Mathematical Optimization of a Magnetic Ruler Layout with Rotated Pole Boundaries

Marzena Fügenschuh (), Armin Fügenschuh, Marina Ludszuweit, Aleksandar Mojsic and Joanna Sokół
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Marzena Fügenschuh: Beuth University of Applied Sciences Berlin
Armin Fügenschuh: Helmut Schmidt University of the Federal Armed Forces Hamburg
Marina Ludszuweit: Helmut Schmidt University of the Federal Armed Forces Hamburg
Aleksandar Mojsic: Helmut Schmidt University of the Federal Armed Forces Hamburg
Joanna Sokół: Helmut Schmidt University of the Federal Armed Forces Hamburg

A chapter in Operations Research Proceedings 2015, 2017, pp 117-123 from Springer

Abstract: Abstract Magnetic rulers for measuring systems are either based on incremental or absolute measuring methods. Incremental methods need to initialize a measurement cycle at a reference point. From there, the position is determined by counting increments of a periodic graduation. Absolute methods do not need reference points, since the position can be read directly from the ruler. In the state of the art approach the absolute position on the ruler is encoded using two tracks with different graduation. To use only one track for position encoding in absolute measuring a pattern of trapezoidal magnetic areas is considered instead of the common rectangular ones. We present a mixed integer programming model for an optimal placement of the trapezoidal magnetic areas to obtain the longest possible ruler under constraints conditioned by production techniques, physical limits as well as mathematical approximation of the magnetic field.

Keywords: Mathematical Approximation; Mixed Integer Programming Model; Parallel Side; Cumulate Length; Reading Head (search for similar items in EconPapers)
Date: 2017
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Persistent link: https://EconPapers.repec.org/RePEc:spr:oprchp:978-3-319-42902-1_16

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DOI: 10.1007/978-3-319-42902-1_16

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