
6. J C Wambold. ‘Road Roughness Effects on Vehicle Dynamics, Measuring Road Roughness and its Effects on Cost and Comfort.’ ASTM STP 884, 1985, pp 179-196.
19. T Mimuro, T Maemura and H Fujii. ‘Development and Application of the Road Profile Measuring System.’ SAE Transactions, 930257, 1993, pp 291-298.
7. ‘International Organization for Standardization, Guide for the Evaluation of Human Exposure to Whole Body Vibration.’ ISO 26311974(E), 1974. 8. M S Janoff. ‘Pavement Roughness and Rideability Field Evaluation.’ NCHRP Report 308, TRB, National Research Council, 1988. 9. G F Hayhoe. ‘Spectral Characteristic of Longitudinal Highway Profiles as Related to Ride Quality.’ Vehicle, Tire, and Pavement Interface ASTM STP 1164, 1992, pp 32-54. 10. ‘ISO Reporting Vehicle Road Surface Irregularities.’ TC108/SC2/WG4 N57, 1982. 11. J Y Wong. ‘Theory of Ground Vehicle.’ John Wiley and Son Inc, Canada, 1993. 12. B D Van Deusen. ‘Analytical Techniques for Design Riding Quality into Auto Motive Vehicles.’ SAE Transactions, vol 76, 670021, 1968. 13. J C Wambold, L E Defrain, R R Hegmon, J Mcghee, J Reichert and E Spangler. ‘State-of-the-art of Measurement and Analysis of Road Roughness.’ Transportation Research Record, vol 836, 1981, pp 21-29. 14. E B Spangler and W J Kelly. ‘GMR road Profilometer — a Method for Measuring Road Profile.’ Highway Research Record, vol 121, Washington, DC, 1966, pp 27-54. 15. W R Hudson. ‘High-speed Road Profile Equipment Evaluation.’ Highway Research Record, vol 189, Washington, DC, 1967, pp 150-163. 16. J R Darlington and P A Milliman. ‘Progress Report on the Evaluation and Application Study of the General Motors Rapid Travel Road
Vol 85, November 2004
20. N Karuppaiah, C Sujatha and V Ramamurthi. ‘Model and Vibration/ stress Analysis of a enger Vehicle by FEM.’ Symposium on International Automotive Technology, January 13-16, Pune, India, 1999. 21. J A Tamboli and S G Joshi. ‘Optimum Design of a ive Suspension System of a Vehicle Subjected to Actual Random Road Excitations.’ Journal of Sound and Vibration, vol 219, no 2, 1999, pp 193-205. 22. A J Healey, E Nathman and C C Smith. ‘An Analytical and Experimental Study of Automobile Dynamics with Random Roadway Inputs.’ Transactions of ASME, Journal of Dynamic Systems, Measurement and Control, vol 99, no 4, 1977, pp 284-292. 23. K Ramji and V K Goel. ‘Coupled Vertical — Lateral Dynamics of Three-wheeled Motor Vehicles.’ Presented at the Seventeenth IAVSD Symposium, Technical University of Denmark, August 20-24, Copenhagen (Lyngby), Denmark, 2001. 24. J W Cooley and J W Tukey. ‘An Algorithm for the Machine Calculation of Complex Fourier Series.’ Math Comp, vol 19, 1965. 25. D S Samuel and R A David. ‘Digital Signal Processing Algorithms.’ Prentice Hall Inc, Englewood Cliff, New Jersy, 1988. 26. R C Britton. ‘Digital Filter Designer’s Handbook.’ McGraw Hill, New York, 1988. 27. P D Welch. ‘The use of Fast Fourier Transform for the Estimation of Power Spectra: a Method Based on Time Averaging over Short, Modified Periodograms.’ IEEE Transactions on Audio and Elctroacoustics, AU-15, vol 2, 1967, pp 70-73.
201
NOTATION Ak (n)
: FFT component
C
: capacitance
fcc
: cut off frequency
fs
: maximum frequency of measured signals
K
: number of segments
N, Csp
: constants
P ( fn )
: power spectrum estimate
R
: resistance
Sqr ( η)
: power spectral density of road surface profile
T
: sampling interval, s
Z0
: vertical undulations of the road surface
Z&1 − Z& 0
: relative velocity of trailer frame and the roadfollowing wheel
Z&&1
: frame vertical absolute acceleration
K Ramji is with Mechanical Engineering Department, College of Engineering, Visakhapatnam 530 003; A Gupta and Prof V Kumar are with Electrical Engineering Department and V H Saran and Prof V K Goel are with Mechanical and Industrial Engineering Department all at IIT Roorkee, Roorkee 247 667. This paper (modified) was received on June 8, 2004. Written discussion on this paper will be received till January 31, 2005.
Vol 85, November 2004
INTRODUCTION With the growing awareness for better highways for an ever increasing traffic loading and concern for aging highway systems, the Government of India has established the National Highway Authority (NHA). The major function of the NHA will be the planning of new routes, preparing maintenance schedules and acceptance or replacement of newly constructed highways. Naturally, appropriate management systems are needed to make objective assessment of highway quality. Generally, highway engineers using a response type single wheel trailer unit, eg, Dipstick or Merlin devices, specify road roughness as the total vertical distance measured by the measuring wheel per kilometer of distance travelled (mm/km). Such specification of road roughness by highway engineers is convenient for the construction and maintenance of roads, but is not useful for providing input to the vehicle model, for evaluation of ride index and enger comfort. These devices do not yield data to obtain the power spectral density (PSD) of the road surface roughness, which is essential for evaluation of vehicle ride behaviour. The purpose of the present work was to measure the road profile in PSD form, which can be used as input to the vehicle model. Vehicle designers also use road roughness data to investigate its effect on vehicle braking and steering behaviour, as the normal tyre forces are affected by road roughness. According to International Standard Organization (ISO)26311, the ride comfort is specified in of root mean square (RMS) acceleration over a frequency range. The pavement surface profile of interest to the highway engineer covers a wavelength range2 of about 0.01 mm to 100 m. This range is too wide to be measured in of a single scale, but can be described and measured in four scales: micro-texture, macro-texture, mega-texture and road roughness. The road roughness usually covers a wavelength from 0.1 m to 100 m. 193
Since, road profiles are random in nature, these are better described by statistical techniques. One such statistical characterization that has been found useful in describing the road roughness is power spectral density. Road surface irregularities are statistically classified by frequency and amplitude distribution by Macaulay3, ie, one can perform a frequency analysis to make an estimate of the amplitudes for various wavelengths present. One method of analyzing random data by Bendat and Piersol4 and Stearns5 is in of its power spectral density (PSD), which is a measure of its mean squared value distribution within a frequency band. It is therefore necessary to measure the road profile and then compute the power spectral density from these data as it will help in the analysis of ride behaviour of vehicles. Wambold6, using a quarter car model to represent the vehicle and using ISO 26317 as the model of subjective response, predicted that car engers should be most sensitive to pavement disturbances within the special frequency range of approximately 0.23 cycles/m to 0.66 cycles/m. On the other hand, Janoff8 presented results that indicated that the car engers respond most strongly to pavement disturbances at spatial frequencies in the range of approximately 0.36 cycles/m to 2.3 cycles/m. These values, translated to temporal frequencies at a travel speed of 80 km/h, give corresponding ranges of approximately 5 Hz to 15 Hz and 8 Hz to 50 Hz, respectively. Hayhoe, et al 9 explained the reason for anomalies in the relationship between the ride quality and the profile characteristics. They found that the profiles contain a large number of pulses — like disturbances and these pulses contribute a significant portion of the energy in the profiles at high frequencies. They argued that the presence of pulses in pavement profiles could be a significant factor in subjective response to road roughness. The ISO10 and Wong11 have proposed a road roughness classification (A-H) based on the power spectral density. Various types of road roughness measuring devices and different kinds of surface roughness along with their measurement criteria have been discussed by Hegmon2, ISO10, Wong11 and Van Deusen12. Road elevation profiles can be measured either by performing close interval rod and level surveys described by Wambold, et al 13, or by using high-speed profilometers discussed by Spangler and Kelly14; Hudson15; Darlington and Milliman16. An inertial profilometer concept implemented at General Motors Research (GMR) laboratories in the 1960 and later developed in 1966, has been widely used for highway evaluation and application by Spangler and Kelly14; Hudson15; Darlington and Milliman16. In the present scenario, the laser based road profile measuring systems given by Prem17; Mimuro and Maemura18; Mimuro, et al 19 are being used to measure vertical undulations of roads in most of the developed countries. On surveying the literature, very few publications discuss the measurement of road undulations for Indian roads. Karuppaiah, et al 20, Tamboli and Joshi21 have made an attempt to measure road roughness for Indian roads in of power spectral 194
density. The PSD of the actual road vertical undulations/ excitations have been represented in the form of an exponential form given by Tamboli and Joshi21 for urban Indian roads and non-urban highways. Several research works12,20-23 have addressed the effect of road roughness on vehicle behaviour and have also described mathematical modelling of power spectral density of road surface profiles. The present paper deals with the development of a profile measuring trailer unit. Measurements of road roughness have been taken on five types of Indian roads and one mosaic floor (for academic interest only) using a PC (personal computer) — based on line data recording system. The results have been presented in the form of a power law equation, which could be used as a road input in vehicle models for evaluation of ride behaviour. ROAD PROFILOMETER A prototype road surface profilometer with three-wheels shown in Figure 1 has been designed and developed by the authors at IIT, Roorkee. The front wheel is a caster wheel while the rear wheels are the driving wheels. The road-following wheel is a solid rubber wheel (another wheel), which maintains with the road surface by a spring and dashpot unit. The specifications and dimension of the trailer frame, solid rubber wheel (road following wheel), caster and other rear wheels are given below: l l
l
The trailer frame is made of angle iron 35 mm × 35 mm size and 6 mm thickness for sufficient rigidity. The road following wheel has a metal rim with a solid rubber tyre of 120 mm dia. The small diameter wheel with large radial stiffness facilitates measurements of low and middle frequency road surface irregularities with good accuracy. The three wheels including the caster wheel of the trailer unit are 3.50 × 10, 4 PR pneumatic tyres, each of 372.5 mm dia.
The trailer unit is instrumented with a transducer to measure relative velocity ( Z&1 − Z& 0 ) between the trailer frame and the road surface (road-following wheel). The accelerometer, mounted on the frame just above the road-following wheel, measures the vertical acceleration ( Z&&1 ) of the frame, the integration of the signal gives the frame vertical velocity ( Z&1 ) . The velocity signal is then added to the relative velocity signal of the frame and the road-following wheel, the resulting signal is integrated to yield the road undulations (vertical displacement, Z0 ) profile. The measurement approach followed in this paper, ie, the single integration of relative velocity between the wheel and frame, rather than merely double integrating the acceleration of the solid rubber wheel, ensures wide acceptability in the measurement of road roughness. The roadfollowing wheel is a solid rubber tyre of 120 mm dia moulded on metal rim. It acts as a mechanical filter, which transmits low and middle frequency road surface undulations but attenuates high frequency (low wavelength) road surface values. IE (I) Journal—CV
Velocity and acceleration transducers Computer for data recording
Trailer
Optocoupler unit
Road profiling wheel Figure 1 Experimental test set-up for measurement of road roughness
( Z&&1 )
( Z&1 − Z& 0 )
The schematic operations of data acquisition are shown in Figure 2. The data (analog signals) obtained from the transducers are stored in digital form on microcomputer mounted on the trolley for data processing later on. In this system, the transducer signals, ie, acceleration and relative velocity are sampled and converted to digital values for use in profile computation. The sampling and computation of the road profile are performed as a function of distance instead of time, which makes the measurements independent of trailer speed and easier to handle. For this purpose an optocoupler, which gives pulses at regular interval of distance travelled, has been mounted on the rear axle, of the trailer. TRANSDUCERS AND DATA PROCESSING
Z&1 − Z& 0
Z&1
–
+
Figure 2 Schematic operation of road profilometer
Vol 85, November 2004
The acceleration of the trailer frame is measured using a strain gauge type accelerometer, suitable for measuring low frequency vibrations of low magnitude, ie, from 0 g to 5 g. Transducers of this type are used in applications requiring small size, small mass and measurement of low frequency (0 Hz - 200 Hz). An internal signal conditioner conditions the signal of the sensing element to a -friendly voltage. The strain gauge type accelerometer pickup was manufactured by Bruel and Kajer and has been already calibrated to International standards. However, before beginning of the experiment, the accelerometer was checked by holding it in hand in horizontal position and rotating it by 90 ° (upside down position), to yield a signal of 1 g on an oscilloscope. At present sensitivity of 1.39 V/g was used. More details of acceleration transducer are given below. Rated output, µ V/g : 553 Strain, µ
:
110.6 195
Frequency response, Hz
:
0–240
Non-linearity
:
1% of rated output
Input resistance, Ω
:
122.8
Output resistance, Ω
:
122.8
Safe temperature, ° C
:
0–50
Safe excitation, V
:
5
The relative velocity pick-up is a cable-activated transducer of 5V/m/s sensitivity, that produces a voltage proportional to the relative velocity between the trailer frame and the roadfollowing wheel. A product of ASM (Automatic Sensorik Messtechnik) of , the unit is precalibrated to International Standards. Internal signal conditioner conditions the signal of the sensing element to -friendly voltage, current or digital pulse. More details of velocity transducer are: Model
:
WGS5-500-10V-T5-L10-HG
Function designation
:
Position and relative velocity transducer
Range
:
0 V-10 V dc signal conditioner
Sensitivity
:
5 V/m/s
Linearity
:
0.1% of measured value
Maximum acceleration
:
60 g
Max velocity
:
10 m/s
Sensor component
:
Tachogenerator
Accuracy
:
0.1 %
It has been described earlier that the vertical undulations (profile) of the road surface are recorded as a function of distance travelled by the trailer unit, which is measured by a single perforated disc mounted on the rear axle of the trailer unit along with an optocoupler. The optocoupler consists of a gallium arsenide infrared emitting diode and a silicon phototransistor mounted in closed proximity. The two are optically coupled but electrically insulated from each other. Whenever an infrared ray from the diode es through the perforation in the disc, a pulse is generated. The three pneumatic tyres (3.50 × 10, 4 PR) of the trailer including the caster wheel are each of 372.5 mm φ . Therefore, the linear distance covered in one wheel rotation is 1170 mm. The optocoupler unit has a perforated disc with 10 equidistant holes on its circumference. Therefore, the distance travelled by the trailer unit between two adjacent holes, which corresponds to two consecutive pulses is 117 mm (or 0.117m), which is also evident from the raw data of bituminous newly laid road given in Table 1. With a 10-hole disc, the distance travelled between two consecutive pulses is 0.117 m. The signals from the two transducers, ie, relative velocity pickup and acceleration pickup are taken to ADC card (8112 HG) using shielded cable, to prevent noise from external electric and 196
magnetic fields being picked up. A 12-bit ADC card (ACL-8112) featuring eight differential inputs, 16 digital inputs/outputs and one timer has been used for data acquisition from transducers. The signals obtained from the transducers are properly filtered using hardware filter before being taken to ADC card, (Figure 2). The hardware filter was a low third order ‘RC’ filter with cut off frequency given by
f cc =
1 2π RC
(1)
The values of C and R were taken as 0.47 µF and 17 kΩ , respectively, which gave the cut off frequency as 20 Hz. Filtered acceleration signal is integrated using a software integrator based on trapezoidal rule. The integrated acceleration signal is again filtered using a band filter. In the absence of filtering, any offset present can cause numerical overflow. Filtered velocity pick-up data are subtracted from integrated acceleration data and signal is again integrated to get the roughness profile. This roughness data (vertical undulations) is used to obtain power spectral density. The scheme of operations is shown in Figure 2. The sampling and computation of the road profile are performed as a function of distance instead of time, which makes the measurements independent of trailer speed and easier to handle. For this purpose an optocoupler, which gives pulses at regular interval of distance travelled, has been mounted on the rear axle of the trailer. In any experimental test program proper care needs to be taken in order to ensure the accuracy and reliability of the test data. Signals obtained from the transducers through ADC card are processed to obtain useful information. The first requirement is to sample the transducer signals and filtering the signals to remove any electrical noise. The accelerometer signals are integrated by software employing the trapezoidal rule to obtain velocity signals. The road surface profile of wavelength of 100 mm or more are normally encountered on typical highways and are of interest to vehicle dynamicist. The profile data was acquired by normally towing the trailer unit at a speed of nearly 1 m/s. Thus, the maximum frequency of measured signals fs was about 10 Hz. Therefore, the minimum sampling frequency, known as the Nyquist rate should be 2 fs or 20 Hz in order to prevent aliasing. Sampling at points which are too far apart will lead to confusion between the low and high frequency components in the original data and is called aliasing. Before choosing the sampling frequency one more important factor, ie, the lowest frequency of interest must be considered, which was chosen as 0.1 Hz. The fast Fourier transform (FFT) is efficient and fast method for computing the discrete Fourier transform (DFT). Computation of DFT required M2 complex operations (addition and multiplication) and hundred of hours of machine time prior to 1965. In 1965, a method for computing the DFT was given by Cooley and Tukey24 that requires approximately Mlog2M operations where M is power of 2. This method of computing Fourier Transform which requires a number of IE (I) Journal—CV
Table 1
Vertical undulations for newly layed road
Distance travelled, m
Vertical undulations, mm/m SEC1 SEC2
Distance travelled, m
Vertical undulations, mm/m SEC1 SEC2
Distance Vertical undulations, travelled, mm/m m SEC1 SEC2
Distance travelled, m
Vertical undulations, mm/m SEC1 SEC2
0.000
–0.423
0.402
5.850
–0.245
3.149
11.700
–2.766
–0.188
17.550
–0.117
0.502
0.117
0.090
0.553
5.967
–1.768
4.341
11.817
–2.440
–0.124
17.667
1.109
1.045
0.234
0.157
–0.388
6.084
–4.348
3.992
11.934
–3.081
–0.562
17.784
0.509
1.289
0.351
0.535
–0.677
6.201
–3.830
4.634
12.051
–2.466
1.102
17.901
–0.626
1.626
0.468
1.789
0.382
6.318
–4.864
3.164
12.168
–1.812
1.917
18.018
0.298
1.296
0.585
1.361
–0.540
6.435
–5.854
2.883
12.285
–1.978
1.083
18.135
0.029
1.186
0.702
1.643
–1.759
6.552
–5.033
2.654
12.402
–1.364
–0.066
18.252
0.546
1.055
0.819
2.444
–1.325
6.669
–5.932
1.406
12.519
–1.061
–0.725
18.369
–0.108
3.199
0.936
1.487
–1.056
6.786
–5.028
2.084
12.636
–2.302
–2.093
18.486
–2.005
3.344
1.053
0.739
–2.557
6.903
–3.600
1.751
12.753
–2.474
–5.441
18.603
–0.244
1.074
1.170
1.919
–1.516
7.020
–4.861
3.295
12.870
–3.875
–6.683
18.720
–1.434
1.901
1.287
0.697
–0.454
7.137
–3.759
2.552
12.987
–1.265
–6.503
18.837
–1.099
0.718
1.404
1.684
–0.887
7.254
–2.492
2.357
13.104
–1.381
–2.050
18.954
0.891
1.343
1.521
1.934
0.155
7.371
–2.290
–0.358
13.221
–1.564
4.335
19.071
0.434
2.352
1.638
0.406
1.694
7.488
–0.748
–1.335
13.338
–0.769
5.148
19.188
1.121
1.246
1.755
1.256
0.772
7.605
–0.325
–1.913
13.455
–2.547
5.120
19.305
1.279
1.039
1.872
2.099
–0.936
7.722
–1.475
–2.451
13.572
–2.537
3.049
19.422
2.348
2.249
1.989
0.650
–0.198
7.839
–3.435
–0.997
13.689
–2.020
0.324
19.539
3.429
2.258
2.106
1.149
–1.116
7.956
–4.675
–0.524
13.806
–3.778
1.992
19.656
1.978
–0.062
2.223
2.247
–1.772
8.073
–4.002
–1.768
13.923
–3.365
1.583
19.773
2.880
–0.246
2.340
2.318
–0.879
8.190
–3.274
–2.109
14.040
–3.220
0.090
19.890
4.053
0.588
2.457
2.344
–0.327
8.307
–3.021
–0.728
14.157
–5.322
0.253
20.007
4.493
0.590
2.574
4.001
–0.503
8.424
–4.009
–2.157
14.274
–4.221
1.983
20.124
5.836
1.423
2.691
2.929
–0.918
8.541
–3.351
–2.807
14.391
2.545
1.964
20.241
–2.290
1.388
2.808
2.695
0.986
8.658
–5.645
–2.435
14.508
–4.165
2.454
20.358
–5.859
2.048
2.925
3.799
0.250
8.775
–4.374
–2.576
14.625
–4.286
4.026
20.475
—
1.937
3.042
3.718
0.184
8.892
0.776
–2.632
14.742
–3.798
5.574
20.592
—
2.835
3.159
3.081
1.121
9.009
0.856
–3.331
14.859
–2.276
5.303
20.709
—
0.302
3.276
3.240
0.418
9.126
1.721
–2.494
14.976
–2.720
5.548
20.826
—
–0.063
3.393
0.019
–0.672
9.243
1.056
–3.000
15.093
–1.404
4.259
20.943
—
–2.559
3.510
0.153
0.133
9.360
1.681
–3.272
15.210
–1.855
6.397
21.060
—
–2.599
3.627
1.881
–0.139
9.477
–1.151
–2.523
15.327
0.922
6.572
21.177
—
–1.697
3.744
2.640
–0.458
9.594
–1.277
–2.396
15.444
–0.244
3.741
21.294
—
–1.605
3.861
2.040
0.272
9.711
–0.148
–4.642
15.561
–0.232
3.292
21.411
—
0.327
3.978
0.853
0.510
9.828
–1.015
–4.646
15.678
0.531
3.547
21.528
—
0.921
4.095
0.498
–0.528
9.945
–0.850
–2.878
15.795
–0.656
1.739
21.645
—
0.668
4.212
0.954
0.533
10.062
–0.13
–4.387
15.912
–0.818
1.931
21.762
—
2.062
4.329
–0.969
2.612
10.179
–0.633
–3.931
16.029
1.349
2.555
21.879
—
0.915 Table 1 Cond
Vol 85, November 2004
197
Table 1
Vertical undulations for newly layed road (Cond)
Distance travelled, m
Vertical undulations, mm/m SEC1 SEC2
Distance travelled, m
Vertical undulations, mm/m SEC1 SEC2
Distance travelled, m
Vertical undulations, mm/m SEC1 SEC2
Distance travelled, m
Vertical undulations, mm/m SEC1 SEC2
4.446
0.264
3.182
10.296
0.833
–0.333
16.146
0.853
2.336
21.996
—
0.065
4.563
1.376
4.113
10.413
1.630
–0.616
16.263
1.051
2.207
22.113
—
0.144
4.680
–2.286
1.653
10.530
2.146
0.641
16.380
1.596
2.886
22.230
—
0.036
4.797
–3.480
1.510
10.647
–3.186
–0.773
16.497
–0.386
2.958
22.347
—
–1.187
4.914
–4.799
0.552
10.764
–7.994
0.933
16.614
–0.079
2.322
22.464
—
–1.548
5.031
–4.202
–0.037
10.881
–1.373
–1.049
16.731
–0.868
2.175
22.581
—
–1.284
5.148
–3.030
–0.540
10.998
3.429
0.816
16.848
–0.993
1.688
22.698
—
–1.400
5.265
–0.944
1.466
11.115
–2.638
–0.458
16.965
–0.298
1.514
22.815
—
–2.778
5.382
–0.456
2.437
11.232
–1.742
–1.824
17.082
–1.629
1.345
22.932
—
–2.839
5.499
–0.702
2.768
11.349
–1.273
–0.444
17.199
–1.022
1.582
—
—
—
5.616
–0.381
3.451
11.466
–13.093
–0.419
17.316
–0.533
1.635
—
—
—
5.733
–1.986
3.300
11.583
–8.608
–0.950
17.433
–0.020
1.810
—
—
—
The signals obtained from the transducers are properly filtered and long wavelength components are attenuated before the data is processed to evaluate road roughness profile. Along with the software filter a low , third order hardware filter with cut off frequency of 20 Hz has also been used. A filter based on the window method of finite impulse response (FIR) has been designed, using the Fourier series method given by Britton26. The Fourier series method of FIR filter design is based upon the fact that frequency response of a digital filter is periodic and is therefore representable as a Fourier series. A desired target frequency response is selected and expanded as a Fourier series, which is truncated to a finite number of that are used in Fourier coefficients. The resulting filter has a frequency response that approximates the original desired target response. 198
The signal so obtained after filtering, were further processed, to bring it to a useful form. The accelerometer signal is to be integrated to obtain the velocity and displacement signals. 0.30 0.25
Series 1
0.20 Magnitude
The signals obtained from transducers are properly filtered and long wavelength components are attenuated before the data is processed to evaluate road roughness profile. Two types of filters, hardware filters and software filters are used for filtering the signals. Software filters are used to remove noise present in transducer signals. Signals from velocity pick-up are filtered using a low filter (0 Hz-10 Hz), while the signals from acceleration pick-up are filtered using a band filter (0.3 Hz10 Hz).
Finite impulse response and magnitude response of band filters and low filters are shown in Figures 3(a) and 3(b) and Figures 4(a) and 4(b), respectively.
0.15 0.10 0.05 0 –0.05 0
50
100
150
200
250
300
–0.10 –0.15
Time, s
Figure 3(a)
Finite impulse response of a band filter (0.3 Hz-9 Hz)
1.2 1.0
Series 1
0.8 Magnitude
operations equal to Mlog2M become known as Fast Fourier Transform. The FFT developed by Cooley and Tukey24 in 1965 is significantly less computationally intensive method for evaluating the DFT and thus particularly attractive for real time spectral analysis using digital signal processing (DSP) technology. The FFT algorithm used for computing DFT has been taken from Samuel and David25. The FFT algorithm requires the number of samples to be an integral power of 2. Since, 29 is equal to 512, with proper adjustment of the delay, a sampling rate of 61 Hz was chosen which gives a resolution of 0.12 Hz in power spectral density, which is acceptable.
0.6 0.4 0.2 0 –0.2
0
10
20
30
Frequency, Hz Figure 3(b) Magnitude response of band filter (0.3 Hz-9 Hz)
IE (I) Journal—CV
0.35
Series 1
0.30 0.25 Magnitude
0.20 0.15
K segments of length L. For each segment of length L, a modified periodogram is calculated. That is, a window W ( j ), j = 0, 1, . . . . . . . . . . , L – 1 is selected and the sequences X1 ( j ) W ( j ), ... ... ..., Xk( j ) W( j ) are formed. The finite Fourier Transforms A1 (n), A2 (n) ... ... ... ... ... , Ak (n) of these sequences is taken. Here
0.10
Ak ( n) =
0.05 0 –0.05 0
50
100
–0.10
150
200
250
300
Figure 4(a) Finite impulse response of a low filter (0 Hz-9 Hz)
Series1
Magnitude
0.8 0.6 0.4 0.2 0 –0.2
0
5
10
15
20
25
30
35
Frequency, Hz
Figure 4(b) Magnitude response of low filter (0 Hz-9 Hz)
Numerical integration is resorted to when the analytical evaluation of integration is either difficult or impossible and when the function to the integration is available at discrete points. However, when it is possible to obtain closed form solution by analytical integration, it must be preferred for its exactness. Consider the integral
I=
z
b a
f(t ) d t
(2)
where f (t) is continuous function of t over a ≤ t ≤ b , and the integral may be evaluated using equal or unequal intervals. In the present work, the integral has been performed based on the Trapezoidal rule employing equal intervals, which is chosen because of its simplicity and reduced errors at high sampling rate. This particular integration technique has poor response characteristics near the Nyquist frequency but presents no difficulty in this application, as the frequencies contained in the signal, are typically less than 10 Hz, well below the Nyquist frequency. The signal corresponding to road surface undulation is obtained which is further processed for power spectral density. Welch27 gave a method for estimation of power spectra by using FFT algorithm. It involves sectioning the record, taking modified periodograms of these sections, and averaging these modified periodograms. The data sample X ( j ) is divided into Vol 85, November 2004
− 2 πijn / L ∑ Xk ( j ) W ( j ) e
j=0
(3)
L K ∑ Ak ( n) UK k = 1
2
(4)
where
1.2 1.0
L −1
The spectral estimate is the average of these periodograms, ie, P ( fn ) =
Time, s
1 L
U =
1 L −1 2 ∑ W ( j) . L j=0
EVALUATION OF ROAD ROUGHNESS Profile data for Indian roads have until recently been unavailable and it is of interest to examine some of their characteristics. Recently Karuppaiah, et al 20 and Tamboli and Joshi21 have published limited information on profile data of Indian roads but no comparisons were made with data available for international roads. Tamboli and Joshi21 have represented the Indian road profile data in an exponential form, which may be computationally more convenient to handle. It has been found in the literature11,12 that the relationship between the power spectral density Sqr ( η) and the spatial frequency ( η) for different ground profiles is usually represented in power law, which generally approximates as S qr ( η ) = C sp η− N
(5)
where η is spatial frequency in cycles/m; Sqr ( η) , power spectral density of road surface profile in m2/cycle/m. N is a dimensionless constant whereas Csp is an empirical constant whose dimensions vary with the value of N. RESULTS AND DISCUSSION In the present work, the road tests were conducted on five different roads and one mosaic floor using the road profilometer designed and developed in Vehicle Dynamics Laboratory (VDL), IIT, Roorkee. Using power series analysis, best-fit curves were obtained for each road profile yielding different values of Csp and N, which are given in Table 2. Five different types of road surfaces consist of four bituminous roads from serial number 1 to 4, one Portland cement concrete (PCC) road at serial 5 and one mosaic floor (similar to very smooth surface) at serial number 6 are evaluated in this study. The tests were performed at slow speeds by pushing the trailer unit on these road surfaces and the mosaic floor with test lengths varying from 21 m to 60 m. The measured data was recorded by a microcomputer, mounted directly on the road profilometer, which computed the power spectral density values. 199
S No
Description of road surface
1
Newly layed
Institute road data C sp N
International road data C sp N
2.2 × 10 − 07
2.7 × 10 − 07
2.0
2.1
surface road (Runway road type of NACA-TN-3305) 2
Smooth road
1.0 × 10 − 06
2.4
2.4 × 10 − 06
2.1
(Smooth runway type of NACA-TN-3484) 3
Rough road
4.9 × 10 − 06
2.2
4.4 × 10 − 06
2.1
3.5 × 10 − 07
2.1
4.8 × 10 − 07
2.1
5.5 × 10 − 07
1.7
6.4 × 10 − 07
1.9
(Highway with gravel) 4
Smooth highway road
5
PCC Road (Runway road type of NASA-TND-510)
6
Mosaic floor
2.2 × 10 − 07
2.2
—
—
Several test runs were carried out along the width of a given road surface like section 1 (SEC 1) and section 2 (SEC 2) and average values of PSD have been reported here. Figure 5 and Figure 6 show vertical undulations and power spectral density values, respectively for a typical institute bituminous road. This was a newly constructed road surface and is similar to air port runway road (NACA-TN-3305)12. The amplitude level Figure 5, indicates the roughness level; higher amplitudes would mean rougher roads. The wave number (or spatial frequency) in Figures 5 and 6 corresponds 0.1 cycles/m to 10 cycles/m or to a wavelength (inversely proportional to spatial frequency) of 10 m
Undulations, mm
10
Sec 1 Sec 2
5 0
0
5
10
15
20
25
–5
Measured road distance position, m
Figure 5 Vertical undulations against measured road distance of bituminous newly layed road
200
1.00E+00 1.00E–01
Spatial frequency, cycles/m 0.1
1.00E–02 1.00E–03
1
Sec 1 Sec 2
10 y=2.17E-07x –2.07E+00 y=2.28E-07x –1.98E+00
1.00E–04 1.00E–05 1.00E–06 1.00E–07 1.00E–08 1.00E–09
Figure 6 PSD as a function of spatial frequency for bituminous newly layed road
at the origin to about 0.1 m towards right. The PSD data for different road surfaces are reported in Table 2, which indicates drop in amplitude with wave number. The rate at which amplitudes decrease with wave number is characterized by the value of N, the larger the value of N, the more steep the decrease in amplitudes. Therefore, measurements were taken on mosaic floors and values of Csp and N are found to be 2.2 × 10 − 7 and 2.2, respectively. The roughness values were found to be nearly the same as that for runway road type NACA-TN-330512. As per ISO specifications, such surfaces could be treated as a good surface. SUMMARY AND CONCLUSIONS Measurements of the actual road roughness profiles, using indigenously designed and developed road profilometer, is presented for five different institute roads and one mosaic floor. The road roughness is represented in of power spectral density as a function of spatial frequency and compared with the data of international roads. Based on ISO surface roughness classification, the roads in IIT, Roorkee could be classified between average, good and very good roads. PSD data for Indian roads will provide additional input for highway engineers in India to develop better management systems for objective assessment of highway quality and an essential input for vehicle designers for achieving better vehicle ride behaviour. It is hoped that this study will stimulate further research on effect of road roughness on the vibration behaviour of Indian vehicles and rider sensitivity to vibrations. ACKNOWLEDGEMENT The research work reported here was carried out under a research scheme financially ed by the Department of Science and Technology, Government of India, New Delhi. The financial is gratefully acknowledged. REFERENCES
–10 –15
Power spectral density, m2/cycles/m
Table 2 C sp and N values for power spectral density functions for various roads
1. ‘ISO 2631 Mechanical Vibration and Shock Evaluation of Human Exposure to Whole Body Vibrations — PART I.’ General Requirements, 1997. 2. R R Hegmon. ‘Some Results from Ongoing Research on Road Roughness.’ Vehicle, Tyre, Pavement Interface ASTM STP 1164, 1992, pp 14-31.
IE (I) Journal—CV
3. M A Macaulay. ‘Measurement of Road Surfaces, Advances in Automobile Engineering — Part I.’ G H Tidbury, (ed), Pergamon Press, Oxford, England, 1963.
Profilometer.’ Highway Research Record, vol 214, Washington, DC, 1968, pp 50-67.
4. J S Bendat and A G Piersol. ‘Random Data: Analysis and Measurement Procedures.’ Wiley-Interscience, New York, 1971.
17. H A Prem. ‘Laser Based Highway-speed Road Profile Measuring System.’ Proceedings of the Tenth IAVSD Symposium on The Dynamics of Vehicle on Roads and Tracks, Prague, 1987, pp 300-304.
5. S D Stearns. ‘Digital Signal Analysis.’ Hayden Book Company INC, Rochelle Park, New Jersey, 1975.
18. T Mimuro and T Maemura. ‘Road Profile Measuring System using Laser Displacement Sensors.’ JSAE Review, vol 11, no 4, 1990.
6. J C Wambold. ‘Road Roughness Effects on Vehicle Dynamics, Measuring Road Roughness and its Effects on Cost and Comfort.’ ASTM STP 884, 1985, pp 179-196.
19. T Mimuro, T Maemura and H Fujii. ‘Development and Application of the Road Profile Measuring System.’ SAE Transactions, 930257, 1993, pp 291-298.
7. ‘International Organization for Standardization, Guide for the Evaluation of Human Exposure to Whole Body Vibration.’ ISO 26311974(E), 1974. 8. M S Janoff. ‘Pavement Roughness and Rideability Field Evaluation.’ NCHRP Report 308, TRB, National Research Council, 1988. 9. G F Hayhoe. ‘Spectral Characteristic of Longitudinal Highway Profiles as Related to Ride Quality.’ Vehicle, Tire, and Pavement Interface ASTM STP 1164, 1992, pp 32-54. 10. ‘ISO Reporting Vehicle Road Surface Irregularities.’ TC108/SC2/WG4 N57, 1982. 11. J Y Wong. ‘Theory of Ground Vehicle.’ John Wiley and Son Inc, Canada, 1993. 12. B D Van Deusen. ‘Analytical Techniques for Design Riding Quality into Auto Motive Vehicles.’ SAE Transactions, vol 76, 670021, 1968. 13. J C Wambold, L E Defrain, R R Hegmon, J Mcghee, J Reichert and E Spangler. ‘State-of-the-art of Measurement and Analysis of Road Roughness.’ Transportation Research Record, vol 836, 1981, pp 21-29. 14. E B Spangler and W J Kelly. ‘GMR road Profilometer — a Method for Measuring Road Profile.’ Highway Research Record, vol 121, Washington, DC, 1966, pp 27-54. 15. W R Hudson. ‘High-speed Road Profile Equipment Evaluation.’ Highway Research Record, vol 189, Washington, DC, 1967, pp 150-163. 16. J R Darlington and P A Milliman. ‘Progress Report on the Evaluation and Application Study of the General Motors Rapid Travel Road
Vol 85, November 2004
20. N Karuppaiah, C Sujatha and V Ramamurthi. ‘Model and Vibration/ stress Analysis of a enger Vehicle by FEM.’ Symposium on International Automotive Technology, January 13-16, Pune, India, 1999. 21. J A Tamboli and S G Joshi. ‘Optimum Design of a ive Suspension System of a Vehicle Subjected to Actual Random Road Excitations.’ Journal of Sound and Vibration, vol 219, no 2, 1999, pp 193-205. 22. A J Healey, E Nathman and C C Smith. ‘An Analytical and Experimental Study of Automobile Dynamics with Random Roadway Inputs.’ Transactions of ASME, Journal of Dynamic Systems, Measurement and Control, vol 99, no 4, 1977, pp 284-292. 23. K Ramji and V K Goel. ‘Coupled Vertical — Lateral Dynamics of Three-wheeled Motor Vehicles.’ Presented at the Seventeenth IAVSD Symposium, Technical University of Denmark, August 20-24, Copenhagen (Lyngby), Denmark, 2001. 24. J W Cooley and J W Tukey. ‘An Algorithm for the Machine Calculation of Complex Fourier Series.’ Math Comp, vol 19, 1965. 25. D S Samuel and R A David. ‘Digital Signal Processing Algorithms.’ Prentice Hall Inc, Englewood Cliff, New Jersy, 1988. 26. R C Britton. ‘Digital Filter Designer’s Handbook.’ McGraw Hill, New York, 1988. 27. P D Welch. ‘The use of Fast Fourier Transform for the Estimation of Power Spectra: a Method Based on Time Averaging over Short, Modified Periodograms.’ IEEE Transactions on Audio and Elctroacoustics, AU-15, vol 2, 1967, pp 70-73.
201
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