Driver Model Based on Mechanical Traveling Wave Principle

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1 Ameican Jounal of Mechanical Engineeing, 014, Vol., No. 6, Available online at Science and Education Publishing DOI: /ajme--6- Dive Model Based on Mechanical Taveling Wave Pinciple SONG Rui-Yin *, LI Yue, ZHOU Ming-Long, LIN Zuan Ningbo Institute of Technology, Zhejiang Univesity, Ningbo, China *Coesponding autho: Received Novembe 5, 014; Revised Decembe 05, 014; Accepted Decembe 08, 014 Abstact A new type of mechanical dive based on taveling wave tansmission pinciple was put fowad. The initial stuctue of the educe was designed and the theoetical models such as dive atio, output toque and output powe wee built up. An initial educe was manufactued and some pefomance paametes wee tested.the expeiment esults illustate that the new type of educe poposed has a lage dive atio featue, and the testing esults accod with the theoetical model. Keywods: educe, taveling wave, theoetical model Cite This Aticle: SONG Rui-Yin, LI Yue, ZHOU Ming-Long, and LIN Zuan, Dive Model Based on Mechanical Taveling Wave Pinciple. Ameican Jounal of Mechanical Engineeing, vol., no. 6 (014): doi: /ajme Intoduction The dive pinciple of a taveling wave has been used in the field of ultasonic wave motos, and it is evident that a taveling wave would be poduced when a paticle oscillates up and down about a fixed point. It is evident that a taveling wave would be poduced when a paticle oscillates up and down about a fixed point, and the dive pinciple of taveling wave has been used in the field of ultasonic wave moto [1,,3,4]. Hee, a new type of educe based on the dive pinciple of a taveling wave has been put fowad. The taveling wave occus when a paticle vibates with cetain fequency poducing taveling waves, and the output waves tansmit in a medium coespondingly. Compaed with the gea educe, this dive has some meits such as simple stuctue, lage dive atio and small dimensions, which can be used in some special fields such as lage dive atio mechanism and MEMS. In this pape, the theoy of mechanical taveling wave dive has been in toduced, the stuctue of the dive was built and some mechanical dive atio expeiments wee pefomed.. Diving Pinciple of Mechanical Taveling Wave igue 1 shows the theoetical model of mechanical taveling wave dive, which mainly includes the taveling wave poduce, elastic laye and output laye. When the equally distibuted olles move, they tow and squeeze the elastic laye, and the paticles of elastic laye move towad the othe side to and fo, the paticles then ecove when the elastic laye is out of touch with the olles. The peiodic motion of stetch-pess-stess makes the paticles of elastic laye move in vetical vibation peiodically. Combining the compound movements of the hoizontal diection movements with the olles and the vetical diection movements of paticles, the mechanical taveling wave occued. igue 1. Pinciple of mechanism taveling wave In the figue, the motion tail of the paticle of the elastic laye is elliptical [4,5,6,7,17,18]. When taveling wave moves towad the ight, the movement diection of the paticles is counte clock wise. When the paticles aive at the wave peak, the diection of the vibation velocity is towad the left. Unde the condition of peload between elastic laye and output laye, the hoizontal movement of the paticles causes fiction foce on the output laye, diving the output laye movement towads the left and vice vesa. The shape of the motion tail fo the elastic paticles is an ellipse (shown in igue 1). Point P 0 is the initial position of the paticle befoe bend defomation of the elastic laye and point P is anothe position of that point afte bending defomation, θ is the bend angle between P and P 0 and u is the vibation displacement along x

2 160 Ameican Jounal of Mechanical Engineeing diection. his the thickness of un-defomed elastic laye and a ectangula coodinate system can be built up along neutal suface of elastic laye. The equation of taveling wave fo neutal suface is as follows [8,9,11,1]: u0 ( xt, ) = Acos( ωt x) (1) whee is the wavelength of taveling wave fo elastic laye Then, the vibation w(x,t) displacement of paticle fom point P 0 to P is as follows: h u0 (,) ( kx ωt wxt = ) x h = Asin( ωt x) () Though a method of patial diffeential equations, the vibation velocity(v x ) fo paticles of the elastic laye is as follows: dw(,) x t vx = h0 ωacos( ωt x) dt = (3) A negative sign means that the motion diection of the paticle is opposite to that of the motion diection fo the taveling wave. If we do not conside the sliding effect between elastic laye and output laye, the output laye velocity(v ) equals the vibation velocity of the elastic paticle at the bending wave cest location. v = vx = h0 ωacos( ωt x) (4) shaft, and the output shaft otates coespondingly based on a taveling wave pinciple. The key pat of the dive is the taveling wave poduce, which includes an elastic laye and cylindical olles unifomly distibuted along the input shaft (shown in igue 3a). Taveling wave poduce can be designed as of seveal shapes such as cicula conical shape, tous shape and disk shape. Cosssection shape of taveling wave poduce is shown in igue 3 (b). igue 3. Stuctue of mechanism taveling wave dive 1-input shaft; -input shaft beaing; 3-base; 4-taveling wave poduce olle; 5- elastic laye; 6-output shaft beaing; 7-output shaft. 4. Modeling fo Mechanical Taveling Wave Poduce 4.1. Dive Ratio of Mechanical Taveling Wave Poduce igue. Velocity cuve of output laye Velocity cuve of output laye is shown in igue. The figue illustates that only a half cycle of the velocity is useful fo the movement of output laye. Without taking the influence of elative sliding into account, by calculating the dashed aea of velocity cuve shown in the figue. The mean velocity of output laye is given by: v h ω A out = 0 (5) 3. Stuctue of Mechanical Taveling Wave Dive Based on the theoy of mechanical taveling wave dive, a mechanical taveling wave dive of a otay type was designed. igue 3 shows the stuctue of the dive, which includes such components as input shaft, output shaft and taveling wave poducing olle etc. In the dive, a seies of cylindical balls ae distibuted equally along the input shaft. Mechanical taveling wave would be poduced on the condition of cylindical olles otating aound input igue 4. seveal paametes of dive igue 4 shows the elationship between paametes fo input shaft, taveling wave poduce and output shaft. R 1, R,, 1 and h epesent distance between input shaft cente and elastic laye cente, input shaft adius, output shaft adius, cuve adius between elastic laye and cylinde ball, adius of cylinde olle and the thickness of elastic laye espectively. Conside that the defomation of the elastic laye is small and that it can be ignoed. Then the wave length of mechanical tavelling wave dive is as follows: ( R h/ ) =, n

3 Ameican Jounal of Mechanical Engineeing 161 while T (wave peiod) is: ( R h/ ) N 60 T = / ( R h/ ) =. n 30 nn Nn We have: ω =. Combined with Equation(5), the 30 aveage velocity of output shaft is obtained as follows: hnn A vout = 40( R h/ ) (6) Evidently, the biggest squeeze defomation of elasticlaye is the amplitude of the elastic laye, i.e. 1 =A. The velocity of cente pat fo elastic laye is obtained as: N N vi = R = R N = ( R 1+ + h / 1) 30 (7) Setting total peload between input shaft and output shaft as, the numbe of olles is n, and the peload fo single olle is: c = / n. The contact aea between olle and the elastic laye is as follows: A accos( 1 c = ) B (8) whee, 1 ( 1 =A) is the defomation depth of the elastic laye, E is elastic modulus of the elastic laye and B is length of the cylindical olle. Conside that the value of the defomation depth of elastic laye( 1 ) is much smalle than that of the cylinde olle(), the stess of the elastic laye is as follows: c σ c = = Ac n.accos( 1 ) B nb 1 1 (9) In a taveling wave length peiod, the stain of elastic laye is given by [8,9]: 1 x L c ( x) = (cos cos ) ( L x L) h ε whee, L is the contact length in a wavelength between input shaft and output shaft. Conside that the stain is poduced in half of the wavelength peiod. The aveage value of the valid stain is as follows: ε ( ) 1 c x = (10) h Based on stess-stain elation fomula: σc = Eεc, the elationship between squeeze defomation and peload is as follows: 1 E = h nb 1 1 Because 1 <<, by simplifying the fomula, the elationship between 1 and (peload) is given by: ( h) 1 3 (11) ( EnB) Then, the total dive atio is as follows: vi 4 R i = = v out hn 1 ( h) 4 R h/ 3 ( EnB) = ( h) hn 3 ( EnB) (1) It is obvious that the total dive atio is influenced by such paametes as thickness of elastic laye, elastic laye mateials, peload, adius of input (output) shaft, numbe of cylindical olles, adius of cylindical olles and amplitude etc. 4.. Output Powe fo Mechanical Taveling Wave Poduce igue 5. The contact model between the elastic laye and fiction laye consideing shea defomation [10-16] iction laye between the elastic laye and output shaft is the key pat to dive the output shaft. Consideing the stiffness of elastic laye is lage than that of fiction laye, it is supposed that fiction laye hasdefomed while elastic laye has no defomation, and the elastic laye has the wavefom shape. Consideing theoy of sheaing defomation and Coulomb fiction law, a contact model between the elastic laye and fiction laye has been built, which is shown in igue 5. In the figue, the inteval [-x,-x 1 ] is the viscous egion, point (-x 1 ) is the demacation point of viscous egion to sliding fiction egion x1 = x Δx. Consideing the influence of the viscous egion, the effective aea between the input laye and output laye deceases, and the output toque coespondingly deceases. Diving foce fom between input shaft and output shaft is given by [9,10]: x0 sgn[ vs( x) v] f1dx T = B x0 x x1 x0 = B[ f1dx + f1dx f1dx] x 0 x 1 x (13) whee, B is the contact width of olle between input shaft and output shaft, f 1 is the hoizontal foce between input

4 16 Ameican Jounal of Mechanical Engineeing shaft and output shaft, and f1 = µ dc, µ d is the dynamic fiction coefficient and c is the peload. It is difficult to accuately measue some paametes such as µ d because the viscous egion and sliding egion ae vaiable with mateials and peload change. So, the equation (13) can be simplified as follows: T d / n (14) whee, ε is constant, which eflects the fiction value. The aveage output toque of the poduce is as follows: T = ntr = nbεµ d / n R d R ( 1+ 1) Then, the output powe is given by: Pout = nt vout d ( h) hnn 3 ( EnL) 40( R h/ ) 5. Testing Device Expeiment (15) (16) A testing device with taveling wave pinciple was manufactued, which is shown in igue 6. In the device, the kinematic chain consists of the electomoto, input shaft, mechanical taveling wave poduce and output shaft. Rotational speed is measued by a speed senso and displacement was measued by a linea scale senso. Hee, a staightedge was used as the output link instead of the output shaft. When the mechanical taveling wave was poduced on the elastic laye, the staightedge would move towad a cetain diection, and the displacement value was measued by a linea scale senso. A feed scew nut device was used as the peload adjuste, and the peload can be adjusted by otating the nut. The mateial used fo the elastic laye is impotant, as it is a key pat of the mechanical taveling wave poduce. Hee, PU (Polycabamate) was selected as the initial mateial used fo the elastic laye, and the thicknesses of the elastic layes was 3mm, 5mm, 7mm and 9mm, espectively. Accoding to Equation (1), we know that the total velocity atio value is dependent on such paametes as thickness of elastic laye, mateial of elastic laye, amplitude of peload, adius of input and output shaft, numbe of olles, adius of olle and amplitude etc. In the expeiment, seveal paametes such as mateial of elastic laye, adius of input and output shaft and adius of olle wee set as constants, while such paametes as thickness of elastic laye, numbe of olles and peload wee set as vaiables. In the testing device, the adius of the input shaft was 0mm and the angula velocity was 136/min; the adius of the cylindical olle was 1.8mm and the length of olle was 9mm, which wee equally distibuted along input shaft length, the diamete of the elastic laye is 48.16mm. Hee, expeiments on total dive atio fo the device by adjusting such paametes as thickness of elastic laye, numbe of cylinde olles and peload wee done Expeiment though Adjusting the Thickness of the Elastic Laye To test the influence of the thickness of the elastic laye vs. total dive atio, seveal elastic layes with a thickness of 3mm, 5mm, 7mm and 9mm wee studied. The peload between the elastic laye and the staightedge was changed by otating the scew nut, and fou displacement cuves ae shown in igue 7. The velocity of the staightedge is almost constant, and the lage dive atio is about Secondly, the displacement value of the staightedge is fom 189mm to 150mm. With the incease of thickness fo the elastic laye, it was evealed that the thickness has an unobvious effect on the total dive atio. igue 7. The displacement of output staightedge on condition of diffeent elastic laye thicknesses (a-3mm, b-5mm, c-7mm, d-9mm) igue 6. Mechanical taveling wave testing device 1-line scale senso, -staightedge, 3- taveling wave poduce, 4-elastic laye, 5-electomoto, 6-input shaft, 7-poload adjuste 5.. Expeiment though Adjusting Peload between Elastic and Staightedge In the expeiment, the peload between elastic and staightedge was adjusted by otating the nut of the scew od, and the adjusted distance was 0.5mm. Hee, two elastic layes with thicknesses of 3mm and 5mm wee used in the expeiment. The cuve of the dive atio VS the defomation of the elastic laye is shown in igue 8. we know that with the incease of peload (i.e. the incease of defomation fo elastic laye) between the elastic laye and the staightedge, the total dive atio deceased in a degee coespondingly, and the total dive atio deceased with the thickness of

5 Ameican Jounal of Mechanical Engineeing 163 elastic laye incease, which coesponds to the theoetical model of the total dive atio. efficiency, which needs to be impoved by theoy and stuctue methods. Refeences igue 8. The cuve of dive atio VS defomation of the elastic laye 5.3. Expeiment though Adjusting Rolle Numbe The numbe of olles is one of the key factos in a mechanical taveling wave poduce. In the expeiment, the numbes of olles wee set to 6,8,1 and 16, and the peload was constant. The cuve of total dive atio VS the olles numbe is shown in igue 9, which has exponential pofile appoximately. This illustates that the total dive atio deceases with the incease of olle numbes, which is consistent with the theoetical model. igue 9. The cuve of dive atio VS the olle numbe 6. Conclusions We found that the total dive atio model and the output powe model of the taveling wave poduce wee built up, and the testing device was built coespondingly. Though a seies of tests, some meits wee dawn as follows: big dive atio and simple stuctue is desiable. Consideing that the mateial of elastic laye and fiction laye have an obvious influence on mechanical behavio of the device, a moe accuate model needs to be established though the method of mico fiction pinciple. uthemoe, it is indicated that the device has low [1] Diwaka, S. V.; Tiwai, Shaligam; Das, Sait K.; Sundaaajan, T. Stability and esonant wave inteactions of confined two-laye Rayleigh-Benad systems [J].Jounal of luid Mechanics. 014, 754: [] Ueha S. Tomikawa Y. Ultasonic motos theoy and applications[m]. Oxfod science Publication, [3] P. LeMoal, P.Cudsin. Optimization of taveling wave ultasonic motos using a thee-dimension analysis of the contact mechanism at the stato oto inteface, Eu.J.Mech.A/solids, 1999, 18: [4] Yang, Lin; Zhao, Chunsheng. lexible suppoting and fixing method fo hybid ultasonic moto using longitudinal and tosional vibation modes [J] JOURNAL O VIBROENGINEERING (9): [5] Glenn, T.S., Ghandi, K.; Atalla, M.J.; Hagood, N.W. Mixeddomain Taveling-wave Moto Model with Lossy (complex) Mateial Popeties[C]: Poceedings of SPIE - The Intenational Society fo Optical Engineeing, 001, 436: [6] Hiata, Hioshi; Ueha, Sadayuki. Design of a Taveling Wave Type Ultasonic Moto[C]: IEEE Tansactions on Ultasonics, eoelectics, and equency Contol, 1995:v 4(): [7] Hagood N W, Mcfal and A J. Modeling of a piezoelectic otay ultasonic moto[j]. IEEE LJC (): [8] Takashi Maneo, Takayuki Tsukimoto, Akia Miyake. inite element analysis of the moto/stato contact in a ing-type ultasonic moto[j]. IEEE Tans on UC, 199, 39(6): [9] Wang Ping; ones, L. S.; YangQun; Guupackiam, S. Cell tansmission model based taffic signal timing in ovesatuated conditions[j]. Jounal of Cental South Univesity. 013, 0(4) [10] Shen, Shengnan; Lee, Heow P.; Lim, Siak P. Thee-dimensional finite element analysis of intefacial delamination in taveling wave ultasonic motos[j]. 014,3(7): [11] Li Huafeng, Zhao ChunshengGuChenglin.Contact Model of Taveling Wave-type Ultasonic Moto[J]. J. HuazhongUniv of Sci. & Tech. ( Natue Science Edition) (10) [1] Kuosawa, Minou Kuibayashi.Ultasonic linea moto using taveling suface acoustic wave[c]:009 IEEE Intenational Ultasonics Symposium and Shot Couses: [13] Zou, G. B, Gao, H. L. Exta high speed hybid potection scheme fo high voltage tansmission line[j]. Intenational Jounal of Electical Powe & Enegy Systems (5) [14] Wang, Shiyu; Xiu, Jie; Cao, Shuqian. Analytical Teatment With Rigid-Elastic Vibation of Pemanent Magnet Motos With Expanding Application to Cyclically Symmetic Powe- Tansmission Systems[J]. Jounal of Vibation and Acousticstansactions of the ASME (). [15] Alijani, abod; Amabili, Maco. Nonlinea vibations and multiple esonances of fluid filled abitay laminated cicula cylindical shells [J].Composite Stuctues () [16] Kim, Heuicheol; Cho, Mi-Gyung; Pak, Jaehong; Bai, Cheolho; Shim, Jaesool. Pediction of gas pulsation of an industial compesso[j].jounal of Cental South Univesity. 013, 0(10) [17] Wang, Tianshi; Lancee, Chales; Beuskens, Robet. Development of a high-speed synchonous mico moto and its application in intavascula imaging [J]. SENSORS AND ACTUATORS A- PHYSICAL.014, 08(10) [18] Monti, Chiaa; Vetella, Ugo Besi; Mugnaini, Giampieo. Test of piezo-ceamic moto technology in ITER elevant high magnetic fields[j]. USION ENGINEERING AND DESIGN. 014, 89(10)