Definitions

# Suspension (vehicle)

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 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. 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.

## Important properties

### 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 when the suspension is constantly forced to the bottom of its stroke causing a reduction in the useful amount of suspension travel which may also lead to harsh bottoming.

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 or stretched.

Spring rate is confined to a narrow interval by the weight of the vehicle, the 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 lbf/in). An example of a linear spring rate is 500 lbf/in. For every inch the spring is compressed, it exerts 500 lbf. 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 lbf force, the second inch exerts an additional 550 lbf (for a total of 1050 lbf), the third inch exerts another 600 lbf (for a total of 1650 lbf). In contrast a 500 lbf/in linear spring compressed to 3 inches will only exert 1500 lbf.

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:

$k = frac\left\{d^4E\right\}\left\{8ND^3\right\} ,$
where d is the wire diameter, E is the spring's elastic modulus (e.g., about 30,000,000 lbf/in² or 207 GPa for steel), and 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. Lets 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 traveled.

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 inline with the wheel contact patch. The result is often that the effective wheel rate under cornering is different than 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 as a ratio of the vehicle's total roll rate. Roll Couple Percentage is critical in accurately balancing the handling of a vehicle.

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.

### 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. Cornering wheel weights requires knowing the static wheel weights and adding or subtracting the unsprung, sprung and jacking forces at each wheel. Some auto racing circles use false terms, or combine things like jacking forces and sprung weight transfer and call it by terms like "side bite". They are either unknowing by ignorance or intentionally confusing competitors by not dealing with vehicle fundamentals and using commonly accepted anthropomorphic terms.

#### 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 center 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 center heights and the sprung center 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 centers that the vehicle rolls around during cornering. The distance from this axis to the sprung center 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 can be thought of as the centripetal force pushing diagonally upward from the tire contact patch into the suspension roll center. The front jacking force is calculated by taking the front sprung weight times the G-force times the front roll center height divided by the front track width. The rear is calculated the same way except at the rear.

### 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. (See Triumph TR3B.)

### Damping

Damping (not to be confused with dampening) 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

See dependent and independent below.

Camber changes with wheel travel and with body roll. A tire wears and brakes best at -1 to -2 degrees of camber from vertical. Depending on the tire, it may hold the road best at a slightly different angle. Small changes in camber, front and rear, are used to tune handling.

### Roll center height

This is important to body roll and to front to rear roll moment distribution. However, the roll moment distribution in most cars is set more by the antiroll bars than the RCH. It may affect the tendency to roll over.

### Instant center

A tire's force vector points from the contact patch of the tire through a point referred to as the "instant center". This imaginary point is the effective geometric point at which the suspension force vectors are transmitted to the chassis. Another way of looking at this is to imagine each suspension control arm mounted only at the frame. The axis that the arm rotates around creates an imaginary line running through the vehicle. Forces, as far as suspension geomentry are concerned, are transmitted either along this axis (usually front to rear) or through this axis at a right angle (usually right to left and intersects the ball joint). When you intersect the force lines of the upper and lower control arms, where they cross is the Instant Center. The Instant Centers when viewed from the front or side may not seem to have much of a relation to each other until you imagine the points in three dimensions. Sometimes the Instant Center is at ground level or at a distant point due to parallel control arms.

The instant center can also be thought of as having the effect of converting multilink suspension into a single control arm which pivots at the Instant Center. This is only true at a given suspension deflection, because an unequal length, multi-link system has an instant center that moves as the suspension is deflected.

### 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 center of gravity. Consider anti-dive first. Locate the front instant centers of the suspension from the vehicle's side view. Draw a line fron the tire contact patch through the instant center, this is the tire force vector. Now draw a line straight down from the vehicle's center of gravity. The anti-dive is the ratio between the height of where the tire force vector crosses the center 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 center 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 raise 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 leaf spring rear 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 suspensions use 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:

### Conventional passive, semi-active/active, and interconnected suspensions

Traditional springs and dampers are referred to as passive suspensions. If the suspension is externally controlled then it is a semi-active or active suspension.

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.

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.

Fully active suspension systems use electronic monitoring of vehicle conditions, coupled with the means to impact vehicle suspension and behavior 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, ie solenoids, in place of hydraulic or pneumatic actuators that have generally been used up until recently. The most advanced suspension system is Active Body Control, introduced in 1999 on the top-of-the-line Mercedes-Benz CL-Class.

With the help of control system, various semi-active/active suspensions could 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 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.

### 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.

## Suspension types

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). Di-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 anti-roll 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.

• Trailing arms
• Panhard rod
• leaf springs used for location (transverse or longitudinal)
• Fully elliptical springs usually need supplementary location links and are no longer in common use
• 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)
• 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.

### Independent suspensions

The variety of independent systems is greater and includes:

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.

## Armoured fighting vehicle suspension

Military AFVs, including tanks, have specialized suspension requirements. They can weigh more than seventy tons and are required to move at high speed over very rough ground. Their suspension components must be protected from land mines and antitank weapons. Tracked AFVs can have as many as nine road wheels on each side. Many wheeled AFVs have six or eight wheels, to help them ride over rough and soft ground.

The earliest tanks of the Great War had fixed suspensions—with no movement whatsoever. This unsatisfactory situation was improved with leaf spring suspensions adopted from agricultural machinery, but even these had very limited travel.

Speeds increased due to more powerful engines, and the quality of ride had to be improved. In the 1930s, the Christie suspension was developed, which allowed the use of coil springs inside a vehicle's armoured hull, by redirecting the direction of travel using a bell crank. Horstmann suspension was a variation which used a combination of bell crank and exterior coil springs, in use from the 1930s to the 1990s.

By the Second World War the other common type was torsion-bar suspension, getting spring force from twisting bars inside the hull—this had less travel than the Christie type, but was significantly more compact, allowing the installation of larger turret rings and heavier main armament. The torsion-bar suspension, sometimes including shock absorbers, has been the dominant heavy armored vehicle suspension since the Second World War.