3W Vehicle Stability-A Case Study

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Vehicle Dynamics

A Case study

3W – Vehicles Stability

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Vehicle Dynamics

Contents

3-Wheeler present issues1. Mechanical design aspect2. Stability during curves3. Road holding aspect

Simple visual analysis of 3-Wheeler stability1. Center of gravity position-Comparison 3W vs. 4W2. Accelerating or braking in a straight line

Logic behind the mathematics of safety marginsAnalysis and mathematics practice tests to perform

Modeling 'unicycle' of Valkenburgh-Klein-Szostak

Modeling using the criterion of Sliding Front Wheel Internal (GRAI)

Model for a 3W rear engine-rear drive

Mathematical development of safety margin calculations

Single front wheel 3-Wheelers

Single Front wheel vs. Front 2 wheels- 3W

Single rear wheel 3-Wheelers


Vehicle Dynamics

First component layout: 3-Wheelers with a single frontwheel, coming from a regular 2-Wheel motorcycle.

The rear may come from an old Volkswagen Beetle, ormay simply be a modified motorcycle rear end:

This group includes the off-road 3-Wheelers that are notsold anymore because of their rollover propensity:

Single front wheel 3-Wheelers


Vehicle Dynamics

Disadvantages:1. A single front wheel which should take most of the braking capacity2. Largest trend reversal because the braking increases the chances of rollover and is

always greater than the accelerations forward, because the three wheels canparticipate in braking

3. The engine drives the back passenger in a frontal collision4. The CG is behind the center of aerodynamic pressure, which is less stable at high

speed5. The full width of the vehicle behind the driver rather than before, which makes

less visibility of the width of the vehicle in tight traffic

Conclusion:This 3-Wheeler component layout with a single front wheel can tip over easily inmost applications and does not offer the best braking performance.It thus present little interest for general public usage.

3W-Single Front wheel


Vehicle Dynamics

Single rear wheel 3-Wheelers

• Third component layout: The 3-Wheelers with rear-engine and a single-rear driving wheel

• Their rear engine and single rear wheel assembly usually comes from aregular 2- Wheel motorcycle

• The 1977 Phantom was among the first well made ones


Vehicle Dynamics

Single Front wheel vs. Front 2-wheels 3W

• These single front wheel 3-Wheelers havelost popularity first precisely because theywould easily rollover when turning, asshown refer to last slide

• Also when braking while going straight,the weight is transferred to only one frontwheel instead of two, which is the case ofthe 3-W with two front wheels.

Rollover while turning-1F2R

Braking force Distribution

1F-2R

2F-1R


Vehicle Dynamics

3-Wheeler present Issues

During forward collisions, the engine at the rear pushesthe passengers in the back and tends to crush themagainst the obstacle

It's the same as for mid-engine sports car and Formula 1race cars

So like for these cars, the passenger protective structuremust be designed to hold back the rear engine in case offorward collisions, in order to insure their safety

These 3-Wheelers sit their passengers side-by-side in bucket seats and hold them backwith safety belts in a protective structure.

Also, these 3-Wheelers must be quite wide and low in order to present a safety marginagainst rollover

2 Front wheel-RE

Mechanical design aspects:


Vehicle Dynamics

Stability during curves:

The engine and transmission constitute a heavy group of components at the back of thevehicle, close to the rear wheel, that does nothing to avoid rollover in curves at highspeeds.

Worse, the vehicle may have to acceleratestrongly and turn at the same time, forinstance at a road crossing like to the right

In this case, weight is transferred to the reardue to the acceleration, which increases theweight on the rear wheel

With all this weight on the rear wheel, theacceleration may be even stronger so that theinterior front wheel can lift off the ground andcause a rollover in front of the incoming traffic 2 Front wheel-RE

Accelerating while turning


Vehicle Dynamics

This can happen while1. Accelerating in a highway entrance or exit.2. It can also happen while leaving a street intersection like at

the right.

3W (RE) spinning about single rear wheel

Font wheels moved further apart to increase wheel track

Second, if the passengers are moved forward, weight isremoved from the rear wheel. So the powerful motorcycleengine can spin this rear wheel and cause the vehicle to spinaround, even more so on wet pavement.

In order to increase stability in curves, the designer of such a 3-Wheeler may move the passengers forward to bring the center ofgravity closer to the two front wheels, that do the work to avoidrollover in curves.But this has two consequences:First, the two front wheels have to be moved farther apart to insert

these passengers, so the vehicle has to be very wide. This explainswhy such 3-Wheelers are typically as wide as a car

Road holding aspect:


Vehicle Dynamics

Study Case:Where the passenger of such a 3-W that spinnedaround when accelerating straight ahead:

In order to accelerate more rapidly, the drivershifted rapidly from first to second to third gear,without releasing the accelerator (Power shift).

When passing from 2nd to 3rd gear, the engineincreased its RPM rapidly so that when the clutchwas released, the engine inertia was able to spinthe rear wheel and spin the 3-Wheeler around.

In practice with this rear-engine (RE) and a single-rear driving wheel concept, designers have to accept an in-between compromise, both limiting ground traction when accelerating and limiting stability in curves.

The problem with this final solution is that both the risk of rolling over in curves and the risk of spinning around may not be eliminated.

3W (RE) spinning about single rear wheel


Vehicle Dynamics

This 3-Wheeler component layout with rear-engine and single-rear driving wheel:

Offers a great opportunity to drive a high performance vehicle offering Formula 1sensations.

But despite its performances in curves and accelerations, it also presents problems:

The chassis must be designed to hold back the rear engine in case of forwardcollisions

If not well designed, the vehicle may rollover when accelerating while turning

And the powerful engine can spin the rear wheel and cause the vehicle to spinaround

Conclusion:


Vehicle Dynamics

Simple visual analysis of 3-Wheeler stability

Thus, the centrifugal force tends to roll the vehicle overtowards the right, around an imaginary point (I)under the righttires, while the gravitational force holds the vehicle back toavoid rollover

We can thus easily understand that if the center of gravity height (h) is greater than the half-track (t)seen from the rear, the resulting force will be aligned over the imaginary point and will thus roll thevehicle over in a curve.

Rollover

point (I)

t

4-W Rear View

CG

Centrifugal Force (F)

Wh

Center of gravity position:Consider a 4-Wheeler as seen fromthe rear

The ratio of the center of gravity height(h) to this half-track(t) thus plays a crucial role indetermining the stability against rollover of a 4-Wheeler.Ideally, this center of gravity height should be low like for a sports car, in order to insure a

safety margin against rollover.

It's as though the centrifugal force and the gravitational forcecombined together into a resulting force exerted on the centerof gravity to turn it around this imaginary point.

If the vehicle is in a curve towards the left, for example, thencentrifugal force is exerted on the center of gravity of thevehicle occupants system, while the vehicle's weight exerts adownward gravitational force


Vehicle Dynamics

In the case of 3-Wheelers, another factor comes intoplay: As can be seen for a 4-Wheeler on the illustration at the

right, the 4-Wheeler rolls over around a linecorresponding to the imaginary point (deep blue) ofthe previous illustration.

But in the case of a 3-Wheeler, the vehicle rather rollsover around a line (blue) going from the unique wheelto one of the two symmetrical wheels.

We can immediately see that the green line between the center of gravity and therollover line is thus shorter than in the case of the 4-Wheeler, even though the CGheight, the length(wheelbase) and the track of the 3-Wheeler are the same as thoseof the 4-Wheeler.

The center of gravity height (red) is thus proportionately greater, which reduces thesafety margin against rollover in curves

Comparison 3W vs. 4W

4-W

3-W

(2F-1R)

Green Line is shorter in case of 3W

CG


Vehicle Dynamics

Moreover, a 3-Wheeler in a curve can also be subject to abraking or accelerating force that will combine with the lateralcentrifugal force, which may further increase chances of rollingover of this 3-Wheeler

For example in the case of the single-front-wheel 3-Wheeler,here above to the right, braking in a curve towards the left willincrease chances of rolling over this 3-Wheeler

So in the case of a 3-Wheeler:1.The CG height: should be low in relation to the half-track(t), like for a 4-W.2.But the CG position also has importance: The farther it is from the two symmetric wheels towards

the single wheel, the shorter is the distance from the center of gravity to the rollover line, whichreduces the safety margin against rollover of the 3-W compared to the 4-W.

- It seems more appropriate to consider overturning, flipping or tipping points or axes

- And to insure an adequate ratio between the vehicle-occupants center of gravity height and thehorizontal distance between the center of gravity and these points or axes, instead of a weightpercentage on the front wheels.

4-W

3-W


Vehicle Dynamics

Accelerating or braking in a straight line

When going straight, a 3-W may be accelerating or brakingthus:

- It may tip backward while accelerating, as in the case of atwo rear wheels 3-Wheeler where the center of gravity islocated too far back

- Or, while braking in the case of a two front wheels 3-Willustrated at the right, it may roll around the blue pointunder the front wheels and tip forward

Summary1. The 3-W’s CG must be low and close to the two symmetrical wheels , that are alone to avoid a

rollover in curves2. But this CG must not be too close to these two symmetric wheels, to avoid tipping backward or

forward.3. Basically, the CG must be located under a pyramid, as shown to the right in the case of a two-

front-wheel 3-Wheeler, to avoid rolling over sideways or tipping forward

1F-2R

2F-1R

CG1 F 2RFront

CG


Vehicle Dynamics

Logic behind the mathematics of safety margins

Specifically:1. The principles of physics and logic behind the mathematical margin of safety against

overturning

2. The mathematical development of these calculations margin of safety in the case of 3-W(2F1R) & Front-wheel-steering

3. The mathematical development in the case of 3W (2F1R) with rear engine,rear wheeldrive

4. Finally analyzing & summarising the results of calculations of margin of safety.

3-Wheeler to a single front wheel are excluded from modeling because they have many disadvantages stated earlier

Necessity for Math: 3-wheels may present a risk of reversal on curved roads. At a minimum, we must

therefore ensure they have a positive margin of safety against overturning

To check their margin of safety against overturning in different operating conditions


Vehicle Dynamics

A variety of mathematical analysis and practical tests have been developed to assessthe safety of vehicles on highways

The SAE (Society of Automotive Engineers) is full of articles on these tests and analysis

Mathematical analysis:1. Determining position of center of gravity2. Margin of safety against overturning3. Dynamic analysis including thousands of vehicle parameters4. Dynamic analysis of vehicle collisions. Practice tests5. Constant radius circle6. Lane change (Emergency lane change)7. Dropped from the steering wheel-steering (Free return ability)8. Releasing the accelerator (Dropped throttle)9. Braking distances

However, since the 3-Wheelers with particular risk of reversal, it is necessary to ensurebefore any other tests or analysis, a 3-Wheels to provides security against overturning

Analysis and mathematics practice tests to perform


Vehicle Dynamics

For stability of 3-Wheelers against overturning

Essentially, this analysis is to:Step 1: Calculate the capacity of tires which generates longitudinal acceleration (Ax /g) and lateral(Ay/g)s applying it to the center of gravity of 3-Wheeler

Step 2: Calculate the limits of longitudinal accelerations (Ax/g) and lateral (Ay/g) in the center ofgravity, beyond which it is a reversal of the vehicle

Step 3: Then ensure that the limits where there is a reversal beyond the capacity of the tires, so thatthe tires slide before the vehicle overturned.

Several authors consider that the coefficients of friction in longitudinal &lateral as Cfy & Cfx for tire against the ground, conform to a law 'elliptical'grip after the right figure

According to "Race Car Vehicle Dynamics," William F. Millikan, Douglas L.Millikan, SAE International, SAE R-146, 1995: Millikan, SAE International

Modeling the capacity of tires


Vehicle Dynamics

Consider just the three wheels of a 3-Wheeler one ortwo front wheels, act according to their ability i.e.‘elliptical’

These tires can therefore generate longitudinalacceleration Ax/g (acceleration or braking) and lateralAy/g (centrifugal / centripetal) from the center ofgravity.

Thus, it is as if these 3-wheels were replaced by a singlewheel and were regarded as a 'unicycle' shown in thirdfigure.

This assumption is valid if the three wheels to participate ideally longitudinal acceleration Ax/g andlateral Ay/g in the center of gravity, as is the case when analyzing the combined lateral accelerationin longitudinal braking, since the three wheels can participate in these accelerations anddecelerations.

(Ax/g)-Longitudinal acceleration

(Ay/g)-Lateral acceleration

If the traction at the front only, or is the back only (RWD). We can not use this assumption of ellipticboundary applied to all three wheels.

Modeling 'unicycle' of Valkenburgh-Klein-Szostak-For Tyres


Vehicle Dynamics

If a 3-W with front wheel-drive guidelines before accelerating at the sametime it rotates clockwise as shown at right, the left front wheel house tothe curve will be reduced due to transfer weight to the front wheel Rightoutside the curve (due to lateral acceleration) and because of weighttransfer to the rear wheel (due to longitudinal acceleration)

So even before the 3 wheels can be reversed, the left front wheel house atthe curve may be too lightweight to withstand high accelerations, whichwill reduce the chances of reversing the 3-W

The margin of safety against overturning of this 3-Wheeler will be higher thanprojected in the modeling of type unicycle of Valkenburgh-Klein-k Szostaabove.

The rear wheel, will not slip as it gets proportionately more weight becausethe rear wheel, will not slip as it 'gets' proportionately more weight becausethe weight transfered to back and it does not participate in the forwardacceleration of the vehicle.

3W(FWD) taking curve while accelerating

Modeling using the criterion of Sliding Front Wheel Internal (GRAI)


Vehicle Dynamics

Model for a 3W rear engine-rear drive

There can not be any slippage Front Wheel internal, which can limit the risk of overturning.

In contrast to these 3-wheel, transferring weight over the rear wheelincreases the propulsive force generated by the wheel back.

In this case, the left front wheel inside the curve may rise and cause areversal in front of vehicles that are coming in the opposite direction.

We can attempt to move the center of gravity closer to the frontwheels to reduce the weight on the rear wheel (the size of the ellipsein front or rear of the rear wheel). This reduces the risk of excessivelongitudinal acceleration and the risk of reversal in acceleration

But if the traction on the back tire is reduced, a very powerful engine of conventional two-wheel motorcycle is very powerful enough to skid the rear wheel not only on wet, but even on dry pavement.


Vehicle DynamicsMathematical development of safety margin calculations-For Vehicle

Curve (Ay/g) max as a function of (Ax/g), beyond which

there is a reversal: Consider the illustration shown in the figure:

Fx- Longitudinal Component of force acting on CG Fy-Lateral Component of force acting on CG (c)Ax-Longitudinal AccelerationAy-Lateral Acceleration

Fx=(W/g)*Ax Fy=(W/g)*Ay

F = Fx*sin λ + Fy*cos λ (F-Rollover Force about axis AB)

Sinλ = (t/2h) ; cosλ=(L/h) also sinλ=*c/(L-x)+ ……(by geom.)

Hence , F = (W/g)*(Ax)(t/2h)+(W/g)*(Ay)*(L/h)Balancing moments about CG,

W c= F z …. (where z-height of CG from ground)Solving this we get

L-wheelbaset- trackwidth

x- CG locn from front wheel centreλ- angle CBD

W- Weight of the vehicle (N)

(Ay/g) L + (Ax/g) (t/2) = [(L-x)/z] (t/2)

3W Vehicle Stability-A Case Study

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