Numerical Simulation and Experimental Analysis of an Active Hydraulic Excitation System Based on Pulsating Flow

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1 Adanced Maerials Research Vols ) pp Online aailable since 2011/Jul/04 a ) Trans Tech Publicaions, Swizerland doi / Numerical Simulaion and Experimenal Analysis of an Acie ydraulic Exciaion Sysem Based on Pulsaing Flow Ziming Kou 1, 2, a, uixian Zhang 1, 3, b, Juan Wu 1, 2, c, Chunyue Lu 1, 4, d 1 College of Mechanical Engineering, Taiyuan Uniersiy of Technology,Taiyuan, China 2 Shanxi Proince Mine Fluid Conrol Engineering Research Cener,Taiyuan, China 3 Elecronic Science and Engineering Deparmen, uanghuai Uniersiy, Zhumadian, China 4 School of Mechanical Engineering Auomaion, Norh Uniersiy of China, Taiyuan, China a [email protected], b [email protected], c [email protected], d [email protected] Keywords hydraulic exciaion; pulsaing flow; he mehod of characerisics; frequency conersion; ibraion excier. Absracs A ibraion wae generaed aciely by hydraulic ibraion excier was sudied, and an experimenal sysem based on he heory of waer hammer was designed. The new deeloped ibraion excier is drien by he moor whose roary speed can be adjused by frequency conerer, by means of which ransien pulsaing flow is generaed regularly. Consequenly he pison of hydraulic cylinder is drien periodically wih he roaion of ibraion excier. Furhermore, mahemaical model was esablished by he mehod of characerisics and compuer code was deeloped o calculae numerical soluion. The simulaion resuls show ha here are differen flow elociies disribued a eery cross secion along he pipe. Measured daa is basically consisen wih he numerical simulaion, which indicaes ha he ibraion parameers of hydraulic cylinder can be conrolled effeciely. Inroducion Mos of he ibraion machines work by ibraion excier based on ineria force, hrough which exciaion force will be generaed periodically. Alhough hydraulic ibraion excier based on pumpconrol and aleconrol has excellen propery, here are sill series of problems such as lower efficiency and negaie influence o equipmen iself. In his sudy, a new ibraion mechanism was presened based on he heory of waer hammer and an experimenal sudy and numerical simulaion were carried ou. Waer hammer commonly occurs in ale or piping sysem. When a ale is closed suddenly a an end of a pipeline sysem, pressure wae will propagae in he pipe, which is known as hydraulic shock. Chuhua Zhang [1] esablished a heoreical model and performed numerical simulaion for hreedimensional flow induced ibraion; uizhe Cao [2] sudied he flucuaion process and opimal conrol of waer hammer in pipes; A.Misra [3] esablished a mahemaical model on selfexcied ibraion of conrol ale due o waer hammer and carried ou numerical analysis caused by fluidsrucure ineracion. Bu unil now no repors are found o uilize hydraulic exciaion force resuled from waer hammer as exciaion source. In ha sense, he presen sudy is enirely new. Sysem composiion and mahemaical model Sysem composiion. In his sudy, he deeloped hydraulic exciaion esing sysem is based on classical waer hammer model, and waer hammer mechanism has been expounded in deail in many published lieraures. The experimenal sysem shown in Fig.1 consiss of pump, hydraulic All righs resered. No par of conens of his paper may be reproduced or ransmied in any form or by any means wihou he wrien permission of TTP, ID , Pennsylania Sae Uniersiy, Uniersiy Park, USA10/03/15,075743)

2 Adanced Maerials Research Vols cylinder, ibraion excier e al. In addiion, an acceleraion ransducer A) is fixed a he boom of pison rod, hree pressure ransducers P) numbered P1, P2 and P3 are disribued along he pipe. Through which, ibraion ampliude and exciaion pressure can be acquired by daa acquisiion card [4]. Fig.1 Schemaic diagram of apparaus Fig.2 Difference grid graph of characerisics Schemaic diagram of experimenal apparaus is shown in Fig.1, where doed line porion is he channel of exciaion pressure generaed aciely. ydraulic cylinder and ibraion excier are locaed in he upsream and downsream respeciely. The new deeloped ibraion excier seres as a check ale openclose rapidly, which is drien by a moor conrolled by frequency conerer. Jus as Fig.1 shows, when he ibraion excier roaes o horizonal posiion, he ale closes in sudden, immediaely he flow elociy of he hydraulic oil close o he ale falls o zero. Consequenly he flow is compressed, leading o he exciaion pressure increase. In he following ime, successie generaed pressure wae will propagae along he pipe a he same way. Only when i reaches hydraulic cylinder in upsream, will he pison be drien o moe upward by pressure wae. Bu once ibraion excier passes by horizonal posiion, he oil will flow back a he role of exernal load and spring, so he pison will be drien o moe downward. Wih he roaing of he ibraion excier, he ale will work alernaely from close o open, generaed pulsaing flow will drie he pison moing up and down, jus like a simple harmonic ibraion. Mahemaical model.based on he Newon s second law and he mass conseraion principle, for onedimensional ransien flow, he basic conrol equaions of waer hammer can be finally deduced and expressed ino wo parial differenial equaions, as Eq.1 and Eq.2 shows [5] 2 c sinα = 0 x g x 1) 1 λ + + ) + = 0 x g x D 2g 2) c= K / ρ 1+ DK / ee 3) Where is pressure head, is ime, is seady flow elociy, c is pressure wae elociy of waer hammer,α is included angle beween pipe axis and horizonal plane,λ is fluid resisance coefficien, D is inernal diameer of pipe, x is posiion coordinaes, g is graiaional acceleraion,k is elasic modulus of fluid, ρ is fluid densiy, e is hickness of pipe wall ande is elasic modulus of pipe. The equaions aboe are firsorder quasilinear hyperbolic parial differenial equaions, which are relaed o wo dependen ariables, and, as funcions of x and.all analyical mehods of waer hammer consider hem as basic equaions, or simplified forms of hem. Bu oward his sysem, for he purpose of reealing is ibraion mechanism, some special boundary condiions

3 2218 Manufacuring Science and Technology, AEMT2011 should be proided. To seek soluion wih he mehod of characerisics, firsly i should be conered ino he characerisic equaions, and hen he equialen ordinary differenial equaions can be worked ou by linear combinaions. Thus is approximae soluion can be calculaed by program based on finie difference equaions. The following are ordinary differenial forms ransformed from parial differenial equaions, as depiced in Eq.4 o Eq.7 below c + dx d d g d +c = + c 4) d d + g λ sin a c + 2D =0 5) c dx d = c 6) d g d c d d g λ sin a c + 2D =0 7) + In essence, Eq.4 o Eq.7 is equal o Eq.1 and Eq.2. The cures labeled c illusraed in Fig.2 correspond o Eq.4 and hose labeled c correspond o Eq.6, which are called characerisic lines. + If Eq.5 and Eq.7 inegrae along cures c and c respeciely, hen he alues of and locaed a he inersecions of he cures a he x, ) coordinaes can be worked ou. Consequenly he characerisic relaions of he parial differenial Eq.1 and Eq.2 can be described by he ordinary differenial Eq.4 o Eq.7, so which is called characerisic equaions. According o calculaion, he pressure wae elociy c is abou 1300m/s, which is obious ha he seady flow elociy is far less han i. So in characerisic equaions can be ignored, ha is why characerisic lines shown in Fig.2 are sraigh lines wih slope of ± c.in Fig.2, he abscissa denoes he spaial sep x, and ime sep is represened by he erical ordinae. Thus, he finie difference mehod was adoped for he discreizaion of he characerisic equaions based on he imespace grid shown in Fig.2 [67].The following Eq.8 o Eq.11 are he corresponding finie + difference equaions along c and c c + xp xa + c) A P g A )=0 g 8) P A a A )+ c P A )+ c sin λ P A )+ 2D A A P A )=0 9) c xp xb c) B P g B )=0 g 10) P B a B ) c P B ) c sin λ P B )+ 2D B B P B )=0 11) In Fig.1, he pipe is diided inon equal pars corresponding o N +1 grid nodes shown in Fig.2,so ime sep as below c + x = c.then hrough he Fig.2, difference Eq.9 and Eq.11 can be ranslaed g g Pi i 1)+ c Pi i 1 )+ c i 1 sina λ x + 2Dc i 1i 1 =0 12)

4 Adanced Maerials Research Vols c g g Pi i+ 1 ) c Pi i+ 1 ) c i+1 λ x sina 2Dc i + 1 i+1 =0 13) Where i =1, 2,, N, corresponding o N nodes shown in Fig.2. Through he discreized difference equaions 12) and 13) aboe, numerical soluions can be obained by programming. Boundary condiions According o he gien schemaic diagram of he hydraulic exciaion sysem shown in Fig.1, he hydraulic cylinder in he upsream can be simplified o a single degree of freedom model F = F sinω under exernal force 0. So i has he same inpu and oupu frequencyω. Through force analysis, if damping is ignored, hen differenial equaions are esablished in Newon's laws shown in Eq.14 and Eq.15 below F0 sinω Qx = m x 14) p 1 = 0 1+ µ sinω ), µ [ 1,1] 15) F Where ampliude of exciaion pressure is 0, ω is angular frequency, m is mass of load, Q is p spring siffness, 1 is exciaion force of hydraulic cylinder and 0 is sysem pressure. As o he downsream, where here is he ibraion excier. The openclose law of he ale is simplified as linear. So is opening aries from 1 o 0, corresponding o full open and full close. Thus, pulsaing flow elociy is described as = 0 1+ µ cosω ), µ [ 1,1] 16) Where 0 is saic flow elociy, is ransien elociy of pulsaing flow. Moreoer, i is obious ha he hydraulic cylinder will ibrae wo periods when he ibraion excier finishes one cycle. Programming and calculaion By VisualBasic6.0 language, a code based on he mehod of characerisics was deeloped, hrough which numerical soluions of difference equaions were obained, reealing ariaion rend of flow elociy along he pipe. Daa can be inpu by ineracie inerface shown in Fig.3a) and numerical soluions of he difference equaions can be obained by program shown in Fig.3b), which are saed as a ex file, followed by sequenial daa processing. a) Inpu form Fig.3 Compuer program prinou b) Oupu form

5 2220 Manufacuring Science and Technology, AEMT2011 Simulaion analysis The same sysem pressure bu differen frequency. By he mehod of characerisics, he flow elociy a he cerain cross secion along he pipe can be calculaed by he deeloped program. For he purpose of reealing hydraulic exciaion mechanism based on waer hammer, he wo main cases should be sudied. One is he same sysem pressure bu differen frequency, he oher is jus he opposie ha is he differen sysem pressure bu same frequency. Of course, he frequency here refers o he se frequency of conerer. For he firs case, he differen frequencies are se as 20z, 35z, 40z and 50z, and he sysem pressure is 3.5MPa, which can be all inpu ino he deeloped program, hen he resuls can be ploed ino cures shown in Fig.4 and Fig.5. Fig.4 shows when he sysem pressure is a consan, he flow elociy a he ibraion excier will rise wih he increasing frequency of conerer, which indicaes ha he ibraion excier, sering as exciaion source, can cause ariaion of he flow elociy. Furhermore, as an acuaor, he flow elociy a he hydraulic cylinder can also change wih ime shown in Fig.5. Fig.4 and Fig.5 show he ariaion of flow elociy where he ibraion excier and he hydraulic cylinder are locaed. Compared wih each oher, i can be seen ha flow elociy a Fig.4 Flow elociy a he ibraion excier Fig.5 Flow elociy a he hydraulic cylinder he ibraion excier is less han ha a he hydraulic cylinder, bu i makes no difference ha he higher se frequency of conerer corresponds o he higher flow elociy under he same sysem pressure. Fig.6 Flow elociy a he ibraion excier Fig.7 Flow elociy a he hydraulic cylinder The same frequency bu differen sysem pressure.fig.6 and Fig.7 show he sysem pressure has no influence on he flow elociy, bu where he ibraion excier are locaed corresponds o he less flow elociy and here is more higher a he hydraulic cylinder. So, for he wo cases aboe, i can be concluded ha he flow elociy in differen cross secions along he pipe will ary wih he frequency of conerer.

6 Adanced Maerials Research Vols Fig.8 The flow elociy a he hydraulic cylinder under differen frequency Fig.8 shows he flow elociy a he hydraulic cylinder is almos linear wih he se frequency of conerer, where he sysem pressure is 3.5MPa and differen se frequency of conerer is 15z, 20z, 25z, 30z, 35z, 40z and 50z. Measured daa hrough experimen Fig.9 shows he measured exciaion pressure a he hydraulic cylinder when sysem pressure is 3.5MPa and frequency of conerer is 32z. Fig.10 shows he measured exciaion pressure a he ibraion excier when sysem is 3MPa bu differen frequencies are 32z, 40z and 50z.Compared beween Fig.9 and Fig.10, i is obious ha he exciaion pressure is higher han he sysem pressure. Bu he exciaion pressure a he ibraion excier increases wih he increasing frequency of conerer. Fig.9 Measured pressure a hydraulic cylinder Fig.10 Measured pressure a ibraion excier Conclusions Numerical simulaion and experimenal analysis on he hydraulic exciaion sysem were carried ou, followed by brief conclusions 1. By mahemaical model based on waer hammer, a hydraulic exciaion sysem was designed. A compuer code based on he mehod of characerisics was deeloped and all parameers can be inpu by a friendly manmachine ineracie inerface, hen oupu resuls were obained by he program. 2. Followed by he deeloped program, numerical simulaions on he flow elociy disribued a differen cross secions were carried ou under differen frequency of conerer. 3. The compuing resuls by program show he flow elociy along he pipe can be adjused almos linearly by frequency conerer. Bu he sysem pressure has no effec on he flow elociy. Moreoer, measured exciaion pressure shows he exciaion pressure is higher han he sysem pressure, and he exciaion pressure a he ibraion excier increases wih he increasing frequency of conerer. Acknowledgemens This work is suppored by he Naional Naural Science Foundaion ). Grea appreciaion also goes o Mine Fluid Conrol Engineering Research Cener of Shanxi Proince and TaiyuanBosch ydraulic Engineering Co. Ld for equipmen suppor.

7 2222 Manufacuring Science and Technology, AEMT2011 References [1] Chuhua Zhang Theoreical Model and Numerical Simulaion of ThreeDimensional Flow Induced Vibraion In Chinese). Journal of Xi an JiaoTong Uniersiy 2007), 415) [2] uizhe Cao, Zhihong e, Zhongyi e The Analyic Research on he Wae Process and Opimal Conrol of Waer ammer in Pipes In Chinese).Engineering Mechanics 2008), 256)2226. [3] A. Misra. K. Behdinan, W.L. Cleghorn Selfexcied ibraion of a conrol ale due o fluid srucure ineracion. Journal of Fluids and Srucures 2002), 165) [4] Ziming Kou, ongzhen Lian Modeling and Moion Simulaion of ydraulic Vibraion SysemIn Chinese). Machine Tool & ydraulics 2009), 3711) [5] Lingxia Yang, Shuhui Li, ec Improemen of fundamenal equaion of waer hammer In Chinese). Shui Li Xue Bao2007), 388) [6] Yudong Sun, Zhongzu Liu, ec Applicaion of MOC o calculaion of fluidsrucural coupling response of piping sysem under impac of waer hammer. Journal of Ship Mechanics 2005), 94) [7] Wenxi Tian, G.. Su, ec Numerical simulaion and opimizaion on aleinduced waer hammer characerisics for parallel pump feed waer sysem. Annals of Nuclear Energy, 2008), 35)

8 Manufacuring Science and Technology, AEMT / Numerical Simulaion and Experimenal Analysis of an Acie ydraulic Exciaion Sysem Based on Pulsaing Flow /