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Multidimensional motion measurement of a bimorph-type piezoelectric actuator using a diffraction grating target

Jong-Ahn Kim, Eui Won Bae, Soo Hyun Kim, Yoon Keun Kwak

2001
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Review of Scientific Instruments
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Precision actuators, such as pick-up actuators for HDDs or CD-ROMs, mostly show multidimensional motion. So, to evaluate them more completely, multidimensional measurement is required. Through structural variation and optimization of the design index, the performance of a measurement system can be improved to satisfy the requirement of this application, and so the resolution of each axis is higher than 0.1 m for translation and 0.5 arcsec for rotation. Using this measurement system, the
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... system, the multidimensional motion and frequency transfer functions of a bimorph-type piezoelectric actuator are obtained. As technologies develop, there is an increasing need for precision actuators which employ piezoelectric transducers or voice coil motors. To obtain more accurate information on precision actuators, multidimensional measurement should be used, since actuators generally show multiaxial motion. For characterization of these actuators, a measurement system requires submicrometer and several arcsec resolutions, in addition to fast measurement speed and a minimal effect on the actuators. Until recently, several systems capable of multidimensional motion measurement have been proposed. 1-5 Among these systems, a measurement system using a diffraction grating target has advantages in various aspects, but it also needs improvements in performance to be applicable to the evaluation of precision actuators, such as pick-up actuators for HDDs or CD-ROMs. 5 In this note, we present a new design method for performance improvement which uses structural variation and optimization of the design index. Finally, the multidimensional motion and frequency transfer functions of a bimorph-type piezoelectric actuator are measured. When a Taylor series expansion is applied to the solution of the forward problem, 5 the change of detector output ␦d versus the input displacement ␦p and the variation of kinematic parameter values ␦q can be formulated as ␦dϭJ"␦pϩQ•␦q. ͑1͒ If ␦d and ␦q are considered as the detector error and the deviation, respectively, from the nominal values of the kinematic parameters in Eq. ͑1͒, then the error source term ␦e is multiplied by the inverse matrix of J and generates a measurement error of each sensing direction ␦p as ␦pϭJ Ϫ1 •͑␦dÀQ•␦q͒ϭS•␦e, ͑2͒ where J and S represent the Jacobian and sensitivity matrix of the measurement system, respectively. From these equations, we can define several design indices representing the performance of the measurement system: the isotropic index, the diagonalization index, the measurement range, and the maximum uncertainty index. The isotropic index, which is the condition number of J, evaluates the uniformity of the sensitivity in each measurement direction. The diagonalization index shows the degree of decoupling between sensing channels, which is calculated from the ratio of diagonal to off-diagonal terms of J. The measurement range is assigned as an inequality constraint in the design process. In Eq. ͑2͒, the maximum singular value of S limits the ratio of ␦p to ␦e, so that it is defined as the maximum uncertainty index. To improve the performance of the measurement system, additional convex lenses are placed between the grating target and the quadrant photodiodes, and the design parameter values are obtained through optimization of these design indices. The convex lens modifies the propagating directions and the intensity distributions of the diffracted rays, so that performance can be enhanced within the constraints. As shown in Fig. 1 , the four design parameters were chosen from the kinematic parameters, such as the distance from the grating target to the convex lenses (Z 0l ,Z 1l ) and the distance from the grating target to the detectors (Z 0d ,Z 1d ). The optimization problem can be solved with Powell's method and the quadratic interpolation method. 6 The design parameter values were obtained as Z 0l ϭ156.9 mm, Z 0d ϭ205.2 mm, Z 1l ϭ128.4 mm, and Z 1d ϭ167.0 mm through the optimization process. The measurement system was constructed using these values and the performance evaluated. The experimental setup and procedures were mostly identical to those in Ref. 5, except that in addition convex lenses were employed and the detectors were replaced by quadrant photodiodes ͑single element size: 2.5 mmϫ2.5 mm; gap between elements: 30 m͒. By applying the sensitivity matrix and the noise level of each detector, the resolution of each sensing direction was calculated as follows: 4 a͒

doi:10.1063/1.1396659
fatcat:bbcypqhb25ec5earhakzwtkpam