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Electromagnetic Microactuators using Non-spiral Planar Microcoils for Robotic Applications
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Available online at www.sciencedirect.com Procedia Computer Science 00 (2018) 000–000
ScienceDirect
www.elsevier.com/locate/procedia
Procedia Computer Science 133 (2018) 545–552
International Conference on Robotics and Smart Manufacturing (RoSMa2018)
Electromagnetic Microactuators using Non-spiral Planar Microcoils for Robotic Applications Krishnapriya Sa*, Himanshu Chandrakara, Rama S Komaragirib, Suja.K.Ja a
Department of Electronics and Communication, NIT Calicut, Kerala, India
b
Department of Electronics and Communication, Bennett University, Noida, India
Abstract Electromagnetic microactuators offer several advantages for robotic applications such as relatively large stroke and low input voltage requirements. Micro coils are significant components for electromagnetic microactuators for generating force required for micro robots. Non-spiral planar microcoils of square and circular geometries are analyzed here considering the fabrication easiness and low power consumption of non-spiral planar coils. Microfabrication of non-spiral planar coil is simpler and requires a single mask process only. Comparison between non-spiral coils and conventional spiral coils are also discussed. Series resistance of non-spiral coil is found out to be lesser than that of spiral coils though magnetic field is slightly lesser for non-spiral coils. The fabrication advantages and low power dissipation of non-spiral structures make them a strong alternative for conventional spiral planar microcoils. Comparison of different planar microcoils shows that the circular non-spiral coil gives better performance than other coil geometries considered here for robotic applications. Circular coil is found to provide a uniform field with lesser parasitic resistance. Electromagnetic microactuator using non-spiral planar circular and square microcoils are also analyzed to compare the performance between the two coil types. The results show that the force generated using non-spiral circular microcoil in the microactuator is adequate for microrobotic applications with an added advantage of uniform magnetic field provided by the circular coils. © 2018 The Authors. Published by Elsevier Ltd. © 2018 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0/) This is an open access article under thescientific CC BY-NC-ND license Peer-review under responsibility of the committee of the(https://creativecommons.org/licenses/by-nc-nd/4.0/). International Conference on Robotics and Smart Manufacturing. Keywords: Electromagnetic microactuator; Non-spiral planar microcoil; Conventional spiral coils; Series resistance.
1. Introduction Micro actuator is one of the important parts of micro robotic devices constructed using Micro Electro Mechanical Systems (MEMS) technology. Among various kinds of actuators, magnetic microactuators possess the advantage of *Krishnapriya.S; Email:[email protected] 1877-0509© 2018 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0/). 1877-0509 © 2018 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0/) Peer-review under responsibility of the scientific committee of the International Conference on Robotics and Smart Manufacturing. 10.1016/j.procs.2018.07.068
Krishnapriya S et al. / Procedia Computer Science 133 (2018) 545–552 Author name / Procedia Computer Science 00 (2018) 000–000
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being non-contact in nature and large force output compared to other types [1]. Microcoil is the backbone of a magnetic microactuator system. Planar microcoils can reduce the device volume up to ten times or lower compared to non-planar microcoils. Planar microcoils also find applications in various aspects of robotics such as wireless power transfer to sub-millimeter robots, micropumps, robotic switches etc. [2-4]. Electromagnetic fields required for
Fig.1. Schematic of a magnetic mobile microrobot using magnetic fields generated by the microcoils [5].
simultaneous independent actuation of multiple microrobots can also be generated using planar microcoils [5]. Such an arrangement for local magnetic field generation is shown in Fig. 1. Planar microcoils can be divided into spiral and non-spiral coil types [5-6]. In spiral coil, center turn is having contact to the lead outside using a via connection which requires additional metal layer during fabrication as shown in Fig. 2, whereas non-spiral type doesn’t require a via interconnection [5-9]. As the two contact leads are coplanar for a non-spiral coil as shown in Fig. 3, it requires only one metal layer while fabrication. Moreover, non-spiral coils are advantageous with regards to its power consumption as the resistance of non-spiral coils are less than that of its spiral counterpart. Non-spiral coils if compared with spiral coils of same geometry, has much lesser resistance at the cost of a lesser magnetic field. Schematic of conventional spiral microcoils of circular and square geometries are shown in Fig. 2. a
b
Fig. 2. Schematic of conventional spiral planar microcoil of (a) circular geometry (b) square geometry [10]
Schematic of non-spiral planar microcoils of circular and square shapes are shown in Fig. 3. Width of each coil turn is designated as w, and spacing between adjacent coil turns is given by g with r1 and rn being the distance from the coil center to the innermost turn, and the distance to the outermost turn.
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Fig. 3. Schematic of non-spiral planar microcoil (a) circular geometry (b) square geometry
In this work, planar microcoils of circular and square shapes are analyzed and compared to choose an optimum geometry for robotic microactuators. Electromagnetic microactuators using circular and square coils are also examined and the force outputs are compared for performance analysis. Finite element analysis (FEA) performed through COMSOL Multiphysics 5.3a simulation software is resorted to conduct the simulation studies on planar microcoils and actuators. 2. Design of Planar Microcoil Design of planar microcoils includes determining the various geometrical parameters of the coil such as internal diameter (D1), external diameter (D), pitch (p), coil width (b) and height (h) as shown in Fig.4. Main electrical parameters such as coil inductance and series resistance of the coil depend upon the geometrical parameters as shown in equations (1) and (3).
Fig.4. Cross section of a square planar microcoil [5]
Series resistance consists of a frequency dependent part and a frequency independent one. The frequency independent coil resistance can be expressed as shown in equation (1). 𝑅𝑅𝑠𝑠 [Ω] = 𝜌𝜌𝜌𝜌 ⁄ℎ𝑏𝑏
(1)
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where Ɩ is the length of the coil, ρ is the resistivity of metal used, h is the thickness of wire and b being the width of a coil turn. Frequency dependence of resistance occurs due to eddy current which forms due to time varying magnetic field. Moreover increase in frequency leads to skin-effect [11]. Therefore the frequency dependent part can be written as shown in equation (2). 𝑅𝑅 [Ω] = 𝜌𝜌𝐷𝐷2 [(1/ℎ𝑏𝑏) + (1/(2𝛿𝛿(ℎ + 𝑏𝑏)) ][(1 − 𝛼𝛼 2 )/𝑝𝑝]ሺʹሻ where α is the fill factor which is zero if it is a complete filled square, D is the diameter of outermost turn and δ is the skin depth which can be calculated as shown in equation (3)[8-11]. Considering the low frequency robotic applications, this frequency dependent resistance can be neglected as the frequencies used are below 30 kHz [8]. (3)
𝛿𝛿 = √[(2𝜌𝜌 ⁄ 𝜔𝜔𝜔𝜔)]
The self inductance (L) can be defined as flux linkage per unit current on the coil. The self inductance of a planar coil of single turn can be expressed as shown in equation (4) [6, 11] where µ is the permeability of coil conductor.
3. Simulation settings
L [H] = [2𝐷𝐷 ⁄𝜇𝜇𝜇𝜇 ][𝑙𝑙𝑙𝑙(4𝐷𝐷/(𝑏𝑏 + ℎ)) + 0.894((𝑏𝑏 + ℎ)/4𝐷𝐷) − 0.660]
(4)
Planar microcoils can be of spiral and non-spiral in nature. Simulation of both types of coils consisting of 5 turns is performed on COMSOL Multiphysics tool to understand the difference between current and field distribution of spiral and non-spiral types. Excitation current is set to a magnitude of 100 mA. Frequency is set as 10 kHz considering low frequency studies. Geometrical parameters selected for the simulation studies is as shown in Table 1. Thickness of the coil is set to 1 µm to make the coil fabrication process easier using e-beam evaporation for coil metal deposition. Table 1. Geometric settings for the simulation studies of planar microcoil
Coil geometric parameters width spacing thickness Innermost-turn radius Outermost-turn radius
Values (µm) 50 50 1 100 550
Values of the different coil geometrical parameters are chosen so as to generate sufficient force in microactuators designed for robotic applications [5]. 4. Simulation Results of Non-spiral Planar Microcoil Simulation results of a circular planar microcoil of spiral type and non-spiral type is shown in Fig. 5. The results show the difference between magnetic field distributions of spiral and non-spiral coils. Spiral coil has a uniform field distribution all over the turns, whereas in a non-spiral coil, the innermost turn possesses the highest field. As the innermost turns in a non-spiral coil has the least resistance owing to its small length compared to outer turns, majority of the excitation current reaches the inner turns of non-spiral coil. Therefore higher flux density is observed at the inner turns compared to the outer turns in a non-spiral coil as shown in Fig. 5.
Krishnapriya et al. / Procedia Computer Science (2018) 545–552 Author name / SProcedia Computer Science 00 (2018)133 000–000
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Fig. 5. Magnetic flux density distribution in a circular planar microcoil of 5 turns of (a) spiral type (b) non-spiral type
a
b a
Fig. 6. Magnetic flux density distribution in a square planar microcoil of 5 turns of (a) spiral type (b) non-spiral type
Simulation experiments were repeated for square geometry and the results obtained are shown in Fig. 6. An irregular magnetic field distribution is observed especially at the four corners of each coil turn for square microcoil as shown in Fig. 6. Magnitudes of magnetic flux densities in spiral coils are almost twice of that of non-spiral microcoil. This can be due to the parallel configuration of turns in non-spiral coil types which reduce the effective coil inductance and thereby the magnetic flux density values. Comparing various coil field distributions shown in Fig. 5 and Fig. 6, circular geometry is found to possess more uniform distribution in each coil turn than that of square geometry. Square coil shows irregular field distributions especially at the corners of each coil turn. Magnitudes of magnetic field are slightly lesser for square spiral coils compared to circular coils. Square coil cannot be a suitable option for robotic microactuator applications due to the irregularities observed in the magnetic field distribution. Series resistance (R) and inductance (L) of the various coil types are also simulated and results are summarized as shown in Fig. 7. Self inductance of non-spiral coil are lesser than that of spiral coils with the inductance of circular non-spiral coil being the lowest as shown in Fig. 7(a). Figure 7(b) shows the ac series coil resistance of spiral and non-spiral coil types of circular and square geometries. Resistance of non-spiral coils is less than that of spiral coils by 3 times which indicates a significant reduction of coil heating losses and hence low power dissipation
Krishnapriya S et al. / Procedia Computer Science 133 (2018) 545–552 Author name / Procedia Computer Science 00 (2018) 000–000
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in non-spiral coil types. The reduction in coil resistance is achieved due to the short-circuited turns’ configuration in non-spiral microcoils. Circular non-spiral gives the least resistance which is an indication of lower coil heating losses. b
a
Fig. 7. Comparison between various coil types: (a) Self inductance (b) Series resistance
The fabrication easiness and reduction in series resistance indicating low power consumption are the main advantages observed for non-spiral coil types albeit at a small reduction of magnetic field compared to spiral coils. Therefore, the non-spiral coil can be chosen as the primary component in magnetic microactuators for robotic applications. As the circular coil shows more regular field distribution and lesser coil resistance compared to the square geometry, a circular planar non-spiral coil can be a better option for the application concerned. Hence a circular non-spiral planar microcoil can be finalized to realize an electromagnetic microactuator for robotic applications. 5. Simulation Results of Microactuator Using Non-spiral Planar Microcoils Based on the observation from the previous section, a non-spiral planar microcoil is selected for setting up microactuator for robotic applications. An electromagnetic microactuator is set up and finite element analysis is conducted using COMSOL Multiphysics to study the force outputs from the actuator. The actuator consists of a magnet and microcoils separated by a fixed vertical distance. The electromagnetic force generated by the interaction between the magnetic fields of the coil and the magnet enables the movement of a mechanical part attached to the actuator. A quartz membrane is used as the movable mechanical part which is actuated by the electromagnetic force. Soft iron material is used for the magnet which is having a remnant magnetization of 1T. Design of the actuator is done in such a way that the force generated is sufficient for the magnetic microrobotic environment [5, 7]. The geometry details of the actuator are given in Table 2. Table 2. Geometric settings for the simulation studies of the microactuator
Geometric parameters Magnet Thickness Magnet Length Coil Thickness Membrane Thickness Membrane length
Values (µm) 50 500 1 10 900
In this work, Microactuator using non-spiral microcoils of circular and square geometry are studied and compared. Frequency of the order of kHz is chosen to have bidirectional actuation for robotic applications [12-14]. Excitation current of 100 mA at a frequency of 10 kHz is applied at the non-spiral coil terminals and the force and magnetic field outputs at the tip of the membrane are observed. This is repeated for various distances of separation between the coil and the magnet. The actuator schematic is shown in Fig.8.
Krishnapriya S et al. / Procedia Computer Science 133 (2018) 545–552 Author name / Procedia Computer Science 00 (2018) 000–000
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Fig 8. 2D Axisymmetric schematic of the microactuator
Fig.9. Electromagnetic force generated at the membrane Vs vertical distance between the coil and the magnet
Finite element analysis results of the microactuator using circular and square microcoils are compared and shown in Fig.9. Electromagnetic force acting on the thin membrane for various vertical distances between the coil and the magnet is plotted as shown in Fig.9. It was found that smaller the vertical gap between the coil and the magnet, higher is the force acting on the flexible membrane. Electromagnetic force of the order of hundreds of microNewton could be obtained which is sufficient for microscale magnetic robots [5, 15]. Force generated using square non-spiral planar microcoils is found to be slightly higher than the force developed using circular non-spiral microcoils. This is due to the higher value of inductance possessed by the square coil as shown in the results of Fig.7 which leads to a larger magnetic field generation. However, considering the uniform magnetic field provided by circular coil, the circular non-spiral microcoil is found to be the most suitable option for the microactuator.
6. Conclusion In this work, comparison between spiral and non-spiral microcoils of circular and square geometry are presented. Electromagnetic microactuators consisting of circular and square microcoils are also discussed using finite element analysis. Non-spiral coil type is found to be advantageous with regards to fabrication easiness and low power consumption compared to a spiral coil. Non-spiral planar microcoil is suitable for robotic applications with miniaturized device structure as it can produce comparable magnetic field as that of a spiral coil. The circular nonspiral generates magnetic field of the order of milli-Tesla with a reduction of coil series resistance compared to square geometry. Though square coil is found to have higher self inductance than that of circular coil, the square coil’s magnetic field is observed to be irregular at the corners of each coil turn. Also parasitic resistance of square coil is higher than that of circular one. Circular coil eliminates proximity effect and yields a uniform field. Therefore circular non-spiral planar microcoil can be chosen as the optimal structure for microactuators in microscale robotic systems. Electromagnetic force generated using circular and square microcoils are also compared and the force is found to be adequate for microrobotic applications.
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References [1]A.C. Hartley, R.E. Miles, J. Corda, N. Dimitrakopoulos, 2008. Large throw magnetic microactuator, in: Mechatronics 18, pp. 459-465. [2] Hiroyuki Fujita, 1996. Future of actuators and microsystem, in: Sensors and Actuators 56, pp. 105–111. [3] Roer Eka Pawinanto, Jumril Yunas, Burhanuddin Yeop Majlis, 2013. Finite Element Analysis on Magnetic Force Generation of Electromagnetic Microactuator for Micropump, in: RSM2013 Proc. Langkawi, Malaysia. [4] Robert Wood, Ramaswamy Mahadevan, Vijay Dhuler, Bruce Dudley, Allen Cowen, Ed Hill, Karen Markus, 1998. MEMS microrelays, in:Mechatronics 8, pp. 535–547. [5] Chowdhury,S,Jing,W,Cappelleri, D. J, 2015. Towards independent control of multiple magnetic mobile microrobots, in:Micromachines 7(1), 3. [6] Krishnapriya S, Rama S Komaragiri, Suja K J, 2017. Modeling and Simulation of Non-spiral Coil for Magnetic Sensing Applications, in: Journal of Mechanical Science and Technology 31(11), pp. 5415-5421. [7] Krishnapriya S, Rama S Komaragiri, Suja K J, 2017. Performance Analysis of Non-spiral Planar Microcoils for Electromagnetic MEMS Actuator, in: Proceedings of 8th ISSS International conference on smart materials, structures and systems [in press]. [8] Wei Ping Wu, Rong Sheng Lu, Xin Long Zhou, Zhong Hua Ni, 2013. The Nuclear Magnetic Resonance Probe Based on a Printed Circuit Board Planar Microcoil, in: Proceedings of 2013 IEEE International Conference on Applied Superconductivity and Electromagnetic Devices, Beijing, China, October 25-27. [9] Krishnapriya S, Rama S Komaragiri, Suja K J, 2016. Significance of Non-spiral Planar Microcoils over Spiral Coils for Biomedical Applications, in: Proceedings of IEEE International Conference on Emerging Electronics, IIT Bombay, pp.1-4. [10] Pan, M., He, Y., Xie, R., & Zhou, 2014, The influence of MEMS on electromagnetic NDT, in: Non-destructive Evaluation/Testing (FENDT), 2014 IEEE Far East Forum: 363-367 [11] C.R. Neagu, H.V. Jansen, A. Smith, J.G.E. Gardeniers, M.C. Elwenspoek, 1997. Characterization of a planar microcoil for implantable microsystems, in:Sensors and Actuators62, pp.599-611. [12] Krishnapriya S, Rama S Komaragiri, Suja K J, 2017. Non-spiral Planar Microcoils for Biomedical Applications, in: Proceedings of 2017 IEEE International Conference on NEMS, CA, USA, pp.780-783. [13]R. Pawinanto, J. Yunas, B. Majlis, B. Bais, and M. M. Said, 2015. Fabrication and testing of electromagnetic mems microactuator utilizing pcb based planar micro-coil, in: ARPN Journal of Engineering and Applied Sciences10, no. 18, pp. 8399-8403. [14] Roer Eka Pawinanto, Jumril Yunas, Muzalifah Mohd. Said, Mimiwaty Mohd. Noor, Burhanuddin, Yeop Majlis , 2014. Design and Fabrication of PCB Based Planar Micro-coil For Magnetic MEMS Actuator, in: IEEE-ICSE2014 Proc. [15] Bi, C., Guix, M., Johnson, B. V., Jing, W., Cappelleri, D. J, 2018. Design of Microscale Magnetic Tumbling Robots for Locomotion in Multiple Environments and Complex Terrains. In: Micromachines 9(2), 68.
ScienceDirect
Available online at www.sciencedirect.com Procedia Computer Science 00 (2018) 000–000
ScienceDirect
www.elsevier.com/locate/procedia
Procedia Computer Science 133 (2018) 545–552
International Conference on Robotics and Smart Manufacturing (RoSMa2018)
Electromagnetic Microactuators using Non-spiral Planar Microcoils for Robotic Applications Krishnapriya Sa*, Himanshu Chandrakara, Rama S Komaragirib, Suja.K.Ja a
Department of Electronics and Communication, NIT Calicut, Kerala, India
b
Department of Electronics and Communication, Bennett University, Noida, India
Abstract Electromagnetic microactuators offer several advantages for robotic applications such as relatively large stroke and low input voltage requirements. Micro coils are significant components for electromagnetic microactuators for generating force required for micro robots. Non-spiral planar microcoils of square and circular geometries are analyzed here considering the fabrication easiness and low power consumption of non-spiral planar coils. Microfabrication of non-spiral planar coil is simpler and requires a single mask process only. Comparison between non-spiral coils and conventional spiral coils are also discussed. Series resistance of non-spiral coil is found out to be lesser than that of spiral coils though magnetic field is slightly lesser for non-spiral coils. The fabrication advantages and low power dissipation of non-spiral structures make them a strong alternative for conventional spiral planar microcoils. Comparison of different planar microcoils shows that the circular non-spiral coil gives better performance than other coil geometries considered here for robotic applications. Circular coil is found to provide a uniform field with lesser parasitic resistance. Electromagnetic microactuator using non-spiral planar circular and square microcoils are also analyzed to compare the performance between the two coil types. The results show that the force generated using non-spiral circular microcoil in the microactuator is adequate for microrobotic applications with an added advantage of uniform magnetic field provided by the circular coils. © 2018 The Authors. Published by Elsevier Ltd. © 2018 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0/) This is an open access article under thescientific CC BY-NC-ND license Peer-review under responsibility of the committee of the(https://creativecommons.org/licenses/by-nc-nd/4.0/). International Conference on Robotics and Smart Manufacturing. Keywords: Electromagnetic microactuator; Non-spiral planar microcoil; Conventional spiral coils; Series resistance.
1. Introduction Micro actuator is one of the important parts of micro robotic devices constructed using Micro Electro Mechanical Systems (MEMS) technology. Among various kinds of actuators, magnetic microactuators possess the advantage of *Krishnapriya.S; Email:[email protected] 1877-0509© 2018 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0/). 1877-0509 © 2018 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0/) Peer-review under responsibility of the scientific committee of the International Conference on Robotics and Smart Manufacturing. 10.1016/j.procs.2018.07.068
Krishnapriya S et al. / Procedia Computer Science 133 (2018) 545–552 Author name / Procedia Computer Science 00 (2018) 000–000
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being non-contact in nature and large force output compared to other types [1]. Microcoil is the backbone of a magnetic microactuator system. Planar microcoils can reduce the device volume up to ten times or lower compared to non-planar microcoils. Planar microcoils also find applications in various aspects of robotics such as wireless power transfer to sub-millimeter robots, micropumps, robotic switches etc. [2-4]. Electromagnetic fields required for
Fig.1. Schematic of a magnetic mobile microrobot using magnetic fields generated by the microcoils [5].
simultaneous independent actuation of multiple microrobots can also be generated using planar microcoils [5]. Such an arrangement for local magnetic field generation is shown in Fig. 1. Planar microcoils can be divided into spiral and non-spiral coil types [5-6]. In spiral coil, center turn is having contact to the lead outside using a via connection which requires additional metal layer during fabrication as shown in Fig. 2, whereas non-spiral type doesn’t require a via interconnection [5-9]. As the two contact leads are coplanar for a non-spiral coil as shown in Fig. 3, it requires only one metal layer while fabrication. Moreover, non-spiral coils are advantageous with regards to its power consumption as the resistance of non-spiral coils are less than that of its spiral counterpart. Non-spiral coils if compared with spiral coils of same geometry, has much lesser resistance at the cost of a lesser magnetic field. Schematic of conventional spiral microcoils of circular and square geometries are shown in Fig. 2. a
b
Fig. 2. Schematic of conventional spiral planar microcoil of (a) circular geometry (b) square geometry [10]
Schematic of non-spiral planar microcoils of circular and square shapes are shown in Fig. 3. Width of each coil turn is designated as w, and spacing between adjacent coil turns is given by g with r1 and rn being the distance from the coil center to the innermost turn, and the distance to the outermost turn.
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Fig. 3. Schematic of non-spiral planar microcoil (a) circular geometry (b) square geometry
In this work, planar microcoils of circular and square shapes are analyzed and compared to choose an optimum geometry for robotic microactuators. Electromagnetic microactuators using circular and square coils are also examined and the force outputs are compared for performance analysis. Finite element analysis (FEA) performed through COMSOL Multiphysics 5.3a simulation software is resorted to conduct the simulation studies on planar microcoils and actuators. 2. Design of Planar Microcoil Design of planar microcoils includes determining the various geometrical parameters of the coil such as internal diameter (D1), external diameter (D), pitch (p), coil width (b) and height (h) as shown in Fig.4. Main electrical parameters such as coil inductance and series resistance of the coil depend upon the geometrical parameters as shown in equations (1) and (3).
Fig.4. Cross section of a square planar microcoil [5]
Series resistance consists of a frequency dependent part and a frequency independent one. The frequency independent coil resistance can be expressed as shown in equation (1). 𝑅𝑅𝑠𝑠 [Ω] = 𝜌𝜌𝜌𝜌 ⁄ℎ𝑏𝑏
(1)
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where Ɩ is the length of the coil, ρ is the resistivity of metal used, h is the thickness of wire and b being the width of a coil turn. Frequency dependence of resistance occurs due to eddy current which forms due to time varying magnetic field. Moreover increase in frequency leads to skin-effect [11]. Therefore the frequency dependent part can be written as shown in equation (2). 𝑅𝑅 [Ω] = 𝜌𝜌𝐷𝐷2 [(1/ℎ𝑏𝑏) + (1/(2𝛿𝛿(ℎ + 𝑏𝑏)) ][(1 − 𝛼𝛼 2 )/𝑝𝑝]ሺʹሻ where α is the fill factor which is zero if it is a complete filled square, D is the diameter of outermost turn and δ is the skin depth which can be calculated as shown in equation (3)[8-11]. Considering the low frequency robotic applications, this frequency dependent resistance can be neglected as the frequencies used are below 30 kHz [8]. (3)
𝛿𝛿 = √[(2𝜌𝜌 ⁄ 𝜔𝜔𝜔𝜔)]
The self inductance (L) can be defined as flux linkage per unit current on the coil. The self inductance of a planar coil of single turn can be expressed as shown in equation (4) [6, 11] where µ is the permeability of coil conductor.
3. Simulation settings
L [H] = [2𝐷𝐷 ⁄𝜇𝜇𝜇𝜇 ][𝑙𝑙𝑙𝑙(4𝐷𝐷/(𝑏𝑏 + ℎ)) + 0.894((𝑏𝑏 + ℎ)/4𝐷𝐷) − 0.660]
(4)
Planar microcoils can be of spiral and non-spiral in nature. Simulation of both types of coils consisting of 5 turns is performed on COMSOL Multiphysics tool to understand the difference between current and field distribution of spiral and non-spiral types. Excitation current is set to a magnitude of 100 mA. Frequency is set as 10 kHz considering low frequency studies. Geometrical parameters selected for the simulation studies is as shown in Table 1. Thickness of the coil is set to 1 µm to make the coil fabrication process easier using e-beam evaporation for coil metal deposition. Table 1. Geometric settings for the simulation studies of planar microcoil
Coil geometric parameters width spacing thickness Innermost-turn radius Outermost-turn radius
Values (µm) 50 50 1 100 550
Values of the different coil geometrical parameters are chosen so as to generate sufficient force in microactuators designed for robotic applications [5]. 4. Simulation Results of Non-spiral Planar Microcoil Simulation results of a circular planar microcoil of spiral type and non-spiral type is shown in Fig. 5. The results show the difference between magnetic field distributions of spiral and non-spiral coils. Spiral coil has a uniform field distribution all over the turns, whereas in a non-spiral coil, the innermost turn possesses the highest field. As the innermost turns in a non-spiral coil has the least resistance owing to its small length compared to outer turns, majority of the excitation current reaches the inner turns of non-spiral coil. Therefore higher flux density is observed at the inner turns compared to the outer turns in a non-spiral coil as shown in Fig. 5.
Krishnapriya et al. / Procedia Computer Science (2018) 545–552 Author name / SProcedia Computer Science 00 (2018)133 000–000
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Fig. 5. Magnetic flux density distribution in a circular planar microcoil of 5 turns of (a) spiral type (b) non-spiral type
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b a
Fig. 6. Magnetic flux density distribution in a square planar microcoil of 5 turns of (a) spiral type (b) non-spiral type
Simulation experiments were repeated for square geometry and the results obtained are shown in Fig. 6. An irregular magnetic field distribution is observed especially at the four corners of each coil turn for square microcoil as shown in Fig. 6. Magnitudes of magnetic flux densities in spiral coils are almost twice of that of non-spiral microcoil. This can be due to the parallel configuration of turns in non-spiral coil types which reduce the effective coil inductance and thereby the magnetic flux density values. Comparing various coil field distributions shown in Fig. 5 and Fig. 6, circular geometry is found to possess more uniform distribution in each coil turn than that of square geometry. Square coil shows irregular field distributions especially at the corners of each coil turn. Magnitudes of magnetic field are slightly lesser for square spiral coils compared to circular coils. Square coil cannot be a suitable option for robotic microactuator applications due to the irregularities observed in the magnetic field distribution. Series resistance (R) and inductance (L) of the various coil types are also simulated and results are summarized as shown in Fig. 7. Self inductance of non-spiral coil are lesser than that of spiral coils with the inductance of circular non-spiral coil being the lowest as shown in Fig. 7(a). Figure 7(b) shows the ac series coil resistance of spiral and non-spiral coil types of circular and square geometries. Resistance of non-spiral coils is less than that of spiral coils by 3 times which indicates a significant reduction of coil heating losses and hence low power dissipation
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in non-spiral coil types. The reduction in coil resistance is achieved due to the short-circuited turns’ configuration in non-spiral microcoils. Circular non-spiral gives the least resistance which is an indication of lower coil heating losses. b
a
Fig. 7. Comparison between various coil types: (a) Self inductance (b) Series resistance
The fabrication easiness and reduction in series resistance indicating low power consumption are the main advantages observed for non-spiral coil types albeit at a small reduction of magnetic field compared to spiral coils. Therefore, the non-spiral coil can be chosen as the primary component in magnetic microactuators for robotic applications. As the circular coil shows more regular field distribution and lesser coil resistance compared to the square geometry, a circular planar non-spiral coil can be a better option for the application concerned. Hence a circular non-spiral planar microcoil can be finalized to realize an electromagnetic microactuator for robotic applications. 5. Simulation Results of Microactuator Using Non-spiral Planar Microcoils Based on the observation from the previous section, a non-spiral planar microcoil is selected for setting up microactuator for robotic applications. An electromagnetic microactuator is set up and finite element analysis is conducted using COMSOL Multiphysics to study the force outputs from the actuator. The actuator consists of a magnet and microcoils separated by a fixed vertical distance. The electromagnetic force generated by the interaction between the magnetic fields of the coil and the magnet enables the movement of a mechanical part attached to the actuator. A quartz membrane is used as the movable mechanical part which is actuated by the electromagnetic force. Soft iron material is used for the magnet which is having a remnant magnetization of 1T. Design of the actuator is done in such a way that the force generated is sufficient for the magnetic microrobotic environment [5, 7]. The geometry details of the actuator are given in Table 2. Table 2. Geometric settings for the simulation studies of the microactuator
Geometric parameters Magnet Thickness Magnet Length Coil Thickness Membrane Thickness Membrane length
Values (µm) 50 500 1 10 900
In this work, Microactuator using non-spiral microcoils of circular and square geometry are studied and compared. Frequency of the order of kHz is chosen to have bidirectional actuation for robotic applications [12-14]. Excitation current of 100 mA at a frequency of 10 kHz is applied at the non-spiral coil terminals and the force and magnetic field outputs at the tip of the membrane are observed. This is repeated for various distances of separation between the coil and the magnet. The actuator schematic is shown in Fig.8.
Krishnapriya S et al. / Procedia Computer Science 133 (2018) 545–552 Author name / Procedia Computer Science 00 (2018) 000–000
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Fig 8. 2D Axisymmetric schematic of the microactuator
Fig.9. Electromagnetic force generated at the membrane Vs vertical distance between the coil and the magnet
Finite element analysis results of the microactuator using circular and square microcoils are compared and shown in Fig.9. Electromagnetic force acting on the thin membrane for various vertical distances between the coil and the magnet is plotted as shown in Fig.9. It was found that smaller the vertical gap between the coil and the magnet, higher is the force acting on the flexible membrane. Electromagnetic force of the order of hundreds of microNewton could be obtained which is sufficient for microscale magnetic robots [5, 15]. Force generated using square non-spiral planar microcoils is found to be slightly higher than the force developed using circular non-spiral microcoils. This is due to the higher value of inductance possessed by the square coil as shown in the results of Fig.7 which leads to a larger magnetic field generation. However, considering the uniform magnetic field provided by circular coil, the circular non-spiral microcoil is found to be the most suitable option for the microactuator.
6. Conclusion In this work, comparison between spiral and non-spiral microcoils of circular and square geometry are presented. Electromagnetic microactuators consisting of circular and square microcoils are also discussed using finite element analysis. Non-spiral coil type is found to be advantageous with regards to fabrication easiness and low power consumption compared to a spiral coil. Non-spiral planar microcoil is suitable for robotic applications with miniaturized device structure as it can produce comparable magnetic field as that of a spiral coil. The circular nonspiral generates magnetic field of the order of milli-Tesla with a reduction of coil series resistance compared to square geometry. Though square coil is found to have higher self inductance than that of circular coil, the square coil’s magnetic field is observed to be irregular at the corners of each coil turn. Also parasitic resistance of square coil is higher than that of circular one. Circular coil eliminates proximity effect and yields a uniform field. Therefore circular non-spiral planar microcoil can be chosen as the optimal structure for microactuators in microscale robotic systems. Electromagnetic force generated using circular and square microcoils are also compared and the force is found to be adequate for microrobotic applications.
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Krishnapriya S et al. / Procedia Computer Science 133 (2018) 545–552 Author name / Procedia Computer Science 00 (2018) 000–000
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