Note for Electrical Machines 1 - EM1 By JNTU Heroes

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LECTURE NOTES ON ELECTRICAL MACHINES-I II B. Tech I semester (JNTU)

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UNIT I Principles of Electromechanical Energy Conversion Topics to cover: 1) Introduction 4) Force and Torque Calculation from 2) EMF in Electromechanical Systems 3) Force and Torque on a Conductor Energy and Coenergy 5) Model of Electromechanical Systems Introduction For energy conversion between electrical and mechanical forms, electromechanical devices are developed. In general, electromechanical energy conversion devices can be divided into three categories: (1) Transducers (for measurement and control) These devices transform the signals of different forms. Examples are microphones, pickups, and speakers. (2) Force producing devices (linear motion devices) These type of devices produce forces mostly for linear motion drives, such as relays, solenoids (linear actuators), and electromagnets. (3) Continuous energy conversion equipment These devices operate in rotating mode. A device would be known as a generator if it convert mechanical energy into electrical energy, or as a motor if it does the other way around (from electrical to mechanical). Since the permeability of ferromagnetic materials are much larger than the permittivity of dielectric materials, it is more advantageous to use electromagnetic field as the medium for electromechanical energy conversion. As illustrated in the following diagram, an electromechanical system consists of an electrical subsystem (electric circuits such as windings), a magnetic subsystem (magnetic field in the magnetic cores and airgaps), and a mechanical subsystem (mechanically movable parts such as a plunger in a linear actuator and a rotor in a rotating electrical machine). Voltages and currents are used to describe the

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Principle of Electromechanical Energy Conversion state of the electrical subsystem and they are governed by the basic circuital laws: Ohm's law, KCL and KVL. The state of the mechanical subsystem can be described in terms of positions, velocities, and accelerations, and is governed by the Newton's laws. The magnetic subsystem or magnetic field fits between the electrical and mechanical subsystems and acting as a "ferry" in energy transform and conversion. The field quantities such as magnetic flux, flux density, and field strength, are governed by the Maxwell's equations. When coupled with an electric circuit, the magnetic flux interacting with the current in the circuit would produce a force or torque on a mechanically movable part. On the other hand, the movement of the moving part will could variation of the magnetic flux linking the electric circuit and induce an electromotive force (emf) in the circuit. The product of the torque and speed (the mechanical power) equals the active component of the product of the emf and current. Therefore, the electrical energy and the mechanical energy are inter-converted via the magnetic field. Concept map of electromechanical system modeling In this chapter, the methods for determining the induced emf in an electrical circuit and force/torque experienced by a movable part will be discussed. The general concept of electromechanical system modeling will also be illustrated by a singly excited rotating system. 2

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Principle of Electromechanical Energy Conversion Induced emf in Electromechanical Systems The diagram below shows a conductor of length l placed in a uniform magnetic field of flux density B. When the conductor moves at a speed v, the induced emf in the conductor can be determined by e  lv  B The direction of the emf can be determined by the "right hand rule" for cross products. In a coil of N turns, the induced emf can be calculated by e  d dt where  is the flux linkage of the coil and the minus sign indicates that the induced current opposes the variation of the field. It makes no difference whether the variation of the flux linkage is a result of the field variation or coil movement. In practice, it would convenient if we treat the emf as a voltage. The above express can then be rewritten as e  d  L di  i dL dx dt dt dx dt if the system is magnetically linear, i.e. the self inductance is independent of the current. It should be noted that the self inductance is a function of the displacement x since there is a moving part in the system. Example: Calculate the open circuit voltage between the brushes on a Faraday's disc as shown schematically in the diagram below. r Shaft r2 r1 Brushes v B SN + 3 SN