Study on the Calculation of Magnetic Force Based on the Equivalent Magnetic Charge Method

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1 Avilble online t Physics Procedi 4 () 9 97 Interntionl Conference on Applied Physics nd Industril Engineering Study on the Clcultion of Mgnetic Force Bsed on the Equivlent Mgnetic Chrge Method Jingng Li,,Qingchng Tn,Yongqi Zhng,Kuo Zhng College of Technology, Ynbin University, Ynji Chin College of Mechnicl Science nd Engineering,, Jilin University, Chngchun Chin Abstrct Mgnetic drivers hve been used widely in the phrmceuticl, chemicl, petroleum, food nd other industries with its perfect seling without contct. Common method of clculting of the mgnetic force re the Mxwell equtions, empiricl formuls, nd he equivlent mgnetic chrge method s well. The Mxwell equtions method is the most complicted nd the empiricl formuls method is the simplest with low ccurcy. The equivlent mgnetic chrge method is simpler thn the Mxwell equtions method nd more ccurte thn the empiricl formuls method. In this pper, the mgnetic force of the mgnetic driver of reciprocte in line is clculted with the equivlent mgnetic chrge method nd ws compred with the experiment. Published by Elsevier by Elsevier B.V. Ltd. Selection Selection nd/or nd/or peer-review peer-review under responsibility under responsibility of ICAPIE of Orgniztion [nme orgnizer] Committee. Open ccess under CC BY-NC-ND license. Keywords: Mgnetic driver; equivlent mgnetic chrge; mgnetic sleeve; fitting curve. Introduction The mgnetic drive is new trnsfer technology of non-contct force or torque using mgnetic force of permnent mgnet mterils or electromgnetic bsed on the theory of modern mgnetic. The device to chieve this technology clled mgnetic driver or mgnetic coupling. The mgnetic drive chieves the trnsmission of force nd torque using the feture of mgnetic field goes through the work spce or the thin distnce sleeve which is different from the mechnicl drive. Such s mgnetic drive pump or gittor, chnges dynmic sel to sttic sel through bolishing trditionl contct sels fter dopts the sel device of mgnetic drive. It elimintes the lekge of shft sel fundmentlly, so the run, drip, lek nd mechnicl sel het, wer of industril pumps, cldron nd other equipment is solved. It cretes fvorble conditions to trnsport of mixing of toxic, flmmble, explosive nd corrosive mterils sfely nd relibly []. The mgnetic driver of reciprocte in line is kind of mchine to trnsfer the motor s rottion to reciprocting motion in line []. It is very complicted to clculte the mgnetic force. Equivlent mgnetic Published by Elsevier B.V. Selection nd/or peer-review under responsibility of ICAPIE Orgniztion Committee. Open ccess under CC BY-NC-ND license. doi:.6/j.phpro...9

2 Jingng Li et l. / Physics Procedi 4 () chrge method is n effective wy for clcultion of mgnetic force. Tn Qingchng etc. hve done some effective work in this re [3][4]. Using Mtlb softwre, this pper clcultes mgnetic force of the mgnetic driver of reciprocte in line in detil nd derives chrcteristic curve between the xis mgnetic force nd the reltive displcement of inner mgnetic sleeve nd outer mgnetic sleeve. At lst, the result of clcultion is compred with the experiment.. Model of mgnetic force The mgnetic force s clcultion model of mgnetic driver of reciprocte in line is shown in Fig.. Mgnetiztion direction of outer mgnetic sleeve 3 4 R 4 3 y R 3 R y z Mgnetiztion direction of inner mgnetic sleeve R o o x + shown s positive mgnetic chrge - shown s negtive mgnetic chrge Figure. The clcultion model of mgnetic force Becuse of the xil symmetry of inner nd outer mgnetic sleeves, the rdil mgnetic force is zero. Therefore, this pper only studies the xis mgnetic force. In ccordnce with the theory of equivlent mgnetic chrge, the xis mgnetic force between inner nd outer mgnetic sleeves cn be expressed s [] Where A is given by: B B r r A R R4 F AArrdrdrdd R R3 Br is the residul mgnetic flux density of inner mgnetic sleeve, r density of outer mgnetic sleeve, is spce permebility which is defined s A is expressed s A, A A ( ) A ( ) A is expressed s A r sin r sin r cos r cos. B is the residul mgnetic flux 7 4 N/A, 3. Clcultion of mgnetic force It needs to solve fourfold integrl for clcultion of mgnetic force. With the id of Mtlb softwre, this pper clcultes the mgnetic force. Becuse of there is only up to triple integrl for solving equtions

3 9 Jingng Li et l. / Physics Procedi 4 () 9 97 in Mtlb, this pper nlyzes eqution () bsed on the principle of differentil clculus, reduces eqution () to triple integrl then clcultes the mgnetic force with the use of Mtlb. This pper prtitions surfces nd (shown s fig.) into n equl prts long the dr direction, so r R ( i )dr, i n. i According to eqution (), when the reltive displcement between inner nd outer mgnetic sleeves (shown s ) is constnt numericl vlue, there is dr dr, so the mgnetic force (shown s F i ) between the i th differentil surfce nd the outer mgnetic sleeve cn be expressed s triple integrl: R4 F Ardr Ardrdd () i i R3 Where r r R ( i )dr in A i. y R d r Figure. Digrm of the differentition R o r i x According to reference [], B B.98 KGs 34 mm, R 5 mm, R 39.4 mm, r r R 45.4 mm, R 8 mm. Mgnetic force F 3 4 i cn be clculted with the commnd of triplequd, Mtlb procedure is s follows: zzi inline(' A ri * d r * r* A',' ',' ',' r'); Fi triplequd( zzi,,*pi,,*pi, R3, R4); Therefore, when the reltive displcement between inner nd outer mgnetic sleeves is constnt numericl vlue, the mgnetic force between inner nd outer mgnetic sleeves cn be expressed s follow: F F F... F F (3) n i i n According to eqution (3), this pper hs clculted mgnetic force of the mgnetic driver for different, shown s Fig.3. It cn be seen in Fig.3 tht the reltionship between xis force F nd, shown s follow: F when. Forwrd long the positive x direction, F is incresing rpidly with the increse of. Axis force F up to the mximum 97 N when. 7 mm. Then F decresed rpidly with the increse of, F when 64. mm. Forwrd long the negtive x direction, the lw of F nd is quite the opposite to the positive x direction.

4 Jingng Li et l. / Physics Procedi 4 () Axil mgnetic force/n Reltive displcement between inner nd outer mgnetic sleeves /mm Figure 3. Performnce curve of reltive displcement between inner nd outer mgnetic sleeves nd xil force 4. Mgnetic force s fitting of the mgnetic driver Axis force is more big in the intervl [-5, +5] thn others, shown s the performnce curve in Fig.3. Otherwise, xis force is very smll in the intervl (-, -5] nd [+5, +). Axis force is symmetricl bout the origin of coordintes, so the fitting intervl of xis force cn be selected in (+5]. This pper obtins fitting curve through fourth-order fitting on xis force using Mtlb commnd of polyfit, the fitting eqution is: 4 3 Ff = (4) The fitting curve of xis force is shown s Fig.4. Axis force/n Theoreticl vlue Clculted vlue Figure 4. Performnce curve of reltive displcement between inner nd outer mgnetic sleeves nd xil force Fitting error nlysis is shown in Tble. It cn be seen tht the xil force fitting errors 46. % in the intervl (, +4]. The reltive displcement between inner nd outer mgnetic sleeves should be controlled in the intervl [-, +] in order to get stble working stte for the mgnetic driver of reciprocte in line. The xil force showing good liner chrcter nd the fitting errors re less thn %, so the fitting result is perfect. TABLE THE FITTING ERRORS OF AXIS FORCE Items The reltive displcement between inner nd outer mgnetic sleeves /mm Theoreticl xis force F /N The reltive displcement between inner nd outer mgnetic sleeves/mm

5 94 Jingng Li et l. / Physics Procedi 4 () 9 97 Fitting xis force F /N f Fitting errors.9%.%.9%.3%.6% 3.%.8% 4.6% 5. Experiments A double-cting hydrulic cylinder is used to provide the lod. The test tble is shown in Fig.5 (), the structure digrm is show in Fig.5 (b) (b) Structure digrm of the test tble. Double-cting hydrulic cylinder. Restrictive vlve 3. Pull pressure sensor 4. distnce sleeve 5. inner mgnetic sleeve 6. outer mgnetic sleeve 7. Slider-crnk mechnism 8. Pin wheel Cycloid motor 9. Displcement sensor. Bridge box Figure 5. Photo nd structure digrm of test tble 5 6 S N N S () Photo of the test tble N S S N 7 DH5937/8 Dynmic Acquisition System 8 Mitsubishi Frequency Converter Computer 5. Sttic experiment Sttic experiment is pplying lod while the mgnetic driver is rest, then strt mgnetic driver t certin frequency nd mesure the mximum sttic lod when outer mgnetic sleeve prts from the inner. The results re shown in Fig.6, The sttic mgnetic crrying cpcity of the driver (xil force) into liner decrese with the strt frequency increses. 5. Dynmic experiment The crnk rdius is 6 mm, the frequency rnge of Mitsubishi Frequency Converter is limited from to 5 Hz (Becuse of serious crwling t low speed nd lrge vibrtion t high speed, ccording to the working condition of the test tble, so the frequency is limited), the opening of the restrictive vlve is controlled to keep full open or hlf open. Chrcteristic of displcement nd xis force between inner nd outer mgnetic sleeves t different frequency is shown in Fig.7. It cn be seen tht the reltionship between

6 Jingng Li et l. / Physics Procedi 4 () Experimentl vlues Fitting line Axis Force/N Strt frequency/hz Figure 6. Sttic lod chrcteristic of the mgnetic driver Axis force/n Reltive displcement between inner nd outer mgnetic sleeves/mm Figure 7. Chrcteristic of displcement nd xis force between inner nd outer mgnetic sleeves t different frequency Axis force/n Restrictive vlve is hlf open Restrictive vlve is full open Reltive displcement between inner nd outer mgnetic sleeves/mm Figure 8. Chrcteristic of displcement nd xis force between inner nd outer mgnetic sleeves t different openning of restrictive vlve reltive displcement nd xis force is independent of the frequency.

7 96 Jingng Li et l. / Physics Procedi 4 () 9 97 Chrcteristic of displcement nd xis force between inner nd outer mgnetic sleeves t different open of restrictive vlve is shown in Fig.8. It cn be seen tht the reltionship between xis force nd reltive displcement hs nothing to do with the opening of restrictive vlve Axis force/n Experimentl vlues Theoreticl curve Reltive displcement between inner nd outer mgnetic sleeves/mm Figure 9. Comprison of theoreticl nd experimentl Fig.9 shows the comprison of theoreticl nd experimentl. It cn be seen tht the experimentl vlues nd theoreticl curve re consistent with the trend, but there is some discrepncy, minly due to the following points: Friction between the inner mgnetic sleeve nd the distnce sleeve. Although the theoreticl clcultion considers no rdil mgnetic force on the ssumption tht the xes of inner nd outer sleeves hve common xis, but in the mnufcturing, instlltion process hve inevitbly resulted in different xes, or xis devition hs occurred, resulting in some of the rdil mgnetic force which leding to incresed friction. Permnent mgnet demgnetiztion. The residul mgnetic flux density B r used in theoreticl clcultion is the fctory clibrtion vlue. Due to demgnetiztion chrcteristic of permnent mgnet, so the residul mgnetic flux density should be less thn the fctory clibrtion vlues. Eddy current losses. It will produce induced current if the distnce sleeve is cut by the lternting mgnetic field, nd the energy will turn into het. This will cuse eddy current heting to the mgnetic driver nd decrese its efficient, the energy trnsforms into lot of het which cn probbly cuse the distnce sleeve overheting, mgnetic sleeves demgnetiztion or other filure [5][6]. Other resons which cn decrese the efficiency of the mgnetic driver, including temperture, electromgnetic fields in the surrounding, etc. Conclusions In this pper, the method to clculte the xis force of mgnetic driver of reciprocte in line is studied, nd some experiments is done. The conclusions re s follows: Using equivlent mgnetic chrge theory to clculte the mgnetic force of mgnetic driver of reciprocte in line is very effective. In certin rnge of the reltive displcement between inner nd outer sleeves, mgnetic force cn be reduced to simpler clcultion model, shown s eqution (4). The reltionship between the reltive displcement of inner nd outer mgnetic sleeves nd xis force re independent of the frequency nd the opening of restrictive vlve.

8 Jingng Li et l. / Physics Procedi 4 () References [] [] [3] [4] [5] [6] Zhng Suolong. STRUCTURE IMPROVEMENT OF MAGNETIC ACTUATION DEVICE FOR KETTLEPETRO- CHEMICAL EQUIPMENT TECHNOLOGY. 999, (5), pp.7-8. ZHAO Guoto, TAN Qingchng, LI Wei. MAGNETIC FORCE TRANSMISSION TECHNOLOGY OF RECIPROCATE IN LINE. CHINESE JOURNAL OF MECHANICAL ENGINEERING. 7, 43(), pp.-4. Tn Qingchng, Meng Huiqin, Xiu shicho. AN INVESTIGATION ON THE DIRECTIONS OF MAGNETIZATION OF PERMANENT-MAGNET BEARINGS. ACTA ARMAMENTARII. 993, 5(), PP Tn Qingchng, Xin Di, Li Wei. Study on trnsmitting torque nd synchronism of mgnet couplings. Journl of Mechnicl Engineering Science. 99, 6(), PP LI Zhipeng, LIU Xu. Energy Loss Anlysis nd Design Study of Mgnetic Pump. MECHANICAL AND ELECTRICAL EQUIPMENT. (), pp.8-3. FENG Zhongming, CHEN Cundong. Clcultion nlysis of turbulence loss in mgnetic pump & its ppliction. Generl Mchinery. 5(4), pp

Studies on Nuclear Fuel Rod Thermal Performance

Studies on Nuclear Fuel Rod Thermal Performance Avilble online t www.sciencedirect.com Energy Procedi 1 (1) 1 17 Studies on Nucler Fuel od herml Performnce Eskndri, M.1; Bvndi, A ; Mihndoost, A3* 1 Deprtment of Physics, Islmic Azd University, Shirz