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Unformatted text preview: 1/12/2006 Copyright 2003 S.D. Sudhoff Page 1 5/ Force and Torque In previous chapters, we have concentrated on predicting the electrical aspects of electromagnetic device performance. In this chapter, we consider the production of electromagnetic force and torque. We will consider two approaches to this subject. The first approach will be energy based. Using this approach, given the relationship between flux linkage, current, and position, an algorithm will be set forth to find a corresponding expression for electromagnetic force / torque. The second approach considered will be field based. In this approach, which is geometry-dependent, we will utilize the Lorenz force equation to obtain an expression for torque for a certain class of rotating electromechanical devices. 5.1 AN ENERGY APPROACH TO FORCE AND TORQUE In this section, an energy based approach to the calculation of force and torque is set forth. In this approach, it is assumed that the relationship between current, flux linkage, and position, i.e. the device flux linkage equation, is known. From this information, a method to derive an expression for force will be set forth. The same method can readily be used to calculate torque. 5.1.1 Magnetic System Description In order to use the methods set forth in this section, the relationship between flux linkage, current, and mechanical position must be known. It will be assumed herein that this relationship can be expressed in one of two forms. In the first form, the flux linkage may be expressed ) , ( x f i λ λ = (5.1-1) where i , λ , and x represent current, flux linkage, and position, respectively. For multi-input systems we have that ) , ( x λ f i λ = (5.1-2) where the bold font indicates a vector (and flux linkage and current have the same dimension). In (5.1-1) and (5.1-2), () λ f is a suitable nonlinear function. The ‘ λ ’ subscript is a reminder that the first argument is flux linkage. The second form of flux linkage equation is used considerably more often than the first and is expressed ) , ( x i f i = λ (5.1-3) 1/12/2006 Copyright 2003 S.D. Sudhoff Page 2 for single-input systems, or, for multi-input systems, ) , ( x i i f λ = (5.1-4) In this case, the ‘ i ’ subscript serves as a reminder that the first argument is a current. 5.1.2 Field Energy Let us now consider an electromechanical device. In general, any such device will involve a magnetic field. The energy stored in this magnetic field will be referred to as the field energy and denoted f W . Energy that is stored in the magnetic field has two possible sources – the electrical system or the mechanical system. The energy entering the stored field from the electrical system is denoted e W ; energy entering the stored field from the mechanical system is denoted m W ....
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This note was uploaded on 09/22/2011 for the course ECE 321 taught by Professor Staff during the Spring '08 term at Purdue.
- Spring '08