3rd International Conference on Mechatronics and Inforation Technology (ICMIT 16) Research and Experients on Electroagnetic Field Induced by Two Coaxial Solenoid Coils of Axially Mag-lev Driving Needle Yang Liua, Xiaoguang Wub, Chi Zhang, Daoyu Wan, Li Zhu school of Mechanical Engineering and autoation, Wuhan Textile University, Wuhan, Hubei 4373, China Eail: aaliceliu93@yeah,net, b6wist@163.co Keywords: Two solenoid coils, Axially ag-lev, Knitting Needle, Electroagnetic field Abstract: The oveent of ag-lev driving needle depends on the interaction of agnetic fields between two solenoid coils and agnet. Inside single cylinder, two solenoid coils are placed vertically and coaxially while the agnet is laid at the botto of the needle base. Based on agnetic-levitation theory and Biot-Savart Law, this paper taking into account the ipacts of utual inductance caused by double coils analyzed and coputed agnetic force when these two coaxial coils were separated into different air-gap heights. By using Gauss eter to easure the agnetic field induced by two coils, we attains that the easuring data accords well with coputing results. Besides, the electroagnetic-peranent driving odel has been built through electroagnetic coupling odule in ANSYS, and through FEM siulation, the curve of electroagnetic force exerted on the agnet as the air-gap height was achieved, and the agnetic field distribution ap of this odel was also attained. Introduction Aong ag-lev devices, whatever radial levitation or axial levitation, it s essential to precisely understand the interrelations of agnetic force between agnetic objects. The coupling proble of electroagnetic fields has recently been one of the research focuses both at hoe and abroad, and such relevant studies can be seen in power electronic syste as study on coupling echanis of transission line syste and agnetic field, study on coupling property of electro agnetis of MRF (Magnetorheological fluid) daper, and agnetic analysis of electroagnetic syste for AC contactor, etc. According to reference[1], by use of Newan forula and coplete elliptic integral, it derived the atheatical forula to calculate agnetic force between two parallel-placed rings which are coaxial and have the sae radius. This paper applied the conclusion presented in reference[1] into two coaxial and equivalent solenoid coils, analyzed and calculated the electroagnetic force existing between the, verified the results through nuerical calculation and practical experients, and finally siulated the agnetic field distribution affected by the coils and agnet by eans of finite-eleent siulation. Magnetic field distribution of single electrified coil on its axis When a piece of etal wire was powered on, it generally will produce a kind of circular agnetic field around itself and the principles is, the larger the current, the ore intensified the agnetic field, and the direction of which can be deterined by Apere s spiral rule of right hand. In the sae anner, after curling the original electrified wire into hollow cylindrical coil around a fixed axis, the direction of agnetic field induced by a single-turn coil can also be ascertained through 16. The authors - Published by Atlantis Press 586
the sae rule[]. Thus, the total agnetic field on the axis of the solenoid coil can be seen as the result of superposition on agnetic fields of N single coil. According to Biot-Savart Law, supposing there is a coil of radius a and it is electrified with current I, the agnetic induction intensity of any point on the axis distancing fro the coil center x is Ia B = µ. (1) ( a + x ) 3/ Based on Eq.1, integrating along the axial path of the coil, the agnetic induction intensity of any point P on the axis of solenoid coil is given. B ' l µ Ir ndx µ nir x, () = db = = 1/ ( r + x ) 3/ r ( r + x ) therein, I is coil current, r is coil radius, n is the nuber of turns of coil per unit length, l 1 and l are the distances fro the point to the two ends of the coil, µ is pereability of vacuu. l1 Electroagnetic force induced by two solenoid coils Nuerical calculation and experients. Fro Eq. it can be seen that, agnetic field intensity caused by single coil decreases very quickly near the two ends of the coil. So in order to strengthen agnetic field on the axis of the coil, two solenoid coils need to be in vertically coaxial arrangeent[3], this way, due to the effects of utual inductance produced by the upper and lower coils, both agnetic fields will be superposed. When exerted the sae current on the, the upper and lower coils will generate agnetic fields of the sae direction. With the assist of repulsion and attraction induced by these two solenoid coils, there would be a superposition on the agnetic fields, which can also strengthen the agnetic field on their axis. When two equal and coaxial circular current loops are separated fro each other with distance h in air, their electroagnetic interacting force can be calculated by therein, r k =, K ( k ) = h + 4r ' I1I h 1+ k F = µ [ K ( k) E( k)], (3) ' 4r + h k π / dx 1 k sin π /, E( k) = (1 k sin x) dx x Matlab nuerical calculation. According to Eq.3, with the application of Matlab nuerical research ethod and substitution of practical values of paraeters, the electroagnetic interacting force F induced by two solenoid coils when they are separated within different distances h has been worked out, and its fitting curve can be seen in Fig 1. Fig 1. Calculating results 587
In Fig 1, the negative values of F indicate agnetic attractions between two solenoid coils ( when both coils were electrified with currents of the sae direction and value ). It can be seen that F induced by these two coils diinishes as the distance h between the increases. When distance h goes to infinity, the agnetic interaction between these two coils tends to zero, that is, there is alost no agnetic distraction between the agnetic fields caused by two coils. However, when distance h gradually reduced to a situation in which the two coils reach contact, the electroagnetic force will go up very high, which indicates an intense agnetic interaction. Experiental data. Applying equal but reverse current to two solenoid coils, the experiental voltage is +1V, electric resistance is 38Ω, the length of single coil is a fixed value, L=16, the nuber of coil turns n is approxiate to 15. The experient uses the CH36 three channels Gauss eter to easure agnetic field on the axis of two solenoid coils. In this experient, the Gauss eter probe whose pereability can be up to thousands high need to be put into these two vertical coils, with the help of highly agnetic sensibility of the probe, it can easily get the accurate values of agnetic field at any point in the field. Based on that, we read the data on the Gauss eter each.5 along the axis of the coils. Respectively easuring the agnetic induction intensity for different air-gap heights, Table 1 has been achieved, which shows the agnetic distribution at the center of the axis of the coils when they are at different air-gap heights. Table1 Experiental data for different air-gap heights h() 1 3 4 5 6 7 8 9 1 B(T) 15.39 14.4 11.74 9.635 7.75 6.94 5.97 5.11 3.93 3.61 Fitting curve of Table 1 can be easily got in Matlab, Fig shows the variation trend of agnetic induction intensity with the air-gap heights. Fig. Fitting curve of experiental data Copared Fig 1 with Fig, it can be seen in Fig 1 that the agnetic induction intensity B at the idpoint of the axis reduces as the air-gap height h increases. Because the weaker the agnetic field, the saller its agnetic force, just as in Fig, when distance h reaches zero, the agnetic attraction between two coils tends to be infinite, but as h increases, F decreases rapidly, approxiate to zero. Thus, it shows that theoretical calculation accords with experiental results. ANSYS electroagnetic siulation and analysis Electroagnetic-peranent agnets FEM odel. The software package of ANSYS Multi-physics supports agnetic-structural analysis, it can be used to deterine the agnetic force iposed on electric conductors or agnetic aterial, and the resulting structural deforation. It has 588
wide applications such as coputing agnetostatic and transient-agnetic force, structural deforation and stress, so that to understand their influences on structure design. Because dual-coil driving needle odel belongs to axisyetric eleent[4], using half of the single needle cylinder to build FEM odel could be a proper way to do the siulation in ANSYS. According to design paraeters of the agnet and solenoid coils, the FEM odels of agnet suspended at different air-gap heights were established, and therefore, the force exerted on the agnet by electroagnetic field can be respectively siulated and analyzed. One of the odels that describes the situation of height h=4 is presented in Fig 3. Fig 3(a). Geoetric odel Fig 3(b). Meshing Fig3. Analytical odel Siulation results. The siulation results can be seen in Fig 4 and Table. Fig 4(a) presents the distribution ap of agnetic lines when the agnetic field induced by two solenoid coils were interfered with other agnetic fields produced by agnet and the lower iron bar. It can be observed that the agnetic field of the iron bar settled in the center of the lower coil interferes with the original agnetic lines ore than that of the agnet did, there are only a few agnetic lines passing through the agnet. Fig 4(b) presents the axonoetric ap of nodal agnetic induction density B. It can also be observed that the agnetic fluid density B approxiate to the iron bar inside the lower coil is uch stronger than that of the agnet which is settled between two coaxial coils. Fig 4(c) and Fig 4(d) display the fitting curves of siulation results. Fig 4(a). Magnetic lines of h=3 Fig 4(b). Magnetic fluid density B 589
Fig 4(c). Curve F V vs h Fig 4(d). Curve F M vs h Fig 4. Siulation results Table Magnetic force exerted on agnet h() 1 3 4 5 6 Fv(N) -.13* 1^- FM(N) -.148* 1^- -.95* -.39* -.838* -.638*.38* 1^-6 -.793* 1^-6.87*.613*.96*.193*.13* 1^-.147* therein, F V represents the force was calculated based on virtual work principle, while F M is the force calculated through MAXWELL equations. 1^- Conclusions In conclusion, this paper applies the coputing principle used to deterine the agnetic force induced by two electric loops into analyze two coaxial solenoid coils driving needle odel, to exaine its electroagnetic properties. (1).The consistency between theoretically nuerical calculating and experiental data validates the accuracy and reliability of the analytical ode. ().The distribution ap of agnetic fluid density and the results of agnetic force exerted on agnet attained by FEM siulation offer iportant design basis and theoretical support for control optiis and structure design of two-coil drive and axially ag-lev needle device. Acknowledgeents The authors acknowledge the financial support fro the Natural Science Foundation of China (51175384 and 513539) and Natural Science Foundation of Hubei Province (14CFA99). References [1] Sihua Zhu, Wanin Yang, Journal of College Physics, 4(1)(5)4-31. [] You Xu, Electroagnetis(П), Science Press, Beijing, PRC(4). [3] Zhicheng Guan, Huafeng, Su, Zhidong Jia, Journal of High Voltage Engineering, 35(11) (9) 735-74. [4] Renxi Hu, Xiuhui Zhang, ANSYS14 self-study anual for analysis of therodynaics, electroagnetis and coupling fields, Posts and Telecounications Press, Beijing, PRC(13). 59