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The simulation and design of an ultrasonic vibrator using coolant through the spindle structure

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The purpose of this study was the design of a vibrator that would be suitable for the ultrasonic tool holder using the “coolant through spindle structure,” as well as to investigate the effects of the shape, material and design of the vibrator on the performance of the tool holder assembly. The COMSOL Engineering simulation program was used for cross verification of resonance frequency and amplitude as well as to analyze the node position of the vibrator using the frequency analysis feature. Comparison of the measured and simulated values of the vibrator resonance frequency showed the error rate to be 2.97% and 2.76% for 2 cells and 4 cells of piezoelectric ceramic respectively. Next, during the experiment measuring by installing varied types of piezoelectric ceramics in the vibrator, it showed that a higher amplitude response could be achieved with PZT-8 piezoelectric ceramics material than was possible with PZT-4 material. The third experiment being conducted by locking the vibrator with varied bolt pretension forces indicated that an increase in bolt pretension force caused a sudden steep drop in initial equivalent impedance which gradually stabilized. During the final experiment, the performance response of the vibrator was also measured using tools of different size and the results showed that there was a difference of 600 Hz in resonance frequency between tools of 10 mm and 8 mm in diameter. Longer tools also resonated at lower frequency, but with higher amplitude. The maximum offset was expressed as 1000 Hz and 11.5 μm.

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The data analyzed and material specifications in this study are included in this article.

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This work was supported by the Ministry of Science and Technology, Taiwan, under Grant MOST 110–2221-E-167–017.

Author information

Authors and Affiliations



All authors contributed to the study conception and design. Material preparation, data collection, and analysis were performed by Bo-Lin Jian, Chia-Chuan Liu, Hao-Yang Lin, and Her-Terng Yau. The first draft of the manuscript was written by Chia-Chuan Liu, and all authors commented on previous versions of the manuscript. All authors read and approved the final manuscript.

Corresponding author

Correspondence to Her-Terng Yau.

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Appendix 1. PZT-4 and PZT-8 piezoelectric constant


PZT-4 piezoelectric constant

$${\mathbf{d}} = \left[ {\begin{array}{*{20}c} 0 & 0 & 0 & 0 & {4.96} & 0 \\ 0 & 0 & 0 & {4.96} & 0 & 0 \\ { - 1.23} & { - 1.23} & {2.89} & 0 & 0 & 0 \\ \end{array} } \right] \times 10^{ - 10} {\text{(C/N)}}$$

PZT-8 piezoelectric constant

$${\mathbf{d}} = \left[ {\begin{array}{*{20}c} 0 & 0 & 0 & 0 & {3.3} & 0 \\ 0 & 0 & 0 & {3.3} & 0 & 0 \\ { - 0.97} & { - 0.97} & {2.25} & 0 & 0 & 0 \\ \end{array} } \right] \times 10^{ - 10} {\text{(C/N)}}$$

Appendix 2. Power amplifier specifications

Power Amplifier specifications (Model No. NF- HAS4051) Source: NF




Max voltage

• ± 150 V

• −50 to 250 V

• −250 to 50 V

Max vurrent

1 Arms, 2.83 Ap-p (40 Hz to 200 Hz),

 ± 0.5 A (DC to 40 Hz)

Slew rate

450 V/μs typ


1 Ω + 3.2 μH max



50 Ω/600 Ω


 × 20, × 40, × 100, × 200, x (1 to 3) variable continuously

Frequency response

500 kHz (+0.5 to −3 dB, 20 Vrms, ± 150 V range)

Appendix 3. Direct reading torque wrenches specifications

Direct-reading torque wrench specifications (Model No. NF- HAS4051) Source: TOHNICHI



Total length

320 mm

Min. torque

50 kgf-cm

Max. torque

500 kgf-cm


5 kgf-cm

Square drive

3/8 inch


\(\pm\) 3%

Appendix 4. Tool specifications





Electroplating length

3 mm

Effective machining length

10 mm

Slot diameter

1.5 mm*2

Through-hole diameter

3 mm

Shank diameter

8, 10 mm


100 pic/mm

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Jian, BL., Liu, CC., Lin, HY. et al. The simulation and design of an ultrasonic vibrator using coolant through the spindle structure. Int J Adv Manuf Technol 123, 1925–1943 (2022).

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