We present a general mesh-free description of the magnetic field distribution in various electromagnetic machines, actuators, and devices. Our method is based on transfer relations and Fourier theory, which gives the magnetic field solution for a wide class of twodimensional (2-D) boundary value problems. This technique can be applied to rotary, linear, and tubular permanent-magnet actuators, either with a slotless or slotted armature. In addition to permanent-magnet machines, this technique can be applied to any 2-D geometry with the restriction that the geometry should consist of rectangular regions. The method obtains the electromagnetic field distribution by solving the Laplace and Poisson equations for every region, together with a set of boundary conditions. Here, we compare the method with finite-element analyses for various examples and show its applicability to a wide class of geometries.

For applications demanding a high torque density and high speed capability, the flux switching permanent magnet machine is an excellent candidate. However, the double salient structure and nonlinear behavior increases the challenge to model the magnetic field distribution and torque output. To date, only the magnetic equivalent circuit (MEC) is employed to model the magnetic field in an analytical manner. However, the MEC method suffers from a coarse discretization and the need for a relative complex adjustment when rotor movement or a parametric sweep is considered. Therefore this paper discusses an alternative technique based on the harmonic or Fourier model which solves these difficulties.Index Terms-Boundary value problem, flux switching, Fourier analysis, permanent magnet machine.

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This paper describes the effects of changing the magnet shape of permanent magnets (PMs) in a Halbach array applied in a slotless tubular actuator. More specifically, the square shaped magnets are replaced by trapezoidal shaped magnets. A semi-analytical magnetic field solution of regular square shaped magnets is presented and used to approximate the airgap field produced by the trapezoidal shaped PMs. The method is based on dividing the magnets into several radial layers and superposition of the fields to calculate the total magnetic field. The results are compared to finite element analysis (FEA) and show excellent agreement. Using this magnetic field solution, the effect of the shape of the magnets on the magnetic field waveform is analyzed by means of a parametric search.

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Abstract-This paper presents the modeling and the experimental verification of a tubular actuator for a pick and place application. To increase the throughput of a placement robot for printed circuit boards, very fast linear motion is required. A moving magnet tubular actuator with axially magnetized magnets is selected. Using a semi-analytical magnetic field description coupled to thermal models, a design is created that potentially could achieve a translator acceleration of 20 g. A prototype of the designed actuator is built and coupled with a Simulink dSpace system to perform extensive measurements to validate the models and investigate the achievable acceleration within a predetermined motion profile. The electro-motive force is measured, and the disturbance forces are identified. The position error is measured during the motion profile with an acceleration of 20 g and a stroke of 30 mm. Furthermore, thermal measurements are performed to check the achievable duty cycle. The built design shows good agreement with the models, and the specified acceleration of 20 g is achieved.

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