Dynamic response of highway trucks due to road surface roughness

Pergamon

Cornpurrs & Structures Vol. 49, No. 6. pp. 1055-1067. 1993 0 1994 Elswier Science Ltd

Printed in Great Britain. 0045-7949/93 56.00 + 0.00

DYNAMIC RESPONSE OF HIGHWAY TRUCKS DUE TO ROAD SURFACE ROUGHNESS

T. L. WANG,? M. SHAHAWY$ and D. Z. HUANGt

tDepartment of Civil and Environmental Engineering, Florida International University, Miami, FL 33199, U.S.A.

$Structures Research and Testing Center, Florida Department of Transportation, Tallahassee, FL 32310, U.S.A.

(Received 1 April 1992)

Alastrati-Vehicle characteristics, vehicle speed and road surface roughness are major factors influencing bridge dynamic response.. In order to improve the previous vehicle model studies, vehicle models with seven or twelve degrees of freedom were developed for H20-44 and HS20-44 trucks, respectively. Vehicle models were validated by comparisons with the real truck dynamic systems.

The road surface roughness was generated from power spectral density (F’SD) functions for very good, good, average, and poor roads. The impact factors of suspension and tire forces were obtained for vehicle models running on different classes of roads at various speeds. A comparison of computed and experimental impact results was also made.

1. INTRODUCTION

Vehicle characteristics, vehicle speed and road surface roughness are some of the major factors that influence the dynamic response of a bridge due to moving loads. In reality, a truck is a very complex mechanical system because of its suspension. Some assumptions need to be made in order to simplify the vehicle characteristics in mathematical modeling analysis.

The dynamic analysis of highway vehicles has been studied since the middle of this century. Brief reviews of the literature can be found in [l-6]. Most of the previous studies have assumed that (1) the vehicle frames are rigid, (2) the interleaf friction forces are considered in a suspension system, (3) spring forces and damper forces are proportional to displacements and a single point. However, all vehicle models were limited to pitch mode vibration and road surface profiles were obtained from field measurement in most of these studies.

Even though Whittemore et al. [6] used frequency domain prediction techniques to simulate pavement load, the techniques were established only for linear systems excited by stationary random inputs.

In this study, the numerical road surface roughness spectrum is generated by using the random number based on the power spectrum density functions. Vehicle nonlinearity can be admitted when the generated road surface roughness is treated as an input function directly. In addition, the new vehicle models will include the roll vibration.

2. VEHICLE MODELS

H20-44 and HS20-44 trucks are two major design vehicles in the American Association of State Highway and Transportation Oflicials (AASHTO)

Specification [7l. Two nonlinear vehicle models with seven and twelve degrees of freedom were developed according to the H20-44 and HS20-44 trucks, respectively.

Figures 1 and 3 illustrate the side and front views of the H20-44 vehicle model. Three rigid masses represent the truck, front wheel/axle set, and rear wheel/axle set, respectively. In the model, the truck was assigned three degrees of freedom, corresponding to the vertical displacement (JJ), rotation about the transverse axis (pitch or O), and rotation about the longitudinal axis (roll or 4). Each wheel/axle set is provided with two degrees of freedom in the vertical and roll directions. The total degrees of freedom in the model are seven.

Similarly, another vehicle model (refer to Figs 2 and 3) with twelve degrees of freedom was developed to represent an HS20-44 truck, consisting of five rigid masses as tractor, semi-trailer, steer wheel/axle set, tractor wheel/axle set, and trailer wheel/axle set. Tractor and semi-trailer were assigned three degrees of freedom (y, 0, and 4) individually. Two degrees of freedom (y and 0) were assigned for each wheel-axle set. The tractor and semi-trailer were interconnected at the pivot point (so-called fifth wheel point, see Fig. 2).

Suspension force consists of the linear elastic spring force and the constant interleaf friction force [8]. The load-displacement relationships for friction force, suspension spring force, and combination of these two forces are shown in Fig. 4. The tire springs are assumed to be linear.

Since the truck is a complex physical system, certain assumptions were made to simplify the model. These assumptions are as follows:

1. The vehicle runs at a constant speed.

1055

1056 T. L. WANG et al.

I- -1

Fig. 1. Side view of an H20-44 vehicle model.

2. All components move with the same velocity in the longitudinal direction.

3. Provision is made in the model for wheel lift. Under this condition, the vertical tire stiffnesses are taken as zero.

4. Each tire contacts the road at a single point. 5. Force inputs are limited to the vertical direction. 6. In suspension systems, damping elements were

assumed to be linear and to be of the viscous type. Damper force is proportional to the velocity. Ten per cent of the critical damping value was used for damping coefficient [6]. In the tires, the damping forces were neglected.

The total potential energy, V = Xvi, of the system is then computed from the spring stiffnesses

and relative displacements, whereas the dissipation energy, D = ZDi, of the system is obtained from the damping forces. The total kinetic energy, T = Xl;, of the system is calculated using the mass, mass moment of inertia, and translational as well as rotational velocities, of the system components. The moment of inertia of all components is assumed to be constant and the weight of each component is considered as the external force on that component.

The equations of motion of the system are derived, using Lagrange’s formulation, as follows:

_dT+dv+aD=o, 8% a4i a4 (1)

Ir ‘6 4

N Is I_ ‘I _ 15

I I I \

k ‘2 *1- 1

I-

t- ‘4 $3+

Fig. 2. Side view of an HSZO-44 vehicle model.

Dynamic response of highway trucks 1057

0 c t1

f YII

d.

Fig. 3. Front view of H20-44 and HS20-44 vehicle models.

where qi and di are the generalized displacements and velocities. Details of derivation are presented in

191. The equations of motion were solved by using a

fourth-order Runge-Kutta scheme [lo, 111, with an integration time step of 0.005 sec. Such a small time step was necessary to avoid numerical instability.

The real percentage of impact acquired from the study is defined as

Imp(%) = 4- 1 x 100% [ 1 (2) sm

in which R, and R, are the absolute maximum responses for dynamic and static studies respectively.

(a) Friction force

tr 18”

-I

h

Fig. 5. Side view of step bump used in vehicle validation.

3. VEHICLE MODEL VALIDATION

In order to check that the mathematical vehicle models properly simulate a real truck dynamic system, it is necessary to validate the models. The 3/4 in-high x 18 in-long and l/2 in-high x 18 in-long step bumps were taken to generate a vertical input for H20-44 and HS20-44 vehicle models respectively, as shown in Fig. 5. The appropriate data used in dynamic simulation of the models was adopted from [8] and is given in [9]. The experimental data was available in [6].

Both damped and undamped suspensions were considered, but tire damping was neglected in this study. Typical tire force histories for H20-44 and HS20-44 vehicle models are shown in Figs 6-9. Impact factors of suspension and tire forces for wide range of vehicle speeds are given in Tables 1 and 2 for H20-44 and Tables 3 and 4 for HS20-44. It may be seen that the impact factors of suspension forces were reduced when a damped suspension system was considered in most cases. However, for tire forces, the impact factors did not change significantly between damped and undamped suspension systems. The comparisons of computed

(b) Suspension spring force

6

(c) Combination of friction and suspension spring forces

Fig. 4. The relationship between the force and displacement in the suspension system.


0’ I 0.3 0.6 0.9 1.2 1.5 1.6

SIMULATION TIME (SEC)

0’ I

0.3 0.6 0.9 1.2 1.5 1.6


Fig. 6. The tire force history of the rear axle of an H20-44 Fig. 7. The tire force history of the rear axle of an H20-44 vehicle with undamped suspension system running at 3/4 in- vehicle with damped suspension system running at 3/4 in-

high step bump and 55 mph. high step bump and 55 mph.

01 0.6 1.3 1.6 2.3 2.6 3.3 3.6 4.3


Fig. 8. The tire force history of the tractor axle of an Fig. 9. The tire force history of the tractor axle of an HS20-44 vehicle with undamped suspension system running HS20-44 vehicle with damped suspension system running at

at l/2 in-high step bump and 35 mph. l/2 in-high step bump and 35 mph.

and experimental impact results of tire forces in different axles are illustrated in Figs 10-13. The agreement between computed and experimental results was found to be very good. The computed impact factors of tire forces almost cover all experimental results.

0’ I

0.6 1.3 1.6 2.3 2.6 3.3 3.6 4.3


4. ROAD SURFACE ROUGHNESS

The typical road surface may be described by a periodically modulated random process. The power spectral density (PSD) is a useful tool for analyzing the periodically modulated random process. The PSD

Table 1. Maximum suspension forces and impact factors of an H20-44 vehicle running at 3/4 in-high step bump for different suspension damping conditions and vehicle soeeds

Maximum static force &ins)

Vehicle speed (mph)

Undamped Damped suspension suspension

Maximum Maximum dynamic Impact dynamic Impact

force factor force factor tkins) (%1 (kit& f%)

15 5.361 44.74 5.164 39.42 20 5.074 36.99 5.048 36.29 25 4.877 31.67 4.865 31.34 30 4.721 27.46 4.705 27.02

Front 3.704 35 4.648 25.49 4.624 24.84 axle 40 4.513 21.84 4.516 21.92

45 4.506 21.65 4.494 21.33 SO 4.444 19.98 4.452 20.19 55 4.324 16.74 4.306 16.25

15 24.158 79.7s 24.163 79.78 20 24.097 79.29 23.990 78.50 25 24.499 82.28 24.051 78.95 30 24.321 80.96 24.129 79.53

Rear 13.440 35 24.449 81.91 24.489 82.21 axle 40 23.438 74.39 23.405 74.14

45 22.193 65.13 22.093 64.38 SO 22.638 68.42 22.622 68.32 5s 22.196 65.15 22.189 65.10

Dynamic response of bigbway trucks

Table 2. Maximum tire forces and impact factors of an H20-44 vehicle running at 3/4 in-high step bump for different suspension damping conditions and vehicle speeds


Maximum Maximum Maximum static Vehicle dynamic Impact dynamic Impact force speed force factor force factor

1059

(kips) 6ph) (kips) (%) Wps) W) 15 9.313 78.19 8.882 68.86 20 8.926 69.70 8.882 68.86 25 8.946 70.08 8.940 69.96 30 8.888 68.97 8.878 68.78

Front 5.260 35 8.950 70.15 8.918 69.54 axle 40 8.942 70.00 8.940 69.96

45 8.892 69.05 8.893 69.07 50 8.964 70.42 8.965 70.44 55 8.952 70.19 8.961 70.36

15 29.330 95.01 29.714 97.57 20 29.480 96.01 29.644 97.10 25 28.874 91.98 28.614 90.25 30 29.758 97.86 29.704 97.50

Rear 15.040 35 29.107 93.53 29.158 93.87 axle 40 28.392 88.78 28.626 90.33

45 29.585 96.71 29.689 97.40 50 29.310 94.88 29.200 94.15 55 29.156 93.86 28.827 91.67

functions for highway surface roughness have been developed by Dodds and Robson [123. They are

S(f#l)=A 2 --“2, 0

f#J>$ 90 ‘O’

(4)

shown as where S(4) is the PSD (m*/cycle/m), b, is the wave

S(r$)=A 2 --, 0 number (cycle/m), A is the roughness coefficient

(b<f#J 90 ‘\O

(3) (m3/cycle), and 4. is the discontinuity frequency = 1/(2n) (cycle/m).

Table 3. Maximum suspension forces and impact factors of an HS20-44 vehicle running at l/2 in-high step bump for different suspension damping conditions and vehicle speeds


Maximum Maximum Maximum static Vehicle dynamic Impact dynamic Impact force speed force factor force factor (kips) (mph) (kips) W) (kips) (%)

15 4.470 53.34 3.971 36.23 20 4.241 45.47 3.941 35.19 25 4.069 39.60 3.878 33.04

Steer 2.915 30 3.860 32.42 3.835 31.57 axle 35 3.848 31.99 3.764 29.12

40 3.735 28.12 3.659 25.52 45 3.651 25.26 3.697 26.82

15 25.133 77.08 23.279 64.02 20 25.538 79.93 22.484 58.42 25 23.441 65.16 22.203 56.44

Tractor 14.193 30 22.148 56.05 23.338 64.43 axle : 21.845 53.92 20.124 41.79

21.852 53.96 21.005 48.00 45 22.131 55.93 21.557 51.89

I5 23.463 61.01 23.218 59.32 20 22.878 56.99 23.218 59.32 25 22.966 57.59 22.908 57.19

Trailer 14.573 30 22.257 52.73 22.816 56.57 axle 35 21.677 48.75 22.347 53.34

40 21.712 48.99 33.351 53.37 45 22.614 55.18 23.012 57.91


Table 4. Maximum tire forces and impact factors of an HS20-44 vehicle running at l/2 in-high step bump for different suspension damping conditions and vehicle speeds

Undamped suspension suspension

Maximum static force (kips)

Steer axle

3.995

Tractor axle

15.994

Trailer axle

16.012

Vehicle speed (mph)

15 20 25 30 35 40 45

Maximum dynamic

force (kips)

6.891 6.524 6.482 6.458 6.501 6.405 6.426

Impact factor (%)

72.49 63.13 62.25 61.65 62.72 60.32 60.84

15 28.741 79.71 20 26.660 66.69 25 25.591 60.01 30 25.971 62.38 3s 25.717 60.79 40 26.387 64.98 45 26.003 62.58

15 25.381 58.51 20 25.242 57.64 25 25.801 61.13 30 25.889 61.68 35 25.845 61.41 40 25.931 61.95 45 25.411 58.70

Maximum dynamic Impact

force factor (kius) (%)

6.518 63.15 6.488 62.40 6.499 62.69 6.470 61.96 6.455 61.57 6.358 59.16 6.476 62.09

29.598 85.06 27.915 74.54 25.993 62.52 26.502 65.70 25.841 61.57 25.990 62.50 25.682 60.58

25.623 60.02 25.602 59.89 25.320 58.13 25.978 62.24 25.828 61.30 25.955 62.09 25.790 61.06

- “NDAYPCD SUSPCNSlDN - DMPCD SUSPENSION 0 CXPCRlYCNTAL DATA

20 30 40 50 60

VEHICLE SPEED (MPH)

i? - UNDAMPED SUSPENSION

100 - DAMPED SUSPCNSION 0: 0

60

60.

h-~. 0

d 0 0 0

g 40. 0 2 0 0

z?i 20.

0

CXPCROIENTU -:-I DATA

0

10 20 30 40 50

VEHICLE SPEED (MPH)

Fig. 10. The comparison of computed and experimental Fig. 11. The comparison of computed and experimental impact results for tire forces of the rear axle of an H20-44 impact results for tire forces of the steer axle of an HS20-44

vehicle running at 3/4 in-high step bump. vehicle running at l/2 in-high step bump.

i?

- t

- UNDAMPED SUSPENSION 100 - DUPED SUSPENSION

g 60 k-.

0 EXPERIMENTAL DATA

’ 60 -. _---- - ---_

iz 8 I

20 30 40

VEHICLE SPEED (MPH)

I

50 20 30 40

VEHICLE SPEED (MPH)

Fig. 12. The comparison of computed and experimental Fig. 13. The comparison of computed and experimental impact results for the tire forces of the tractor axle of an impact results for the tire forces of the trailer axle of an

HS20-44 vehicle running at l/2 in-high step bump. HS20-44 vehicle running at l/2 in-high step bump.

120 -

Dynamic response of highway trucks

!c:,:t ,. . . I WI 0 64 128 192 256

DISTANCE ALONG THE ROAD (M) [ai *mt s&s

DISTANCE ALONG THE ROAD (M) @a) Iam \ina

gj 1::: t.1 m 0

D&k ALO: THE ROE (N) 256

ib) Lett line

Fig. f4. Vertical highway surface pro&s in a very good Fig. 16, Vertical highway surface profiles in an average road. road.

The values of wi and w, varied from 1.36 to 2.28 [I2]. In order to simplify the description of road surface roughness, both wi and w, are assumed the value of two. Equations (3) and (4) are converted as follows:

S(gl)=A $ -2. 0 0

2 2.0

2 ii 1.0 s iz 0.0

s w -1.0

5: 2 -2.0 VI 0 84 128 182 258

DISTANCE ALONG THE ROAD (M) ,a> Righr ‘in*

2 2 0

DIST:CE ALOZTHE ROE(M) 256

(b, I&r line

Fig, IS. Vertical highway surface profdes in a good road.

3 1 I 2 -4.0 0 64 125 182 256

DISTANCE ALONG THE ROAD (Id) (a) ni+t LLmz

E 2.0

z” 1.0

g 0.0

s -1.0

2 -2.0 s\

It was found that the comparison between nume~cal and analytical PSDs agreed fairly well [9].

The random numbers which have approximate white noise properties were generated first [ 131. Then, these random numbers were passed through the first order recursive filter [14]. Finally, the output function will be the road surface roughness. The detail of the procedure has been discussed by Wang [lo]. In this study, the values of 5 x 10m6, 20 x 10m6, 80 x lo-‘* and 256 x lOA m*/cycle were used according to Intemational Organization for Standardization (ISO) specifications [15] as the roughness coefficient A for the classes of very good, good, average, and poor roads, respectively. The sample length was taken as 256m (839.9 ft) and 2048 (2”) data points were generated for this distance. The average vertical highway surface profiles of right and left lines from five simulations are shown in Figs 14-17 for very good, good, average, and poor roads respectively.

5. SUMMARY AND CONCLUS?ONS

According to the real H20-44 and HS20-44 trucks, two nonlinear vehicle models with seven and twelve degrees of freedom were developed and validated by the experimental data. Four different classes of road surface roughness were generated for very good, good, average, and poor roads. The maximum dynamic forces and entire force histories were recorded in 800-B simulation length when vehicle models with damped suspension system were running on the different classes of roads. Typical force histories of suspension and tire for H20-44 and HS20-44 vehicles


u 4.0

E E 2.0

6 0.0 3 0 E -2.0

u" iz

-4.0

5 -6.0 VI 0 64 128 192 256

DISTANCE ALONG THE ROAD (Id) (oi) Hlqht Line

52 6.0 , -1

L

2 -6.0 3. 0-l 0

DIST:CE ALOETHE ROE(M) 25R

(b) Left line

Fig. 17. Vertical highway surface profiles in a poor road.

m 0.6 1.6 2.6 3.0 4.6 5.6 6.6


Fig. 18. The suspension force history of the rear axle of an H20-44 vehicle with damped suspension system running at

75 mph and average road surface condition.

5 VI Ol 1.2 2.2 3.2


Fig. 20. The suspension force history of the tractor axle of an HS20-44 vehicle with damped suspension system running

at 75 mph and average road surface condition.

1.2 2.2 3.2 4.2 5.2 6.2 7.2


Fig. 21. The tire force history of the tractor axle of an HS20-44 vehicle with damped suspension system running at

75 mph and average road surface condition.

O-0 VERYGOODROADSWRPACE A-.& GOODROAG SURFACE 0-o AVRRAGE ROAD SURFACE o-----v POOR ROM SURFACE

0’ 10 20 30 40 50 60 70 60

VEHICLE SPEED (MPH)

Fig. 22. Impact results of suspension forces for the front axle of an H20-44 vehicle with damped suspension system.

25, I

z 140 -

a 20 O-0 VERY GOOD ROAD SURFACE

5 R 120 d--a GOOD ROAD SURFACE

O--O AVERAGE ROAD SVRFACE

2 15 ; 100. o-----v POOR ROAD SURFACE

,./’ .v...

?? E 60.

.o/--

~c.p_.._--- p x--._s

10

cr 2 v... ,... ..‘. 2 60. -.._,v ,-I+-o-_-O

F:

5

t; 40. o/ o----o

d e__-4-__‘L-----9----e---~---r~

0 20. 0.6 1.6 2.6 3.6 4.6 5.6 6.6

2

SIMULATION TIME (SEC) 0

10 20 30 40 50 80 70 60

Fig. 19. The tire force history of the rear axle of an H20-44 VEHICLE SPEED (MPH)

vehicle with damped suspension system running at 75 mph Fig. 23. Impact results of suspension forces for the rear axle and average road surface condition. of an H20-44 vehicle with damped suspension system.


Table 5. Maximum suspension forces and impact factors of front axle of an H20-44 vehicle with damped suspension system for different road surface conditions and vehicle speeds

Road surface conditions very good Good Average Poor

Maximum Maximum Maximum Maximum Maximum static VehiCle dynamic Impact dynamic Impact dynamic Impact dynamic rmpact force speed fOW2 factor force factor force factor force factor (kips) (mph) Orips) (“/I (kips) (“/I (kipsl Wl (kips) Wl

15 4.008 8.20 4.146 11.92 4.444 19.97 5.050 36.32 25 3.996 7.87 4.166 12.46 4.421 19.34 5.188 40.06 35 4.947 9.26 4.183 12.93 4.847 30.84 6.l65 66.44

3.704 45 4.064 9.71 4.199 13.36 4.950 33.63 6.244 68.57 55 4.054 9.43 4.296 15.99 4.954 33.74 6.182 66.89 65 4.102 10.73 4.370 17.98 5.170 39.57 5.739 54.94 75 4.084 10.24 4.368 17.91 5.660 52.79 5.995 61.85

Table 6. Maximum suspension forces and impact factors of rear axle of an H20-44 vehicle with damped suspension system for different road surface conditions and vehicle speeds

Maximum static Vehicle force speed fkiP@ (mph)

15 25 35

IJ.440 45

:: 75

very good


force factor &bsl <“/of

Road curface conditions Good Average


force factor force factor fkips) @f &ips) W-t

Poor


force factor Rips> (%I

17.274 28.53 17.804 32.47 18.679 38.98 22.553 67.81 17.275 28.53 17.840 32.74 20.203 50.32 21.271 58.26 17.561 30.67 17.976 33.75 20.241 50.60 23.304 73.39 17.518 30.34 18.003 33.95 21.442 59.54 24.976 85.83 17.435 29.72 18.057 34.36 21.336 58.75 25.586 90.37 17.463 29.93 18.290 36.08 21.161 57.45 27.657 105.78 17.570 30.73 18.859 40.32 21.264 58.21 25.771 91.75

Table 7, Maximum tire forces and impact factors of front axie of an H20-44 vehicle with damped suspension system for different road surface conditions and vehicle speeds

Road surface conditions Very good Good Average Poor

Maximum Maximum Maximum Maximum Maximum static Vehicle dynamic Impact dynamic Impact dynamic Impact dynamic Impact force speed force factor force factor force factor force factor (kipsl (mph) tkipsl WI <kipsI (“Al Ikipsf (%f (kipsl WI

:: 5.462 5.516 4.87 3.83 5.660 5.823 10.70 7.69 6.230 6.442 22.47 18.43 7.544 8.412 43.42 59.92 35 5.525 5.04 5.940 12.92 7.183 36.55 9.863 87.51

5.260 45 5.588 6.23 5.978 13.64 7.480 42.20 9.960 89.36 55 5.627 6.98 6,199 17-67 7.729 46.94 9.71 I 84.61 65 3.636 7.15 6.183 17.54 9.046 71.97 9.6i8 82.85 75 5.643 7.29 6.261 19.03 9.384 78.40 10.265 95.16

O--O YeBY GO00 RDAD SURFACE *--a GDOB ROAD SURFACE 4---o AYERAGS RDAD SURFACE (I -... P POOR ROAO SURFACE l . FXPERMXTAL DATA

.=--~..,_~_..~-~- _,d..V

,’

Fig. 24. Impact results of tire forces for the front axle of an H20-44 vehicle with damped suspension system.

Fig. 25. The comparison of computed and experimental impact results of tire forces for the rear axle of an H20-44

vehicle with damped suspension system.

1064 T. L. WANG et ai.

140 . 160 o- 0 VERY DOOD RQAD SUfWACL o-0 WRY GOOD ROAD SURFACE

G 140 A-.4 Gooll ROAD SumwE

O---o AW$RAGE ROAD SURFACE O--P POOR ROAD SURFACE ; 120 v----v POOR ROAD SURFACE

10 20 30 40 50 60 70 50 10 20 30 40 50 80 70 80

V~HIC~SP~~D(MPH) VEHIC~SP~ED(MPH)

Fig. 26. Impact results of suspension forces for the steer Fig. 27. Impact results of suspension forces for the tractor axle of an HS20-44 vehicle with damped suspension system. axle of an HS20-44 vehicle with damped suspension system.

Table 8. Maximum tire forces and impact factors of rear axle of an H20-44 vehicle with damped suspension system for different road surface conditions and vehicle speeds

static force (hips)

IS.040

Vehicle speed (mph)

1.5 25 35 45 55 65 75

Very good


force factor &ipsl (%I

15.799 15.967 16.018 6.50 16.066 6.82 16.138 7.30 16.306 8.42 16.227 7.89

Road surface conditions Good Average

~-


force factor force factor Chips) WI @ripsI (%I

16.407 9.09 17.673 17.51 16.783 11.59 19.408 29.04 17.083 13.58 19.906 32.35 17.306 15.07 21.421 42.42 17.592 16.97 20.759 38.02 17.681 17.56 21.596 43.59 18.543 23.29 22443 49.22

Poor


force factor

(k&N (“,I

22.165 47.37 20.809 38.36 23.165 54.02 26.091 73.47 25.358 68.60 25.894 72.17 26.853 78.55

Table 9. Maximum suspension forces and impact factors of steer axle of an HS20-44 vehicle with damned suspension system for different road surface conditions and vehicle speeds

_ _


Maximum Maximum Maximum Maximum Maximum static Vehicle dynamic Impact dynamic Impact dynamic Impact dynamic Impact force speed force factor force factor force factor force factor

&ins) (mph) &ins) WI &ins) (%) @ins) W) (kins) WJ)

15 3.350 14.93 3.479 19.35 3.680 26.25 4.625 58.67 25 3.373 15.72 3.551 21.81 3.881 33.15 4.505 54.53 35 3.360 15.28 3.677 26.15 4.045 38.76 5.028 72.50

2.915 45 3.433 17.78 3.683 26.33 4.063 39.37 5.318 82.42 55 3.379 15.92 3.510 20.41 4.875 67.24 6.069 108.20 65 3.385 16.12 3.576 22.67 4.504 54.52 5.508 88.95 75 3.411 17.03 3.593 23.24 4.365 49.76 N/A WA

Table 10. Maximum suspension forces and impact factors of tractor axle of an HS20-44 vehicle with damned suspension system for different road surface conditions and vehicle speeds

Very good

Maximum Maximum static Vehicle dynamic Impact force

tsm% force factor

(hips) (hips) Wl

15 19.083 34.45 25 19.142 34.87 35 19.499 37.38

14.193 45 19.252 35.65 55 19.221 35.42 65 19.024 34.04 75 19.033 34.11

Road surface conditions Good Average


force factor force factor (hips) W) (hips) W)

19.763 39.25 20.798 46.54 19.353 36.36 20.719 45.98 20.000 40.91 20.63 I 45.36 20.222 42.48 22.300 57.12 20.311 43.11 23.371 64.67 20.773 46.36 22.340 57.40 20.087 41.53 22.211 56.50

Poor


force factor

@ins) W)

22.856 61.04 23.435 65.12 25.662 80.81 28.500 100.80 28.324 99.56 26.323 85.47

WA N/A


01 ’ 1 10 20 30 40 60 60 70 80

VEHICLE SPEED (MPH) VEHICLE SPEED (YPH)

Fig. 28. Impact results of suspension forces for the trailer Fig. 29. Impact results of tire forces for the steer axle of an axle of an HS20-44 vehicle with damped suspension system. HS20-44 vehicle with damped suspension system.

Table 11. Maximum suspension forces and impact factors of trailer axle of an HS20-44 vehicle with damped suspension system for different road surface conditions and vehicle speeds


Maximum Maximum Maximum Maximum Maximum static Vehicle dynamic Impact dynamic Impact dynamic Impact dynamic Impact force

?ms force factor force factor force factor force factor

otips) otips) (%) (kips) (%) (kips) (%) (kips) W) 15 18.862 29.43 19.342 32.73 21.560 47.95 26.376 80.99 25 19.059 30.79 19.849 36.20 20.991 44.04 24.079 65.23 35 19.178 31.60 20.476 40.51 22.221 52.48 31.295 114.74

14.573 45 19.152 31.42 19.988 37.16 23.344 60.19 26.473 81.66 55 18.972 30.18 19.711 35.26 22.818 56.58 28.589 %.I7 65 19.433 33.35 20.176 38.45 22.301 53.03 29.283 100.94 75 19.273 32.25 20.832 42.95 22.87 1 56.94 N/A N/A

Table 12. Maximum tire forces and impact factors of steer axle of an HSZO-44 vehicle with damped suspension system for different road surface conditions and vehicle sneeds

Maximum Maximum static Vehicle dynamic force speed force (kips) (mph) (kips)

15 4.294 25 4.365 35 4.348

3.995 45 4.422 55 4.475 65 4.521

Very good Road surface conditions

Good Average Poor

Impact factor (%)

7.49 9.25 8.84

10.68 12.00 13.17

Maximum dynamic

force otips)

4.474 4.612 4.912 4.845 4.960 5.035

Maximum Impact dynamic factor force (%) (kips)

factor (%)

11.99 4.893 22.48 15.43 5.314 33.01 22.96 5.443 36.25 21.28 6.074 52.03 24.15 6.703 67.79 26.02 6.023 50.76

Maximum dynamic

force Orips)

6.461 6.821. 7.040 8.774 8.455 8.572

Impact factor (%)

61.73 70.74 76.22

119.62 111.64 114.56

75 4.562 14.18 5.033 25.99 6.822 70.76 N/A N/A

Table 13. Maximum tire forces and impact factors of tractor axle of an HS20-44 vehicle with damped suspension system for different road surface conditions and vehicle speeds


Maximum Maximum Maximum Maximum Maximum static Vehicle dynamic Impact dynamic Impact dynamic Impact dynamic Impact force force factor force factor force factor force factor (kivs) (kius) (%) (kips) (%) (kips) (%) fkins) I%)

15 17.804 11.32 19.507 21.97 21.910 36.99 24.960 56.06 25 17.874 11.76 19.524 22.08 21.549 34.74 29.212 82.65 35 18.377 14.90 20.991 31.25 22.724 42.08 28.563 78.59

15.994 45 18.613 16.38 21.919 37.05 25.667 60.48 39.058 144.21 55 18.892 18.12 21.552 34.76 26.469 65.50 33.769 111.14 65 18.402 15.06 21.730 35.87 25.530 59.63 29.674 85.54 75 18.441 15.30 20.608 28.85 25.746 60.98 N/A VA

10 20 30 40 50 60 70 80

VEHICLE SPEED (MPH)

Fig. 30, The comparison of computed and experimental impact results of tire forces for the tractor axle of an

HS20-44 vehicle with damped suspension system.

70 0-o SIBElI AXLE

i? 60 A---A TRACTORAXLE

o---o TRAILER AXLE

w 507

01 , ’ ’ 12 14 18 18 20 22 24 28 28 30

Lz @T)

12 14 16 18 20 22 24 26 28 30

L2 W')

Fig. 32. Impact results of suspension forces in an HS20-44 Fig. 33. Impact results of tire forces in an HS20-44 vehicle vehicle with damped suspension system running at 55 mph with damped suspension system running at 55 mph and and good road surface condition for different L, values. good road surface condition for different L, values.

running at 75 mph and average road surface condition are shown in Figs 18-21. A summary of the impact factors of suspension and tire forces for different road surface conditions and vehicle speeds is given in Tables 5-14 and ill~trat~ in Figs 22-31. The different distances between the tractor and trailer axles (L,) of an HS20-44 vehicle have also been studied. The results are shown in Table 15, Figs 32 and 33.

The conclusions of this study are summarized as follows:

1. The impact factors of both suspension and tire forces increased with vehicle speed in most cases.

2. The impact factors were affected slightly by the vehicle speeds in very good and good roads for both

o----o VRRY woo ROAO SuRFACL

F 100 A- -d GOOD ROM SURFACE O----o AVERAGE ROAD SURFACE v-.-.0 POOR ROAU SURFACE

___o----_&- _-0-_---a-- -

0 10 20 30 40 50 80 70

VEHICLE SPEED (MPH)

Fig. 31. Impact results of tire forces for the trailer axle of an HS20-44 vehicle with damped suspension system.

70 0-o SCEER AXLE

G SD .%---A TRACTOR AXLE

O--o TRAILER AXLE

suspension and tire forces. However, the vehicle speeds influence the impact factors significantly in average and poor roads.

3. The impact factors of both suspension and tire forces obtained from the poor road are the highest among these four different road surface conditions for speed varied from 15 to 75 mph. The lowest impact factors are always found in the very good road.

4. In Tables 13 and 14, it may be seen that the impact factors of tire forces of tractor axle are much higher than those of trailer axle in HS20-44 vehicle.

5. When values of L, changed, the impact factors of all three axles of HS20-44 vehicle varied slightly. However, Figs 32 and 33 show that the highest

Table 14. Maxims tire forces and impact factors of traiier axle of an HS20-44 vehicle with damped suspension system for different road surface conditions and vehicle speeds


-

Maximum Maximum Maximum Maximum Maximum static Vehicle dynamic Impact dynamic Impact dynamic Impact dynamic Impact force speed force factor force factor force factor force factor (kipsl (mph) (hips) (%l Chips) (%l @ipsl W) Wpsl Wl

15 17.059 6.54 17.743 10.81 19.007 18.70 25.085 56.66 25 17.470 9.10 17.952 12.11 19.959 24.65 22.258 39.00 35 17.401 8.67 18.673 16.61 20.308 26.83 28.01 I 74.93

16.012 4.5 17.450 8.98 18.482 15.42 22.922 43.15 25.813 61.21 55 17.588 9.84 19.164 19.68 21.423 33.79 27.585 72.27 65 17.823 11.31 18.970 18.47 21.476 34.12 28.116 . 75.59 75 17.801 11.17 19.863 24.05 21.720 35.64 N/A N/A

Dynamic response of highway trucks

Table 15. Maximum suspension forces, tire forces, and impact factors of an HS20-44 vehicle with damped suspension system running at 55 mph and good road surface condition for different L, values

Suspension Tire

Maximum Maximum Maximum Maximum static dynamic Impact static dynamic Impact

JG* force force factor force force factor (ft) (kips) (kips) (%) (kips) (kips) (%)

1067

Steer axle

Tractor axle

Trailer axle

14 16 18 20 22 24 26 3.541 28 3.539

14 16 18 20 22 24 26 28

20.311 20.648 20.639

14.193 19.531 20.120 20.578 20.070 19.904

14 16 18 20 22 24 26

19.711 19.768 19.754

14.573 19.613 19.746 19.788 19.770

3.510 3.510 3.548

2.915 3.574 3.501 3.506

28 19.786

20.41 20.40 21.72 22.61 20.11 20.29 21.48 21.40

43.11 45.48 45.42 37.61 41.76 44.99 41.41 40.24

35.26 35.65 35.56 34.58 35.50 35.79 35.66 35.77

4.960 4.960 4.861

3.995 4.870 4.821 4.867 5.007 5.026

21.552 21.744 21.323

15.994 20.332 20.957 21.181 21.955 21.093

19.164 19.019 18.929

16.012 19.097 18.924 18.869 19.105 19.014

24.15 24.15 21.68 21.90 20.67 21.84 25.33 25.80

34.76 35.96 33.32 27.13 31.03 32.44 37.28 31.89

19.68 18.78 18.21 19.26 18.18 17.84 19.32 18.74

*L2 is the distance between the tractor and trailer axles.

impact factors were obtained when L, = 14-16 ft and 26-28 ft for both suspension and tire forces.

6. Some experimental data obtained by Whittemore et al. [6] were used to compare with computed data. A comparison of computed and experimental impact results for tire forces is presented in Figs 25 and 30. It can be seen that the computed impact values agree very well with the experimental data.

REFERENCES

1. S. J. Fenves, A. S. Veletsos and C. P. Siess, Dynamic studies of bridge on the AASHO road test. Highway Research Board, Report 71, National Academy of Scienses, Washington, DC (1962).

2. S. J. Fenves, A. S. Veletsos and C. P. Siess, Dynamic studies of the AASHO road test bridge. Hiahwav Research Board, Report 73, National Academy of Sciences, Washington, DC (1962).

3. S. Levy and J. P. D. Wilkinson, The Component Element Merhod in Dynamic. McGraw-Hill, New York (1976).

4. G. R. Potts and H. S. Walker, Nonlinear truck ride analysis. J. Engng for Industry, Trans. ASME, May, 597-602 (1974).

5. A. S. Veletsos and T. Huang, Analysis of dynamic response of highway bridges. J. Engng Mech. Div., AXE %, 593620 (1970).

6. A. P. Whittemom, J. R. Wiley, P. C. Schultz and D. E. Pollock, Dynamic pavement loads of heavy highway

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Documents

Dynamic response of highway trucks due to road surface roughness