# Longitudinal Composite-Mode Linear Ultrasonic Motor for Motion Servo System of Probe Station

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Construction and Working Principle

#### 2.1. Construction

#### 2.2. Working Principle

_{x}is the vibrating amplitude along the X direction, U

_{y}is the vibrating amplitude along the Y direction, and φ is the response phase shift between two working modes.

## 3. Simulation Via FEM

^{3}, Young’s modulus of 113 GPa, and Poisson’s ratio of 0.33. The physical parameters of the piezoelectric ceramics are listed as below:

^{S}is the dielectric constant matrix, and

**c**

^{E}is the stiffness matrix.

#### 3.1. Modal Analysis

#### 3.2. Sensitivity Analysis of Geometrical Parameters

_{sj}are determined by the partial derivative of modal frequency f

_{sj}to geometrical parameter P

_{j}. As the exact functional relationship between modal frequency and the geometrical parameter is not clear, the sensitivity could be approximately calculated by the ratio of the frequency difference caused by the variation in geometrical parameter ΔP

_{j}to ΔP

_{j}During the manufacturing process of the stator, the value of sensitivity is guidance for designing the tolerance of the geometrical dimension.

_{sj}and f

_{asj}are the modal frequencies of the symmetrical and anti-symmetrical modes, respectively, f

_{sjv}and f

_{sj0}are the modal frequencies of the symmetrical modes after and before the variation in geometrical parameter P

_{j}, respectively, and f

_{asjv}, f

_{asj0}are those of the anti-symmetrical mode, respectively [32].

#### 3.3. Harmonic Analysis

## 4. Experimental Investigation

#### 4.1. Impedance Analysis

#### 4.2. Operational Testing

## 5. Conclusions and Discussion

## Supplementary Materials

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 4.**Two working modes with the same longitudinal local modes: (

**a**) Rectangular piezoelectric vibrators vibrate with the same phases; (

**b**) rectangular piezoelectric vibrators vibrate with the opposite phases.

**Figure 6.**Relationship between amplitude ratio, phase shift, and ellipse trajectory: (

**a**) The relationship between phase shift and ellipse trajectory; (

**b**) the relationship between amplitude ratio and ellipse trajectory.

**Figure 11.**Harmonic response analysis curve: (

**a**) Harmonic response curve under single-phase excitation; (

**b**) harmonic response curve under dual-phase excitation.

**Figure 17.**Frequency speed curve: (

**a**) Frequency speed curve with single-phase excitation; (

**b**) frequency speed curve with dual-phase excitation.

Parameter | a | R | b | c | f | k | m | h | s |

Value (mm) | 120° | 1.5 | 1 | 17 | 0.5 | 3 | 5 | 1.45 | 90° |

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**MDPI and ACS Style**

Wang, Y.; Chen, Z.; Shi, Y.; Cui, C.; Cheng, F. Longitudinal Composite-Mode Linear Ultrasonic Motor for Motion Servo System of Probe Station. *Actuators* **2020**, *9*, 111.
https://doi.org/10.3390/act9040111

**AMA Style**

Wang Y, Chen Z, Shi Y, Cui C, Cheng F. Longitudinal Composite-Mode Linear Ultrasonic Motor for Motion Servo System of Probe Station. *Actuators*. 2020; 9(4):111.
https://doi.org/10.3390/act9040111

**Chicago/Turabian Style**

Wang, Yin, Ziyan Chen, Yunlai Shi, Changcai Cui, and Fang Cheng. 2020. "Longitudinal Composite-Mode Linear Ultrasonic Motor for Motion Servo System of Probe Station" *Actuators* 9, no. 4: 111.
https://doi.org/10.3390/act9040111