Electromagnet Gripping in Iron Foundry Automation Part II: Simulation

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1 238 Electromagnet Gripping in Iron Founry Automation Part II: Simulation Rhythm-Suren Wahwa Department of Prouction an Quality Engineering, NTNU Tronheim, 7051, Norway Abstract This paper compares the simulation an initial experimental results for robust part hanling by raially symmetric cylinrical electromagnetic gripper heas, that are use in founry manufacturing assembly operation. Knowlege of the irect holing force is essential to etermine if a given electromagnet is capable of preventing part slipping uring pick an place operation. Energy base moel an the magnetic circuit moel have been escribe. The latter is evelope further an compare with results from a FEA software. It was foun that the magnetic circuit moel, although simple in form, was limite in its ability to accurately preict the holing force over the entire range of conitions investigate. The shortcomings in the moel were attribute to its inability to accurately moel the leakage flux an non-uniform istribution of the magnetic flux. A finite element allowe for the ability to couple the mechanical an magnetic moels. The finite element moel was use to preict the magnetic fiel base off the solutions to the mechanical ( ) an the magnetic moel ( B ). Keywors: Founry Automation, Hanling Electromagnet Design 1. Introuction Robot grippers are use to position an retain parts in an automate assembly operation. Electromagnet grippers offer simple compact construction with no moving parts, uncomplicate energy supply, flexibility in holing complex parts an reuce number of set-ups, an are thus suitable to ferrous metalcaste parts. However, their use is limite to ferrous materials (Iron, Nickel, Cobalt), electromagnet size is irectly epenant on require prehension force; resiual magnetism in the part when hanle when using DC supplies requires the aitional of a emagnetizing operation to the manufacturing process. Smart materials, commonly classifie accoring to their energy transuction moe as piezo-electrics, shape memory alloys, an magnetostrictives, have been shown to be useful in low banwith application, an micro gripping applications,but they still have limitations in a high volume manufacturing environment [1]. An electromagnet consists of at least one pair of north an south magnetic poles that are separate by an airgap. In this way, there is practically no magnetic fiel present when a current flows through the coil, because air presents a very high reluctance to the magnetic flux. When a part is place on the surface of the electromagnet in such a way that it connects a north an south pole, the magnetic flux can be establishe, given that the part is mae of a ferromagnetic material. The magnetic flux will prouce a force of attraction between the part an the electromagent, as mentione in the previous section. Two parts mae of the same material an having the same geometry an imensions coul experience a ifferent force of attraction on a given electromagnet if the contact conitions between the workpiece an the electromagnet are ifferent for the two of them. Of one of the parts has a rougher surface or has a larger flatness error, the contact interface will have larger airgaps that have to be transverse by the magnetic flux in orer to complete the magnetic circuit. The users of electromagnets in iron founries know that factors such as material harness, surface contact conitions, an electromagnet esign influence the holing force. Most of the available literature in founry automation is of a commercial nature [2,3,4]. The author believes that a preictive moel for etermining the holing force will enable the esign of the optimum operating geometry an/or conitions to prevent part slip uring robot hanling/assembly. Consequently, the nee for costly an time intensive experimentation will be minimize. This paper compares the results from the magnetic circuit moel an energy moel with available commercial software COMSOL 4.0,for a cylinrical raially symmetrical electromagnet. 2. Moeling Electromagnetic Behavior Several energy base moels have been create in an attmept to capture the non-linear behaviour or electromagents. Moeling techniques bu Dapino et. al [5] inclue a thermoynamic approach for estimating magnetization to fiel. Aitional moeling techniques have been reporte by Sablik an Jiles [6], where internal energy minimization is use to ensure mechanical

2 239 equilibrium. Analytical methos have also been epevlope, but mainly for preicting magnetostrictive performance [7]. When analyzing complex geometries finite element metho generally gives more accurate results. The inustrial set-up for the experiments was escribe in [1], an the following sections, the energy base moel, magnetic circuit moel an the FEA moel use to simulate experimental ata are explaine. As a basis for comparison, the analytical metho for calculating magnetization factor for cylinrical electromagnets is compare to FEA preictions where the effect of airgaps an varying current through the electromagnet coil on the holing force is investigate. Comsol Multiphysics 4.0 magentostatics (with currents) is the finite element moel was use in the research. To etermine the magentization effect via FEA approach the external fiel is calculate by etermining the magnetic fiel at a point of interest in space at a certain istance from the magnet, in the absence of the sample part. The magnetization factor was calculate for several aspect ratios, where the thickness of the sample always remaine 2-inches. The airgap was varie to change the aspect ratio, an the effect of electromagnet coil heating over a perio of 20 minutes (~robot assembly cycle time) was observe. 3. Magnetic Fiel Distributions This section analyzes ifferent basic electromagnet setups an their effects on the magnetic properties of a system. Magnetic fiel istributions will be use for each setup to emphasize key ifferences between ifferent esigns. As a basis for comparison, the analytical metho for calculating the magnetization factor of a cylinrical core is compare to FEA preictions,where the effect of aspect ratio on magnetization is investigate. A COMSOL Multiphysics 4.0 magnetostatic (with currents) finite element moel was create with a geometry consisting of a rectangular core immerse in a coil, surroune by an air omain with imensions of three times the largest imension of the ro an coil (Figure 1). Figure 1: COMSOL Magentostatics (with currents) geometric ro coil setup. Equation 1 gives a general expression for etermining the effective magnetic fiel within a sample, with a known value of N (magnetization factor) [7]. Since calculation of the effective magnetic fiel ( H ) requires a knowlege of eff N (geometry epenent), the magnetic fiel within the sample is normally ifficult to calculate (especially for complicate geometries). H eff H ext H H ext N M (1) Ellipsoial geometries have been shown to have a relatively constant magnetic fiel istribution, leaing to one value of magnetization factor for the entire geometry. An analytical expression for calculating the emagnetization factor as a function of a imensional ratio (k) was evelope by [8] (Equation 2). The imensional ratio, k, is etermine by iviing the length of the semimajor axis by the semiminor axis. It was esire to simulate the magnetic fiel behavior along the raius an length of the ro. A 2D axisymmetric, magnetostatics (with currents) moel was utilize. The ro was place at the r = 0 location an was surroune by a coil. The ro an coil setup is surroune by an air omain (μr = 1) with imensions that are three times the length of the coil, which is the largest component of the circuit. A current ensity of 3e6 A/m2 was assigne to the geometry corresponing to the coil. A relative permeability of 50 was assigne to the ro for the experiment. Figure 2 shows a 2D axisymmetric streamline of the magnetic fiel when the magnetic sample (μr = 50) is place insie the coil. It is evient that ue to the emagnetization effect, the magnetic fiel leaks throughout the length of the ro (i.e., some streamlines fail to travel the full istance of the sample). However, if a magnetic circuit is incorporate into the esign of the transucer, then the flux leakage can be rastically reuce. In Figure 3, a steel flux return path is ae to the same setup as in Figure 2, with μr = 2000 for the steel. The use of a well efine magnetic circuit will allow for the full use of the material capabilities, as there is negligible fiel lost ue to flux leakage. (2) Ros having a raius of 0.25-inches were analyze for aspect ratios of 1, 2, an 4 (0.5, 1, an 2-inch long ros respectively). The magnetic ro is assume to have a

3 240 constant permeability of 50. The steel flux return path iscusse in the secon case has a permeability of The current ensity use here is 3e6 A/m2 for all cases. First, the magnetic fiel istribution was stuie for the no steel flux return case. The raial magnetic fiel istribution (at the mi-height of the ro) was stuie for the no steel flux return case, for cylinrical ros with aspect ratios of 1, 2, an 4, an all with raii of inches. The magnetic fiel ata for each aspect ratio was non-imensionalize accoring to its maximum magnetic fiel value. The raial position was also nonimensionalize (i.e., max fiel is one, an outer raius position is one). their centerline to the outer raius. Aitionally, it is evient that the magnetic fiel increases from the center of the ro an reaches a maximum at the en of the ro for all aspect ratio cases. It shoul also be note that the relationships shown in Figure 4 are parabolic. This parabolic magnetic fiel behavior plays a key role in the element type that is chosen for the mesh. Figure 4: Nonimensional raial magnetic fiel verses non imensional position for a ro an coil setup with varying aspect ratios. The ashe lines show ros with ifferent imensions that yiel the same imensions as the ros shown in the soli lines. All ata is normalize to its respective maximum magnetic fiel. Figure 2: 2D axisymmetric view of magentic fiel streamlines showing lines of flux leakage resulting from ro an coil setup. Figure 3: 2D axisymmetric view of magentic fiel streamlines showing flux leakage for ro an coil with steel flux return path. Figure 4 shows the non-imensional results for the three ifferent aspect ratios. There are two sets of ata shown for each aspect ratio. The ashe lines correspon to ros with length an with of half the sample shown by the re lines. Using these imensions gives the same aspect ratio. It is evient that the non-imensional magnetic fiel istribution oes not vary for ros of the same aspect ratio. It is important to note that this is only true when comparing magnetic fiel istributions of the same shape. Also, these istributions are unique to the specific coil esign an applie current ensity. Further, Figure 4 shows that lower aspect ratio samples experience a larger amount of non-imensional magnetic fiel leakage from Next, the magnetic fiel istribution along the length of the ro was stuie for the no steel flux return case, for cylinrical ros with aspect ratios of 1, 2, an 4, an all with raii of 0.25-inches. Again, the magnetic fiel ata for each aspect ratio was non-imensionalize accoring to its maximum value. The magnetic fiel behaviour escribe in the aboe two cases is summarize in Table 1. As the aspect ratio is increase, the percentage ifference between the maximum an minimum magnetic fiel through ifferent locations along the raial span ecreases. On the contrary, the percentage ifference between maximum an minimum magnetic fiel along the length increases for samples with higher aspect ratio ratios. Differences in magnetic fiel of 80.9% were seen along the length of a 2-inch, 0.25-inch iameter sample. Table 1. Percentage ifference of magnetic fiel along raius an length of cylinrical samples with raii of 0.25-inches an lengths of 0.5, 1, an 2-inches (aspect ratio ratios of 1, 2, an 4) for ro an coil setup. The raial magnetic fiel istribution (at the mi-height of the ro) was stuie for the steel flux return case, for the same cases as one for the no steel flux return path stuies. It was clear that the presence of the steel flux return path increases the magnetic fiel within the sample, as well as

4 241 creates a more uniform istribution of magnetic fiel. Table 2 summarizes the magnetic fiel behavior. It can be observe that as the aspect ratio increases, the percentage ifference between the maximum an minimum magnetic fiel through the raial span ecreases. In contrast, the percentage ifference between maximum an minimum magnetic fiel along the length increases for samples with higher aspect ratios. Differences in magnetic fiel of 6.5% were seen along the length of a 2-inch, 0.25-inch iameter sample. However, in comparison to Table 1, the steel flux return path eliminates a large amount of the flux leakage leaing to small percentage ifferences in magnetic fiel along the raius an length of the sample. Where is the flux linkage, which is equal to the magnetic flux ( ) in the system times the number of turns in the coil ( N ) generating the magnetic fiel. It can be seen from Eq. (4) that the store energy in the magnetic fiel, an thus the mechanical force, is a function of the magnetic flux (or flux ensity) present in the system. Thus, the available force for a specific evice with a given MMF is etermine by the reluctance of the evice. Magnetic Circuit Moel The magnetic circuit approach is an analytical metho, analogous to electric circuit analysis, for moeling electromagnetic evices [9,10]. Cherry et al. in a classic paper [11], emonstrate the uality between electric an magnetic circuits. The below Magnetic circuit moel was erive in [1]. Table 2. Percentage ifference of magnetic fiel along raius an length of cylinrical samples with raii of 0.25-inches an lengths of 0.5, 1, an 2-inches (aspect ratios of 1, 2, an 4) for ro, coil, an steel flux return path. It was clear that the spatial variation of magnetic fiel varies greatly with the setup. The above parametric stuy suggeste that it is important to inclue a flux return path. It was also foun that it is esirable to use samples of lower aspect ratio, as the percentage change in magnetic fiel is much smaller for lower aspect ratio samples. Seeing these, the magnetic circuit was moele before experimentation. 4. Magnetic Moels Energy Base Moel In the magnetic fiel, the energy associate with the system is istribute throughout the space occupie by the fiel. Assuming no losses, the energy store in the system per unit volume when increasing the flux ensity from zero to B is: Wf B HB 0 From this expression, a relation for the mechanical force can be obtaine by the metho of energy or coenergy. These two methos are erive from the principle of conservation of energy an are very well ocumente in the literature such as Sen 1989, Fitzgeral The expression for the force obtaine with the energy metho is: (3) Figure 5: Equivalent Magnetic Circuit of the Magnet-Part System The results from the above magnetic circuit moel were compare with COMSOL FEA moel escribe below. COMSOL FEA Moel The magnetic moel was create using a 2D axisymmetric magnetostatics (with currents) moule. The air omain was assigne the imensions of with an length equal to three times the maximum imension of the electromagnet. The air an aluminum parts were assigne a μr = 1, steel casing a μr = 2000, an the center ro was assigne a variable permeability via μr(b,σ). The magnetic fiel is assigne via a current ensity which has units of current per unit area. The air omain with normal mesh use for this stuy of a 2D axisymeetric ro an coil setup is shown in Figure 6 there is a traeoff between computational efficiency an moel accuracy, as a finer mesh normally requires more memory an computational time, but generally gives a more accurate solution. W F 2 m B A x cons tan t 0. (4)

5 242 Experimental ata was recore for ifferent magnetic fiel intensities with varying electromagnet aspect ratios an solenoi currents. The preicte results were within 10% accuracy with the FEA moel, when compare to the experiments. Figure 6: COMSOL moel of normal meash moel for raially symmetric electromagnet. When assigning a mesh to a geometry, one must also efine what is known as a shape function. A shape function linear, quaratic or cubic- efines the relationship between a particular variable. Pian an Lee [12] have shown that the conventional elements such as 3-noe triangular an 4-noe quarilateral elements will lea a stiffness matrix with all infinite values. The inability of these elements to give accurate results when ealing with incompressible problems shoul be consiere when selecting a mesh type. The magnetic problem iscusse in this research involves the magnetic form of Gauss s Equation, which employs an incompressibilty conition. Consiering this, the use of conventional 3-noe triangular an 4-noe quarilateral elements when solving magnetostatics problems was avoie. Other important bounary conitions inclue axial symmetry an continuity. Axial symmetry is efine for 2D axisymmetric moels at r = 0, an assumes a symmetric conition such that the properties of the system o not vary azimuthally.the continuity bounary conition enforces continuity of the tangential components of the magnetic fiel via: n x (H2 H1) = 0. This bounary conition is use at the junction of two ifferent subomains with ifferent magnetic properties. Figure 7: COMSOL moel of temperature graient for raially symmetric electromagnet. Figure 8: COMSOL moel of surface temperature for raially symmetric electromagnet. Figure 9: COMSOL moel of magnetic flux ensity for raially symmetric electromagnet. 5. Conclusions an Future Work It was shown that a steel flux return path greatly reuces the raial an longituinal variations of fiel. The part texture attributes (surface roughness an texture) affect the holing forces of an electromagnet gripper. Upcoming effort in this area will present the effect of these attributes on normal an tangential holing forces, an etails of the experiemental analysis. 6. References [1] Wahwa, R.S., Lien,T. Electromagnet Gripping in Iron Founry Automation Part I: Principles an Framework, IJCSI, Vol 6, Issue 6, Nov 2011

6 243 [2] Robust Prehension for ferrous metalcaste prouct families, Proceeings of MITIP 2011 [3] Anonymous, New shelf robot saves vital space in the founry environment, The Inustrial Robot. Befor: Vol. 33, Iss. 2; p. 145 [4] Anonymous, The Castings Center selects STRIM, Eucli, an Prelue Software, The Inustrial Robot. Befor: Vol. 23, Iss. 6; p. 6 [5] Wetzel, S. GM s Iron Finishing Automation, Moern Casting, 2008; 98,1 ABI/INFORM Complete pg.38 [5] P. G. Evans, M. J. Dapino, an J. B. Restorff, "Bill Armstrong memorial symposium: free energy moel for magnetization an magnetostriction in stresse Galfenol alloys," in Proceeings of SPIE, Behavior an Mechanics of Multifunctional an Composite Materials, San Diego, CA, 2007, p. p [6] M. J. Sablik an D. C. Jiles, "Couple Magnetoelastic Theory of Magnetic an Magnetostrictive Hysteresis," Ieee Transactions on Magnetics, vol. 29,no. 4, pp , Jul [7] J. Atulasimha, "Characterization an Moeling of the Magnetomechanical Behavior of Iron-Gallium Alloys," Ph Dissertation Department of Aerospace Engineering, MD, [8] S. Chikazumi, Physics of Magnetism: John Wiley an Sons, Inc., [9] Hoole, S.R, Computer Aie Analysis an Design of Electromagnetic Devices, 1989 [10] Law, J.D., Moeling of Fiel Regulate Reluctance Machines, PhD Thesis, University of Wisconsin- Maison,1991 [11] Cherry, E.C.: The uality between interlinke electric an magnetic circuits an the formation of transformer equivalent circuits, Proc. Phys. Soc., 1949, 62, p.101 [12] T. H. H. Pian an S. W. Lee, "Finite-Elements for Nearly Incompressible Materials," Aiaa Journal, vol. 14, no. 6, pp , Acknowlegments Financial support from the AutoCast Consortium an the Norwegian Research Council is gratefully acknowlege. First Author Rhythm Suren Wahwa is a PhD stuent at the epartment of prouction an quality engineering, NTNU. She has worke in the Manufacturing Automation inustry for five years. Current research interests inclue assembly automation, optimization techniques, assembly simulation an inustrial robotics. She was the presient of Society of Women Engineers at the University of Michigan. She has a Masters Degree in Mechanical Engineering from University of Michigan, an Bachelors egree in Manufacturing Processes Automation Engineering.