Franck Levassort

Jean-Marc Gregoire

Marc Lethiecq

HIGH-FREQUENCY ULTRASONIC TRANSDUCERS Fabrication, Characterisation, Performance

Introduction

High-frequency ultrasound devices have been developing in many fields such as electronic filters and resonators, material characterisation (acoustic microscopes), non-destructive testing and medical diagnostics. This paper will deal with ultrasonic transducers which are designed for imaging applications, particularly for medical diagnosis in organs such as skin, eye and blood vessels, as well as for non-destructive evaluation and small animal examinations. This field has generated a great deal of research as well as commercial products, attested by many publications in both specialised and general scientific journal [START_REF] Sherar | Ultrasound backscatter microscopy images the internal structure of living tumour spheroids[END_REF][START_REF] Berson | High frequency (20 MHz) ultrasonic devices: advantages and applications[END_REF][START_REF] Ermet | High frequency ultrasonic imaging and its applications in skin[END_REF][START_REF] Foster | Advances in ultrasound biomicroscopy[END_REF]. The frequency range starts around 20 MHz, and extends up to 100 MHz.

I. General transducer requirements I.1. Electroacoustic requirements

The classical single-element transducer is composed of a piezoelectric plate or disc poled along the thickness direction, whose thickness defines the resonance frequency of the device (Figure 1). The piezoelectric element (typically a ferroelectric ceramic), has an acoustic impedance (i.e. around 33 MRa) much higher than biological tissues (close to that of water, i.e. 1.5 MRa). This large difference leads to poor acoustic matching and low axial resolution. Consequently, other layers are added to this active layer. First, on its rear face, a thick layer is bonded (backing) [START_REF] Kossof | The effects of backing and matching on the performance of piezoelectric ceramic transducers[END_REF]. It serves as a mechanical support for the active element, but acoustic energy flows by the rear face. The closer the backing acoustic impedance is to that of the active layer, the more energy is lost. The consequence is a lower sensitivity but a higher axial resolution. The attenuation coefficient and the thickness of the backing layer must be sufficient so that no energy can be radiated back to the active layer, because this would produce parasitic echoes. Secondly, on the front (i.e. between the piezoceramic and the propagation medium), a matching layer is used. Its design is optimised in order to increase the energy transfer from the active layer to the tissues [START_REF] Desilets | The design of efficient broadband piezoelectric transducers[END_REF][START_REF] Inoue | Design of ultrasonic transducers with multiple acoustic matching layers for medical application[END_REF]. The thickness of this matching layer is generally around a quarter-wavelength at the resonance frequency, and its acoustic impedance is intermediate between those of the piezoceramic and tissues. The use of a matching layer thus improves the sensitivity of the transducer. Moreover, since the acoustic energy can better flow towards the tissues, the duration of acoustic resonance in the active layer is decreased. Consequently, the matching layer also improves axial resolution. Influence of these two elements on the impulse and frequency responses transducers is shown in Figure 1 and a trade-off has to be found for each application. The active layer is typically a PZTbased material, while matching layers and backings are polymer-based.

I.2. Radiation pattern requirements

The radiation pattern of a focused single-element transducer is defined by the size of the active element (D) and the focal distance (F) (Figure 2). In the case where a lens is used for focusing, (F) can be deduced from the lens curvature (R c ) and the sound wave velocities in the lens and propagation media (Figure 3). Lateral resolution is linked to the width of the acoustic beam and is optimum at the focal distance. Approximate expressions of this lateral resolution (R lateral ), depth of field (DOF) and axial resolution (R axial ) for a spherical shape transducer are defined (eq. 1). The ratio between the focal distance and the diameter of the piezoelectric element, called the f-number (f # ), allows to define the trade-off between lateral resolution and depth of field. λ is the wavelength at nominal frequency and BWR -6dB is the relative bandwidth at -6 dB.

= # F f D , ≈ λ × lateral # R f , ≈ λ× 2 # DOF 7 f , - λ ≈ axial 6dB R 2BWR (1)
The resolutions and depth of field can change of several orders of magnitude according to frequency. High frequencies lead to high resolutions but, due to increase of attenuation in tissues, the depth of penetration in the explored medium is reduced. The acoustic properties of the explored medium as well as of the driving electronics also influence the imaging performance [START_REF] Foster | Advances in ultrasound biomicroscopy[END_REF][START_REF] Lethiecq | Piezoelectric materials for ultrasonic medical diagnostics[END_REF].

Typical size

For typical fixed values for medical imaging as the centre frequency at 50 MHz (i.e. a f-number of 2.5, a focal distance at 7.5 mm, a relative bandwidth (-6dB) at 60%), the corresponding diameter D is at 3 mm, the thickness of the piezoelectric element (ceramic) is around 45 µm, the axial and lateral resolutions are respectively around 30 and 75 µm, and the depth of field around 1.3 mm. These resolutions correspond to those generally required for skin imaging.

II. Piezoelectric materials II.1. General requirements

For the piezoelectric material, in particular for medical applications, two of the most important material parameters are the effective electromechanical coupling coefficient k eff of the main vibration mode used and the acoustic impedance Z. The k eff factor represents the piezoelectric activity of the material in the considered mode of vibration, in other words the capability of the material to convert electrical energy into acoustic energy (or viceversa) in a short time; it should of course be as high as possible. This factor depends not only on the material properties but also on the geometry of the active element. In medical imaging applications, all vibration modes are longitudinal, i.e. the displacements are in the poling direction which defines the thickness dimension. For large plates or discs (thickness much lower than lateral dimensions), the thickness coupling factor k t is used. For bars or pillars (thickness higher than lateral dimensions), the factor is k 33 . For the intermediate case of an array element (one small and one large lateral dimensions with a thickness value between them), k' 33 factor is defined [9]. The value of the dielectric constant also has an important role on the electrical matching. (Z) for a wide range of available piezoelectric materials. It can be observed that no material allows to obtain both high coupling and low acoustic impedance (ideal area in Figure 4). The best trade-off must be found among these materials. For almost all medical transducers applications, PZT piezoceramics are used because of their high coupling factor, even if their acoustic impedance is high, since this can be compensated for by using acoustic matching layers in the transducer structure. For a given application, properties such as dielectric constant and grain size allow to choose a specific material reference. A large range of properties can be found from relatively low (a few hundred) to very high (a few thousand) relative dielectric constants with grain sizes from one to ten micrometers. For large area devices such as single element transducer, a moderate dielectric constant allows good electrical matching to cables and electronics (which are typically at 50 to 80 ohms) (area 1), while array elements require much higher dielectric constants (area 2).

II.2. Characterisation

Measurements of the complex electrical impedance as a function of frequency of the piezoelectric materials allow, with an equivalent electrical scheme [START_REF] Krimholtz | New equivalent circuit for elementary piezoelectric transducers[END_REF], to obtain dielectric, mechanical and electromechanical properties by a fitting process. In some cases, standards on piezoelectricity [9, 11] can be used: the experimental curves are then exploited directly using simple formulas. The standard set-up is composed of a network analyser with its impedance test kit and a spring clip fixture to make electrical contacts with the electroded piezoelectric material (Figure 5(a)). These contacts have a great importance in particular at high frequency, since to stay in free resonator condition, their sizes must be very small in comparison with the size of the measured sample and the forces applied must not perturbate the resonance mode. Moreover, the quality of the contact is very important to avoid a too large contact impedance. Figure 5(b) shows the typical resonance of a PZT disk made by tape-casting which has an antiresonant frequency around 50 MHz. At high frequency, the piezoelectric element is often deposited on a substrate during the fabrication process (Figure 5(a)) and the experimental electrical impedance depends on this substrate. With an electrical equivalent circuit, such as KLM which is well adapted to multilayer structures (electrodes, piezoelectric layer and substrate), and knowing all the acoustic properties of electrodes and substrate, the fitting process allows to obtain the properties of the piezoelectric layer (Figure 4 (c)) [START_REF] Hue | Preparation and electromechanical properties of PZT/PGO thick films on alumina substrate[END_REF][START_REF] Lukacs | Thickness mode material constants of a supported piezoelectric film[END_REF].

m ) = ∆ a m f Q f (4)
where ∆f corresponds to the frequency width at half the maximum resistance; ♦ Dielectric losses appear as an offset on resistance curves, the measurement can be made at twice the anti-resonant frequency and they can change with frequency.

Several authors [START_REF] Foster | Characterization of lead zirconate titanate for use in miniature highfrequency (20-80 MHz) transducers[END_REF][START_REF] Zipparo | Piezoceramics for high frequency (20 to 100 MHz) single-element imaging transducers[END_REF][START_REF] Hue | Comparison of several methods to characterize the high frequency behavior of piezoelectric ceramics for transducer applications[END_REF] have proposed specific measurement methods to obtain high-frequency properties of piezoelectric materials.

II.3. Polymers/Copolymers

Piezopolymers such as PVDF or copolymers [START_REF] Kawaii | The piezoelectricity of poly(vinylidene fluoride)[END_REF][START_REF] Foster | A history of medical and biological imaging with polyvinylidene fluoride (PVDF) transducers[END_REF] can be purchased as films with thickness of one to a few tens of microns which can be directly used for high frequency applications. Their coupling factors are relatively low (between 15 and 30%) and relative clamped dielectric constant is low (around 5). These two last properties tend to give a relatively low sensitivity and the electric matching is difficult. But their acoustic impedance is low and close to that of tissues (between 4 and 5 MRa), so acoustic matching is not indispensable (Table 1).

Table 1 : Main properties of a P(VDF-TrFE) piezoelectric copolymer film. The second main and determinant advantage is that the flexibility of the film allows a direct focusing and avoids the addition of a lens (Figure 6). Even with a relatively low (k t ), these materials are widely used for high frequency transducer fabrication in the range of from 20 MHz to over 100 MHz.

material ε ε ε ε 33 S /ε ε ε ε 0 v l (m/s) k t (%) δ δ δ δ e (%) δ δ δ δ m (%) Z (MRa) ref P(VDF-TrFE) 4
II.4. Ceramic thick films Many processes are possible and have been developed [START_REF] Wolny | Piezoceramic thick films -Technology and applications. State of art in Europe[END_REF] such as screen-printing, tape-casting, spin or dip coating processes and spray techniques [START_REF] Gentry | Thick film sol PZT Transducer using dip coating[END_REF][START_REF] He | Preparation of PZT(53/47) thick films deposited by a dipcoating process[END_REF][START_REF] Kobayashi | Piezoelectric thick film ultrasonic transducers fabricated by spray technique[END_REF][START_REF] Thiele | Processing and properties of screen-printed lead zirconate titanate piezoelectric thick films on electroded silicon[END_REF] to make piezoelectric thick films (few tens of microns). The three first ones are widely used techniques, in particular for imaging applications. In each case, the samples (generally circular shape) are made directly in final shape and avoid machining, namely lapping, which can represent a critical step where micro-cracks or breakdown can appear. The tapes can be used to manufacture thin self-supported disks as shown on Figure 7. Table 2 summarises several representative characteristics of self-supported samples where properties are slightly lower than those of bulk ceramics (in particular k t ) but their actual performance allow to integrate these elements in transducers which deliver satisfying properties. The substrates used for the deposited thick films can be used in two ways. First, the substrate can be chosen to be used directly as a backing for the transducer [START_REF] Kosec | Screen-printed Pb(Zr,Ti)O3 thick films for ultrasonic medical imaging applications[END_REF]. Many conditions are necessary for this in terms of sintering temperature (for the thick films) and acoustic properties for the transducer.

Porous PZT can be a good choice (Figure 8(a)). This method leads to an integrated device. Secondly, the substrate can be chosen only as an intermediate material. For example, The PZT thick film is deposited on an aluminium substrate (Figure 8(b)) [START_REF] Lukacs | Single element high frequency (>50 MHz) PZT sol gel composite ultrasound transducers[END_REF]. On the other side, epoxy resin loaded with Ag powder is added as the future backing. Finally, the Al substrate is etched and a new electrode is deposited on the front face of the thick film. This method allows to optimise the choice of these two materials for the future transducer. For these two cases, properties of the piezoelectric thick films are given in Table 3 where the performance obtained can be relatively high, but the reproducibility remains an important problem to be solved. Moreover, the choice of the bottom electrode material and thickness can also greatly influence the final properties.

II.5. Composites

In combining a high coupling piezoceramic (such as a soft PZT) and a low acoustic impedance polymer, it is possible to obtain simultaneously the two essential requirements as mentioned in section II.1. Different spatial arrangements (described by the connectivity [START_REF] Newnham | Connectivity and piezoelectric-pyroelectric composites[END_REF]) between the two phases are possible and influence directly the homogenised material performance. For high frequency applications, 1-3, 2-2 and 0-3 piezo-composites have been investigated. The 1-3 connectivity is of great interest and delivers high performance (Figure 9(a)). This connectivity corresponds to ceramic pillars in a polymer matrix. For example, with a ceramic volume fraction around 40%, the value obtained for k t is higher than that of the ceramic alone (Figure 9(b)). The most common process for 1-3 piezo-composite fabrication is the "dice and fill" technique which appeared at the beginning of the 80's [START_REF] Savakus | PZT-Epoxy piezoelectric transducers: a simpliflied fabrication procedure[END_REF]. Other methods such as lost mould, fused deposition, injection-moulding techniques have been widely used [START_REF] Janas | Overview of fine-scale piezoelectric ceramic/polymer composite processing[END_REF][START_REF] Su | Routes to net shape electroceramic devices and thick films[END_REF][START_REF] Meyer | High frequency 1-3 composite transducers fabricated from alkoxide-derived PZT fibers[END_REF]. At high frequency, the spatial scale for all these methods (i.e. periodicity) limits the good vibration in thickness mode generally around 25 MHz. Alternative method is to develop ceramic fibres which are aligned in random positions and embedded in a polymer matrix as a 1-3 composite [START_REF] Jadidian | Development of fine scale piezoelectric ceramic/polymer composites via incorporation of fine PZT fibers[END_REF][START_REF] Meyer | Development of ultra-fine scale piezoelectric fibers for use in high frequency 1-3 transducers[END_REF]. Table 4 summarises a few results of fibres and composites properties. Relatively high fibre volume fraction is necessary to obtain good thickness vibration mode and non-uniform distribution of fibres can deliver low transfer of stress between matrix and ceramic fibres and non uniform strain distribution [START_REF] Snook | Design, Fabrication, and evaluation of high frequency, single-element transducers incorporating different materials[END_REF]. Piezo-composite performance obtained is slightly higher than that of bulk ceramic (as k t ) due to a lower acoustic impedance.

2-2 piezo-composites (Figure 10(a)), corresponding to alternative layers of piezoceramic and polymer are also developed for high frequency applications, in particular for linear arrays. For this, the thickness of each layer must be very low. To make a linear array at 30 MHz, a first fabrication process had been described [START_REF] Ritter | A 30-MHz piezo-composite ultrasound array for medical applications[END_REF] where polished ceramic plates (thickness around 30 µm) were bonded with epoxy resin containing polystyrene microspheres (diameter around 6 µm). To decrease the thickness, tape-casting technology and fugitive carbon ink layer has been recently developed (a) (b) [START_REF] Kwon | Ceramic/polymer 2-2 composites for high frequency transducers by Tape-casting[END_REF]. By a slow heating, carbon ink is eliminated, the composite is then sintered and space between ceramic layers is filled by epoxy resin under vacuum (Figure 10(b)). With these materials, linear arrays with a centre frequency over 35 MHz are conceivable.

Table 4 : Properties of 1-3 piezo-composites integrated ceramic fibre. 0-3 piezo-composite, which corresponds to ceramic particles embedded in a polymer matrix (Figure 11) can also be used. Thin layers can be achieved using tape-casting or screen-printing process. Moreover, as for piezoelectric polymer, shaping is easy due to the polymer matrix. The effective properties corresponding to this connectivity are relatively poor and to obtain sufficient electromechanical performance, high ceramic volume fraction is necessary (over 60%) [START_REF] Levassort | A matrix method for modeling electroelastic moduli of 0-3 piezocomposites[END_REF][START_REF] Levassort | Effective electroelastic moduli of 3-3(0-3) piezocomposites[END_REF]. This leads to a mixed connectivity between 0-3 and 3-3 and limits the flexibility. II.6. Hollow spheres PT hollow spheres (few millimetre diameter) [START_REF] Meyer | Pre-focused lead titanate >25 MHz singleelement transducers from hollow spheres[END_REF] are made using sacrificial polystyrene balls which are tumbled and mixed with a powder slurry. The thickness deposited can be controlled (Figure 12(1)). After calcination and sintering, the PT hollow sphere is immersed in melting wax (2) (the thickness of the melting wax allows to control the diameter of the shell) and the spheres are polished to obtain the shell (3). The thickness variations obtained are apparently low (around 10%). Finally, the shell is removed (4), electroded and poled [START_REF] Kossof | The effects of backing and matching on the performance of piezoelectric ceramic transducers[END_REF]. This fabrication technique allows to obtain directly the final shape with low f-number. Properties measured on a sample from [START_REF] Meyer | Pre-focused lead titanate >25 MHz singleelement transducers from hollow spheres[END_REF] are given in Table 5.

Fibre material V f (%) φ φ φ φ (µm) k t (%) ε ε ε ε 33 /ε ε ε ε 0 ρ ρ ρ ρ (kg/m 3 ) v l (m/s) δ δ δ δ e (%) Q m T co (

III. Transducer fabrication III.1. Spherically shaped transducers

This fabrication technique, described by Lockwood et al. [START_REF] Lockwood | Fabrication of spherically shaped ceramic transducers[END_REF], has allowed to increase significantly the sensitivity of focused transducers, for centre frequencies around 50 MHz, compared to the more classical polymer-based devices. This method has been applied to both ceramic and single crystals (Figure 13). First, bulk ceramic is bonded on a malleable substrate (typically conductive epoxy layer) (1). Ceramic is then lapped to required thickness (generally few tens of microns) (2). The third step is the lapping of the substrate generally to around 100 microns and machining of the structure to final diameter. The two-layer composite is then heated and pressed into a spherically shaped well. The diameter of the well is the focal distance of the transducer (4). The shell is cooled and removed from the well (5). Finally, an attenuating backing is added.

Figure 13 : Diagram describing the main steps to obtain a spherically shaped ceramic transducer.

III.2. Cross section diagrams

Two possibilities exist for focusing. The first is the use of a spherically-shaped active element (Figure 14(a)), the second is the addition of lens (Figure 14(b)). In the case of a lens, a matching layer is first deposited on the flat piezoelectric element (section I.1) and by a moulding step, the lens is added (section I.2) (Figure 14(b)). For a press-focused transducer, the addition of a curved matching layer with constant thickness is more difficult. This can be made by spin coating for loaded epoxy, or by evaporation of a Parylene TM layer. Depending on the conductivity of the backing, electrical contacts are either made in this backing or on the rear face of the piezoelectric element. For the front face, the contact is made directly on the top electrode. A coaxial cable or SMA connector is finally added.

III.3. Cable

Cables always have an influence on the electroacoustic response of a transducer but it becomes more critical at high frequencies. The choice of the cable properties (impedance, length) must be taken into account in the optimisation process [START_REF] Chen | Optimization of pulse transmission in a high frequency ultrasound imaging system[END_REF]. On Figure 15, electroacoustic time and frequency responses of a high frequency single-element transducer (where performance has been first optimised without cable (see section IV.2)), are given for different cable lengths. Results clearly show that the cable can affect both the sensitivity and the bandwidth.

III.4. Overview of published results

The two next Tables (Tables 6 and7) give an overview of published results on high-frequency transducers using materials and/or process described in previous sections. Table 6 specifies essentially the characteristics (fabrication process, dimensions or material used) while Table 7 gives the corresponding performance such as bandwidth and sensitivity [START_REF] Lukacs | Single element high frequency (>50 MHz) PZT sol gel composite ultrasound transducers[END_REF][START_REF] Snook | Design, Fabrication, and evaluation of high frequency, single-element transducers incorporating different materials[END_REF][START_REF] Cannata | Design of efficient, broadband singleelement (20-80 MHz) ultrasonic transducers for medical imaging applications[END_REF][START_REF] Knapik | A 100-200 MHz ultrasound biomicroscope[END_REF] (if authors give these values). Concerning the sensitivity, the comparison between values is not always possible since the definition used by different authors is not identical. no no e: thickness of the piezoelectric material; f c : transducer centre frequency; F: focal distance;

F # : f-number; Z b : acoustic impedance of the backing -corresponding material; Z m1 and Z m2 : acoustic impedances of the first and second matching layers -corresponding material.

In these nine high-frequency transducers, a wide range of centre frequencies is observed (between 31 and 200 MHz). The press-focused process is essentially used. A majority of transducers have been designed to have a f-number between 2 and 3. With PT hollow sphere, this f-number is lower. For backing material, epoxy loaded with silver particles is mainly used. For matching layers, technology takes a very important place and generally only one matching layer is added. These matching layers are often in Parylene TM which allows uniform and repeatable deposition of controlledthickness layers. [START_REF] Snook | Design, Fabrication, and evaluation of high frequency, single-element transducers incorporating different materials[END_REF] 3 yes 47 ---23.7 Fiber composite [START_REF] Li | Samarium and manganese-doped lead titanate ceramic fiber/epoxy 1-3 composite for high-frequency transducer application[END_REF] 5 no 118 ---29.3 PT hollow sphere [START_REF] Meyer | Pre-focused lead titanate >25 MHz singleelement transducers from hollow spheres[END_REF] 2 no 33 ---20.1 PZT thick film [START_REF] Lukacs | Single element high frequency (>50 MHz) PZT sol gel composite ultrasound transducers[END_REF] 1 n o 5 2 2 0 2 9 5 -4 6 D: aperture; tuning: addition or not of a self inductor and a transformer; BW: bandwidth at -6dB;

AR: axial resolution (-6dB); LR: lateral resolution (-6dB); IL: insertion loss.

In accordance with properties given in section II for piezoelectric materials, LiNbO 3 and PT based single-element transducers deliver best performance for medical imaging corresponding to a good trade-off between resolution and sensitivity. Press-focused process seems to deliver better performance than lens-focused process [START_REF] Cannata | Design of efficient, broadband singleelement (20-80 MHz) ultrasonic transducers for medical imaging applications[END_REF]. Attenuation due to various lens thickness decreases the sensitivity (around -6dB for LiNbO3 transducers [START_REF] Cannata | Design of efficient, broadband singleelement (20-80 MHz) ultrasonic transducers for medical imaging applications[END_REF]) even if bandwidth is slightly increased. Moreover, LiNbO 3 single crystal seems to be a good candidate since the lapping is not limited by grain size. Finally, the transducer (LiNbO 3 based) with two matching layers (Ag epoxy and parylene) gives, as expected, the highest performance.

IV. Performance

IV.1. Modelling Electroacoustic behaviour of transducers includes electrical input impedance (that will govern energy transfer between the imaging system and the transducer), pulse-echo response (whose amplitude is linked to sensitivity and duration to axial resolution), and frequency response equal to the Fourier transform of pulse-echo response (which defines centre frequency and bandwidth). All these curves can be predicted with the assumption of single axis vibration, using equivalent electrical circuits such as KLM [START_REF] Krimholtz | New equivalent circuit for elementary piezoelectric transducers[END_REF][START_REF] Van Kervel | A calculation scheme for the optimum design of ultrasonic transducers[END_REF] or others [START_REF] Lockwood | Modeling and optimization of high-frequency ultrasound transducers[END_REF]. All transducer layers are taken into account as well as electrical elements such as electrical matching and cables. Finite element methods are also available [START_REF] Assaad | Finite element modelling of ultrasonic transducers using the ATILA code[END_REF][START_REF] Marechal | Electro-acoustic response at the focal point of a focused transducer as a function of the acoustical properties of the lens[END_REF] in cases where no assumptions can be made on acoustic modes.

Acoustic radiation patterns allow to define lateral resolution, which is high when lateral beam dimensions are low, and acoustic noise level (the off-axis power level measured in dB using the onaxis power level as a reference). The appearance of side lobes (which exist whenever there are amplitude steps on the surface defined by the transducer front face) or grating lobes (which are due to space sampling in arrays) tends to increase acoustic noise level. Lateral resolution is responsible for image sharpness and low parasitic lobe levels ensure the absence of artefacts in the lateral direction. Radiation pattern calculations can be performed by applying Huygen's principle (i.e. the transducer surface is assumed to be a series of point-sources, and the pressure radiated at any point is the sum of pressures radiated by each of the point-sources [START_REF] Kino | Acoustic waves: devices imaging and analog signal processing[END_REF]). For simple geometry (circular, annular or rectangular transducers), analytical results have been derived (impulse diffraction theories), and allow more efficient calculations [START_REF] Penttinen | The impulse response and pressure nearfield of a curved ultrasonics radiators[END_REF][START_REF] Selfridge | A theory for the radiation pattern of a narrow strip acoustic transducer[END_REF].

IV.2. Optimisation Methods based on minimisation index have been developed [START_REF] Thijssen | Optimisation of ultrasonic transducers[END_REF][START_REF] Rhyne | Computer optimisation of transducer transfer using constraints on bandwidth, ripple and loss[END_REF] in addition to analytical approaches [START_REF] Desilets | The design of efficient broadband piezoelectric transducers[END_REF][START_REF] Mc Keighen | Design guidelines for medical ultrasonic arrays[END_REF]. The main difficulty is first to choose the parameters and their contribution to the index. These parameters are determined as a function of the application and independently of the transducer configuration. Moreover, their calculations require only the electroacoustic response of the transducer. For medical imaging, transducers must have good resolution while keeping high sensitivity and the best trade-off must be found between these two conditions. To quantify these properties, as described on Figure 16, the three following parameters are defined: d6, d30 (related to resolution) and amp (related to the sensitivity). Weighting parameters (noted α, β, γ) are applied to d6, d30 and amp. Different trials have shown that α=8, β=8 and γ=3 lead to a performance index well adapted to medical imaging requirements:

PI=α(d6/T 0 )+β (d30/T 0 )+γ(amp× T 0 ) (

T 0 is the period corresponding to the centre frequency of the transducer. Other performance indexes can be defined [START_REF] Thijssen | Optimisation of ultrasonic transducers[END_REF][START_REF] Desmare | Optimisation method for ultrasonic transducers used in medical imaging[END_REF]. From an initial configuration of the transducer, the electroacoustic response and then the PI are first calculated using for example the K.L.M. model. With a minimisation method such as, for example, the simplex method, transducer characteristics are modified by iteration to obtain the minimal index and the corresponding optimised configuration.

IV.3. Results & comparison

Five different piezoelectric materials have been retained for comparison. P(VDF-TrFE) copolymer, LiNbO 3 single crystal, lead titanate (PbTiO 3 ) ceramic, soft PZT ceramic and finally a new PMN-PT single crystal will be compared. For all these simulations, three parameters have been fixed: the transducer centre frequency (50 MHz), the active area of the piezoelectric element (diameter of 3 mm i.e. an area of 7.07 mm 2 ) and the length of the 50 ohms coaxial cable (1.5 m). The active material thickness is adjusted to reach the 50 MHz frequency and one matching layer is considered for all these optimisations. A self inductor and a transformer are also taken into account (Figure 17). Table 8 gives all the parameters of piezoelectric materials used for the simulations (values from literature). The optimisation of the performance of each transducer allows to determine the characteristics of the matching layer (acoustic impedance and thickness), of the backing (only its acoustic impedance since this medium is supposed semi-infinite), the value of the self inductor and the ratio of the transformer. The results are summarised in Table 9 with the values of the insertion loss (calculated as the ratio between the received power and the power delivered by the generator in pulse echo mode) and the bandwidth at -6 dB. These simulations do not take into account the possibility of focusing by addition of lens. These results allow, for an identical configuration, to quantify the gain and compare the piezoelectric materials. Impulse responses are presented in Figure 18. Due to is relatively low k t , the P(VDF-TrFE) based transducer delivers a relatively low sensitivity in comparison with all other simulations. The results for PbTiO 3 and soft PZT are similar. The electrical matching allows to compensate the differences in dielectric constants. The LiNbO 3 single crystal delivers a similar bandwidth but a lower sensitivity since the dielectric constant is low. Finally, the PMN-PT single crystal gives the best tradeoff in terms of sensitivity and bandwidth. V. Transducer characterisation V.1. Passive materials Ultrasonic spectroscopy is generally used for measurement of high frequency properties of passive materials. The method is described in [START_REF] Wang | High frequency properties of passive materials for ultrasonic transducers[END_REF] to measure velocity and attenuation. Experimental set-up is given in Figure 19. Particular attention must be paid to the water properties such as attenuation which can not always neglected at high frequency. Recently, an alternative method to characterise thin passive layers was described [START_REF] Wang | Characterizing ultra-thin matching layers of high-frequency ultrasonic transducer based on impedance matching principle[END_REF]. The method is well adapted to obtain the characteristics of matching layers (thickness around 10 microns) directly at high frequency. The principle is to deposit the layer (∼λ/4) on a known substrate (acoustic properties and dimensions). Then, all the signals from the thin layer are used to obtain phase velocity and attenuation (Figure 20(a)). Another possibility is to use a resonance technique. For this, a thin piezoelectric disk (with resonance frequency over 30 MHz) is bonded to a substrate. The electromechanical and acoustic properties of the disk and substrate are previously measured. The thin passive layer is deposited on the front face of the piezoelectric disk and the modified electrical impedance is measured and fitted with KLM model to deduce the acoustic properties of the thin layer. For these two methods, velocities are obtained with good accuracy, but not the attenuation. Velocities of a Ag epoxy or Parylene TM matching layers have been measured by both methods.

V.2. Electroacoustic measurements

Electrical input impedance can be measured directly using a network or an impedance analyser, the front face of the transducer being in contact with a tissue-mimicking media or water. Typical frequency ranges are from one tenth of the resonance frequency of the piezoelectric layer to over twice this frequency. Pulse-echo response is obtained by exciting the transducer by an electrical impulse of duration less than half a period of the active element resonance, and by measuring the echo reflected by a large acoustic mirror immersed in water. The waveform is usually digitised, which allows FFT to be used in order to derive frequency response curves. At half amplitude of the normalised envelope echo, pulse duration at -6dB corresponding axial resolution is calculated (Figure 21). If a burst is generated instead of a pulse, sensitivity can also calculated as described in Figure 21 with the amplitude ratio of the echo and the burst for a given frequency. Specifically for high-frequency transducers, phantoms including tungsten wires (few microns diameter) with different axial and lateral spacing (typically from 500 to 30 µm) are fabricated and the images obtained when transducers are integrated in an imaging system allow to evaluate resolutions while avoiding the problem of point-target.

Interferometric laser probes can be used to measure acoustic wave displacements. With this method, excellent spatial resolution can be obtained and the high sensitivity allows to measure displacements of 10 -3 nm/Hz 1/2 [START_REF] Royer | Mesures optiques de déplacement d'amplitude 10 -4 à 10 2 Angström. Application aux ondes élastiques[END_REF]. The phase variation between the reflected optical beam (on a mirror) and a reference beam corresponds to a displacement. For a focused transducer, a very thin metallised membrane can be placed perpendicularly to propagation axis (z) of the transducer. For each z value, the displacement is measured on the membrane and the radiation pattern in reconstructed [START_REF] Royer | Quantitative imaging of transient acoustic fields by optical heterodyne interferometry[END_REF]. Another possibility is to use the experimental set-up described in Figure 23 where optical beam and mirror are perpendicular to the axis (z) of the transducer [START_REF] Jia | Optical heterodyne detection of pulsed ultrasonic pressures[END_REF]. In this case the phase variation in only due to the optical index variation induced by acoustic pressure. water This is an integral measurement, data is collected for several directions in the (x, z) plane and a tomographic reconstruction allows to obtain the pressure field. This process can be repeated at different depths to obtain the complete radiation field [START_REF] Bou Matar | Characterization of airborne transducers by optical tomography[END_REF][START_REF] Remenieras | Acoustic pressure measurement by acousto-optic tomography[END_REF]. Using this technique, measurements have been performed on a 20 MHz single element transducer.

The results are given in Figure 24 [START_REF] Grégoire | Echographie haute-résolution : technologie et applications en dermatologie et ophtalmologie[END_REF].

VI. Conclusion & Perspectives

High-frequency single-element transducers have been the focus of many research projects in the past years, and several technologies have been developed, some of which are industrially exploited.

Polymer-based transducers have first been produced, but more recently ceramic and single crystalbased devices have proven to deliver higher performance. The trend is now moving towards array transducers [START_REF] Ritter | A 30-MHz piezo-composite ultrasound array for medical applications[END_REF][START_REF] Lacaze | 20 MHz ultrasound array for medical imaging: from design to image evaluation[END_REF], following first attempts in the early 90's [START_REF] Lethiecq | Miniature high frequency array transducers based on new fine grain ceramics[END_REF] around 20 MHZ. The aim is now to produce linear arrays in the 25 to 50 MHz range. Some authors are investigating high-frequency 2D arrays [START_REF] Buma | A high-frequency, 2D array element using thermoelastic expansion in PDMS[END_REF], as well as new technologies such as optical arrays [START_REF] Hamilton | High frequency ultrasound imaging with optical array[END_REF] and capacitive micro-machined devices [START_REF] Oralkan | Capacitive micromachined ultrasonic transducers: Next-generation arrays for acoustic imaging?[END_REF].

Figure 1 :

 1 Figure 1 : (a) Classical diagram of a single-element transducer. (b) and (c) Frequency and impulse responses of : black line : piezoelectric element (water on front face and air on rear face), grey line : piezoelectric element+backing, white line : with matching layer.

Figure 2 :

 2 Figure 2 : Shape-focused transducer.Figure3: Lens-focused transducer.

Figure 3 :

 3 Figure 2 : Shape-focused transducer.Figure3: Lens-focused transducer.

DFFFigure 4

 4 Figure4represents values of the thickness mode coupling factor (k t ) versus the acoustic impedance (Z) for a wide range of available piezoelectric materials. It can be observed that no material allows to obtain both high coupling and low acoustic impedance (ideal area in Figure4). The best trade-off must be found among these materials. For almost all medical transducers applications, PZT piezoceramics are used because of their high coupling factor, even if their acoustic impedance is high, since this can be compensated for by using acoustic matching layers in the transducer structure. For a given application, properties such as dielectric constant and grain size allow to choose a specific material reference. A large range of properties can be found from relatively low (a few hundred) to very high (a few thousand) relative dielectric constants with grain sizes from one to ten micrometers. For large area devices such as single element transducer, a moderate dielectric constant allows good electrical matching to cables and electronics (which are typically at 50 to 80 ohms) (area 1), while array elements require much higher dielectric constants (area 2).

PZT:Figure 4 :

 4 Figure 4 : (a) Electromechanical coupling factor in thickness mode (k t ). (b) Relative dielectric constant at constant strain (ε 33r S ) versus of the acoustic impedance (Z) for a wide range of piezoelectric materials.

Figure 5 :♦

 5 Figure 5 : (a) Experimental set-up for electrical impedance measurements. (b) Experimental and theoretical complex impedance (fit) of high frequency piezoelectric disk in free resonator conditions. (c) Experimental and theoretical impedance (real part) (fit) of high frequency piezoelectric thick film on alumina substrate. Typical parameters characterised are the following: ♦Resonant (f r ) and antiresonant (f a ) frequencies which correspond respectively to maximum of real admittance and real impedance; ♦The thickness coupling factor (vibration corresponding to a thickness mode) can be calculated with π π = r r t a a f f k c o t ( ) 2 f 2 f (2); ♦ The longitudinal wave velocity =

Figure 6 :

 6 Figure 6 : (a) Copolymer sheet. (b) High frequency copolymer based transducer.

Figure 7 :

 7 Figure 7 : Tape-casted self supported disk photographs. (a) (b) from Ferroperm piezoceramics (Denmark), (c) from Laboratoire de Céramique (EPFL, Switzerland).

Figure 8 :

 8 Figure 8 : (a) Cross section of optical microscope photograph of screen-printed PZT thick film on porous PZT substrate. (b) Schematic screen-printing process with intermediate substrate.

Figure 9 :

 9 Figure 9 : (a) Schematic representation of a 1-3 piezo-composite sample. (b) Typical variation of the thickness coupling factor (k t ) of a 1-3 piezo-composite as a function of the volume fraction of the ceramic.

  Figure 10 : (a) Schematic representation of a 2-2 piezo-composite sample. (b) Schematic cross-section of a high frequency 2-2 piezo-composites used. (c) Schematic representation of Interdigital Pair Bonding process.

Figure 11 :

 11 Figure 11 : Schematic representation of a 0-3 piezo-composite sample.

Figure 12 :

 12 Figure 12 : Main steps for the shell fabrication based on hollow sphere.

d 33 :

 33 piezoelectric coeffcient; δ δ δ δ e : dielectric losses; δ δ δ δ m : mechanical losses.

Figure 14 :

 14 Figure 14 : Cross-sections of schematic representation of transducers (a) press-focused and (b) lens-focused.

Figure 15 :

 15 Figure 15 : (a) Schematic view of the simulated single-element transducer. (b) Electroacoustic time responses. (c) Frequency responses.

Figure 16 :

 16 Figure 16 : Parameters used for performance index calculation from the transducer electroacoustic response.

Figure 17 :

 17 Figure 17 : Scheme of simulated transducers.

  thickness of the piezoelectric material; Z b and Z m1 : acoustic impedances of the backing and matching layer; e m1 : thickness of the matching layer normalised by a quarter-wavelength; tuning: addition or not of a self inductor and a transformer; BW: bandwidth at -6dB; IL: insertion loss.

Figure 18 :

 18 Figure 18 : Electroacoustic responses of the five simulated transducers.

Figure 19 :

 19 Figure 19 : Set-up of measurement of longitudinal velocity and attenuation by ultrasonic spectroscopy.

Figure 20 :

 20 Figure 20 : (a) Experimental set-up for thin layer (∼λ/4) characterisation by transmission method. (b) Experimental set-up for thin layer characterisation by resonance method.

Figure 21 :

 21 Figure 21 : Measurements of the axial resolution and sensitivity.V.3. Radiation diagram measurementsRadiation patterns can be measured in transmit mode using a point hydrophone receiver which scan the half space in front of the transducer. Alternatively, in transmit/receive mode, a point-target is scanned, and the amplitude of the echo is plotted as function of target position. The effective diameter of the hydrophone or target must be very small: much lower than the beam width and lower than a wavelength in water. The target must not generate parasitic echoes. Lateral resolution and depth of field are measured as specified in Figure22.

Figure 22 :

 22 Figure 22 : Measurements of the lateral resolution and depth of field from the radiation pattern.

Figure 23 :

 23 Figure 23 : Experimental set-up for acoustic pressure measurement by optical method.

Figure 24 :

 24 Figure 24 : Spatio-temporal evolution of acoustic beam (20 MHz transducer) between z=7 and 19mm (1mm step).

Table 2 :

 2 Properties of self supporting samples made by tape-casting.

	Materials			ε ε ε ε 33 S /ε ε ε ε 0 k t (%) f a (MHz) ρ ρ ρ ρ (kg/m	3 ) δ δ δ δ m (%)	ref
	Pz21 (PNNZT)	1920	43	33.9	7420	4.7	[25]
	Pz29 (PZT)		1035	35.5	34.1	6900	6.0	[25]
	PZT			675	43	46	-	3.6	[26]
	ε ε ε ε 33	S	/ε ε ε ε

0 : clamped dielectric constant; k t : thickness coupling factor; f a : antiresonant frequency; ρ ρ ρ ρ: density; δ δ δ δ m : mechanical losses.

Table 3 :

 3 Properties of screen-printed samples on different substrates.

	material	process	substrate e (µm) ε ε ε ε 33	S	/ε ε ε ε 0 v l (m/s) k t (%) δ δ δ δ e (%) δ δ δ δ m (%) Z (MRa)	ref
	PZT/PGO Screen-printing	PZT	35.5	334	3240	47	4.7	4.8	-	[27]
	PZT/PGO Screen-printing	Al 2 O 3	39	342	3940	39.7	2.0	1.5	-	[27]
	PZT	Spin coating	Al	20	220	3950	24.4	-	-	21.8	[28]
	ε ε ε ε 33 S /ε ε ε ε 0 : clamped dielectric constant; v l : longitudinal wave velocity; k t : thickness coupling factor; δ δ δ δ e : dielectric losses; δ δ δ δ

m : mechanical losses; Z: acoustic impedance.

Table 5 :

 5 Properties of shell samples.

	Material -shell	ε ε ε ε 33
	PT	280	~50	48-52	68	<2	12-17	[44]
	ε ε ε ε 33

T /ε ε ε ε 0 f a (MHz) k t (%) d 33 (pC/N) δ δ δ δ e (%) δ δ δ δ m (%) ref T /ε ε ε ε 0 : clamped dielectric constant; f a : antiresonant frequency; k t : thickness coupling factor;

Table 6 :

 6 Overview of published results on high-frequency transducers (part 1).

	Material	e (µm) f c (MHz)	shaping	F # /F (mm)	Z b (MRa)-material	Z m1 (MRa)-material	Z m2 (MRa)-material
	P(VDF-TrFE) [19]	17	34	prefocused	2.7/6	15 -Ag epoxy	no	no
	PVDF[36]	9	48.1	prefocused	2-3/-	3.15 -pure epoxy	no	no
	LiNbO 3 crystal [47]	-	7 8	prefocused	2/-	5.9 -Ag epoxy 7.3 -Ag epoxy 2.6 -parylene
	LiNbO 3 crystal [36]	60	44.5	lens (epoxy)	2-3/-	5.9 -Ag epoxy 7.3 -Ag epoxy	no
	LiNbO 3 crystal [48]	-	200	prefocused	1.15/0.8	4.3 -Ag epoxy	no	no
	PT ceramic [36]	32	45.1	prefocused	2-3/-	5.9 -Ag epoxy	3-parylene	no
	Fiber composite [39]	32	31	prefocused	-/17.5	Porous polymer	no	no
	PT hollow sphere [44] 70-90	39.8	-	-/1.43	6 -Ag epoxy	parylene	no
	PZT thick film [28]	-	7 2	prefocused	-/2.8	Ag epoxy

Table 7 :

 7 Overview of published results of high-frequency transducers (part 2).

	P(VDF-TrFE) [19]	2.2	no	70	51	-	-
	PVDF [36]	3	no	118	-	-	-45.6
	LibO 3 crystal [47]	3	yes	73	-	-	-13.5
	LiNbO 3 crystal [36]	3	yes	74	-	-	-21.3
	LiNbO 3 crystal [48]	0.7	-	22	12	14	-18
	PT ceramic

Material

D (mm) tuning BW (%) AR (µm) LR (µm) IL (dB)

Table 8 :

 8 Piezoelectric material parameters for high-frequency single element transducer simulations.

	Material	k t (%) ε ε ε ε 33 S /ε ε ε ε 0 ρ ρ ρ ρ (kg/m	3 ) v l (m/s) δ δ δ δ e (%) δ δ δ δ m (%) Z (MRa)
	P(VDF-TrFE) [19]	33	4.1	1932	2380	6.9	4.0	4.6
	LiNbO 3 crystal [36]	49	28	4640	7340	0.1	0.01	34.1
	PT ceramic [36]	49	200	6900	5200	0.9	0.83	35.9
	PZT soft ceramic [60]	50	800	7900	4390	2.5	2.7	34.7
	PMN-33%PT [61]	62	712	8060	4645	-	-	37.4
	k t : thickness coupling factor; ε ε ε ε 33 S /ε ε ε ε 0 : clamped dielectric constant; ρ ρ ρ ρ: density; v l : longitudinal wave velocity; δ δ δ δ e : dielectric losses; δ δ δ δ m : mechanical losses; Z: acoustic impedance.

Table 9 :

 9 Design and performance parameters of high-frequency single element transducers.

Material e (µm) Z b (MRa) Z m1 (MRa) e m1 (×λ/4) tuning BW(%) IL(

dB) P(VDF-TrFE)

		22.4	1.2	2	1.5	Yes	71	26
	LiNbO 3 crystal	69.6	4.5	4	1.2	Yes	70	23.4
	PT ceramic	51.0	4.3	4.3	1.2	Yes	53	19.7
	PZT soft ceramic 43.1	4	4.2	1.2	Yes	54	20.6
	PMN-33%PT	44.3	2.7	4	1.0	Yes

Acknowlegement

The authors would like to thank co-workers of LUSSI/GIP ULTRASONS in Tours & Blois and colleagues from teams involved in HF ultrasound around the world for fruitful discussions and cooperation.


Modeste Assemien
email: nguetta.assemien@ec-lyon.fr

Simon Pouget
email: simon.pouget@eiffage.com

Alain Le Bot
email: alain.le-bot@ec-lyon.fr

NOISE INDUCED BY DYNAMIC CONTACT FORCES OF A RUB-BER CYLINDER ROLLING ON ROAD PAVEMENT SAMPLES

Keywords: dynamic force, rolling noise, pavement

Tire/road noise, also called rolling noise, is an important part of vehicle noise. The mechanical interactions between tire pattern and the road asperities is a major contributor to mechanisms at the origin of tire/road contact noise. This paper presents an experimental study of the dependence between the dynamic contact forces and the rolling noise. A measurement campaign was carried out on asphalt pavement samples to achieve this aim. It is found that the mean value of the normal contact force, responsible of the rolling noise, remains constant and the level in dB of this force increases linearly with the logarithm of the rolling speed.

Introduction

Road traffic noise has become a serious environmental pollution problem for human being problems and an important part of environmental noise [START_REF] Sandberg | Tyre/road reference book[END_REF]. It is widely known that road traffic noise has negative influences on human health [START_REF] Lambert | European Network on Noise and Health[END_REF]. Tire-road noise is a wide-band noise ranging from 100 Hz to 5000 Hz [START_REF] Iwao | A study on the mechanism of tire/road moise[END_REF] and considered to be the most dominant cause of road traffic noise above 30 km/h [START_REF] Anfosso-Lédée | Bruit de roulement automobile : influence du revêtement de chaussée[END_REF]. Rolling noise arises from a complex combination of physical processes which can be categorized into three groups: mechanical mechanisms caused by tangential and radial vibrations of the tire, aerodynamic mechanisms specifically air-pumping, Helmholtz and pipe resonances, and amplification effect, also called horn effect [START_REF] Kuijpers | Tyre/road noise models in the last two decades : a critical evaluation, Proceedings of Inter-Noise 2001[END_REF]. In literature, several relationships are used to study the phenomenology of the noise induced by the rolling speed between rough surfaces. The level of the noise in dB can be investigate by physical quantities such as the sound pressure level L p [START_REF] Yokoi | A Fundamental Study on Friction Noise(5th report, The influence of random surface roughness on frictional noise)[END_REF][START_REF] Othman | Surfaces roughness measuring using dry friction noise[END_REF][START_REF] Stoimenov | The roughness effect on the frequency of frictional sound[END_REF], the vibrational level L v [START_REF] Abdelounis | An experimental study on roughness noise of dry rough flat surfaces[END_REF] and contact force level L F [START_REF] Cesbron | Experimental study of tyre/road contact forces in rolling conditions for noise prediction[END_REF].

The purpose of this paper is to measure the dynamic contact forces between a rubber cylinder and asphalt concretes samples and find the influence of the rolling speed on the normal contact force level.

The paper is structured as follows. Section 2 describes the experimental device and the procedure of measurement. In section 3 experimental results and discussion are presented. A conclusion giving the summary of the main outcomes closes the paper.

Experimental setup 2.1 Experimental device

The experimental device, also called LUG, shown in Fig. 1 is composed of concrete bloc with mass of 600 kg supported by four air springs. The rubber cylinder is fixed to a high precision spindle and the pavement sample is screwed at the center of top plate on the concrete bloc with its aluminum support. The rotations of the rubber cylinder and the plate are controlled with two different brushless synchronous motors with a rotational speeds ranging from 0.001 to 1000 rpm. The reactions of the spindle are measured by six cantilever strain gage force sensors which are connected to electronic amplifiers. Forces and moments can be controlled and recorded through a computer.

Experimental procedure

The experiment consists of a freely rotating rubber cylinder in contact on the top surface of a road sample. A constant rotation speed of 20 rpm is applied onto the road sample. A wheel whose surface is made of rubber is put into contact against the upper surface of the sample with a controlled static force ranges from 0 to 100 N. The tests are realized with a normal contact force of 35 N and a sweep is set for the rotation speeds from 0 to 500 rpm. At each step, the duration of measurement is 10 s with a total of 11 steps. The dynamic forces signals are acquired with sampling frequencies of 300 Hz and 10 kHz.

Road samples

The six pavements samples used for the experiment campaign shown in Fig. 2 concretes with aggregate size 0/6 mm. Thin asphalt are suitable and are known for their good acoustic performances. The sixth, labelled EN18153, is a semi grained asphalt with aggregate size 0/10 mm. This is a medium macro-texture asphalt concrete considered as a reference because this is the most used on the road network and parking. The composition of the six samples are summarized in Table 1.

Results and discussion

Time fluctuation of dynamic contact forces

The time fluctuations of longitudinal, lateral and normal forces are shown by Fig. 3 for sample EN18153 at speed 450 rpm (1.2 m/s). The absolute value of mean values of longitudinal and lateral forces, respectively 1.6 N and 3 N are negligible compare to the value of the mean value of normal force which is 36 N. This result is the same for all the asphalt concretes samples and rolling speeds. The means values of dynamic forces are constant and the data confirmed that the normal contact force is responsible of the rolling noise. The mean value of the normal contact force (see Fig. 4) is the same for the tested road samples and almost equal to initial load 35 N. At a given speed, the time evolution of the normal force is influenced by the texture of the pavement samples.

Rolling noise induced by normal contact force

In the literature, the overall noise level was largely studied. Sandberg and Ejsmont [START_REF] Sandberg | Tyre/road reference book[END_REF] proposed an empirical law between the noise level and the vehicle speed (Eq. ( 1)).

L = A + B log 10 V. ( 1
)
where L is the noise level in decibels, V the vehicle speed, A and B the regression coefficients.

In previous studies, several authors have used the same law (Eq. ( 1)) to predict the values of speed exponent n. Using the sound pressure level L p (Eq. ( 2)), Dubois [START_REF] Dubois | Modèle de contact dynamique pneumatique chaussée par approche multi-aspérités: application au bruit de roulement[END_REF] has shown that n = 1.7 and Yokoi et al. have found that n varies between 0.6 and 1.1.

L p ∝ 20 log 10 V n (2)
ICSV27, Annual Congress of International Institute of Acoustics and Vibration (IIAV), 11-16 July 2021

Concerning the relation between vibrational level L v (Eq. ( 3)), the values of the speed exponent found by Abdelounis at al. [START_REF] Abdelounis | An experimental study on roughness noise of dry rough flat surfaces[END_REF] are ranged from 0.7 to 0.96.

L v ∝ 20 log 10 V n (3)
The normal force level is the physical quantity used in the present study to investigate the rolling noise. We make the assumption that the values of longitudinal and lateral forces are equal to zero. From our measurement the normal force level in dB is expressed by the following relationship:

L F = 20 log 10 ( σ F σ ref ) (4)
where

σ F = ( 1 N N i=1 (F i -F z ) 2 ) 1/2
is the standard deviation of normal contact force, N the number of time samples, F i the instantaneous values of the normal force, F z the mean value of the normal force and σ ref = 10 -6 N. The normal force level can also be expressed as a scaling law (Eq. ( 5)):

L F = 20 log 10 V V ref m ( 5
)
where L F is the level of normal force, V the rolling speed m the speed exponent and

V ref = 1 m/s.
The evolution of the level of normal force is a linear increasing function of the logarithm of the rolling speed (see Fig. 5). The tested asphalts concretes may be classified in two groups, the first group is composed of samples EN18131, EN18155 and EN18156 with high level of normal force in dB and the second group composed of EN18132, EN18133 and EN18153 with lower level of normal force. The range of the speed exponent m is from 0.38 to 1.11. The results are in agreement with the previous investigations. In previous studies, the exponent of the rolling speed is ranged from 1 to 2.5 [START_REF] Kuijpers | Tyre/road noise models in the last two decades : a critical evaluation, Proceedings of Inter-Noise 2001[END_REF][START_REF] Anfosso-Lédée | Bruit de roulement automobile : influence du revêtement de chaussée[END_REF]. These values of the slope take into account mechanical vibrations and aerodynamical phenomena [START_REF] Sandberg | Tyre/road reference book[END_REF]. The difference between the values expected for the slope n and our results is due to the fact that in the present study, only the mechanism of vibrations is highlighted.

Conclusion

In this paper, an experimental study has been performed to measure the dynamic contact forces between a rubber cylinder and pavement samples. The results show that the normal force is responsible of the rolling noise and the mean value of this force is the same for the tested samples. The normal contact force level is a linear increasing function of the logarithm of the rolling speed.

Figure 1 :

 1 Figure 1: Experimental device. Rubber cylinder (Radius : 31.5 mm, width : 26 mm, thickness of the rubber : 5 mm), Pavement (thickness : 50 mm, radius : 49.5 mm)

Figure 2 :

 2 Figure 2: View of the six pavement samples used.

Figure 3 :

 3 Figure 3: Time fluctuation of dynamic contact forces. Fx longitudinal force, Fy lateral force and Fz normal force.

Figure 4 :

 4 Figure 4: Time evolution of the normal force at 500 rpm (1.34 mm/s) for the six samples.

Figure 5 :

 5 Figure 5: Relationship between L F , the level of normal force and the logarithm of the rolling speed of the rubber cylinder.

Table 1 :

 1 Composition of the asphalt concretes

	Pavement sample code	Type of asphalt concrete	Aggragate size	Sand	Stone
	EN18131	Thin asphalt	0/6 mm	0/2 mm (9.0%) 4/6 mm (82.0%)
	EN18132	Thin asphalt	0/6 mm	-	1/2 mm (15.4%) 4/6 mm (73.9%)
	EN18133	Thin asphalt	0/6 mm	0/2 mm (9.0%) 1/2 mm (9.0%) 4/6 mm (72.9%)
	EN18153	Semi grained asphalt 0/10 mm	0/4 mm (42.8%) 4/6 mm (8.0%) 6/10 mm (41.5%)
	EN18155	Thin asphalt	0/6 mm	-	1/2 mm (12.4%) 4/6 mm (73.9%)
	EN18156	Thin asphalt	0/6 mm	0/2 mm (9.0%) 1/2 mm (9.0%) 4/6 mm (72.9%)

ICSV27, Annual Congress of International Institute of Acoustics and Vibration (IIAV), 11-16 July 2021