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

actuators

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

Ai Mizuno 1,*, Koki Oikawa 1, Manabu Aoyagi 1,* ID , Hidekazu Kajiwara 1, Hideki Tamura 2 and Takehiro Takano 2

1 Graduate School of Engineering, Muroran Institute of Technology, 27-1, Mizumoto, Muroran, Hokkaido 050-8585, Japan; [email protected] (K.O.); [email protected] (H.K.) 2 Department of Information and Communication Engineering, Tohoku Institute of Technology, Sendai, Miyagi 982-8577, Japan; [email protected] (H.T.); [email protected] (T.T.) * Correspondence: [email protected] (A.M.); [email protected] (M.A.); Tel.: +81-143-46-5504 (M.A.)

Received: 5 January 2018; Accepted: 20 February 2018; Published: 27 February 2018

Abstract: Spherical ultrasonic motors (SUSMs) that can operate with multiple degrees of freedom (MDOF) using only a single stator have high holding torque and high torque at low speed, which makes reduction gearing unnecessary. The simple structure of MDOF-SUSMs makes them useful as compact actuators, but their development is still insufﬁcient for applications such as joints of humanoid robots and other systems that require MDOF and high torque. To increase the torque of a sandwich-type MDOF-SUSM, we have not only made the vibrating stator and spherical rotor larger but also improved the structure using three design concepts: (1) increasing the strength of all three vibration modes using multilayered piezoelectric actuators (MPAs) embedded in the stator, (2) enhancing the rigidity of the friction driving portion of the stator for transmitting more vibration force to the friction-driven rotor surface, and (3) making the support mechanism more stable. An MDOF-SUSM prototype was tested, and the maximum torques of rotation around the X(Y)-axis and Z-axis were measured as 1.48 N·m and 2.05 N·m, respectively. Moreover, the values for torque per unit weight of the stator were obtained as 0.87 N·m/kg for the X(Y)-axis and 1.20 N·m/kg for the Z-axis. These are larger than values reported for any other sandwich-type MDOF-SUSM of which we are aware. Hence, the new design concepts were shown to be effective for increasing torque. In addition, we measured the transient response and calculated the load characteristics of rotation around the rotor’s three orthogonal axes.

Keywords: ultrasonic motor (USM); spherical rotor; multiple degrees of freedom (MDOF); high-power; annular vibrator; sandwich; multilayer piezoelectric actuator (MPA)

1. Introduction In recent years, developments in robot technology have increased the demand for downsized and simpliﬁed actuator systems. The actuator system with multiple degrees of freedom (MDOF) is one way to meet this demand. Spherical motors that can operate with MDOF using only a single stator were proposed [1–5], and such systems are effective for downsizing. MDOF motion is often required under conditions of low speed with large torque. However, a spherical electromagnetic motor (SEMM) has characteristics of low torque at high speed [6–13]. In contrast, an ultrasonic motor has the potential to be an MDOF drive source due to higher performance with respect to a SEMM; it has high torque at low speed, high holding torque, and no need for reduction gearing. For these reasons, MDOF ultrasonic motors and MDOF spherical ultrasonic motors (SUSMs) have been studied [14–27].

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The authors previously reported MDOF-SUSMs using annular vibrating stators that can excite multiple vibration modes [28–31]. Our results showed that the sandwich-type MDOF-SUSM is effective for increasing torque despite its compact size [28,29]. The sandwich structure refers to a spherical rotor held between two annular vibrating stators. The MDOF motion of the rotor can be realized even if only one stator is used with a rotor support mechanism, so two active stators increases the torque for all three rotational axes. This simple structure has both a rotor support and a preload mechanism. Although the MDOF-SUSM is useful as a compact actuator, it is still insufﬁcient in applications such as larger joints of a humanoid robot and other systems that require both MDOF and high torque. For a robot manipulator, which is the expected application of the SUSM, a shoulder joint requires a motor with high torque and high rigidity because some wrist and elbow motors apply a load to the shoulder joint motor. Most MDOF-SUSMs are useful for low-load applications, such as small robotic wrist joints and hands, because of their high torque per unit weight. However, their maximum torques range up to only about 200 mN·m [14,15,20–22,25,28–31]. These torques are insufﬁcient for high-load applications, such as wrist and shoulder joints, because these applications require high torque of at least 10 N·m [15]. The MDOF-SUSM simply cannot generate output torque at the same level as a same-size motor with one degree of freedom. To make the MDOF-SUSM with annular vibrating stator previously reported [29], a thin piezoceramic (PZT) disk with divided electrodes was bonded to the surface of the stator. This excitation method has the advantage of simple structure and compact size, and it is adopted in many types of ultrasonic motors. However, the method has a disadvantage in that it generates force using the piezoelectric lateral effect, which is weak in comparison to the piezoelectric longitudinal effect. To obtain high torque, it is necessary to change the method for exciting vibration modes to a more effective method that produces higher-power excitation. In this study, a high-torque sandwich-type MDOF-SUSM using a new annular vibrating stator with a strong excitation structure was developed based on three design concepts: (1) Stronger excitation is produced by utilizing the piezoelectric longitudinal effect of multilayered piezoelectric actuators (MPAs) having a high mechanical quality factor; (2) The rigidity of the friction driving portion of the stator is increased; (3) A more stable support mechanism is developed. The MPAs embedded in the vibrating stator can strongly excite the three different vibration modes necessary for the stator to drive rotation. Furthermore, it is possible to suppress the attenuation of the excited vibration force by increasing the rigidity of the friction driving portion of the stator. This results in increased rotor driving force, and a further torque increase can be expected due to its capacity for higher preload. Thus, this paper describes the effectiveness of strong excitations by MPAs and the design and driving method of a new vibrating stator. Some performance characteristics of a prototype MDOF-SUSM using the new stator are reported and compared to the performance of the previous type that had a 20 mm-diameter spherical rotor [29]. Hereafter, the previous type is called the φ20 mm type. The obtained performance of both MDOF-SUSMs cannot be compared directly because their spherical rotors and stators have different sizes, so the torque per unit weight of stator was also determined to serve as a performance index.

2. Operating Principle The operating principle of the sandwich-type MDOF-SUSM is shown in Figure1. The motor’s annular stator can independently excite three different vibration modes: the bending vibration mode (B21-mode), the radial vibration mode (R1-mode), and the non-axisymmetric vibration mode (((1,1))-mode). The B21’-mode and ((1,1))’-mode are the same-shape orthogonal modes of the B21-mode and the ((1,1))-mode, respectively. A spherical rotor can be rotated around three axes by combining two of these vibration modes. Actuators 2018, 7, 8 3 of 17 Actuators 2018, 7, x 3 of 17

FigureFigure 1. 1.OperatingOperating principle principle of the multiple of the multiple degrees of degrees freedom of spherical freedom ultrasonic spherical motor ultrasonic MDOF-SUSM motor usingMDOF-SUSM annular vibrating using annular stators. vibrating stators.

2.1.2.1. Rotation Rotation around around X(Y)-Axis X(Y)-Axis

WhenWhen B B2121-mode-mode or or B B2121’-mode,’-mode, and and R R1-mode1-mode are are combined, combined, the the bending bending vibration vibration generates generates a a rotationrotation torque torque in in the the vertical vertical plane plane and and the the radial radial vibration vibration controls controls the the friction friction of of the the contact contact surface surface betweenbetween thethe rotorrotor and and stator. stator. Therefore, Therefore, the spherical the spherical rotor can rotor rotate can around rotate the around X(Y)-axis the continuously X(Y)-axis continuouslyvia an elliptical via displacement an elliptical displacement motion generated motion in generated the stator. in The the resonance stator. The frequencies resonance offrequencies B21-mode of(B 21B’-mode)21-mode and(B21’-mode) R1-mode and need R1-mode to be closeneed to to each be close other to because each other the stator because must the simultaneously stator must simultaneouslygenerate both vibrations generate both with vibrations a single driving with a frequency. single driving frequency.

2.2.2.2. Rotation Rotation around around Z-Axis Z-Axis ◦ WhenWhen ((1,1))-mode ((1,1))-mode and and ((1,1))’-mo ((1,1))’-modede are are excited excited with with a a phase phase diffe differencerence of of 90°, 90 ,an an elliptical elliptical displacementdisplacement motion occurs inin thethe Z-planeZ-plane of of the the stator. stator. The The rotor rotor receives receives a frictional a frictional rotary rotary force force and androtates rotates around around the Z-axisthe Z-axis based based on traveling-wave on traveling-wave ultrasonic ultrasonic motion. motion.

3.3. Construction Construction Design Design and and Driving Driving Method Method 3.1. Vibrating Stator Construction 3.1. Vibrating Stator Construction The design of the annular vibrating stator is shown in Figure2. For strong excitation, two concepts The design of the annular vibrating stator is shown in Figure 2. For strong excitation, two are incorporated. concepts are incorporated. The first concept is the excitation of the stator by embedded MPAs made of hard piezoelectric The first concept is the excitation of the stator by embedded MPAs made of hard piezoelectric material provided with a high mechanical quality factor, which has inner losses less than those of a material provided with a high mechanical quality factor, which has inner losses less than those of a soft material. The MPA is constructed by alternately stacking several tens to several hundreds of thin soft material. The MPA is constructed by alternately stacking several tens to several hundreds of thin piezoelectric ceramic sheets and electrodes. The polarizations of the ceramic sheets are in the thickness piezoelectric ceramic sheets and electrodes. The polarizations of the ceramic sheets are in the direction, and they are opposite to each other. Positive and negative electrodes are connected in parallel. thickness direction, and they are opposite to each other. Positive and negative electrodes are Hence, a high electric field is applied to each ceramic sheet, so that large force and displacement in the connected in parallel. Hence, a high electric field is applied to each ceramic sheet, so that large force thickness direction are generated by applying a low voltage. The MPA was adopted after comparing and displacement in the thickness direction are generated by applying a low voltage. The MPA was the excitation performance of an MPA embedded in a vibrating bar and a PZT plate bonded to an adopted after comparing the excitation performance of an MPA embedded in a vibrating bar and a equivalent vibrating bar. It was confirmed that the excitation by an MPA embedded in the vibrator PZT plate bonded to an equivalent vibrating bar. It was confirmed that the excitation by an MPA embedded in the vibrator generated a stronger excitation at low applied voltage. The details are described in Appendix A. Figure 2 shows how the MPAs are arranged and embedded in the inner

Actuators 2018, 7, 8 4 of 17

Actuators 2018, 7, x 4 of 17 generated a stronger excitation at low applied voltage. The details are described in AppendixA. Figure2 shows how the MPAs are arranged and embedded in the inner and outer surfaces of the new Actuatorsand outer 2018 ,surfaces 7, x of the new stator. A pair of MPAs is embedded in each square hole on4 bothof 17 stator. A pair of MPAs is embedded in each square hole on both surfaces. surfaces. and outer surfaces of the new stator. A pair of MPAs is embedded in each square hole on both surfaces.

(a) (b)(c)

Figure 2. 2. NewNew(a) stator stator construction construction using using SUS304 SUS304(b steel.)( steel. (a) Outside; (a) Outside; (b) Inside; (b) Inside; and ( andc) Cross-section (cc)) Cross-section A-A’. A-A’. FigureThe other 2. New concept stator construction is the increased using SUS304rigidity steel. of th (ae) friction-drivingOutside; (b) Inside; portion and (c) Cross-sectionof the stator. A-A’. The new stator design was given high structural rigidity by increasing the thickness of the inner ring of the TheThe other other concept concept is is the the increased increased rigidity rigidity of of th thee friction-driving friction-driving portion portion of of the the stator. stator. The The new new stator, where it contacts the rotor, in comparison with the proportionate thickness of the φ20 mm statorstator design design was was given given high high structural structural rigidity rigidity by by increasing increasing the the thickness thickness of of the the inner inner ring ring of of the the type shown in Figure 3. This was done to suppress the attenuation of the strong excited vibration stator,stator, where itit contactscontacts thethe rotor, rotor, in in comparison comparison with with the the proportionate proportionate thickness thickness of the of φthe20 φ mm20 mm type force and to increase the driving force to the rotor. The designed stator has four spherically shaped typeshown shown in Figure in Figure3. This 3. was This done was to done suppress to suppre the attenuationss the attenuation of the strong of the excited strong vibration excited forcevibration and surfaces for partial but stable contact with the spherical rotor [29]. For rotation around the X(Y)-axis, forceto increase and to the increase driving the force driving to the force rotor. to Thethe designedrotor. The stator designed has fourstator spherically has four spherically shaped surfaces shaped for the spherical contact surface has an effective portion that generates friction to rotate the rotor and a surfacespartial but forstable partial contact but stable with contact the spherical with the rotor sphe [29rical]. For rotor rotation [29]. For around rotati theon X(Y)-axis, around the the X(Y)-axis, spherical non-effective portion that produces a braking force. This is why a partial contact surface is needed. thecontact spherical surface contact has an surface effective has portion an effective that generatesportion that friction generates to rotate friction the rotorto rotate and the a non-effective rotor and a non-effectiveportion that producesportion that a braking produces force. a braking This is whyforce. a This partial is why contact a partial surface contact is needed. surface is needed.

(a) (b)(c)

Figure 3. φ20 (mma) type stator construction using( SUS304b)( steel. (a) Outside; (b) Inside; andc) (c) Cross-section A-A’. FigureFigure 3. 3. φ20φ mm20 mm type type stator stator construction construction using SUS304 using SUS304steel. (a) Outside; steel. (a ()b Outside;) Inside; and (b) (c Inside;) Cross-section and (c ) A-A’.FigureCross-section 4 shows A-A’. the strain distribution of the stator in each vibration mode, as simulated by finite element analysis (FEA). We assumed the stator made of an austenitic stainless steel, SUS304 (18Cr-8Ni) Figure 4 shows the strain distribution of the stator in each vibration mode, as simulated by finite basedFigure on Japan4 shows JIS standard, the strain which distribution was a ofquite the statorpopular in eachmaterial. vibration The material mode, as characteristics simulated by ﬁniteusing element analysis (FEA). We assumed the stator made of an austenitic stainless steel, SUS304 (18Cr-8Ni) FEAelement were analysis Young’s (FEA). modulus We assumed of 197 GPa, the statordensity made of 8000 of an kg/m austenitic3, and stainlessPoisson’s steel, ratio SUS304 of 0.33. (18Cr-8Ni) To excite based on Japan JIS standard, which was a quite popular material. The material characteristics using thebased vibration on Japan mode JIS standard, effectively, which MPAs was awere quite arra popularnged material.at large-strain The material portions. characteristics The dimensional using FEA were Young’s modulus of 197 GPa, density of 8000 kg/m3, and Poisson’s ratio of 0.33. To excite parametersFEA were Young’s of the stator modulus are ofshown 197 GPa, in Figure density 5. of Th 8000e X(Y)-axis kg/m3, androtation Poisson’s of the ratio motor of 0.33. is driven To excite by the the vibration mode effectively, MPAs were arranged at large-strain portions. The dimensional combinationvibration mode of R effectively,1-mode and MPAs B21-mode were or arranged B21’-mode at large-strain vibrations; portions.therefore, The their dimensional resonance frequencies parameters parameters of the stator are shown in Figure 5. The X(Y)-axis rotation of the motor is driven by the wereof the brought stator are close shown each in other Figure by5. tuning The X(Y)-axis the diameters rotation and of the thicknesses motor is driven of each by part the combinationof the stator by of combination of R1-mode and B21-mode or B21’-mode vibrations; therefore, their resonance frequencies modalR -mode FEA. and The B -moderesonance or B frequencies’-mode vibrations; for a range therefore, of values their for resonance each dimensional frequencies parameter were brought are were1 brought close21 each other21 by tuning the diameters and thicknesses of each part of the stator by shownclose each in Figure other by6. The tuning dimensions the diameters of the and stator thicknesses were determined of each part using of thethese stator simulations, by modal which FEA. modal FEA. The resonance frequencies for a range of values for each dimensional parameter are Theassumed resonance a spherical frequencies rotor diameter for a range of of 50.8 values mm. for each dimensional parameter are shown in Figure6. shown in Figure 6. The dimensions of the stator were determined using these simulations, which The dimensions of the stator were determined using these simulations, which assumed a spherical assumed a spherical rotor diameter of 50.8 mm. rotor diameter of 50.8 mm.

Actuators 2018, 7, 8 5 of 17 ActuatorsActuators 2018 2018, ,,7 7, ,,x xx 55 of of 17 17

((aa)) ((bb)()(cc))

FigureFigure 4. 4. Strain StrainStrain distribution distributiondistribution in inin the thethe stator statorstator during duringduring each eacheach vibration vibrationvibration mode. mode.mode. ( (a(a) )R R1-mode,11-mode, ( b(b) )B B212121-mode,-mode, and and Figure 4. Strain distribution in the stator during each vibration mode. (a)R1-mode, (b)B21-mode, and (c(c) )((1,1))-mode. ((1,1))-mode. Animations Animations of of simulated simulated vibration vibration modes modes and and an an elliptical elliptical displacement displacement motion motion are are (c) ((1,1))-mode. Animations of simulated vibration modes and an elliptical displacement motion are availableavailable as as Supplement Supplement Materials. Materials. available as Supplement Materials.

FigureFigure 5. 5. Dimensional DimensionalDimensional parameters parametersparameters of ofof the thethe new newnew stator. stator. stator.

RR=38,=38, R R=42,=42, R R=25.4,=25.4, T T=18,=18, T T=4=4 RR=56,=56, R R=50,=50, R R=25.4,=25.4, T T=18,=18, T T=4=4 R22=38, R33=42, R44=25.4, T11=18, T22=4 R11=56, R33=50, R44=25.4, T11=18, T22=4 2626 2626 R1-modeRR1-modeR-mode-mode R1-modeRR1-modeR-mode-mode R1-modeR11-mode R1-modeR11-mode B21-modeBB21-modeB -mode-mode B21-modeB2121-mode B21-modeB21-modeBB2121-mode-mode 2424 2424 21 (kHz) 2222 (kHz) 2222 22 (kHz) 22 (kHz) (kHz) (kHz)

2020 2020 Resonance frequency Resonance frequency Resonance frequency Resonance frequency Resonance frequency 4646 48 48 50 50 52 52 54 54 56 56 Resonance frequency 46 48 50 52 54 56 3838 40 40 42 42 44 44 46 46 48 48 RR (mm)(mm) RR (mm)(mm) R11 (mm) R22 (mm) ((aa)) ((bb)) RR=56,=56, R R=38,=38, R R=25.4,=25.4, T T=18,=18, T T=4=4 RR=56,=56, R R=38,=38, R R=44,=44, T T=18,=18, T T=4=4 R11=56, R22=38, R44=25.4, T11=18, T22=4 R11=56, R22=38, R33=44, T11=18, T22=4 2626 2626 26 RR1-modeR-mode-mode 26 R1-modeRR1-modeR-mode-mode R1-modeR1-modeR11-mode R1-modeR11-mode B21-mode B21-modeBB21-modeB -mode-mode B21-modeBB21-modeB2121-mode-mode B21-modeB2121-mode 2424 21 2424 (kHz) (kHz) (kHz) (kHz) 2222 (kHz) 2222 (kHz) 22

2020

Resonance frequency 20 Resonance frequency

Resonance frequency 20 Resonance frequency 2222 23 23 24 24 25 25 26 26 4040 42 42 44 44 46 46 48 48 50 50 22 23 24 25 26 RR (mm)(mm) RR (mm)(mm) R33 (mm) R44 (mm) ((cc)) ((dd))

Figure 6. Cont.

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R1=52, R2=40, R3=45, R4=25.4, T2=4 R1=52, R2=40, R3=45, R4=25.4, T1=18 26 60 R1-modeR1-mode R1-modeR -mode 50 1 B21-modeB21-mode 24 B21-modeB21-mode 40 30 (kHz) (kHz) 22 20 20 10 Resonance frequency Resonance frequency 13 14 15 16 17 18 19 20 2 6 10 14 18 T1 (mm) T2 (mm) (e) (f)

FigureFigure 6.6. Simulated resonance frequency characteristicscharacteristics for the statorstator dimensionaldimensional parametersparameters identified in Figure 5. (a) R1; (b) R2; (c) R3; (d) R4; (e) T1; and (f) T2. identiﬁed in Figure5.( a)R1;(b)R2;(c)R3;(d)R4;(e)T1; and (f)T2.

3.2. Motor Structure 3.2. Motor Structure The basic construction of the new MDOF-SUSM design is shown in Figure 7. The stators, The basic construction of the new MDOF-SUSM design is shown in Figure7. The stators, spherical spherical rotor and support rings were made of the stainless steel SUS304. To achieve high torque rotor and support rings were made of the stainless steel SUS304. To achieve high torque with strong with strong excitation, the structural stability of the preload mechanism is important. Supporting excitation, the structural stability of the preload mechanism is important. Supporting beams of beams of the φ20 mm type stator shown in Figure 3 could reduce negative effects on the vibration the φ20 mm type stator shown in Figure3 could reduce negative effects on the vibration mode. mode. However, such a structure was weak against the force in the preload direction, so that large However, such a structure was weak against the force in the preload direction, so that large preload preload was hardly applied. Moreover, the φ20 mm type stator was apt to become unstable by its was hardly applied. Moreover, the φ20 mm type stator was apt to become unstable by its own output own output torque. Therefore, supporting beams of the prototype stator had relatively high rigidity torque. Therefore, supporting beams of the prototype stator had relatively high rigidity in preload in preload direction and radial direction. Each stator is fixed to a support ring at four points of direction and radial direction. Each stator is ﬁxed to a support ring at four points of supporting beams. supporting beams. The assembled support rings are used for preload adjustment. This construction The assembled support rings are used for preload adjustment. This construction aims to provide a aims to provide a uniform preload and its easy setting at three points without affecting the vibration uniform preload and its easy setting at three points without affecting the vibration modes. Hence, modes. Hence, the support ring was designed by tuning its outer diameter, that is, its radial wall the support ring was designed by tuning its outer diameter, that is, its radial wall thickness and axial thickness and axial width, by FEA. The forced vibration of the stator was analyzed by FEA under the width, by FEA. The forced vibration of the stator was analyzed by FEA under the condition that condition that the certain voltage of natural frequency of R1-mode was set to MPAs. The vibration the certain voltage of natural frequency of R1-mode was set to MPAs. The vibration amplitudes of amplitudes of R1-mode at 12 evaluation spots shown in Figure 8a were calculated about each R1-mode at 12 evaluation spots shown in Figure8a were calculated about each dimension of support dimension of support ring. If R1-mode was affected and deformed by the support ring, the evaluation ring. If R1-mode was affected and deformed by the support ring, the evaluation spots at the inner spots at the inner circumference of the stator had different vibration amplitude. If not, the vibration circumference of the stator had different vibration amplitude. If not, the vibration amplitude at all amplitude at all evaluation spots should be almost the same. Negative effects on the vibration mode evaluation spots should be almost the same. Negative effects on the vibration mode were evaluated were evaluated by calculating the standard deviation (SD) which evaluates the degree of dispersion by calculating the standard deviation (SD) which evaluates the degree of dispersion in vibration in vibration amplitude at the evaluation spots. The distribution of displacement is unaffected by the amplitude at the evaluation spots. The distribution of displacement is unaffected by the maximum maximum vibration amplitude due to linear analysis, even though the maximum vibration vibration amplitude due to linear analysis, even though the maximum vibration amplitudes obtained amplitudes obtained in each simulation were different. Therefore, the SD of the simulated vibration in each simulation were different. Therefore, the SD of the simulated vibration amplitude normalized amplitude normalized with its maximum value was suitable for the evaluation. The simulation with its maximum value was suitable for the evaluation. The simulation results, shown in Figure8b, results, shown in Figure 8b, confirmed that support ring effects on the vibration modes could be conﬁrmed that support ring effects on the vibration modes could be reduced by adjusting the radial reduced by adjusting the radial wall thickness to 15 mm and the axial width to 12 mm. The SDs of wall thickness to 15 mm and the axial width to 12 mm. The SDs of 0.048 and 0.039 were obtained on 0.048 and 0.039 were obtained on the stator with and without the designed support ring, respectively. the stator with and without the designed support ring, respectively. Thus, the stator support ring Thus, the stator support ring design considered the displacement deviation, given an approximation design considered the displacement deviation, given an approximation of the resonance frequencies of of the resonance frequencies of the vibration modes. The FEA results for stator resonance frequency the vibration modes. The FEA results for stator resonance frequency were: 21.32 kHz for B21-mode, were: 21.32 kHz for B21-mode, 21.41 kHz for R1-mode, and 24.30 kHz for ((1,1))-mode. 21.41 kHz for R1-mode, and 24.30 kHz for ((1,1))-mode.

Actuators 2018, 7, 8 7 of 17 Actuators 2018, 7, x 7 of 17 Actuators 2018, 7, x 7 of 17

Figure 7. Component parts of sandwich structure used in the new stator.stator. Figure 7. Component parts of sandwich structure used in the new stator.

(a) (b) (a) (b) Figure 8. Analysis of support ring effects on stator. (a) Fixed portions of support ring and evaluation Figure 8. Analysis of support ring effects on stator. (a) Fixed portions of support ring and evaluation Figurespots in 8. theAnalysis rotor contact of support portion ring of effects the stator; on stator. (b) (Calculateda) Fixed portions standard of supportdeviation ring of the and normalized evaluation spotsspots in in the the rotor rotor contact contact portion portion of of the the stator; stator; (b ()b Calculated) Calculated standard standard deviation deviation of of the the normalized normalized simulated vibration amplitude of the stator at the evaluation spots during R1-mode excitation in finite simulated vibration amplitude of the stator at the evaluation spots during R1-mode excitation in finite simulatedelement analysis vibration (FEA). amplitude of the stator at the evaluation spots during R1-mode excitation in ﬁnite elementelement analysis analysis (FEA). (FEA). 3.3. Driving Method 3.3.3.3. Driving Driving Method Method The arrangement of MPAs in the new stator is shown in Figure 9. Each vibration mode is excited The arrangement of MPAs in the new stator is shown in Figure 9. Each vibration mode is excited by twoThe ports arrangement on opposite of MPAs sides inof thethe newstator: stator Port is A shown and Port in Figure B, or 9Port. Each C and vibration Port D. mode The isvibration excited by two ports on opposite sides of the stator: Port A and Port B, or Port C and Port D. The vibration bymode two can ports be onselected opposite by applying sides of the a sinusoidal stator: Port volt A andage of Port the B, appropriate or Port C and phase Port difference D. The vibration to each mode can be selected by applying a sinusoidal voltage of the appropriate phase difference to each modeMPA, canas shown be selected in Table by applying1. Moreover, a sinusoidal rotational voltage movement of the in appropriatethe three axis phase directions difference is generated to each MPA, as shown in Table 1. Moreover, rotational movement in the three axis directions is generated MPA,by combining as shown the in two Table vibration1. Moreover, modes rotational that are movement excited in ineach the port, three as axis shown directions in Table is generated2. by combiningby combining the twothe vibrationtwo vibration modes modes that arethat excited are excited in each in each port, port, as shown as shown in Table in Table2. 2.

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FigureFigure 9. 9. ArrangementArrangement of of MPAs MPAs in the stator.

TableTable 1. Excitation method of each vibration mode. Phase Difference (deg) Vibration Mode Phase Difference (deg) Vibration Mode 1 2 0 0 R1-mode

0180 180 0 B21-mode R1-mode 180180 0 180((1,1))-mode B21 -mode 180 0 ((1,1))-mode Notes:  MPA pair on opposite sides (Port A–B or Port A–D)  MPA pair on the inside and outside

(1–2Notes: in each1 MPA port) pair on opposite sides (Port A–B or Port A–D) 2 MPA pair on the inside and outside (1–2 in each port).

Table 2. Operation method of each rotation. Table 2. Operation method of each rotation. Vibration Mode Rotation Vibration Mode Ports A–B Ports C–D DirectionRotation Direction Ports A–B Ports C–D R1-mode B21-mode Around X-axis R1-modeB21’-mode B21R-mode1-mode Around Around Y-axis X-axis B21’-mode((1,1))-mode ((1,1))’-mode R1-mode Around Around Z-axis Y-axis ((1,1))-mode ((1,1))’-mode Around Z-axis

4. Structure and Measured Characteristics 4. Structure and Measured Characteristics 4.1. Stator Dimensions 4.1. Stator Dimensions Figure 10 shows an assembled stator for the prototype MDOF-SUSM. The MPAs were Figure 10 shows an assembled stator for the prototype MDOF-SUSM. The MPAs were embedded embedded into rectangular holes formed in the stator, and they were secured in the holes with metal into rectangular holes formed in the stator, and they were secured in the holes with metal wedges, wedges, as shown in Figure 10c. The stator dimensions were determined by FEA simulation. as shown in Figure 10c. The stator dimensions were determined by FEA simulation. Figure 11a,b show Figure 11a,b show dimensional drawings of designed prototype stator and the φ20 mm type stators, dimensional drawings of designed prototype stator and the φ20 mm type stators, respectively. For the respectively. For the generation of high torque, the prototype stator was designed for a spherical rotor generation of high torque, the prototype stator was designed for a spherical rotor 50.8 mm in diameter, 50.8 mm in diameter, which is about 2.5 times larger than the rotor of the φ20 mm type, and the main which is about 2.5 times larger than the rotor of the φ20 mm type, and the main part of the stator was part of the stator was about 2.7 times larger than that of the φ20 mm type. It is understood that the about 2.7 times larger than that of the φ20 mm type. It is understood that the prototype stator was not prototype stator was not simple upsizing of the φ20 mm type. simple upsizing of the φ20 mm type.

Actuators 2018, 7, 8 9 of 17 ActuatorsActuators 2018 2018, 7, ,7 x, x 9 9of of 17 17 Actuators 2018, 7, x 9 of 17

(a()a ) (b(b)()(c)c ) (a) (b)(c) FigureFigure 10. 10. Photographs Photographs of of stator stator used used in in the the prototype prototype MDOF-SUSM. MDOF-SUSM. (a ()a Outside) Outside view view and and (b (b) Inside) Inside FigureFigure 10. 10. PhotographsPhotographs of of stator stator used used in in the the prototype prototype MDOF-SUSM. MDOF-SUSM. ( (aa)) Outside Outside view view and and ( (bb)) Inside Inside view.view. ( c()c Structure) Structure of of embedded embedded MPA MPA secured secured to to the the stator stator using using metal metal wedges. wedges. view.view. ( (cc)) Structure Structure of of embedded embedded MPA secured to the statorstator usingusing metalmetal wedges.wedges.

(a()a ) (b(b) ) (a) (b) FigureFigure 11. 11. Dimensional Dimensional drawings drawings of of stators stators designed designed for for used used in in the the MDOF-SUSM. MDOF-SUSM. (a ()a Prototype) Prototype and and FigureFigure 11. 11. DimensionalDimensional drawings drawings of of stators stators designed designed for for used used in in the the MDOF-SUSM. MDOF-SUSM. ( (aa)) Prototype Prototype and and (b(b) )φ φ2020 mm mm type. type. ((bb)) φφ2020 mm mm type. type. 4.2.4.2. Admittance Admittance Characteristics Characteristics 4.2.4.2. Admittance Admittance Characteristics Characteristics FigureFigure 12 12 shows shows the the admittance admittance loops loops for for each each vibration vibration mode mode of of the the prototype prototype stator, stator, as as FigureFigure 1212 showsshows the the admittance admittance loops loops for eachfor each vibration vibration mode mode of the prototypeof the prototype stator, as stator, measured as measuredmeasured by by an an impedance impedance analyzer. analyzer. The The resonance resonance frequencies frequencies of of each each vibration vibration mode mode were were close close measuredby an impedance by an impedance analyzer. analyzer. The resonance The resonance frequencies frequencies of each of vibration each vibration mode weremode close were toclose the toto the the results results from from FEA FEA simulation. simulation. In In th the eprototype, prototype, the the dynamic dynamic admittances admittances for for B B2121-mode,-mode, toresults the results from FEA from simulation. FEA simulation. In the prototype, In the prototype, the dynamic the admittances dynamic foradmittances B21-mode, for R1 -mode,B21-mode, and RR1-mode,1-mode, and and ((1,1))-mode ((1,1))-mode were were 1.08 1.08 S, S, 0.52 0.52 S, S, and and 1.48 1.48 S, S, respectively. respectively. These These values values are are very very large, large, R((1,1))-mode1-mode, and were ((1,1))-mode 1.08 S, 0.52 were S, and 1.08 1.48 S, S,0.52 respectively. S, and 1.48 These S, respectively. values are veryThese large, values and are a large very current large, andand a alarge large current current flow flow was was expected. expected. In In addition addition, ,the the resonance resonance quality quality factors factors were were obtained obtained as as andﬂow a waslarge expected. current Inflow addition, was expected. the resonance In addition quality, the factors resonance were obtainedquality factors as 426 were for B21 obtained-mode,504 as 426426 for for B B2121-mode,-mode, 504 504 for for R R1-mode,1-mode, and and 301 301 for for ((1,1))-mode. ((1,1))-mode. This This confirmed confirmed that that the the prototype prototype stator stator 426for Rfor1-mode, B21-mode, and 504 301 for for R ((1,1))-mode.1-mode, and 301 This for conﬁrmed ((1,1))-mode. that This the prototypeconfirmed stator that the had prototype good electrical stator hadhad good good electrical electrical performance performance despite despite its its large large and and somewhat somewhat complicated complicated structure. structure. hadperformance good electrical despite performance its large and despite somewhat its large complicated and somewhat structure. complicated structure.

FigureFigure 12. 12. Admittance Admittance loops loops for for each each vibration vibration mode mode in in the the prototype prototype stator. stator. FigureFigure 12. 12. AdmittanceAdmittance loops loops for for each each vibration vibration mode mode in in the the prototype prototype stator. stator.

Actuators 2018, 7, 8 10 of 17 Actuators 2018, 7, x 10 of 17

4.3. Vibration Vibration Displacement Displacement Figure 13 shows the the vibration vibration displacements displacements on on th thee surface surface of of the the prototype prototype stator, stator, as as measured measured by aa laserlaser Doppler Doppler vibrometer vibrometer (Ono (Ono Sokki, Sokki, LV-1800). LV-1800). The measurement The measurement positions werepositions the normalizedwere the normalizedposition, which position, was deﬁnedwhich was in thedefined inserted in the ﬁgure inserted of Figure figure 13 ofa, Figure on the 13a, upper on the surface upper of surface the stator of thein B stator21-mode in B and21-mode the outer and the surface outer of surface the stator of the in stator R1-mode in R and1-mode ((1,1))-mode. and ((1,1))-mode. The excitations The excitations of each ofvibration each vibration mode met mode the designmet the objectives. design ob Atjectives. an applied At an voltage applied of8 voltage Vpp, a vibration of 8 Vpp, amplitude a vibration of µ amplitude7.27 m was of obtained7.27 μm was in B 21obtained-mode near in B21 the-mode point near of contact the point between of contact the rotor between and stator.the rotor For and reference, stator. Forthis reference, value was this about value 48.5 was times about larger 48.5 than time thes larger vibration than amplitude,the vibration 0.15 amplitude,µm, of the 0.15φ20 μm, mm of type the φ [2920]. mmMoreover, type [29]. the maximumMoreover, vibrationthe maximum amplitudes vibration of Ramplitudes1-mode and of ((1,1))-mode R1-mode and were ((1,1))-mode about 27 timeswere aboutand about 27 times 28 times and largerabout than28 times those larger of the thanφ20 those mm type, of the respectively. φ20 mm type, Hence, respectively. the embedded Hence, MPAs the embeddedsucceeded inMPAs generating succeeded strong in generating excitations. strong excitations.

(a)(b)(c)

Figure 13. Vibration displacement measured measured on on the prot prototypeotype stator surface during each vibration mode. (a) B21-mode; (b) R1-mode; and (c) ((1,1))-mode. mode. (a)B21-mode; (b)R1-mode; and (c) ((1,1))-mode.

4.4. Maximum Maximum Torque Torque The prototype sandwich-type MDOF-SUSM is shown in Figure 14. Table 3 lists the resonance The prototype sandwich-type MDOF-SUSM is shown in Figure 14. Table3 lists the resonance frequencies and input admittances of both stators assembled with their support rings, as measured frequencies and input admittances of both stators assembled with their support rings, as measured by an impedance analyzer. The difference in the resonance frequencies of the two stators was by an impedance analyzer. The difference in the resonance frequencies of the two stators was approximately 60 Hz. The measured resonance frequencies agreed very well with the FEA simulation approximately 60 Hz. The measured resonance frequencies agreed very well with the FEA simulation results. Moreover, because both stators had similar input admittances, both could be excited by the results. Moreover, because both stators had similar input admittances, both could be excited by the same drive frequency and applied voltage for the same level of torque generation. In the same drive frequency and applied voltage for the same level of torque generation. In the measurement measurement of the vibration amplitude at the evaluation spots shown in Figure 8a, the SDs of 0.077 of the vibration amplitude at the evaluation spots shown in Figure8a, the SDs of 0.077 and 0.046 were and 0.046 were obtained on the stator with the designed support ring and without it, respectively. obtained on the stator with the designed support ring and without it, respectively. The inﬂuence of The influence of the support ring in the measurement was larger than that in the simulation, however, the support ring in the measurement was larger than that in the simulation, however, its SD was still its SD was still suppressed lower. Figure 15 shows the measured maximum torque and the input suppressed lower. Figure 15 shows the measured maximum torque and the input power for each axis power for each axis rotation with respect to the voltage applied to the prototype MDOF-SUSM. The rotation with respect to the voltage applied to the prototype MDOF-SUSM. The maximum torque maximum torque was measured by a force gauge and an arm attached to the spherical rotor, and the was measured by a force gauge and an arm attached to the spherical rotor, and the input power was input power was measured by a high-frequency power meter. The common drive frequency of the measured by a high-frequency power meter. The common drive frequency of the upper and lower upper and lower stators was 22.0 kHz when the rotor rotated around the X(Y)-axis and 24.95 kHz stators was 22.0 kHz when the rotor rotated around the X(Y)-axis and 24.95 kHz when the rotor rotated when the rotor rotated around the Z-axis. The preload between the two stators was adjusted using around the Z-axis. The preload between the two stators was adjusted using the spring-tensioned the spring-tensioned screws that attach the support rings to each other. We confirmed that torque screws that attach the support rings to each other. We conﬁrmed that torque could be increased using could be increased using the 3-point preload adjustment. the 3-point preload adjustment. At the preload of 20.58 N, the maximum torque of rotation around X(Y)-axis had the peak value, At the preload of 20.58 N, the maximum torque of rotation around X(Y)-axis had the peak value, but that around Z-axis had no peak and it was not saturated until the applied voltage of 35 Vpp. but that around Z-axis had no peak and it was not saturated until the applied voltage of 35 Vpp. Maximum torques at applied voltages of 40 Vpp and 45 Vpp were measured to search the value of the Maximum torques at applied voltages of 40 Vpp and 45 Vpp were measured to search the value of largest maximum torque. However, those continued to increase. At those applied voltages, the value the largest maximum torque. However, those continued to increase. At those applied voltages, the of electric current exceeded the current measuring range of the power meter used in experiment, so value of electric current exceeded the current measuring range of the power meter used in experiment, that data of input power was not provided. Large input power was necessary to generate large 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

Actuators 2018, 7, 8 11 of 17

Actuators 2018, 7, x 11 of 17 maximum torque. Most of the input power was consumed as heat loss. A temperature rise of MPA ◦ was thethe mostmost intense, intense, and and the the temperature temperature at theat surfacethe surface of MPA of MPA rose uprose to aroundup to around 60 C at 60°C the applied at the voltageapplied ofvoltage 30 Vpp ofwith 30 V offsetpp with of offset 15 V andof 15 input V and power input of power around of 160around W. 160 W.

Actuators 2018, 7, x 11 of 17 was the most intense, and the temperature at the surface of MPA rose up to around 60°C at the applied voltage of 30 Vpp with offset of 15 V and input power of around 160 W.

Figure 14. Photograph of assembled prototyp prototypee of the sandwich-type MDOF-SUSM.

Table 3. Basic characteristics of stators with support ring attached. fr = 22.0 kHz , VB21 = 30 Vpp fr = 24.95 kHz 2 120 3 180 ● Basic Characteristics of Stator R1-ModeT preload 20.58 B21 N-Mode ((1,1))-Mode 2.5 ○ T preload 11.76 N 150 1.5 Resonance frequency (kHz)90 22.15 21.88 24.98 Upper stator ▲ P preload 20.58 N (W) (W) Admittance (S)N·m) 2 0.45△ 1.38 2.17 120 (N·m) P

( preload 11.76 N P P T T Resonance frequency (kHz) 22.09Z 21.87 24.94 1 LowerFigure stator 14. Photograph of assembled60 prototype 1.5of the sandwich-type MDOF-SUSM. 90 Admittance (S) 0.44Y 1.25 1.86 X ● T preload 20.58 N 1 60 Input Power ○ T Input Power Max TorqueMax 0.5 Z preload 11.76 N 30 TorqueMax fr = 22.0 kHz , VB21 = 30 ▲Vpp fr = 24.95 kHz 2 Y P preload 20.58 N 120 0.53 30180 X △ P preload 11.76 N ● T 0 0 0 preload 20.58 N 0 2.5 ○ T preload 11.76 N 150 1.5 0 1020304090 0 1020304050 ▲ P preload 20.58 N Applied Voltage V (V ) Applied Voltage V (V ) (W) ((1,1)) pp R1 pp (W) N·m) 2 △ 120

(N·m) P

( preload 11.76 N P P T T 1 (a) 60 1.5 Z (b) 90 Y X Figure 15. Maximum torque● Tandpreload electric 20.58 N input power with1 respect to applied voltage. (a) Rotation60 Input Power ○ T Input Power Max TorqueMax 0.5around X(Y)-axis andZ (b) Rotationpreload around 11.76 N Z-axis.30 TorqueMax Y ▲ P preload 20.58 N 0.5 30 X △ P Table 3. Basic preloadcharacteristics 11.76 N of stators with support ring attached. 0 0 0 0 0 10203040 0 1020304050 Basic Characteristics of Stator R1-Mode B21-Mode ((1,1))-Mode Applied Voltage VR1 (Vpp) Applied Voltage V((1,1)) (Vpp) Resonance frequency (kHz) 22.15 21.88 24.98 Upper stator (a) Admittance (S) 0.45 1.38(b ) 2.17 Resonance frequency (kHz) 22.09 21.87 24.94 LowerFigure stator 15.15. Maximum torque and electric input powerpower withwith respectrespect toto appliedapplied voltage.voltage. (a) RotationRotation Admittance (S) 0.44 1.25 1.86 around X(Y)-axis andand ((bb)) RotationRotation aroundaround Z-axis.Z-axis.

Table 4 comparesTable the maximum3. Basic characteristics torque and of torque stators pewithr unit support weight ring of attached. the stators of the prototype Table4 compares the maximum torque and torque per unit weight of the stators of the prototype MDOF-SUSM and the φ20 mm type [29]. The prototype MDOF-SUSM achieved an obvious increase MDOF-SUSMBasic and Characteristics the φ20 mm type of [Stator29]. The prototype RMDOF-SUSM1-Mode B achieved21-Mode an obvious((1,1))-Mode increase in in torque. The maximum torques of rotation around the X(Y)-axis and Z-axis were obtained as torque. The maximumResonance torques of frequency rotation around (kHz) the X(Y)-axis 22.15 and Z-axis 21.88 were obtained 24.98 as 1.48 N·m 1.48Upper N∙m andstator 2.05 N∙m, respectively. The torque per unit weight of stator was about 1.24 times the and 2.05 N·m, respectively. TheAdmittance torque per (S) unit weight of stator0.45 was about 1.38 1.24 times the 2.17value of the value of the φ20 mm type for X(Y)-axis rotation and about 1.18 times that of the φ20 mm type for φ20 mm type for X(Y)-axisResonance rotation frequency and about (kHz) 1.18 times 22.09that of the φ20 21.87 mm type for Z-axis 24.94 rotation. Z-axisLower rotation. stator Friction material was not used for contacting surfaces, so that an intense abrasion Friction material was not usedAdmittance for contacting (S) surfaces, so that 0.44 an intense abrasion 1.25 occurred 1.86 for friction occurred for friction between the same metal of stainless steel. However, the maximum torque was between the same metal of stainless steel. However, the maximum torque was hardly changed during hardly changed during torque examinations. torqueTable examinations. 4 compares the maximum torque and torque per unit weight of the stators of the prototype

MDOF-SUSM and the φ20 mm type [29]. The prototype MDOF-SUSM achieved an obvious increase in torque. The maximum torques of rotation around the X(Y)-axis and Z-axis were obtained as 1.48 N∙m and 2.05 N∙m, respectively. The torque per unit weight of stator was about 1.24 times the value of the φ20 mm type for X(Y)-axis rotation and about 1.18 times that of the φ20 mm type for

Z-axis rotation. Friction material was not used for contacting surfaces, so that an intense abrasion occurred for friction between the same metal of stainless steel. However, the maximum torque was hardly changed during torque examinations.

Actuators 2018, 7, 8 12 of 17

Actuators 2018, 7, x 12 of 17 Table 4. Comparison of torque performance between prototype and φ20 mm type. Table 4. Comparison of torque performance between prototype and φ20 mm type. Performance Characteristic Rotation Prototype φ20 mm Type [29] Performance Characteristic Rotation Prototype φ20 mm Type [29] Around X(Y)-axis 1.48 at 30 0.058 at 80 Max torque (N·m at Vpp) Around X(Y)-axis 1.48 at 30 0.058 at 80 Max torque (N∙m at Vpp) Around Z-axis 2.05 at 40 0.084 at 140 Around Z-axis 2.05 at 40 0.084 at 140 Around X(Y)-axis 0.87 0.70 Torque/weight (N·m/kg) Around X(Y)-axis 0.87 0.70 Torque/weight (N∙m/kg) Around Z-axis 1.20 1.02 Around Z-axis 1.20 1.02

Figure 16 compares the maximum torques and to torquesrques per unit weight for various MDOF-SUSMs previously reported [[15,16,20,29].15,16,20,29]. The maximum torq torqueue obtained by the new design design was was much much larger larger thanthan those those obtained obtained by other other motors. motors. The The targeted targeted maximum maximum torque of 10 N N∙·m,m, suitable suitable for for high-load high-load applications like shoulder joints, was not achieved, but the torque per unit weight increased and the maximum torque was about 5 to 7 7 times times greater greater as as compared compared to to the the other other MDOF-SUSMs MDOF-SUSMs having high maximum torques, torques, as as shown in Figure 16.16. The mo mostst of MDOF-SUSMs for the comparison have not used a friction friction material. material. Especially, Especially, φ20 mm type which was previous ty typepe with the similar similar structure structure did not use a friction material. If If a a friction friction mate materialrial was was used, used, the the maximum maximum torque torque would would decrease. decrease. The friction condition was severe, but was set as a comparison condition.

■：Commercial product (ref. 16) 2 ○：X Prototype △：X φ20 mm type (ref. 29) ◆：ref. 20 φ 1.5 ●：Z Prototype ▲：Z 20 mm type (ref. 29) ◇：ref. 15 m/kg) ·

0.5 Max torqueperMax unit weight (N 0 0 0.5 1 1.5 2 2.5 Max torque (N·m)

Figure 16. Comparison of maximum torque and torque per unit weight for various MDOF-SUSMs. Figure 16. Comparison of maximum torque and torque per unit weight for various MDOF-SUSMs.

4.5. Current Current and Power Factor Figure 17a,b17a,b show the measured effective values for current and power factor corresponding to thethe applied voltage voltage shown shown in in Figure Figure 15,15, respectively respectively.. The The prototype needed needed to to be be driven with with large large inputinput power power and and high high current, current, as as shown shown in in Figures Figures 15 15 and and 17, 17 because, because of the of thelarge large capacitance capacitance of the of MPAs,the MPAs, which which made made the power the power factor factor low (Figure low (Figure 15). As 15 ).a result, As a result, the maximum the maximum output output current current of the amplifiersof the ampliﬁers (BP4610, (BP4610, NF Co., NF Co.,Yokohama, Yokohama, Japan) Japan) was was reached reached before before the the full full potential potential torque performance of the prototype motor was attained.attained. Hence, Hence, the the measured maximum torques torques were limitedlimited by by the the ability ability of of the the amplifiers ampliﬁers to to supply supply current. current. If Ifthe the driving driving current current supply supply were were larger, larger, a largera larger maximum maximum torque torque and and torque torque per per unit unit weight weight could could be be obtained. obtained. Therefore, Therefore, future future studies studies will will explore the improvement of the power factor for the driving circuit.

ActuatorsActuators 201820182018,, , 777,, , xx 8 1313 ofof 1717

fr = 22.0 kHz, V = 30 V 25 fr = 22.0 kHz, VB21B21 = 30 Vpppp 1 frfr== 24.9524.95 kHz kHz 25 1 2525 11

20 0.8 IIpreload 20.58 N 20 0.8 2020 preload 20.58 N 0.80.8 θ θ θ ) θ ) ) Ipreload 11.76 N ) Ipreload 11.76 N rms cos rms rms cos cos rms 15 0.6 cos

(A 15 0.6 15 0.6

I (A (A preload 20.58 N 15 0.6

I (A I preload 20.58 N I I I Ipreload 11.76 N preload 11.76 N I 10 cosθ 0.4 10 cosθpreloadpreload 20.58 20.58 N N 0.4 1010 0.40.4 Current Current Current Current Current Current Power factor

cosθ factor Power

Power factor preload 11.76 N cosθpreload 11.76 N factor Power Z 55 Z 0.20.2 5 cosθ ZZ 0.2 5 cosθpreloadpreload 20.58 20.58 N N 0.2 cosθpreload 11.76 N Y cosθpreload 11.76 N Y YY X X XX 00 00 00 00 00 10203040 10203040 00 10203040 10203040 Applied voltage VR1 (Vpp) Applied voltage V((1,1)) (Vpp) Applied voltage VR1 (Vpp) Applied voltage V((1,1)) (Vpp) ((aa)) ((bb))

FigureFigure 17. 17. EffectiveEffective currentcurrent andand powerpower factor factor with with respect respect to to applied applied voltage. voltage. (( aa)) Rotation Rotation aroundaround X(Y)-axisX(Y)-axis and and ( (bb)) Rotation Rotation around around Z-axis. Z-axis.

4.6 Transient Response and Load Characteristics 4.64.6. Transient Transient Response Response and and Load Load Characteristics Characteristics Figure 18a–d shows the transient response of the X-axis and Z-axis rotation speeds for preloads Figure 18a–d18a–d shows the transient response of the X-axis and Z-axis rotation speeds for preloads of 11.76 N and 20.58 N, as measured with a high-speed digital camera (1200 fps). The rise time was of 11.76 11.76 N N and and 20.58 20.58 N, N, as as measured measured with with a high-speed a high-speed digital digital camera camera (1200 (1200 fps). fps). The Therise time rise timewas calculated using the rise curve of the rotation speed estimated by fitting each measured point. The wascalculated calculated using using the rise the curve rise curve of the of rotation the rotation speed speed estimated estimated by fitting by fitting each eachmeasured measured point. point. The estimated rise times were about 4 ms to 8 ms. The load characteristics were simulated by the moment estimatedThe estimated rise times rise times were wereabout about4 ms to 4 8 ms ms. to The 8 ms. load The characteristics load characteristics were simulated were simulated by the moment by the of inertia of the rotor, the rise curve, and the calculated rise time [32]. Figure 19a–d shows the ofmoment inertia of of inertia the rotor, of the the rotor, rise the curve, rise curve,and the and calculated the calculated rise time rise time[32]. [Figure32]. Figure 19a–d 19 a–dshows shows the simulated load characteristics of X-axis and Z-axis rotations for preloads of 11.76 N and 20.58 N. The simulatedthe simulated load load characteristics characteristics of X-axis of X-axis and andZ-axis Z-axis rotations rotations for preloads for preloads of 11.76 of 11.76 N and N 20.58 and 20.58 N. The N. speed-load curves were derived from the gradient of the rise curve. The efficiency-load curves were speed-loadThe speed-load curves curves were were derived derived from fromthe gradient the gradient of the of rise the curve. rise curve. The efficiency-load The efficiency-load curves curves were estimated from the mechanical output and the electrical input power shown in Figure 15. The wereestimated estimated from fromthe mechanical the mechanical output output and and the theelectrical electrical input input power power shown shown in in Figure Figure 15.15. The maximum torque almost agreed with the measured value shown in Figure 13. Maximum efficiencies maximum torque almost agreed wi withth the measured value shown in Figure 13.13. Maximum efficiencies efficiencies of about 0.2% to 1.4% were obtained. The causes of the low efficiency were likely the high current of about 0.2%0.2% toto 1.4%1.4% were were obtained. obtained. The The causes causes of of the the low low efficiency efficiency were were likely likely the highthe high current current flow flow and low power factor, as well as friction loss between the rotor and stator. Moreover, the MPAs, flowand lowandpower low power factor, factor, as well as aswell friction as friction loss between loss between the rotor the androtor stator. and stator. Moreover, Moreover, the MPAs, the MPAs, which which were made of hard piezoelectric material provided with high mechanical quality factor, had werewhich made were of made hard of piezoelectric hard piezoelectric material material provided provided with high with mechanical high mechanical quality factor, quality had factor, large heathad large heat loss when driven at high frequency. Therefore, the first step for improving the efficiency largeloss when heat loss driven when at highdriven frequency. at high frequency. Therefore, Th theerefore, first step the forfirst improving step for improving the efficiency the efficiency will be to will be to provide a power factor improvement circuit. willprovide be to a provide power factor a power improvement factor improvement circuit. circuit.

frfr== 22.022.0 kHzkHz ,, VVB21 == 3030 V Vpp ,, PreloadPreload 20.5820.58 N N fr = 24.95 kHz , Preload 20.58 N 4040 B21 pp 22 80 fr = 24.95 kHz , Preload 20.58 N 2 Applied voltage VR1 = 25 Vpp 80 2 Applied voltage VR1 = 25 Vpp Applied voltage V((1,1)) = 25 Vpp Applied voltage V((1,1)) = 25 Vpp STST ST Z ST 30 Z 1.5 30 Y 1.5 6060 1.51.5

(rpm) Y Z (rpm) (rpm) X Z (rpm)

S X S S Y S

(N·m) Y (N·m) (N·m) X (N·m)

T X T

20 1 T 20 1 4040 11 T Torque Torque Torque 10 0.5 20 0.5 Torque Rotation speed 10 0.5 Rotation speed 20 0.5 Rotation speed Rotation speed

00 00 00 00 00 5 5 10 10 15 15 20 20 25 25 00 5 5 10 10 15 15 20 20 25 25 TimeTime (ms)(ms) TimeTime (ms)(ms) ((aa)) ((bb)) Figure 18. Transient response of rotation speed and torque with preload of 20.58 N. (a) Rotation Figure 18.18. TransientTransient response response of of rotation rotation speed speed and and torque torque with with preload preload of 20.58 of N.20.58 (a) RotationN. (a) Rotation around around X(Y)-axis; and (b) Rotation around Z-axis. aroundX(Y)-axis; X(Y)-axis; and (b) Rotationand (b) Rotation around Z-axis.around Z-axis.

Actuators 2018, 7, 8 14 of 17 Actuators 2018, 7, x 14 of 17

fr = 22.0 kHz , V = 30 V , Preload 20.58 N fr = 24.95 kHz , Preload 20.58 N 40 B21 pp 2 80 2 Applied voltage V =25 V Applied voltage VR1 = 25 Vpp ((1,1)) pp S η S η 60 1.5 30 1.5 Z Z (rpm) (rpm)

Y (%) (%) S

S Y

X η X η 20 1 40 1 Efficiency Efficiency Efficiency 10 0.5 20 0.5 Rotation speed Rotation speed

0 0 0 0 00.511.5 0 0.5 1 1.5 Torque (N·m) Torque (N·m) (a) (b)

FigureFigure 19.19. LoadLoad characteristics characteristics with with preload preload of 20.58 of N.20.58 (a) RotationN. (a) Rotation around X(Y)-axis, around andX(Y)-axis, (b) Rotation and (aroundb) Rotation Z-axis. around Z-axis.

5. Conclusions 5. Conclusions A high-torque sandwich-type MDOF-SUSM was designed for high-load applications. The A high-torque sandwich-type MDOF-SUSM was designed for high-load applications. The design design features a new annular stator that can strongly excite three different vibration modes using features a new annular stator that can strongly excite three different vibration modes using MPAs. MPAs. The operating principle and sandwich structure of the prototype MDOF-SUSM are similar to The operating principle and sandwich structure of the prototype MDOF-SUSM are similar to those those of a previously reported φ20 mm type. However, the new prototype not only is larger but also of a previously reported φ20 mm type. However, the new prototype not only is larger but also has a high-power excitation method and stable support mechanism. Moreover, the rigidity of the has a high-power excitation method and stable support mechanism. Moreover, the rigidity of the friction driving portion of the stator was enhanced to more effectively transmit the excited vibration friction driving portion of the stator was enhanced to more effectively transmit the excited vibration force to the friction-driven surface. As a result, the prototype had very high torque compared with force to the friction-driven surface. As a result, the prototype had very high torque compared with other MDOF-SUSMs, confirming the effectiveness of the excitation method and structural changes. other MDOF-SUSMs, confirming the effectiveness of the excitation method and structural changes. The torque performance of the prototype MDOF-SUSM was limited by the output current of the The torque performance of the prototype MDOF-SUSM was limited by the output current of the amplifiers used during the performance examination. The load characteristics were calculated by amplifiers used during the performance examination. The load characteristics were calculated by measuring the transient response of the rotor rotation speed. The efficiency was low due to heat loss measuring the transient response of the rotor rotation speed. The efficiency was low due to heat loss in in the MPAs and a low power factor. If the electric power factor of stators can be improved to reduce the MPAs and a low power factor. If the electric power factor of stators can be improved to reduce the the current required to drive the motor, the maximum torque, torque per unit weight, and efficiency current required to drive the motor, the maximum torque, torque per unit weight, and efficiency will will likely increase. likely increase.

SupplementarySupplementary Materials: TheThe following following are are available online at www.mdpi.com/xxx/s1www.mdpi.com/2076-0825/7/1/8/s1 . Acknowledgments: ThisThis work was partially supported by JSPS Kakenhi Grant Number 26289023. Author Contributions: Koki Oikawa designed the structure, pe performedrformed the fundamental experiments, and and wrote a part of the paper; Ai Mizuno conceived to improve the performance and and performed performed the the experiments; experiments; ManabuManabu Aoyagi Aoyagi directed directed the the whole whole of of this this study; study; Hidek Hidekazuazu Kajiwara Kajiwara analyzed analyzed the the performance; performance; Hideki Hideki Tamura Tamura and Takehiro Takano contributed to the creation of the basic design concept and analyzed data; Ai Mizuno and andManabu Takehiro Aoyagi Takano wrote contributed the final version to the ofcreation the paper. of the basic design concept and analyzed data; Ai Mizuno and Manabu Aoyagi wrote the final version of the paper. Conflicts of Interest: The authors declare no conflict of interest. The founding sponsors had no role in the design Conflictsof the study; of Interest: in the collection, The authors analyses, declare orno interpretationconflict of interest. of data; The infounding the writing sponsors of the had manuscript, no role in the and design in the ofdecision the study; to publish in the thecollection, results. analyses, or interpretation of data; in the writing of the manuscript, and in the decision to publish the results. Appendix A. Comparison of Excitation Methods by MPAs and PZT Plate AppendixA performance A. Comparison comparison of Excitation was madeMethods for by two MPAs excitation and PZT methods: Plate (1) a PZT plate with polarizationA performance in the thicknesscomparison direction was made bonded for two to the excitation surface ofmethods: a steel (1) bar a andPZT (2)plate an MPAwith 3 polarization(6 × 6 × 5 mm in the) made thickness of hard direction piezoelectric bonded ceramics to the surface embedded of a steel into bar a and similar (2) an bar. MPA Both (6 piezoelectric× 6 × 5 mm3) madedevices of were hard manufactured piezoelectric products.ceramics Theirembedded physical into and a similar piezoelectric bar. Both properties piezoelectric are shown devices in Table were A1 . manufacturedThe PZT plate andproducts. MPA vibratorsTheir physical are shown and piezoele in Figurectric A1 a,b,properties respectively. are shown The PZTin Table plate A1. was The bonded PZT plateat the and center MPA of thevibrators bar. The are MPA shown was in embedded Figure A1a,b, into arespectively. rectangular holeThe PZT formed plate on was the bar,bonded and at it wasthe 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 (B1-mode) and the first longitudinal mode (L1-mode).

Actuators 2018, 7, 8 15 of 17 secured in the hole with metal wedges, as shown in Figure 10c. The vibrator could independently exciteActuators the 2018 ﬁrst, 7, bendingx mode (B1-mode) and the ﬁrst longitudinal mode (L1-mode). 15 of 17

(a) (b)

FigureFigure A1.A1. PhotographsPhotographs ofof rectangularrectangular barbar vibrators.vibrators. ((aa)) BondedBonded PZTPZT plateplate andand ((bb)) EmbeddedEmbedded MPA.MPA.

TableTable A1.A1. PhysicalPhysical andand piezoelectricpiezoelectric propertiesproperties ofof PZTPZT andand MPA.MPA. Item Unit PZT MPA Item Unit PZT MPA Dielectric properties ε33T/ε0 1400 1460 T CurieDielectric temperature properties ε33 /ε0 °C 1400315 1460 310 ◦ DielectricCurie temperatureloss tanδ % C 315 0.3 310 0.4 Dielectric loss tanδ % 0.3 0.4 d31 ×10−12− 12m/V −132 −120 Piezoelectric strain constant d31 ×10 m/V −132 −120 Piezoelectric strain constant −12−12 d33 d33 ×10×10 m/Vm/V 296 296 315 315 DensityDensity ρ ρ ×10×103 3kg/mkg/m3 3 7.767.76 7.6 7.6 Poison’sPoison’s ratio ratio 0.310.31 0.31 0.31 10 Young’s modulus Y11 ×10 Pa 7.6 8.2 Young’s modulus Y11 ×1010 Pa 7.6 8.2 Mechanical quality factor Qm 1800 2000 Mechanical quality factor Qm 1800 2000

WhenWhen anan ACAC voltage of 5 V pppp waswas applied applied at at the the resonance resonance freq frequency,uency, measured measured force force factors factors of ofboth both vibration vibration modes modes of ofeach each vibrator vibrator were were obtained obtained (Table (Table A2). A2 ).The The force force factor factor is isan an indicator indicator of ofthe the conversion conversion efficiency efﬁciency from from electrical electrical energy energy to tokinetic kinetic energy. energy. The The force force factor factor was was calculated calculated by bymotional motional current current divided divided by byvibration vibration velocity velocity at the at theresonance resonance frequency. frequency. TheThe motional motional current current was wascalculated calculated by observing by observing the theinput input voltage voltage and and cu currentrrent to to the the piezoelectric piezoelectric element usingusing anan oscilloscope.oscilloscope. The vibration velocityvelocity was measured on thethe surfacesurface ofof thethe barbar usingusing aa laserlaser DopplerDoppler vibrometer.vibrometer. TheThe measurementmeasurement pointpoint waswas setset wherewhere thethe maximummaximum vibrationvibration velocityvelocity waswas obtained,obtained, speciﬁcallyspecifically thethe upperupper surfacesurface endend ofof thethe barbar inin B1-modeB1-mode andand thethe sideside endend ofof thethe barbar inin L1-mode.L1-mode. TheThe forceforce factorfactor ofof B1-modeB1-mode forfor thethe embeddedembedded MPAMPA waswas aboutabout 3.73.7 timestimes largerlarger thanthan thatthat forfor thethe bondedbonded PZTPZT plate.plate. InIn addition,addition, thethe forceforce factorfactor ofof L1-modeL1-mode forfor thethe embeddedembedded MPAMPA waswas aboutabout 5.25.2 timestimes largerlarger thanthan thatthat ofof thethe bondedbonded PZTPZT plate.plate. AsAs aa result,result, thethe excitationexcitation ofof thethe vibratorvibrator byby anan embeddedembedded MPAMPA generatedgenerated aa largerlarger forceforce thanthan couldcould bebe obtainedobtained withwith thethe PZTPZT plate.plate. ThisThis isis becausebecause thethe MPAMPA utilizesutilizes thethe piezoelectricpiezoelectric longitudinallongitudinal effect,effect, which which has has a a larger larger force force factor. factor.

TableTable A2.A2. ResultsResults ofof forceforce factorfactor measurementmeasurement ofofPZT PZTand andMPA MPA type type vibrators. vibrators.

ResonanceResonance VibrationVibration Velocity Velocity MotionalMotional CurrentCurrent ForceForce Factor Factor ModeMode FrequencyFrequency (kHz) (kHz) (mm/s(mm/s rms) rms) (mA rms)rms) (N/V)(N/V) PZTPZT MPA MPA PZT PZT MPA MPA PZT PZT MPA MPA PZT PZT MPAMPA B1-mode 8.98 8.10 21.2 290 2.84 144 0.134 0.497 B1-mode 8.98 8.10 21.2 290 2.84 144 0.134 0.497 L1-modeL1-mode 29.7 29.7 27.7 27.7 6.85 6.85 492 492 2.31 2.31 863 863 0.3370.337 1.751.75

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