Modelling of piezoelectric transducers applied to piezoelectric motors: a comparative study and new perspective

Sensors and Actuators A 110 (2004) 336–343

Modelling of piezoelectric transducers applied to piezoelectric motors: a comparative study and new perspective J.L. Pons∗ , H. Rodr´ıguez, F. Seco, R. Ceres, L. Calderón Instituto de Automática Industrial, CSIC, Ctra. Campo Real km. 0200, Arganda del Rey, Madrid 28500, Spain Received 20 September 2002; received in revised form 3 June 2003; accepted 10 June 2003

Abstract There has been a great deal of interest devoted to modelling and simulation of electromechanical transducers, and in particular to piezoelectric transducers, during the last decades. Modelling of the electro-mechanical phenomena is a complex matter: transducers comprise laminated structures of varying thickness, consideration of piezoelectric forcing, non-uniform electric field inside the ceramic . . . Several approaches for modelling the laminate structure have been reported, i.e. classical lamination theory, first order and higher order shear deformation theories. Likewise, the constitutive equations of the piezoelectric media have been included in FEA approaches. In addition, non-uniform electric fields, both linear and quadratic, were analysed. The particular case of travelling wave ultrasonic motors is addressed. This paper reports the comparative results of modelling all these plus additional transducer effects on the accuracy and presents the application to the classical electro-mechanical modelling of the stator of piezoelectric motors. Modelling results are compared with experimental data. © 2003 Elsevier B.V. All rights reserved. Keywords: Modelling; Piezoelectric transducers

1. Introduction Piezoelectric transducers, and in particular piezoelectric motors, have been developed since the 1970s. In parallel to these developments, modelling and simulation approaches have been proposed with the aim of providing analysis and design tools for these electro-mechanical devices. Accurate modelling of piezoelectric transducers requires appropriate models for the mechanical behaviour of laminate structures, the inclusion of the constitutive equation of the piezoelectric media and the consideration of non-uniform electric field in the ceramic. Hagood and McFarland [1], presented a complete model of a piezoelectric motor in which teeth dynamics, shear deformations and rotary inertia of the structural transducer body are not considered. In addition, a uniform thickness is assumed. Friend and Stutts [2] introduced the classical lamination theory applied to piezoelectric motors in which shear and rotary inertia are neglected. Hagedorn and Wallashek [3] demonstrated a simple model in which rotary inertia, shear and non-uniform stator thickness are introduced. However, their model does not include the piezoelectric domain.

∗ Corresponding author. Tel.: +34-918711900; fax: +34-918717050. E-mail address: [email protected] (J.L. Pons).

0924-4247/$ – see front matter © 2003 Elsevier B.V. All rights reserved. doi:10.1016/j.sna.2003.06.002

Other authors have introduced forcing due to piezoelectric domain. In particular, Heyliger and Saravanos [4] and Gopinathan et al. [5] demonstrated the need of including a model of the electric field in the piezoelectric domain, and again Hagedorn et al. [6] introduced for the first time a non-uniform linear electric field variation. In addition, when particularising to piezoelectric motors, the rotor–stator contact problem is still under consideration. The use of models based on distributed springs to simulate the behaviour of rotor–stator interface has been proposed, see Ming and Peiwen [7], as a means of obtaining accurate enough models to enable a performance estimation of TWUMs. In a recent paper, Zharii [8] proposed an analytical model in which a contact mechanics approach at the rotor–stator interface is considered to render an evaluation of the motor performance. However, a not very good estimation is obtained for speed, torque and friction loses probably due to the fact that the friction viscoelastic interface material as well as rotor flexion were neglected. Hagood and McFarland [1] computed, as a step in their simulation process, a contact pressure distribution based in the so-called elastic foundation model. In addition to this, Hirata and Ueha [9] have introduced a two-dimensional elastic contact model that is used in combination with an electrical equivalent circuit model in order to propose a design method for TWUMs.

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In this paper, we introduce a novel electro-machanical modelling strategy based on the use of laminated plate theories over annular subdomains [10]. This strategy allows including the effect of shear, rotary inertia, linear variation of electric field in the piezoelectric domain, teeth dynamics and radial varying thickness. The proposed strategy is valid for modelling general-purpose piezoelectric transducers but will be applied to the stator of an ultrasonic motor. The comparative results of including all these effects will be demonstrated.

2. Stator modelling approach The proposed novel modelling approach is based on the use of laminated plate theories over annular sub-domains. In general, three types of electromechanical domains, see Fig. 1, can be found in piezoelectric transducers: 1. Type I: Isotropic material—useful to model single material regions; 2. Type II: Isotropic material plus piezoelectric domain; and 3. Type III: Orthotropic material plus piezoelectric domain—useful to model material regions with different stiffness properties in orthogonal axes, i.e. teeth of piezoelectric motor. 2.1. Effect of shear and rotary inertia The effect of rotary inertia and shear deformation is introduced in our model by considering first order shear deformation theory with rotary inertia. The displacement field

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associated to this theory is shown in the Eq. (1). u(r, θ, z, t) = u0 (r, θ, t) + zψr (r, θ, t) v(r, θ, z, t) = v0 (r, θ, t) + zψθ (r, θ, t)

(1)

w(r, θ, z, t) = w0 (r, θ, t) where u0 , v0 and w0 represent the displacement at a point on the neutral plane; ψr the rotation angle of the normal to the neutral plane around the r coordinate axis; and ψθ the rotation angle of the normal to the neutral plane around the θ coordinate axis, see Fig. 2 for a graphical representation. According to the displacement field from Eq. (1), shear deformation results in that sections perpendicular to the neutral plane before deformation no longer remain perpendicular after deformation. This can be seen in Fig. 2. The deformation field corresponding to the displacement described by Eq. (1) can be found according to Eq. (2) ∂u ∂ψr +z = ε0r + zκr0 ∂r ∂r 

1 ∂v z ∂ψθ εθ = +u + + ψr = ε0θ + zκθ0 r ∂θ r ∂θ εr =

εz = 0

(2)

1 ∂w εθz = ψθ + r ∂θ 1 ∂w εrz = ψr + r ∂r 0 εrθ = · · · = ε0rθ + zκrθ

In Eq. (2), εr , εθ and εz are the normal strains in directions, r, θ and z, respectively. εθz , εrz and εrθ are the shear strains.

Fig. 1. Definition of annular subdomains, domain type I includes one single elastic material, domain type II includes a laminate structure of both elastic and piezoelectric material, and domain type III includes, in addition, the teeth layer.

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evaluated under conditions of no mechanical load. Likewise, superscript E refers to the condition of no electrical field. 2.2. Teeth dynamics The inclusion of teeth dynamics is provided through the proper definition of type III elements. Up to know, most of the work on modelling of piezoelectric transducers has just considered teeth kinematics and teeth inertia. Here, we propose to include teeth dynamics through orthotropic elements in which radial and angular stiffness are independently considered. This is done according to the definition of the flexural stiffness coefficients in Eq. (5). D11 =

YIT θ1

Yθ1 h3m 12(θ1 − θt + α3 θt )  + C = D66 2θ1

D22 = Fig. 2. Effect of shear deformation on resulting displacements: the rotation angle, ψr , when shear deformation is allowed no longer can be assumed to be equal to the rotation of the neutral plane, (∂w0 /∂r).

For compactness, both normal and shear stress and strain are referred to with subscripts 1–6, respectively. In addition, κr0 and κθ0 are curvatures in radial and circumferential directions, respectively. Following the model approach, the constitutive equations of both piezoelectric and non-piezoelectric domains are worked out by considering a state of plane stress. This follows from the fact that the outer lateral surface of the stator, i.e. r = re in Fig. 2, is unloaded and thus σ z is negligible. In Eq. (3), the resultant forces acting on the annular domains are introduced.      A] [B B] [A {N} {ε} = B ]T [C C] {M} {κ} [B (3)      Q1 A55 A45 ε5 = Q2 A45 A44 ε4

D66

(5)

where Y is the Young modulus, IT the teeth torsional stiffness, α = (hm /H) and all other parameters are defined according to transducer geometry, see Fig. 3. 2.3. Radial varying thickness In the application of the first order shear deformation theory with rotary inertia, uniform thickness is just a simplifying constrain. In this theory, the matrices A , B and D which relate equivalent force and torque to deformation and

In Eq. (3), Ni , Mi and Qi are normal forces, resultant bending moments and shear forces, respectively. In addition, when the piezoelectric annular domains are considered, the constitutive equations of the piezoelectric ceramic are introduced:    S   κ3 e31 e31 0 D3  E3                     σ1    −e31 CE CE   0  ε1  11 12  = (4)    −e31 CE CE  σ2  ε2  0          12 22               E σ6 ε6 0 0 0 C66 where Cij , eij and ki are elastic, piezoelectric and dielectric constants, respectively. Superscript S refers to the coefficient

Fig. 3. Geometric parameters used in the definition of teeth dynamics.

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curvature are defined according to: M  zm+1  (m) (Aij , Bij , Dij ) = (1, z, z2 )Cij dz m=1 zm

(6)

In order to take varying thickness into account, z is defined as a linear function of r, the radius, and introduced in Eq. (6). As a result, matrices A , B and D can be expressed as A (r) = A0 + A1 r B (r) = B0 + B1 r + B2 r 2

(7)

D (r) = D0 + D1 r + D2 r 2 + D3 r 3 A thorough analysis of the mathematical formulation behind Eq. (7) is out of the scope of the present paper. Nevertheless, the reader is referred to [11] for a detailed mathematical formulation of the structure of matrices A i , B i and D i .

The electrostatic approximation of Maxwell equations applies to our problem. This is due to the fact that excited elastic waves have a much shorter wavelength than the electromagnetic counterpart. As a consequence the approximation of Eq. (8) can be used. ∇ ×E =0 ∇ ·D=0

(8)

where E and D are the electric field and displacement, respectively. In Eq. (8), we have decided to include a general expression of both electric field and displacement respectively. However, due to the geometrical construction of the ultrasonic motor stator, just their axial component will be non-zero, i.e. E3 and D3 . In order to meet Eq. (8), the electric field can be defined as the gradient of the electric potential ϕ. Moreover, taking into account that the electric displacement is only in the z direction, Eq. (8) can be rewritten accordingly: E3 = −grad ϕ(r, θ, z, t) ∂D3 =0 ∂z

(9a)

In Eq. (9a), the electric field is computed out of the gradient of the electric potential in axial direction. Later on, when computing the linear electric field, Eq. (11), through the piezoelectric ceramic, the following boundary conditions will be used on the electrical potential: grad ϕ(r, θ, z2 ) = 0 grad ϕ(r, θ, z3 ) = Φ(θ)v(t)

If we now consider Eq. (4), we note that D depends also on stator deformation εi through coefficient e31 . As supposed in Eq. (1), the mechanical displacement field varies linearly in the z direction. As a consequence, it cannot be assumed a constant electric displacement through the piezoelectric domain. Accordingly, the following linear variation of the electric field is supposed: ˜ 0 (r, θ, t) + E ˜ 1 (r, θ, z, t)z E3 (r, θ, z, t) = E

(9b)

In Eq. (9b), Φ(θ) is a function of the circumferential co-ordinate helpful in describing the electrode pattern used to electrically excite the ultrasonic motor. On the other hand, v(t) is used to describe the time dependence of the electric potential.

(10)

In Eq. (10), the linear electric field in the axial direction, ˜ 0 (r, θ, t), i.e. E3 , has been split into a constant component, E independent of the axial variable z, and a linear component ˜ 1 (r, θ, t). By combining Eqs. (1), (3), (9a) in z, defined by E and (10), and taking into account the boundary conditions of Eq. (9b), the following linear electric field distribution in the piezoelectric domain is found: E3 = −

2.4. Linear variation of electric field

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Φ(θ)v(t) e31 − S (kr + kθ )(2z − z3 − z2 ) hp k3

(11)

where hp define the axial thickness of the piezoelectric ceramic, z2 and z3 define the axial co-ordinates of the piezoelectric ceramic and all the other parameters were introduced previously. 2.5. Rotor–stator interface models In general, the motion transmission between stator and rotor in a TWUM can be regarded as a highly non-linear problem in which three parameters play an important role: normal displacement at the interface, tangential speed and surface traction, [8]. The problem is non-linear in that normal pressure depends on tangential velocity which in turn is a function of the normal displacement. In addition, the size of the contact area is also unknown, and the location of sticking and sliding areas are only determined when solving the problem. In Fig. 4, normal pressure, FN , tangential force, FR , rotor velocity, vr , velocity at the stator contact points, ve (θ), traction stress, τ, and normal pressure, p(θ), are schematically shown. The classical way of introducing friction is through contact mechanics. A thorough analysis of the problem of contact mechanics at the rotor–stator interface is out of the scope of the present paper, the reader is referred to [11,12] for a discussion on the proposed approach. Here, just the main lines of the approach are outlined. The introduction of contact forces (the result of the contact problem) into the equation of motion, Eq. (13), is through their variational work, see Eq. (12):  δWN = δ p(r, θ, t)uz r dr dθ  δWR = δ µd (vrad )p(r, θ, t)ur (z0 )r dr dθ (12)  δWC = δ µd (vcir )p(r, θ, t)uθ (z0 )r dr dθ In computing the variational work of Eq. (12), an exponentially decaying function of the contact velocity in radial and circumferential directions, see Fig. 5, was used as the

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method is based on the modified Hamilton principle for electro-mechanical systems. According to the Hamilton principle the equation of motion is derived from:  t1  t1 δLdt + δ(WN + WT )dt = 0 (13) t0

t0

where L is the Lagrangian function comprising both the electrical enthalpy density and the kinetic energy. In addition, for a complete formulation of the problem involving the rotor–stator interface, the variational work of normal and shear forces, WN and WT , respectively, could be included as outlined in Section 2.5. In addition, WT can be written as WT = WR + WC in order to take into account both radial and circumferential components of the contact force. The stator displacement was approximated by the product of a radial varying function, φi (r), and sinusoidal functions, cos(nθ) and sin(nθ), of the circumferential variable. The wavelength of the latter, n, was assumed to be equal to the wavelength of the flexural stator vibration as determined by the electrode pattern, see Eq. (14). (c)

Fig. 4. Model of the rotor–stator interface: the viscoelastic model leads to contact and non-contact areas. The resulting contact forces are introduced in the derivation of the equation of motion through their variational work.

dynamic friction coefficient, µd (vrad ) and µd (vcir ), respectively. In order to work out the pressure distribution, a viscoelastic foundation model, see Fig. 14 [12], was used. The other parameters in Eq. (12) will be introduced in the next section, i.e. Eq. (14).

3. Simulation and experimental results In our approach we used the Ritz method to find an approximate solution of the resulting equations. The Ritz

Φi = φi (r)cos(nθ) (s)

Φi = φi (r)sin(nθ) This way, the displacement field is:  (1) (c) −jwt ur ≈ u1 = m i=1 Ui Φi e  (2) (s) −jwt uθ ≈ u2 = m i=1 Ui Φi e  (3) (c) −jwt uz ≈ u3 = m i=1 Ui Φi e  (4) (c) −jwt ψr ≈ u4 = m i=1 Ui Φi e  (5) (s) −jwt ψθ ≈ u5 = m i=1 Ui Φi e

(14)

(15)

(j)

where, Ui are nodal displacements at node “i” in the direction “j” which will be computed during the numerical simulation of the proposed paper.

Fig. 5. Exponentially decaying dynamic friction coefficient as a function of relative speed at the contact interface as it has been used in the derivation of contact forces.

J.L. Pons et al. / Sensors and Actuators A 110 (2004) 336–343 Table 1 Comparative results on the model accuracy after experimental verification Model

Frequency (kHz)

Error (%)

Experimental FEA Full model Classical linear theory Uniform thickness Uniform E field No teeth dynamics

48.7 50.48 46.53 27.2 44.6 45.29 45.6

– 3.6 4.5 44.1 8.4 7 6.4

The final system of equations is obtained by combining the resultant forces from Eq. (3), the strain–displacement relations from Eq. (2), and the approximate displacement field from Eq. (15). Once this is done, the system of equations adopts the form of Eq. (16). [K]U + w2 [M]U = F

(16) (j)

where U comprises the coefficients Ui and F the electrical excitation. The solution was applied to the full stator model and to partial models in which one of the above stated stator effects were not considered. The experimental verification was carried out by means of a laser interferometer. The 5th flexural mode of the stator was excited by using specifically designed electrodes and the circumferential as well as radial stator displacement was recorded during stationary excitation. Table 1 shows the comparative results of the simulation of the 5th vibration mode of a piezoelectric motor together with an experimental verification of the accuracy of our model and a comparison with FEA results. The experimental comparison has been based on an analysis of modal response, i.e. modal frequency and modal shape.

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The proposed model has not explicitly considered the effect of losses at high electric fields (usually found in ultrasonic motors). Since modal response is independent to a great extent of electrical excitation, we think that this approach provides us a means of neglecting the effect on electrical excitation on the different models. However, it should be noted that the effect of losses has been indirectly taken into account by keeping the value of the stator vibration velocity far below the saturated vibration velocity. This, as reported by Uchino’s results, see [13], ensures that no drastic reduction of the quality factor is experienced and thus heat generation is kept within acceptable limits. Also the non-linear behaviour of the elastic coefficient has not been considered in any of the proposed models. It is expected that the effect this might have on their performance is equivalent, and thus for comparison purposes the approach remains valid. Nevertheless, this is an important matter that will be included in further works. In addition a solution was also provided for the rotational motion of the piezoelectric motor. A specifically designed testing bench was developed to obtain torque–speed motor performance as well as transient response. The testing bench can be seen in Fig. 6. In order to experimentally test the stator model, a simulation of the resonance and forced response of the stator was carried out. In parallel, the vibration map of a commercial ultrasonic motor, the Shinsei USR30, was obtained under equivalent conditions with a laser interferometer. Fig. 7 shows the experimental and simulated torque–speed relation for the USR30. It can be seen that the simulation accuracy was higher close to the maximum rotational velocity of the motor. The simulation of the stall torque was around 25% lower than the measured experimental stall torque. Several reasons can be given for this mismatch between experimental and simulated values. First, the proposed

Fig. 6. Testing set-up for experimental validation.

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Fig. 7. Model experimental validation: experimental and modelled performance.

model is an approximation of the viscoelastic behaviour of the interface material. The introduction of contact mechanics models for accurate modelling of the interface is computationally expensive. The proposed model is a parametrical one in which design and optimisation processes are possible, and where a trade-off had to be reached between computational efficiency and accuracy. Secondly, the torque–speed curves shown in Fig. 7 include also the stator model and thus the partial contribution of interface and rotor models to the modelling error is comparatively lower. A third possible reason for the modelling error could arise from the fact that the rotor model does not include rotor flexion since it was assumed to behave as a rigid body.

4. Conclusions Our paper presents a comprehensive analysis of the effect on simulation accuracy of including physical phenomena in the model of electromechanical transducers. In particular, the case of piezoelectric transducers is studied and a specific focus on ultrasonic motors is approached. We can conclude that our model predicts with high accuracy the experimental results. The simulation error was always below 5% as compared to experimental data. In general, the lower effect on accuracy was due to the inclusion of teeth dynamics. When no teeth dynamics is considered accuracy is reduced by just 2%. However, the higher impact on accuracy is related to the use of classical linear theory to model stator mechanical behaviour.

When including the rotor–stator model, full rotational simulation could be obtained. Despite the simplifying assumptions of this model, the torque–speed curves as obtained from the model fit reasonably well experimental data. The larger mismatch is found in the region of the stall torque. Due to the parametric nature of our approach and to its relatively low computational cost, design optimization of piezoelectric transducers is feasible. It has comparative advantages to FEA approaches. In particular computing time is two orders of magnitude lower for the proposed model as compared to FEA. References [1] N. Hagood, A.J. McFarland, Modeling of a piezoelectric rotary ultrasonic motor, IEEE Trans. Ultrason. Ferroelectr. Freq. Control 42 (2) (1995) 210–224. [2] J.R. Friend, S. Stutts, The dynamics of an annular piezoelectric motor stator, J. Sound Vib. 204 (3) (1997) 421–437. [3] P. Hagedorn, J. Wallashek, Travelling wave ultrasonic motors, Part I: Working principle and mathematical modeling, J. Sound Vib. 155 (1) (1992) 3–46. [4] P. Heyliger, D.A. Saravanos, Exact free-vibration analysis of laminated plates with embedded piezoelectric layers, J. Acoust. Soc. Am. 98 (3) (1995) 1547–1557. [5] S.V. Gopinathan, V.V. Varadan, V.K. Varadan, Detailed study of electromechanical fields in piezolaminates, Proc. SPIE 1 (1999) 438– 448. [6] P. Hagedorn, T. Sattel, D. Speziari, J. Schmidt, G. Diana, The importance of rotor flexibility in ultrasonic travelling wave motors, Smart Mater. Struct. 7 (1998) 352–368. [7] Y. Ming, Q. Peiwen, Performances estimation of a rotary travelling wave ultrasonic motor based on two-dimension analytical model, Ultrasonics 39 (2001) 115–120.

J.L. Pons et al. / Sensors and Actuators A 110 (2004) 336–343 [8] O.Y. Zharii, An exact mathematical model of a travelling wave ultrasonic motor, Proc. 1994 Ultrason. Symp. 1 (1994) 545–548. [9] H. Hirata, S. Ueha, Design of a travelling wave type ultrasonic motor, IEEE Trans. Ultrason. Ferroelectr. Freq. Control 42 (2) (1995) 225– 231. [10] H. Rodr´ıguez, R. Ceres, L. Calderón, J.L. Pons, Modeling of the traveling wave piezoelectric motor stator: an integrated review and new perspective, Bol. Soc. Esp. Cerám. Vidrio, in press, (2003). [11] H. Rodr´ıguez, Modelado, Diseño y Control de Motores Piezoeléctricos de Onda Viajera: su aplicación a manos protésicas y robóticas, PhD Thesis, U. Politécnica de Madrid, 2002. [12] J.L. Pons, H. Rodr´ıguez, R. Ceres, L. Calderón, Novel modeling technique for the stator of traveling wave ultrasonic motors, IEEE Trans. on Ultr. Ferr., and Freq. Contr. in press (2003). [13] K. Uchino, S. Hirose, Loss mechanisms in piezoelectrics: how to measure different losses separately, IEEE Trans. Ultrason. Ferroelectr. Freq. Control 48 (1) (2001) 307–321.

Biographies José L. Pons received a BS degree in Mechanical Engineering from the Universidad de Navarra Engineering in 1992, the MS degree in 1994 from Universidad Politécnica de Madrid and a PhD degree in 1996 from the Universidad Complutense de Madrid. From 1994 to 1999, Dr. Pons was a research assistant at the Systems Department of the Intituto de Automática Industrial. He has spent several research stays at the Katholieke Universiteit Leuven in Belgium, Arts/MiTech Lab at the SSSUP Sant’Anna in Pisa, Teknische Universit in Munich, Germany and MIT in US. His research interests include new sensor and actuator technologies, signal processing and digital control and their application to microsystems and technical aids for the disabled. In 1997, Dr. Pons received the Fundación Artigas Prize in Mechanical Engineering for the most outstanding doctoral dissertation in the engineering disciplines. The Consejo Superior de Investigaciones Cient´ıficas also awarded his contribution to the discipline of mechanical engineering with the Silver Medal award in 1998. He currently holds a research position at the Instituto de Automática Industrial, CSIC, and is member of Institute of Electrical and Electronics Engineers. Humberto Rodr´ıguez received the BS degree in electro-mechanical engineering from the Technological University of Panama, Panama, the MS degree in mechanical engineering from the University of Alabama at

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Tuscaloosa and the Doctorate in industrial engineering from the Polytechnic University of Madrid, Spain, in 1990, 1992 and 2002, respectively. Currently, he is with the department of Mechanical Engineering at the Technological University of Panama. His research interests include the modelling and design of piezoelectric sensors and actuators, specially piezoelectric motors, and the design and control of robotic systems for special applications. Fernando Seco, was born in Madrid, Spain. He received a degree in Physics from the Universidad Complutense in Madrid in 1996, and is currently working towards a PhD degree in Science at the Instituto de Automática Industrial (IAI). His dissertation deals with the development of a linear position sensor based on the transmission of ultrasonic signals. His research interests include the electromagnetic generation of mechanical waves in metals, the propagation of sound in waveguides and the processing of ultrasonic signals. Ramón Ceres was born in 1947 in Jaén, Spain. He graduated in Physics (electronic) from Universidad Complutense de Madrid in 1971 and received the PhD degree in 1978. After a first stay for 1 year, in the LAAS-CNRS in Toulouse (France), be has been working at the Instituto de Automática Industrial (IAI), a dependent of the Spanish National Council for Science Research. For the period 1990–1991, he worked in an electronics company (Autelec) as R and D director. Since the beginning, Dr. Ceres has developed research activities on sensor systems applied to different fields such as continuous process control, machine tools, agriculture, robotics and disabled people. On these topics he has published more than 80 papers and congress communications, and he has several patents in industrial exploitation. At present, Dr. Ceres belongs to the Spanish Delegation of the IMT (Brite-Euram) Committee, being deputy director of the IAI. Leopoldo Calderón was born in 1947 in Lumbrales (Spain). He graduated in physics from the Universidad de Sevilla in 1974 and received the doctoral degree in 1984 from the Universidad Complutense de Madrid. Since 1974, Dr. Calderón has been working in the Instituto de Automática Industrial developing many research activities in the field of automation of processes and especially on the study of sensors (focused on ultrasonic sensors) and their processing and application. As a consequence of this activity, Dr. Calderón has published many scientific papers and is author of different patents. He has also participated in different national and international scientific programmes and congresses.