机械专业毕业设计外文翻译外文文献

A Multi-DOF Ultrasonic Motor Using In-plane Deformation of PZT Elements and Its Driving CircuitMinghui Zhang, Mantian Li and Lining SunRobotics InstituteHarbin Institute of TechnologyHarbin, Heilongjiang Province, Chinapeterzmh@Abstract - Due to the increasing number of DOFs of systems and the reducing the volume and weight of the devices, multi-degrees-of-freedom (DOF) actuators have become more useful in the field of robotics. And the general features of ultrasonic motors are also suitable for constructing a direct-drive multi-DOF actuator. So, a new multi-DOF ultrasonic motor using in-p lane deformation of PZT elements is introduced in this p ap er. Then its working p rincip le and requirement for driving circuit are analyzed. At last, a driving circuit is p rop osed accordingly which generates sinusoidal actuating signals with a FPGA part (a Direct Digital Synthesizer (DDS) array is synthesized in it) and amplifies them with high voltage power operational amplifiers. It is characteristic of indep endent adjustment of amp litude and frequency for each outp ut signal and indep endent adjustment p hase between any two of outp ut signals. The circuit meets the requirement of the motor.Index Terms - ultrasonic motor; multi-degree of freedom; in-plane deformation; driving circuitI.I NTRODUCTIONMulti-DOF ultrasonic motor is a new kind of multi-DOF actuator. With it or other multi-D OF actuators, dexterous multi-DOF can be generated easily, and at the same time the volume and weight of the devices are also reduced greatly. And comparing to other multi-D OF actuators, multi-D OF ultrasonic motors can be easily miniaturized. What’s more, they also have many other excellent characteristics such as high torque at low speed, high stationary limiting torque, absence of electromagnetic radiation, less noise, and simplicity of design. Some of the characteristics assure capability of ultrasonic motors as multi-DOF actuators, usable as direct-drive actuators. Especially, a multi-D OF ultrasonic motor with compact stator and simple driving circuit is very suitable for robot eye control, laser handling, and other applications [1].Therefore, many multi-D OF actuators based on the principle of ultrasonic motors have been proposed in the past. Toyama developed a spherical ultrasonic motor in which three or four ring-shaped vibrators are arranged around a spherical rotor [2]. Takfumi designed an ultrasonic actuator with multi-degree of freedom using bending and longitudinal vibration of a single stator, which has been applied in an auditory tele-existence robot [3, 4]. Takemura proposed a bar-shaped ultrasonic motor capable of generating three-DOF motion and a plate type multi-D OF ultrasonic motor whose rotor was larger in the size of volume [5, 6]. Otokawa constructed an arrayed-type multi-DOF ultrasonic motor based on a selection of reciprocating vibration modes [7]. Almost all these multi-D OF ultrasonic motors generate vibration by expanding and contracting with the coupling commonly associated with the piezoelectric d33 (strain) or e33, (stress) coefficients.In order to obtain the optimum working character, a driving circuit for the ultrasonic motor should be developed. And to study the multi-D OF ultrasonic motor directly and easily, it is better that the driving frequency and voltage of the output signal must be adjustable, and the phase between the outputs should also be controllable [8, 9]. Takemura have proposed a self-oscillation driving circuit for the plate type multi-D OF ultrasonic motor they developed. Experimental results confirm the rotor can be rotated using the self-oscillation driving circuit and the maximum rotational speed of the rotor is about 70 rpm [6]. And King Long has also designed three kinds of driving circuits for a three-degree freedom of spherical piezoelectric ultrasonic motor [10].In this paper, a new multi-D OF ultrasonic motor is introduced, which generates vibration with the coupling associated with the piezoelectric d31 (strain) or e31, (stress) coefficients and the piezoelectric d15 (strain) or e15, (stress) coefficients. Then, a special driving circuit based on DDS is developed. The sinusoidal driving signals are generated from the DDS array synthesized a FPGA part and amplified by high voltage power operational amplifiers. The frequency and amplitude of the four output signals from the driving circuit are all adjustable independently; and the phase between any of them can also be adjusted.II.S TRUCTURE A ND P RINCIPLEA. Structure of the statorA square beam has two bending modes whose resonance frequencies are equal to each other. And with calculated dimensions, it may have one longitudinal mode which is orthogonal to them and its resonance frequency also corresponds to them. The second bending mode frequencies in any direction for circular cylinders are equal to each other and the first longitudinal mode frequency can be very close to them. The stator of the motor presented in this study combines the circular and square cross sections.The outside surface of a hollow metal cylinder is flattened on four sides at 90 degrees to each other and four rectangular piezoelectric plates are bonded onto these four flattenedProceedings of the 2007 IEEE International Conference on Mechatronics and Automation August 5 - 8, 2007, Harbin, Chinasurfaces [Fig. 1]. The PZT plate has five electrodes; four are deposited on the top surface while the fifth one is deposited on the bottom surface of the PZT plates. On the top of PZT plates, two electrodes are connected across corners as one input, and the inputs on the symmetric positions of the stator are defined as one input electrode group. And the bottoms of PZT plates are electroded uniformly and they are ground. With the application of an alternating current (AC) voltage potential across the thickness of the piezoelectric plate, the plate will expand and flex due to the coupling commonly associated with the piezoelectric d31(strain) or e31, (stress) coefficients and the piezoelectric d15(strain) or e15, (stress) coefficients [11, 12]. With the configuration shown, the plate deforms in-plane and makes longitudinal and bendingvibration of the base.(a)(b)Fig.1 Structure of the stator. (a) orthographic view ; (b) top viewB. Vibration modesFig. 2 shows the driving principle of the multi-D OF ultrasonic motor. The rotor can rotate around three perpendicular axes. A longitudinal vibration and two bending vibrations of the stator are used as shown in Fig. 2. Fig. 2(a) shows the natural vibration modes of the stator that are used when the rotor rotates around the z axis. Figs. i and iii show the second bending mode of the stator in the x-z plane (mode A), and Figs. ii and iv show the second bending mode of the stator in the y-z plane (mode B). When these two natural vibration modes, A and B, are combined at a phase difference of 90°, the tip of the stator rotates around the z axis. Then, the spherical rotor in contact with the stator’s head also rotates around the z axis by frictional force. Fig. 2(b) shows the natural vibration modes used when the rotor rotates around the x axis. Figs. i and iii show the first longitudinal mode of the stator along the z axis (mode C), and Figs. ii and iv show the mode B. when an electrical excitation is imposed between electrode group ‘A’ or ‘B’ and ground, these two natural vibration modes, B and C, are combined at a phase difference of 90°, and the tip of the stator rotates around the x axis. Then, the spherical rotor also rotates around the x axis due to frictional force. Excitation of input electrode group ‘A’ and ground will cause the counterclockwise rotation by right-hand rule, while excitation of input electrode group ‘B’ and ground will cause the clockwise rotation. The rotor rotates around the y axis when the mode A and the mode C are combined in the same way as the case of Fig. 2(b). The point to notice is that the natural frequencies of these three natural vibration modes, A, B, and C, should be as close as possible. Table I shows the input phases for the PZT plates needed for excitation eachrotation.(a) (b)Fig.2 Driving principle of the multi-DOF ultrasonic motor. (a) around z axis;(b) around x axisWhen a driving voltage is applied on electrodes A1 and A2, vibration modes B and C can be excited the same time. Accordingly, the tip of the stator rotates around the x axis counterclockwise. Then, the spherical rotor in contact with the stator’s head also rotates around the x axis counterclockwise by frictional force. Similarly, the spherical rotor rotates around the x axis clockwise, when a driving voltage is applied on electrodes B1 and B2. And the excitation on electrodes C1 and C2 will cause the counterclockwise rotation of the rotorand he excitation on electrodes D 1 and D 2 will cause the clockwise rotation of the rotor, as well. The rotor will rotate around z axis counterclockwise with electrodes A1 and C1 being excited simultaneously at a phase difference of 90° and rotate around z axis clockwise with electrodes B1 and D 1 being excited simultaneously at a phase difference of 90° .C. GeometrySince the design is complicated, finite element analysis method is used to conduct modal and harmonic analysis of the ultrasonic motor, including the linearized piezoelectric material properties. In this way, a feasible design can be developed from the concept with reasonable assurance that the results of the analysis would resemble the behavior of an actual actuator. Fig. 3(a) and (b) show the calculated first longitudinal mode and the calculated second bending mode of the stator, respectively. The calculated natural frequencies ofthese modes are very close, about 57 kHz [Table I].(a) (b)Fig.3 Vibrating modes of stator. (a) second bending mode; (b) firstlongitudinal modeTABLE IN ATURAL F REQUENCIES O F T HE S TATORVibrating modeNatural frequency(KHz) First longitudinal mode along z axis (L1) 56.7 Second bending mode in the x-z plane (B2) 56.6Second bending mode in the y-z plane (B2) 56.6The basic configuration of the motor is shown in Fig. 4.The rotor is made of stainless steel. The stator of the prototypemotor consists of a hollow metal tube (brass) with an outerdiameter of 10 mm and inner diameter of 6 mm, length of 16mm, and four rectangular piezoelectric plates withdimensions, 16 mm in length, 8 mm in width, and 1 mm inthickness. The outside surface of the metal cylinder is on foursides at 90 degrees to each other. The PZT plates (PZT4,Kunshan Jingfeng Electric Corp., Ltd.), which are poled in thethickness direction, are bonded onto to the flat orthogonalsurfaces of the cylinder using a conductive epoxy [Fig.1 (b)].The stator is held on the base with four screws. And the supporting points are on the nodal plane.Fig.4 Assembly diagram of MDOF USMIII. D RIVING C IRCUITA. StructureFor driving ultrasonic motors, a generation of the desired natural vibration of the stator is one of the most important points. Considering the requirement for excitation of each rotation, we propose a driving circuit for multi-D OFultrasonic motors which can generate four independent alternating excitation signals. The amplitude and frequency of each signal can be adjusted individually; the phase betweenany two of the four excitations can be adjusted individually, aswell. Fig. 5 shows the schematic diagram of the driving circuit. The circuit includes the D SP controller, the FPGA part inwhich a D D S array are synthesized, D /A modules, low pass filters (LPF) and power amplifiers (PA). The DSP controllerreceives commands, encoder values and other feedbacks, andthen controls the digital potentiometer and the FPGA partcorrespondingly. The D SP controller communicates with theFPGA part through a dual port RAM. The frequency andphase information for each output is written in RAM by DSPcontroller and read by the FPGA part which uses it as theparameter for the D D S array. The four D D S modules in theD D S array generate the four excitation outputs respectively.Actually, the output signal of DDS module is coded sinusoidalsignal, and must be transformed to step sinusoidal wave byD/A module and smoothed by low pass filter. After amplifiedby the power amplifier, the smooth ultrasonic sinusoid waveserves as the excitation signal.Fig.5 Schematic diagram of the driving circuitB. Working principle Since the output voltage of the D /A module is proportional to its reference voltage and the amplitude of the driving circuit output is also proportional to the output voltage of the D/A module, the amplitude of the driving circuit output can be adjusted by setting the reference voltage of the D /A module. D igital potentiometers are used to modify the reference voltage. All digital potentiometers get their values from the DSP controller and update the values simultaneously with the unique chip select signal. The adjustment of the frequency of the outputs and phase between outputs is realized by D D S and described as the follows. Fig. 6 shows the schematic diagram of a DDS, where K is the frequency control word, f c is the frequency of the input clock signal, N is the digital capacity of DDS. At every rising edge of input clock, the accumulator accumulates in step length of K . The output of accumulator is added with P and its result acts as the address of the wave pattern ROM. All the information of wave is stored in the ROM. The output of ROM is turned into step wave in D /A converter [13]. After passing the low pass filter, the step wave is smoothed and all the harmonic components are removed. In the D D S system, the accumulator, the adder and the ROM in the imaginary line block are synthesized in FPGA, while others parts are individual electrical components.The frequency of the DDS output signal is: K f f N cout2where f out is the frequency of the output. The frequency is inratio of the frequency control word K , so f out can be adjusted proportionally by changing the value of K . Thus the frequency range of DDS output is from f c /2N to f c /2, when the frequency control word is in a span from ‘1’ to ‘N-1’. But in order to guarantee the output accuracy, there at least need to be four sampling points in one period. The maximum of K is N-2, that is, the highest frequency of the DDS output is f c/4.Fig.6 Schematic diagram of DDSIn the implement process of DDS, the phase control word P is added with the result of the frequency accumulator at every rising edge of the input clock. Consequently, a shift of 2ʌ•P/2N is generated in the output wave. Thus, the phases of output signals can be easily adjusted with modifying the phase control word and the resolution of phase adjustment is2ʌ/2N .C. Power amplifier In order to generate continuous output in ultrasonic range, high voltage power operational amplifiers (Apex Microtechnology Corp.) are adapted to realize power amplification. They are characteristic of high voltage, high output current output, high slew rate and low quiescent current. So they are very appropriate to drive piezoelectric elements. The high voltage power operational amplifier can be used just like ordinary operational amplifier(R F = 5 kȍ, R IN = 150 kȍ,R CL = 3.3 ȍ), as showed in Fig.7, where R CL is the current limit resistor. And considering the capacity loads and closed loop stability, the type of high voltage power operational amplifier is PA90. And the qualification of the power amplifier circuit is as follows: the closed loop gain is 30; the maximum peak-to-peak amplitude of the output is 300V; the highest frequency is 100 KHz with 2.2 nF capacityloads.Fig.7 Power amplifierIn order to demonstrate the driving circuit, a 2.2 nF capacitive load is added to the driving circuit. Actually, the capacity of the piezoelectric plates is less than 2.2 nF. Fig. 8 shows the output signal of the driving circuit measured by the DS5102C oscilloscope, a digital oscilloscope of Rigol Electric Corp.. All the figures are captured with 50V/div(y axis) and 5ȝs/div(x axis). Fig.8(a) shows that the voltage of output can be adjusted from 0 to 300V. Fig.8(b) shows that the frequency of output can be adjusted from 0 to 100 kHz. And fig.8(c) shows that the phase of two outputs also can be adjusted.(a)(b)(c)Fig.8 Output signals of the driving circuit. (a) amplitude adjustment(b)frequency adjustment (c) phase adjustmentIV. C ONCLUSIONSIn this study, the driving principle for a multi-D OF ultrasonic motor using in-plane deformation of the PZT elements is proposed. And its requirement for the driving circuit is also analyzed. Accordingly, the driving circuit based on D D S is developed which consists of the D SP controller, the FPGA part in which a D D S array are synthesized, D /A modules, low pass filters and power amplifiers. The driving circuit is characteristic of the amplitude and frequency of each output, and the phase between any two of the outputs can be adjusted continuously and independently. So it can be used in the experimental study of multi-DOF ultrasonic motors.A CKNOWLEDGMENTThis study is supported by the National Natural Science Foundation of China #50575056. Authors also would like to thank the staff of Kunshan Jingfeng Electric Corp.. for their help in manufacturing the piezoelectric ceramics.R EFERENCES[1] K. Takemura, T. 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