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Motorcycle Dynamics (book)
No full textChapter 1: Kinematics of Motorcycles
The kinematic study of motorcycles is important, especially in relation to its effects on the dynamic behavior of motorcycles. Therefore, in this chapter, in addition to the kinematic study, some simple examples of the dynamics behavior of motorcycles are reported in order to show how kinematic peculiarities influence the directional stability and maneuverability of motorcycles.
Chapter 2: Motorcycle Tires
The tire is one of the motorcycle's most important components. Its fundamental characteristic is its deformability, which allows contact between the wheel and the road to be maintained even when small obstacles are found.
In addition to improving the comfort of the ride, the tire improves adherence, an important characteristic both for the transfer to the ground of large driving and braking forces, and for the generation of lateral forces. The performance of a motorcycle is a largely influenced by the characteristics of its tires. in order to understand their importance, one must consider that control of the vehicle's equilibrium and motion occurs through the generation of longitudinal and lateral forces that correspond with the contact patches of the tires with the road plane. The forces originate as a result of action taken by the rider through the steering mechanism, the accelerator and the braking system.
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Chapter 3: Rectilinear Motion of Motorcycles
The behavior of motorcycles during rectilinear motion depends on the longitudinal forces exchanged between the tires and the road, the aerodynamic forces originating during this motion, and the slope of the road plane. The study of rectilinear motion highlights certain dynamic aspects that are also important for safety, such as the motorcycle's behavior during braking with a possible forward overturning, and in acceleration, with possible wheeling.
Chapter 4: Steady Turning
During steady turning motion the motorcycle can have neutral, under or oversteering behavior. To maintain equilibrium the rider applies a torque to the handlebars that can be zero, positive, in the same direction of the handlebar rotation, or negative, i.e., applied in the direction opposite to the rotation of the handlebar. These characteristics are important and concur to define the sensation of the motorcycle's handling.
Chapter 5: In-Plane Dynamics
A motorcycle without suspension moving over irregular ground presents difficulties in steering because of the loss of wheel grip on the road plane, and because of rider discomfort. Small bumps on the ground are easily absorbed by the tires, but for adequate absorption of larger bumps, the motorcycle needs appropriate suspension.
A motorcycle with suspension, from a dynamics point of view, can be considered as a rigid body connected to the wheels with elastic systems (front and rear suspension). The rigid body constitutes the sprung mass (chassis, engine, steering head, rider), while the masses attached to the wheels are called unsprung masses.
Suspension had to satisfy the following three purposes:
* to allow the wheels to follow the profile of the road without transmitting excessive vibration to the rider. This purpose concerns rider comfort, that is the isolation of the sprung mass from the vibration generated by the interaction of the wheels with road irregularities;
* to ensure wheel grip on the road plane in order to transmit the required driving and braking forces;
* to ensure the desired trim of the vehicle under various operating conditions (accelerated motion, braking, entering and leaving turns).
The degree of required comfort varies according to the use of the vehicle. For example, in racing vehicles, comfort is less important than the motorcycle's capacity to keep the wheels in contact with the ground and to assume the desired trim. However, in other vehicles the suspension is expected to serve other purposes. For example, in cross-country vehicles the suspension serves to isolate the sprung mass from continuous impact generated by the vehicle jumps. For this reason, suspension in cross-country vehicles has greater wheel travel than in touring vehicles, and more so than in racing vehicles.
As to the trim, it much be stressed that it depends on the stiffness of the suspension. The load can be quite variable in motorcycles (one or two passengers, possibly with baggage); and further, load transfer between the front and rear wheel occurs in both acceleration and braking.
Chapter 6: Motorcycle Trim
In the previous chapters, the forces operating on the motorcycle were calculated: resistant forces, driving force and dynamic loads on the wheels, in different conditions of both stationary and non stationary motion, in acceleration and in braking. In this chapter, variations in the trim taken by the motorcycle in various driving conditions will be studied instead, and the importance covered by the chain force will be highlighted.
The term vehicle trim implies the geometric configuration that the motorcycle takes in different conditions in steady-unsteady motions, in acceleration and in braking.
As shown below, the motorcycle's trim depends on the stiffness characteristics of the front and rear wheel suspension, on the forces operating on the motorcycle, and on the inclination angle of the chain and the swinging arm.
Chapter 7: Motorcycle Vibration Modes and Stability
As everyone knows, the front and/or rear end of a motorcycle in motion can start to oscillate around the steering axis, especially if the wheels are unbalanced. This phenomenon is easy to observe experimentally, for example by gradually slowing down the motorcycle from a fairly high speed. Oscillations can be observed at certain speed if the front wheel is, statically or dynamically, out of balance. They reach their maximum amplitude and then decrease as speed decreases until they disappear completely. Rear-end oscillations can be observed when traveling over a transversal bump or by exciting the rear frame with an impulsive movement of the trunk. Front end oscillations exhibit their greatest amplitude at a higher speed than rear-end oscillations do. At a low speed it can also be easily observed that the motorcycle tends to fall over sideways, regardless of what the rider does. These experimental observations of motorcycle dynamics who that there are three major modes:
* capsize, a non oscillation mode used and controlled by the rider;
* weave, an oscillation of the entire motorcycle, but mainly the rear end;
* wobble, an oscillation of the front end around the steering axis which does not involve the rear end in any significant way.
In this chapter, firstly we will study these modes using simplified models and later on the in-plane and out of plane modes will be studies by means of an eleven degree of freedom models.
Chapter 8: Motorcycles Maneuverability and Handling
A motorcycle's dynamic properties are described using terms like maneuverability, handling and stability. Maneuverability and handling describe the motorcycle's ability to execute complicated maneuvers, and how difficult it is for the rider to perform them. Stability, on the other hand, means a motorcycle's ability to maintain equilibrium in response to outside disturbances like an uneven road surface or gusts of wind
Sensore per la misurazione della forza di smorzamento in un ammortizzatore motociclistico
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A Motorcycle Multi-Body Model for Real Time Simulations Based on the Natural Coordinates Approach
No full textThis paper presents an eleven degrees of freedom, non-linear, multi-body dynamics model of a motorcycle. Front and rear chassis, steering system, suspensions and tires are the main features of the model. An original tire model was developed, which takes into account the geometric shape of tires and the elastic deformation of tire carcasses. This model also describes the dynamic behavior of tires in a way similar to relaxation models. Equations of motion stem from the natural coordinates approach. First, each rigid body is described with a set of fully cartesian coordinates. Then, links between the bodies are obtained by means of algebraic equations. This makes it possible to obtain simple equations of motion, even though the coordinates are redundant. The model was implemented in a Fortran code, named FastBike. In order to test the code, both simulated and real slalom and lane change maneuvers were carried out. A very good agreement between the numerical simulations and experimental test was found. The comparison of FastBike's performance with those of some commercial software shows that first is much faster than others. In particular, real time simulations can be carried out using FastBike and it can be employed on a motorcycle simulator
The relation between contact patch geometry and the mechanical properties of motorcycle tyres
No full textThe mechanical properties of motorcycle and scooter tyres have a large influence on the handling
and stability of these vehicles. When a two-wheeled vehicle moves along a curvilinear path, there
are large camber angles (up to 50◦); hence, tyres have a curved cross-section and the contact patch
moves and changes its shape when the roll and steer angles are modified by the rider. This paper
describes experimental research aimed at studying the influence of the camber angle, vertical load
and inflation pressure on the shape of the contact patch and the forces and moments of the tyres. The
experimental tests were carried out by means of a rotating-disc machine. The contact patches were
measured by making use of a pressure-indicating film. The camber force and twisting torque were
related to the vertical load and inflation pressure through the dimensions of the contact patch. Newbestfitting
equations were developed starting from the brush model. Many experimental results dealing
with front and rear tyres are presented and the merits and limitations of the best-fitting equations are
discussed
Elaboration and quantitative assessment of manoeuvrability for motorcycle lane change
No full textThe desire to quantitatively assess vehicle manoeuvrability and handling has led to the development of various expressions, or metrics, which typically relate system input to system output. With regard to motorcycle manoeuvrability, a notable example of such a measure, or metric, is the Koch index [Koch, J., 1978, Experimentelle und Analytische Untersuchungen des Motorraad-Fahrer Systems. Dissertation, Berlin.]. This article describes the development of a new metric applied to lane change (LC) tests and coined 'LC roll index'. This metric takes into account the peak-to-peak values of the rider-input steering torque divided by the peak-to-peak roll rate response of the vehicle and normalizes this quantity by the forward velocity. In addition to this new metric, an analytical expression is developed, which in many cases summarizes a motorcycle's LC performance in a single, terse, analytical term. Experimental results are presented for three vastly different motorcycles: a scooter, a street, and a touring motorcycle performing variations of the LC manoeuvre. Numerous test runs for each vehicle are analysed and the results are summarized along with those presented in the recent literature. Finally, simulation results are presented to highlight the correlation between the proposed indices and handling
Instantaneous screw axis of two-wheeled vehicles in typical manoeuvres
No full textThe motion of the rear frame of a two-wheeled vehicle is characterized by the motion of the
instantaneous screw axis, which is also known as the Mozzi axis. The first objective of this study
is to analyse the evolution of the instantaneous screw axis during typical manoeuvres. The second is
to highlight that the analysis of the motion of the instantaneous screw axis gives useful information
about the manoeuvre and the riding technique. Entering in a curve and lane-change manoeuvres are
considered and both the experimental and numerical results are analysed
Model simulation - The latest dynamic simulation developments for motorcycle tires
No full textMotorcycle tires mechanics is rather different from car tires mechanics because motorcycle tires have toroidal-shaped cross sections and the contact area is smaller than car tires’ contact area. Moreover, in a curve motorcycle tires are always rolled and a significant part of tire forces is due to the presence of roll angle. Therefore, specific models of motorcycle tires are necessary.
In the first section of this paper the main features of motorcycle tire models that are used for multi-body simulation by the Motorcycle Dynamics Research Group of Padua University are described. The need for a detailed understanding of the elastic properties of tire carcass is highlighted.
Then, results of an experimental analysis of tire carcass elastic characteristics are shown and several models that are useful to understand tire carcass elastic behavior are presented. Finally, the stiffness parameters that define tire elastic behavior according to the proposed models are identified
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