# Examination of High-Torque Sandwich-Type Spherical Ultrasonic Motor Using with High-Power Multimode Annular Vibrating Stator

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Operating Principle

_{21}-mode), the radial vibration mode (R

_{1}-mode), and the non-axisymmetric vibration mode (((1,1))-mode). The B

_{21}’-mode and ((1,1))’-mode are the same-shape orthogonal modes of the B

_{21}-mode and the ((1,1))-mode, respectively. A spherical rotor can be rotated around three axes by combining two of these vibration modes.

#### 2.1. Rotation around X(Y)-Axis

_{21}-mode or B

_{21}’-mode, and R

_{1}-mode are combined, the bending vibration generates a rotation torque in the vertical plane and the radial vibration controls the friction of the contact surface between the rotor and stator. Therefore, the spherical rotor can rotate around the X(Y)-axis continuously via an elliptical displacement motion generated in the stator. The resonance frequencies of B

_{21}-mode (B

_{21}’-mode) and R

_{1}-mode need to be close to each other because the stator must simultaneously generate both vibrations with a single driving frequency.

#### 2.2. Rotation around Z-Axis

## 3. Construction Design and Driving Method

#### 3.1. Vibrating Stator Construction

^{3}, and Poisson’s ratio of 0.33. To excite the vibration mode effectively, MPAs were arranged at large-strain portions. The dimensional parameters of the stator are shown in Figure 5. The X(Y)-axis rotation of the motor is driven by the combination of R

_{1}-mode and B

_{21}-mode or B

_{21}’-mode vibrations; therefore, their resonance frequencies were brought close each other by tuning the diameters and thicknesses of each part of the stator by modal FEA. The resonance frequencies for a range of values for each dimensional parameter are shown in Figure 6. The dimensions of the stator were determined using these simulations, which assumed a spherical rotor diameter of 50.8 mm.

#### 3.2. Motor Structure

_{1}-mode was set to MPAs. The vibration amplitudes of R

_{1}-mode at 12 evaluation spots shown in Figure 8a were calculated about each dimension of support ring. If R

_{1}-mode was affected and deformed by the support ring, the evaluation spots at the inner circumference of the stator had different vibration amplitude. If not, the vibration amplitude at all evaluation spots should be almost the same. Negative effects on the vibration mode were evaluated by calculating the standard deviation (SD) which evaluates the degree of dispersion in vibration amplitude at the evaluation spots. The distribution of displacement is unaffected by the maximum vibration amplitude due to linear analysis, even though the maximum vibration amplitudes obtained in each simulation were different. Therefore, the SD of the simulated vibration amplitude normalized with its maximum value was suitable for the evaluation. The simulation results, shown in Figure 8b, confirmed that support ring effects on the vibration modes could be reduced by adjusting the radial wall thickness to 15 mm and the axial width to 12 mm. The SDs of 0.048 and 0.039 were obtained on the stator with and without the designed support ring, respectively. Thus, the stator support ring design considered the displacement deviation, given an approximation of the resonance frequencies of the vibration modes. The FEA results for stator resonance frequency were: 21.32 kHz for B

_{21}-mode, 21.41 kHz for R

_{1}-mode, and 24.30 kHz for ((1,1))-mode.

#### 3.3. Driving Method

## 4. Structure and Measured Characteristics

#### 4.1. Stator Dimensions

#### 4.2. Admittance Characteristics

_{21}-mode, R

_{1}-mode, and ((1,1))-mode were 1.08 S, 0.52 S, and 1.48 S, respectively. These values are very large, and a large current flow was expected. In addition, the resonance quality factors were obtained as 426 for B

_{21}-mode, 504 for R

_{1}-mode, and 301 for ((1,1))-mode. This confirmed that the prototype stator had good electrical performance despite its large and somewhat complicated structure.

#### 4.3. Vibration Displacement

_{21}-mode and the outer surface of the stator in R

_{1}-mode and ((1,1))-mode. The excitations of each vibration mode met the design objectives. At an applied voltage of 8 V

_{pp}, a vibration amplitude of 7.27 μm was obtained in B

_{21}-mode near the point of contact between the rotor and stator. For reference, this value was about 48.5 times larger than the vibration amplitude, 0.15 μm, of the ϕ20 mm type [29]. Moreover, the maximum vibration amplitudes of R

_{1}-mode and ((1,1))-mode were about 27 times and about 28 times larger than those of the ϕ20 mm type, respectively. Hence, the embedded MPAs succeeded in generating strong excitations.

#### 4.4. Maximum Torque

_{pp}. Maximum torques at applied voltages of 40 V

_{pp}and 45 V

_{pp}were measured to search the value of the largest maximum torque. However, those continued to increase. At those applied voltages, the value of electric current exceeded the current measuring range of the power meter used in experiment, so that data of input power was not provided. Large input power was necessary to generate large maximum torque. Most of the input power was consumed as heat loss. A temperature rise of MPA was the most intense, and the temperature at the surface of MPA rose up to around 60°C at the applied voltage of 30 V

_{pp}with offset of 15 V and input power of around 160 W.

#### 4.5. Current and Power Factor

#### 4.6. Transient Response and Load Characteristics

## 5. Conclusions

## Supplementary Materials

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## Appendix A. Comparison of Excitation Methods by MPAs and PZT Plate

^{3}) made of hard piezoelectric ceramics embedded into a similar bar. Both piezoelectric devices were manufactured products. Their physical and piezoelectric properties are shown in Table A1. The PZT plate and MPA vibrators are shown in Figure A1a,b, respectively. The PZT plate was bonded at the center of the bar. The MPA was embedded into a rectangular hole formed on the bar, and it was secured in the hole with metal wedges, as shown in Figure 10c. The vibrator could independently excite the first bending mode (B

_{1}-mode) and the first longitudinal mode (L

_{1}-mode).

Item | Unit | PZT | MPA | |
---|---|---|---|---|

Dielectric properties | ε_{33}^{T}/ε_{0} | 1400 | 1460 | |

Curie temperature | °C | 315 | 310 | |

Dielectric loss | tanδ | % | 0.3 | 0.4 |

Piezoelectric strain constant | d_{31} | ×10^{−12} m/V | −132 | −120 |

d_{33} | ×10^{−12} m/V | 296 | 315 | |

Density | ρ | ×10^{3} kg/m^{3} | 7.76 | 7.6 |

Poison’s ratio | 0.31 | 0.31 | ||

Young’s modulus | Y_{11} | ×10^{10} Pa | 7.6 | 8.2 |

Mechanical quality factor | Q_{m} | 1800 | 2000 |

_{pp}was applied at the resonance frequency, measured force factors of both vibration modes of each vibrator were obtained (Table A2). The force factor is an indicator of the conversion efficiency from electrical energy to kinetic energy. The force factor was calculated by motional current divided by vibration velocity at the resonance frequency. The motional current was calculated by observing the input voltage and current to the piezoelectric element using an oscilloscope. The vibration velocity was measured on the surface of the bar using a laser Doppler vibrometer. The measurement point was set where the maximum vibration velocity was obtained, specifically the upper surface end of the bar in B1-mode and the side end of the bar in L1-mode. The force factor of B1-mode for the embedded MPA was about 3.7 times larger than that for the bonded PZT plate. In addition, the force factor of L1-mode for the embedded MPA was about 5.2 times larger than that of the bonded PZT plate. As a result, the excitation of the vibrator by an embedded MPA generated a larger force than could be obtained with the PZT plate. This is because the MPA utilizes the piezoelectric longitudinal effect, which has a larger force factor.

Mode | Resonance Frequency (kHz) | Vibration Velocity (mm/s rms) | Motional Current (mA rms) | Force Factor (N/V) | ||||
---|---|---|---|---|---|---|---|---|

PZT | MPA | PZT | MPA | PZT | MPA | PZT | MPA | |

B_{1}-mode | 8.98 | 8.10 | 21.2 | 290 | 2.84 | 144 | 0.134 | 0.497 |

L_{1}-mode | 29.7 | 27.7 | 6.85 | 492 | 2.31 | 863 | 0.337 | 1.75 |

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**Figure 1.**Operating principle of the multiple degrees of freedom spherical ultrasonic motor MDOF-SUSM using annular vibrating stators.

**Figure 2.**New stator construction using SUS304 steel. (

**a**) Outside; (

**b**) Inside; and (

**c**) Cross-section A-A’.

**Figure 3.**ϕ20 mm type stator construction using SUS304 steel. (

**a**) Outside; (

**b**) Inside; and (

**c**) Cross-section A-A’.

**Figure 4.**Strain distribution in the stator during each vibration mode. (

**a**) R

_{1}-mode, (

**b**) B

_{21}-mode, and (

**c**) ((1,1))-mode. Animations of simulated vibration modes and an elliptical displacement motion are available as Supplement Materials.

**Figure 6.**Simulated resonance frequency characteristics for the stator dimensional parameters identified in Figure 5. (

**a**) R

_{1}; (

**b**) R

_{2}; (

**c**) R

_{3}; (

**d**) R

_{4}; (

**e**) T

_{1}; and (

**f**) T

_{2}.

**Figure 8.**Analysis of support ring effects on stator. (

**a**) Fixed portions of support ring and evaluation spots in the rotor contact portion of the stator; (

**b**) Calculated standard deviation of the normalized simulated vibration amplitude of the stator at the evaluation spots during R

_{1}-mode excitation in finite element analysis (FEA).

**Figure 10.**Photographs of stator used in the prototype MDOF-SUSM. (

**a**) Outside view and (

**b**) Inside view. (

**c**) Structure of embedded MPA secured to the stator using metal wedges.

**Figure 11.**Dimensional drawings of stators designed for used in the MDOF-SUSM. (

**a**) Prototype and (

**b**) ϕ20 mm type.

**Figure 13.**Vibration displacement measured on the prototype stator surface during each vibration mode. (

**a**) B

_{21}-mode; (

**b**) R

_{1}-mode; and (

**c**) ((1,1))-mode.

**Figure 15.**Maximum torque and electric input power with respect to applied voltage. (

**a**) Rotation around X(Y)-axis and (

**b**) Rotation around Z-axis.

**Figure 17.**Effective current and power factor with respect to applied voltage. (

**a**) Rotation around X(Y)-axis and (

**b**) Rotation around Z-axis.

**Figure 18.**Transient response of rotation speed and torque with preload of 20.58 N. (

**a**) Rotation around X(Y)-axis; and (

**b**) Rotation around Z-axis.

**Figure 19.**Load characteristics with preload of 20.58 N. (

**a**) Rotation around X(Y)-axis, and (

**b**) Rotation around Z-axis.

Phase Difference (deg) | Vibration Mode | |
---|---|---|

① | ② | |

0 | 0 | R_{1}-mode |

180 | 180 | B_{21}-mode |

180 | 0 | ((1,1))-mode |

Vibration Mode | Rotation Direction | |
---|---|---|

Ports A–B | Ports C–D | |

R_{1}-mode | B_{21}-mode | Around X-axis |

B_{21}’-mode | R_{1}-mode | Around Y-axis |

((1,1))-mode | ((1,1))’-mode | Around Z-axis |

Basic Characteristics of Stator | R_{1}-Mode | B_{21}-Mode | ((1,1))-Mode | |
---|---|---|---|---|

Upper stator | Resonance frequency (kHz) | 22.15 | 21.88 | 24.98 |

Admittance (S) | 0.45 | 1.38 | 2.17 | |

Lower stator | Resonance frequency (kHz) | 22.09 | 21.87 | 24.94 |

Admittance (S) | 0.44 | 1.25 | 1.86 |

Performance Characteristic | Rotation | Prototype | ϕ20 mm Type [29] |
---|---|---|---|

Max torque (N∙m at V_{pp}) | Around X(Y)-axis | 1.48 at 30 | 0.058 at 80 |

Around Z-axis | 2.05 at 40 | 0.084 at 140 | |

Torque/weight (N∙m/kg) | Around X(Y)-axis | 0.87 | 0.70 |

Around Z-axis | 1.20 | 1.02 |

© 2018 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Mizuno, A.; Oikawa, K.; Aoyagi, M.; Kajiwara, H.; Tamura, H.; Takano, T. Examination of High-Torque Sandwich-Type Spherical Ultrasonic Motor Using with High-Power Multimode Annular Vibrating Stator. *Actuators* **2018**, *7*, 8.
https://doi.org/10.3390/act7010008

**AMA Style**

Mizuno A, Oikawa K, Aoyagi M, Kajiwara H, Tamura H, Takano T. Examination of High-Torque Sandwich-Type Spherical Ultrasonic Motor Using with High-Power Multimode Annular Vibrating Stator. *Actuators*. 2018; 7(1):8.
https://doi.org/10.3390/act7010008

**Chicago/Turabian Style**

Mizuno, Ai, Koki Oikawa, Manabu Aoyagi, Hidekazu Kajiwara, Hideki Tamura, and Takehiro Takano. 2018. "Examination of High-Torque Sandwich-Type Spherical Ultrasonic Motor Using with High-Power Multimode Annular Vibrating Stator" *Actuators* 7, no. 1: 8.
https://doi.org/10.3390/act7010008