Abstract-Multiple sets of solutions for the selective harmonic elimination pulse-width modulation method for inverter control exist. These sets present an independent solution to the same problem but further investigation reveals that certain sets may offer an improved overall harmonic performance. In this paper, a minimization method is discussed as a way to obtain these multiple sets of switching angles. A simple distortion harmonic factor that takes into account the first two most significant harmonics present in the generated waveform is considered in order to evaluate the performance of each set. The bipolar waveform is thoroughly analyzed and two cases are considered; single-phase patterns which eliminate all odd harmonics and three-phase counterparts which eliminate only the nontriplen odd harmonics from the line-to-neutral pattern but such harmonics are naturally eliminated from the line-to-line waveform. Experimental results support the theoretical considerations reported in the paper. Index Terms-Selective harmonic elimination pulse-width modulation (SHEPWM).

A five-level symmetrically defined multilevel selective harmonic elimination pulsewidth modulation (MSHE-PWM) strategy is reported in this paper. It is mathematically expressed using Fourier-based equations on a line-to-neutral basis. An equal number of switching transitions when compared against the well-known multicarrier phase-shifted sinusoidal PWM (MPS-SPWM) technique is investigated. For this paper, it is assumed that the four triangular carriers of the MPS-SPWM method have nine per unit frequency resulting in seventeen switching transitions for every quarter period. For the proposed MSHE-PWM method, this allows control of sixteen harmonics and the fundamental. It is confirmed that the proposed MSHE-PWM offers significantly higher converter bandwidth in the standard range of the modulation indices. Moreover, when the bandwidth is reduced to be equal with the one offered with the MPS-PWM, the modulation index can be increased resulting in a higher gain and at a reduced switching frequency overall. Selected solutions for the switching transitions are presented and verified experimentally in order to confirm the effectiveness of the proposed technique. Index Terms-Multilevel Converter, optimization, phase-shifted sinusoidal pulsewidth modulation (PS-PWM), pulsewidth modulation (PWM), selective harmonic elimination (SHE).

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Milling is today the most effective, productive and flexiblemanufacturing method for machining complicated or sculptured surfaces. Ball-end tools are used for machining 3D freeform surfaces for dies, moulds, and various parts, such as aerospace components, etc. Milling data, such as surface topomorphy, surface roughness, non-deformed chip dimensions, cutting force components and dynamic cutting behaviour, are very helpful, especially if they can be accurately produced by means of a simulation program. This paper presents a novel simulation model, the so-called MSN-Milling Software Needle program, which is able to determine the surface produced and the resulting surface roughness, for ball-end milling. The model simulates precisely the tool kinematics and considers the effect of the cutting geometry on the resulting roughness. The accuracy of the simulation model has been thoroughly verified, with the aid of a wide variety of cutting experiments. Many roughness measurements were carried out on workpieces, which were cut using a 5-axis machining centre. The calculated roughness levels were found to be in agreement with the experimental ones. The proposed model has proved to be suitable for determining optimal cutting conditions, when finishing complex surfaces. The software can be easily integrated into various CAD-CAM systems.

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