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Determination of anti-pitch geometry – acceleration [1/3] •
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Similar to anti-squat Opposite direction of D’Alembert’s forces.
Front wheel forces and effective pivot locations
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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 [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
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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.
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Lateral load transfer during cornering Notation and assumptions in the analysis are: •
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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 m sg acts vertically downwards through G; The inertia forces m uf a 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
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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) M s about the roll axis, i.e Assuming linear relationship between M φ and φ Mφ = ksφ 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 •
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– – – –
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Prevent high frequency vibration from being transmitted –
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Inconsistent with roll resistance in cornering Roll stiffening using ant-roll bars Spring can hit limits Additional springs as bump stops Use rubber bush connections
Good road grip (Good handling) – Hard response
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Steel springs •
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– 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
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Leaf spring analysis • • • •
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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
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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 •
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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
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Hydro-pneumatic springs •
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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
Basic diaphragm accumulator spring
Principles of a hydro-pneumatic suspension spring
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Anti-roll bars (stabilizer) • •
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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
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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. •
Total roll stiffness k rs is equal to the sum of the roll-stiffness produced by the suspension springs k ,r sus and the roll stiffness of the anti-roll bars k r,ar ,
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Roll bar contribution to total roll stiffness
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Dampers – types and characteristics •
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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
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Dampers – types and characteristics •
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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 forcevelocity axes Ratios of 3:1
Damper characteristics
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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 –
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At low speeds orifices are effective At higher pressure valves open up
Shaping of damper characteristics
lot of scope for shaping and fine tuning of damper characteristics Typical curves for a three position (electronically) adjustable damper
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Road surface roughness and vehicle excitation •
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Road surfaces have random profiles -> nondeterministic. 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
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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
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Human response to whole body vibration •
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Human body –complex assemblage of linear and nonlinear elements Range of body resonances - 1 to 900 Hz For a seated human –
–
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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
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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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• • • •
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Human response to whole body vibration •
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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 –
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0.1 to 0.63 Hz for motion sickness. most sensitive range is from 0.1 to 0.315 Hz
RCB – Reduced Comfort Boundary
Whole-body RCB vibration criteria, (a) RCB for vertical (z-axis) vibration (b) RCB for lateral ( x
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Analysis of vehicle response to road excitation •
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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
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Analysis of vehicle response to road excitation •
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Much useful information can be derived from simpler vehicle models. The two most often used for passenger cars are the halfvehicle 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
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Response to road excitation Pitch and bounce characteristics Equivalent stiffness is calculated as •
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Generalized co-ordinates are z and θ
Notation for pitch –bounce analysis
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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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Response to road excitation Roots of the equation are
Distance of O1 & O2 (Oscillation centres)from G
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Response to road excitation •
If inertia coupling ratio is –
O1 and O2 are at suspension centers
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it becomes a 2 DOF (2 mass) system
(0.8 for sports cars ,1.2 for some If w < wfront , T > T drive and on a cars) bump nf
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No coupling of front and
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Two equivalent masses
<
nr
nf
nr
one gets a feeling of in phase motion rear suspensions and minimal pitching better ride
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Suspension performance analysis •
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Quarter car model Frequency ranges –
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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 Road holding •
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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
rs = kt/ks
(b)
(a) ride Effect of suspension stiffness on sprung and unsprung mass transmissibilities, (a) sprung mass transmissibility, (b) unsprung mass transmissibility
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Effect of Suspension Damping sprung and unsprung mass transmissibilities, (a) sprung mass transmissibility, (b) unsprung mass transmissibility
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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
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Refined non-linear analysis •
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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
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Controllable suspensions • •
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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
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Slow active controlled suspensions •
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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
