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2002-01-3105
Integral Suspension System for Motor Vehicles Based on
Passive Components
Josep Fontdecaba i BujCREUAT S.L
Copyright 2002 Society of Automotive Engineers, Inc.
ABSTRACT
This paper presents the theory and results of a passive
suspension system implementation that links the fourwheels vertical movements through a central device.This arrangement is made to define a passive kinematicslink between all wheels vertical movements that definethe elasticity and damping of all vehicle movements, roll,pitch and rebound, as well as the resistance to axlecrossing.
The analisys made is opposite to the traditional one-quarter-vehicle analisys, and exploits the passivesystems to provide advantages sought with activesystems.
INTRODUCTION
Conventional passive suspension systems are based onone-per-wheel suspension elements that support thebody of the vehicle and transversal components that addstiffness to reduce the roll movement. These two kinds ofelements define the suspension characteristics and thedynamics of the vehicle.
Suspension elements associated to each wheel providethe main elasticity component of the suspension, as wellas the damping means to extinguish the vehicle bodyoscillations induced by the travel of the vehicle. Thesesuspension elements define the stiffness and damping
characteristics of all vehicle body movements such asrebound, roll, pitch and axle crossing.
Transversal elements, usually built as torsion bars,oppose the roll movement of the vehicle body and arecommonly referred to as anti-roll bars. There are severalarrangements of this transversal link, but in all cases, theaim is to increase the stiffness of the suspension to theroll movement without modifying the stiffness to reboundand pitch.
Our analisys is based on an arrangement that links alwheels vertical movements at one time, not onlytransversely. To do so, a central device is provided tohelp define the specific elasticity and damping for everyvehicle movement in an independent way. This allows
the suspension designer to independently set theelasticity and damping characteristics for:
1. Roll2. Pitch3. Rebound4. Axle crossing.
These four (4) system movements correspond to the 4degrees of freedom that the four wheels independenvertical movements provide.
There are several ways to implement the kinematicsrelationships to have the right elasticities and dampingmovements. In all cases, we have chosen passivecomponents that do not drag any energy from thesystem except for additional features like height control.
Our study also includes two different implementations ofthe system that either use:
1. Hydraulic components2. Mechanical components
Both implementations have particular advantages. Wehave built several prototypes and the development of thesystem follows its own course.
CENTRALIZED SUSPENSION CONCEPT
To provide the proper relationship between all wheevertical movements we have worked with a layout thaincludes suspension elements individually linked to eachwheels movements, and a central device that providesthe kinematics links between the individual wheemovements.
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From an intuitive point of view, the central device can bedesigned to define the system movements such as pitch,roll and rebound. The resilient and damping elementspresent in the central device will characterize the maindynamic behavior of the whole vehicle
On the other hand, the individual suspensioncomponents associated with each wheel will be moredirectly involved with the individual wheel movements
The analisys of the system will nevertheless demonstratethe important is the system as a whole in defining notonly the system movements such as pitch, roll andrebound, but also the system capacity to deal withindependent movements in each wheel.
SYSTEM LAYOUT
We can define the system layout as in the followingfigure, where the vertical movements in each wheel arelinked to the individual suspension elements, and fromthem transmitted to the central device. This centraldevice is in charge of distributing the efforts and
movements in order to define the dynamics of the vehicleas well as distribute the weight between the wheels.
Figure 1
To build a passive system according to this layout we
have needed to physically transmit the efforts and movesfrom each individual suspension component to thecentral device. In a hydraulic solution, this is relativelyeasy by means of hydraulic conduits, but on amechanical implementation, the movements have to betransmitted by means of connection links or torsion bars.
The central device must provide links that connectwheels simultaneously in a transversal, longitudinal anddiagonal way. Each link can then be connected to thevehicle body, so the weight is transmitted to the wheels.
CENTRAL DEVICE SUSPENSION COMPONENTS
The suspension components in the central device musprovide the extra elasticity for the movements tharequire a softer characteristic. This is usually the case forthe rebound and pitch movements.
The central device should also provide the axle-crossingcapacity independent from all other suspensioncomponents. This is, in fact, the main advantage ocentralizing the suspension characteristics that couldhardly be obtained otherwise.
INDIVIDUAL SUSPENSION COMPONENTS
The suspension components associated with each wheemovement are placed as a filter to the movements andforces transmitted to the central device. This means thatthe stiffness of both resilient and damping componentsshould, if alone, provide a greater or equal stiffness thanany system movement such as rebound, roll and pitch. Inour case, this will be the roll stiffness.
SYSTEM IMPLEMENTATION
By the time this paper is written, several prototypes havebeen built, and others are being built now. There areseveral ways to define the central and individuasuspension devices, and two solutions are being sought:
1. Hydraulic implementation2. Mechanical implementation
The implementation of the system that we have followedis based on a central device that acts rigidly to the rolmovements, so the roll is completely defined by thesuspension elements associated with each wheel. We
can do this since we needed the stiffest component forthe roll movement, and the central device added thenecessary elasticity to soften the other movements suchas rebound and pitch.
The axle crossing is completely controlled by the centradevice. We also provided the means to disable thisfeature in case it was needed.
HYDRAULIC IMPLEMENTATION
In the hydraulic implementation, each individual wheel isconnected to the vehicle body by means of simple-acting
cylinders that transmit the vertical movements to thehydraulic fluid.
The individual suspension elements are thehydropneumatic expansion chambers connected to thecircuit near the cylinder on each wheel.
Each cylinder is then connected to the hydraulic centradevice by means of pipes of convenient size. The centradevice has the additional elasticity elements that providesome of the system parameters of the suspension.
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Heave extra elasticity and
damping components
Pitch extra elasticity and
damping components
Isostatic valve
Roll elasticityand dampingcomponents
The following layout indicates the hydropneumaticexpansion chambers in charge of providing both theelasticity and damping of the system:
Figure 2
The hydraulic implementation includes the valve in thecentral device to disconnect the axle crossing. This valve
has proven necessary in limit situations. The free axlecrossing makes the suspension system isostatic, this is:the weights are independent of the surface irregularities.This feature unfortunately disables the system to copewith limit static or dynamic situations where more thanhalf the vehicle weight falls on one wheel.
The hydraulic implementation has an interesting feature,which is that it can easily add a damping module to eachexpansion chamber, therefore providing the adequatedamping coefficient to each system movement.
An immediate advantage of this feature is that we canincrease the damping coefficient for roll movements tocompensate for the increased stiffness wanted toaugment the stability.
MECHANICAL IMPLEMENTATION
In the mechanical implementation, each individual wheelis connected to the transmission means that link thewheel vertical movements with the central device.
Depending on the vehicle suspension geometry, wefound it convenient to use either angled levers withconnection links or torsion bars that transmit themovements to the central device.
By using torsion bars, we provide transmission meansthat have their own elasticity, simplifying theimplementation of the individual elasticity components.
The mechanical implementation provides the simplicityand robustness of mechanical components.Nevertheless, it is difficult to provide individual dampingthat would be associated to the torsion bars in the layoutpresented above. In general, the mechanicalimplementation can provide the same degree of freedom
to define elasticity elements, but makes it difficult for thedesign of the damping elements.
The image below shows the layout of a mechanicasystem on a typical all-terrain vehicle:
Figure 3
Damping elements are in this case easily mountedbetween each individual wheel and the vehicle body, noallowing the benefits predicted before.
Nevertheless, when connecting links are used, it iseasier to implement the individual damping elements andzero the damping of axle-crossing movements.
ELASTICITY ANALISYS
To analyze the passive system we will ignore thesuspension geometry and other details that, althoughvery important on a vehicle dynamics analisys, have littleto do with the concepts being presented here.
We will consider a four-wheeled vehicle, whereeach wheel can moveideally in a vertical directionin respect to the vehiclebody, and that interactswith it through a force in thedirection of the movement.
WHOLE VEHICLE MOVEMENTS ANALISYS
Lets analyze every freedom degree associated to wheemovements from a global point of view:
REBOUND MOVEMENT
We can characterize the rebound movement by theuniform displacement of each wheel against the vehiclebody. When all wheels are in contact with a planasurface, this displacement is equal to the vehicle bodydisplacement.
32
1 0
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In this case, wecan define aelasticityconstant thatrelates forcesincrements anddisplacements inthe reboundmovement in thefollowing way:
(f0+f1+f2+f3) = Kh (x0+x1+x2+x3)
Where Kh is the elasticity associated with the reboundmovement. Note that we will consider all elasticitieslinear for simplification purposes.
PITCH MOVEMENT
We can characterize the pitch by contrary displacementof each front wheel in one direction, and rear wheel inthe opposite direction.
When all wheels are in contact with a planar surface, thisdisplacement produces the pitch movement in thevehicle.
In this case, we candefine a elasticityconstant that relatesforces incrementsand displacementsfor pitch movementin the following way:
(f0+f1-f2-f3) = Kp (x0+x1-x2-x3)
Where Kp is the elasticity associated with the pitchmovement.
ROLL MOVEMENT
Similarly to pitch andrebound, we candefine a elasticityconstant that relatesforces incrementsand displacements inroll movements in the
following way:
(f0-f1+f2-f3) = Kr (x0-x1+x2-x3)
Where Kris the elasticity associated to roll movement.
AXLE CROSSING MOVEMENT
Axle crossing movement is not associated to any vehiclebody movement such as pitch, roll and rebound. It is,though, associated with the weight distribution and thecapability to adapt to uneven surfaces.
Nevertheless,when analyzingthe forcesassociated to thismovement we candefine a similarelasticity constantin the followingway:
(f0-f1-f2+f3) = Kx (x0-x1-x2+x3)
Where Kxis the elasticity associated to roll movement.
SYSTEM ELASTICITY CONCEPT
With the previous analisys, we have defined foursystem constants that define the relationship betweenindividual wheel movements and system effects:
1. (f0+f1+f2+f3) = Kh (x0+x1+x2+x3)
2. (f0+f1-f2-f3) = Kp (x0+x1-x2-x3)
3. (f0-f1+f2-f3) = Kr (x0-x1+x2-x3)
4. (f0-f1-f2+f3) = Kx (x0-x1-x2+x3)
We can extend this simplified definition to a relationshipbetween forces and displacements through a elasticitiesmatrix:
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
f0
f1
f2
f3
Kh
0
0
0
0
Kp
0
0
0
0
Kr
0
0
0
0
Kx
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
x0
x1
x2
x3
In this case we can define a general elasticities matrix[R] through a base change as
R0 0,
R1 0,
R2 0,
R3 0,
R0 1,
R1 1,
R2 1,
R3 1,
R0 2,
R1 2,
R2 2,
R3 2,
R0 3,
R1 3,
R2 3,
R3 3,
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1Kh
0
0
0
0
Kp
0
0
0
0
Kr
0
0
0
0
Kx
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
Where Ri,j defines the forces induced in each wheelj by
displacements in wheel i. In particular this matrix is
interesting as the diagonal Ri,i shows the forces induced
in each wheel i when it experiments a displacementwhich translates into a messure of comfort.
INDIVIDUAL ELASTICITY CONCEPT
When the system experiences a vertical movement onlyin one wheel, such as is the case with small bumpstransversed at a speed where the vehicle bodymovement has not yet had the time to react, we cancalculate the forces involved combining the previousequations:
Assuming x1=0, x2=0and x3=0, and a vertical movemen
in one wheel with x00
f3
x3
f2
x2f0
x1
f1
x0
-f3
-x3
-f2
-x2 f0
x1
f1
x0
f3
x3
-f2
-x2 -f0
x1
f1
-x0
f3
x3
-f2
-x2 f0
-x1
-f1
x
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f0
f1
f2
f3
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1Kh
0
0
0
0
Kp
0
0
0
0
Kr
0
0
0
0
Kx
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
x0
0
0
0
which translates into:
f0
f1
f2
f3
1
4
Kh Kp+ Kr+ Kx+
Kh Kp Kr Kx+
Kh Kp Kr+ Kx
Kh Kp Kr Kx+
x0
Looking at the diagonal members of matrix matrix [R] wesee that they accomplish that:
Ri i,f0
x0
1
4Kh Kp+ Kr+ Kx+( )
We can define the equivalent independent elasticity Ri,i
on wheel i as the force induced when the wheelexperiments a vertical displacement in respect to thevehicle body while the other wheels do not:Conventionalsuspension
Conventional suspension systems: springs and bars
We can confirm this result comparing it with aconventional suspension case. If we know that everywheel is connected to the vehicle body through a spring
of known elasticity Ks, and antiroll bars that provide a
elasticity of Kb between transversal wheels, we candefine the system elasticities as:
Kh
0
0
0
0
Kp
0
0
0
0
Kr
0
0
0
0
Kx
Ks
0
0
0
0
Ks
0
0
0
0
Ks 2 Kb+
0
0
0
0
Ks 2 Kb+
Note that both Krand Kx are related to the antiroll barssince the wheel displacements associated to both rolland axle crossing act against such transversal resilientelements, while rebound and pitch do not.
If we assume that front and rear axles are not equal, withfront and rear different values for springs and anti-rollbars, then the elasticities matrix will become in the form:
a
b
0
0
b
a
0
0
0
0
c
d
0
0
d
c
where:
a1
2Ksf Ksr+( )
b1
2Ksf Ksr( )
c1
2Ksf 2 Kbf+( ) Ksr 2 Kbr+( )+
d1
2
Ksf 2Kbf+( ) Ksr 2 Kbr+( )
Note: For simplicity we assume here that the spring andanti-roll bars are applied vertically on the wheel hubCertain correction factors need to be made depending onthe suspension geometry of the vehicle.
If we consider asymetrc front/rear suspensioncomponents, we can find that the individual elasticitycomponent is different front and rear:
R0 0, R1 1,1
2a b+ c+ d+( ) Ksf Kbf+
R2 2, R3 3,1
2a b c+ d( ) Ksr Kbr+
Beeing Ksf and Kbf the front springs and antiroll barts
elasticity, and Ksr and Kbr the rear springs and antirolbarts elasticity:
This result is obvious as we all know that in that type owheel movement, only the spring between that wheeand the vehicle body is compressed, and the anti-roll bathat connects it with the transversely opposed wheel
For the time beeing, and to simplify the core analisys wewill keep the front/rear symetry and keep Ksf=Ksr and
Kbf=Kbr.
DAMPING ANALISYS
Similarly to the elasticity analisys, we can define systemdamping constants that characterize the damping of thefour system wheel movements, as well as the analisysfor the induced individual wheel reaction .
SYSTEM DAMPING CONCEPT
As with elasticity, we will consider the damping a lineavalue calculated on the wheel velocity with respect to thevehicle body.
With this in mind, we can define the coefficients:
1. Ch : Damping for the rebound movement
2. Cp : Damping for the pitch movement
3. Cr: Damping for the roll movement
4. Cx : Damping for the axle crossing movement
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Based on the vertical velocity in each wheel in respect tothe vehicle body, we can define the forces caused bysuch speeds with the set of damping coefficients definedbefore as:
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
f0
f1
f2
f3
Ch
0
0
0
0
Cp
0
0
0
0
Cr
0
0
0
0
Cx
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
v0
v1
v2
v3
INDIVIDUAL DAMPING COCEPT
Similarly to the elasticity analisys, when the systemexperiences a vertical movement only in one wheel, suchas is the case with small bumps transversed at a speedwhere the vehicle body movement has not yet had thetime to react, we can calculate the forces involvedcombining the previous equations.
Assuming v1=0, v2=0and v3=0, and a vertical movement
speed in one wheel with v00, we get:
f01
4Ch Cp+ Cr+ Cx+( ) v0
Therefore we can define Ci,i the equivalent independent
damping at wheel i, as the force induced when the wheelexperiments a vertical velocity in respect to the vehiclebody while the other wheels do not:
D0 0,f0
v0
1
4Ch Cp+ Cr+ Cx+( )
In general, on a conventional suspension using oneshock absorber per wheel, we can find that the individualelasticity component Di,i at each wheel i is:
Di i,1
4Ch Cp+ Cr+ Cx+( ) Cd
The simplicity of this result already give us hints of thelimitations of using only one damper per wheel.
Conventional suspension: four dampers
Conventional suspension systems have no damping
associated to the anti-roll bars. If we proceed with ananalisys similar to the elasticity, we can confirm thiscase. If we know that every wheel is connected to thevehicle body through a single damper, and the dampingcoefficient is Cd we can define the system dampingcoefficients as:
Ch
0
0
0
0
Cp
0
0
0
0
Cr
0
0
0
0
Cx
Cd
0
0
0
0
Cd
0
0
0
0
Cd
0
0
0
0
Cd
Note: For simplicity we assume here that all dampersare applied vertically on the wheel hub. Certaincorrection factors need to be made depending on thesuspension geometry of the vehicle.
OPTIMAL CENTRAL DEVICE
Conventional suspension systems do not establishlongitudinal or diagonal links between vertica
movements of wheels. The conventional use of anti-rolbars restricts the system elasticity and dampingconstants under the following constraints:
Kh = Kpand Ch = Cp
Kr= Kxand Cr= Cx
These two limitations create three different problems thacompromise all conventional suspension systems:
1. The link between Pitch and Rebound elasticity anddamping coefficients make the oscillationfrequencies depend on wheel base, thereforerestricting the axles distances in the vehicle design
2. The link between Roll and Axle Crossingcompromises the traction capabilities when stabilityis sought and vice versa.
3. The compromise to damp both pitch and roll with thesame set of dampers usually leaves roll damping tooweak and vertical movements damping too stiff.
It would be desirable to design a suspension systemwhere all system parameters can be chosen arbitrarily tosuit the needs of the suspension so three criteria aremet:
1. Kh Kpand Ch Cpso the design of the vehicledynamics can optimize the pitch and reboundoscillation movements for the vehicle characteristicsthat are sought.
2. Krand Crare independent, so the damping of rollmovemens can be adjusted to the vehicle roll inertiaand other stability considerations.
3. Kx and Cx are minimized to favor traction and brakingcapacity, as well as to decrease the individual
reaction Ki and Ci in each wheel to increase thecomfort felt by the vehicle passengers.
FREE AXLE CROSSING: ISOSTATICITY
Freeing the axle-crossing has several advantages as wehave pointed out. Nevertheless, it implies a weighdistribution that does not depend on the surfaceirregularities. We can see that :
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0
0
0
0
Kh
0
0
0
0
Kp
0
0
0
0
Kr
0
0
0
0
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
x0
x1
x2
x3
implies a solution with one degree of freedom:
x0 x3 x1 x2
Assuming a complete symetry in the suspension design,then this solution is:
x0 z3 x1 x2
The existence of this solution makes the systemisostatic, this is, given any value of x0, x1, x2 and x3 thereis a combination of rebound, roll and pitch movementsthat repositions the vehicle body to make:
f0 f1 f2 f3 0
This is the isostatic solution from the suspension point ofview. If we analyze the distribution of weights, then wecan determine that the weights in each wheel Wiaccomplishes that:
W0 W3+ W1 W2+
This is: Half the weight of the vehicle is supported by oneset of wheels diagonally opposed, and the other half bythe other diagonal. In fact, this relationship is obtainedthrough the central device, as it acts as a balancebetween the two diagonal sets of wheels.
This arrangement has, though, one disadvantage, as itcannot allow one wheel to support more than half theweight of the vehicle. That situation could be reached inextreme situations, by either static loads or dynamicforces. In that case, the system would unload one wheeland the diagonally opposite would reach the travel limit.
To solve this situation, the central device must be locked,that is, the axle crossing must be restricted. There aretwo ways to detect this situation:
1. Detecting vehicle accelerations (lateral and
longitudinal)2. Detecting wheel load decrease
We have built our prototypes on the second premise, asit covers both static and dynamic conditions.
ELASTICITIES ANALISYS
For a conventional suspension system, we have foundthe individual spring constant to be:
Ki = Ks+Kb
Where Ks is the spring elasticity and Kb the anti-roll baelasticity.
Keeping all system elasticities Kh, Kp and Kr unaltered
we can decrease Ki by minimizing the axle-crossingelasticity in the following way:
Kh0
0
0
0Kp
0
0
00
Kr
0
00
0
0
Ks0
0
0
0Ks
0
0
00
Ks 2 Kb+
0
00
0
0
From where we get:
Ki1
4Kh Kp+ Kr+ Kx+( )
3
4Ks
1
2Kb+
This means that the individual wheel elasticity is
decreased between 25% and 50% when compared withthe conventional individual elasticity.
Therefore, the forces determined on the wheel passingover a bump will be smaller than in a conventionasystem. Nevertheless, we need to neglect the effect onall other wheels that add up to produce the same effectson the vehicle body, which are still determined by system
parameters Kh, Kp and Kr.
DAMPING ANALISYS
A similar analisys can be followed for the dampingcharacteristics. Nevertheless, and to compare it with therestrictive Ch = Cp = Cr, we can find that
Ch
0
0
0
0
Cp
0
0
0
0
Cr
0
0
0
0
0
Cd
0
0
0
0
Cd
0
0
0
0
Cd
0
0
0
0
0
Obtaining:
Ci1
4Ch Cp+ Cr+ Cx+( )
3
4Cd
This means that the individual damping is decreased
25% when compared with the conventional individuadamping, while maintaining the same dampingcharacteristics for the system movements such as pitchroll and rebound.
It is important to note that these individual elasticity anddamping decreases do not alter any of the globasuspension characteristics from a chassis control pointof view. This is important, as they would alter the
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oscillation frequencies and the stability for which thesuspension was designed.
Conventional Example
Lets take a sports car suspension as an example. Letsassume that the springs and anti-roll bars have thefollowing rates:
Ksf 18 kNm
Ksr 22 kNm
Kbf 75kN
mKbr 15
kN
m
Then, if we ignore the suspension geometry and assumethese values applied on the wheel hubs, the elasticitiesmatrix would be:
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
120
2
0
0
2
20
0
0
0
0
220
116
0
0
116
220
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
177
159
0
0
159
177
0
0
0
0
63
41
0
0
41
63
=
If we free cross-axle movements, we get:
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
120
2
0
0
2
20
0
0
0
0
220
0
0
0
116
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
93
75
84
84
75
93
84
84
26
26
37
15
26
26
15
37
=
Which shows how forces are distributed it over all wheelswhen an individual input is taken. This can clearly beseen on the first column of the resulting matrix, where itindicates the effect on each wheel for an input in wheel
0.
While this is interesting by itself, it is more interesting tosee the effect on damping elements.
Lets assume the following damper characteristics:
Cdf 3.5kN
m s1
Cdr 2.5
kN
m s1
This translates into a damping matrix of:
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1 3
.5
0
0
.5
3
0
0
0
0
3
.5
0
0
.5
3
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
3.5
0
0
0
0
3.5
0
0
0
0
2.5
0
0
0
0
2.5
=
Freeing axle crossing we would get:
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
13
.5
0
0
.5
3
0
0
0
0
3
0
0
0
.5
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2.625
0.875
0.875
0.875
0.875
2.625
0.875
0.875
0.625
0.625
1.875
0.625
0.625
0.625
0.625
1.875
=
Which shows how the damping forces are distributedover all wheels reducing the maximum value of anywheel component.
To optimize further these values we could consider yet:
a) Increase the damping of roll to attain areasonable fraction of the critical damping ofthe roll movement.
b) Slightly decrease the damping of pitch andrebound to attain a similar fraction of thecritical damping of these two movements.
It is also of interest to note that the torsional forces onthe vehicle body created by both the elasticity anddamping elements have been reduced despite the factthe roll stiffness has been maintained.
EXPERIMENTAL RESULTS
Several prototypes have been built to confirm thetheorys advantages. In this paper we focus the study inthe hydraulic implementation made on a 1990 RangeRover model, known because of the traction capabilityand the tendency to roll.
All tests have been conducted at IDIADA, who has runthe tests independently with its own equipmentinstrumentation and personnel, and has postprocessedand analyzed the data obtained.
TESTED CONFIGURATIONS
We have conducted tests on three diferentconfigurations of the suspension:
1. Original suspension2. Axle free HARD3. Axle free SOFT
These suspensions have been characterized by fouelasticity and damping matrices as follows:
Kconfiguration: System Elasticities Matrix kN/mRconfiguration: Individual Elasticities Matrix kN/mCconfiguration: System Damping Matrix kN/(ms
-1)
Dconfiguration: Individual Damping Matrix kN/m(ms-1
)
The original vehicle was characterized by the followingsuspension parameters:
Front springs: 23 kN/m
Rear springs: 33 kN/m
Wheel spring: 230 kN/m
Front dampers(b/r avrg.): 2.9 kN/m
Rear dampers(b/r avrg.): 4.3 kN/m(*)
Front roll center Z: 340mm
Front Springs base: 1000mm
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Rear Springs base: 1100mm
Wheels base: 1650mm
Rear roll center Z: 480mm
Anti roll bars: none
Weight: 2123 Kg
C.G. height 650mm (aprox)
X_Inertia: 420Kgm2
(aprox)
Y_inertia: 3700Kgm2
(aprox)
(*): Rear dampers equivalent constant
Taking into account the vehicle suspension geometry,two live axes, the spring and wheel bases, we canconfigure this suspension with the following matrices that
we will identify as Conf 1 during the instrumented tests:
Koriginal
28
5
0
0
5
28
0
0
0
0
18
4
0
0
4
18
:= Roriginal
18.5
4.5
0
0
4.5
18.5
0
0
0
0
27.5
5.5
0
0
5.5
27.5
=
Coriginal
4.4
1.5
0
0
1.5
4.4
0
0
0
0
2.3
0.5
0
0
0.5
2.3
= Doriginal
2.6
0.3
0.25
0.25
0.3
2.6
0.25
0.25
0.25
0.25
4.1
1.8
0.25
0.25
1.8
4.1
=
Note the poor anti-roll efficiency of springs in this type ofsuspension geometry.
These matrices, when taken into account the wheelspring effect, configure the vehicle own frequencies of:
froll 1.384 Hz= fpitch 1.096Hz= fheave 1.092Hz=
The same vehicle was used to install the prototypesystem with free axle-crossing built with hydrauliccomponents.
It is to be noted that the non-linearity of hydropneumaticsprings would require some additional analisys that fallsoutside the scope of this paper. The hydraulic conduitsand the fluid viscosity have pressure losses associatedthat will make the axle crossing not completely free. Wewill ignore these effects for the linear characteristicsobtained from the tests.
The tested prototypes are:
Prototype Conf 2 with high anti-roll effect and free axle-crossing:
Khard
23.7
0.8
0
0
0.8
23.7
0
0
0
0
65.6
0
0
0
10.3
0
= Rhard
25.275
2.375
13.825
13.825
2.375
25.275
13.825
13.825
18.975
18.975
31.225
6.725
18.975
18.975
6.725
31.225
=
Chard
3.1
0.4
0
0
0.4
3.1
0
0
0
0
4
0
0
0
0.1
0
= Dhard
2.775
0.725
1.025
1.025
0.725
2.775
1.025
1.025
0.975
0.975
2.325
0.375
0.975
0.975
0.375
2.325
=
And its own frequencies once wheels are taken intoaccount:
froll 2.197Hz= fpitch 1.016Hz= fheave 1.013Hz=
Prototype Conf 3 with intermediate anti-roll effect andfree axle-crossing:
Ksoft
26.1
4.5
0
0
4.5
26.1
0
0
0
0
30.2
0
0
0
8.3
0
= Rsoft
16.275
5.325
5.475
5.475
5.325
16.275
5.475
5.475
9.625
9.625
24.925
5.675
9.625
9.625
5.675
24.925
=
Csoft
2.6
0.1
0
0
0.1
2.6
0
0
0
0
3
0
0
0
0
0
= Dsoft
2.1
0.6
0.75
0.75
0.6
2.1
0.75
0.75
0.75
0.75
2
0.5
0.75
0.75
0.5
2
=
And its own frequencies:
froll 1.729Hz= fpitch 1.062Hz= fheave 1.058Hz=
The damping values on the prototypes were choosen toobtain an adequate fraction of the critical damping. Notehow roll damping was increased along with rolstiffeness, while pitch damping was decreased.
TESTS PERFORMED
the following tests were performed during July-2002 athe IDIADA AUTOMOTIVE TECHNOLOGY facilities:
Steady State Circular Test (ISO 4138)
Pseudo-Random steering Input Test (ISO 7401TR 8725)
Step Steer test ((ISO 7401)
Energy Level Measurement
These tests where performed with the aim to measurethe chassis control and the effect of the free axlecrossing. The two changes were supposed to have adirect effect on the vehicle behaviour and comfort.
We also wanted to measure the effect on handling andcornering, which some results show.
All tests have been carried out at IDIADA Automotivetechnology center on every configuration
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RESULTS OF STEADY CIRCULAR TEST (ISO 4138)
AVERAGE (LEFT-RIGHT response)
Parameter Unit Conf 1 Conf 2 Conf 3
steer,Ackermann [] 81.754 84.361 84.252
ratio [-] 21.667 22.358 22.329
K, linear [/ m/s] 6.601 5.178 5.913
K, 5 m/s [/ m/s] 22.052 19.910 31.873
K, linear [/ m/s] 0.999 0.497 0.872K, linear [/ m/s] -0.595 -0.571 -0.582
K, 5 m/s [/ m/s] -1.061 -1.007 -1.402
(/)max [s-1] 0.169 0.170 0.166
vx, (/)max [kph] 49.214 47.457 47.566
max [] 6.263 3.881 6.258
ay,max [m/s2] 5.988 6.211 5.805
vx,max [km/h] 58.552 59.084 57.942
/7
0
/7
0
sm
linear
sm
[* m/s] 3.791 3.104 3.077
Normalised responses in respect to ratio
K / ratio, linear [/ m/s2] 0.304 0.234 0.266
K / ratio, 7 m/s [/ m/s2] 1.005 0.897 1.447
Normalised responses in respect to ratio and wheelbaseK / (ratio*WB) , linear [/ m/s
2] 0.115 0.089 0.101
K / (ratio*WB), 7 m/s [/ m/s2] 0.381 0.340 0.549
From this test we have extracted two results withsignificant differences on roll and understeer gradient foraverage right-left response:
The first relevant aspect of this tests is data related to rollgradient in the linear range from 0ms
-2to 4ms
-2:
AVERAGE (LEFT-RIGHT response)
Experimental Unit Conf 1 Conf 2 Conf 3
K, linear [/ m/s] 0.999 0.497 0.872
The roll gradient K, improves on the prototypes Conf 2
and Conf 3. Nevertheless it can be noted that the resultsare highly conditioned by the relatively soft tires used.
Tires static elasticity has been meassured to be230N/mm which, along with the wheel and spring basehas been taken into account to provide the followingtheoretic results:
TheoreticWheel K [/ m/s] 0.126 0.126 0.126
Suspension K [/ m/s] 0.862 0.278 0.513
Total K [/ m/s] 0.988 0.404 0.640
Both prototype configurations display a higher Rollgradients than expected. We may look into the nonlinearity of hydropneumatic springs and the center-ofmass position to explain the discrepancy.
The second relevant aspect i data related to understeegradient in the linear range from 0ms
-2to 4ms
-2:
Experimental Unit Conf 1 Conf 2 Conf 3
K / ratio, linear [/ m/s2] 0.304 0.234 0.266
The understeer gradient K / ratio in Conf 2 and Conf 3shows a more neutral vehicle. This is assumed to be theresult of the isostaticity that reduces the weighdifferences in all wheels.
To calculate spring forces we can define bodymovements related to the spring compressions as:
Heave
Pitch
Roll
Axle X
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
x0
x1
x2
x3
To calculate the forces in a pure roll movement on a flatsurface we can use then the elasticities matrix in thefollowing manner :
f0
f1
f2
f3
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1 K0 0,
K1 0,
K2 0,
K3 0,
K0 1,
K1 1,
K2 1,
K3 1,
K0 2,
K1 2,
K2 2,
K3 2,
K0 3,
K1 3,
K2 3,
K3 3,
0
0
Roll
0
Provided the simetries that take place in the prototypevehicles used, the Roll value is 4 times the springcompression/extension on roll (wheel equivalendisplacement).
In our case, under a lateral accelleration of 4ms-2, theoriginal vehicle experiments a roll that compresses outersprings to a wheel-equivalent displacement of abou40mm, while inner springs experiment a similaextension.
If we calculate the suspension forces distribution on thewheels for the original configuration on a flat surface andat an accelleration of 4ms
-2we get about 30% more
antiroll effect on the rear axle, thus reducing theundersteer behaviour of the vehicle in Conf 1:
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
128
5
0
0
5
28
0
0
0
0
18
4
0
0
4
18
N
mm4
0
0
40mm
0
0.56
0.56
0.88
0.88
kN=
Nevertheless, any solution that involves freeing the axlecrossing would neutralize the steer effect related tosuspension stiffeness as can be seen in the followingcalculation using the same elasticities matrix for a Roll of40mm at each wheel:
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1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
128
5
0
0
5
28
0
0
0
0
18
0
0
0
4
0
N
mm4
0
0
40mm
0
0.72
0.72
0.72
0.72
kN=
With our prototipes, and the accordingly reduced roll forthe same acceleration, the wheel forces distribution
becomes neutral in Conf 2:
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
123.7
.8
0
0
.8
23.7
0
0
0
0
65.6
0
0
0
10.3
0
N
mm4
0
0
11mm
0
0.722
0.722
0.722
0.722
kN=
And in Conf 3:
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
126.1
4.5
0
0
4.5
26.1
0
0
0
0
30.2
0
0
0
8.3
0
N
mm4
0
0
24mm
0
0.725
0.725
0.725
0.725
kN=
Note: The forces here calculated only include thecomponent induced through the suspension due to thebody roll, not the reaction to the lateral accelerationapplied to the center of roll. Such reaction would add tothe above values the forces in the rear and front wheels
1
2
a M 480 mm
WheelBase 1309N=
.and:
1
2
a M 340 mm
WheelBase 927N=
.
respectively.
The change in forces distribution would have had agreater impact on weight distribution on any car where
the suspension didnt have so little effect against roll. Inthis way the steer component change becomes almostneglectable. Tests results confirm this end, showing avery small (probably neglectable) reduction in theundersteering former suspension. The following diagramshows how slip angles are not significantly influenced bythe better distribiution of weights introduced in Conf 2
and Conf 3.
-7.5 -5 -2.5 0 2.5 5 7.5
-10
-7.5
-5
-2.5
0
2.5
5
7.5
10
Conf 1
Conf 2
Conf 3
RIGHT
Sideslip angle []
LEFT
-- -- -- Rear
--------- Front
Lateral acceleration [m/s]
Figure 4: Sideslip Angle vs. Lateral Accelleration
The remaining understeer gradient obtained at IDIADA isprobably the result of tire pressures used (front: 1.9baand rear: 2.4 bar) since any other factor related togeometry design remained unchanged. For all threeconfigurations, wheel pressures were determinant. to theinherent understeer behaviour.
During the handling tests, though, this and otheprototypes have shown a more balanced weighdistribution (thus a higher cornering grip) has becomemore evident on irregular surfaces, and specially withlarge slip values. In these situations, the steering of thevehicle is more predictable due to the reduced forcefluctuations, thus slip fluctuations, introduced by roadbumps.
RESULTS PSEUDO-RANDOM STEERING INPUTTEST (ISO 7401, TR 8725)
The random steering test was performed to measure theresponse at a different frequencies of steering input. Thefollowing two figures show the three configurationswhere we can appreciate how Conf 2 and Conf 3
elliminate the gain near frequency 1Hz detected in Conf1 due to the original suspension underdamped roll.
Figure 4: Roll versus Lateral Accelleration
Node 1 shows the soft and underdamped roll behaviourin the original suspension Conf 1. while Conf2 and
Conf3 stay much more controlled in the range of bodyfrequencies from 0 to 2Hz.
Node 2 should be neglected as it is the result omoderate roll angles under small accelleration valuesNevertheless, it is to be noted that even in that case
Conf2 and Conf3 keep roll and roll rate under controalthough we are closer to the higher roll own frequency.
Node 2Node 1
0.5 1 1.5 2 2.5 3
0
0.5
1
1.5
Conf 1
Conf 2
Conf 3
-0.4
-0.3
-0.2
-0.1
0
0.1
0.2
-180
-120
-60
0
60
120
180
0.5 1 1.5 2 2.5 3
0
0.5
1
Delay ()
Coherence
: ay-roll
Delay (sec)
Gain [/m/s2]
Frequency (Hz)
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0.5 1 1.5 2 2.5 3
0
5
10
15
Conf 1
Conf 2
Conf 3
-0.4
-0.3
-0.2
-0.1
0
0.1
0.2
-180
-120
-60
0
60
120
180
0.5 1 1.5 2 2.5 3
0
0.5
1
Delay ()
Coherence
: ay-rollR
Delay (sec)
Gain [/s/m/s2]
Frequency (Hz)
Figure 5: Roll velocity versus Lateral Accelleration
RESULTS STEP STEER TEST ((ISO 7401)
The step steer test shows the effect of a single steeringmovement. This is useful to measure the effect of aseparate input.
The diagrams obtained show clearly the roll control whencompared to the original suspension. This is attainedwith the specific damping to roll.
Figure 6: Step Steer Time diagrams
RESULTS ENERGY LEVEL MEASUREMENT
The increment of damping to roll should reduce thecomfort measurements. Nevertheless, an adequatedamping of pitch and rebound movements have reducethe measurements at the seat reel.
The following chart shows the results on the threeconfigurations:
RMS energy levels
0,000
0,500
1,000
1,500
2,000
2,500
3,000
3,500
4,000
Roll Pitch RollR PitchR Seat Rail
Signal
RMS
level
Original
Isostatic 1
Isostatic 2
Figure 7: Autopower results
The Autopower frequency analisys shows the expectedresponse at higher frequencies due to the increaseddamping to roll.
0 1 2 3 4 5 6 7 8 9
-60
-50
-40
-30
-20
-10
0roll
pitch
0 1 2 3 4 5 6 7 8 9
Autopowerlevel[ d
B]
-60-50-40-30-20-10
010
rollR
pitchR
0 1 2 3 4 5 6 7 8 9
-40-30
-20
-10
0
conf 1 conf 2 conf 3
Seat Ra
Range Rover at 90 km/h
Frequency (H
Figure 8: Autopower Frequency Analisys
CONCLUSIONS
The centralized suspension system provides two majoadvantages for suspension design.
First advantage is the availability of extra parameters todesign the elasticity and damping coefficients of avehicle suspension. Current suspension designs, where
underdamped roll movements is common place, can beimproved by implementing an appropiate damping forpitch, roll and rebound. This should help to maximizecomfort as it can avoid excessive damping of pitch andrebound in the conventional suspension compromisescurently taken.
Second advantage is the better weight distribution onstatic and dynamic conditions. This effect has beenproved to favour the neutral characteristics of thevehicle, but the main consequence is a reduction of theeffect of road irregularities on the vehicle steeringcontrol.
Reduced roll rate
peak forConf 2 and
Conf 3
0 1 2 3 4 5 6 7 8
80
85
90
95
100
105
vx
[kp
h]
Conf 1 Conf 2 Conf 3
0 1 2 3 4 5 6 7 8
-10
0
10
20
30
40
50
de
lta
[]
0 1 2 3 4 5 6 7 8
-6
-5
-4
-3
-2
-1
0
1
slip
[]
Front
Rear
0 1 2 3 4 5 6 7 8
-1
0
1
2
3
4
5
6
ay
[m/s]
0 1 2 3 4 5 6 7 8
0
1
2
3
4
5
roll[]
0 1 2 3 4 5 6 7 8
-0.75
-0.5
-0.25
0
0.25
0.5
0.75
1
pitch
[]
0 1 2 3 4 5 6 7 8
-7.5
-5-2.5
0
2.5
5
7.5
10
rollR
[/s]
0 1 2 3 4 5 6 7 8
-3
-2
-1
0
1
2
3
4
pitchR
[/s]
0 1 2 3 4 5 6 7 8
-2.5
0
2.5
5
7.5
10
12.5
15
yawR
[/s]
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Subjective evaluations demonstrate a specially bettersteering control cornering over slipery surfaces. This isjustified by the reduced effect that bumps and surfaceirregularities cause on the wheel forces, and thus on theslip angle fluctiations. This stresses how important is theachieved better distribution of vehicle weight on dynamicconditions.
And important enough, the tests show how theseimprovements on chassis control have been attainedwith a rather moderate change on comfortmeasurements.
FUTURE RESEARCH
Our current developments are the design of acommercially viable suspension system.
Our plans include three areas of future research:
1. Optimal use of non-linear hydropneumaticsprings
2. Pneumatic springs
3. Semiactive damping modules
The experience so far is that stiffness to both pitch androll can be controlled without sacrifying excessivecomfort by designing apropriate spring devices that areprogressively stiff, which is feasible when usinghydropneumatic or air springs.
Pneumatic springs applied to the suspension system willprovide the desired weight-independency of oscillationfrequencies that neither mechanical nor hydropneumaticsystems provide. There are several other advantages ofusing semiactive components that we want to
experiment within the future.
Semiactive damping modules are the obvious step for apassive system that already provides many benefits tothe suspension characterization. The use of suchcomponents can add:
Weight-dependent damping
Adaptive damping
Geometry control is now being studied by many groupsat one axle level. With a centralized system, we canstudy the advantages that the full vehicle model analisys
provides.
ACKNOWLEDGMENTS
We acknowledge the help from the IDIADA team to helpus on the preparation of the instrumented vehicles andthe analisys of the results, as well as the S.I.P. for the aidin their off-road facilities.
REFERENCES
1. Performance of Limited Bandwidth Active
Suspension Based on a Half Car Model. (S.M. El-
Demersdash, University of Helwan) (981118)
2. Optimization of Active and Passive Suspension
Based on a Full Car Model (ElSayed M. ElBaheiry
and Dean C. Karnopp, University of California
Davis). (951063)
3. Influence of Active Suspensions on the Handling
Behaviour of Vehicles Experimental and
Theoretical results G.Keuper, K.H.Senger, R.StollerR.Walter - Robert Bosch GmbH. (945061)
CONTACT
Josep Fontdecaba, an Industrial Engineer Graduatedfrom the Universitat Politcnica de Catalunya. Hescurrently leading the development of the CREUATsuspension system at CREUAT [email protected]
ADDITIONAL SOURCES
IDIADA AUTOMOTIVE TECHNOLOGY, LAlbornar POB20 E-43710 Santa Oliva (Tarragona) Spain
S.I.P. Outdoor Activities, Carretera s/n 25289 Bassella(Lleida) Spain.
DEFINITIONS, ACRONYMS, ABBREVIATIONS
System Elasticity: Set of Elasticity values related to althe vehicle body movements plus axle crossing once weconsider grouped wheel movements for pitch, reboundroll and axle crossing.
System Damping: Set of damping values related to althe vehicle body movements plus axle crossing once weconsider grouped wheel movements for pitch, reboundroll and axle crossing
Individual Elasticity: Elasticity related to one wheewhen it moves while the vehicle body and all othewheels are kept still.
Individual Damping: Desiliency related to one wheewhen it moves while the vehicle body and all othewheels are kept still.
Isostatic Valve: Valve in the hydraulic version of thecentral device that determines whether the suspensionbecomes isostatic or not.
SYMBOLS:
steer,Ackermann Steering angle at very low speed
ratio Overall steering ratio
K Understeering gradient
K Roll gradient
K Sideslip gradient
(/)max Maximum of yaw velocity / delta gain
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vx, (/)max Forward speed at maximum of (/)max
max Maximum roll angle
ay,max Maximum lateral acceleration
vx,max Maximum forward speed
/7
0
/7
0
sm
linear
sm
Area between recorded steering angle andlinear regression of steering angle
K / ratio Normalised understeer gradient
K/ / ratio Normalised sideslip gradient
K / (ratio*WB) Steer coefficient (= Stability factor)
K/ / (ratio*WB) Directional coefficient
- All the gradients are calculated withrespect to ay
Notes:
- The linear range has been defined from 0to 4 m/s
