Abstract—Lead zirconate titanate (PZT) stacks are commonly used for submicron resolution actuation, fast response times and high sensitivity. They are usually modeled as expansion generators without external load. This paper proposes an electromechanical model for a commercially available micro-piezoelectric actuator (PEA) which comprises pre-stressed PZT stacks and external amplifier flexure frame for closed loop force control. The proposed model avoids the need to measure the piezoelectric charge which is usually required in conventional electromechanical models. The mechanical part of the PEA was modeled as a linear, lumped, double mass-spring-damper system and the related parameters were experimentally identified. The PEA system was characterised under load-free and load-applied conditions, and the electromechanical coupling ratios which describe the energy transfer from the electrical domain (voltage) to the mechanical domain (endpoint displacement/force) were experimentally determined. Index Terms—Electromechanical modeling, micro-piezoelectric actuator, parameter identification, force control. NOMENCLATURE v in total input voltage of the PEA system, V v e effective voltage of the PEA system, V v z voltage on amplifier resistance, V f ext external applied force to the PEA, N f pzt exerted force by the PZT stacks, N n em electromechanical coupling factor, NV -1 t em electromechanical coupling factor, mV -1 z resistance of the PEA amplifier, Ω c constant capacitance of the PEA,F k pzt stiffness of the PZT stacks, Nm -1 k s stiffness of PEA preload springs, Nm -1 m 1 , m 2 equivalent mass of the PEA, kg k 1 , k 2 equivalent stiffness of the PEA, Nm -1 b 1 , b 2 equivalent damper value of the PEA, Nsm -1 x 1 endpoint displacement of the PEA, m x 2 modelling displacement of the PEA, m δ total electric transformed displacement, m h nonlinear hysteresis displacement, m S strain tensor T stress tensor, Nm −2 Manuscript received June 15, 2012; revised October 18, 2012. J. Liu, E. Ahearne, and G. Byrne are with the Advanced Manufacturing Science (AMS) Research Centre, School of Mechanical and Materials Engineering, University College Dublin, Ireland (e-mail: jinghang.liu@ucd.ie, eamonn.ahearne@ucd.ie, gerald.byrne@ucd.ie). W. J. O'Connor is with the School of Mechanical and Materials Engineering, University College Dublin, Ireland (e-mail: william.oconnor@ucd.ie). E electric field vector, Vm -1 X output displacement, m V exerted voltage to the PZT stacks, V ˆ 33 s elastic compliance, m 2 N −1 d 33 material constants, mV −1 or CN −1 A cross-section of the PZT cylinder, mm 2 l length of the PZT cylinder, m k stiffness of the PEA, Nm -1 i ω the i th resonance frequency in Bode plot (i=1,2), rads −1 I. INTRODUCTION Chemical mechanical polishing (CMP) is described as “the process of smoothing and planarising synergistically aided by combined chemical and mechanical effects” [1] which is widely used for planarisation in semiconductor manufacturing. The Advanced Manufacturing Science (AMS) Research Centre at UCD is pioneering a new concept for advanced process control, called multifunctional intelligent tooling (MIT), with the potential to provide a major improvement in the interfacial pressure control between the silicon wafer and polishing pad [2]–[3]. In the proposed system, a long range micro-piezoelectric actuator is used as a force generator rather than its more common use in motion control. Models for relating voltage to displacement in PZT stacks can be divided into two major types: models based on or partly derived from PZT linear constitutive equations [4], and electromechanical models describing the electrical and mechanical energy transformations considering the nonlinear hysteresis between voltage and charge [5]–[9]. Constitutive equation based models treat the stacks as a linear component by ignoring the nonlinear behaviour of PZT, to which hysteresis is the most significant contributor. By contrast, electromechanical models adopt hysteresis operators to describe the nonlinear relationship between voltage and charge. Accordingly, charge measurement is essential since charge is the only index to indicate the accuracy of the hysteresis model. However, charge measurement is not recommended or not possible for some applications, for example where the disassembly for identification would have negative consequences for the whole system. This arises when the PZT stacks are pre-stressed and housed by the flexure amplifier mechanism, as in the PEA used in this project. In addition, the charge measurement is usually costly and has limited sensitivity. II. ELECTROMECHANICAL MODEL OF THE PEA The actuator used here is a commercial product, Modelling of Piezoelectric Actuator (PEA) for Advanced Process Control in Chemical Mechanical Polishing (CMP) Jing-Hang Liu, William J. O’Connor, Eamonn Ahearne, and Gerald Byrne IACSIT International Journal of Engineering and Technology, Vol. 5, No. 2, April 2013 202 DOI: 10.7763/IJET.2013.V5.542