Frequency analysis of the flat plank tyre tester for validation of tyre

Frequency analysis of the flat
plank tyre tester for validation of
tyre transmissibility
J.J.Nieuwenhuijsen
DCT 2008.072
Bachelor’s thesis
Coaches:
Dr. Ir. I. Lopez
R.R.J.J. van Doorn
Technical University Eindhoven
Department Mechanical Engineering
Dynamics and Control Group
June 17, 2008
Summary
At the Eindhoven Technical University (TU/e) a model is developed to simulate the transmissibility of a specific tyre hence the need is born to validate
this model with measurements. Since no device is present at the TU/e which is
known to be usable for these measurements the question arose whether the flat
plank tyre tester is usable for these measurements since this tester is already in
use for stiffness and relaxation tests on tyres. The experiments which the flat
plank is used for are quasi static measurements but for transmissibility measurements frequency response experiments are required. The research this report
describes is done to find out whether the flat plank is usable for transmissibility
measurements.
The experiments carried out during this research had two aims, obtaining
the dynamics of the flat plank tyre tester and obtaining the transmissibility of
the tyre under investigation. The experiments concerning the first aim involve
(a) apply an impulse to the point on the flat plank axle where usually a tyre is
mounted, (b) mount the tyre of interest and apply an impulse at a wheelnut with
which the tyre is mounted and (c) repeat experiment (b) but in this case the
tyre is pressed against the road surface with a force of 2750N. The experiments
concerning the second aim involve excitation of the tyre circumference with a
chirp signal. This experiment was repeated with and without the tyre pressed
to the road surface with a force of 2750N.
The dynamics of the flat plank appear to be so rich of resonances that
it would be possible that the response as result of the transmissibility isn’t
distinguishable of the flat plank dynamics. The transmissibility experiments
confirm this prediction and show that the flat plank isn’t usable as a device to
perform transmissibility measurements.
2
Samenvatting
Aan de Technische Universiteit Eindhoven (TU/e) is een model ontwikkeld dat
de transmissibility van een specifieke autoband beschrijft. Omdat dit een nieuwe
ontwikkeling is is de behoefte ontstaan om dit model te valideren met metingen.
Op dit moment is er op de TU/e geen instrument beschikbaar om de transmissibility te meten, er is echter wel een instrument beschikbaar waarmee stijfheidsen relaxatiemetingen kunnen worden gedaan aan auto- en motorbanden. De
vraag is nu of deze flat plank tyre tester ook geschikt is om transmissibilitymetingen te doen. De experimenten waarvoor de flat plank nu gebruikt wordt
zijn quasi-stationair, terwijl voor metingen aan de transmissibility frequency response metingen nodig zijn. Het onderzoek dat dit verslag beschrijft is gedaan
om erachter te komen of de flat plank tyre tester geschikt is voor het meten van
de transmissibility van een autoband.
De experimenten die gedaan zijn gedurende dit onderzoek hadden twee doelen, het in kaart brengen van de flat plank en het meten van de transmissibility
voor de band waarvan een model is gemaakt. De experimenten met betrekking
tot het eerste doel houden in (a) impulsexcitatie van de meetas op het punt
waar normaal gesproken een band gemonteerd is, (b) montage van de band op
de meetas en impulsexcitatie op een wielmoer waarmee de band is gemonteerd
en (c) herhaling van experiment (b) maar nu met de band tegen het wegdek
gedrukt met een kracht van 2750N. De experimenten met betrekking tot het
tweede doel houden in dat het loopvlak van de band geëxciteerd wordt met een
chirp-signaal. Dit experiment werd herhaald met de band tegen het wegdek
gedrukt met een kracht van 2750N.
De dynamica van de flat plank is zo rijk aan resonanties dat het mogelijk kan
zijn dat de responsie ten gevolge van de transmissibility niet te onderscheiden
is van de dynamica van de flat plank. De experimenten met betrekking tot de
transmissibility bevestigen dit en laten zien dat de flat plank niet geschikt is
voor het meten van de transmissibility.
3
Contents
Summary
2
Samenvatting
3
1 Introduction
1.1 Background . . . . .
1.2 Goal . . . . . . . . .
1.3 Approach . . . . . .
1.4 Scope of this report
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2 Background
2.1 Model . . . . . . . . . . . . . . . .
2.1.1 Finite Elements . . . . . . .
2.1.2 Mode shapes . . . . . . . .
2.2 Simulations . . . . . . . . . . . . .
2.2.1 Effect of initial deformation
2.2.2 Effect of acoustic resonance
2.3 Experimental mode shapes . . . .
2.4 Transmissibility . . . . . . . . . . .
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3 Experiments
3.1 Description of the flat plank . . . . . . .
3.2 Experiments to carry out . . . . . . . .
3.2.1 Dynamics of the flat plank . . .
3.2.2 Validation of tyre transmissibility
3.3 Additional hardware . . . . . . . . . . .
3.3.1 System for data acquisition . . .
3.3.2 Other necessary hardware . . . .
3.3.3 Settings . . . . . . . . . . . . . .
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4 Results
4.1 Axle dynamics . . . . . . .
4.1.1 Influence of the tyre
4.1.2 Influence of load . .
4.2 Transmissibility . . . . . . .
4.2.1 Influence of load . .
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5 Conclusion and recommendations
29
5.1 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
5.2 Recommendations . . . . . . . . . . . . . . . . . . . . . . . . . . 29
A z-direction FRF
31
B Measured mode shapes
33
C Experiments
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C.1 List of equipement . . . . . . . . . . . . . . . . . . . . . . . . . . 34
C.2 SigLab settings . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34
C.3 Amplifier settings . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
D m-files
36
D.1 Plot shaker results . . . . . . . . . . . . . . . . . . . . . . . . . . 36
D.2 Plot hammer results, no tyre mounted . . . . . . . . . . . . . . . 38
D.3 Plot hammer results, with tyre mounted . . . . . . . . . . . . . . 40
Bibliography
43
5
Chapter 1
Introduction
1.1
Background
Noise generated by traffic is becoming a serious issue nowadays. Exterior noise
is disturbing for other road users and people living along the road while interior
noise influences the comfort experienced by the driver and passengers. Two
sources are responsible for the noise, the engine and the tyre/road contact. The
engine noise is dominant at lower speeds while the tyre/road noise is dominant
at higher speeds (breakpoint at about 30 km/h for passenger cars). The trend is
that tyre/road noise is getting more important because engine noise is reduced
and wider tyres are used. With the introduction of hybrid-electric propulsion
it is likely that the engine noise is reduced even further and thus the tyre/road
noise will become even more dominating [1].
Vibrational mechanisms occurring in the tyres with a frequency range of 50
to 500 Hz cause axle forces which are transduced by the suspension to the car
structure and there causing interior noise. An approach to reduce interior noise
is to reduce the vibrations at the source which means that the tyre transmissibility needs to be improved. This property relates the axle forces to the forces
in the tyre/road contact. Improvement of the transmissibility with respect to
interior noise asks for theoretical knowledge in the form of a model. Since tyres
are very complex products these days, they can be build out of dozens of materials and can consist of multiple layers, tyre models can get very complex but
still don’t represent the properties and thus the behavior of a tyre well enough.
At the Eindhoven Technical University (TU/e) research is done to improve the
quality of tyre models [1] and a model of tyre transmissibility is developed so
experimental data is needed for validation.
At the TU/e an instrument is already available to perform for example
relaxation and stiffness measurements on automotive tyres. This instrument
is the flat plank tyre tester which was transferred from the Delft Technical
University (TUD) to the TU/e in 2003 [4]. With this instrument it is possible
to apply known forces and known displacements to a tyre and measure the
resulting forces on the axle. The development of the new, more complicated
models, asks for frequency response measurements although experience on the
flat plank is gained with quasi-static measurements only. Therefore it isn’t sure
whether the flat plank is usable for frequency response measurements and thus
6
for validation of the new transmissibility models.
1.2
Goal
The goal of this report will be to investigate whether validation of frequency
response models of tyres regarding the transmissibility is possible on the flat
plank tyre tester. This goal is divided in two parts:
1. Obtaining the frequency response plot of the flat plank dynamics
2. Obtaining the tyre transmissibility associated with the tyre under investigation
The development of a model of the Yokohama 185/70 R14 88T tyre by
master thesis student R. van Doorn gives direct occasion to this research hence
this tyre will be the tyre under investigation.
1.3
Approach
To get insight in the flat plank dynamics it is necessary to obtain the frequency
response function (FRF) of the axle and to get insight in the influence of the
weight of a mounted tyre and of the stiffness induced by an applied load to this
FRF. Three experiments are carried out to obtain these results, all three involve
impulse excitation of the flat plank axle with a measuring hammer. The input
force of the hammer as well as the output force measured by the axle are logged
so a frequency response plot can be made. The first experiment involves impulse
excitation of the axle itself without anything mounted or loaded. For the second
and third experiment the tyre is mounted onto the flat plank axle. The second
experiments involves excitation of the axle while the tyre is unloaded. The third
experiment is the same as the second but with the tyre pressed against the road
surface with a load of 2750N.
To see whether the transmissibility can be obtained with the flat plank the
circumference of the tyre is excited with a shaker feeded with a chirp signal
while the tyre is mounted on the flat plank. The input force generated by the
shaker as well as the output force measured by the axle are logged again for
obtainment of a frequency response plot. This experiment is repeated with and
without an applied load of 2750N according to the simulations carried out in
[1].
If the flat plank is usable for validation of the tyre transmissibility, the
transmissibility resonances will be clearly visible in the frequency response plots
obtained with the shaker measurements. If the flat plank is unusable for these
kind of measurements mainly the dynamics of the flat plank itself will be visible
in the shaker measurement frequency response plots.
1.4
Scope of this report
This report is build up of five chapters. After this introduction the model developed by R. van Doorn is discussed in the second chapter, along with a discussion
of the validation of the modal analysis performed by J. Fioole. A description of
7
the flat plank with it’s current measurement capabilities can be found in chapter
three. The third chapter also describes the experiments which are carried out
and the extra hardware that is needed to perform the required measurements.
The fourth chapter lays out and discusses the results of the experiments and the
remaining chapter contains the conclusion and the recommendations for further
research. The appendices contain the results that are left out of the main text
for readability as well as the mode shapes obtained in [2], directives to repeat
the experiments and the m-files used to obtain the frequency response plots
from the measurement data.
8
Chapter 2
Background
2.1
Model
This section discusses the model developed by R. van Doorn. All the information, graphics and numbers in this section are extracted from [1], which is
his master thesis report. For a more detailed description about the model and
consideration that led to this model, the author refers to this report.
2.1.1
Finite Elements
The tyre of which the model is build is the Yokohama 185/70 R14 88T, it isn’t
analytical, but a 3D Finite Element (FE) model. Such a model is a 3D visual
representation of an object, in this case the tyre, which is divided in a finite
number of small parts, called elements, that are geometrically interconnected
by nodes. The distribution of elements is called the mesh. The distribution in
the cross-section is depicted in 2.1(a), the distribution in the surface is depicted
in 2.1(b). The geometry of the complete tyre is generated by revolving the
cross-section mesh along the rotational symmetry axis of the tyre.
(a)
(b)
Figure 2.1: Two dimensional cross-section with different components indicated (a) and
the inflated 3D tyre (b), where the colors indicate the deformation due to the inflation
pressure.
For the research of R. van Doorn the shape of the tyre and the resulting axle
9
forces are of interest. Because the rim and axle aren’t modeled, the assumption
is made that the sum of the forces acting in every node on the rim is the
resultant axle force. The initial conditions define the initial shape of the tyre
which is influenced by the inflation pressure of 200 kPa, this initial deformation
is depicted in figure 2.1(b). The boundary conditions define which degrees of
freedom every node has in this case. The nodes connected to the rim for example
cannot move in any direction because the rim is assumed to be undeformable.
The nodes where the excitation is applied on the other hand, have prescribed
forces in time. These initial and boundary conditions can be changed to carry
out different simulations.
Figure 2.2: Location of the different materials in the FE model.
It has to be remarked that the model that R.
of four materials. Although a real tyre consists
stated in chapter 1, the complexity of the model
relevant properties of the tyre. How the materials
is depicted in figure 2.2.
2.1.2
van Doorn modified is build
of much more materials, as
is sufficient to represent the
are distributed over the tyre
Mode shapes
When the wavelength of a vibration fits an integer number of times in the
circumference of the tyre, so called standing waves arise. This means that
certain points on the circumference vibrate heavily while others don’t move at
all.These movements cause the tyre to vibrate in a certain ’steady’ shape, the
mode shape or eigenmode. Examples of the mode shapes of the tyre are depicted
in figure 2.3. It must be remarked that the amplitudes of the mode shapes are
strongly amplified in this figure. The frequency at which the mode shapes arise
are called resonance frequencies. The mode shapes are named (k,a) where k is
the number of wavelengths around the circumference and a is the number of
half wavelengths in axial direction at a point where the shape is at an extreme
radial displacement.
Mode shapes are very important in the analysis of the transmissibility because the response of the tyre is described by superposition of the mode shapes.
2.2
Simulations
Because of the limitations of the flat plank it is not possible to validate all the
simulations discussed in [1]. Only the simulations that can be validated on the
flat plank are discussed in this report. This comes down to simulations with
10
(a) mode(1,0) at f=78 Hz
(b) mode(3,0) at f=121 Hz
(c) mode(3,1) at f=132 Hz
Figure 2.3: Three mode shapes of the undeformed tyre, the colors represent the amount
of displacement.
excitation parallel to the road surface and both with or without the effect of
deformation.
At each resonance frequency of the undeformed tyre two mode shapes arise.
The shape of these modes are identical, the only difference is an offset in the
angular position of the modes. For every simulation applies that mode shapes
are only visible in the transmissibility if the integral of the axle forces around
the circumference is nonzero. If the integral is equal to zero, all the force vectors
cancel each other out and no nett force is applied to the axle. As can be seen in
figure 2.4, only the modes with one wavelength around the circumference, eq.
the (1,x ) modes, result in an axle force for an undeformed tyre.
Figure 2.4: Mode shapes of an undeformed tyre with arrows representing the force
vectors. Only in mode (1,0) the force vectors aren’t canceled out.
2.2.1
Effect of initial deformation
For this simulation the effect of the weight of the car is taken into account. A
constant load of 2750N is applied to a limited number of nodes at the circumference to represent this weight.
The two mode shapes that arose at the same frequency for an undeformed
tyre, split up in two mode shapes that aren’t identical of shape anymore and
arise both at a different frequency. One of these modes has a force integral equal
to zero (the ’0’ mode), while the other hasn’t (the ’extremum’ mode). Therefore
only the extremum mode will be visible in the transmissibility as stated above.
In figure 2.5 the effect of deformation on the transmissibility is clearly visible,
the extremum modes that arise are clearly seen. The effect of the acoustic
resonance isn’t taken into account in this figure, this effect will be discussed in
the next section.
11
Figure 2.5: The simulated transmissibility plot for both the undeformed and deformed
tyre with a load of 2750N.
2.2.2
Effect of acoustic resonance
Until this point the air inside the tyre isn’t taken into account. To let the tyre
model be as close to reality as possible, it is necessary to include air inside the
tyre. The interaction of the air with the tyre must be taken into account too.
For the resulting acoustic resonances the same holds as for all resonances, only
the modes with a none-zero force integral will be visible in the transmissibility,
so only the first acoustic mode which has similar shape as the first structural
mode will be visible. In figure 2.6(a) the acoustic resonance is clearly visible at a
frequency of 228 Hz, this peak is much sharper than the peaks of the structural
modes because of the small damping factor in the air. It’s also easy to see that
taking the acoustics into account shifts down the frequencies of the structural
modes slightly.
The deformation has a significant effect on the acoustic resonance. The
deformation causes the acoustic mode to split in two modes, a horizontal and
a vertical mode. It is known that the vertical mode is mainly contributing
the transmissibility. The acoustic effect amplifies all the structural modes but
mainly the first structural mode closely above the acoustic resonance, which is
clearly visible in figure 2.6(b). The acoustic resonance frequency will shift down
a little due to the deformation, in contrast to the structural eigenfrequencies
which shift up a little.
2.3
Experimental mode shapes
Report [2] discusses experiments carried out to validate the theoretical mode
shapes from section 2.2 and fine tune the modal parameters of the model. The
results obtained in chapter 4 should coincide with the eigenfrequencies obtained
in [2].
The frequencies of the experimental modes shapes are depicted in table 2.1.
The remark has to be made that the (1,a) eigenmodes are omitted in this table
because the frequency at which they appeared is out of the range of agreement
with the simulation results and with the other experimental results discussed in
12
(a)
(b)
Figure 2.6: Effect of including acoustics on the transmissibility of an undeformed (a)
and a deformed (b) tyre.
Table 2.1: Experimentally obtained eigenfrequencies of the tyre.
Mode
2
3
4
5
6
Without load
113 Hz
139 Hz
165 Hz
194 Hz
221 Hz
With load
110.5 Hz
138 Hz
166 Hz
196 Hz
222 Hz
2750N
123 Hz
152.5 Hz
179 Hz
209 Hz
239 Hz
[1]. The experimental mode shapes corresponding to table 2.1 can be found in
appendix B.
2.4
Transmissibility
The theoretical transmissibilities of the undeformed and deformed tyre to be
validated are similar to the continuous lines in figure 2.6. It’s impossible to obtain the dashed lines in this figure, because it is impossible to omit the acoustic
effect in a real tyre. The experimental transmissibilities must agree with the
eigenfrequencies in table 2.1, but they will differ from the theoretical transmissibilities because of the following reasons:
For both undeformed and deformed measurements
• The flat plank registers the resulting axle force in three perpendicular
directions (x,y,z). So three separate transmissibility plots will be obtained
from which only the two in radial directions (x,y) are useful according to
[1].
• The weight of the rim isn’t taken into account in the simulations while it’s
impossible to perform measurements on the flat plank without a rim. This
will result in a shift downwards for the frequencies of the mode shapes.
For deformed measurements only
13
• It’s impossible to excite the tyre on the flat plank in the contact patch.
The plots depicted in 2.6 are results of a simulation with the applied force
in the contact patch, which is off course the most realistic way to simulate
the transmissibility. When a car drives on a road the tyre is excited in the
contact patch after all.
• For the simulation of the excitation in the contact patch, the deformation isn’t modeled as a road surface but as a constant load. When the
deformation is modeled as a (more realistic) road surface, it is impossible
to simulate excitation of the tyre in the contact patch. In stead of excitation in the contact patch, excitation at the side is applied during the
experiments.
The simulated transmissibilities in x- and z-direction for road surface deformation and the excitation at the side can be found as a continuous line in figure
2.7.
14
(a)
(b)
Figure 2.7: Transmissibility in x- (a) and z-direction (b) as to be validated by measurements on the flat plank.
15
Chapter 3
Experiments
3.1
Description of the flat plank
The flat plank (figure 3.1) is situated in de Automotive Engineering Science Laboratory of the department Mechanical Engineering of the Eindhoven Technical
University. The flat plank is a device developed by the Technical University of
Delft and is transferred to Eindhoven in 2003. With the flat plank it is possible to press a tyre with a constant displacement or a constant load to a road
surface. The road surface is above the tyre and the tyre is lifted up against the
road surface.
Many parameters involved in the position and orientation of the tyre and
the road surface can be adjusted and measured but not all are relevant for this
report, so only the relevant specifications are described in this section. A full
description of the flat plank tyre tester can be found in [4].
Figure 3.1: Flat plank tyre tester
A tyre that has to be examined has to be attached to a rim. This rim has
to be mounted on the axle which can rotate in the measuring hub. This hub is
attached to the supporting frame with certain degrees of freedom which can be
locked for specific measurements.
The variables of interest are the axle forces in longitudinal, axial and vertical
directions represented by respectively x, y and z. In the measuring axle 5 strain
gauge bridges are installed, the voltages outputted by these bridges are used
to derive the forces of interest. In figure 3.2 the setup of the bridges and the
directions of the forces are depicted [3].
16
Figure 3.2: Overview of the axle, strain gauge bridges and the orientation of forces
and moments
3.2
Experiments to carry out
Every time domain signal can be transformed into a frequency domain signal.
This means that every real signal can be represented as a signal that consists of
multiple periodic signals with their own frequencies. So it is possible to predict
the behavior of a system if the response to a range of frequencies is known.
Therefor the goal of the experiments is to obtain a frequency response plot.
Such a frequency response plot is a visualization of the response of the system
to different input frequencies.
A frequency response measurement consists of two graphs that belong together, a magnitude and a phase plot. The horizontal axis of a magnitude plot
contains a finite range of frequencies, the vertical axis shows whether the output
signal is amplified or weakened relative to the input signal at these frequencies.
The horizontal axis of a phase plot contains the same range of frequencies as
the magnitude plot, but the vertical axis shows how much the output signal is
delayed relative to the input signal, this is called phase shifting.
When a certain frequency is amplified much stronger than the surrounding
frequencies and the phase is shifted −π rad, this frequency is called a resonance
frequency or peak. When a certain frequency is weakened much stronger than
the surrounding frequencies and the phase is shifted +π rad, this frequency is
called an antiresonance frequency.
3.2.1
Dynamics of the flat plank
First it is necessary to derive the frequency response plot from the axle itself so
the resonance peaks of the flat plank are known. Second a frequency response
plot is derived with the tyre attached to the axle. The frequency shift of the
existing peaks and resonances and possibly new peaks and resonances represent
the influence of the attached tyre. Third the tyre is pressed against the road
surface, again shifted and new peaks and antiresonances must become visible
that represent the influence of the load. To exclude the transmissibility from
these measurements it is necessary to excite the axle in all three situations.
To perform a frequency response measurement but not repeating the same
experiment with a single frequency for many times to get a reasonable resolution,
an input signal is needed which contains a wide range of frequencies. Both a
chirp signal and a random signal contain a wide range. To apply these signals to
17
the axle it is convenient to generate these signals on a computer and connect an
actuator which is fed with the signal, the actuator of choice would be a shaker.
A disadvantage of this method is that the shaker must be attached firmly and
without play to the axle. There are no adapters that are suited for this job, so
an option would be to make one especially for this project.
Another signal that contains a wide range of frequencies besides a chirp or
random signal is an impulse signal. An impulse force can be generated by a
hit from a hammer. The hammer needs to be equipped with a force sensor in
the head portion of the hammer to measure the impact force. Such a device
is available in the Dynamics and Control Technology (DCT) laboratory of the
faculty of mechanical engineering.
The hammer of the DCT laboratory is equipped with a PCB 208A05 sensor
and an arnite tip. This sensor doesn’t need an amplifier, so it can be directly
connected to a data acquisition card. The material of the tip in combination
with the material of the target restricts the duration of the impulse and therefore
the frequency range of the applied force. The auto spectrum of the hammer is
nearly flat in the frequency range of interest, which is 50Hz to 500Hz, as can
be seen in figure 3.3. Therefore this hammer is suited to perform the required
measurements.
Figure 3.3: Auto spectrum of the measuring hammer with arnite tip
For measurements on the axle alone the axle of the flat plank is hit at the
point where usually the tyre is mounted. For measurements on the axle with
the tyre mounted a wheelnut is hit. The wheelnut to be hit is chosen so the
direction of the hit will cross the center axis of the axle. The resulting axle
forces are measured by the strain gauge bridges that are already installed in the
flat plank.
3.2.2
Validation of tyre transmissibility
J. Fioole carried out his experiments with the tyre mounted on the flat plank
axle and a shaker hanging under the road surface([2]) as depicted in figure 3.4.
18
With this shaker he excited the circumference of the tyre at a fixed point and
measured the acceleration at multiple points at the circumference.
Figure 3.4: Setup of the experiments to validate the transmissibility with the shaker
hanging under the road surface.
For validation of the tyre model the same method of excitation is used as
in [2], but the axle forces will be measured in stead of the acceleration. The
shaker is suited for this measurements because an adaptor to attach it to a tyre
already exists and the tyre isn’t as stiff as the flat plank axle. This shaker will
be fed with a chirp signal analog to the experiments in [2].
If the flat plank is suited for the validation it must be possible to distinguish
the peaks and antiresonances of the flat plank from the peaks and resonances
of the tyre. Hopefully the peaks of the tyre are clearer than the peaks of the
flat plank itself. Because it would be possible then to subtract the peaks of no
interest and remain the peaks of interest, which is the frequency response of the
tyre alone.
3.3
3.3.1
Additional hardware
System for data acquisition
The output voltages of the strain gauge bridges are amplified and read out on
a computer on which a Labview program is running. This program is especially
written for measurements on the flat plank. The main disadvantage of this program is that it’s designed for quasi static measurements and not for frequency
response measurements. To make the existing setup suitable for frequency response measurements the existing program has to be adapted or a new program
has to be written. Because it is possible that the flat plank will not be suitable
for this kind of measurements it is decided to look for a data acquisition solution
that doesn’t need writing a program. The disadvantage of using another system
than Labview is that the system needs to be build up every time measurements
are carried out, because the flat plank needs to be available for measurements
that use the Labview program.
The analysis of the measurements will be carried out in MATLAB, therefore
it’s desirable that the measurement data can be easily exported to MATLAB.
Other requirements are the availability of proper anti aliasing filters and the
availability of the system itself at the faculty of mechanical engineering. SigLab
19
is a system that answers the demands of this research, so that will be the data
acquisition system for this project. The biggest advantage of SigLab is that
it is controlled by a special MATLAB program that stores the measurements
directly in a MATLAB structure. An additional advantage is that SigLab is
able to average multiple measurements and to store the averaged values in the
structure. The chosen measurement settings are also stored in this structure.
3.3.2
Other necessary hardware
Because the strain gauges cannot be connected to SigLab directly an amplifier
is needed. The amplifier that is installed for use with Labview is well-suited
for measurements with the strain gauges and the output connectors are of the
same type as the input connectors of SigLab, the output voltage range of the
amplifier also matches the input voltage range of SigLab. So the strain gauges
stay connected to the amplifier as they are and the outputs of the amplifier are
disconnected from the Labview computer and connected to SigLab.
There are three forces of interest and one reference input signal is needed.
One SigLab unit is equipped with 4 inputs, so that seems to be perfect. Unfortunately the three forces are measured with 5 strain gauge bridges as discussed
in section 3.1. Fy is measured with one strain gauge, both Fx and Fz are measured with two strain gauges each. The strain gauges for Fx are placed in such
a way that the forces on the two single strain gauges added together are equal
to Fx . This means that if the output voltages of these strain gauges are added,
the resulting voltage represents Fx . The reasoning concerning the voltage of Fz
is analog to that of Fx .
To overcome the problem that five strain gauges have to be read in SigLab
while only three inputs are available, a double summation unit is used to add
the voltages of the bridges Gx1 and Gx2 and the voltages of the bridges Gz1
and Gz2 from figure 3.2. This results in the signal route as depicted in figure
3.5. The SigLab unit is connected to a laptop and both the SigLab unit and
the summation unit need there own power supply but these are left out of the
figure for simplicity.
Figure 3.5: Overview of the signal route during experiments
20
3.3.3
Settings
In order to obtain useful data it is necessary to make proper settings in SigLab
and on the strain gauge amplifier. The important settings with their values
and motivations for these settings are listed below. All settings are listed in
appendix C.
SigLab settings
1. The frequency range of the transmissibility will be from 50Hz to 500Hz
according to [1], hence the bandwidth is set to 1kHz. SigLab automatically
adapts the samplerate to a proper value of 2560 samples per second.
2. The record length is 8192 samples which is the longest record SigLab
allows given the samplerate. The record length is chosen to be as long
as possible to prevent occurrence of leakage without the use of a window.
This is possible since the record length is 3.2 seconds (8192/2560) so the
response of the system is died out before the end of the record is reached.
Amplifier settings
1. The cutoff frequency is set to 20kHz, the highest cutoff frequency available
on the amplifier.
2. The amplification factor is set as high as possible to have the highest output voltage that’s possible in order to restrict the amount of noise present
in the output signal. The height of the amplification factor is limited by
overload which can occur in the amplifier itself as well as in SigLab. In
practice the overload occurs in the amplifier because the amplifier can
output a maximum of 10V while SigLab allows a maximum input of 10V.
• The amplification factors of the two channels for the x-direction are
set to 5000.
• The amplification factors of the two channels for the z-direction are
set to 5000 in case the tyre is unloaded while factors of 1000 are set in
case the tyre is loaded. The load points in the z-direction and therefore generates a constant signal that is to high for an amplification
factor of more than 1000.
21
Chapter 4
Results
Because of limitations of the flat plank it is only possible to validate the transmissibility model with excitation in the x-direction, so only the results obtained
by excitation in the x-direction will be discussed in this chapter. According to
the results in [2] there will be no eigenfrequencies above 400Hz, all results in
this chapter are therefore plotted in a frequency range of 0Hz to 400Hz.
Only the forces in x- and z-direction are of interest according to [1], so
the results obtained in y-direction are left out of this report, although these
measurements are logged in the SigLab structure.
4.1
Axle dynamics
At first a FRF of the dynamics of the flat plank itself is obtained. This is
done by excitation of the measuring axle with the measuring hammer without
a tyre being mounted. The results obtained for the output forces in x- and
z-direction are depicted in figure 4.1. The most striking peaks are indicated and
the corresponding frequencies are depicted in table 4.1 for comparison with the
results of the other experiments.
The first thing that stands out is that the coherence of the reaction force in
z-direction is much worse than the coherence of the reaction force in x-direction.
This significant difference appears because the z-direction is perpendicular to
the x-direction. Therefore the excitation force has no component in the reaction
force direction which results in a bad coherence.
It is easy to see that dynamics of the flat plank itself are present in the
frequency range where the dynamics of the tyre are expected, that is the range
of 50Hz to 500Hz. This could be a problem if the dynamics of the flat plank are
overpowering the transfer function of the transmissibility.
4.1.1
Influence of the tyre
The second experiment is carried out with the tyre mounted on the axle. The
excitation with the hammer is applied on a wheelnut that is horizontally aligned
with the center of the axle. The response of the system is depicted in figure 4.2,
the most striking peaks are indicated again.
22
(a)
(b)
Figure 4.1: Magnitude, phase and coherence of the axle transfer function, obtained by
excitation with the measuring hammer on the flat plank axle in x-direction. No tyre
was mounted and no load was applied.
23
Table 4.1: Resonance peaks of the flat plank measuring axle
Peak
xa
xb
xc
xd
xe
xf
xg
No tyre, no load
9.7Hz
75.3Hz
138.4Hz
185.6Hz
254.4Hz
303.1Hz
Tyre, no load
7.2Hz
69.4Hz
140.6Hz
184.3Hz
220.3Hz
245.0Hz
295.9Hz
Tyre and load
7.5Hz
78.8Hz
140.9Hz
186.3Hz
221.3Hz
247.2Hz
294.7Hz
When the tyre is mounted on the measuring axle, the resonance peaks are
expected to shift down in frequency because of the extra weight that is added
to the system. As can be seen in table 4.1 this holds for all the indicated peaks
except for peaks xc. When comparing figure 4.1 with figure 4.2 it can be seen
that not only peak xc is shifted up but some non-indicated peaks are shifted up
as well. It isn’t possible to give an explanation for the upwards shifts within
the scope of this report, a more detailed research about the dynamics of the flat
plank could explain it.
Another peak that stands out is peak xg, it just appears when the tyre
is mounted. This resonance is likely to be the (1,2) eigenmode of the tyre
which is also present in the simulated transmissibility of figure 2.6(a). It’s not
possible to give a well-founded explanation why this peak appears, while it isn’t
expected that the transmissibility would play a role in this experiment since the
circumference of the tyre isn’t excited. It could be possible that the inertia of
the circumference is causing this mode to become visible, but then the other
mode shapes are expected to be visible as well, which isn’t the case.
Because of the bad coherence of the response in z-direction the corresponding
FRF are left out of this section but can be found in appendix A.
4.1.2
Influence of load
The third experiment is carried out exactly as the previous experiment, described in section 4.1.1, with that difference that the tyre is pressed against the
road surface with a force of 2750N. The response of the system is depicted in
figure 4.3, the most striking peaks are indicated again. The results in z-direction
are omitted again, because of their bad coherence as explained in the previous
section. The results are depicted in appendix A.
As can be seen in table 4.1 the indicated peaks are shifted upwards in frequency with exception of peak xg, so this result is almost exactly as expected
because extra stiffness is added by pressing the tyre to the surface, which results
in an upward shift of peaks.
As indicated in the previous section (4.1.1) peak xg is a strange one in the
first place because of it’s appearance in plots where the transmissibility isn’t
expected to play a role. Therefore further investigation is needed to explain
why this peak is present in the first place and shifted down instead of up in the
second place.
24
Figure 4.2: Magnitude, phase and coherence of the axle transfer function, obtained by
excitation with the measuring hammer on a wheelnut that’s horizontally aligned with
the center of the axle. The tyre was mounted but no load was applied.
Figure 4.3: Magnitude, phase and coherence of the axle transfer function, obtained by
excitation with the measuring hammer on a wheelnut that’s horizontally aligned with
the center of the axle. The tyre was mounted and a load of 2750N was applied.
25
4.2
Transmissibility
Two experiments are carried out with the shaker to obtain the transmissibility
of the tyre as described in section 3.2.2. One experiment is carried out without
a load on the tyre, another experiment is carried out with the tyre pressed to
the road surface with a load of 2750N. The results obtained by the measurements without a load are depicted in figure 4.4, the results obtained by the
measurement with a load of 2750N are depicted in figure 4.5.
In the ideal situation figure 4.4 would look like figure 2.6(a). But as can
be seen in figure 4.4 more peaks arise than expected. Resonance (1,2) from
figure 2.6(a) could coincide with the resonance arising just below 300Hz in figure
4.4. Unfortunately a resonance is also present just below 300Hz in figure 4.2
(which depicts results with a mounted tyre but no applied load) in which the
transmissibility has no influence at all. Therefore it is unlikely that resonance
(1,2) from figure 2.6(a) would be marked as a transmissibility resonance without
knowing it’s frequency beforehand.
Figure 4.4: Magnitude, phase and coherence of the combined tyre/axle transfer function, obtained by excitation with the shaker on the circumference of the tyre. The
tyre was mounted but no load was applied.
The other peak that should arise in figure 4.4 is peak (1,0) from figure 2.6(a).
A peak is present at this frequency, but in figure 4.1(a) (which depicts results
with a mounted and loaded tyre) a peak is also present around this frequency,
so this peak probably wouldn’t be marked as a transmissibility resonance just
like peak (1,2) wouldn’t.
The only resonance that would be marked as a transmissibility resonance
for certain is the acoustic resonance indicated with (ac) in figure 2.6(a). This
peak is obviously present in figure 4.4 at 237Hz while no peak is present in
26
figure 4.2 at this frequency. It is discussed in section 2.2.2 that the acoustic
resonance has a very small damping factor. Therefore the small damping factor
of the experimentally obtained peak is also a convincing indication that it is
the acoustic resonance. Moreover this measured frequency is in pretty good
agreement with the theoretical prediction of 228Hz in [1].
4.2.1
Influence of load
The results of the excitation with a load of 2750N are expected to be like figure
2.7. The results for both the x- and z-direction are depicted in figure 4.5 and
aren’t much alike figure 2.7. The reason that the z-direction isn’t left out of the
results here, is that direction-separated simulation results are provided in [1]
and that many differences are present between these two figures. The vertical
lines that are visible in both the figures 4.5 represent the frequencies at which
resonances should be visible according to the results obtained in [2].
The peak that is expected at 123Hz is present in the plot for the z-direction
only while an antiresonance appears at that frequency in the plot for the xdirection. This is explainable from the fact that the mode shape at this frequency has a resultant force in the z-direction and is symmetrical in the xdirection.
The resonance appearing at 150Hz can be accidently interpreted as the resonance that is expected at 152.5Hz. The peak in the phase, though, is an
indication that it isn’t a resonance of the system because a phase shift would
occur rather than a phase peak. This peak is more likely to be a k*50Hz peak
from the power network.
The acoustic resonance is clearly visible in both the plots for the x- and
z-direction but appears at 233.1Hz in the x-direction and at 239.1Hz in the zdirection. This isn’t as expected from figure 2.6 where the resonances for both
directions appear at 239Hz. It’s certain that the peak in x-direction isn’t the
symmetric part of the split that occurs with loading of the tyre, because it isn’t
expected to be visible and is a mode shape at 222Hz according to [2].
It’s clear that only a minority of the expected frequencies is visible in figure
4.5 obtained from excitation of the tyre circumference with the shaker and hence
the tyre transmissibility isn’t derivable from these figures.
27
(a)
(b)
Figure 4.5: Magnitude, phase and coherence of the combined tyre/axle transfer function for the x-direction (a) and z-direction (b), obtained by excitation with the shaker
of the circumference of the tyre. The tyre was mounted and a load of 2750N was
applied.
28
Chapter 5
Conclusion and
recommendations
5.1
Conclusion
A lot of effort is made at the TU/e to improve tyre models hence a need exists to
validate these models. Because validation of frequency response models which
concern the transmissibility isn’t possible at the TU/e, a search is initiated for
a device that’s useable for these kind of experiments. Currently the flat plank
tyre tester is present which is capable of measuring axle forces generated by an
automobile tyre. Because experience is gained with quasi static measurements
only, the possibilities of measuring frequency responses have to be examined.
Experiments are carried out which survey the dynamics of the flat plank.
Unfortunately these experiments revealed that the dynamics of the flat plank
are very rich, a lot of resonances and antiresonances are present in the frequency
response plots.
The rich dynamics of the flat plank doesn’t have to be a problem, as long
as the dynamics of the tyre are dominant over these of the flat plank, but this
isn’t the case. The dynamics of the tyre aren’t clearly visible in the transfer
function estimate from axle to shaker. Therefor the flat plank tyre tester isn’t
usable for easy validation of the transmissibility of a tyre.
5.2
Recommendations
• In order to use the flat plank as a tool to validate tyre transmissibility
models after all, it could be useful to find a mathematical method to
calculate the difference between the frequency response measurements of
the flat plank itself and the ones that include the tyre transmissibility so
the transmissibility is isolated. With this approach it is also necessary
to improve the coherence of the frequency response measurements in zdirection for comparison with simulation results.
• Performing a modal analysis of the construction of the flat plank can
be useful to change the construction of it in such a way that most of
29
the dynamics are taken away so validation of the transmissibility will be
possible.
• Another possibility could be to especially build a device that is usable to
validate the transmissibility models. When this approach is chosen it is
wise to take the measuring axle of the flat plank as an example. That’s
because the measuring axle is sensitive enough the register the frequency
response obtained by excitation with the shaker, while a load of 2750N is
applied to the tyre at the same time.
30
Appendix A
z-direction FRF
The frequency response plots that aren’t depicted in chapter 4 for reasons that
are discussed in this chapter as well, are depicted below.
Figure A.1: Magnitude, phase and coherence of measurements for measurements with
the shaker to obtain the transmissibility in the z-direction .
31
(a)
(b)
Figure A.2: Magnitude, phase and coherence of measurements in the z-direction with
the hammer, without (a) and with a load of 2750N (b).
32
Appendix B
Measured mode shapes
Figure B.1: Mode shapes obtained by experiments discussed in [2].
33
Appendix C
Experiments
C.1
List of equipement
• Tyre under investigation (prepared for shaker mounting)
• Adapter to mount the tyre on the axle
• Flat plank tyre tester
• Amplifier already installed in the flat plank setup
• Double summation unit
• SigLab plus the notebook that comes with it
• Measurement hammer (to obtain flat plank dynamics)
• Shaker (to obtain transmissibility)
• Coaxial cables
C.2
SigLab settings
• The channel to which the measuring hammer is wired is set to BIAS. This
setting feeds the sensor in the hammer so there is no need for a separate
amplifier. This setting is also used for the sensor used with the shaker for
the same reason.
• The channels to which the strain gauges are connected are set to AC. The
other available option is DC but AC gives a higher resolution.
• The frequency range of the transmissibility will be from 50Hz to 500Hz
according to [1], hence the bandwidth is set to 1kHz. SigLab automatically
adapts the samplerate to a proper value of 2560 samples per second.
• The record length is 8192 samples which is the longest record SigLab
allows given the samplerate. The record length is chosen to be as long
as possible to prevent occurrence of leakage without the use of a window.
This is possible since the record length is 3.2 seconds (8192/2560) so the
response of the system is died out before the end of the record is reached.
34
• The anti-aliasing filters are turned on to prevent high frequencies from
occurring as lower frequencies.
• To get satisfying results it is necessary to average over multiple excitations.
The coherence didn’t improve significantly with more than 10 excitations,
so SigLab is set to automatically stop the measurements when 10 frames
are obtained.
• When the hit of the hammer is too powerful overload occurs on a channel
which leads to unreliable results. SigLab contains a setting that is called
overload reject which reject a frame when an overload occurred on one of
the channels, so this is turned on for ease of use.
• Triggering is turned on so logging of a new frame is initiated when an input
signal, either the hammer or the shaker, is detected. To make sure the total
excitation is recorded the trigger delay is set to -7% so the registration of
the frame will start 7% of the record length ahead of the trigger.
• To feed the shaker a chirp signal is set with a frequency range of 0Hz to
1kHz.
C.3
Amplifier settings
• The cutoff frequency is set to 20kHz, the highest cutoff frequency available
on the amplifier.
• The amplification factor is set as high as possible to have the highest output voltage that’s possible in order to restrict the amount of noise present
in the output signal. The height of the amplification factor is limited by
overload which can occur in the amplifier itself as well as in SigLab. In
practice the overload occurs in the amplifier because the amplifier can
output a maximum of 10V while SigLab allows a maximum input of 10V.
– The amplification factors of the two channels for the x-direction are
set to 5000.
– The amplification factors of the two channels for the z-direction are
set to 5000 in case the tyre is unloaded while factors of 1000 are
set in case the tyre is loaded. The load points in the z-direction
and therefore generates a constant signal that is too high for an
amplification factor of more than 1000.
• The amplifier is zeroed to remove offsets generated by gravity and a potential load before every new measurement. It appears that small offsets
randomly occur for no obvious reason, so therefore this procedure is repeated regularly.
35
Appendix D
m-files
The m-files used to make the frequency response plots of the results are depicted
in this appendix. The constants needed to convert voltage to force for the
hammer and the shaker are obtained from datasheets of the manufacturers of
the sensors. The constants needed to convert voltage to force for the strain
gauge bridges are obtained from the Labview program that is used to perform
quasi-static measurements.
D.1
%
%
%
%
%
%
%
%
%
%
%
%
Plot shaker results
VERWERKING METINGEN MBV SHAKER
De krachten worden met rekstrookjes gemeten op kanalen 2 en 3 en 4
de sensor op de shaker op kanaal 1.
toelichting op variabelen:
Richting
meetrichting
cutoff
bovengrens waartot geplot wordt [Hz]
belast
plot belaste of onbelaste toestand
shakerc
omrekenconstante van [V] naar [N] voor de shaker
brugc
omrekenconstante van [V] naar [N] voor de rekstroken
K
versterkingsfactor ingesteld op meetversterker
%% Clear de workspace en close alle figuren
clear all
close all
%% bepaal welke resultaten moeten worden getoond
Richting = ’x’;
cutoff = 400;
belast = ’n’;
% ’x’, ’y’, of ’z’
% ’w’ (wel) of ’n’ (niet) belast
36
%% Laad de juiste file
if belast == ’n’
File = [’unloaded chirp2’]; % bronbestand weggeschreven door SigLab
elseif belast == ’w’
File = [’loaded2 2750N chirp2’]; % bronbestand weggeschreven door SigLab
end
load([File,’.vna’], ’-mat’);
%% Laad relevante vectoren met duidelijker var-namen
% SLm.xcmeas(1,ch).xfer en SLm.xcmeas(1,ch).coh bevatten respectievelijk de
% gemeten overdracht en bijbehorende coherentie van kanaal ’ch’ naar kanaal 1
shakerc = 890.15;
% [N/V]
if Richting == ’x’
ch = 2;
K = 5000;
brugc = 3.82;
elseif Richting == ’y’
ch = 3;
K = 2000;
brugc = 3.85;
elseif Richting == ’z’
ch = 4;
if belast == ’n’
K = 5000;
elseif belast == ’w’
K = 1000;
end
brugc = 1.97;
end
xfer = SLm.xcmeas(1,ch).xfer;
coh = SLm.xcmeas(1,ch).coh;
f = SLm.fdxvec;
cutoff = find(f >= cutoff,1);
f = f(1:cutoff);
coh = coh(1:cutoff);
xfer = xfer(1:cutoff);
Mag = 20*log10(abs(xfer*200000/K*9.81/brugc/shakerc));
Phase = angle(xfer)/2/pi*360;
37
%% Maak de vectoren voor de resonanties van Joost
if belast == ’w’
x = [110.5 123 138 152.5 166 179 196 209 222 239];
if Richting == ’z’
y = [-40 40];
elseif Richting == ’x’
y = [-60 20];
end
else
x=[];
end
%% plot figuren van frequentie analyse
h=figure(’Position’,[200 200 560 640]);
hold on
subplot(3,1,1), plot(f,Mag,’b’);
hold on
for n = 1:length(x)
X = [x(n) x(n)];
subplot(3,1,1), plot(X,y,’r’);
end
title([’magnitude -- ’,Richting,’-direction’]);
xlabel(’f [Hz]’);
ylabel(’mag [-]’);
grid
subplot(3,1,2), plot(f,Phase,’b’);
title([’phase -- ’,Richting,’-direction’]);
xlabel(’f [Hz]’);
ylabel(’phase [degree]’);
grid
subplot(3,1,3), plot(f,coh,’b’);
title([’coherence -- ’,Richting,’-direction’]);
xlabel(’f [Hz]’);
ylabel(’mag [-]’);
grid
print(h, ’-r300’, ’-dpng’, [’Shaker meet’,Richting,’ linf ’,belast,’_belasting’]);
saveas(h, [’Shaker meet’,Richting,’ linf ’,belast,’_belasting’], ’fig’);
D.2
Plot hammer results, no tyre mounted
% VERWERKING METINGEN MBV HAMER
38
%
%
%
%
%
%
%
%
%
%
%
%
De krachten worden met rekstrookjes gemeten op kanalen 1 en 3 en 4
de krachtsensor op de hamer op kanaal 2.
toelichting op variabelen:
MeetRichting meetrichting
Slagrichting slagrichting
cutoff
bovengrens waartot geplot wordt [Hz]
belast
plot belaste of onbelaste toestand
hamerc
omrekenconstante van [V] naar [N] voor de hamer
brugc
omrekenconstante van [V] naar [N] voor de rekstroken
K
versterkingsfactor ingesteld op meetversterker
%% Clear de workspace en close alle figuren
clear all
close all
%% Laad de juiste file
SlagRichting = ’x’;
MeetRichting = ’x’;
Richting = MeetRichting;
% ’x’,’y’ of ’z’
% ’x’,’y’ of ’z’
File = [’Hamer slag’,SlagRichting,’ geen_band geen_belasting’]; % bronbestand
% weggeschreven door SigLab
load([File,’.vna’], ’-mat’);
%% Laad relevante vectoren met duidelijker var-namen
% SLm.xcmeas(1,ch).xfer en SLm.xcmeas(1,ch).coh bevatten respectievelijk de
% gemeten overdracht en bijbehorende coherentie van kanaal ’ch’ naar kanaal 2
cutoff = 400;
hamerc = 4450;
% [N/V];
if Richting == ’x’
ch = 2;
K = 5000;
brugc = 3.82;
elseif Richting == ’y’
ch = 3;
K = 2000;
brugc = 3.85;
elseif Richting == ’z’
ch = 4;
K = 5000;
brugc = 1.97;
39
end
xfer = SLm.xcmeas(1,ch).xfer;
coh = SLm.xcmeas(1,ch).coh;
f = SLm.fdxvec;
cutoff = find(f >= cutoff,1);
f = f(1:cutoff);
coh = coh(1:cutoff);
xfer = xfer(1:cutoff);
Mag = 20*log10(abs(xfer*200000/K*9.81/brugc/hamerc));
Phase = angle(xfer)/2/pi*360;
%% plot figuren van frequentie analyse
h=figure(’Position’,[200 200 560 640]);
subplot(3,1,1), plot(f,Mag,’b’);
title([’magnitude -- ’,Richting,’-direction’]);
xlabel(’f [Hz]’);
ylabel(’mag [-]’);
grid
subplot(3,1,2), plot(f,Phase,’b’);
title([’fase -- ’,Richting,’-direction’]);
xlabel(’f [Hz]’);
ylabel(’phase [degree]’);
grid
subplot(3,1,3), plot(f,coh,’b’);
title([’coherence -- ’,Richting,’-direction’]);
xlabel(’f [Hz]’);
ylabel(’mag [-]’);
grid
print(h, ’-r300’, ’-dpng’, [’Hamer slag’,SlagRichting,’ meet’,Richting,’
linf geen_band geen_belasting’]);
saveas(h, [’Hamer slag’,SlagRichting,’ meet’,Richting,’ linf geen_band
geen_belasting’], ’fig’);
D.3
Plot hammer results, with tyre mounted
% VERWERKING METINGEN MBV VERSNELLINGSOPNEMER
%
40
%
%
%
%
%
%
%
%
%
%
%
De krachten worden met rekstrookjes gemeten op kanalen 1 en 3 en 4
de krachtsensor op de hamer op kanaal 2.
toelichting op variabelen:
MeetRichting meetrichting
Slagrichting slagrichting
cutoff
bovengrens waartot geplot wordt [Hz]
belast
plot belaste of onbelaste toestand
hamerc
omrekenconstante van [V] naar [N] voor de hamer
brugc
omrekenconstante van [V] naar [N] voor de rekstroken
K
versterkingsfactor ingesteld op meetversterker
%% Clear de workspace en close alle figuren
clear all
close all
%% Laad de juiste file
SlagRichting = ’x’;
MeetRichting = ’z’;
belast = ’n’;
% ’x’,’y’ of ’z’
% ’x’,’y’ of ’z’
% ’n’ of ’w’
File = [’Hamer slag’,SlagRichting,’ wel_band ’,belast,’_belasting’]; % bronbestand
% weggeschreven door SigLab
load([File,’.vna’], ’-mat’);
%% Laad relevante vectoren met duidelijker var-namen
% SLm.xcmeas(1,ch).xfer en SLm.xcmeas(1,ch).coh bevatten respectievelijk de
% gemeten overdracht en bijbehorende coherentie van kanaal ’ch’ naar kanaal 2
cutoff = 400;
hamerc = 4450;
% [N/V];
if MeetRichting == ’x’
ch = 2;
K = 5000;
brugc = 3.82;
elseif MeetRichting == ’y’
ch = 3;
K = 2000;
brugc = 3.85;
elseif MeetRichting == ’z’
ch = 4;
if belast == ’n’
K = 5000;
elseif belast == ’w’
41
K = 1000;
end
brugc = 1.97;
end
xfer = SLm.xcmeas(1,ch).xfer;
coh = SLm.xcmeas(1,ch).coh;
f = SLm.fdxvec;
cutoff = find(f >= cutoff,1);
f = f(1:cutoff);
coh = coh(1:cutoff);
xfer = xfer(1:cutoff);
Mag = 20*log10(abs(xfer*200000/K*9.81/brugc/hamerc));
Phase = angle(xfer)/2/pi*360;
%% plot figuren van frequentie analyse
h=figure(’Position’,[200 200 560 640]);
subplot(3,1,1), plot(f,Mag,’b’);
title([’magnitude -- ’,MeetRichting,’-direction’]);
xlabel(’f [Hz]’);
ylabel(’mag [-]’);
grid
subplot(3,1,2), plot(f,Phase,’b’);
title([’phase -- ’,MeetRichting,’-direction’]);
xlabel(’f [Hz]’);
ylabel(’phase [degree]’);
grid
subplot(3,1,3), plot(f,coh,’b’);
title([’coherence -- ’,MeetRichting,’-direction’]);
xlabel(’f [Hz]’);
ylabel(’mag [-]’);
grid
print(h, ’-r300’, ’-dpng’, [’Hamer slag’,SlagRichting,’ meet’,MeetRichting,’
linf wel_band ’,belast,’_belasting’]);
saveas(h, [’Hamer slag’,SlagRichting,’ meet’,MeetRichting,’ linf wel_band ’,
belast,’_belasting’], ’fig’);
42
Bibliography
[1] R.R.J.J. van Doorn, Physically based modelling of vibrations and force
transmission of deformed rotating tyres, 2008.
[2] J.C.J. Fioole, Experimental Modal Analysis of an Automobile Tire, 2008.
[3] R.T. Uil, Non-lagging effect of motorcycle tyres, 2006.
[4] R.E.A. Blom, J.P.M. Vissers, L.L.F. Merkx, Manual for the Flat plank tyre
tester, 2003.
43