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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 locations Figure 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 square brackets is zero.

anti-squat and anti-pitch performance depends on the following 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 act directly 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 at A plus a moment (the roll moment) Ms about the roll 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

Tf and Tr are the front and rear track widths of the vehicle

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Load transfer due to sprung mass inertia force

The sprung mass is distributed to the roll centers at front and rear axles. Centrifugal force distribution is Corresponding load transfers 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 in motor vehicle

Robust and simple used for heavy applications

Hotchkiss type- to provide both vertical compliance and lateral constraint for the wheel travel

change in length of the spring produced by bump loading is accommodated by 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 the number, length, width and thickness of the leaves

Angling of the shackle link used to give a variable rate

When the angle < 90 , the spring rate will increase (i.e. rising rate) with bump loading

Figure from Smith,2002

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Coil springs

Light and compact form of compliance for weight and packaging constraints

Little maintenance and provides Opportunity for co-axial mounting with a damper Variable rate springs produced either by varying the

coil 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 of spring and consequently very cheap

The principle of operation is to convert the applied load FW into a torque FW R producing twist in the bar

Stiffness related to diameter, length of the torsion bar and the torsion modulus of the material

Principle of operation of a torsion bar spring

Figure from Smith,2002

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Hydro-pneumatic springs

Spring is produced by a constant mass of gas (typically nitrogen) in a variable volume enclosure

As the wheel deflects in bump, the piston moves upwards transmitting the motion to the fluid and compressing the gas via the flexible diaphragm

The gas pressure increases as its volume decreases to produce a hardening spring characteristic

Systems are complex (and expensive) 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 bar

connected to the wheel supports and

Central length of bar attached to body of the vehicle

Attachment points need to be selected to ensure that bar is subjected to Torsional loading without bending

Anti-roll bar layout

Figure from Smith,2002

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Anti-roll bars (stabilizer)

Conditions: One wheels is lifted relative to

the other, half the total anti-roll stiffness acts downwards on the wheel and the reaction on the vehicle body tends to resist body roll.

If both wheels lift by the same amount the bar is not twisted and there is no transfer of load to the vehicle body.

If the displacements of the wheels are mutually opposed (one wheel up and the other down by the same amount), the full effect of the anti-roll stiffness is 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 piston

Damper types, (a) dual tube damper, (b) free-piston monotube damper

Figure from Smith,2002

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Dampers types and characteristics

In dealing with road surface undulations in the bump direction (damper being compressed) relatively low levels of damping are required compared with the rebound motion (damper being extended)

These requirements lead to damper characteristics which are asymmetrical when 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 are achieved by a combination of orifice flow and flows through spring-loaded one-way valves At low speeds orifices are

effective At higher pressure valves

open up

lot of scope for shaping and fine tuning of damper characteristics

Shaping of damper characteristics

Typical curves for a three position (electronically) adjustable damper

Figure 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 poor minor road at 20 m/s is shown

Figure from Smith,2002

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Human response to whole body vibration

Human body complex 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 BS 6841 (BSI, 1987)

whole-body vibration from a supporting surface to either the feet of a standing person or the buttocks of a seated person

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 48 Hz corresponding to the thoraxabdomen resonance

most sensitive range for transverse vibration is from 1 to 2 Hz corresponding to headneck resonance

ISO 2631 discomfort boundaries 0.1 to 0.63 Hz for motion

sickness. most sensitive range is from 0.1

to 0.315 Hz

Whole-body RCB vibration criteria, (a) RCB for vertical (z-axis) vibration (b) RCB for lateral (x and 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 for the vehicle body (pitch, bounce and roll)

Vertical degree of freedom at each of the four unsprung masses.

This model allows the pitch, bounce and roll

The suspension stiffness and damping rates are derived from the individual spring and damping 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 vehicle models.

The two most often used for passenger cars are the half-vehicle model and the quarter vehicle model.

These have four and two degrees of freedom respectively.

Reduced number of degrees of freedom

In the case of the half vehicle model, roll information is lost and for the quarter vehicle model pitch 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 bounce characteristics

Equivalent stiffness is calculated as

Generalized co-ordinates are 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

<

If wnf < wnr, Tnf > 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 or wheel hop

Suspension designer has selection of characteristics and parameter values for suspension springs and dampers to achieve the desired suspension performance

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Suspension performance analysis

Lowest transmissibility (best ride) is produced with the softest suspension

good road holding requires a hard suspension low transmissibility at the

wheel-hop frequency and in the mid-frequency range between the two resonances 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 of damping, but results in poor isolation in the mid-frequency

Wheel-hop resonance also requires high levels of damping for its control, 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 damper non-linearities,

random road excitation assessment of ride, tyre force

fluctuation and clearance space limitations

highly non-linear analysis Requires simulations in the

time domain ISO weighted acceleration

response of the sprung mass denoted by the Discomfort Parameter 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-board

pump controlled by signals derived from transducers fitted to the sprung and unsprung masses.

Signals are processed in a controller according to some control law to produce a controlled force at the actuator

With practical limitations taken into account, ride can be improved by 2030% for the same wheel travel and dynamic tire load when compared with a passive suspension

Fully active suspension

Figure from Smith,2002

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Slow active controlled suspensions

Low bandwidth (up to approximately 6 Hz).

The aim of this form of suspension is to control the body mode to improve ride.

Above its upper frequency limit it reverts to a conventional passive system which cannot be bettered for control of the wheel-hop mode.

Such systems require much less power than the fully active system, with simpler forms of actuation.

The potential performance gains are less than those for a fully active systems, but the viability is much improved.

Slow active suspension

Figure from Smith,2002

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Another Controllable suspension

Passive damper is replaced with a controllable one.

Designed to produce a controlled force when called upon to dissipate energy and then switches to a notional zero damping state when called upon to supply energy.

Performance potential of this suspension closely approaches that of a fully active system under certain conditions, but the hardware and operational costs of this type of suspension are considerably less

Performance is impaired by changes in payload which alter the suspension working space : overcome by combining the controllable damper with some form of self-leveling system

Semi-active suspension

Figure from Smith,2002