1 of 39 Determination of anti-pitch geometry – acceleration [1/3] • Similar to anti-squat • Opposite direction of D’Alembert’s 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 θ = 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. 4 of 39 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 φ 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 Mφ and φ Mφ = ksφ 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 9 of 39 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 10 of 39 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 Leaf spring design by the swinging shackle

Figure from Smith,2002 11 of 39 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 θ < 90° , the spring rate will increase (i.e. rising rate) with bump loading

Figure from Smith,2002 12 of 39 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.

13 of 39 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 14 of 39 Hydro-pneumatic springs

• Spring is produced by a constant mass of gas (typically nitrogen) in a variable volume Basic diaphragm accumulator spring 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 Principles of a hydro-pneumatic expensive) and maintenance suspension spring

Figure from Smith,2002 15 of 39 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 16 of 39 Anti-roll bars (stabilizer)

Conditions: Total roll stiffness krs is equal to the sum • One wheels is lifted relative to of the roll-stiffness produced by the the other, half the total anti-roll suspension springs kr,sus and the roll stiffness acts downwards on the stiffness of the anti-roll bars kr,ar, 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 Roll bar contribution to total roll stiffness is produced.

Figure from Smith,2002 17 of 39 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 Damper types, (a) dual tube damper, pressurized free piston (b) free-piston monotube damper

Figure from Smith,2002 18 of 39 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 19 of 39 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 Shaping of damper characteristics effective – At higher pressure valves open up • lot of scope for shaping and fine tuning 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 frequency ‘n’

κ = 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 RCB – – 0.1 to 0.63 Hz for motion Reduced sickness. Comfort – most sensitive range is from 0.1 Boundary to 0.315 Hz

Whole-body RCB vibration criteria, (a) RCB for vertical (z-axis) vibration (b) RCB for lateral (x Figure from Smith,2002 and y axis vibration) 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 Half and quarter model, roll information is lost and vehicle models, (a) for the quarter vehicle model half vehicle model, pitch information is also lost (b) quarter vehicle model

Figure from Smith,2002 27 of 39 Response to road excitation

Pitch and bounce characteristics • Equivalent stiffness is calculated as

• Generalized co-ordinates Notation for pitch–bounce analysis are z and θ

Figure from Smith,2002 28 of 39 Response to road excitation

• Equations simplify as

•If B=0 – the equations are uncoupled •On a bump only pitching occurs – not desired

n, bounce  A

n, pitch  C 29 of 39 Response to road excitation

Roots of the equation are

Distance of O1 & O2 (Oscillation centres)from G

Figure from Smith,2002 30 of 39 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 someIf wnf < w frontnr, Tnf > T nrdrive and on a cars)bump one gets a feeling of in phase motion – No coupling of front and rear suspensionsand minimal pitching – Two equivalent masses better ride

< 31 of 39 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

32 of 39 Suspension performance analysis Road holding • Lowest transmissibility (b) r = k /k (best ride) is produced s t s with the softest suspension • good road holding requires a hard suspension – low transmissibility at the wheel-hop frequency and (a) in the mid-frequency range ride between the two resonances Effect of suspension stiffness on sprung and unsprung mass transmissibilities, (a) sprung mass transmissibility, (b) unsprung mass transmissibility Figure from Smith,2002 33 of 39 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 34 of 39 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 37 of 39 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 38 of 39 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 39 of 39 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 Semi-active suspension system

Figure from Smith,2002