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Design and Optimization of a Lorentz-Force-Driven Planar Motor

He Zhang, Baoquan Kou

2016
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Applied Sciences
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This paper describes a short-stroke Lorentz-force-driven planar motor which can realize three-degree-of-freedom motions in high-precision positioning systems. It is an extended version of our previous publication. Based on the analytical model, the force expression concerning the main dimensional parameters is derived. Compared with the finite element simulation, the optimization method in this paper is completely based on the mathematical model, which saves considerable time and has clear
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... and has clear physical meaning. The effect of the main parameters on the motor performances such as force, force density, and acceleration are analyzed. This information can provide important design references for researchers. Finally, one prototype is tested. The testing values for the resistance and inductance of the square coil agree well with the analytical values. Additionally, the measured forces show a good agreement with the analytical force expression, and the force characteristics show a good symmetry in the x and y directions. structure. Therefore, it has broad application prospects in 2-D positioning systems, especially in the high precision applications. According to the working principle, planar motors can be divided into four types, which are reluctance-type planar motor, induction-type planar motor, synchronous-type planar motor, and Lorentz-force-driven planar motor. A planar stepping motor belongs to reluctance-type motors and it is the earliest planar motor [12, 13] . A planar stepping motor is comprised of two linear stepping motors. The movers of the two linear stepping motors are integrated into one moving part in mutually perpendicular directions. The stator is a 2-D tooth-slot array. The advantages of the planar stepping motor are no accumulated error and simple structure, but the low frequency oscillation, losing steps, and low speed limit its range of applications. A switched reluctance planar motor is another type of reluctance-type motor, which was proposed by Pan et al. [14, 15] . The stator is composed of several blocks, each of which is made of silicon steel sheets instead of solid iron. Therefore, the eddy current effect and the processing cost is reduced. In 1999, Fujii et al. [16] proposed a planar induction motor. The primary is an iron ring winded with windings, and the secondary is a magnetic plate. This motor can achieve not only the long-stroke planar motion, but also the rotary motion. However, there are some disadvantages, such as its complex manufacturing process, low air-gap magnetic flux density, and low operating speed. The 2-D electromagnetic force of the synchronous-type planar motor is from the interaction between a permanent magnet array and coil array. In recent years, this type of planar motors was deeply researched, and many novel topologies were put forward. The earliest synchronous planar motor was proposed by Kim [17], in which there are four groups of linear synchronous units. Each unit can be seen as a slotless linear motor which is composed of a 1-D Halbach magnet array and three-phase windings. In 2002, Cho et al. [18] proposed a new synchronous planar motor, which is composed of a 2-D permanent-magnet array and four 1-D coil arrays. The performances of several 2-D permanent-magnet arrays are compared with each other. In 2007, a novel moving-magnet synchronous planar motor was proposed by Jansen et al. [19] . The motor consists of a 2-D permanent-magnet array and a 2-D coil array. In the 2-D coil array, there are two groups of track-shape coils which are orthogonal and arranged in turn. Obviously, this moving-magnet topology has no moving cables and the heat from a coil array can be easily reduced by adopting cooling solutions. The above three types of motors are long-stroke planar motors, in which the moving range is usually hundreds of millimeters. However, high-accuracy performance at a millimeter level is often required in many applications. In this case, the Lorentz-force-driven planar motor [20] [21] [22] is the best solution due to the inherent features of unlimited resolution, high linearity, no force-ripple, etc. Actually, it is more often the case that high accuracy and long stroke are both required in some systems [23, 24] . Therefore, the coarse-fine scheme is usually adopted, in which the Lorentz-force-driven planar motor is located on top of the system in order to achieve the precision compensation. The Lorentz-force-driven planar motor needs to be well designed and optimized to simplify the system-level structure and improve the integral dynamic performance, because it lies on the top of the positioning system. Compared with the long-stroke motors at the bottom, the optimization work for the short-stroke motors can do more contributions to the improvement of system performance. At present, the finite element method is usually used in most of the studies in the established literature concerning the design and optimization for planar motors. Obviously, it is a time-consuming method to analyze the planar motors that cannot be completely described by a 2-D finite element model. In this study, we describe a short-stroke Lorentz-force-driven planar motor. The analytical model containing the air-gap magnetic field, inductance and force expression is built. Based on the model, the main design parameters are determined and the specific influences of the main parameters on motor performances are analyzed. Three important indexes (i.e., the force, force density, and acceleration) are optimized and the reasonable values for the dimensional parameters are concluded. Compared with [1], the main dimensions' equation is transformed to the force equation in this paper, which is more important for motor optimization. Additionally, the analytical expressions for the force density and acceleration are derived, and the corresponding variation curves are given, which are very important references for this type of motor. Finally, based on the optimization results, reasonable Appl. Sci. 2017, 7, 7 3 of 14 ranges for the main parameters are given, which can balance the force, the force density, and the acceleration for the proposed planar motor. Structure and Working Principle The proposed short-stroke Lorentz-force-driven planar motor, shown in Figure 1 , has a moving-magnet scheme, in which the magnet part is the mover (secondary) and the coil part is the stator (primary). The primary is composed of an array of coils, and the secondary is composed of permanent magnets and two back-irons. The four square coils in the primary are controlled by four separate controllers. Compared with round-shaped coils, the effective edges of the square coils in the magnetic field can be fully used, which increases the force level. Actually, the proposed planar motor is combined by four Lorentz-force-driven units. The motor can realize three-degree-of-freedom motion through controlling the current combination of the four driving units. As shown in Figure 2 , the Lorentz-force-driven unit consists of three parts: upper magnets, lower magnets, and one square coil. The double-sided structure is adopted to increase the air-gap magnetic field. Appl. Sci. 2017, 7, 7 3 of 15 very important references for this type of motor. Finally, based on the optimization results, reasonable ranges for the main parameters are given, which can balance the force, the force density, and the acceleration for the proposed planar motor. Structure and Working Principle The proposed short-stroke Lorentz-force-driven planar motor, shown in Figure 1 , has a movingmagnet scheme, in which the magnet part is the mover (secondary) and the coil part is the stator (primary). The primary is composed of an array of coils, and the secondary is composed of permanent magnets and two back-irons. The four square coils in the primary are controlled by four separate controllers. Compared with round-shaped coils, the effective edges of the square coils in the magnetic field can be fully used, which increases the force level. Actually, the proposed planar motor is combined by four Lorentz-force-driven units. The motor can realize three-degree-of-freedom motion through controlling the current combination of the four driving units. As shown in Figure 2 , the Lorentz-force-driven unit consists of three parts: upper magnets, lower magnets, and one square coil. The double-sided structure is adopted to increase the air-gap magnetic field.

doi:10.3390/app7010007
fatcat:6ulp22td7zbjxcei2xsylnmfuu