The aim of this assignment is to investigate and research into various automotive suspensions system configurations and the methodologies used to design, analyse and physically test them.
ABSTRACT:-
This paper reviews the suspension systems used in vehicle. Different type of suspension system along with the configuration and working are discussed. The advantage and disadvantage of each suspension system is mentioned.
Along with it suspension system in context to vehicle handling, ride quality and durability is discussed. Factors like understeer and oversteer affecting ride and handling is also discussed. Effect of vibration on human perception of ride and quality. One more important aspect, durability of suspension system and ways to test the durability is mentioned.
1. INTRODUCTION:-
Suspension has been used since two centuries in some form or another. In present times automobile chassis is mounted on the axles, not direct but through some form of springs [2].Which results in isolation of the vehicle body from the road shock and also active safety. In order to eliminate these road shocks suspension systems are used.
A suspension system should hold the wheels of the car in their proper relationship to the road and to the car [1]. It should be maintained even if the condition of the road is degraded, direction of travel or the speed of the car. The wheels must follow the contour of the road. With the bump it must rise and dip during holes. So basic function is to absorb the energy of vertically accelerated wheels and keep the frame and body undisturbed while the wheel follows the bump.
Figure 1: General layout of suspension system
2. FUNCTIONS OF THE VEHICLE SUSPENSION SYSTEM:-
To isolate the occupants or cargo from levels of shock and vibration induced by the road surface [2].
To preserve the stability of the vehicle in rolling and pitching
To enable the wheels to maintain contact with the road, ensuring stability and control.
To maintain the road wheels in correct geometry (proper steer and camber) during driving.
React to the control forces produced by the tires i.e. longitudinal acceleration and braking force.
To safeguard the occupants from road shocks.
3. DESIGH CONSIDERATION FOR A SUSPENSION SYSEM:-
3.1 Vertical loading: -
The wheel when subjected to a bump or pit, depending on the nature of the irregularity of road, suspension is subjected to vertical forces which are absorbed by the springs. Furthermore when the front wheel strikes the bump it is set into vibrations and dies down exponentially due to damping and same occurs at the rear. Human comfort mainly depends on how low the vibration frequencies are. Hence to keep the vibration frequency low, pitching tendency is used.
Rolling: -
The centre of gravity of vehicle is considerably above. Due to this reason while taking a turn, the centrifugal force acts outwards on the C.G while the road resistance acts inwards at wheels. This phenomenon gives rise to a couple turning the vehicle about the longitudinal axis called rolling. Anti roll bar is used to avoid rolling tendency of the vehicle. [2]
Dive and Squat: -
The acceleration torque causes the front to lift and on application of brakes causes the front to dive. All these forces are transferred to the spring by the suspension linkages
Side Thrust: -
When a vehicle is in motion there are many forces are present like wind, cambering of road and centrifugal force which altogether gives rise to a force called side thrust. These forces are absorbed by springs or panhard rods.
Unsprung weight:-
It's nothing but the weight of the suspension, axle and tires. When the wheels pass over bumps, the unsprung mass stores the energy of the vertical moment of the bump. This is later passed on to the car body in the form of shock. So reduction in weight of the unsprung mass is an important criterion.
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4. LAYOUT OF SUSPENSION SYSTEM:-
The suspension system is a combination of spring, damper and linkages.
SPRING: - The spring is the heart of the suspension system. Its main function is to absorb the vertical moment due to bump and shock produced from the road surface. Various types of springs are
Steel spring
Rubber spring
Plastic spring
Air spring
Hydraulic spring
Depending on their function or use, they can be further classified as
Laminated/Leaf spring
Helical spring
Anti roll bar/Torsion bar
Fig 2:- Leaf spring Fig 3:- Helical spring
Fig 4:- Anti Roll Bar
DAMPER: - The main function of the damper is reducing the oscillation of the spring when it passes over a bump or a hole. They are required to cause a rapid die-away of any vibrations forced either randomly or periodically at the natural frequency of the suspension system and thus introducing a state of resonance [6].
SUSPENSION LINKAGES: - Linkages connect the vehicle body to the wheel & allows the moment between the two. Linkages allow locating hard points in the suspension & maintaining the correct geometry.
5. TYPES OF SUSPENSION SYSTEM: -
5.1 SOLID AXLE SUSPENSION SYSTEM:-
Fig 5 :- Solid Axle suspension system
In this type of suspension system the wheels are mounted on either side of a rigid axle.When the wheel are subjected to bump it does not result in parallel up and down motion.This gives rise to gyroscopic torques and contribute to a predisposition towards wheel shimmy.They are mainly used on the rear of trucks and most of cars.These suspension system advantage is that the wheel camber is not due to the body roll,hence there is less wheel camber when the vehicle turns besides the compression from the tyres on the outside turns.The tire wear is minimum in this type of supension.
5.1. 1. Hotchkiss Drive :-
Fig 6 : Hotchkiss drive [7]
These are the commonly used rigid axle suspension system. The axle is located by semi elliptical leaf spring and is driven by longitudinal driveshaft with universal joints. The leaf spring is connected on either end to the chassis and at the centre to axle. They are still widely used light and heavy commercial vehicle.
5.2 INDEPENDANT SUSPENSION SYSTEM:-
The independent suspension allow each wheel to move irrespective of the opposite wheel .The various advantage over solid axle suspension system are
It has resistance to steering steering vibrations such as such as wheel wobble and shimmy.
Reduction in weight of the system
Usage of softer springs, better ride comfort
Spring deflection does not alter steering geometry
Increase in space for the engine
Result of all the above advantages the usage of independent suspension has grown in modern vehicle.
5.2. 1. Double Wishbone Type Suspension:-
Fig 7 : Double whisbone
This type of supension consist of two links which are parallel to each other in ride condition.The links are made in a shape of an wishbone which helps in resisting braking torque and also provide stifness.The wishbone consist of three pivot points of which two inner bearings are connected to the frame and outer ball joint attaching the whisbone to stub axle. Wishbone layout helps in positioning of wheels and vehicle load and inturn resist the acceleration, braking and cornering forces.The strut is placed above the lower wishbone which gives the necessary vertical support. The advantage of this type of suspension is that you analyze the effect of each moving joint and tune the suspension. The double whisbone suspension can also be called as S-L A (Short-Long Arm) suspensions in which upper arms arms are shorter when compared to lower ones , resulting in wheel track being constant and inturn avoiding wheel scrub.The main disadvantage of this type system is that it is more complex than others.
5.2. 2. Mac Pherson type suspension:-
Fig 8: Mac Pherson
It is one of the widely used suspension system. It houses a long telescopic tube incorporating the damper, is pivoted to the body at the top and connected to stub axle at the lower end with the help of a ball joint. The wishbone is hinged to the cross member and positions the wheel and also resists accelerating, braking and side forces [2].when compared to other systems it is much simple and light, resulting in low unsprung weight. It maintains the camber in up & down moment .Room in the engine compartment is maximum because of this system.
5.2. 3. Multi-Link Suspension: -
It has the same principal, but the arms of the upper and lower wishbone are separate. These arms are fixed to the top and bottom of the spindle thus forming a spindle shape. One unique feature is that spindle turns for steering; it alters the geometry of all four arms. They have better road holding properties but on contrary are complex in design and expensive.
Fig 9 : Multi link suspension
5.2. 4. Vertical Guide Suspension: -
In this configuration of supension the kingpin is directly attached cross member of the frame, result of which it moves up and down with the wheel motion .In this the track, wheel base & wheel attitude remain the same but results in decreased stability.
Fig 10: Vertical guide suspension
5.2. 5. Trailing Link Suspension:-
It consist of an coil spring, attached to the trailing link which itself is attached to the shaft carrying the wheel hub .When the wheel moves up and down it winds and unwinds the spring. Coil spring can be replaced by torsion bars at some places.The camber angle and wheel track always remain the same but front and rear wheel distance shifts.
Fig 11: Trailing link suspension
5.2. 6. Swinging Half Axle Suspension :-
The wheels are bolted on to the half axles, which are pivoted on their ends to the chasis member at the middle of the car. The main diasavantage is that the up and down movement of the wheel results in changes of the camber angle.
Fig 12 : Swinging half axle suspension
5.2. 7. De-Dion Suspension :-
This system is a balane between live and independent system.The De-Dion axle has the differential and drive attached to the chassis. The wheel are mounted on a transverse dead tube axle. The axle tube is hollow to provide drive shaft access to the hubs. It is otherwise known as an semi-independant system.The main disavantage is that it is an complex structure.[1]
Fig 13 : De-Dion suspension
5.2. 8. Air Suspension System :-
The below sketch is an skematic diagram of an air suspension . Genrally the air suspension uses two types of spring which are bellow type or spring type.Either of which used are always used in a whisbone system. When a vehicle is subjected to a bump the pressure inside the spring increases. Resuting in compression, stiffer the spring becomes .The main advantage is that it produces three times more softer ride than conventional springs.
Fig 14 : Air suspension system
The system consist of four air springs which are used instead of conventional springs. The air passes from the filter to compressor where it is compressed to 240Mpa and then into the accumulator tank [2]. The accumulator tank also consist of safety valves. And after which the high pressure air passes through lift control and the levelling valves leading to the air spring.The main advantage of this type of system is that it give an comfortable ride.
5.2. 9. Hydrolastic Suspension:-
The hydrostatic suspension consist of displacer units which are fitted to all four wheels. The displacer unit are connected by fluid with help of a small bore pipe. In the displacer unit, rubber which is subjected to compression and shear is used as spring and fluid under pressure is the damping meduim. Stem connects to wheel through suitable linkages so that its movent is similar to up and down movement of the wheel.The main advantage of this system is that pitch is virtually eliminated.
Fig 15: Hydrolastic suspension
5.2. 10. Hydragas Suspension System:-
The below diagram shows the arrangement of this system. It is seen that the effective piston area acting on the diaphragm increses during a bump and decreses during rebound. Nitrogen gas which under compression and pressure from diaphragm acts as the spring.The posItion of damper valve is similar to hydrostatic but the only difference is the connecting pipes are below which means that liquid flow between the front and rear units does not pass through the damper valves. The main advantage is the low pitch frequency and good ride.
Fig 16 : Hydragas system
5.2. 11. ACTIVE SUSPENSIONS: -
Fig 17 : Bose® Electromaganative active suspension
A suspension is fully active when the spring and dampers of a passive suspension are replaced by hydralic struts. It was first implemented in a car by lotus.
A system is active when it uses a fast-acting, closed-loop control system.Such a system uses hydralic rams, servovalves and sensors. Closed loop control system requires the interconnection of these elements to feedback signals from the hydralic rams by means of sensor to activate the control device, which inturn feeds the signals back to the arms. This teconology allows car manufacturer to have high ride quality and ride handling. The main disavantage of this system is increased complexity and cost.[4]
6. VEHICLE HANDLING:-
Vehicle handling refers clearly to a system which allows the driver directional control of the vehicle with sufficent efficency to choose the best path around corners, to avoid other objects and to manouver the car efficently at low speeds.[1]
6. 1.Low Speed Turning:-
In a low speed turn the tires do not develop any lateral forces.Thus they roll without any slip angle while the vehicle must negotiate the turns as shown in the figure below.
Fig 18 : Geometry of a turning vehicle
When the rear wheel do not have any slip angles, the turn center must lie on the projection of rear axle. The pependiculars from the front wheels should pass through the turn center. If they do not pass through the same point, the front wheels fight against each other alongwith experiencing scrub in the turn.
The exact geomentry of the front wheel is defined by the Ackerman geomentry.These angles are mainly dependant on the wheelbase and angle of turn. If not correct results in tire wear. With correct geomentry the steering torques increases with steer angle which results in a natural feel of the feedback through the steering wheel for the driver.The other significant feautre is the offtracking occuring at the rear wheels. This phenomem is considerd for vehicles with long wheelbase such as trucks and buses.
6. 2.High speed cornering :-
During a high speed corner there is a difference in turning equation because of the lateral acceleration. To curb the lateral accelaration the tires develop lateral forces and slip angles, which are present at each wheels.
Tire conering forces :-
Fig 18: Tire cornering force properties
Fy is the conering force. The conering forces increases with slip angle at a given tire load .The relationship between lower slip angles and lateral force is linear.It is given by the equation
..........(A) (for low slip angles)
Cα = Proportionality constant of conering stifness
The conering stifness depends on many variables like tire size, type, wheel width and tread.Which shows that speed is not the only one which affects the cornering stifness.
6. 3.Slip angle :-
Slip angle is defined as angle between the rolling wheel's actual direction of travel and the direction towards which it is pointing.
6. 4.Concept of understeer,oversteer and neutralsteer:-
6.4. 1.Neutralsteer:-
When both the front and rear wheel have the same slip angle , the vehicle is said to be in neutral steer.
Fig 19: Neutral steer
6.4. 2.Understeer:-
When the slip angle of the front wheel is greater than that of rear wheel , radius of the turn increases.This shows that for a given rotation of steering wheel the vehicle turns less sharply.In simple words the vehicle moves away from its normal intended course and bring it back to the right path one has steer more than required.
Fig 20 : Understeer
6.4. 3.Oversteer:-
When the slip angle of the front wheel is less than that of rear wheel , radius of turn is decreased.Which results in the vehicle turning more sharply than for the given rotation of the steering wheel. In simple words, the vehicle moves away from its normal direction of motion and in order to bring it to the right path one has to steer less than required.
Fig 21: Oversteer
When compared with above two , understeer is less undesirable, though both are not required, because the driver always reacts naturally by steering in the desired direction.In oversteer greater care is required, due to which the vehicles are generally desighed with understeer condition at normal speed.As the speed increases the scenario changes first to neutral steer and then to oversteer.
6. 5.Vehicle handling improvement:-
There are few ways in which handling can be improved. One of the basic one is the Tire pressure, which can be adjusted to improve the handling. If the pressure is high it gives rise to cornering forces for a given load and slip angle.Variation in tyre sizes can help to get understeer and oversteer which are useful during some instances, but anti roll bars are the one maiinly used.In other case altering the roll stifness at the front or rear can give rise to understeer or oversteer, in order to limit the maximum lateral acceleration.Low grip tyres are used in some instances to prevent tipping of a vehicle by reducing the conering capacity.
7.VEHICLE RIDE:-
The vehicle experience different types of vibration.The term "ride" is usually associated with the tactile and visual vibration, aural vibrations are categorized as noise. Considering the frequency of vibration, the spectrum of vibration is classified as ride (0-25 Hz) and noise (25-20000 Hz). Vibration is an important criteria by which people judge the desigh and construction quality of the car.So car manufacturer must develop objective engineering methods for dealing with ride as performance mode of the vehicle.
The ride quality is a factor of relatively low frequency bounce and rebound of the suspension when subjected to a bump.This bump results in a series of oscillation according to the natural frequency of the system.The ride is more comfortable when the natural frequency ranges between 60 - 90 cycles per minute or 1-1.5 Hz, above which the occupants perceives the ride as harsh.
The below figure shows the dynamic ride system through which the ride perception of the vehicle be determined by the occupants.
Fig 22: Ride dynamic system
7. 1.Excitation sources :-
They are genrally catogerized into two types i.e road roughness and on-board sources.Rotating components such as tire/wheel assemblies, the driveline and the engine are the source for on-board vibration.
7.1. 2.Road roughness:-
Road roughness includes everything from potholes to the deviation in road surface, reflecting the practical limits of precision with which roads can be laid and maintained. Roughness is described as the elevated profile over which the vehicle passes. This profile is similar to category of broad-band random signals which can be defined by the profile itself or the statistical properties.One of the most useful reperesentation is the power spectral density function (PSD). The elevation profile is measured over a length of road and with help of fourier transform series is converted into a series of sine waves.The plot of amplitude vs frequency is the PSD. Spatial frequency is expressed as the wavenumber with units as cycle/foot.
Fig 23: Typical spectral densities of road elevation profiles.
The PSD for average road properties is given by the equation
GZ (V) = GO [1+ (VO/V) 2] / (2Î v) 2.
Where:
GZ (V) = PSD amplitude.
V = wave number.
GO = Roughness magnitude parameter.
VO = Cut-off wave number.
7.1. 3.On board excitation sources:-
TIRE/WHEEL ASSEMBLY :-
This assembly is mostly soft and compliant in order to absorb vibration to isolate the ride system. However imperfection due to manufacturing limitation of the assembly may result in nonuniformities. These uniformities results in variation in force and moments on the ground it rolls and then act as a source for ride vibration when transmitted to axle of the vehicle.
DRIVELINE EXCITATION:-
The rotating driveline consists of the driveshaft, gear reduction and the differential on the drive axle and axle shaft connecting to the wheels. The driveshaft with spline has the main potential for exciting ride vibrations. The rear axle gearing and rest of the driveline also generate vibrations but the frequency generated is above the ride (>25Hz) hence they are considered as noise.
ENGINE/TRANSMISSION :-
The powered delivered in an engine is mainly due to the cyclic process due to which torque developed is also not constant. The crankshaft at each power stroke of a cylinder consists of a series of pulses. The flywheel acts as an inertia damper along with the inertias and compliances in the transmission. The torque output from the driveshaft consists of a steady state component plus superimposed torque variation. This variation in torque induces excitation forces which result in vibrations. The vibration is in six directions three translation and three rotational.
7.2. Vehicle dynamic response:-
The vehicle dynamic system when considered starts best with basic properties of vehicles on its suspension system - i.e. motion of the body and axles. At low frequencies, the body which is sprung mass moves as an integral unit on the suspension. The unsprung masses consisting of wheels and axles also move as rigid bodies resulting in excitation force on unsprung mass as input and output of which is the vibration of the body. The dynamic response can be calculated by the input-output relationships. The ratio between the output and input can be described as gain and the term "Transmissibility" is used to denote the word gain. Which is non dimensional.
7.2. 1.Suspension isolation:-
The sprung mass supported by primary suspension system is a type of road isolation shared by all vehicles. It is first level of isolation system known as quarter car model.
Fig 24: Quarter car model
It consist of a sprung mass(M) on the suspension system represented by a spring with a stiffness (Ks) along with an damper (Cs)which is then connected to unsprung mass (m).The tire is represented as a spring of stiffness (Kt ). Sprung mass resting on the suspension and tires are capable of motion in vertical direction. The effective stiffness of suspension and tire spring in series is called as "Ride rate".
RR = KS.KT / (KS + KT)
Where:
RR = Ride rate
KS = suspension stiffness
KT = Ride stiffness
The natural frequency at each corner in the absence of damping is given by
Where:
W=mg=weight of unsprung mass
g= acceleration due to gravity
When damping is present as in the case of the suspension resonance occurs at damped natural frequency given by
Where:
In modern passenger cars the damping ration is between 0.2-0.4 for a good ride. The resonant frequency in the equation above is usually quite close to the natural frequency because of the influence of damping. At 0.2 the damped natural frequency is 98% of undamped natural frequency and 0.4damping the ratio is 92%.
7.2. 2.Suspension stiffness:-
The suspension spring rules in establishing the ride rate and also the natural frequency in the vertical mode. Road acceleration inputs increases in amplitude at higher frequency, the best isolation is achieved by keeping the natural frequency as low as possible. The figure below shows acceleration spectra calculated for a quarter car models.
The natural frequency is in a range between 1-2Hz and plotted in a linear scale. The area under the curve shows the relative level of mean square acceleration over frequency.
Fig 25: Mean square acceleration vs. Frequency
As shown above the lowest acceleration occurs at frequency of 1Hz. At higher natural frequency, the acceleration peak in 1-5Hz range increases, reflecting a greater transmission of road acceleration input and mean square acceleration increases by several hundred percent . In addition stiffer springs can elevate the natural frequency to 10Hz, allowing more acceleration transmission in the high frequency range. Which shows soft suspension is good for ride isolation. The natural frequency range for a normal car is 1-1.5 Hz and for performance car between 2-2.5Hz sacrificing the ride.
7.2. 3.Suspension damping:-
Fig 26: Effect of damping on suspension isolation behaviour
The next in line is the damper which works in tandem with the spring. The main function of the damper is to dissipate the energy put into the system by bump. At 40% damping similar to the road cars the frequency range is between 1.5-2 .At 100% damping the bounce motion are well controlled, if pushed further would result in vehicle bounce due to stiff suspension.
7.2. 4.Active control:-
To improve the ride performance, use of active components has been developed in recent years. The active components are hydraulic cylinder which can exert forces in the suspension on command from an electronic controller.
Fig 27: Acceleration vs. suspension travel for passive suspension
The above figure represents the passive system. Soft suspension would represent a luxury car and a stiffer one for sports car. So increase in damping increases acceleration but reduces suspension travel. In case of active suspension electronic control senses the acceleration of sprung and unsprung masses to vary the force in proportion to these variables. In curve 1 optimization to minimize vertical acceleration and travel results in performance but less in for optimal road handling. Best benefit in active system can be obtained by control of sprung mass motion near resonant frequency.
Fig 28: Acceleration vs. Suspension travel for active suspension
Active system reduces the resonant amplitude of the sprung mass at sprung mass resonant frequency because it exerts force to minimize the amplitude.
7.3 Ride perception:-
Ride is a subjective perception, it is nothing but the level of comfort experienced during a travel. So the ride perceived is a cumulative product of many factors. So it is Upto an individual of how he perceives the ride. The minimum tolerance for a human in vertical vibration is between the frequency range of 4-8 Hz. The frequency above and below this range the tolerance increases in proportion to frequency. Human sensitivity for the fore/aft vibration is different from the vertical; the main reason is the maximum sensitivity occurs in the range of 1-2Hz.
Perception of ride quality is degraded by virtually any disturbance experienced by the occupant. The sensitivity of human varies according to disturbance. High frequency vibration of wind and drive train noise must be minimized and insulated for ride isolation.
The ride quality depends on collection of factors of how it is constructed and how well it is insulated which finally results in good ride quality.
Fig 29: Human Tolerance for vertical vibration
Fig 30: Human tolerance limit for fore/aft vibration
8. VEHICLE DURABILITY:-
Due to increased competition in global car industry, vehicle development schedule have decreased from 4 years to less than 2 years today. The challenge for the car developers is that to meet these condensed timelines without negatively affecting the quality and performance attributes such as warranty, crash worthiness, NVH (noise, vibration and harshness) and driver comfort. At the most fundamental core of any development is vehicle durability testing. The success of a durability program lies in ability to satisfy all possible requirements. In order to assist durability testing many use the virtual testing method coupled with traditional durability testing.
8.1. Vitrual testing method
8.1. 1.Virtual proving ground:-
These were created from the Nuneaton based proving ground drawings. These were first reproduced in the CAD geometry, meshed in hypermesh and processed in Matlab to create ADAMS road files. The main disadvantage is that important durability surface such as pàve and cobblestone slalom could not be made to exact requirements.
The latest method involves measuring such surfaces directly using a combination of high speed photography and laser techniques.
Fig 31: Virtual proving ground
8.1. 2.Virtual test rig:-
Fig 32: Virtual test rig
The measurements have also been used to drive displacement driven virtual durability test rig. The rig helps in driving the tire contact patches with help of an actuator. The actuator functions in a way similar to the disturbances in the proving ground surface. The above figure shows the profile of the surface directly under the tire contact patch is used to drive the rig taking into account averaging effect of the tire. The measured track data can alternatively be used to drive 4-post hydraulic test rig.
8.2. Traditional durability test
8.2. 1.Road test:-
In road testing before the final product is launched into the market it is taken on the road and tested for performance in actual road condition. Examples of special durability surfaces are at MIRA and the well known of these are the "Belgian Pàve", which not only produced rapid deterioration in hydraulic damper performance but structural breakages of various forms as well. Also there are various features such as bumps, pot holes, tramlines and rail crossing, broken edges and also hill sections. These are repeated in a continous cycle which is other words is the durability cycle. Such tests help to get behaviour of the vehicle behaviour in actual condition. [1]
Fig 33: Pàve surface test Fig 34: Resonance road test
Fig 35: Road test
8.2. 2.Laboratory testing:-
All major manufacturers and engineering consultancies have extensive range of test rigs. Most of which are servo-hydraulic, although many have rotating machinery too. The shaker rigs are driven by a real time signal of disturbance inputs which are recorded in a car on a test surface. The input signals to the shaker rig are modified using iterative control software such that a similar car on the test rig experiences the same disturbances as were recorded on the test surface. It is important that the phase relationship among the various inputs should be retained accurately on the test rig. The lab testing comes into limelight when the road testing becomes expensive. [1]
Fig 36: 4 Poster Test Rig
Fig 37: 4 Poster Test Rig
9. CONCLUSION:-
Suspension systems are one of the most critical part of a car. Various suspension types are available each suitable for specific application. Ride and handling have prime importance in an automotive suspension. The Dampers when set to soft result in good ride but on the expense of handling and vice versa. So it's a tough job to achieve an optimum balance of ride and handling. Active suspensions have started making their mark in the high end luxury car market. And also vehicle testing has become the prime importance to ensure its durability in the long run.
LIST OF FIGURES:-
Fig 1: General layout of suspension system
Fig 2: Leaf spring
Fig 3: Helical spring
Fig 4: Anti Roll Bar
Fig 5: Solid Axle suspension system
Fig 6: Hotchkiss drive
Fig 7: Double wishbone
Fig 8: Mac Pherson
Fig 9: Multi link suspension
Fig 10: Vertical guide suspension
Fig 11: Trailing link suspension
Fig 12: Swinging half axle suspension
Fig 13: De-Dion suspension
Fig 14: Air suspension system
Fig 15: Hydrolastic suspension
Fig 16: Hydragas system
Fig 17: Bose® Electromaganative active suspension
Fig 18: Geometry of a turning vehicle
Fig 18: Tire cornering force properties
Fig 19: Neutral steer
Fig 20: Understeer
Fig 21: Oversteer
Fig 22: Ride dynamic system
Fig 23: Typical spectral densities of road elevation profiles
Fig 24: Quarter car model
Fig 25: Mean square acceleration vs. Frequency
Fig 26: Effect of damping on suspension isolation behaviour
Fig 27: Acceleration vs. suspension travel for passive suspension
Fig 28: Acceleration vs. Suspension travel for active suspension
Fig 29: Human Tolerance for vertical vibration
Fig 30: Human tolerance limit for fore/aft vibration
Fig 31: Virtual proving ground
Fig 32: Virtual test rig
Fig 33: Pàve surface test
Fig 34: Resonance road test
FIG 35: Road test
Fig 36: 4 Poster Test Rig
Fig 37: 4 Poster Test Rig
NOMENCLATURE
ζ =damping ratio.
Cs=Suspension damping coefficient
RR=Ride Rate
Ks =suspension stiffness.(lb/ft)
Kt =tyre stiffness.(lb/ft)
M =Sprung mass or mass of vehicle, (lb)
m =unsprung mass, (lb)
g =gravitational acceleration (ft/sec2)
α =Slip angel. (deg)
RR =Ride Rate
PSD =Power Spectral Density
SAE =Society of Automotive Engineering
Hz =Hertz unit of frequency
