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Determination of anti-pitch geometry
acceleration [1/3]
Similar to anti-squat
Opposite direction of
DAlemberts forces.
Front wheel forces and effective pivot locationsFigure from Smith,2002
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Determination of anti-pitch geometry
acceleration [2/3]
It follows that the change in the front spring force
is:
where kf= front suspension stiffness.
Similarly for the rear wheels.
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Determination of anti-pitch geometry
acceleration [3/3]Pitch angle
Zero pitch occurs when = 0, i.e. when the term in squarebrackets is zero.
anti-squat and anti-pitch performance depends on thefollowing vehicle properties suspension geometry,
suspension stiffnesses (front and rear) and
Tractive force distribution.
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Lateral load transfer during cornering
Notation and assumptions in the analysis are:
G is the sprung mass centre of gravity;
The transverse acceleration at G due to
cornering is a;
The sprung mass rolls through the angle
about the roll axis; The centrifugal (inertia) force on the
sprung mass msa acts horizontally through
G;
The gravity force on the sprung mass msg
acts vertically downwards through G;
The inertia forces mufa and mura actdirectly on the unsprung masses at the
front and rear axles. Each transfers load
only between its own pair of wheels.Steady-state cornering analysis
Figure from Smith,2002
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Load transfer due to the roll moment
[1/2]
Replace the two forces at G with the same forces atA plus a moment (the roll moment) Ms about theroll axis, i.e
Assuming linear relationship between M and
M = ks
ks = total roll stiffness
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Load transfer due to the roll moment
[2/2]
ksf+ ksr = ks Load transfer sin two axles are
Tfand Tr are the front and rear track widths of thevehicle
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Load transfer due to sprung mass
inertia force
The sprung mass isdistributed to the rollcenters at front and rearaxles.
Centrifugal forcedistribution is
Corresponding loadtransfers are
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Load transfer due to the unsprung
mass inertia forces
Total load transfer
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Suspension components
Need for compliance between unsprung and sprung mass.
Requirements:
Good isolation of the body(Good ride) Soft response Inconsistent with roll resistance in cornering
Roll stiffening using ant-roll bars Spring can hit limits
Additional springs as bump stops
Prevent high frequency vibration from being transmitted Use rubber bush connections
Good road grip (Good handling) Hard response
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Steel springs
Semi-elliptic springs earliest developments inmotor vehicle
Robust and simple usedfor heavy applications
Hotchkiss type- to provideboth vertical complianceand lateral constraint forthe wheel travel
change in length of thespring produced by bumploading is accommodatedby the swinging shackle
Leaf spring design
Figure from Smith,2002
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Leaf spring analysis
Wheel load FW , is vertical.
FC is parallel to the shackle
Two load member
The stiffness (rate) of the
spring is determined by thenumber, length, width andthickness of the leaves
Angling of the shackle linkused to give a variable rate
When the angle < 90 ,the spring rate will increase(i.e. rising rate) with bumploading
Figure from Smith,2002
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Coil springs
Light and compact form of compliance for weight andpackaging constraints
Little maintenance and provides
Opportunity for co-axial mounting with a damper
Variable rate springs produced either by varying thecoil diameter and/or pitch of the coils along its length
Disadvantages:
Low levels of structural damping, there is a possibility
of surging (resonance along the length of coils) Spring as a whole does not provide any lateral support
for guiding the wheel motion.
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Torsion bars
Very simple form ofspring and consequentlyvery cheap
The principle of operation
is to convert the appliedload FW into a torque FW R producing twist in thebar
Stiffness related to
diameter, length of thetorsion bar and thetorsion modulus of thematerial Principle of operation of a torsion bar spring
Figure from Smith,2002
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Hydro-pneumatic springs
Spring is produced by aconstant mass of gas (typicallynitrogen) in a variable volumeenclosure
As the wheel deflects in bump,
the piston moves upwardstransmitting the motion to thefluid and compressing the gasvia the flexible diaphragm
The gas pressure increases asits volume decreases to
produce a hardening springcharacteristic
Systems are complex (andexpensive) and maintenance
Principles of a hydro-pneumatic
suspension spring
Basic diaphragm accumulator spring
Figure from Smith,2002
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Anti-roll bars (stabilizer)
Reduce body roll
Ends of the U-shaped barconnected to the wheelsupports and
Central length of barattached to body of thevehicle
Attachment points needto be selected to ensure
that bar is subjected toTorsional loading withoutbending
Anti-roll bar layout
Figure from Smith,2002
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Anti-roll bars (stabilizer)
Conditions:
One wheels is lifted relative tothe other, half the total anti-rollstiffness acts downwards on thewheel and the reaction on thevehicle body tends to resist body
roll. If both wheels lift by the same
amount the bar is not twisted andthere is no transfer of load to thevehicle body.
If the displacements of the
wheels are mutually opposed(one wheel up and the otherdown by the same amount), thefull effect of the anti-roll stiffnessis produced.
Roll bar contribution to total roll stiffness
Total roll stiffness krs is equal to the sum
of the roll-stiffness produced by the
suspension springs kr,sus and the roll
stiffness of the anti-roll bars kr,ar,
Figure from Smith,2002
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Dampers types and characteristics
Frequently called shock
absorbers
Main energy dissipators
in a vehicle suspension Two types: dual tube,
Mono tube.
In mono tube Surplus fluid
accommodated by gas
pressurized free pistonDamper types, (a) dual tube damper,
(b) free-piston monotube damper
Figure from Smith,2002
f
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Dampers types and characteristics
In dealing with road surfaceundulations in the bumpdirection (damper beingcompressed) relatively lowlevels of damping are
required compared with therebound motion (damperbeing extended)
These requirements lead todamper characteristics
which are asymmetricalwhen plotted on force-velocity axes
Ratios of 3:1 Damper characteristics
Figure from Smith,2002
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Dampers types and characteristics
Damper designs areachieved by acombination of orificeflow and flows throughspring-loaded one-wayvalves At low speeds orifices are
effective
At higher pressure valvesopen up
lot of scope for shapingand fine tuning of dampercharacteristics
Shaping of damper characteristics
Typical curves for a three position
(electronically) adjustable damperFigure from Smith,2002
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Road surface roughness and vehicle
excitation
Road surfaces have random profiles -> non-
deterministic.
Methods based on the Fourier transform
Power spectral density S(n) of the height
variations as a function of the spatial
frequency n
= the roughness coefficient
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Road surface roughness and vehicle
excitation
Substituting
The variation of S( f ) for a
vehicle traversing a poorminor road at 20 m/s is
shown
Figure from Smith,2002
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Human response to whole body
vibration
Human bodycomplex assemblage of linear and non-linear elements
Range of body resonances - 1 to 900 Hz
For a seated human 12 Hz (headneck)
48 Hz (thoraxabdomen)
Perception of vibration motions diminishes above 25
Hz and emerges as audible sound. Dual perception (vibration and sound) up to several
hundred Hz is related to the term harshness
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Human response to whole body
vibration Motion sickness (kinetosis) low frequency , normally in
ships
ISO 2631 (ISO, 1978) and the equivalent British Standard BS6841 (BSI, 1987)
whole-body vibration from a supporting surface to eitherthe feet of a standing person or the buttocks of a seatedperson
The criteria are specified in terms of
Direction of vibration input to the human torso
Acceleration magnitude Frequency of excitation
Exposure duration
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Human response to whole body
vibration Most sensitive frequency range
for vertical vibration is from 48Hz corresponding to the thoraxabdomen resonance
most sensitive range for
transverse vibration is from 1 to2 Hz corresponding to headneck resonance
ISO 2631 discomfort boundaries 0.1 to 0.63 Hz for motion
sickness.
most sensitive range is from 0.1to 0.315 Hz
Whole-body RCB vibration criteria, (a) RCB for
vertical (z-axis) vibration (b) RCB forlateral (xand y axis vibration)Figure from Smith,2002
RCB
Reduced
Comfort
Boundary
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Analysis of vehicle response to road
excitation Most comprehensive of these
has seven degrees of freedom
Three degrees of freedom forthe vehicle body (pitch,bounce and roll)
Vertical degree of freedom ateach of the four unsprungmasses.
This model allows the pitch,bounce and roll
The suspension stiffness anddamping rates are derivedfrom the individual spring anddamping units Full vehicle model
Figure from Smith,2002
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Analysis of vehicle response to road
excitation Much useful information can be
derived from simpler vehiclemodels.
The two most often used forpassenger cars are the half-vehicle model and the quarter
vehicle model. These have four and two degrees
of freedom respectively.
Reduced number of degrees offreedom
In the case of the half vehicle
model, roll information is lost andfor the quarter vehicle modelpitch information is also lost
Half and quarter
vehicle models, (a)
half vehicle model,
(b) quarter vehicle
model
Figure from Smith,2002
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Response to road excitation
Pitch and bouncecharacteristics
Equivalent stiffness iscalculated as
Generalized co-ordinatesare z and
Notation for pitchbounce analysis
Figure from Smith,2002
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Response to road excitation
Equations simplify as
If B=0 the equations are uncoupled
On a bump only pitching occurs not desired
,
,
n bounce
n pitch
A
C
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Roots of the equation are
Distance of O1 & O2 (Oscillation centres)from G
Response to road excitation
Figure from Smith,2002
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Response to road excitation
If inertia coupling ratio is
O1 and O2 are at suspension centers
it becomes a 2 DOF (2 mass) system
(0.8 for sports cars ,1.2 for some front drive cars)
No coupling of front and rear suspensions
Two equivalent masses
Tnr and on a bump
one gets a feeling of in phase motion
and minimal pitching
better ride
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Suspension performance analysis
Quarter car model
Frequency ranges
Low - 1 to 2 Hz resonance of sprung mass
High - 1011 Hz resonance of un-sprung orwheel hop
Suspension designer has selection of
characteristics and parameter values forsuspension springs and dampers to achievethe desired suspension performance
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Suspension performance analysis
Lowest transmissibility(best ride) is producedwith the softestsuspension
good road holdingrequires a hardsuspension
low transmissibility at thewheel-hop frequency andin the mid-frequency rangebetween the tworesonances Effect of suspension stiffness on sprung and
unsprung mass transmissibilities, (a) sprung
mass transmissibility, (b) unsprung mass
transmissibility
(a)
(b)
Figure from Smith,2002
rs = kt/ks
ride
Road
holding
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Effect of Suspension Damping
sprung and
unsprung mass
transmissibilities,
(a) sprung mass
transmissibility,
(b) unsprung
mass
transmissibility
Control of the sprung mass resonance requires high levels ofdamping, but results in poor isolation in the mid-frequency
Wheel-hop resonance also requires high levels of damping for itscontrol, but with the same penalties in the mid-frequency range
0.3 used for passenger cars
Figure from Smith,2002
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Refined non-linear analysis
suspension spring and dampernon-linearities,
random road excitation
assessment of ride, tyre forcefluctuation and clearance
space limitations highly non-linear analysis
Requires simulations in thetime domain
ISO weighted acceleration
response of the sprung massdenoted by the DiscomfortParameter D is evaluated
ISO weighting characteristic for
vertical vehicle body acceleration
Figure from Smith,2002
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Controllable suspensions
Hydraulic Control Speed of response, high
bandwidth, up to 60 Hz
Actuator is driven by an on-boardpump controlled by signalsderived from transducers fitted to
the sprung and unsprung masses. Signals are processed in a
controller according to somecontrol law to produce acontrolled force at the actuator
With practical limitations taken
into account, ride can beimproved by 2030% for thesame wheel travel and dynamictire load when compared with apassive suspension Fully active suspension
Figure from Smith,2002
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Slow active controlled suspensions
Low bandwidth (up to approximately6 Hz).
The aim of this form of suspension isto control the body mode to improveride.
Above its upper frequency limit it
reverts to a conventional passivesystem which cannot be bettered forcontrol of the wheel-hop mode.
Such systems require much lesspower than the fully active system,with simpler forms of actuation.
The potential performance gains are
less than those for a fully activesystems, but the viability is muchimproved.
Slow active suspension
Figure from Smith,2002
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Another Controllable suspension
Passive damper is replaced with acontrollable one.
Designed to produce a controlledforce when called upon to dissipateenergy and then switches to anotional zero damping state whencalled upon to supply energy.
Performance potential of thissuspension closely approaches thatof a fully active system under certainconditions, but the hardware andoperational costs of this type ofsuspension are considerably less
Performance is impaired by changesin payload which alter the suspensionworking space : overcome bycombining the controllable damperwith some form of self-levelingsystem
Semi-active suspension
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