Modeling and Optimization of Novel Actuators Produced by Solid Freeform Fabrication
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ceramics during World War II that has seen piezoelectric materials progress from a laboratory phenomenon to a multi-billion dollar a year industry. Piezoelectric ceramics are used in devices such as microphones, loud speakers, ink jet printers, medical imaging equipment and recently, in 'smart' skis and bats [2]. Haertling [3] notes that while the strain of the piezoelectric ceramic itself is appealing for small (1000lgm) are needed for applications such as linear motors and switches. Recent efforts have focused on novel actuator designs for improved displacement performance [3-7]. Actuator performance is dependent on three complex factors, the properties of the ceramic, the design of the actuator and its drive technique [8]. The present investigation will focus on actuator design. With the development of Solid Freeform Fabrication techniques, such as the Fused Deposition of Ceramics (FDC) process [9], that enable the ready fabrication of complex shapes, the current investigation will study the effect of actuator geometry, poling direction and applied potential direction on the displacement performance of several novel piezoelectric actuators having either a dome, spiral or telescoping shape. BACKGROUND The analytical theory of piezoelectricity has been developed since the early 1900s [1]. In linear piezoelectricity, the linear elastic equations are coupled with the charge equation of 159 Mat. Res. Soc. Symp. Proc. Vol. 625 ©2000 Materials Research Society
electrostatics. For an orthotropic piezoelectric material, the constitutive relations, expressed in terms of stress, are given as [10] Sij = Sijkl OTkl+ dkj Ek
(1)
Di = dikl
(2)
OTkl+ &k Ek
where ok, and Sjj are the components of the stress and strain tensor, respectively, Ek the components of the electric field vector, Di the components of the electric displacement vector, Sijkl the components of the elastic compliance matrix, diki the components of the piezoelectric matrix, and Eik the components of the dielectric permittivity matrix. For piezoelectric and permittivity coefficients, dikb, and eCk,respectively, the first subscript 'i' denotes the direction of the electric field vector. Properties for the piezoelectric material used in this study, PZT-5H, are given in Table 1. It should be noted that the properties are given with x3 direction as its poling direction. Table 1: Elastic, piezoelectric and dielectric constants of PZT-5H [11]. Elastic Compliance sli S33 S12 S13 S4 4 mZ/N)
16.5
20.7
-4.78
-8.45
43.5
Piezoelectric Constant
d15
d24
d 31
d32
d 33
(10-12 C/N)
741
741
-274
-274
593
Dielectric Permittivity
6£1
-22
£33
(10-9 F/m)
15.05
15.05
13.01
( 10-11
S66
42.6
Due to the complexity of the constitutive relations and material properties, analysis of piezoelectric materials is difficult. Analytical solutions are limited to a few cases having simple geometries and boundary conditions. As a result, computational methods such as finite element analysis (FEA) have proven a valuable tool in the study of piezoelectric devices. B
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