Principles Of Interconnected Suspension

Part1: Modal Suspension Analysis

If there is one topic in racecar suspension engineering that stands out as the defining issue of the 1990s, it is the trend towards new ways of interconnecting individual wheel suspension systems. Hydraulic and mechanical 'third-spring' devices are the variations currently receiving greatest attention. There are a number of other possibilities, particularly since remote reservoir dampers have become so popular. Not only will designers have to become conversant with these possibilities, but rule-makers, setup specialists and drivers will also need to understand them. Fortunately, this need not be difficult. It does, however, require an appropriate conceptual framework.

The avenue to this conceptual framework is Modal Suspension Analysis. This approach involves looking at the entire four wheel suspension as a single system, and breaking down, or resolving, its motions into four fundamental modes.

These modes are roll, pitch, heave, and warp.

Any possible position or motion of the suspension system can be described as some number of inches (or millimetres) of roll, pitch, heave. and warp. Furthermore, the system will provide discrete wheel rates (or wheel rate curves or functions) in the different modes. All forms of non-rigid suspension interconnection - anti-roll bars, third spring units, Z-bars. and the various hydraulic, pneumatic and elastomeric equivalents - work by adding wheel rate in some modes, while leaving other modes unaffected. By examining these modal stiffening effects. we can understand and predict any interconnection's effect on vehicle behavior.

Table 1: Suspension Modes
	Right & Left Wheel Pairs	Front & Rear Wheel Pairs	Diagonal Wheel Pairs
Roll	Synchronous motion, in opposite directions	Oppositional motion, in same direction	Oppositional motion, in opposite front/rear directions
Pitch	Oppositional motion, in same direction	Synchronous motion, in opposite direction	Oppositional motion in same front/rear direction
Heave	Synchronous motion, in same direction	Synchronous motion, in same direction	Synchronous motion, in same direction
Warp	Oppositional motion, in opposite directions	Oppositional motion, in opposite directions	Synchronous motion, in opposite directions

Alternetively Click Here For Diagrams Of The Above

The Modes Defined

If we want to describe what an individual wheel suspension system does, the simplest thing we can say is that it lets the wheel go up and down relative to the body or sprung mass. That is, it compresses and extends. A really complete description would add camber change. toe change, lateral and longitudinal wheel movement, and so on. But fundamentally, what the suspension does is compress and extend.

Compression/extension is a single, bi-directional mode of movement. If we consider combinations of wheels, we can have combinations of compression and extension. A pair of wheels can compress or extend synchronously (same direction) or oppositionally (opposite directions). Any possible position or movement of that wheel pair can be described as some many inches (or millimetres) of oppositional and synchronous movement.

For example, if we have Sin of compression (from static ride height) on one wheel and 2in of compression on the other, we can express that as 1.5in of synchronous movement plus 0.5in of oppositional movement. If we have a four-wheeled car, we can pair those wheels in three possible ways: right and left pairs; front and rear pairs; diagonal pairs. These wheel pairs can move synchronously or oppositionally, in four possible combinations. Those four combinations define the four modes of suspension movement. Table 1 is a table of verbal definitions of the four modes, in terms of wheel pair movement. The panels on each page illustrate the modes pictorially. Some readers will recognise roll, pitch, and heave as terms describing body or sprung mass motions. Sprung mass motion, like suspension motion, is resolvable into modes. We need to understand these in order to deal with suspension movement, particularly since suspension roll, pitch, and heave are not the same as body roll, pitch and heave - although they are related.

Actually, there are six modes of sprung mass motion - three angular, three linear. Angular motion around a longitudinal axis is roll. Angular motion around a transverse axis is pitch. Angular motion around a vertical axis is yaw. Linear motion along a longitudinal axis is forward or backward travel. Linear motion along a transverse axis is sideslip. Linear motion along a vertical axis is heave. This terminology is far older than the automobile. It was invented centuries ago by sailors, to describe the motions of watercraft. We can use it to describe the motions of any object, as long as we can agree which end is the front, and which side is the top. Applying this conceptual framework to aircraft and cars was natural and inevitable.

Resolving suspension motion into modes involved a bit more thought, and happened later. It was not just a re-application of nautical and aeronautical dynamics; ships and aircraft do not have suspension systems. (Well, aircraft do, but only for takeoff and landing.)

According to the vehicle dynamics pioneer, Bill Milliken, the earliest reference to four mode suspension analysis appeared in a French engineering paper in the late 1930s. The concept did not attract widespread interest in the following decades, but it became vitally important when 'active' suspension appeared in the 1970s. An active suspension controls its four hydraulic rams with a single computer. An engineer programming such a computer obviously needs a way to analyse the suspension system as a whole, and determine appropriate compress/extend commands for the four corners. A fully active suspension uses sensors to read road contours, and accelerometers to read accelerations in three axes. From these inputs, the system derives modal suspension reactions needed to produce desired sprung mass behavior. It then sums these to determine desired wheel position, or position change, at each wheel at a particular instant. To illustrate how this modal summing works, suppose our suspension is in a condition of Sin of right roll. That means we have Sin of compression (from static position) on both right wheels, and Sin of extension on both left wheels. Note that this is how the suspension moves when the sprung mass rolls rightward, if the road surface is perfectly flat. Note also that we express the suspension roll in linear units, whereas body roll is measured in degrees. Now let's add 0.5in of forward pitch. We now have 0.5in compression at each front wheel, and 0.5in extension at each rear, added to the previous roll mode movements. So, we have 1.5in compression at the right front, 0.5in compression at the right rear, 1.5in extension at the left rear, and 0.5in extension at the left front.

If we add 0.5in of downward (or compressive) heave, and 0.1in left warp, we get 2.1in compression at the right front, O.9in compression at the right rear, O.9in extension at the left rear, and 0.10in extension at the left front. This combination might be found in a racecar entering a banked left turn, on the brakes. If the banking angle is of the magnitude normally seen on oval tracks, the car's sprung mass will actually roll left, even though the roll component of the suspension motion is to the right. This illustrates that sprung mass roll is not the same as suspension roll, and may not even be in the same direction. A similar distinction applies to pitch and heave. Here's one way to think of it: The track surface - actually, the four patches of it under the tyres 'moves' in roll, pitch, heave and warp as the racecar goes along it. The sprung mass moves in roll, pitch, and heave as it goes down the road. The suspension's motions make up the difference.

Note that the sprung mass does not have a warp mode. Actually, if the sprung mass twists, it does have a warp mode. And of course it does twist - but hopefully not very much, so we customarily think of it as rigid. We also ignore deflections of the tyres - alternatively, we include the tyres as part of the suspension . The absence of a sprung mass warp mode is important. It may be the key to the future advances in passive suspension technology, as we shall see.

Modal Effects in Passive Suspension

Most of us still work entirely with passive suspension. It doesn't do us much good to try to predict or control the motions of our suspension to the nearest millimetre, from instant to instant. We don't try to - although we may monitor its positions in detail with electronic data-acquisition, once we have it operating The value of modal analysis for us lies in predicting the stiffness of our suspension in various situations, so that we can understand the effects that different designs and setups will have on wheel loadings and roadholding. As most readers will be aware, we want soft suspensions to let the wheels follow road irregularities with minimum load change At the same time, we need stiff suspension, to control sprung mass attitude and position. And we need an appropriate distribution of stiffness to control relative wheel loadings and get the desired oversteer/understeer balance.

Other subtleties enter in, as well. We would like to have natural frequencies in pitch and heave that will help the car ride as level as possible over large and small disturbances If our racecar gets downforce from ground-effects we need to control ground clearance more tightly than we'd otherwise want to, particularly at the front. To generalise, though, for most applications we'll get the best combination of roadholding and sprung mass control with a suspension that is stiffest in roll, also fairly stiff in pitch, softer in heave, and very soft in warp. This is easy to ask for, but not so easy to deliver. The devices we call anti-roll bars, and all other non-rigid connections of wheel pairs, are tools we can use to get closer to the optimum. The simplest suspension, from the standpoint of modal wheel rate analysis, is a fourwheel independent system with no anti-roll bars or other interconnections - just a spring and a damper for each wheel. Such a system has the same wheel rate in all four modes. Early four-wheel independent suspensions were often built this way, and setups like this are still popular for street rods.

The problem with this approach is that we cannot control sprung mass roll adequately except by using very stiff springs. Also, the wheel rates we need for our desired over favourable relationship of natural frequencies in pitch and heave. There are instances where the simple fourspring chassis has a chance of working adequately. It helps if the car has a low centre of mass, a wide track, and tyres of modest grip. If the car is set up as low as possible for reasons of appearance, stiff springs may be required due to lack of fender and ground clearance. The setup may consequently have sufficient roll stiffness without further measures, especially if hard driving is not contemplated .

Simpler anatomically, but more complex in its wheel rate behavior, is a basic four-spring, two-beam-axle chassis. Beam axle suspensions invariably have a greater wheel-to-spring motion ratio in oppositional motion than in synchronous motion. Wheel rate varies inversely with the square of motion ratio. So the wheel rate in oppositional motion is substantially softer than in synchronous motion. This disparity increases as spring spacing becomes narrower, relative to track. A four-spring, beam axle car consequently is stiffer in pitch and heave than in roll and warp. its relatively high roll centres, and its immunity to wheel camber change with roll, allow it to corner better than we might expect. its soft warp rate helps it absorb 'one-wheel' bumps easily, and minimises torsional loads to the sprung structure. An interesting variation is the beam axle chassis with transverse torsion bars located outside the wheelbase. This layout, pioneered by Kurtis in Indycar racing, is still the norm in American sprint cars and midgets. These cars have their stiffest wheel rate in pitch. They are a bit softer in heave, and very soft in roll and warp, especially at the front. The roll centres are high - usually at axle height.

One often hears school-trained engineers express amazement that these beam-axle "dinosaurs" can go so fast on bumpy dirt tracks. No doubt big tyres, stout motors, big wings (when present), and light weight are significant contributors. But I also believe sprint car chassis work as well as they do because they're warp-soft. Beam axle chassis really do have inherent disadvantages. They produce too much lateral tyre scrub when the front or rear wheel pair moves oppositionally. Their unsprung mass inertia is too great, especially in synchronous motion at the rear. Warp-softness is their only major advantage over present-day independent suspension. The fact that beam-axle cars can run as well as they do suggests how significant this one advantage is, and logically leads us to wonder what we might achieve with a comparably warp-soft independent suspension.

With independent suspension, we cannot use high roll centres. To avoid inordinate tyre scrub and jacking effects, we must have the roll centres near ground level. We therefore need a fairly high wheel rate in roll. To obtain this, and also obtain a soft wheel rate in warp, we need to take a fresh look at non-rigid wheel pair interconnection. That will be our focus in Part 2 of this article.

Author Mark Ortiz is an independent racecar chassis consultant based in Wisconsin, USA. He specialises in setup coaching by telephone and can be reached on (1) 715 835 3292

 Part 2: Methods of Non Rigid Interconnection & Their Effects NEXT WEEK!