21/3/2000
Stefano Garbin, stefano_garbin@libero.it
Comparisons between simulations and reality
The aim of virtual prototyping is the development of a product entirely made with computers, using particular softwares and mathematical models to simulate reality.
We will mainly use the "Multibody System Analysis", i.e. kinematical and dynamical analysis of rigid bodies joined together with several kinds of constraints.
In this paper will be described the creation of a motorcycle's virtual model (particularly an Aprilia RSV 1000 ), and a driving control able to simulate a pilot and his bike on real pieces of road.
Among the various multibody codes existing, the choice was MSC Working Model 3D, for his power and flexibility.
The model is composed by several rigid bodies: front and rear wheel, rear fork, front unsprung components, front fork, frame and motor, pilot.
Mass and inertia properties and suspension characteristics are those declared by Aprilia; all of the unknown properties were measured here at the M.D.R.G.'s lab, or guessed looking at similar motorcycles.
The calculations of forces and torques acting between tyres and road's surface, and the control which has to keep the balance and drive the motorcycle-rider sysem along a fixed trajectory, were implemented in a new software called "Difficult Rider". This software was written in Visual Basic and works together with Working Model using OLE technology (Object Linking and Embedding).
Particularly at every integration step Working Model passes to Difficult Rider the positions and the linear and angular velocities of wheels, receiving back forces and torques acting between tyres and road's surface, and the steering torque to drive the bike.
The first fundamental part of Difficult Rider is surely the tyre's mathematical model.
Input data, received from Working Model, are the positions and the linear and angular velocities of wheels. By means of some coordinate changes we calculate the contact point, its absolute velocity (VP) and the same velocity without the rotational term (VT). At this point we can calculate longitudinal slip and sideslip angle (lambda).
The knowledge of these parameters is necessary because we use them to calculate, by means of Pacejka's "magic formula", longitudinal, lateral and vertical forces, and also self-aligning and overturning torques.
The second fundamental part of Difficult Rider is the control applied to the steer, which has to keep the balance of the system motorbike-rider and drive it along a particular path.
This kind of control is based on the "look ahead" technique: what does everybody do to drive a vehicle? We look ahead and guess in which position our bike could be with respect to the path to be followed, and then we apply a torque to the steer to reduce the previewed error.
The "look ahead" control behaves exctly in the same manner: starting from motorbike's actual configuration (position and velocities of center of mass) it calculates in which position with respect to the trajectory the bike should be after a certain time "t". Using this distance "d", its derivative, camber angle and camber speed it calculates steering torque with this formula:
The path to be followed is defined by a parametric function X= X(L), Y=Y(L), whereX and Y are the coordinates on the ground plane, L is the distance covered by the bike. To easily draw trajectories we have created a graphical tool called "track generator".
The virtual prototype was involved in several standard manoeuvres, such as constant radius curves and slaloms at various speeds; the same thing was done with the real motorcycle, carrying a telemetry system. A lot of kinematical and dynamical quantities were masured and recorded; in the following graphs you can see some of them.
This is a constant radius turn (radius = 8 m, speed = 7 m/s). In order, there is camber angle, steering angle and steering torque vs time; the blue line represents telemetry, the red one is the simulation.
The correspondance between telemetry and simulations is very good, so we may say that the model is quite accurate.
Steering torque has a negative value: this means for example that if the bike is turning right, we apply a leftwise torque.
In the next graphs you can see a slalom manoeuvre (pitch = 21 m, speed = 15 m/s): there are camber speed, yaw rate and steering torque vs time. The green line represents telemetry, the red one is the simulation with Dunlop tyres, the blue one with Metzeler tyres.
After the virtual model was validated, it was involved in some manoeuvres where we first kept constant camber angle, and then turning radius. The speed was increased from 5 m/s up to the limits of the tyres.
In the following graph, steering angle is plotted vs lateral acceleration.
A very interesting parameter to understand motorbike's handling characteristics is the ratio between steering torque and lateral acceleration vs speed. As you can see in the following graph, we obtained a particular family of curves which characterizes motorbike's geometric and inertial configuration.
By reducing caster angle of 5 degrees we obtain a new family of curves (the black ones), which is lower and left with respect to the original one. This means a worst handling and also a worst performance (because the new curves are shorter).
Looking at this work we may say that there is a good correspondance between simulations and reality, which was tested in several typical manoeuvres. We also developed a new control to simulate running on real portions of road, and we obtained interesting results about motorcycle's handling characteristics. Moreover a new sotware was developed ("Difficult Rider"... remember Peter Fonda and Dennis Hopper?): it is powerful and user-friendly.
Absolute reference: it is attached to the ground, and Z axis is perpendicular to road surface.
Relative reference: it is attached to the motorcycle; Z axis is perpendicular with respect to the bike, X axis is longitudinal (defines the running direction), Y axis is trasversal.
Camber angle : angle between Z axis, perpendicular to road surface, and motorcycle's simmetry plane (plane Z-X in relative reference).
Yaw angle : rotation with respect to Z axis of absolute reference.
Pitch angle: totation about Y axis of relative reference.
Steering torque : it is the torque applied to steer axis to simulate the action of our arms on steer.
Motorcycle dynamics: Official site of the Motorcycle Dynamics Research Group (M.D.R.G.), the only one in Italy and one of the few in the world really involved in motorcycle research.
Aprilia S.P.A: A famous italian motorcycle brand, which has collaborated to several research prjects of M.D.R.G.
MSC Working Model: One of the most famous software for dynamical analysis and now also for F.E.A.
MPEG slalom movie (2.35 Mb): Simulation of a slalom made with Working Model and Difficult Rider.
MPEG curve movie (2.63 Mb): Simulation of a constant radius turn by gradually increasing speed.
