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

Transcription

1 Determination of anti-pitch geometry acceleration [1/3] 1 of 39 Similar to anti-squat Opposite direction of D Alembert s forces. Front wheel forces and effective pivot locations

2 Determination of anti-pitch geometry acceleration [2/3] 2 of 39 It follows that the change in the front spring force is: where k f = front suspension stiffness. Similarly for the rear wheels.

3 Determination of anti-pitch geometry Pitch angle acceleration [3/3] 3 of 39 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 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 m s a acts horizontally through G; The gravity force on the sprung mass m s g acts vertically downwards through G; The inertia forces m uf a and m ur a 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

5 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 5 of 39 Assuming linear relationship between M φ and φ M φ = k s φ k s = total roll stiffness

6 Load transfer due to the roll moment [2/2] 6 of 39 k sf + k sr = k s Load transfer sin two axles are T f and T r are the front and rear track widths of the vehicle

7 Load transfer due to sprung mass The sprung mass is distributed to the roll centers at front and rear axles. inertia force 7 of 39 Centrifugal force distribution is Corresponding load transfers are

8 Load transfer due to the unsprung mass inertia forces 8 of 39 Total load transfer

9 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 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 by the swinging shackle Leaf spring design

11 11 of 39 Leaf spring analysis Wheel load F W, is vertical. F C 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

12 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 13 of 39 Torsion bars Very simple form of spring and consequently very cheap The principle of operation is to convert the applied load F W into a torque F W 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

14 14 of 39 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 Basic diaphragm accumulator spring Principles of a hydro-pneumatic suspension spring

15 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

16 16 of 39 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, Roll bar contribution to total roll stiffness

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

18 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 forcevelocity axes Ratios of 3:1 Damper characteristics

19 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 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

20 Road surface roughness and vehicle excitation 20 of 39 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

21 Road surface roughness and vehicle excitation 21 of 39 Substituting The variation of S( f ) for a vehicle traversing a poor minor road at 20 m/s is shown

22 Human response to whole body vibration 22 of 39 Human body complex assemblage of linear and nonlinear 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 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 23 of 39

24 Human response to whole body vibration 24 of 39 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 Hz RCB Reduced Comfort Boundary Whole-body RCB vibration criteria, (a) RCB for vertical (z-axis) vibration (b) RCB for lateral (x and y axis vibration)

25 Analysis of vehicle response to road excitation 25 of 39 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

26 Analysis of vehicle response to road excitation 26 of 39 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

27 27 of 39 Response to road excitation Pitch and bounce characteristics Equivalent stiffness is calculated as Generalized co-ordinates are z and θ Notation for pitch bounce analysis

28 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 n, pitch C A

29 29 of 39 Response to road excitation Roots of the equation are Distance of O 1 & O 2 (Oscillation centres)from G

30 30 of 39 Response to road excitation If inertia coupling ratio is O 1 and O 2 are at suspension centers it becomes a 2 DOF (2 mass) system (0.8 for sports cars,1.2 for some If w nf < wfront nr, T nf > T nr drive and on a cars) bump No coupling of front and rear suspensions Two equivalent masses one gets a feeling of in phase motion and minimal pitching better ride <

31 31 of 39 Suspension performance analysis Quarter car model Frequency ranges Low - 1 to 2 Hz resonance of sprung mass High 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 32 of 39 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 r s = k t /k s (b) Road holding (a) ride Effect of suspension stiffness on sprung and unsprung mass transmissibilities, (a) sprung mass transmissibility, (b) unsprung mass transmissibility

33 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

34 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

35 37 of 39 Controllable suspensions Hydraulic Control Speed of response, bandwidth, up to 60 Hz high 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

36 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

37 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 system Semi-active suspension