Characterization of three-dimensional dynamics of piezo-stack actuators B. Arda Gozen, O. Burak Ozdoganlar n Department of Mechanical Engineering, Carnegie Mellon University, Pittsburgh, PA 15213, USA article info Article history: Received 8 December 2011 Received in revised form 27 March 2012 Accepted 28 March 2012 Available online 13 April 2012 Keywords: Piezo-stack actuator FRF Dynamic characterization Non-linear response Laser doppler vibrometry abstract This paper presents a methodology for the characterization of dynamic behavior of piezoelectric-stack actuators. Piezo-stack actuators are used in many fields to obtain high- accuracy displacements and vibrations, commonly in multiple dimensions. However, obtaining accurate motions from piezo-stack actuators require thorough characterization of their non-linear dynamic response characteristics in three dimensions. In this work, a laser Doppler vibrometer-based precision characterization system is created to measure the three-dimensional dynamic motions of the piezo-stack actuators within a wide frequency range. A measurement reference frame is obtained by arranging three laser beams in a mutually orthogonal configuration. A set of stepped-sine tests are conducted at different levels of excitation amplitudes by individually exciting each of the stacks (of a multi-stack piezo actuator) and measuring the three-dimensional response in the measurement reference frame. The resulting dynamic response is decomposed into its components that occur at harmonics and non-harmonics of the excitation frequency. A power analysis is then conducted to determine the amount of contribution of each response component (harmonic or non-harmonic) in the overall response. The response behavior is then represented using a new approach constructed by extending the conventional frequency response function (FRF) description to higher-harmonic and non-harmonic components. The application of the approach is demonstrated by testing two three-axis piezo-stack actuators. & 2012 Elsevier Ltd. All rights reserved. 1. Introduction Driven by the recent advances in the nanotechnology [1,2], precision engineering [3], and metrology [4,5] fields, there is a strong need for obtaining three-dimensional motions with nanometer-level accuracy within a broad range of frequencies. Piezoelectric actuators are commonly chosen to fulfill this need due to their capability of generating nano- scale motions with sub-nanometer resolution. To obtain long range and multi-dimensional motions, the piezoelectric actuators are assembled into stacks (see Fig. 1). Dynamic motions of the piezo-stack actuators are three-dimensional in nature due to their complex modes of deformation that strongly depend upon their mechanical assembly and boundary conditions. Although three-dimensional motions can be generated using multi-axis piezo-stack actuators, mechanical assembly, boundary conditions, and the non-linear dynamic behavior brings significant complexities. Therefore, the use of piezo-stack actuators for obtaining specific (e.g., elliptical) high-accuracy motions at high frequencies require a thorough Contents lists available at SciVerse ScienceDirect journal homepage: www.elsevier.com/locate/ymssp Mechanical Systems and Signal Processing 0888-3270/$ - see front matter & 2012 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.ymssp.2012.03.021 n Corresponding author. Tel.: þ1 412 268 9890; fax: þ1 412 268 3348. E-mail address: ozdoganlar@cmu.edu (O. Burak Ozdoganlar). Mechanical Systems and Signal Processing 31 (2012) 268–283