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On the structural vibrations of bicycles: influence of materials and construction technology on the modal properties
No full textStructural vibrations of bicycles and bicycle components have drawn the interest of research-ers and designers since many years, mainly because they have a large influence on rider com-fort. For the improvement of comfort in-plane vibrations (with displacements in the sym-metry plane of the bicycle) are the most important and sometimes in plane modes have been studied. In recent years also the out-of-plane structural modes of vibration have been considered, because the cyclists’ experience and recent researches show that they may interfere with the typical modes of vibration of the vehicle in motion (capsize, weave and wobble) that determine stability and safety. In this paper the modal analysis approach is used for identifying the out-of-plane modes of some bicycles with similar geometric properties: a utility bicycle with steel frame, a sport bicycle with Ergal frame and two sport bicycles in carbon. The tests are carried out with hammer excitation. The results show that in the range 10-125 Hz all the tested bicycles have some typical modes (e.g.: torsion mode, frame bending). The dependence of the natural frequencies and modal dampings of the typical modes on the material and construction technology is analyzed and discussed. The new modes that sometimes appear when the structural properties of frame and fork are modified are presented and analyzed. Finally, the possible influence of the identified structural modes on bicycle stability is discussed
Identification and improvement of the dynamic properties of the components of two-wheeled vehicles
Full text linkSingle track vehicles dynamic is a very complex topic that involves many different branches of the scientific knowledge, such as vibration mechanics, stability and control, materials science and biomechanics. Although the first studies on the stability of a single track vehicle were carried out at the end of the XIX century, the technological progress that has improved the properties of the employed materials and the craving for better performances oblige the scientific world to an everlasting research activity, carried out both on whole vehicles and on single components.
This Ph. D. thesis summarizes the research activities carried out at the Motorcycle Dynamics Research Group of the University of Padova and describes the tested mechanical components, the testing equipments, the experimental data, the elaboration criteria and the final results obtained after a three years work.
The experimental methodologies employed in order to carry out the research activities are presented in the first chapter. Both the hardware and the software of each experimental bench will be described. In addition, the theoretical principles on which the testing rigs are based and the principles with which it processes the output of the measuring sensors will be illustrated.
Subsequent chapters shift the focus on the results obtained on the various analyzed components. The second chapter presents the results of the tests carried out on motorcycles frames , with or without engine; the third chapter describes the results of the measurements made on motorcycles swingarms; the fourth chapter describes the results of tests performed on motorcycle front forks; the fifth chapter presents the results of tests conducted on front and rear motorcycle and scooter tires; shifting the attention to another type of two-wheeled vehicle, the sixth chapter presents the results of the tests carried out on bicycles and bicycle components. Finally, the seventh chapter describes the results of measurements conducted on tires typically used for wheelchairs
The twist axis of frames with particular application to motorcycles
No full textThe static and dynamic properties of the frame and the front fork of a single track vehicle play a critical role from the
point of view of vehicle stability. A turning point in the study of motorcycle stability was established by the introduction
of lumped stiffness elements to characterize the critical compliances of the motorcycle elements, this approach being still
in use with advanced multibody codes. Nonetheless, up to now very few scientific studies have been carried out to
identify the parameters that account for the stiffness and damping properties of motorcycle front forks and frames. This
work addresses the problem of identifying the parameters needed for developing lumped element models of motorcycles
from experimental results. Two motorcycle frames are studied performing static, dynamic, and modal tests by means of a
specific testing equipment. The frames have been tested in two different conditions: fixing them at the steering head or at
the swing-arm pivot.
In the first section of the paper a general definition of the twist axis, based on the concept of ‘‘Mozzi’’ or instantaneous
screw axis, is presented. The twist axis is used for characterizing the deformation patterns of the tested frames. The
static twist axis is identified loading the frames at low rate by means of a servo-hydraulic actuator and measuring the
deformation of a reference plate by means of three laser sensors; the dynamic twist axis is identified exerting an
impulsive excitation and measuring the vibration of a reference plate by means of three accelerometers. In the last
section of the paper, experimental results obtained on motorcycle frames are shown. A method to identify the stiffness
properties of the frames from the measured twist axes is presented. Results obtained with the proposed method are in
good agreement with the ones presented in literature.
Out-of-plane vibrations and relaxation length of the tyres for single-track vehicles
No full textThe properties of tyres have a large influence on the stability of single-track vehicles. This paper focuses on the characterization
of the dynamic properties of tyres. In the first section of the paper, modal analysis of the tyres is presented.
Two motorcycle tyres and four scooter tyres are modally tested in order to measure the natural frequencies and the
damping coefficients of the first typical modes of vibration. Tests are carried out for seven different inflation pressures in
order to study how the pressure affects the properties of the tyres. The modal stiffnesses and the damping coefficients
are identified for each mode of vibration. The second section of the paper focuses on the characterization of the transient
properties of the tyres according to a ring model, in which the tyre tread is a ring connected to the rim with a series
of springs and dampers. A comparison between a first-order model, which takes into account only the modal stiffnesses,
and a second-order model, which considers also the self-aligning torques and the modal damping coefficients, is made. A
prediction of the relaxation length according to the first-order model is presented. The relaxation length is calculated
considering the term due to the measured contact patch, the terms due to the stiffnesses of the lateral and camber
modes and the residual stiffness term, which accounts for the modes with ring deflection. In the last section, the predicted
relaxation lengths are compared with those measured by means of a tester machine
Ranking of the importance of design parameters on the stability of a bicycle
No full textThis paper focuses on the open loop stability of a bicycle. The basic Whipple Carvallo Bicycle
Model (WCBM) is improved including the effect of front fork lateral compliance. Experimental
tests for the identification of fork properties are presented and discussed. Stability analysis is
carried out by means of a MATLAB numerical code. In order to rank design parameters
numerical calculations are carried out with the Design Of Experiments (DOE) approach
considering two levels of eight design parameters. The effect of design parameters on the autostability
range is analysed. Results show that an increased wheelbase decreases stability,
whereas increased trail and caster angle improve stability. The forward displacement of the
centre of mass of the rear frame increases stability as well
Identification of the critical stiffnesses of motorcycles in static and dynamic conditions
No full textStiffness of structural elements has a significant effect on
the dynamics of single-track vehicles, because it influences the
stability of the typical modes of this class of vehicles (weave
and wobble). Up to date no specific method for measuring the
critical stiffnesses of front fork, chassis and swingarm is
universally recognized. This measurement is difficult chiefly
for two reasons. When a structural element of a single-track
vehicle is loaded at one end it undergoes both bending and
torsion deformation and stiffness has to be decomposed into the
bending and torsion components. The stiffness characteristics
measured in static conditions may be rather different from the
ones measured in the presence of dynamic loads, owing to the
excitation of vibration modes. The concept of Mozzi or twist
axis is used in this paper for giving a lumped element
representation of stiffness of structural elements of single-track
vehicles. Then the differences between stiffness characteristics
measured in static and dynamic conditions are highlighted and
analyzed. Finally, a novel method is proposed for the
decomposition of stiffness, it makes use of the axes of the
bending and torsion modes. These axes are identified by means
of impulsive tests measuring the frequency response functions
of three points of a rigid plate that moves with the loaded end
of the structural element. Experimental results dealing with
swingarm, chassis and front fork are presented
The modal twist axis: A method for describing the dynamical characteristics of single track vehicles
No full textStatic and dynamic properties of single-track vehicles
components (such as frames, front forks and swing-arms) play
a fundamental role from the point of view of vehicle stability,
which is a key issue of single-track vehicles dynamics and
safety. Nowadays, the stability of a vehicle is studied by means
of multi-body codes, in which it is possible to implement
models of the tires and of the components of the vehicle.
Actually, the chassis and the forks of motorcycles are
mechanical systems with distributed mass and stiffness
properties, but in most simulation codes the elastic properties of
the structural elements are modeled with lumped stiffness and
damping elements. Very few research has been carried out on
the identification of the lumped elements, of their natural
frequencies and damping from laboratory tests.
In the first section of the paper, the concept of modal twist
axis is proposed to characterize the dynamic deformability of a
structural element. The twist axis is defined as the intersection
between the un-deformed plane of the structural element and
the plane tangent to the free end of the structural element in
deformed condition. If the identification of the twist axis is
carried out in resonance condition, the modal twist axis is
found. A method for measuring the modal twist axis position
and orientation is described. It is based on impulse excitation
by means of a modally tuned hammer and three accelerometers
which are used for defining the deformed plane.
In the second section of the paper, experimental results
obtained on two motorcycle frames are shown. In order to
know the modal shapes of the components at the measured
natural frequencies, modal analysis is carried out. A correlation
between the modal twist axis position and the mode of
vibration is shown and discussed. In order to study the
influence of the constraints on dynamic properties, the frames
are tested in two different constraint conditions: rear
constrained and front constrained.
The last section of the paper shows the experimental
results obtained by applying the proposed method to other
motorcycle components, such as a front fork and a frame with
the engine
Identification of the characteristics of motorcycle and scooter tyres in the presence of large variations in inflation pressure
No full textStability and safety of road vehicles are largely affected by tyre properties. Single-track vehicles are
characterised by weakly damped modes of vibration (weave and wobble) and therefore this phenomenon
is even more important. This article focuses on the study of both steady-state and transient
properties of motorcycle and scooter tyres in the presence of very low and very high inflation pressures.
The steady-state properties are defined as lateral forces (side-slip and camber forces) and yaw
torques (self-aligning and twisting). The transient properties are described in terms of relaxation
length, which represents the distance needed to reach a certain percentage of the steady-state value
of the tyre force. Experimental tests are carried out on a specific rotating disk machine. Three sets
of tyres are analysed. Steady-state properties are measured by increasing step by step the values of
camber and side-slip angles. Transient properties are studied carrying out tests with harmonic sideslip
excitation and measuring the phase lag between the excitation (input) and the tyre force (output).
Experimental results show important variations in tyre properties with inflation pressure with general
trends of all the tested tyres and particular features related to the tyre’s geometry. After the analysis
and discussion of experimental results, the measured data are fitted by means of a specific version
of the Magic Formula. The dependence of the Magic Formula’s coefficients on inflation pressure is
analysed and interpolation curves are given
Experimental and numerical investigation on the motorcycle front frame flexibility and its effect on stability
No full textIt is well known that front fork flexibility may have a significant effect on motorcycle stability. This work addresses the problem of developing lumped element models of the front fork from experimental results. The front forks of an enduro motorcycle and of a super sport motorcycle are characterized performing static, dynamic and modal tests by means of specific testing equipment. The concept of wheel twisting axis is proposed to characterize static and dynamic deformability of the front fork. Modal analysis results show the presence of two important modes of vibration of the front assembly in the low frequency range: the lateral mode and the longitudinal mode. Different lumped models are discussed and a new model that takes into account information obtained from static and dynamic tests is proposed. Simulations are carried out by means of a multibody code and show the effect of the front assembly deformability on the weave and wobble vibration modes
THE EFFECT OF FRONT FORK COMPLIANCE ON THE STABILITY OF BICYCLES
No full textIn this paper the effect of front fork compliance on
uncontrolled bicycle stability is analyzed. First the benchmark
model of a bicycle is improved to take into account either
torsion compliance or bending compliance of front fork, a
lumped element approach is adopted introducing additional
joints restrained by rotational springs and dampers. Two models
having three degrees of freedom are developed and
implemented in MATLAB codes to perform stability analysis.
Then series of experimental tests are carried out on an
advanced carbon fork and a standard steel fork, the modal
analysis approach is adopted. Experimental methods and results
are presented and discussed. A specific method is developed for
identifying the stiffness and damping properties from the
bending and torsion modes of the forks. Results obtained with
the proposed method agree with data presented in literature.
Finally, the identified stiffness and damping parameters are
implemented in the simulation codes and some numerical
simulations are carried out. Results presented in the paper show
a small influence of torsion compliance on stability and a large
influence of bending compliance on high speed stability
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