Frequency responses of spherically contoured rectangular AT-cut quartz crystal resonators fabricated by fixed abrasive method

Jeong, Hee-Won; Aoki, Tetsuya; Hatsuzawa, Takeshi

doi:10.1016/j.ijmachtools.2004.04.010

Cited by 6 publications

(4 citation statements)

References 11 publications

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“…However, finishing time from 200 through 300 hours for 5000 blanks remains as a problem in the actual production. We have proposed a fixed abrasive polishing method to make the polishing time short, and confirmed a short polishing time of 9 hours (4) (5) .…”

Section: Introductionmentioning

confidence: 70%

“…analyzer R3754B (Advantest Corp.). Spectrums obtained for non-polished blank, conventional barrel polishing and finished by this mechanism are compared in Fig.7, although the resonant frequency of (b) is different because of the blank thickness (4) (5) . While the conventional method achieved larger resonance magnitude with small sub-peaks, spurious peaks located more than 16 MHz in the proposed method are suppressed by the polishing, and main resonance becomes dominants, which shows the usefulness of the mechanism.…”

Section: Experimental Results Imentioning

confidence: 99%

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High Speed Surface Micro-Polishing for Spurious Reduction of Small Quartz Crystal Blanks

et al. 2007

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Non-member Surface polishing is required for small crystal blanks to eliminate frequency spurious generated by the infinite rectangular shape. From the productivity viewpoint, bi-convex or plano-cylindrical surface are generally used to realize the energy trapping at the central part of the blanks. So far barrel polishing is the common fabrication technology to obtain bi-convex surface, however, the surface is finished insufficiently and fabrication process takes longer time as the blank size becomes small. To solve this difficulty, two types of new surface micro-polishing mechanisms with fixed abrasive and arrayed blank arrangement are experimentally examined to obtain plano-cylindrical surface. The fastest finishing time of 10 s for a blank is achieved together with the spurious elimination.

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Section: Introductionmentioning

confidence: 70%

Section: Experimental Results Imentioning

confidence: 99%

High Speed Surface Micro-Polishing for Spurious Reduction of Small Quartz Crystal Blanks

et al. 2007

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“…The oscillation mode of rectangular AT-cut quartz resonators has been studied in several works [31][32][33]. It is known with precision that the AT-cut quartz resonator fundamental oscillation mode is in the thickness shear mode, as depicted in figure 6.…”

Section: Probe Dynamics and Sensitivitymentioning

confidence: 99%

Gentle and fast atomic force microscopy with a piezoelectric scanning probe for nanorobotics applications

Acosta¹,

Polesel-Maris²,

Thoyer³

et al. 2013

Nanotechnology

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A novel dual tip nanomanipulation atomic force microscope (AFM) platform operating in ambient conditions is presented. The system is equipped with a high frequency quartz piezoelectric self-sensing scanning probe for fast imaging and a passive cantilever for manipulation. The system is validated by imaging and selective pushing/pulling of gold colloid beads (diameters from 80 to 180 nm). This provides a more compact integration compared to an external optical lever and avoids several of its drawbacks such as optical interference and noise, and recalibration in the case of a moving cantilever and a fixed laser source and photodiode sensor. Moreover, as the quartz oscillator exhibits oscillation amplitudes in the sub-picometer range with a resonant frequency in the megahertz range, this dynamic force sensor is ideal for fast AFM imaging. Experiments show an increase by five times in imaging speed compared to a classical AFM system.

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“…Li et al [39,40] investigated the trapped thickness-shear modes of a contoured AT cut resonator with Legendre equation and hypergeometric function for the thickness, and quartz crystal plate with periodical contour by power series expansion technique. The quartz crystals are usually beveled into spherical shape to restrict the vibrating area of the plate within its central region, that is the energy trapping effect [41]. However, the cross section in the middle is more likely to be elliptical.…”

Section: Introductionmentioning

confidence: 99%

Geometric eccentricity effect on thickness-shear vibration of an elliptical flexoelectric crystal plate

et al. 2023

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In this paper, a thickness-shear vibration model for a two-dimensional finite flexoelectric crystal plate with slowly varying thickness and elliptical cross section is presented. The influences of eccentricity and flexoelectricity on the fundamental frequencies of thickness-shear vibration and electric potential distributions under short circuit boundary condition are investigated. The proposed model uses the first order McLaughlin series to approximate the elliptical function and the first derivative of elliptical function is ignored since the plate thickness varies slowly. For the finite plate, the symmetric mode in length and antisymmetric mode in thickness are adopted for the displacement function. In addition, only the shear strain gradient through the thickness is used in the mathematical model for the thin and long flexoelectric crystal plate. By implementing the variational principle, the governing equations are obtained and further solved by the Galerkin method. The obtained frequencies of thickness-shear mode are expressed in terms of eccentricity and length-to-thickness ratio. The results show that the eccentricity has great influence on the nondimensional fundamental frequencies. A small reduction in eccentricity results in significant increment of the nondimensional frequency implying that it is possible to increase the fundamental frequency by changing the cross section of the elliptical flexoelectric plate. The flexoelectric effect is also found to affect the nondimensional frequency and electric potential distribution significantly. Thus, for accurate design of nano/micro scale high precision and high frequency flexoelectric/piezoelectric devices, flexoelectricity must be taken into consideration.

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Frequency responses of spherically contoured rectangular AT-cut quartz crystal resonators fabricated by fixed abrasive method

Cited by 6 publications

References 11 publications

High Speed Surface Micro-Polishing for Spurious Reduction of Small Quartz Crystal Blanks

High Speed Surface Micro-Polishing for Spurious Reduction of Small Quartz Crystal Blanks

Gentle and fast atomic force microscopy with a piezoelectric scanning probe for nanorobotics applications

Geometric eccentricity effect on thickness-shear vibration of an elliptical flexoelectric crystal plate

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