Fig. 1. An example of a racing motorcycle at full acceleration; the 2D model includes the rear suspension and the actuator simulating the chain transmission, between the engine and the rear wheel.
V. Cossalter, R. Berritta
Department of Mechanical Engineering - University of Padova
www.aprilia.com
www.lista.it
5th International conference "High-tech cars and engines", Modena,
Italy, june 3rd-4th, 1999
Sommario
Il ricorso ai codici di calcolo, cosiddetti "multi-body", consente di realizzare con precisione e con completezza l’analisi dinamica del comportamento dei veicoli su strada tramite la simulazione al calcolatore.
In questo lavoro vengono presentate delle simulazioni sviluppate con il codice Working Model che riguardano alcuni aspetti connessi alla sicurezza del motociclo.
In particolare viene studiato il comportamento del veicolo in fase di accelerazione e la dipendenza dell’impennamento del veicolo dall’assetto della sospensione posteriore e dal sistema di trasmissione del moto.
Vengono inoltre simulate due modalità di caduta in curva; la caduta tipo low-side dovuta allo scivolamento laterale della ruota posteriore, e la caduta, tipo high side, che si verifica quando la ruota posteriore perde prima aderenza per poi riacquistarla improvvisamente, con l’effetto di sbalzare in alto il pilota.
Abstract
The use of the so-called "multi-body" approach has allowed significant steps towards improving the precision and thoroughness of the dynamical analysis of vehicle behaviour on the road.
In this paper a unique analysis is made of the emergency manouvres of a two wheeled vehicle by means of MSC Working Model commercial simulation software by MSC Working Knowledge. Innovative plug-in and original Visual Basic routines developed at Padua University were used to fully implement all the elements relevant to vehicle dynamics, as the tyre and the driver's movements while driving the vehicle. This analysis can be done without loosing the possibility of interacting with model during the calculation and without increasing the overall computational time.
The behaviour of the vehicle during acceleration is studied. In particular, the dependence of the behaviour on the rear suspension arrangement is highlighted.
Low side and high side falls, while making a turn, are simulated. In particular, the high side phenomena, which happens when the rear tyre looses contact and suddenly get it back again, is explained.
Introduction
The dynamic analysis of a motorcycle is very complex due to its own instability, especially at low speed: without the rider's control, a motorcycle can fall not only when the motorcycle is stopping but also when it is running in straight uniform motion [ 1] .
Motorcycle multi-body analysis makes possible to simulate dynamic behaviour in situations taken to the limits, which are extremely dangerous for the drivers. Simulations are used to test the influence of a vehicle's geometry, mass distribution, tyre properties and various kinds of suspensions and steering mechanism on vehicle safety.
Multi-body System Analysis codes (MSA) have an increasing importance in testing the performances of a virtual prototype, that is to say not only estimating but also optimising the characteristics of a vehicle before building even the first actual prototype.
Therefore, it is possible to reduce the development costs and the time to market by figuring out all possible design solutions at the early design phase.
MSC Working Model motorcycle model
The MSC Working Model 2D Code [ 2] makes possible to analyse motorcycle plane dynamics during acceleration and braking situations on smooth or coarse roads. 2D modelling is very accurate as it takes into account engine torque, damper properties, tyre characteristics, vertical loads, etc.
Fig. 1. An example of a racing motorcycle at full acceleration; the 2D model includes the rear suspension and the actuator simulating the chain transmission, between the engine and the rear wheel.
In order to have a full three-dimensional modelling, it is necessary to use the more complex 3D simulation codes. The MSC Working Model Motion code can perform full three-dimensional multi-body simulations [ 3] . Due to a motorcycle's instability, a rider control is needed when driving in all the required manoeuvres. A mathematical model of the motorcycle tyre is also necessary because, due to the high roll angles reached by turning motorcycles, its behaviour is rather different from the automotive tyre. The tyre model developed is made with an external and additional Visual Basic code that calculates the forces and torques acting on each tyre.
The reaction of the road surface on the tyre is represented by three forces (vertical load, longitudinal and lateral forces), acting at the geometric contact point, and by three torques (overturning, rolling resistance and yaw torques), acting along the three independent axes.
These torques depend only on tyre deformation and on the asymmetric distribution of the contact stresses on the contact area. In this way, the effect of geometry is separated from the effect of stress distribution on the contact patch [ 4,5] .
Forces and torques are calculated using the Visual Basic external code that, thanks to experimental data, provides correct values depending on tyre orientation, loads and velocity. At each integration step these forces and torques are transferred to the multi-body software, Working Model, for time domain integration.
Fig. 2 and 3 show 3D examples of racing motorcycles set up for MSC Working Model Motion 3D simulations.
Fig. 2. MSC Working Model Motion interface with motorcycle model.
Fig. 3. The motorcycle model.
Three simulation examples
Case 1. Two dimensional analysis of motorcycle behaviour during acceleration
One of the most important aspects of motorcycle dynamic behaviour during its acceleration phase is the wheeling phenomenon which takes place when the driving force reaches a certain limit.
This common behaviour depends not only on the engine torque, but also on the rear suspension geometry and on the arrangement of the transmission between the engine and the rear wheel.
We will now consider three kinds of motorcycles and their different behaviours:
Chain transmission
With reference to Fig. 4, the intersection at point A is between the upper chain branch and the line passing through the tyre centre and the swinging arm pivot.
The line linking the rear wheel contact point Pr with the previously described point A is called chain force line; the angle between this line and the road plane is called chain force angle s.
The resultant force (Fr) of the load transfer force and the driving force (applied at the contact point of the tyre) with the plane road forms an angle called load transfer angle t.
The line along resultant Fr is called the load transfer line.
Fig. 4. Equilibrium at the swinging arm, the chain force line and the load transfer line.
The chain force ratio  is defined as the ratio between the load transfer torque and the torque generated by the sum of the chain force and the driving force; it depends on the rear suspension geometry and is equal to:
The chain force ratio depends on:
Three cases are possible:
Cardan shaft trasmission
With reference to a Cardan shaft transmission, the chain force ratio has a different formula:
This ratio is expressed as a function of the geometric characteristics of the suspension and also as a ratio between the tangent of the load transfer angle and the tangent of a virtual chain force angle. It corresponds to a straight line passing through the contact point Pr and the swinging arm pivot A, as shown in Fig. 5.
Fig. 5. Arm equilibrium with Cardan shaft transmission.
Load transfer angle t, with a Cardan shaft transmission, is generally smaller than angle s, therefore ratio R is smaller than one: the suspension is always extended during the driving phase.
Ratios about the unitary value are attainable by adopting long forks.
Four-bar linkage suspension with Cardan shaft transmission
As shown in Fig. 6, ratio R can be expressed as a function of the tangents of load transfer angle t and virtual chain force angle s. This angle is defined by the straight line passing through the instant centre of the connecting rod (point A) and the contact point of the rear wheel.
Fig. 6. Motorcycle equilibrium with four-bar linkage.
Motorcycle behaviour during acceleration
We will now consider three motorcycles equipped with different rear suspension (supposing that they have equal inertial and geometric characteristics) and subjected to the same driving force. We will investigate their behaviour during acceleration.
In the initial condition, we suppose that the motorcycles speed is 100 km/h; then the engine increases the torque transmitted to the rear wheel; the wheel accelerates and transfers the driving force to the road, by means of the longitudinal slip between the tyre and road surface.
Fig. 7. Motorcycles with different kinds of rear suspensions.
With regards to the motorcycles with the traditional rear swinging arm and chain transmission, three different vehicles with three different chain force ratios are considered:
High ratio values improve the rear suspension compression during the driving phase and reduce the wheeling phenomenon, as Fig. 8 shows, in which the vertical displacement of the handlebar is represented.
On the other hand, chain force ratios lower than one improve the wheeling phenomenon and suspension extension.
The figure shows that when R =1 and R =1.3 the front tyre wheels up and after 0.8 -1 s it falls down, while when R =0.7, the motorcycle is always wheeling up.
Fig. 8. Motorcycle wheeling up at various chain force ratios.
Fig. 9. Motorcycles wheeling up with Cardan shaft transmission.
Fig. 9 deals with a motorcycle equipped with a Cardan shaft transmission. It shows that in this case the front wheel raises so easily in the numerical simulation under investigation that without a torque control the motorcycle falls backwards. The wheeling up phenomenon depends on the rear fork length.
The four-bar linkage suspension with Cardan shaft transmission behaves more safely. In the case here considered the instant centre ( point A in fig. 6) is located about the top of the front wheel. Hence, the behaviour of this motorcycle is similar to the one of a motorcycle equipped with a traditional swinging arm with a high chain force ratio.
The BMW Paralever suspension is based on this kinematical concept.
Case 2. Three-dimensional analysis of motorcycle behaviour at "Low-side" fall
We will now consider a motorcycle braking the rear wheel while in a curve, as shown in Fig. 10 .
Frame 1 - Due to the braking longitudinal slip, the side force, necessary for maintaining equilibrium, is obtained with a slip angle greater than the one necessary in curve without the presence of the braking force.
Frame 2 - In these conditions it is quite possible for the side force produced by the rear wheel to be insufficient; consequently the rear wheel begins to slip.
Frame 3 - In order to follow the desired trajectory, the driver turns the handle-bar.
Frame 4 - With regards to the braking action, the driver can decide to stop or to continue acting on the rear wheel, in order to get more control of the motorcycle. If the braking action is constant the rear tire continues slipping to external side.
Frame 5 - The motorcycle tilts and falls laterally. In the fall motion the vehicle also drags the driver down. If the driver has not been hit by other vehicles, the fall could be not dangerous, in the sense that the motorcycle does not fall against the driver.
Fig. 11 shows an example of such analysis made with the multi-body code.
Fig. 10. 'Low-side' fall.
Fig. 11. Simulation of a 'low-side' fall.
Case 3. Three-dimensional analysis of motorcycle behaviour at "high-side" fall
The example in Fig. 12 shows the simulation of a ’high-side’ fall, which is closely related to vehicle stability and the interdependence between lateral and longitudinal tyre forces.
Frame l - in a curve the rider starts to brake the rear wheel, therefore the longitudinal braking force increases, as does the total friction force;
Frame 2 - the total friction force reaches the limit value, the rear wheel loses grip and the motorcycle moves outward;
Frame 3 - the rider makes a mistake, reducing the braking force suddenly, and the rear wheel takes grip again;
Frame 4 - the large side slip, which is still present, generates a lateral force impulse; the impulse torque around the centre of mass produced by the lateral force is not balanced by the torque caused by tyre load;
Frame 5 -The result is that the motorcycle is violently twisted and pushed upwards.
Fig. 12. 'High-side' falling action.
Fig. 13. Relationship between longitudinal slip and side slip.
Tyre behaviour during a ’high-side’ may be better understood by looking at Fig. l3, which shows the available lateral tyre force when a longitudinal tyre force is present.
In the left plot the parameter of the curves is the longitudinal slip k; in the right plot the parameter of the curves is the side slip angle l.
In both cases, the envelope of the families of curves is the friction ellipse.
The initial condition is represented by point A in which a lateral force is present and the side-slip angle is about 1.5°. When the driver starts to brake the rear wheel, the point moves in the horizontal direction and the side-slip angle increases in order to keep the lateral force constant in presence of an increasing longitudinal force. The loss of grip takes place at point B when the friction ellipse is reached; a large side-slip angle (of about 3°) is present. When the rider releases the brake, the rear wheel takes grip again; the new condition is represented by point C, where there is still a large side-slip angle but where the longitudinal slip is negligible. Hence, the lateral force impulse takes place, because the lateral force increases suddenly from the value of point B to the value of point C.
Fig. 14. A simulated ‘High-side’ sequence.
Conclusions
The results presented in this paper show that using dynamic simulation nowadays it is possible to predict motorcycle dynamic behaviour and to compare alternative design choices without carrying out a lot of expensive (and sometimes dangerous) experimental tests.
The simulations carried out by means of the 2D multi-body code clearly highlighted the effect of rear suspension design on the wheel-up phenomenon.
The 3D multi-body code made it possible to analyse the causes of low-side and high-side falls, which are relevant to vehicle safety.
References