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                       control signal and the hydraulic pressure/flow is the energy source. The hydraulic cylinder acts as the
                       energy conversion device that converts fluidic energy to mechanical energy. For a typical electromechan-
                       ical actuator, such as a DC motor (Fig. 20.3), the power amplification block is the motor driver that
                       amplifies signal level (low current/power) control signal to the higher power (large current) signal that
                       is used to convert electrical energy to mechanical energy through the electromagnetic principle.
                         In this chapter, we will first present an overview of common types of electromechanical actuators.
                       They will be classified by the respective energy conversion mechanism. The power electronic components,
                       such as diodes, thyristors, and transistors, which are used for power amplification and modulation, will
                       be presented followed by discussion of common power amplification building blocks. We will conclude
                       by discussing some issues related to interfacing with electromechanical actuators.
                       Type of Electromechanical Actuators—Operating Principles
                       Converting electrical energy to mechanical energy is the common thread among different electrome-
                       chanical actuators. Physics provided us with many different mechanisms either through direct conversion
                       such as piezoelectric or through an intermediate medium such as a magnetic field. We will present an
                       overview of the more common electromechanical actuators by their energy conversion mechanism:
                       electromagnetic, electrostatic, and piezoelectric. The following discussion is intended to provide intro-
                       ductory information about the types of electromechanical actuation and is by no means exhaustive.
                       Detailed discussion of each can be found in subsequent chapters, where they will be discussed in more
                       detail.
                       Electromagnetics—Magnetic Field
                       Electromagnetic is the most widely utilized method of energy conversion for electromechanical actuators.
                       One of the reasons for using magnetic fields instead of electric fields is the higher energy density in magnetic
                       fields. The air gap that separates a stationary member (stator) and a moving member of an electrome-
                       chanical actuator is where the electromechanical energy conversion takes place. The amount of energy
                       per unit volume of air gap for magnetic fields can be five orders of magnitude higher than that of electric
                       fields.
                         Lorentz’s law of electromagnetic forces and Faraday’s law of electromagnetic induction are the two
                       fundamental principles that govern electromagnetic actuators. Before going into the detail of electro-
                       magnetics, we will first introduce the concept of magnetic field and flux.
                         Magnetic flux φ exists due the presence of a magnetic field. The magnetic field strength   (in A/m)
                                                                                             H
                       and the magnetic flux density   (in tesla [T]) are related by the permeability of the material. In a vacuum,
                                             B
                       the magnetic flux density is directly proportional to the magnetic field strength and is expressed by
                                                                ⋅
                                                         B =  µ 0 H                              (20.1)
                       where µ 0  = 4[T m/A] is the permeability constant. For other magnetic or ferromagnetic materials the
                       relationship is given by
                                                      B =  µ r H  ⋅  ⋅                           (20.2)
                                                             () µ 0 H
                              H
                       where µ r ( ) is the relative permeability of the material. Figure 20.4 shows typical B-H and µ-H curves.
                       Lorentz’s Law of Electromagnetic Force
                       When a current carrying conductor is placed in a magnetic field, it will be subjected to an induced force
                       given by
                                                                ×
                                                          F =  i B                               (20.3)
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