Suspension Stiffness
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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