汽油機(jī)曲柄連桿機(jī)構(gòu)中活塞的有限元分析,汽油機(jī)曲柄連桿機(jī)構(gòu)中活塞的有限元分析,汽油機(jī),曲柄,連桿機(jī)構(gòu),活塞,有限元分析 Tieying University, Piezoelect configuration and flexibility of shape. Not only have the linear ultrasonic driving mechanisms been applied in pre- Many kinds of linear ultrasonic motors have been described in the literature. Concepts of traveling wave, standing wave, surface acoustics wave, and large strain have been investigated in the papers. Liu concluded that the proper ratio of the length to the width of a thin rectan- tor of the motor is comprised of a metal plate and eight pie- zoelectric ceramic plates. It is easy for the stator with such a construction to be clamped. The working mode is a com- posite in-plane bimode. The design concept presented in this paper is much promising for the applications in high- torch motors with smaller size. * Corresponding author. Tel./fax: +86 10 62772787. E-mail address: (C. Lu). Ultrasonics 44 (2006) e585e589 cision positioning systems, subminiature driving system, automobile, optics system, national defense and so on, but also have inspired many new conceptual applications in fields such as micro electromechanics and nanotech- nology, precision manipulators and micro robots. Linear ultrasonic driving techniques have a nice application foreground. gular piezoelectric ceramics plates should be 4.0 10. Zumeris, who is from Nanomotion Ltd., Israel has trans- ferred the technology of ceramic plate linear ultrasonic motor with bimodal in-plane vibration for commercial applications 11. A linear ultrasonic motor with double-driving feet at the same side is designed in this paper. The laminated plate sta- 1. Introduction Recently, linear ultrasonic motors have been of signif- icant research interests. Compared with ordinary electro- magnetic motors, the linear ultrasonic motors have such advantages as high torque per volume, operation at the precision level of nanometers, good control characteristics at start and stop, good ability to maintain its own position when stopped, ability to work in vacuum environment, no restriction through induction, simple type ultrasonic motors were proposed 16. Some standing wave bimodal linear ultrasonic motors with in-plane vibra- tions has been developed because of their good character- istics, such as higher force (torque) per volume, higher driving velocity and higher positioning precision, which should satisfy the increasing miniaturization demand of the motors 79. These motors use single rectangular piezoelectric ceramic plate as stators and some of them have one driving foot bonded to one end of the stators. The methods for structure design and control of the motor Study of a new type linear ultrasonic Cunyue Lu * , Tian Xie, Department of Physics, Tsinghua Available online Abstract A new type linear USM with double-driving feet has been developed. brass plate. Piezoelectric ceramics plates are polarized along the thickness angle brass plate. Double-driving feet are assembled on the same side plane bimode, which consists of the first longitudinal in-plane vibration USM is determined carefully by FEA. The characteristics of the prototype C211 2006 Elsevier B.V. All rights reserved. Keywords: Linear ultrasonic motor; Laminated plates; Vibration in plan; 0041-624X/$ - see front matter C211 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.ultras.2006.05.191 motor with double-driving feet Zhou, Yu Chen Beijing 100084, China 9 June 2006 The stator consists of eight piezoelectric ceramic plates and one and are symmetrically bonded to the two surfaces of one rect- of the brass plate. The working vibration mode is a composite in- mode and the second bending one. The basic size of the linear motor were measured experimentally. ric ceramic 2. Working principle 2.1. General structure As a prototype example, a compact ultrasonic motor based on bimode was fabricated, as illustrated in Fig. 1. It consists of a stator and a pressing mechanism including a box, a bolt and a plastic cushions. The stator is made of a thin brass plate with eight piezoelectric ceramic plates bonded to the upper and down surfaces symmetrically. There are two driving feet at the same side of the brass sets are excited by a signal of Asin(xt + u). The metal plate is the ground. Actually, the frequency of longitudinal mode and the bending one of the stator can not agree well because of the influence of such facts as an error of manu- facture and variety of temperature. So, for the sake of the bimode vibrations on the stator being eectively excited, an exciting frequency f d between the longitudinal mode fre- quency f l and bending one f b was chosen, as shown in Fig. 3. There is a phase dierence u between the two exciting signals, which should cause a phase dierence between the vibrations. Fig. 4 shows that if the exciting frequency f d changes, the phase of resonance vibration changes too. The more the exciting frequency be close to the modal fre- quency of the stator, the greater the phase of the resonance vibration changes. The driving frequency changes, the phase dierence of the resonance vibrations changes too. e586 C. Lu et al. / Ultrasonics 44 (2006) e585e589 plate. Piezoelectric ceramic plates were polarized along the thickness direction. The polarization direction of the four piezoelectric ceramic plates bonded to the upper sur- face of the brass plate is against the direction of the other four plates bonded to the down surface of the brass plate. A bolt and some plastic cushions were used to fix the stator in the metal shell. The pressure between the stator and the slider can be adjusted, so the motor can work under dier- ent pressure force desired. In order to reduce the influence of the clamp on the vibration of the stator, the fixed point should near the nodal plane of the vibration of the stator. 2.2. Working principle The working bimode of the stator consists of the first longitudinal vibration mode and the second bending vibra- tion mode of the stator. Fig. 2(a) shows that the particles on the friction face of the driving feet vibrate transversely in the first longitudinal vibration mode of the stator. Fig. 2(b) shows that the particles on the friction face of the driving feet vibrate vertically when the stator vibrates in the second bending vibration mode. If there is a certain phase dierence between the two modes, the track of parti- cles on the friction face of the driving feet should be an ellipse when the stator vibrates in the bimode, as illustrated in Fig. 2(c). The metal shell was fixed on the operating plat- form. Two feet of the stator drive the slider to make a lin- ear motion. The friction pair is ceramic to ceramic. If the phase dierence of the vibrations changes, the shape of the ellipse track of the particles changes too. Thus the move speed of the slider changes. Commonly, the desired phase dierence of the two vibrations is 90C176 so that the slider can be driven eciently. Fig. 1. The stator of the motor with metal shell. 2.3. Exciting mechanism The vibration exciting method of the stator is shown in Fig. 3. Eight piezoelectric ceramic plates are classified into four pairs. Each pair includes two ceramic plates symmet- rically bonded to the both sides of the brass plate. The diagonal two pairs of piezoelectric ceramic plates are excited by a sine signal of Asin(xt), and the other diagonal Fig. 2. The vibration modes of the stator: (a) the first longitudinal mode, (b) the second bending mode and (c) the composite in-plane bimode. Fig. 3. The exciting method. The velocity consistency of the two driving feet is another important factor aecting the driving capability of the stator. Dierent mounting location of the driving feet brings on dierent vibration amplitude, as well as dif- ferent driving force provided by the two feet. The vibration behaviors of the stator were calculated by using the electromechanical coupling dynamic model. The applied voltage on the electrodes of the PZT plates is 4.05 4.1 4.15 x 10 4 Frequeny, kHz Frequency of the first longitudinal mode Frequency of the second bending mode s 44 (2006) e585e589 e587 The traveling direction of the drive can be changed by switching the one pair crossing connected electrodes to another pair. This changes the bending mode phase by p and results in reversing the direction of surface elliptical motion. The velocity of the slider can be changed by adjust- ing the exciting voltage or phase dierence of the two excit- ing signals. When the frequency f l and f b are the same, the phase dif- ference of the two vibrations changes very little as the frequency f d varies. So, it is very important to make the frequency of the two vibrations be as consistent as possible. 3. Structure design of the motor An electromechanical coupling dynamic model of the stator is built using a FEM software ANSYS for the struc- ture design. Only when the natural frequency of the first longitudinal mode is close to the second bending one of the stator, the needed bimode could be eectively excited on the stator. Therefore the frequency consistency of the two modes should be considered when the stator being designed and manufactured. Fig. 5 shows the predicted frequencies of the vibration modes as functions of the length of the brass plate. It can be found from Fig. 5 that both the frequencies of the lon- gitudinal and bending vibration modes decreases with the length of brass plate, but the frequency of the bending mode decreases faster. This modeling revealed that an eective method of frequency consistence adjustment Fig. 4. The frequency and the phase of the vibration modes. C. Lu et al. / Ultrasonic would be changing the length dimension of the brass plate. The calculated length of the brass plate is 40.5 mm. The natural frequency of the bending mode is 39980 Hz, and the frequency of the longitudinal mode is 40010 Hz. The frequencies are approximately equal to each other. In consideration of the errors from calculation and man- ufacturing, the brass plate was made at first with 41 mm in length, which was 0.5 mm longer than the calculated value. By reducing the length of the brass plate gradually, the consistency of the mode frequencies of the stator can be achieved in virtue of frequency measuring instruments. Double-driving feet strategy was adopted. The two feet drive by turns. The two driving feet should be arranged symmetrically because of the requirement of the reverse driving. The shape of the driving feet is rectangle. For keeping the friction pair contacting well in order that the slider can be driven steadily, the flexural amplitude of the con- tacting face on each foot should be consistent in the direc- tion of bending vibration. The position of the driving feet on the stator influences the consistence of the vibration velocity of the feet. There are five equidistant nodes on each meshed feet of the FEM model, as shown in Fig. 6. The relation of the flexural amplitude of the nodes on each foot versus the cen- tre distance between the two feet was calculated, as shown in Fig. 7. While the centre distance equals to 13.7 mm, the flexural amplitudes of the five nodes were nearly the same. 39 39.5 40 40.5 41 3.95 4 Length, mm Fig. 5. The relation between the modal frequency and the length of the brass plate. 40 V. The driving frequency is 40080 Hz. A constant Fig. 6. Five equidistant nodes on each meshed feet. 12 13 14 15 16 1.2 1.4 1.6 1.8 2 x 10 -6 Distance, mm Amplitude, m 1.4 1.6 1.8 x 10 -6 node1 node2 node3 node4 node5 node1 node2 node3 node4 node5 Fig. 9. The size of the stator. e588 C. Lu et al. / Ultrasonics 44 (2006) e585e589 damping ratio of 0.003 is set for use in the harmonic response. The vibration amplitudes of a ridge on the stator, where the driving feet mounted, were calculated and plot- ted in Fig. 8. U X is the displacement in the direction of the longitudinal vibration. U Y is the displacement in the direction of the bending vibration. U Z is the displacement in the direction of thickness vibration. USUM is the com- posite displacement. It is shown that the displacement U Z is 12 13 14 15 16 1.2 Distance, mm Amplitude, m Fig. 7. Vibration of the feet. as tiny as to be ignored. The displacement U Y is symmetri- cally distributed. The flexural amplitude reaches its maxi- mum at the situation that the distance between the centers of two feet equals to 13.7 mm, and the amplitude is basically symmetrical. U X is not symmetrically distrib- uted. The U X amplitude of the right foot is a little greater Fig. 8. The calculated vibration amplitudes of a ridge on the stator, where the driving feet mounted. than that of the left foot. Thus, the composite displacement USUM of the right foot is a little greater than that of the left foot too. Since only when the distance between the centers of two feet is 13.7 mm, the flexural amplitude U Y reaches its max- imum and the vibration speed of the nodes on the diving feet keeps consistent in the direction of bending vibration, the size of the stator is determined as shown in Fig. 9. The size of the rectangular brass plate is 40.5 mm in length, 11 mm in width and 2 mm in thickness. The piezo- electric ceramic plates are 17 mm in length, 4 mm in width and 0.8 mm in thickness. 4. Experimental investigations The frequency response characteristic of the stator mea- sured with impedance analyzer is shown in Fig. 10. The res- onant frequency of the first longitudinal vibration mode is 38.8 kHz, while the resonant frequency of the second bend- ing vibration mode is 40.8 kHz. The bending vibration fre- Fig. 10. The measured resonant frequency of the stator. quency is about 2 kHz higher than the longitudinal one. 36 37 38 39 40 41 42 0 20 40 60 80 100 Frequency, kHz Driving speed, mm/s Left foot Right foot Voltage=50Vrms Fig. 11. The relation between the driving speed and the frequency. Fig. 11 shows the relation between the driving speed and vibration mode and the second in-plane bending vibration mode can be easily regulated to the same by adjusting the length of the brass plate. The characteristics of the proto- type motor were measured experimentally. The motor has a maximum speed of 94.5 mm/s when the driving electric voltage is about 50 V in rms and the frequency is 38.6 kHz. Acknowledgements The authors thanks for the financial supports from the National Natural Science Foundation of China (No.50235010). References 1 S. Ueha, Y. Tomikawa, M. Korosawa, K. Nakamura, Ultrasonic Motors: Theory and Application, Clarendon Press, Oxford, 1993. 25 30 35 40 45 50 55 60 65 20 30 40 50 60 70 80 90 100 voltage, Vrms Driving speed, mm/s Left foot Right foot Frequency=39.6kHz Fig. 12. The relation between the driving speed and the driving voltage. C. Lu et al. / Ultrasonics 44 (2006) e585e589 e589 the driving frequency. The driving electric voltage is about 50 V in rms. At a resonant frequency of 38.6 kHz, the motor has a maximum speed of 94.5 mm/s. In the fre- quency range from 38.6 to 40.8 kHz, the speed varies above 42 mm/s. The driving speed of the motor varies proportionally with an applied voltage. This result is in agreement with a no-load working condition of the slider, as shown in Fig. 12. The exciting frequency is about 39.6 kHz. 5. Conclusions A new type linear USM with double-driving feet has been developed. The stator consists of eight piezoelectric ceramic plates and one brass plate. 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