In this work the proposed model for  type-disk, ultrasonic motor rotating, elliptic movement to surface beam. A sinusoidal vibration of the vertical displacement in the z-direction, Assume that the vertical displacement of the neutral plane, equals the product of the slope of the neutral plane and half of the beam height, the tangential velocity vs at the upper surface is given

Dan DOBROTA

Gabriel CHIRCULESCU

Oana CHIVU

Directory of Open Access Journals

                                  Fiabilitate si Durabilitate - Fiability & Durability    no 2(6)/ 2010                                Editura “Academica Brâncuşi” , Târgu Jiu, ISSN 1844 – 640X  49 THEORETICAL AND EXPERIMENTAL CONTRIBUTIONS CONCERNING THE PROPOSED MODEL FOR THE DISC-TYPED ROTARY ULTRASONIC MOTOR   Asist. dr.eng. Oana CHIVU, Polytechnic University of Bucharest,  Prof. dr.eng. Dan DOBROTA, ”Constantin Brancusi” University of Targu-Jiu,  Dr. eng. Gabriel CHIRCULESCU, Rovinari Energy Complex  Abstract - In this work the proposed model for  type-disk, ultrasonic motor rotating, elliptic movement to surface beam. A sinusoidal vibration of the vertical displacement in the z-direction, Assume that the vertical displacement of the neutral plane, equals the product of the slope of the neutral plane and half of the beam height, the tangential velocity vs at the upper surface is given.  Keywords: elastic-body, sinusoidal vibration, ultrasonic.  1. Introduction Employing the fundamental theories for ultrasonic motors, we will extend to applying them to rotary ultrasonic motors. Instead of a beam, we now consider an elastic-body ring shown in figure 1 below.     Fig. 1.  Visualization from a beam to a ring.  Treating the beam as an infinite body that carries flexural waves. Cutting a length equal to the wavelength multiplied by m times and joining the two ends together forms a ring. A sinusoidal vibration of the vertical displacement in the z-direction can be expressed as:  ⎟⎠⎞⎜⎝⎛ ++⎟⎠⎞⎜⎝⎛ +−= mmmmmmn xlmDxlmtsimCw ϕπωφπω 2sin2                                     (1) where  fm  and   m are appropriate phase angles and l is equal to the wavelength multiply by m. The relationship between the vibrational mode number n, and the number of waves cycles present on the ring is: n = 2m                                                                 (2)                             2.Elliptical motion at the beam’s surface  Figure 2 below illustrates how points on a beam’s surface rotate in a counter-clockwise direction as the flexural wave travels from left to right. Assume that the vertical displacement of the neutral plane can be describe by : w = ξo sin( ωt – kx )                                                              (3)                                   Fiabilitate si Durabilitate - Fiability & Durability    no 2(6)/ 2010                                Editura “Academica Brâncuşi” , Târgu Jiu, ISSN 1844 – 640X  50   Fig. 2.  Points at beam’s surface rotate counterclockwise in an elliptical motion.  As depicted in figure 2, the displacement u in the x direction equals the product of the slope of the neutral plane and half of the beam height.   u = ( kξoh/2) cos(ωt – kx )             (4)  Since k = 2π/λ, we obtain,  u = ( πξoh/λ ) cos(ωt – kx)                                  (5)             We observe that the ratio of the minor to the major axis of an ellipse is given by πh/λ.By differentiating equation (5) with respect to time, we will derive the tangential velocity of each point at the beam’s surface as follows,   ( )kxthdtdu−−= ωλωπξ sin                                                 (6) We have assumed that phases A and B are identical except with a 900  phase difference in position and time . Let ξA and ξB   be the amplitudes at the neutral plane of phases A and B respectively Then we will have, w = ξA sin ωt sin kx + ξB cos ωt cos kx                                                xwhuϑϑ2−=                                                                      (7) The tangential velocity vs at the upper surface is given by  ( )kttkxthktxwhtuv BAs sinsincoscos222ωξωξωϑϑϑϑϑ+−=−==                       (8)    To find the position of the crest, we let ∂w/∂x = 0. Thus,                                       ξA sin ωt cos kx = ξB cos ωt sin kx                                                    (9)  From this equation, we obtain the following,                                     Fiabilitate si Durabilitate - Fiability & Durability    no 2(6)/ 2010                                Editura “Academica Brâncuşi” , Târgu Jiu, ISSN 1844 – 640X  51            ( )[ ]wtwtAkxABB22 cot1coscosξξξξ+⎟⎠⎞⎜⎝⎛=                                                          (10)                            ( ) wtkxAB22 cot11sinξξ+                                                              (11)  Substituting these terms into Equation (8), we acquire the tangential velocity at the,                                   [ ] ( )[ ]wtwthkvBABAtops 2222 cossin2ξξξξω+−=                                            (12)                       Since k=2π/λ,                         [ ] ( )[ ]wtwthkvBABAtops 2222 cossin ξξλξξω+−=                                                   (13)                   When  , ξA = ξB = ξo,                  [ ] ( ) ( )πλωξλξω22 00⎟⎠⎞⎜⎝⎛−=−=hhkv tops                                                                    (14) According to Equation (14), we know that the velocity in the transverse direction is equal to  ξoω . By knowing this fact, the velocity of the crest is obtained at the end of the shorter arm. Taking moment about the fulcrum point at the neutral plane of the beam, we arrive with the conclusion that the longer arm of the lever has a length λ of   divided by 2π  while the shorter arm has a length h/2. This analogy applied directly to the actual motor where the comb teeth are considered to be short arms of the lever. The comb teeth are regarded as a row of the levers as shown in Figure 3.   Fig. 3.  The ‘lever’ principle modeling the comb teeth of an ultrasonic motor.  3. Conclusions 1° A rotary ultrasonic motor has a resolution limit. An ultrasonic motor can produce extremely fine position changes until the sub-nanometric field and small variations in operating voltage can be converted into continuous movements; 2° Piezo positioning systems can produce a force of tens of thousands of Newtons (units operating there that can support loads of several tons), making movements with nanometer resolution; 3° Experimentally it is found that ultrasonic motors have a response time of microseconds Odin;                                   Fiabilitate si Durabilitate - Fiability & Durability    no 2(6)/ 2010                                Editura “Academica Brâncuşi” , Târgu Jiu, ISSN 1844 – 640X  52 4° Elements of an ultrasonic motor operates without wear. An engine displacement based on dynamic ultrasonic solid no-wear. 5° Experimentally been found not require lubrication. Ultrasonic motors do not need any lubricant and makes them ideal for high vacuum applications. 6° Ultrasonic motors can operate at cryogenic temperatures. Piezo effect is based on electric fields and produce up to near zero degrees Kelvin is only important point Curie temperature.   References  [1] AMZA, Gh., Niţoi, D., Elements for designes and modeling of an ultrasonic motor, Timişoara, 2001.   [2] Hirata, H., and Ueha, S. Design of a travelling wave type ultrasonic motor. In IEEE Transactions on Ultrasonic, Ferroelectrics, and Frequency Control, pages 225-231, Vol. 42, No. 2, March 1995. [3] Hu, J. H., Nakamura, K., and Ueha, S. Characteristics of a noncontact ultrasonic motor using acoustic levitation. In IEEE Ultrasonics Symposium, pages 373-376, Vol. 1, November 1996.    

THEORETICAL AND EXPERIMENTAL CONTRIBUTIONS CONCERNING THE PROPOSED MODEL FOR THE DISC-TYPED ROTARY ULTRASONIC MOTOR

http://doaj.org/search?source=%7B%22query%22%3A%7B%22bool%22%3A%7B%22must%22%3A%5B%7B%22term%22%3A%7B%22id%22%3A%22c9e0298d64a849f9b8ce05ecd4341743%22%7D%7D%5D%7D%7D%7D

THEORETICAL AND EXPERIMENTAL CONTRIBUTIONS CONCERNING THE PROPOSED MODEL FOR THE DISC-TYPED ROTARY ULTRASONIC MOTOR

Abstract

Similar works

Full text

Available Versions

Directory of Open Access Journals