[PDF] Determination of anti-pitch geometry – acceleration [1/3]

14313_616_suspension_3.pdf

1 of 39 Determination of anti-pitch geometry

- acceleration [1/3]

Similar to anti-squat

Opposite direction of

D͛Alembert͛s forces.

Front wheel forces and effective pivot locations

Figure from Smith,2002

2 of 39 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.

3 of 39 Determination of anti-pitch geometry

- acceleration [3/3]

Pitch angle

Zero pitch occurs when ɽ с 0, i.e. when the term in sƋuare 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 ͚a͛;

The sprung mass rolls through the angle ʔ

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

5 of 39 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 Mʔ and ʔ

Mʔ = ksʔ

ks = total roll stiffness

6 of 39 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

7 of 39 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

8 of 39 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 ɽ < 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

20 of 39 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 freƋuency ͚n͛

ʃ с the roughness coefficient

21 of 39 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

22 of 39 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

1-2 Hz (head-neck)

4-8 Hz (thorax-abdomen)

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

23 of 39 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

24 of 39 Human response to whole body

vibration

Most sensitive frequency range for vertical vibration is from 4-8 Hz corresponding to the thorax-abdomen resonance

most sensitive range for transverse vibration is from 1 to 2 Hz corresponding to head-neck 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

25 of 39 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

26 of 39 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 ɽ

Notation for pitch-bounce 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 Z

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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 - 10-11 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 20-30% 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