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Suspension is the term given to the system of springs, shock absorbers and linkages that connects a vehicle to its wheels. Suspension systems serve a dual purpose, contributing to the car's roadholding/handling and braking for good active safety and driving pleasure, and keeping vehicle occupants comfortable and reasonably well isolated from road noise, bumps, and vibrations. These goals are generally at odds, so the tuning of suspensions involves finding the right compromise. It is important for the suspension to keep the road wheel in contact with the road surface as much as possible, because all the forces acting on the vehicle do so through the contact patches of the tyres. The suspension also protects the vehicle itself and any cargo or luggage from damage and wear. The design of front and rear suspension of a car may be different.

History
Leaf springs have been around since the early Egyptians.
Ancient military engineers used leaf springs in the form of bows to power their siege engines, with little success at first. The use of leaf springs in catapults was later refined and made to work years later. Springs were not only made of metal, a sturdy tree branch could be used as a spring, such as with a bow.

Horse Drawn Vehicles
By the early 19th century most British horse carriages were equipped with springs, wooden springs in the case of light one-horse vehicles to avoid taxation, and steel springs in larger vehicles. These were made of low-carbon steel and usually took the form of multiple layer leaf springs.
The British steel springs were not well suited for use on America's rough roads of the time, and could even cause coaches to collapse if cornered too fast. In the 1820s, the Abbot Downing Company of Concord, New Hampshire developed a system whereby the bodies of stagecoaches were supported on leather straps called "thoroughbraces", which gave a swinging motion instead of the jolting up and down of a spring suspension (the stagecoach itself was sometimes called a "thoroughbrace")

Automobiles
Automobiles were initially developed as self-propelled versions of horse drawn vehicles. However, horse drawn vehicles had been designed for relatively slow speeds and their suspension was not well suited to the higher speeds permitted by the internal combustion engine.
In 1903 Mors of Germany first fitted an automobile with shock absorbers. In 1920 Leyland used torsion bars in a suspension system. In 1922 independent front suspension was pioneered on the Lancia Lambda and became more common in mass market cars from 1932.

Spring Rate
The spring rate (or suspension rate) is a component in setting the vehicle's ride height or its location in the suspension stroke. Vehicles which carry heavy loads will often have heavier springs to compensate for the additional weight that would otherwise collapse a vehicle to the bottom of its travel (stroke). Heavier springs are also used in performance applications where the loading conditions experienced are more extreme.
Springs that are too hard or too soft will both effectively cause the vehicle to have no suspension at all. Vehicles that commonly experience suspension loads heavier than normal have heavy or hard springs with a spring rate close to the upper limit for that vehicle's weight. This allows the vehicle to perform properly under a heavy load when control is limited by the inertia of the load. Riding in an empty truck used for carrying loads can be uncomfortable for passengers because of its high spring rate relative to the weight of the vehicle. A race car would also be described as having heavy springs and would also be uncomfortably bumpy. However, even though we say they both have heavy springs, the actual spring rates for a 2000 lb race car and a 10,000 lb truck are very different. A luxury car, taxi, or passenger bus would be described as having soft springs. Vehicles with worn out or damaged springs ride lower to the ground which reduces the overall amount of compression available to the suspension and increases the amount of body lean. Performance vehicles can sometimes have spring rate requirements other than vehicle weight and load.

Mathematics Of The Spring Rate
Spring rate is a ratio used to measure how resistant a spring is to being compressed or expanded during the spring's deflection. The magnitude of the spring force increases as deflection increases according to Hooke's Law. Briefly, this can be stated as:

F = -kx \

Where:

F is the force the spring exerts
k is the spring rate of the spring
x is the displacement from equilibrium length i.e. the length at which the spring is neither compressed nor stretched

Spring rate is confined to a narrow interval by the weight of the vehicle, load the vehicle will carry, and to a lesser extent by suspension geometry and performance desires.
Spring rates typically have units of N/mm (or lb/in). An example of a linear spring rate is 500 lb/in. For every inch the spring is compressed, it exerts 500 lb. A non-linear spring rate is one for which the relation between the spring's compression and the force exerted cannot be fitted adequately to a linear model. For example, the first inch exerts 500 lb force, the second inch exerts an additional 550 lb (for a total of 1050 lb), and the third inch exerts another 600 lb (for a total of 1650 lb). In contrast a 500 lb/in linear spring compressed to 3 inches will only exert 1500 lb.
The spring rate of a coil spring may be calculated by a simple algebraic equation or it may be measured in a spring testing machine. The spring constant k can be calculated as follows:

k = \frac{d^4G}{8ND^3} \

Where:

d is the wire diameter
G is the spring's shear modulus (e.g., about 12,000,000 lb/in² or 80 GPa for steel)
N is the number of wraps and D is the diameter of the coil

Wheel Rate
Wheel rate is the effective spring rate when measured at the wheel. This is as opposed to simply measuring the spring rate alone.
Wheel rate is usually equal to or considerably less than the spring rate. Commonly, springs are mounted on control arms, swing arms or some other pivoting suspension member. Consider the example above where the spring rate was calculated to be 500lbs/inch, if you were to move the wheel 1 inch (without moving the car), the spring more than likely compresses a smaller amount. Let’s assume the spring moved 0.75 inches, the lever arm ratio would be 0.75 to 1. The wheel rate is calculated by taking the square of the ratio (0.5625) times the spring rate. Squaring the ratio is because the ratio has two effects on the wheel rate. The ratio applies to both the force and distance travelled.
Wheel rate on independent suspension is fairly straight-forward. However, special consideration must be taken with some non-independent suspension designs. Take the case of the straight axle. When viewed from the front or rear, the wheel rate can be measured by the means above. Yet because the wheels are not independent, when viewed from the side under acceleration or braking the pivot point is at infinity (because both wheels have moved) and the spring is directly in line with the wheel contact patch. The result is often that the effective wheel rate under cornering is different from what it is under acceleration and braking. This variation in wheel rate may be minimized by locating the spring as close to the wheel as possible.

Roll Couple Percentage
Roll couple percentage is the effective wheel rates, in roll, of each axle of the vehicle just as a ratio of the vehicle's total roll rate. Roll Couple Percentage is critical in accurately balancing the handling of a vehicle. It is commonly adjusted through the use of anti-roll bars, but can also be changed through the use of different springs.
A vehicle with a roll couple percentage of 70% will transfer 70% of its sprung weight transfer at the front of the vehicle during cornering. This is also commonly known as "Total Lateral Load Transfer Distribution" or "TLLTD".

Weight Transfer
Weight transfer during cornering, acceleration or braking is usually calculated per individual wheel and compared with the static weights for the same wheels.
The total amount of weight transfer is only affected by 4 factors:

Distance between wheel centres (wheelbase in the case of braking, or track width in the case of cornering)
Height of the centre of gravity
Mass of the vehicle
Amount of acceleration experienced.

The speed at which weight transfer occurs as well as through which components it transfers is complex and is determined by many factors including but not limited to roll centre height, spring and damper rates, anti-roll bar stiffness and the kinematic design of the suspension links.

Unsprung Weight Transfer
Unsprung weight transfer is calculated based on the weight of the vehicle's components that are not supported by the springs. This includes tires, wheels, brakes, spindles, half the control arm's weight and other components. These components are then (for calculation purposes) assumed to be connected to a vehicle with zero sprung weight. They are then put through the same dynamic loads. The weight transfer for cornering in the front would be equal to the total unsprung front weight times the G-Force times the front unsprung centre of gravity height divided by the front track width. The same is true for the rear.

Sprung Weight Transfer
Sprung Weight Transfer is the weight transferred by only the weight of the vehicle resting on the springs, not the total vehicle weight. Calculating this requires knowing the vehicles sprung weight (total weight less the unsprung weight), the front and rear roll centre heights and the sprung centre of gravity height (used to calculate the roll moment arm length). Calculating the front and rear sprung weight transfer will also require knowing the roll couple percentage.
The roll axis is the line through the front and rear roll centres that the vehicle rolls around during cornering. The distance from this axis to the sprung centre of gravity height is the roll moment arm length. The total sprung weight transfer is equal to the G-force times the sprung weight times the roll moment arm length divided by the effective track width. The front sprung weight transfer is calculated by multiplying the roll couple percentage times the total sprung weight transfer. The rear is just the total minus the front transfer.

Jacking Forces
Jacking forces are the sum of the vertical force components experienced by the suspension links. The resultant force acts to lift the sprung mass if the roll centre is above ground, or compress it if underground. Generally, the higher the roll centre, the more jacking force is experienced.

Travel
Travel is the measure of distance from the bottom of the suspension stroke (such as when the vehicle is on a jack and the wheel hangs freely), to the top of the suspension stroke (such as when the vehicles wheel can no longer travel in an upward direction toward the vehicle). Bottoming or lifting a wheel can cause serious control problems or directly cause damage. "Bottoming" can be either the suspension, tires, fenders, etc. running out of space to move or the body or other components of the car hitting the road. The control problems caused by lifting a wheel are less severe if the wheel lifts when the spring reaches its unloaded shape than they are if travel is limited by contact of suspension members.

Damping
Damping is the control of motion or oscillation, as seen with the use of hydraulic gates and valves in a vehicles shock absorber. This may also vary, intentionally or unintentionally. Like spring rate, the optimal damping for comfort may be less than for control.
Damping controls the travel speed and resistance of the vehicles suspension. An undamped car will oscillate up and down. With proper damping levels, the car will settle back to a normal state in a minimal amount of time. Most damping in modern vehicles can be controlled by increasing or decreasing the resistance to fluid flow in the shock absorber.

Camber Control
Camber changes due to wheel travel, body roll and suspension system deflection or compliance. In general, a tire wears and brakes best at -1 to -2 degrees of camber from vertical. Depending on the tire and the road surface, it may hold the road best at a slightly different angle. Small changes in camber, front and rear, can be used to tune handling. Some race cars are tuned with -2~-7 degree camber depending on the type of handling desired and the tire construction. Often times, too much camber will result in the decrease of braking performance due to a reduced contact patch size through excessive camber variation in the suspension geometry. The amount of camber change in bump is determined by the instantaneous front view swing arm (FVSA) length of the suspension geometry, or in other words, the tendency of the tire to camber inward when compressed in bump.

Roll Centre Height
This is important to body roll and to front to rear roll stiffness distribution. However, the roll stiffness distribution in most cars is set more by the antiroll bars than the RCH. The height of the roll centre is related to the amount of jacking forces experienced.

Instant Centre
Due to the fact that the wheel and tire's motion is constrained by the suspension links on the vehicle, the motion of the wheel package in the front view will scribe an imaginary arc in space with an “instantaneous centre" of rotation at any given point along its path. The instant centre for any wheel package can be found by following imaginary lines drawn through the suspension links to their intersection point.
A component of the tire's force vector points from the contact patch of the tire through instant centre. The larger this component is, the less suspension motion will occur. Theoretically if the resultant of the vertical load on the tire and the lateral force generated by it points directly into the instant centre, the suspension links will not move. In this case all weight transfer at that end of the vehicle will be geometric in nature. This is key information used in finding the force-based roll centre as well.
In this respect the instant centres are more important to the handling of the vehicle than the kinematic roll centre alone, in that the ratio of geometric to elastic weight transfer is determined by the forces at the tires and their directions in relation to the position of their respective instant centres.

Anti-Dive And Anti-Squat
Anti-dive and anti-squat are expressed in terms of percentage and refer to the front diving under braking and the rear squatting under acceleration. They can be thought of as the counterparts for braking and acceleration as jacking forces are to cornering. The main reason for the difference is due to the different design goals between front and rear suspension, whereas suspension is usually symmetrical between the left and right of the vehicle.
Anti-dive and anti-squat percentage are always calculated with respect to a vertical plane that intersects the vehicle's centre of gravity. Consider anti-dive first. Locate the front instant centres of the suspension from the vehicle's side view. Draw a line from the tire contact patch through the instant centre, this is the tire force vector. Now draw a line straight down from the vehicle's centre of gravity. The anti-dive is the ratio between the heights of where the tire force vector crosses the centre of gravity plane expressed as a percentage. An anti-dive ratio of 50% would mean the force vector under braking crosses half way between the ground and the centre of gravity.
Anti-squat is the counterpart to anti-dive and is for the rear suspension under acceleration.
Anti-dive and anti-squat may or may not be desirable depending on the suspension design. Independent suspension using multiple control arms can be an issue if the percentage is too high (say over 30%). A percentage of 100% in this case would indicate the suspension is taking 100% of the weight transfer under braking instead of the springs. This effectively binds the suspension and turns the independent suspension into no suspension like a go-cart. However, in the case of leaf spring rear suspension the anti-squat can often exceed 100% (meaning the rear may actually rise under acceleration) yet because there isn't a second arm to bind against and the suspension can freely move. Traction bars are often added to drag racing cars with rear leaf springs to increase the anti-squat to its maximum. This has the effect of forcing the rear of the car in the air and the tires onto the ground for better traction.

Flexibility And Vibration Modes Of The Suspension Elements
In modern cars, the flexibility is mainly in the rubber bushings.

Isolation From High Frequency Shock
For most purposes, the weight of the suspension components is unimportant, but at high frequencies, caused by road surface roughness, the parts isolated by rubber bushings act as a multistage filter to suppress noise and vibration better than can be done with only the tires and springs. (The springs work mainly in the vertical direction.)

Contribution To Unsprung Weight And Total Weight
These are usually small, except that the suspension is related to whether the brakes and differential(s) are sprung.

Space Occupied
Designs differ as to how much space they take up and where it is located. It is generally accepted that MacPherson struts are the most compact arrangement for front-engined vehicles, where space between the wheels is required to place the engine.

Force Distribution
The suspension attachment must match the frame design in geometry, strength and rigidity.

Air Resistance (Drag)
Certain modern vehicles have height adjustable suspension in order to improve aerodynamics and fuel efficiency. And modern formula cars, that have exposed wheels and suspension, typically use streamlined tubing rather than simple round tubing for their suspension arms to reduce drag. Also typical is the use of rocker arm, push rod, or pull rod type suspensions, that among other things, places the spring/damper unit inboard and out of the air stream to further reduce air resistance.

Cost
Production methods improve, but cost is always a factor. The continued use of the solid rear axle, with unsprung differential, especially on heavy vehicles, seems to be the most obvious example.

Springs And Dampers
Most conventional suspensions use passive springs to absorb impacts and dampers (or shock absorbers) to control spring motions.
Some notable exceptions are the hydropneumatic systems, which can be treated as an integrated unit of gas spring and damping components, used by the French manufacturer Citroën and the hydrolastic, hydragas and rubber cone systems used by the British Motor Corporation, most notably on the Mini. A number of different types of each have been used:

Passive Suspensions
Traditional springs and dampers are referred to as passive suspensions - most vehicles are suspended in this manner.

Springs
Leaf spring – AKA Hotchkiss, Cart, or semi-elliptical spring
Torsion beam suspension
Coil spring
Rubber bushing
Air spring

Dampers Or Shock Absorbers
The shock absorbers damp out the (otherwise resonant) motions of a vehicle up and down on its springs. They also must damp out much of the wheel bounce when the unsprung weight of a wheel, hub, axle and sometimes brakes and differential bounces up and down on the springiness of a tire. The regular bumps found on dirt roads (nicknamed "corduroy", but properly washboarding) are caused by this wheel bounce.

Semi-Active And Active Suspensions
If the suspension is externally controlled then it is a semi-active or active suspension - the suspension is reacting to what are in effect "brain" signals. As electronics have become more sophisticated, the opportunities in this area have expanded.
For example, a hydropneumatic Citroën will "know" how far off the ground the car is supposed to be and constantly reset to achieve that level, regardless of load. It will not instantly compensate for body roll due to cornering however. Citroën's system adds about 1% to the cost of the car versus passive steel springs.
Semi-active suspensions include devices such as air springs and switchable shock absorbers, various self-levelling solutions, as well as systems like Hydropneumatic, Hydrolastic, and Hydragas suspensions. Mitsubishi developed the world’s first production semi-active electronically controlled suspension system in passenger cars, the system was first incorporated in the 1987 Galant model. Delphi currently sells shock absorbers filled with a magneto-rheological fluid, whose viscosity can be changed electromagnetically, thereby giving variable control without switching valves, which is faster and thus more effective.
Fully active suspension systems use electronic monitoring of vehicle conditions, coupled with the means to impact vehicle suspension and behaviour in real time to directly control the motion of the car. Lotus Cars developed several prototypes, from 1982 onwards, and introduced them to F1, where they have been fairly effective, but have now been banned. Nissan introduced a low bandwidth active suspension in circa 1990 as an option that added an extra 20% to the price of luxury models. Citroën has also developed several active suspension models (see hydractive). A recently publicised fully active system from Bose Corporation uses linear electric motors, i.e. solenoids, in place of hydraulic or pneumatic actuators that have generally been used up until recently. The most advanced suspension system[citation needed] is Active Body Control, introduced in 1999 on the top-of-the-line Mercedes-Benz CL-Class.
Several electromagnetic suspensions have also been developed for vehicles. Examples include the electromagnetic suspension of Bose, and the electromagnetic suspension developed by professor Laurentiu Encica. In addition, the new Michelin wheel with embedded suspension working on an electromotor is also similar.
With the help of control system, various semi-active/active suspensions realize an improved design compromise among different vibrations modes of the vehicle, namely bounce, roll, pitch and warp modes. However, the applications of these advanced suspensions are constrained by the cost, packaging, weight, reliability, and/or the other challenges.

Interconnected Suspensions
Interconnected suspension, unlike semi-active/active suspensions, could easily decouple different vehicle vibration modes in a passive manner. The interconnections can be realized by various means, such as mechanical, hydraulic and pneumatic. Anti-roll bars are one of the typical examples of mechanical interconnections, while it has been stated that fluidic interconnections offer greater potential and flexibility in improving both the stiffness and damping properties.
Considering the considerable commercial potentials of hydro-pneumatic technology (Corolla, 1996), interconnected hydropneumatic suspensions have also been explored in some recent studies, and their potential benefits in enhancing vehicle ride and handling have been demonstrated. The control system can also be used for further improving performance of interconnected suspensions. Apart from academic research, an Australian company, Kinetic, is having some success (WRC: 3 Championships, Dakar Rally: 2 Championships, Lexus GX470 2004 4x4 of the year with KDSS, 2005 PACE award) with various passive or semi-active systems, which generally decouple at least two vehicle modes (roll, warp (articulation), pitch and/or heave (bounce)) to simultaneous control each mode’s stiffness and damping, by using interconnected shock absorbers, and other methods. In 1999 Kinetic was bought out by Tenneco.
Historically, the first mass production car with front to rear mechanical interconnected suspension was the 1948 Citroën 2CV. The suspension of the 2CV was extremely soft, it had low roll stiffness, but its pitch stiffness was increased by using an interconnected suspension. The leading arm/trailing arm swinging arm, fore-aft linked suspension system together with inboard front brakes had a much smaller unsprung weight than existing coil spring or leaf designs. The interconnection transmitted some of the force deflecting a front wheel up over a bump, to push the rear wheel down on the same side. When the rear wheel met that bump a moment later, it did the same in reverse, keeping the car level front to rear. The 2CV had a design brief to be able to be driven at speed over a ploughed field. It originally featured friction dampers and tuned mass dampers. Later models had tuned mass dampers at the front with telescopic dampers/shock absorbers front and rear.
Some of the last post war Packard models also featured interconnected suspension. The original Mini and some more recent British Leyland models also featured interlinking, when fitted with Moulton's Hydrolastic or Hydragas suspensions.

Suspension Geometry
Suspension systems can be broadly classified into two subgroups , dependent and independent. These terms refer to the ability of opposite wheels to move independently of each other.
A dependent suspension normally has a beam (a simple 'cart' axle) or (driven) live axle that holds wheels parallel to each other and perpendicular to the axle. When the camber of one wheel changes, the camber of the opposite wheel changes in the same way (by convention on one side this is a positive change in camber and on the other side this a negative change). De Dion suspensions are also in this category as they rigidly connect the wheels together.
An independent suspension allows wheels to rise and fall on their own without affecting the opposite wheel. Suspensions with other devices, such as sway bars that link the wheels in some way are still classed as independent.
A third type is a semi-dependent suspension. In this case, the motion of one wheel does affect the position of the other but they are not rigidly attached to each other. A twist-beam rear suspension is such a system.

Dependent Suspensions
Dependent systems may be differentiated by the system of linkages used to locate them, both longitudinally and transversely. Often both functions are combined in a set of linkages.
Examples of location linkages include:

Satchell link
Panhard rod
Watt's linkage
WOBLink
Mumford linkage
Leaf springs used for location (transverse or longitudinal):

o Fully elliptical springs usually need supplementary location links and are no longer in common use
o Longitudinal semi-elliptical springs used to be common and still are used in heavy-duty trucks. They have the advantage that the spring rate can easily be made progressive (non-linear)
o A single transverse leaf spring for both front wheels and/or both back wheels, supporting solid axles was used by Ford Motor Company, before and soon after World War II, even on expensive models. It had the advantages of simplicity and low unsprung weight (compared to other solid axle designs).

In a front engine, rear-drive vehicle, dependent rear suspension is either "live axle" or deDion axle, depending on whether or not the differential is carried on the axle. Live axle is simpler but the unsprung weight contributes to wheel bounce.
Because it assures constant camber, dependent (and semi-independent) suspension is most common on vehicles that need to carry large loads as a proportion of the vehicle weight, that have relatively soft springs and that do not (for cost and simplicity reasons) use active suspensions. The use of dependent front suspension has become limited to heavier commercial vehicles.

Semi-Independent Suspension
In a semi-independent suspension the wheels of an axle are able to move relative to one another as in an independent suspension but the position of one wheel has an effect on the position and attitude of the other wheel. This effect is achieved via the twisting or deflecting of suspension parts under load. The most common type of semi-independent suspension is the twist beam.

Independent Suspensions
The variety of independent systems is greater and includes:

Swing axle
Sliding pillar
MacPherson strut/Chapman strut
Upper and lower A-arm (double wishbone)
Multi-link suspension
Semi-trailing arm suspension
Swinging arm
Leaf springs

Transverse leaf springs when used as a suspension link, or four quarter elliptics on one end of a car are similar to wishbones in geometry, but are more compliant. Examples are the front of the original Fiat 500, the Panhard Dyna Z and the early examples of Peugeot 403 and the back of the AC Ace and AC Aceca.
Because the wheels are not constrained to remain perpendicular to a flat road surface in turning, braking and varying load conditions, control of the wheel camber is an important issue. Swinging arm was common in small cars that were sprung softly and could carry large loads, because the camber is independent of load. Some active and semi-active suspensions maintain the ride height, and therefore the camber, independent of load. In sports cars, optimal camber change when turning is more important.
Wishbone and multi-link allow the engineer more control over the geometry, to arrive at the best compromise, than swing axle, MacPherson strut or swinging arm do, however the cost and space requirements may be greater. Semi-trailing arm is in between, being a variable compromise between the geometries of swinging arm and swing axle.