Jtam-A4.dvi


JOURNAL OF THEORETICAL

AND APPLIED MECHANICS

53, 1, pp. 109-117, Warsaw 2015
DOI: 10.15632/jtam-pl.53.1.109

VIBRATION ANALYSIS FOR VEHICLE WITH VACUUM PACKED

PARTICLES SUSPENSION

Michał Makowski, Robert Zalewski

Warsaw University of Technology, Faculty of Automotive and Construction Machinery Engineering, Warsaw, Poland

e-mail: michal.makowski@simr.pw.edu.pl; robertzalewski@wp.pl

The paper concerns an effect of the damping force controlling a vehicle suspension system.
The investigated vehicle suspension system consists of innovatoryVacuumPackedParticles
controllable damperswhich allow controlling the vehicle body vibration.Themain objective
of performed and presented in the paper studies is to determine properties of the Vacuum
PackedParticles (VPP) damper and propose a preliminary control strategy. The control in
the vehicle suspension system can be realized by controlling the underpressure resulting in
various jammingmechanisms in the granular core. Some algorithms of vibration control are
also proposed and discussed.

Keywords: VacuumPacked Particles, vibration damping, semi-active, smart materials

1. Introduction

For more than twenty years, innovative developments in the vehicle suspension design have
focused on increasing the safety and comfort levels. For years, many automotive companies
have carried out research aimed at continuous control of vehicles suspension. These efforts have
resulted in a rapid development of advanced electronics and drive control systems as well as
devices and structures which can be employed to achieve the goal.

At themoment, thanks to advances inmeasurement technology andmicroprocessor control,
the development of a new generation of smart materials may lead to wide implementation
of concepts of semi-active damping systems into everyday life. Especially interesting in this
field seems to be application of technology based on the properties of the so called ‘intelligent’
materials includingmagnetorheological (MR) (Zalewski andPyrz, 2013) electrorheological (ER)
(Skup, 2009) and piezoelectric materials (Mikulowski et al., 2013). In this paper, the authors
would like to focus on the new type of smart structures – Vacuum Packed Particles (VPP)
(Zalewski and Pyrz, 2013). Former works of the authors aimed at the constitutive modelling of
VPPs behaviour using both analytical (Zalewski, 2010) and stochastic identification procedures
(Pyrz and Zalewski, 2010).

In the car industry, researchers anddesigners have longbeen investigating newways toutilize
the so-called “smart” suspension systems in order to reduce harmful vibrations. The essential
part of existing solutions involved active or semi-active devices designed to dissipate kinetic
energy in a controlled way. Smart suspension systems have suffered from the lack of a time-
-control loop putting accuracy of their control in question. It has been recently suggested that
the time-control loop can be involved into intelligent suspension systemsbymeans of semi-active
magnetorheological dampers (MRDs) (Holnicki-Szulc et al., 2008; Makowski and Knap, 2013).
Semi-active MRDs consist of magnetorheological fluids (MRF), which can significantly change
their physical propertiesuponapplication ofmagnetic field. In late 1990s,Carlson andGoncalves
(2008) introduced an MRD applicable to the on-and-off-highway vehicle suspension system. It
was experimentally confirmed that the capability to control the damping force in a vehicle



110 M.Makowski, R. Zalewski

suspension system can be simply achieved by MRDs. Other researches proposed additional
know-how in the field of developing effective vehicle and aircraft suspension systems with use of
MRDs under different optimization criteria (Duysinx et al., 2005). At the same time, laboratory
tests devoted to controlling the active suspension vehicle including various types of active or
semi-active devices were carried out (March and Shim, 2007). It should be also mentioned that
the controlled hydraulic dampers are now in-use in several manufactured vehicle suspension
systems, where their dissipative features are adapted in time to the current vehicle load and
road conditions (Prada et al., 2014).

In previous works by Bajkowski et al. (2012) main attention was paid to discussion of pro-
blems encounteredduringexperimental researchofMRdampers family.Conductingexperiments
on variousMRdevices, the authors found some similarities betweenMRfluids and vacuumpac-
ked particles (Zalewski and Pyrz, 2010).
Themain aim of the present work is to investigate issues associated with control algorithms

for an adaptive (semi-active) suspension system of a vehicle equipped with a new type of semi-
-active dampers. Numerical simulations results of the vehicle suspension system equipped with
a VPP damper are presented and discussed in details.

2. Experimental tests of granular cores

According to previously mentioned similarities of MRFs and VPPs, the authors conducted a
set of experiments on specially developed granular samples. The investigated granular cores are
the main part of innovative granular damper prototypes used as a part of modelled vehicle
suspension system. In the discussed experimental research of VPP, four different types of a
loosematerial have been investigated (PMMA, polypropylene, polystyrene, ABS). The size and
dimensions of a single grain are almost the same in each case.A typical grain is a cylinder having
approximately 3mm length and 1mm in diameter.
The specially prepared experimental sample (Fig. 1) has been subjected to triangular displa-

cement excitation (Fig. 5) and various underpressure values from 0.01 to 0.09MPa.

Fig. 1. Scheme of the special granular structure testing specimen; 1 – handle, 2 – steel disc, 3 – valve,
4 – encapsulation, 5 – grains

Fig. 2. Displacement-time triangular excitation

The excitation frequency has been 0.25Hz. Selected force responses for Polypropylene grains
under a wide range of generated underpressures are shown in Fig.3. All loading tests have been
performed on theMTS 809 standard testing machine.



Vibration analysis for vehicle with Vacuum Packed Particles suspension 111

It is worthmentioning that the applied in experimental research excitation program (Fig. 2)
doesnot introduce inertial forces into theoverall systemexceptpoints,where thevelocity changes
direction. This allows for an accurate measurement of the force response.

Fig. 3. Force-displacement diagrams for polypropylene grains and various underpressure values

An increase in the underpressure value results in an apparently larger force response. Me-
asurements depicted in Fig. 3 reveal a significant difference in granular structures behaviour
according to loadingdirections.Elongatedgranular structuresbehave totally differentwhencom-
pressed. This phenomenon is clearly reflected in a non-symmetrical shape of force-displacement
diagrams illustrated in Fig. 3.
The force response for 0.09MPa is about 10 times greater (in the compression region) than

for 0.01MPa. The underpressure is a very convenient parameter for controlling the mechanical
properties of vacuum packed particles.

3. Granular damper design

The main advantage of the considered granular damper prototype over popular controllable
devices is the economical aspect. The granular material used in described prototypes is about
100 times cheaper in comparison to well commercialised MR shock absorbers.
Althoughgranular devices could successfully competewithotherpopular solutions in selected

engineering applications, during experimental research of granular systems a lot of additional
problemscanbeencountered.Suchproblemsare typical for innovatoryornon-classical structures
or engineering materials. Some of proposed solutions that enable their minimization or even
negligence can be found in Zalewski and Pyrz (2013).
According to previously developed standards, a preliminary granular damper prototype has

been designed. A basic scheme of its lower and upper bases also a global overview is depicted in
Figs. 4 and 5, respectively.

4. Model of the vehicle

The mechanical model of a vehicle in form of a rigid plate is shown in Fig. 6. This simplified
model is described by the oscillating mass m and mass moments of inertia Iy, position of the
center of mass a1 and a2. The parameter xk specifies the location of the checkpoint K (for
example, driver’s position).
The investigated suspension system is also described by the spring stiffness k1 and k2, and

shock absorberswithviscous friction characterized bydamping coefficients cT1, cC1 and cT2, cC2.



112 M.Makowski, R. Zalewski

Fig. 4. Lower (left) and upper (right) bases of the investigated granular damper prototype

Fig. 5. Scheme of the granular damper prototype

Fig. 6. Simplified model of a vehicle

The upper indexes c and t correspond to experimentally observed non-symmetrical damping
characteristics of granular devices (Fig. 3).Vibrations of the vehiclemodel result fromkinematic
excitations described by functions ξ1(t) and ξ2(t).
Previous works of authors revealed the viscous-like behavior of Vacuum Packed Particles.

For example, in Zalewski and Pyrz (2013) or Pyrz and Zalewski (2010) uniaxial tests conducted
on granular cores were discussed. They showed that the response of the material is influenced
by the strain rate applied in experiments. Additionally, in Zalewski and Szmidt (2014) the same
phenomenonwas found in periodically loaded samples. In the authors opinion the global viscous
properties of VPP’s are incorporated with nonlinear friction contacts occurring between single
grains of the structure.
The vehicle model has been described in the coordinates

X= [z,Φy]
T (4.1)

where X1 = z is the vertical displacement of vehicle, X2 = Φy – angle of rotation around the
transverse axis of the vehicle.



Vibration analysis for vehicle with Vacuum Packed Particles suspension 113

The flat model of the vehicle has been described by means of the following set of ordinary
differential equations

MẌ+H(S+T)=0 (4.2)

where M = diag(m,Jy). Matrix H describes the allowed configuration space to the forces Si
and Ti

H=
[

H1 H2

]

=

[

1 1
−a1 a2

]

(4.3)

The spring force S and friction force T in the damper are described by means of the following
relationship

S= [S1,S2]
T = [f1(U1),f2(U2)] T= [T1,T2]

T = [F1(V1,w1),F2(V2,w2)] (4.4)

wherewi (i=1,2) is the control parameter (the value of underpressure).
The values of suspension displacements Ui and velocity Vi (i = 1,2) are calculated from

following formulas

Ui(t)=H
T
i X+ξi(t) Vi(t)=H

T
i X+ ξ̇i(t) (4.5)

where ξi (i=1,2) are functions describing roughness of the pavement.
The damper forces T(t) are determined on the basis of the assumed control algorithm F,

which is described later. Then, the equation of vibration of the vehicle turns into the following
form

MẌ+HS(U)+HT=0 T(t)=F(U(t),V(t)) (4.6)

where F is a function describing the algorithm for designating signals applied to the granular
core.
Formula (4.9) describes the damper forces T(t) in the selected time moment. It is defined

based on the proposed control strategy which is dependent on the control criteria presented in
Section 5. The optimal friction force is determined on the basis of the deflection of the spring
elements in the suspension and the current velocity value. Basing on the characteristic depicted
inFig. 7a for a selected value of the velocity, theT(t) force is chosen in suchaway as tominimize
the comfort indicator coefficient (5.5).

5. Control algorithm

A control algorithm has been developed assuming the need to meet two criteria: improvement
of driving comfort and reduction of wheel force variations. The control of the comfort criterion
can be achieved by minimizing the vertical body accelerations (which is a measure of exposure
to fatigue resulted by vibration nuisance). However, there is a problemof criteria conflict.While
the vehicle body acceleration is minimized, the force wheel variation grows significantly.
The control is possible in a given set of the allowed friction forces

T∈Ω(V ) := {Ti ∈ R1, i=1,2}

Ti =

{

VicTi for V ­ 0, cTi ∈ [cTmin,cTmax]
VicCi for V < 0, cCi ∈ [cCmin,cCmax]

(5.1)

Collection of the allowed friction forcesΩ(V ) is schematically shown in Fig. 7a. It is limited
by a set of damping coefficients cCmin, cCmax and cTmin, cTmax dependent on the speed V .



114 M.Makowski, R. Zalewski

Thedamping coefficients depend on the allowed underpressure values pmin and pmax. In Fig. 7b,
the real experimental data for the VPP’s damper prototype is depicted. Various force-velocity
characteristics have been recorded for different underpressure values. Additionally, the assumed
values ofpmin andpmax are illustrated.Basing on the experimental results, the idealizeddamping
characteristic used in the numerical tests has been proposed (Fig. 7a).

Fig. 7. (a) Set of the allowable solutionsΩ(V), (b) real response of the granular damper

In the comfort criterion, the value of friction in any time is determined by minimizing an
absolute value of the acceleration of the fixed pointK, which corresponds (for example) to the
position of the driver.

The value of this acceleration is described by the formula

ak =G
T
Ẍ G= [1,xk]

T (5.2)

where xk is the parameter specifies the location of the checkpointK,G – vector determines the
position of the pointK.

On the basis of equation (4.2), the acceleration of the pointK is described by the following
formula

ak =−GTM−1H(S+T)= a0(t)+DTT (5.3)

where

D
T :=−GTM−1H a0(t) :=DTS(U(t)) (5.4)

The comfort indicator is assumed and adopted in the form

κ(T, t) =
∣

∣a0(t)+D
T
T
∣

∣ (5.5)

The first criterion of minimizing the vehicle body acceleration is the optimization problem of
finding the best friction force in the SGS damper. The problem is formulated in the following
form

TK(t)∈ArgminT∈Ω(V)
∣

∣a0(t)+D
T
T
∣

∣ (5.6)

whereArgmin is the set of solutions inwhich theminimized functional is convexbutnot strictly
convex. A detailed description of the optimization problem solution and control algorithm is
described in (Makowski and Knap, 2013).



Vibration analysis for vehicle with Vacuum Packed Particles suspension 115

6. Numerical simulation of the vehicle with SGS suspension

In order to implement the optimal selection of friction forces in the granular damper, a simplified
vehicle model has been developed inMatlab/Simulink environment.

The following values of parameters have been employed for the vehicle model in compu-
ter simulations: the oscillating weight m = 1200kg, spring stiffness k1 = k2 = 47500N/m,
a1 = a2 =1.6m and xk =0.5 m. In order to solve the optimization problem, it has been neces-
sary to define the limits of the dimensionless damping factor. According to the non-symmetrical
characteristics of the VPP damper introducing the dimensionless damping coefficient γ (6.1),
the following parameters have been assumed in the controlling algorithm γCmin = 0.05 and
γCmax = 1.0, cCmax = 750Ns/m, cCmin = 15000Ns/m, γTmin = 0.017 and γTmax = 0.3 and
cTmin = 250Ns/m, cTmax = 5000Ns/m. Additionally, numerical tests without control have
been carried out for the constant γ =0.3 parameter (c=4500Ns/m)

γC =
cCi

2
√
kim

γT =
cT i

2
√
kim

(6.1)

The simulation studies have been carried out for a harmonic sinusoidal kinematic excitation
defined by formula

ξi = ξ0 sin(ωt+βi) i=1,2 (6.2)

where

β1 =0 β2 =2π
( a1

a1+a2

)

Thenumerical tests have been performed for the excitation frequency 2.25Hz and amplitude
0.02m. The characteristic depicted in Fig. 8 presents acceleration of the pointK in versus time
for the active and inactive controlling parameter.

Fig. 8. Acceleration values of the selectedK point with and without application of the control
algorithm (f =2.25Hz)

Basing on the above presented simulation results, lower acceleration values are observed for
the controlled damping process according to the comfort criterion. In such a case, the damping
coefficient is changeable in accordance to the applied excitation rule.

Numerical results for vertical accelerations of the selected point K are depicted in Fig. 9.
Similarly to theprevious results, the controlling strategy providesmuch lower acceleration values
in comparison to the non-controlled process.



116 M.Makowski, R. Zalewski

Fig. 9. Acceleration values for the selectedK point with and without application control algorithm
(f =1.5Hz)

7. Conclusions

Results of numerical simulation and experimental investigations of a granular damper prototype
have been presented in the paper. The experimental studies have been carried out to evaluate
the granular damper dissipation characteristics.

The results of numerical simulations of the investigated devices have been used to propose
a fast and efficient algorithm allowing improvements to passenger comfort. The proposed algo-
rithm can be used to calculate the appropriate value of the signal to control semi-active devices
with respect to two opposing criteria: comfort (reduction of vertical accelerations) and safety
(reduction of wheel force variations).

The presented results of vehicle simulation demonstrated that it is possible to significantly
reduce vertical accelerations using the controlled granular dampers (shock absorbers). The pro-
posed vehiclemodel and control algorithm can beused to simulate other controlled dampers like
magnetorheological, electrorheological or electrohydraulic. It is also possible to link the model
and algorithm with external systems such as MBSAdams.

References

1. Bajkowski J., Jasiński M., Mączak J., Radkowski S., Zalewski R., 2012, The active
magnetorheological support as an element of damping of vibrations transferred from the ground to
large-scale structure supports,Key Engineering Materials, 518, 350-357

2. Carlson J.D., Goncalves F., 2008, Controllable fluids come of age, 11th International Confe-
rence on New Actuators/5th International Exhibition on Smart Actuators and Drive, Conference
Proceedings Book Series: Actuator-International Conference and Exhibition on NewActuators and
Drive Systems, 477-480

3. Duysinx P., Bruls O., Collard J.F., Fisette P., Lauwerys J.S., 2005, Optimization of
mechatronic systems: application to a modern car equipped with a semi-active suspension, 6th
World Congresses of Structural and Multidisciplinary Optimization, Rio de Janeiro, Brazil

4. Holnicki-Szulc J., Pawłowski P., Mikułowski G., Graczykowski C., 2008, Adaptive im-
pact absorption and applications to landing devices,Advances in Science and Technology, 56, 609,
609-613

5. Makowski M., Knap L., 2014, Reduction of wheel force variations with magnetorheological
devices, Journal of Vibration and Control, 20, 10, 1552-1564



Vibration analysis for vehicle with Vacuum Packed Particles suspension 117

6. March C., Shim T., 2007, Integrated control of suspension and front steering to enhance vehicle
handling, Proceedings of the Institution of Mechanical Engineers, Part D: Journal of Automobile
Engineering, 221, 4, 377-391

7. Mikulowski G.,Wiszowaty R., Holnicki-Szulc J., 2013, Characterization of a piezoelectric
valve foranadaptivepneumatic shockabsorber,SmartMaterials andStructures,22, 125011(12pp)

8. Prada J.G.,Vinolas J., CarreraX., 2014,Gas damper: potential vehicle performance studied
on a full-car model, International Journal of Vehicle Design, 64, 214-239

9. Pyrz,M., Zalewski, R., 2010,Modeling of granularmedia submitted to internal underpressure,
Mechanics Research Communications, 37, 2 141-144

10. Skup Z., 2009, Factors influencing load transmission through electrorheological cylinder clutch,
Journal of Theoretical and Applied Mechanics, 47, 91-107

11. Zalewski R., 2010, Constitutive model for special granular structures, International Journal of
Non-Linear Mechanics, 45, 3, 279-285

12. Zalewski R., Nachman J., ShillorM., Bajkowski J., 2014,Dynamicmodel for amagnetor-
heological damper,Applied Mathematical Modelling, 38, 2366-2376

13. Zalewski R., Pyrz M., 2010,Modeling and parameter identification of granular plastomer con-
glomerate submitted to internal underpressure,Engineering Structures, 32, 8, 2424-2431

14. Zalewski R., Pyrz M., 2013, Experimental study andmodeling of polymer granular structures
submitted to internal underpressure,Mechanics of Materials, 57, 75-85

15. ZalewskiR., SzmidtT., 2014,Application of special granular structures for semi-activedamping
of lateral beam vibrations,Engineering Structures, 65, 13-20

Manuscript received June 17, 2014; accepted for print July 24, 2014