International Journal of Mechanical Engineering and Technology (IJMET)
Volume 10, Issue 04, April 2019, pp. 689–697, Article ID: IJMET_10_04_067
Available online at http://www.iaeme.com/ijmet/issues.asp?JType=IJMET&VType=10&IType=4
ISSN Print: 0976-6340 and ISSN Online: 0976-6359
© IAEME Publication
Scopus Indexed
REDUCING PITCH ANGLE AND SUSPENSION
JOUNCES OF A TRUCK WHEN BRAKING ON
RAILWAY CROSSING BY CONTROL OF SEMIACTIVE SUSPENSION
N. L. Pavlov
Department of Combustion Engines, Automobile Engineering and Transport,
Faculty of Transport,
Technical University of Sofia, 8 Kliment Ohridski Blvd., 1000 Sofia, Bulgaria
ABSTRACT
This paper presents pith plane dynamic model of a cargo truck. Numerical
simulations for determination of a pitch angle and deflection in front and rear
suspension under braking on railway crossing are conducted. The change of the
braking force is presented by trapezoidal form, similar to the theoretical law of
variation of braking deceleration in the braking diagram of road vehicles. For the
railway crossing profile trapezoidal function is used too. The numerical simulations
are carried out in program field of MATLAB. After conducting tests for determination
of a braking dynamics and braking properties of a truck in road conditions, the pith
plane model is validated. Possibilities for pitch angle and suspension jounces
reduction are given. A fifth wheel assembly, displacement sensors and data
acquisition system are used in the road tests.
Key words: Dynamic model, truck, simulation and road test
Cite this Article: N. L. Pavlov, Reducing Pitch Angle and Suspension Jounces of a
Truck When Braking on Railway Crossing by Control of Semi-Active Suspension,
International Journal of Mechanical Engineering and Technology 10(4), 2019, pp.
689–697.
http://www.iaeme.com/IJMET/issues.asp?JType=IJMET&VType=10&IType=4
1. INTRODUCTION
Road transport and commercial vehicles are constantly being studied and improved, and proof
of this is the availability of various publications on the topic. Along with the fuel economy
and the exploitation efficiency of the road freight transport [1, 2 and 3], the problems of the
dynamics of commercial vehicles are a question of present interest [4, 5]. When the road
vehicles are under braking on the vehicle body acts a powerful disturbance as a torque. Its
magnitude is proportional to the inertia force and, on the other hand to the mass centre height
of the vehicle [6, 7 and 8]. The action of the torque is accompanied by longitudinal tilting of
the vehicle body (pitch angle) due to the presence of elastic suspension. This results in
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Reducing Pitch Angle and Suspension Jounces of a Truck When Braking on Railway Crossing by
Control of Semi-Active Suspension
redistribution the normal reactions of the front and rear wheels. The phenomenon is most
pronounced in vehicles with a short base and a high mass centre, for unladed trucks or tractors
with a detached semitrailer. When the ground vehicles brakes, the wheel suspension travel
may be spend and shocks may occur as a result of the inclusion of the jounce stops at
maximum suspension deflection [9]. The phenomenon is known as a suspension "slam" or
"jounce", which is an amalgamation of the words jump and bounce. In suspension
terminology, it means the most compressed condition of a spring. These phenomena are even
more pronounced when vehicle passing through convex irregularities such as some railway
crossings (Fig. 1). This type of crossings has a profile corresponding to a single bump of
triangle or trapezoidal irregularity.
Figure 1 A primer of a railway crossing like single road irregularity
2. DYNAMIC MODEL
In order to find the pitch angle and the suspension deflection values when the truck
simultaneously braking and crossing over the railway, the dynamic model based on the
authors’ model presented in [9] used to study the braking only, without any road irregularities.
The present model is shown in Fig. 2. It takes into account the mass of the vehicle, its
moment of inertia around the transverse axis, the elasticity of the front and rear suspension
and the damping of the shock absorbers. The railway crossing is presented as irregularity with
trapezoidal form.
Figure 2 Dynamic model of a truck when braking on railway crossing
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Braking is a process of creating and control the artificial resistance of the vehicle motion.
The braking of the vehicle is mainly accomplished by creating braking moments from the
brake mechanisms on the wheels [10]. Due to friction in the contact path, a tangential reaction
Rx directed opposite of the direction of motion arises under the action of the braking moment.
Then in braking mode for the differential equation of motion along x-axis is obtained:
mx   R x
(1)
Since the mass center of the vehicle lies above the center of elasticity of the suspension at
any distance, the inertia force that is always directed against the acceleration, in the case of
braking, creates torque. Because the trucks have elastic suspension of the body on the wheels,
the resulting torque deflects the suspension elastic elements and tilts the vehicle forward at an
angle θ around the center of elasticity – c. e. If the center of mass (m) is relocated to the point
C placed in the horizontal plane of the center of elasticity (c. e.) it will not affect linear z-axis
oscillations. To study the angular oscillations during braking, it is necessary to add the torque
(moment) M = Fj.h (Fig. 3). After reducing the inertial force Fj and relocating the center of
gravity to the plane of the center C, also is necessary to reduce the coordinate system in an
appropriate manner. This is accomplished by relocating the start of the x-z coordinate system
at a distance h, at point C, which is accepted as a new coordinate of the mass center.
Figure 3 Dynamic model after reduction of inertia force and adding the torque M = Fj.h
The torque M is added as a disturbance in the differential equation of the angular
displacement around the y-axis. The change of the braking torque is presented by trapezoidal
form, similar to the theoretical law of variation of braking deceleration in the braking diagram
of road vehicles. The differential equations of motion of vertical and angular displacements
are:








mz  1 z  a   2 z  b  c1 z  a   c 2 z  b  
c1 q1  c 2 q 2  1 q1   2 q 2
J  1 a z  a   2 b z  b  c1 az  a   c 2 bz  b  
c1 aq1  c 2 bq2  1 aq1   2 bq 2  M
(2)
(3)
where q1 and q 2 are the coordinates of the road irregularities respectively under the front
and rear axle of the truck, and also their derivatives q1 and q 2 , i.e. the velocities with which
the wheels of the truck are moved along the vertical axis.
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Reducing Pitch Angle and Suspension Jounces of a Truck When Braking on Railway Crossing by
Control of Semi-Active Suspension
For the inertia force can be writing:
Fj  m. j  Rx  Rx1  Rx 2
(4)
where j is braking deceleration;
Rx1 and Rx2 are the longitudinal reactions in the contact between the wheels and the road under
braking.
In the used model the following assumptions have been accepted [9]:
- the characteristics of the elastic and damping elements are linear;
- the vehicle moves horizontally;
- the aerodynamic drag is ignored;
- the rolling resistance forces are ignored;
- the influence of the inertia moments of the rotating parts is ignored;
- the body angle is small (up to 15 °) and sin   , cos  1 .
The dimensions of the railway crossing are given in Fig. 4 below:
Figure 4 Dimensions of the railway crossing
3. NUMERICAL SIMULATIONS
The simulations were performed using MATLAB with the given in Table 1 parameters:
Table 1 Simulation parameters
Parameter
Full mass of the truck
Moment of inertia
Front suspension stiffness
Rear suspension stiffness
Distance
Distance
Distance
Static load – front axle
Static load – rear axle
Symbol
m
J
c1
c2
h
a
b
Gw1
Gw2
Value
7500
33582
166600
230625
1,2
2,32
1,93
33,355
40,221
Unit
kg
kg.m2
N/m
N/m
m
m
m
kN
kN
The minimal and maximal damping coefficients of suspension β1 and β2 are defined in the
work [9]. The accepted values for the front suspension are:
β1low=9520 N.s/m
β1high=30000 N.s/m
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N. L. Pavlov
For the rear suspension:
β2low=12300 N.s/m
β2high=35000 N.s/m
The simulation results of a pith angle and suspension deflection with two different
damping coefficients are shown in Fig. 5 and Fig 6.
Figure 5 Effect of the shock absorber damping ratio (β) on the pitch angle θ when the truck brakes on
the railway crossing with maximum acceleration j=8 m/s2. Subscribe l when βlow, h when βhigh
In the figures 5 and 6 can be seen how increasing the damping reduce the truck pitch angle
and eliminate the suspension jounce.
Figure 6 Effect of the shock absorber damping ratio (β) on the front z1 and rear z2 suspension
deflection when the truck brakes on the railway crossing with maximum acceleration j=8 m/s2.
Subscribe l when βlow, h when βhigh. The black line shows the maximum of the dynamic suspension
travel deflection
The principal diagram of a possible control system for reducing the pitch angle and
suspension jounce is shown in Fig. 7. The controller receives signals from the displacement
sensors and generates control signals to the shock absorbers.
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Reducing Pitch Angle and Suspension Jounces of a Truck When Braking on Railway Crossing by
Control of Semi-Active Suspension
Figure 7 Principal diagram of a pitch angle control system
Kpitch is a controller; Sp, Sz1 and Sz2 – sensor signals; 1 – brake pedal; 2 – pedal displacement sensor; 3,
4 – front shock absorbers; 5, 6 – rear shock absorbers; 7 – front axle displacement sensor; 8 – rear axle
suspension sensor
4. MODEL VALIDATION
For model validation was conducted road tests with real truck (Fig. 8). The distance, speed
and acceleration of the truck when braking were measured by using “fifth wheel” measuring
device (Fig. 9). Displacement sensors on front and rear axle, brake air pressure sensors and
speed sensor for wheel slip determination were mounted on the truck (Fig. 10). The procedure
of the road test is described in work [11]. Some numerical simulation results of braking on
horizontal road are compared with the results obtained in the road tests (Fig. 11 and 12).
Figure 8 The truck in road tests conditions
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Figure 9 “Fifth wheel” measuring device assembly and data acquisition devices in the cabin
a)
b)
Figure 10 Brake air pressure sensor 1a, truck speed sensor 1b, front axle displacement sensor 2a, rear
axle displacement sensor 2b
Figure 11 Measured and calculated - results for the pitch angle when braking
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Reducing Pitch Angle and Suspension Jounces of a Truck When Braking on Railway Crossing by
Control of Semi-Active Suspension
Figure 12 Measured and calculated - results for the front suspension deflection z1 and the rear
suspension deflection z2 when braking
Road tests have not been conducted on a railway crossing, but the author's opinion is that
conducted test on horizontal road gives sufficient information for model validation.
5. CONCLUSIONS
The paper presents a dynamic model allowing the study of the pitch angle and the suspension
deflection when a truck braking on a railway crossing. The braking process was simulated
using MATLAB program and validated with road brake tests. The principle of the pitch angle
and suspension deflection reducing is outlined and a scheme of the control system is
presented.
ACKNOWLEDGMENTS
This work was supported by Research and Scientific Centre of Technical University of Sofia,
Bulgaria.
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