Jingcai Wang
email: ajingcai.wang@ensam.eu

Laurent Langlois
email: blaurent.langlois@ensam.eu

Muhammad Rafiq

Régis Bigot
email: dregis.bigot@ensam.eu

Hao Lu
email: eluhao@sjtu.edu.cn

Experimental & Numerical Study of the Hot Upsetting of Weld Cladded Billets

Keywords: Bimaterial, Forgeability, Stainless steel, Weld cladding

 . Slab model and finite-element simulation are conducted to parametrically study the potential forgeability of the bimaterial cladded billet. The viscoplastic law is adopted to model the friction at the die/billet interface. The friction condition at the die/billet interface has a great impact on the final material distribution, forging effort and cracking occurrence. With Latham and Cockcroft Criterion, the possibility and potential position of cracks could be predicted.

I.

Introduction

Bimaterial cladded workpiece could satisfy the complex functional requirements as well as attain a compromise between performances and manufacturing costs. The selection of its manufacturing processes is decided by various elements such as mechanical and metallurgical properties, productivity and costs. The classical fabrication process of cladded products sequentially includes the preform manufacturing, forming process, weld cladding process and finishing process. After the forming process, the preforms become complex to be weld cladded, conducting the problem of low efficiency and bad quality control of the following weld cladding process. The presented work has changed the order of the fabrication process. Performing the weld cladding process before the forming process, a simple preform is weld cladded and then forged to obtain the final complex form required. Higher productivity and better quality control are expected to obtain. At the same time, the final metallurgical structure of the cladding material is optimized by the hot plastic forming. The objective of this article is to study the ability of a weld cladded billet under hot forging to obtain a desired form with defect free material distribution and structure. A bimetal could fabricate by various process such as diffusion bonding, rolling, extrusion, simultaneous plastic deformation [START_REF] Vamsi Krishna | Analysis of deformation during simultaneous plastic deformation of dissimilar powder metallurgical preforms[END_REF] , cladding and powder metallurgy technique [START_REF] Krishna | Co-extrusion of dissimilar sintered P/M preforms-an explored route to produce bimetallic tubes[END_REF] etc. Mehmet Şimşir et al. have produced a bimetal bulk consisting of stainless steel (SS316L) and structural steel (30CrNiMo8) by shell mold casting technique [START_REF] Şimşir | An investigation into stainless steel/structural-alloy-steel bimetal produced by shell mould casting[END_REF] . The authors have characterized the metallurgy and mechanical properties of the bulk, but never the forgeability. Presently, little work is available on the forgeability of bimaterial cladded billet. Joseph Domblesky et al. have studied the forgeability of welded preforms. Two cylindrical billets of same metal and different metals are butted by general friction weld. The authors find that such preforms have adequate workability based on upsetting and side pressing tests, although flow tends to be concentrated in the lower strength alloy for bi-metal preforms [START_REF] Domblesky | Welded preforms for forging[END_REF] . Later, the authors investigate the mechanical properties and microstructural evaluation of these forged welded preforms by tensile testing. The results show that for same-metal specimens the microhardness and microstructure after hot working are fairly uniform and consistent with the surrounding base metal pieces in the weld vicinity. For the bi-metal ones, an asymmetric hardness gradient is generated [START_REF] Domblesky | Mettalographic evaluation of welded forging preforms[END_REF] . K. Essa et al. [START_REF] Essa | Upsetting of bi-metallic ring billets[END_REF] have done a work similar to the work presented in this paper. The authors have studied the cold upsetting of bi-metallic ring type billets which consists of a solid inner C15E cylinder and a ring of mild steel (C45E) fitting around the former cylinder by friction. The objective is to find a success process for cold forging of such bi-metallic billets. The results show that under certain conditions, bi-metallic billets may be upset while maintaining a good interfacial contact between the two components within a range of geometries. The presented work concentrates on the hot forgeability of a low carbon steel (C15) billet coated by austenitic stainless steel (SS316L) by MIG cladding. A series of upsetting tests with different ratios and using different friction conditions at 1050°C are performed. Slab model and finite-element model are introduced. Comparison is performed between the experimental results and the numerical results. Upsetting is considered as a forgeability testing of the bi-material. The intended applications concern hot forming of raw preforms like cylindrical billet or flat sheet partially cladded [START_REF] Rafiq | Hot forming of a cladded component by automated GMAW process[END_REF] .

II. Upsetting of weld cladded billet

The hot upsetting test is a basic hot ductility test consisting of compressing a series of cylindrical specimens to various levels. The limit for compression without radial or peripheral cracking is considered to be a measure of forgeability. The upsetting tests are performed to understand the fundamentals of material flow and the initiation of cracking during the deformation to obtain the forgeability limits of cladded specimens.

Principle of experiments

In the upsetting test, a billet is upset between two plat dies at 1050°C until a crack appears. Depending on the appearance of cracks, the upset ratio of the next trial is increased or decreased. The increase or decrease step is adjusted referring to the total specimen height. From the last test without cracks, the upset increment step is reduced to refine the applicable range. The cladded specimens are obtained by cutting a weld cladded bar. A mild steel bar (0.15%C, 0.45%Mn, 0.2%Si, 0.023%P and 0.023%S) with a diameter of Ø27mm is cladded by stainless steel (0.02%C, 1.8%Mn, 0.33%Si, 0.023%P, 0.013%S, 17.5%Cr, 2.55%Mo and 12.2%Ni) wire (Ø1.0mm) by MIG process on rotating welding platforms. The bar is then cut into 45mm-high specimens. The main parameters of the MIG cladding process are shown in Table 1. Fig. 1 shows the longitudinal section of the cladded billet. The substrate/cladding interface exhibits a wavy morphology. The mean cladding thickness is about 3mm. For a billet of 45 mm, there are about 10 beads. The cladding is composed of juxtaposed bead rings instead of a coil. There is an overlapping on the beginning of the bead by the end of the same bead. The overall dilution rate between the filler material and the substrate is about 10%. This relatively low value for MIG cladding is achieved owing to overlapping. The upsetting tests were performed on a hydraulic press machine, with a mark of Loire ACB, with a maximum load of 6000 kN. The specimens were heated 15 minutes at 1050°C under normal atmosphere in an electric furnace, while the dies were not preheated. The tribological condition at the die/billet interface was an input of the experimental parametric study. Therefore, the tests were performed with lubricated and dry smooth dies as well as striated dies. Theses dies respectively corresponded to low, strong and sticking friction on the die/billet interface. The lubricant was a mixture of water and graphite. It was deposited on the smooth die by a brush before each test. There are many concentric circular grooves on the plan of the striated die. The distance between two successive grooves was about 1mm with a depth of 1 mm. The specimens were taken out of the furnace and upset immediately. The upset velocity was constant about 30mm/s. The specimen was upset to various ratios with the help of stop blocks placed between the die holders.

Modelling

The upsetting test is also studied numerically. This part is devoted to study the crack occurrence in bi-material cladded billet, estimate the material distribution, predict the forging effort and evaluate the effect of process parameters.

a. Slab model

The slab model, based on classical slab model of non-cladded billet upsetting, integrates the continuity condition through substrate/cladding interface. Fig. 2 shows the geometrical and other parameters of the model. A viscoplastic law is applied for modelling the friction condition at the die/billet interface.

Fig. 2 Slab model of weld cladded billet

The slab model is based on several assumptions: -The cladded billet and the substrate/cladding interface remain cylindrical during the deformation; -The temperature of the billet is constant and uniform during the upsetting; thermal exchange with dies and dissipated energy are neglected; -The material behavior can be modeled by a simplified Spittel thermo-viscoplastic law; -Plasticity can be governed by the von Mises criterion; -Friction at die/billet interface can be represented by a viscoplastic law. According to the cylindrical symmetry and considering the mass conservation principle, the velocity field is obtained as below: (1) where is constant and corresponds to the upsetting velocity. The magnitude of the sliding speed at die/billet interface during the deformation is as below:

(2)

The plastic strain rate is uniform in the cladded billet and given by Eq. 3.

(3)

The equivalent plastic strain is given by Eq. 4.

(4) where h 0 is the initial height of the billet. In order to get the stress tensor of billet, von Mises plasticity criterion is applied with conditions that the deviatory stress is parallel to strain rate and the equivalent stress is equal to the flowing stress of the material. In this condition, one can get:

Lower die r z Upper die h slab R e v r, z = - rh 2h e r + z • h h e z ℎ v g = r h 2h ε p = - 1 2 0 0 0 - 1 2 0 0 0 1 h h ε = ln ! h 0 h " (5)
Where σ is the complete stress tensor, σ 0 is the flow stress of the material and σrr is the normal stress in the radial direction.

The fundamental principle of applied statics is applied to the slab bounded by: ( 6), ( 7), (8) Considering the following equilibrium in the direction :

(9

)
Where τ is the tangential stress at the die/billet interface corresponding to friction. τ is negative and opposes the sliding of material on the die. Developing the relationship of order 2 one can get:

(10)

The relation between the friction stress and the thermomechanical conditions at die/billet interface is modeled by a viscoplastic law:

(11

)
where α is the friction factor, σ 0 is the flowing stress and P f is the friction exponent. According to Eq. 2, 10 and 11, the general expression of the radial stress is given as:

(12

)
where C is an integrating constant and K is given by Eq. 13.

(

) 13
According to the considered zone in the billet (substrate or cladded layer), the value of K, σ 0 , P f and C of Eq. 12 have to be adapted. The radial stress is continuous through the susbtrate/cladding interface and is equal to zero at the external free surface of the billet. Considering these boundary conditions, Eq. 12 leads to:

(14) (15)
Considering the axi-symetry of the problem,the forging effort is given by the following equation:

(16) σ = $ σ rr 0 0 0 σ rr 0 0 0 σ rr -σ 0 % r ∈ 'r, r + dr); θ ∈ ,θ - dθ 2 , θ + dθ 2 -; z ∈ '0, h) e r
h σ rr + dσ rr r + dr dθ -hrσ rr dθ -2hσ rr !sin θ 2 " dr -2τrdrdθ = 0

dσ rr = -2 τ h dr τ = -ασ 0 v g P f σ rr = Kσ 0 • r P f +1 + C K = α • 2 1-P f h • 6 h h 7 P f • 1 P f + 1 σ rr = K σ 0s r P f +1 + σ 0r -σ 0s R P f +1 -σ 0r R + e P f +1 r ∈ '0, R) σ rr = Kσ 0r r P f +1 -R + e P f +1 r ∈ 'R, R + e) F = -2π ; σ zz R+e 0 rdr
The axial stress σ zz is function of the flowing stress and the radial stress as it can be seen in Eq. 5.

Finally, the forming load is given by Eq. 17.

(

) With (18) 17
R and e are functions of the initial geometry (h 0 , e 0 , R 0 ) of the billet and the upsetting height.

According to the principle of volume conservation:

(21) The flowing stress of the substrate could be calculated from the equivalent plastic strain and strain rate. It's described by a simplified Hansel-Spittel law (see Eq. 22) that is well suited to represent the hot forming behavior of metals:

(22)
The law with associated coefficients is only valid for given range of temperatures, strain and strain rate data for each material. The forging effort, calculated by the slab model, depends only on:

-The initial geometry of the cladded billet (h 0 , e 0 , R 0 ) -The friction factor at the die/billet interface -The flowing stress of the two materials

b. Finite-element model

The finite-element model is implemented on the platform of Forge2011®. Considering the symmetry of the problem, a 2-D axe-symmetric hot forging model is adopted. The rheological law used by the software is a simplified Hansel-Spittel law in the form of equation ( 22). The bilateral sticking criterion is applied to the substrate/cladding interface although there is practically weld cladding interface between them. A high heat exchange coefficient (2×10 4 Wm -2 K -1 ) is applied in order to reduce the temperature discontinuity at the interface regardless of the heat flux. Special attention is paid on the substrate/cladding interface geometry, refining the grids of the interface zone in order to better control the continuity conditions through the interface. The simulation model is shown in Fig. 3. Two types of substrate/cladding interface, cylindrical and wavy (sine) morphology, are adopted and compared in the study. The latter is implemented in order to estimate the effect of the wavy morphology of the substrate/cladding interface. Fig. 3 also shows the geometrical parameters of the sine-wavy interface. A weak heat exchange (2×10 3 Wm -2 K -1 ) is applied to the die/billet interface. The tribology is described by viscoplastic law. The dies are considered to be rigid.

c. Simulation parameters

The coefficients of the Spittel law of the substrate and cladding materials for slab model and finite element simulation are given in Table 2. They are extracted from the Forge2011® database and correspond to thermo-viscoplastic behavior of low carbon steel C15 and stainless steel SS316L. The effects of dilution resulting from the cladding process are neglected. Three levels of friction conditions are considered. The sticking condition, corresponding experimentally to upsetting tests performed with striated dies, cannot be taken into account by the slab model. For the upsetting tests performed with dry and lubricated smooth dies, the parameters of the viscoplastic friction law are given in Table 3.

Table 3 Parameters of the hydraulic press

Friction conditions α P f Lubricated die 0.3 0.15 Dry die 0.5 0.15

The forming velocity is 30mm/s. The initial dimensions of the cladded billet are given in Fig. 1. For finite element calculation, a dwell time of 5 seconds is introduced before upsetting in order to take into account the experimentally unavoidable time between the moment when the billet is placed on the lower die and the moment when the upsetting starts.

III. Results and discussion

With experimental and numerical studies, the final results of hot upsetting tests of weld cladded billet are analyzed. The analysis is focused on the material distribution, forming load and hot damage generated during deformation. The slab model results only concern the forming load.

Material distribution

Fig. 4 shows the material distribution obtained experimentally and after finite element calculation.

The longitudinal cross section of upset cladded billets are etched by Nital 2% for a few seconds. The material distribution is observed visually in the macrographs of longitudinal section as shown in Fig. 4. The hot forged substrate consists of a central trunk surrounded by a ring covered by the deformed cladded layer.

The material distribution varies with the tribology condition at the die/billet interface. The elongation of the cladded layer depends on the tribological conditions. The cladded layer becomes thinner or thicker after upsetting. In the case of sticking conditions the layer is thinned during forming. The obtained thickness is no more uniform (see Fig. 4). A zone with cladded layer thinning can be observed experimentally and by finite element simulation for tests performed with striated dies. The dissymmetry of material distribution between the upper and lower surface might be caused by the dwell time (about 5 seconds) between placing the billet on the lower die and forging. The billet has heat exchange with the lower die during the dwell time. Therefore, the material in the lower part of the billet is colder, causing larger flowing stress. This phenomenon emphasizes the important effect of heat exchange on material distribution of hot-upset cladded billet.

Fig. 4 Comparison of numerical and experimental results of materials distribution obtained with striated die (corresponding to sticking friction), lubricated and dry smooth dies

The finite element simulation is able to predict the material distribution, the effect of friction conditions and thermal exchange with the tool. The modeling of the wavy morphology of the bimaterial interface is necessary for accurate prediction of the thickness of cladded layer and to observe the detail shape of the interface. However, the overall distribution of the materials can be also predicted with smooth interface model as shown in Fig . 4.

Forming load

The evolution of forming load is traced experimentally and numerically. Comparisons are performed to evaluate the slab model and simulation model. Experimentally, the forming load and displacement of upper die are directly provided by the sensors in the hydraulic press machine. The forging effort is calculated from the pressure in the main cylinder of the machine with a precision corresponding to about ±5kN. Fig. 5 shows the evolution of forging effort for tests performed with different types of dies.

Fig. 5 Evolution of forging efforts for tests performed with different types of dies

The forging load-versus-displacement curves are quite similar to that of mono-material billet upsetting. At the end of the test, forming load increases sharply because of many factors: the increase of the billet diameter, the deformation rate increases during the forging (the forming velocity being constant), the accumulation of friction forces leading to an increase in hydrostatic pressure and the cooling of the billet with thermal exchange. The effect of friction condition is similar to that of upsetting of mono-material. The higher the friction conditions are the higher the forming load is for a given upsetting rate. Slab model and simulation are able to reproduce the effect of friction on the forming load. The developed slab model is not able to simulate sticking condition. The evolution of forging efforts is similar to the experimental result; the effect of friction factor is more sensitive at the end of upsetting. For finite element model, there is no notable difference concerning the forming load obtained with the smooth and wavy substrate/cladded layer interface.

Compared with the simulation results, the forming load obtained by slab model is higher. This is a well-known result, the kinematical assumption for slab model leading to overestimation of the stress and the associated forming load. In Fig. 7, one can note that the forming load measured experimentally between 5% and 50% is higher than that of finite element simulation or slab model. The difference is not caused by bad friction coefficient because its effect is mainly sensitive at the end of the upsetting. It might be due to the fact that the behavior of the cladded layer is modeled by the Spittel law of SS316L without considering the effect of dilution. In order to better estimate the forming load, it would be necessary to identify the behavior law of the cladded material.

Hot damage

Longitudinal and circumferential cracks, which occur only in the cladded layer and never propagate into the substrate, are observed on billet upset with striated dies at an upsetting ration around 70% (see Fig. 8). The circumferential cracks locate in the thinnest zone of the cladded layer on the top or lower surface of the billet. For smooth dies, lubricated or not, only longitudinal cracks are observed in tests with upsetting ratios higher than 70%. Circumferential cracks are specific feature for cladded billet. (

) 23
Where ε is the effective strain, σ max is the maximum principal stress if it's positive; otherwise it's equal to zero. σ eq is the von Mises equivalent stress. The probability of crack occurrence increases if the value of the indicator La is larger. According to Fig. 9, the Zone A and B are places with maximum values of La. Zone B corresponds to longitudinal crack and Zone A to circumferential cracks. The configuration of substrate/cladded layer interface impacts little the overall distribution of La. The occurrence and the location of circumferential cracks could be predicted even with smooth interface model. With Forge 2011®, the evolution of La for certain grids in Zone A and B are drawn (see Fig. 10). For 70% upset, the value of La in Zone A is larger than that in Zone B. The two curves intersect at the point where the upsetting ratio is slightly less than 70%. The simultaneous occurrence of two types of cracks in the billet tends to give the critic value of La for the hot ductility of the cladded billet at 1050°C. According to Fig . 10, the critic value is close to 0.6.

IV. Conclusions and perspective

The research proposes to characterize the hot forging of weld cladded billet by hot upsetting test. A parametric study of upsetting test concerning the friction conditions at die/billet contact is carried out by slab model and finite element simulation. The application involves the case of stainless steel cladded on carbon steel. In experimental tests, two types of cracks occur: longitudinal crack and circumferential crack. The latter occurs with striated die (equivalent to sticking condition). The curve of forging effort as function of upsetting ratio is typical for upsetting test. Friction has same effect on forging effort as for the upsetting test of mono-material billet. A slab model is developed considering a visco-plastic friction law at die/billet contact. It permits getting the analytical expression of forging effort as function of upsetting ratio and certain processing parameters such as friction coefficients.

With Latham and Cockcroft Criterion, the finite element simulation allows predicting the possible position of crack observed experimentally regardless of the accuracy of the geometrical modeling of the substrate/cladded layer interface. More precisely, it seems unnecessary to take into account the periodic aspect of the substrate/cladding interface to predict overall material distribution, the forging effort and the crack occurrence. Wavy morphology should be considered to obtain more accurate cladding thicknesses. The circumferential crack is specific to cladded billet due to overall mechanical interaction between the substrate and the cladded layer. This crack is the result of the lack of hot ductility of the cladded material, the initial material distribution and the hot forging process parameters like friction.

Fig. 1

 1 Fig.1The longitudinal section of a weld cladded specimen

RFig. 3

 3 Fig. 3 Model with sine curve interface and model with straight interface

Fig. 6

 6 Fig. 6 Evolution of forging efforts (a) for slab model, (b) for finite element model with wavy interface

Fig. 7

 7 Fig. 7 Comparison of experiment, slab model and simulation

Fig. 8

 8 Fig. 8 Section of billet upset at 1050°C with striated die In Forge2011®, it is possible to estimate the probability of the damage of billet by calculating the Latham and Cockcroft coefficient. The indicator La is used to predict crack occurrence. Its expression is given by Eq. 23:

Fig. 9

 9 Fig. 9 Distribution of indicator La for simulation with sticking friction

Fig. 10

 10 Fig. 10 Evolution of the indicator La for simulation corresponding to different friction conditions For simulations performed with viscoplastic friction conditions, La remains lower in Zone A than in Zone B. This explains why circumferential cracks are only observed for upsetting tests with striated dies.

Table 1

 1

			Parameters of MIG cladding process
	Parameters	Nozzle-to-bar distance [mm]	Wire feed speed [mm/s]	Voltage [V]	Welding speed [mm/s]	Protection gas [% in volume]	Generator	Welding machine
						Ar96%,		6-axes
	Value	16	4.2	22	5.3	CO 2 3%,	CY385MPR	polyarticular
						H 2 1%		robot (SCS)

Table 2

 2 Coefficients of Hansel-Spittel Law for hot upsetting simulation

	Material	Coefficients of simplified Hansel-Spittel Law A (Mpa) m 1 m 2 m 3 m 4
	C15	890.4543 -0.00234 -0.12626 0.13938 -0.0477
	SS316L 8905.34 -0.00383 0.01246 0.09912 -0.02413

The results obtained by upsetting test could be the base for identification of the behavior law of the constitutive material of the cladded layer. Indeed, this last one is the result of the solidification of a mix of the filler material and the substrate and is a priori unknown. Further investigations have to be conducted about the evolution of the cladded microstructure during forming and subsequent cooling. Residual stresses within the cladded layer as result of the thermal expansion difference between the substrate and the cladded layer have to be considered.

V.


Prof Elie Johan Lefeuvre

Dr Marion Moulin

Dr Emile Woytasic

Dr Gaël Martincic

Dr Guy Pillonnet

Prof. Lemarquand

Iman Shahosseini
email: iman.shahosseini@u-psud.frwww.ief.u-psud.fr

Johan Moulin

Marion Woytasic

Emile Martincic

Gaël Pillonnet

Guy Lemarquand

Electromagnetic MEMS Microspeaker for Portable Electronic

Keywords: electromagnetic, microspeaker, MEMS, silicon membrane, piston electromagnetic, microspeaker, MEMS, silicon membrane, piston SPL: Sound Pressure Level, FEM: Finite Element Method, SOI: Silicon On Insulator, DRIE: Deep Reactive Ion Etching, RIE: Reactive Ion Etching

This work presents the conception, the microfabrication, and the electroacoustic characterization of a new electromagnetic microspeaker based on silicon. The objectives are to get improved sound quality compared to that of conventional microspeakers, while keeping the electroacoustic efficiency as high as possible. An optimized stiffening silicon microstructure let the sound radiator be extremely light and rigid. The mobile part is suspended to the fixed part by silicon suspension springs, which enable large out-of-plane displacement. The acoustic radiator is actuated by an electromagnetic motor, composed of a fixed permanent magnet and a planar coil located on top of the silicon radiator. The piston-like motion of the radiator favored by this structure is very beneficial for the sound quality. Electro-mechano-acoustic characterization of the microfabricated microspeaker showed that the radiator surface could run out-of-plane with displacements higher than ±400 µm, with no mechanical and electrical failure. For an electrical power of 0.5 W, the microspeaker was capable to generate a sound pressure level of 80 dB at 10 cm, from 330 Hz up to 20 kHz frequency. The efficiency reaches 3×10-5, that is to say three times more than typical efficiency of conventional microspeakers. Moreover, as characterization results showed, the existence of very few structural modes and the low electroacoustic distortions evidence the high sound quality of the microspeaker.

I. Introduction

Today, conventional microspeakers are widely spread in electronic mobile devices such as smart phones, tablets, laptops, personal digital assistants (PDA), etc.

However, the electroacoustic performances of these microspeakers remain limited in terms of power efficiency and sound quality. Their poor efficiency has a significant impact on power consumption. Indeed, when using a cellular phone in hands-free mode, nearly a third of battery power is consumed by the audio system [START_REF] Lee | High-level power management of audio power amplifiers for portable multimedia applications[END_REF]. Audio systems are typically composed of two main parts, the amplifier and the electroacoustic transducer. For mobile applications, class-D amplifiers are broadly used in the audio system, because of their very high power efficiency, more than 70%, good signal-to-noise ratio (SNR), low distortions, and small size, which simplifies their integration [START_REF] Groeneweg | Analog signal processing for a class D audio amplifier in 65 nm CMOS technology[END_REF][START_REF] Lin | Enhanced design of filterless class-D audio amplifier[END_REF]).

On the contrary, conventional microspeakers have efficiency typically in range of 0.001 % -0.01 %, and their non-linearities are the bottleneck both for power efficiency and sound quality [START_REF] Chao | Dynamical modeling and experimental validation of a micro-speaker with corrugated diaphragm for mobile phones[END_REF][START_REF] Lee | Design and analysis of microspeaker to improve sound characterizatics in a low frequency range[END_REF]. The former drawback affects also the device autonomy and the playback time. The latter limits the bass rendering and sound reproduction fidelity. This is mainly due to narrow frequency bandwidth (typically from 800 Hz to 10 kHz), mechanical and electromagnetic nonlinearities, and numerous structural modes existing in the frequency bandwidth [START_REF] Chao | Dynamical modeling and experimental validation of a micro-speaker with corrugated diaphragm for mobile phones[END_REF][START_REF] Kwon | Development of slim rectangular microspeaker used for minimultimedia phones[END_REF][START_REF] Hwang | New development of combined permanent-magnet type microspeakers used for cellular phones[END_REF].

Regarding these aspects of the problem, Microelectromechanical Systems (MEMS) technologies offer attractive high precision manufacturing and interesting miniaturization potential to permit going beyond limitations of conventional technologies. Besides, thanks to MEMS batch processing potential, there is a possibility to keep the final cost low. This is a good point for the MEMS industry, which could answer a demand of more than one billion microspeakers per year [START_REF] Lefeuvre | Potential of MEMS technologies for manufacturing of high-fidelity microspeakers[END_REF].

Concerning MEMS microspeakers, a few works reported efficiency enhancement [START_REF] Chen | A low-power milliwatt electromagnetic microspeaker using a PDMS membrane for hearing aids application[END_REF][START_REF] Je | A compact and low-cost MEMS loudspeaker for digital hearing aids[END_REF]Yi and Kim 2005;[START_REF] Cheng | A silicon microspeaker for hearing instruments[END_REF]). Most of the works did not present good results about either sound quality or sound pressure level (SPL). Reported MEMS electrodynamic microspeakers generated only 106 dB SPL at 1 kHz in a 2 cm 3 coupler [START_REF] Chen | A low-power milliwatt electromagnetic microspeaker using a PDMS membrane for hearing aids application[END_REF][START_REF] Je | A compact and low-cost MEMS loudspeaker for digital hearing aids[END_REF][START_REF] Rehder | Balanced membrane micromachined loudspeaker for hearing instrument application[END_REF], whereas reported piezoelectric MEMS microspeakers generated only 100 dB at 9.3 kHz at 1 cm [START_REF] Cho | Dependence of material properties on piezoelectric microspeakers with AlN thin film[END_REF]. Due to low sound intensities and limited bandwidth, the use of these MEMS microspeakers were more considered for hearing aids than for any other application. Acoustic shortcomings are even more significant for other MEMS microspeakers using electrostatic or thermo-acoustic actuation [START_REF] Rangsten | Electrostatically excited diaphragm driven as a loudspeaker[END_REF][START_REF] Roberts | Electrostatically driven touchmode poly-SiC microspeaker[END_REF][START_REF] Xiao | Flexible, stretchable, transparent carbon nanotube thin film loudspeakers[END_REF].

This work aims to develop a MEMS microspeaker, which stands far beyond other MEMS electroacoustic transducers in terms of SPL and sound quality, and can rival existing non-MEMS microspeakers in sound quality and efficiency. The objective is to get 80 dB SPL at 10 cm, within a frequency bandwidth of 300 Hz to 20 kHz.

Regarding the objectives of this work, the electrodynamic actuation, which drives today's loudspeakers and microspeakers, is actually the most appropriate for several reasons. Indeed, this actuation principle enables higher power densities. It does not require high driving voltage, which is often necessary for electrostatic actuators. Its intrinsic non-linear behavior is weak, contrary to piezoelectric actuators, which exhibit significant hysteresis effect. Moreover, the device performance would not be influenced by the presence of residual stress in the radiator surface, which is one of the major problems reported about MEMS piezoelectric microspeakers. However, the main drawback of electrodynamic actuation is the difficulty of integration of permanent magnets with strong magnetic field with today's MEMS technologies [START_REF] Je | A compact and low-cost MEMS loudspeaker for digital hearing aids[END_REF][START_REF] Kim | High performance piezoelectric microspeakers and thin speaker array system[END_REF]Yi et al. 2009;[START_REF] Lee | Piezoelectric microphone built on circular diaphragm Sensors and Actuators[END_REF].

This paper presents first the architecture of the MEMS microspeaker, while comparing to other MEMS and non-MEMS structures. Then, the microfabrication steps based on SOI (Silicon On Insulator) substrate are detailed in section III.

Section IV presents the results of electro-mechanic and electro-acoustic characterizations. Finally, the last section underlines the main achievements and outlines the perspectives of this work.

II. Device architecture

To generate acoustic waves, the conventional microspeakers use the vibration of a semi-flat diaphragm, which is clamped to the frame in the perimeter and free in the center (Fig. 1-a). The flexibility of the diaphragm is usually favored near its perimeter thanks to diagonal corrugations or thickness variation, while a slight dome shape stiffens the center part. In this way, the outer part of the diaphragm plays the role of the suspension and the center part the role of the rigid membrane used in classical loudspeakers [START_REF] Lee | Design and analysis of microspeaker to improve sound characterizatics in a low frequency range[END_REF][START_REF] Chao | Dynamical modeling and experimental validation of a micro-speaker with corrugated diaphragm for mobile phones[END_REF]. The actuation principle relies on the Lorentz force F Lorentz , originated by the interaction between the magnetic field B created by the permanent magnets and the electric current I passing through the copper coil of length l [START_REF] Chen | An optimized Cu-Ni nanocomposite coil for lowpower electromagnetic microspeaker fabrication International Solid-State Sensors[END_REF].

  l Lorentz l d B I F 0 . .   (1)
In the case of the MEMS microspeakers, reproduction of the slight dome shape used for the diaphragm of conventional microspeakers is not easy. Therefore, in most of former MEMS microspeakers, a very flexible and flat diaphragm is to play the role of both the radiator surface and the suspension simultaneously. As Fig. 1-b shows, the elastic diaphragm, usually made out of polyimide, parylene or SU-8 epoxy, is clamped to the substrate all along its perimeter [START_REF] Chen | A low-power milliwatt electromagnetic microspeaker using a PDMS membrane for hearing aids application[END_REF][START_REF] Chen | An optimized Cu-Ni nanocomposite coil for lowpower electromagnetic microspeaker fabrication International Solid-State Sensors[END_REF][START_REF] Je | A compact and low-cost MEMS loudspeaker for digital hearing aids[END_REF].

Though the small mass of polymer diaphragms is in favor of power efficiency, diaphragms are very soft and they have consequently numerous structural modes within the frequency bandwidth. This is actually one of the main reasons for the poor sound quality.

To overcome this drawback, instead of a flexible diaphragm, we propose here to use a rigid membrane for the acoustic radiator. To provide the required out-ofplane displacement, a set of flexible springs is added between the membrane and the substrate (Fig. 1-c). Such structure presents piston-like motion for the sound generation, which is much better for the sound quality than the drum-like diaphragm vibration, used in aforementioned MEMS microspeakers [START_REF] Pierce | Acoustics[END_REF]). However, apart from the stiffness, the lightness is also an important aspect, which should be taken into account because of its huge impact on the electroacoustic efficiency. To meet these criteria, previous works of the authors showed that a good trade-off between mass and rigidity of the radiator surface can be set using monocrystalline silicon material and a particular microstructure optimized for stiffening and reducing the membrane mass (Lefeuvre at al. 2012;Shahosseini et al. 2012-a). In this way, most of the membrane proper modes are shifted out of the audible frequency band, and the membrane motion remains like a piston in low and medium frequencies, at which human ear is the most sensitive [START_REF] Rossing | Handbook of Acoustics[END_REF].

Due to its excellent mechanical properties, silicon single-crystal is appropriate for the suspension springs as well. This material exhibits linear strain-stress behavior and it has outstanding resistance to mechanical fatigue. The latter property is very interesting for our application, because the suspension should resist at least one billion strain cycles within microspeaker lifetime [START_REF] Legros | Fatigue of single crystalline silicon: Mechanical behaviour and TEM observations[END_REF][START_REF] Kamiya | Finite fatigue lifetime of silicon under inert environment[END_REF][START_REF] Chida | Silicon linear actuator driven by electrochemomechanical strain of polypyrrole film[END_REF].

To determine the membrane surface and its displacement, the microspeaker acoustic power P acoustic should be calculated first. For the targeted sound pressure level L dB of 80 dB at the distance a of 10 cm from the acoustic source, Eq (2) yields an acoustic power of 12.6 µW [START_REF] Skudrzyk | The foundations of acoustics[END_REF]. For a loudspeaker with a circular radiator surface having a piston-like displacement, the emitted acoustic power depends on the displaced air volume and the frequency f, as shown in Eq. (3). In this expression, the displaced air volume is decomposed into the radiator surface diameter d and its displacement x peak [START_REF] Lehmann | Les transducteurs electro et mecano-acoustiques, haut-parleurs et microphones[END_REF].

From (3) it can be deduced that for a preset acoustic power, lower working frequency asks for higher displaced air volume. For the microspeaker of this work, at extreme working conditions, i.e. 80 dB SPL at 10 cm at 300 Hz, an air volume of 120 mm 3 should be displaced. If the target had been set for the same sound pressure level but starting from 800 Hz, which is the case of the conventional microspeakers, only 17 mm 3 air volume should be displaced (Fig. 2).

Thus, the design of a MEMS microspeaker capable of displacing seven times larger air volume than the non-MEMS microspeakers is a challenge.

According to Eq. ( 3), by setting the acoustic power and the frequency, the system variables becomes limited to two parameters, the acoustic radiator diameter and its out-of-plane displacement. To comply with the required acoustic power and frequency bandwidth, the product of these two geometrical parameters should be at least 120 mm 3 .

To do so, a trade-off between these parameters has to be made. Indeed, for the sake of integration, the device overall surface should be limited. The out-of-plane displacement should be also limited, in order to keep the mechanical stress in the springs as low as possible.

In the first approach, the radiator surface diameter was set to 15 mm, leading to ±350 µm out-of-plane displacement in the extreme working conditions. The undertaken exhaustive study of suspension springs by finite element method (FEM) resulted in a proper design, for which the reduction of stress concentration zones permitted the silicon suspension springs to resist large out-of-plane displacements. Moreover, experimental tests confirmed the linear behavior of the suspension for out-of-plane displacements as large as 2 mm (Shahosseini-a et al. 2012). The microcoil should be ideally located on the membrane edge, as close as possible to the magnet, where the magnetic flux density is maximal. In this way, as Eq. ( 4) shows, the driving force per current unit, the force factor, can be maximized.

r factor B l F      (4)
However, in order to prevent the coil damage near springs clamp areas, where outof-plane displacements raise the mechanical stress, the coil is shaped in special geometrical form. For the microcoil turns, electromagnetic optimization led to conceive a 14-turn copper coil with a cross-section of 3530 µm 2 . Because of the microfabrication limits, the coil thickness was set to 30 µm, with 20 µm space between turns.

The microcoil was fed by two conductor tracks located on top of two of the six suspension springs. Each track enabled the electrical connection to the amplifier at one end. At the other end, one track made an electric contact with the coil's exterior end, and the other track with the coil's interior end.

III. Microfabrication process

The device microfabrication steps, based on an SOI substrate, are shown in Fig. 4.

First, a layer of 200 nm thick silicon oxide is deposited on front side of the SOI substrate by plasma enhanced chemical vapor deposition (PECVD). This insulation layer prevents short-circuit between conductors. After few nanometers titanium sputtering to ameliorate the adhesion between the silicon oxide and the copper films, the copper target is sputtered at 2 µbar by applying 210 W till depositing 1 µm thick layer on the substrate (Fig. 4-a). After patterning the copper surface by photolithography resist of Shipley S1818, the wafer is immersed in the copper etch solution for a chemical etching of almost 4 minutes (Fig. 4-b). Once the copper tracks are defined, a second insulator layer of silicon oxide is deposited by PECVD at 550 mtorr. After S1818 resist patterning, the silicon oxide is anisotropicaly etched using reactive ion etching (RIE) with 325 W power (Fig. 4c). This layer lets the microcoil have two contact points in its inner and outer ends with the conductor tracks.

To pattern the suspension beams in front side of the substrate, first the silicon oxide is etched by RIE, and after the 20 µm thick top side silicon layer of the SOI substrate is etched by DRIE (Fig. 4-d). The S1828 resist showed a good masking durability for these two steps of etching. After an oxygen plasma treatment to ameliorate the surface adhesion of the silicon oxide, a 200 nm Ti/Cu seed layer is sputtered on the substrate. Then, the copper coil is micromolded (Fig 4-e). For this purpose, a specific process of resist photolithography was developed to succeed patterning of 35 µm thick Clariant AZ4562 resist. Afterwards, the copper microcoil is electroplated in an electrolyze cell in which the electrolyte was agitated by a magnetic bar at 200 rpm (Fig. 4-f). The most homogenous coil thickness was realized through applying -25 mA/cm 2 current density and an anode-cathode distance of 2 cm. After solving the resist micromold in acetone, the Ti/Cu seed layer is removed by ion beam etching (IBE), and the coil turns become insulated from each other (Fig. 4-g).

Before proceeding to silicon backside etching, the substrate front side structures, especially the microcoil, should be protected from further process damages. For this purpose, the front side is first spin coated by 35 µm thick Clariant AZ4562 resist (Fig. 4-h). Then, the substrate backside is spin coated and patterned using 10 µm thick Clariant AZ4562 resist (Fig. 4-i). Then, through DRIE Bosch processing of 300 µm thick silicon, the substrate is etched on backside. At this level, all bulk silicon material on back side of suspension springs is removed; at the same time, the silicon membrane is structured on back side (Fig. 4-j). Then, the buried silicon oxide layer, which serves as etching stop layer, is removed from the openings in backside by RIE. This step sets free the mobile part of the microspeaker (Fig. 4k). Fig. 5 shows the microfabricated device before bonding of the magnet. An inset of the 300 µm thick microstructured silicon membrane is also shown on this figure. After the micromachining steps, a bulk annular NdFeB magnet with an axial magnetization of 1.5 T is mounted on the device in order to complete the electromagnetic motor.

IV. Electro-mechano-acoustic characterization

The first measurement concerned the force factor of the electromagnetic motor.

For this purpose, the membrane out-of-plane static displacement was measured as a function of the coil DC current, using a Keyence LKG5000 laser displacement sensor (Shahosseini et al. 2012-b). To make sure that the membrane moves parallel to its initial position, measurements were carried out for different zones on the membrane surface. The displacement values remained identical to each other, thus confirming the good axial positioning of the magnet with the microcoil.

This measurement was carried out in a static mode, so the electromagnetic force was only balanced by the elastic force of the suspension springs. In this case, the product of force factor F factor and the injected current I is equal to the product of the suspension stiffness k suspension and the membrane displacement x:

x k F I suspension factor    (5)
The suspension stiffness was first measured to be 5 N/m. The force factor was then calculated for each value of the DC current and the corresponding displacement. Fig. 6 shows the force factor determined by measurements and by FEM simulations as a function of the membrane out-of-plane displacement. These results show that the force factor remains nearly 0.1 N/A for membrane displacements of -100 µm to +100 µm. In other words, for medium and high frequencies, for which the membrane displacement is small, the force factor remains constant. However, the force factor varies of 40% for displacements from +300 µm to -300 µm. This is due to the fact that the magnetic flux density is not uniformly distributed for upward and downward displacements. Both simulated and measured force factors have the same pace as function of the membrane displacement, but there is 25% difference between experimental and FEM simulation results. This can be explained by the magnetic field of the magnet, which may be lower in practice than the value given by the manufacturer.

The membrane dynamic displacement was then measured using a laser Doppler vibrometer Polytech-PI. The membrane displacement as a function of frequency is depicted in Fig. 7 for an electrical power of 12 mW. The first resonance peak at 460 Hz corresponds to the piston mode. After few small peaks and dips between 2 and 3 kHz, the second major peak appears at 10 kHz. It corresponds to the drum mode vibration of the membrane. For higher frequencies up to 20 kHz, the existence of other modes cannot be distinguished. This measurement shows the effectiveness of the rigid silicon membrane to push most of the structural modes out of the microspeaker bandwidth.

Acoustic characterizations were performed in an anechoic chamber. A B&K 4938 microphone was set in the radiator surface axis, at 10 cm distance from the microspeaker. Fig. 8 shows the SPL response as a function of frequency for an input power of 0.5 W. The targeted 80 dB SPL is available from 330 Hz up to 20 kHz. Compared to previous works, we have obtained in particular much lower starting frequency, 330 Hz instead of 800 Hz for conventional microspeakers and more than 1 kHz for previous MEMS microspeakers. This enables better bass rendering of the transducer. Moreover, the microspeaker electroacoustic efficiency is of 3×10 -5 , that is to say almost three times higher than that of conventional microspeakers.

As intermodulation distortion is usually responsible of significantly deterioration of the perceived audio quality of loudspeakers and microspeakers, we have performed such analysis on our MEMS microspeaker, but only a few intermodulation harmonics were observed. Fig. 9 plots the frequency spectrum of acoustic intermodulation, with an electrical signal composed of two pure sinusoids respectively at 600 Hz and 1700 Hz. In this unfavorable case, some intermodulation harmonics are visible at 3.4, 5.7, 10.8, and 11.4 kHz. These intermodulation harmonics have sound pressure level of 35 to 40 dB lower than the main signal, meaning that they will be barely audible. This underlines the outstanding sound quality of the microspeaker.

For both static and dynamic measurements, the copper conductor tracks sputtered on the silicon suspension springs showed very good durability. This is an important point, because it could affect the lifetime of the microspeaker. For durability tests, a microfabricated device was under test for a long time. After one year of permanent operation, which corresponds to more than 20 billion strain cycles, no electrical failure could be detected.

V. Conclusion and perspectives

This paper proposed a new design for MEMS microspeakers with high sound quality and high sound intensity properties. These specifications make the device an appropriate choice to be part of high fidelity audio systems for mobile electronic devices.

For the first prototype, the membrane diameter was set to 15 mm. The electromagnetic actuator and the suspension springs were designed to provide at least 350 µm out-of-plane displacement. The device modular fabrication took place in clean room using silicon technology. The main technical challenges were micromolding the copper coil and setting free the mobile part of the microspeaker device once the microcoil electroplated.

The static electromechanical test showed that the membrane could reach an outof-plane displacement of more than 400 µm with no electrical and mechanical failure of the copper conductor tracks and the silicon springs. Acoustic measurements confirmed a sound pressure level of 80 dB at 10 cm distance from the microspeaker, starting from 330 Hz and up to 20 kHz. Compared to conventional microspeakers, higher sound intensity is available in lower frequencies, thus making possible better bass rendering. The linearity and high sound quality generation are other achievements of this work. The radiator surface presents just very few resonance peaks in the bandwidth, and as intermodulation test results strand, very little distortion of the signals could be detected in the frequency response.

Ongoing studies focus on complete electroacoustic characterization to measure the microspeaker total harmonic distortion and the microspeaker impedance as a function of the frequency. Besides this, with the goal of obtaining a stronger and uniform force factor, other magnet and coil configurations will be also studied.

For the sake of better integration, the impact of the global size reduction of the microspeaker on its electroacoustic performances will be also investigated.

Fig. 3

 3 Fig. 3 depicts the disposition of the suspension springs in the MEMS microspeaker of this work. An inset of the membrane backside is also included to show the stiffening microstructure, composed of radial and circular ribs. As for the actuation, an annular permanent magnet attached to the fixed part of the device creates the magnetic field. With this magnet configuration, the driving force is created through interaction between the radial component of the magnetic flux density B r and the planar microcoil deposited on top of the silicon membrane.

Fig. 1

 1 Fig. 1 Schematic view of electrodynamic microspeakers cross-section: (a) conventional microspeaker, (b) MEMS microspeaker with elastic diaphragm, (c) MEMS microspeaker of this work, with rigid acoustic radiator and flexible suspension springs

Fig. 2 Fig. 6 Fig. 9

 269 Fig. 2 Displaced air volume as a function of frequency for 80 dB SPL at 10 cm: (a) air volume at 300 Hz, (b) air volume at 800 Hz Fig. 3 Schematic view of the proposed MEMS microspeaker structure and its components, with an inset of the backside ribbed microstructure of the membrane Fig. 4 Microspeaker microfabrication steps on SOI substrate: (a) silicon oxide PECVD and Cu sputtering, (b) copper conductor tracks patterning, (c) silicon oxide PECVD and patterning, (d) first silicon oxide RIE etching and front side silicon DRIE etching, (e) Ti/Cu seed layer deposition and coil micromolding, (f) copper microcoil electroplating, (g) Ti/Cu seed layer IBE etching, (h) front side resist spin coating, (i) backside patterning, (j) backside silicon DRIE etching, (k) buried silicon oxide RIE etching Fig. 5 Microfabricated MEMS microspeaker before assembling the magnet, with a backside view of the microstructured membrane Fig. 6 Static measurements and FEM simulation results of the force factor as a function of the membrane out-of-plane position Fig. 7 Radiator surface out-of-plane peak displacement as a function of frequency for 12 mW input power Fig. 8 SPL response measured at 10 cm distance from the microspeaker as a function of frequency for 0.5 W input power Fig. 9 Frequency spectrum for two sinusoidal electrical signals at frequencies f a =600 Hz and f b =1.7 kHz, and the resulted intermodulation signals at f 1 =2f b , f 2 =f a +3f b , f 3 =f a +6f b , and f 4 =2f a +6f b

Figure 1

 1 Figure 1 Click here to download Figure: Fig 1.doc

  Figure 1 Click here to download Figure: Fig 1.doc

  Figure 5 Click here to download Figure: Fig 5.doc

Figure 9

 9 Figure 9 Click here to download Figure: Fig 9.doc

ACKNOWLEDGMENTS

This work has been funded by the French Agence Nationale pour la Recherche (ANR). The authors would like to thank the staff of the University Technological Center IEF-MINERVE for their help and technical support.