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

Transcription

1 Frequency analysis of the flat plank tyre tester for validation of tyre transmissibility J.J.Nieuwenhuijsen DCT 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

2 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

3 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

4 Contents Summary 2 Samenvatting 3 1 Introduction Background Goal Approach Scope of this report Background Model Finite Elements Mode shapes Simulations Effect of initial deformation Effect of acoustic resonance Experimental mode shapes Transmissibility Experiments Description of the flat plank Experiments to carry out Dynamics of the flat plank Validation of tyre transmissibility Additional hardware System for data acquisition Other necessary hardware Settings Results Axle dynamics Influence of the tyre Influence of load Transmissibility Influence of load

5 5 Conclusion and recommendations Conclusion Recommendations A z-direction FRF 31 B Measured mode shapes 33 C Experiments 34 C.1 List of equipement C.2 SigLab settings C.3 Amplifier settings D m-files 36 D.1 Plot shaker results D.2 Plot hammer results, no tyre mounted D.3 Plot hammer results, with tyre mounted Bibliography 43 5

6 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

7 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

8 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

9 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 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

10 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. van Doorn modified is build of four materials. Although a real tyre consists of much more materials, as stated in chapter 1, the complexity of the model is sufficient to represent the relevant properties of the tyre. How the materials are distributed over the tyre is depicted in figure 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

11 (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 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

12 Figure 2.5: The simulated transmissibility plot for both the undeformed and deformed tyre with a load of 2750N 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

13 (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 Without load With load 2750N Hz Hz 123 Hz Hz 138 Hz Hz Hz 166 Hz 179 Hz Hz 196 Hz 209 Hz Hz 222 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

14 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

15 (a) (b) Figure 2.7: Transmissibility in x- (a) and z-direction (b) as to be validated by measurements on the flat plank. 15

16 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 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

17 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 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

18 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 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

19 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 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

20 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 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 G x1 and G x2 and the voltages of the bridges G z1 and G z2 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

21 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 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

22 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 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

23 (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

24 Table 4.1: Resonance peaks of the flat plank measuring axle Peak No tyre, no load Tyre, no load Tyre and load xa 9.7Hz 7.2Hz 7.5Hz xb 75.3Hz 69.4Hz 78.8Hz xc 138.4Hz 140.6Hz 140.9Hz xd 185.6Hz 184.3Hz 186.3Hz xe 254.4Hz 220.3Hz 221.3Hz xf 303.1Hz 245.0Hz 247.2Hz xg 295.9Hz 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 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

25 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

26 4.2 Transmissibility Two experiments are carried out with the shaker to obtain the transmissibility of the tyre as described in section 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

27 figure 4.2 at this frequency. It is discussed in section 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] 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 x- direction. 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 x- direction. 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 z- direction. 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

28 (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

29 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 z- direction 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

30 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

31 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

32 (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

33 Appendix B Measured mode shapes Figure B.1: Mode shapes obtained by experiments discussed in [2]. 33

34 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

35 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 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 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