Chapter 3. Mathematical Model of Electromagnetic Brakes 3.1. Introduction

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Abstract	Precise mathematical models of the brakes are important for the purpose of simulation and control. In this chapter we review different models available for electromagnetic brakes and propose a new model which has better performance in least-squares sense. The electromagnetic brake is a relatively primitive mechanism, yet it employs complex electromagnetic and thermal phenomena. As a result, the calculation of brake torque is a complex task. Both empirical and analytical approaches have been applied. To explain the magnetic function of an electromagnetic retarder, the Maxwell principles may be applied to the following physical arrangement: a ferro-magnetic disc with a permeability, µ , and an electric conductivity, ρ , rotates at the face of a ring of magnetic poles of alternate polarity. Each pole produces a magnetic excitation flux, N 0 , which is proportional to the excitation current within the coil as long as the core is not saturated. The lines of magnetic flux, N, form loops within the disc through the very small air gap which is arranged between the discs and the poles. When the disc rotates, as a first approximation, this flux varies in a sinusoidal function of time at a given point within the disc according to the following expression:
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