1、Words and Expressions electromagnetism n. 电磁，电磁学 electrical apparatus 电器，电器设备 motor n. 电动机 generator n. 发电机 fractional adj. 分数的，几分之一 magnetic field n. 磁场 coupling device 连接设备 static transformer 静态变压器 electrical power distribution circuits 送变电电路 circuit breakers 电路断路器 automatic switches 自动闸 relay 继电器
2、 quantity n. 变量，数量 magnetic flux n. 磁通量 simplify the computations 估算 Amperes Circuital Law 安培环路定律 horizontal plane 水平面 right-hand rule 右手（螺旋）法则 flux density 磁密度 tesla n. 特斯拉，磁通密度的单位 permeability n. 磁导率，磁导系数 henries 亨利（电感单位） henries/meter 亨利 /米 （磁导率的单位） absolute permeability 绝对磁导率 relative permeabili
3、ty 相对磁导率 Deltamax 克镍铁磁性合金 ferromagnetic material 铁磁性材料 effective area n. 有效面积 normal component n. 法线方向分量 weber n. 韦伯，磁通的单位 common flux 共有磁通 Magnetic Field Intensity H 磁场强度 electrical machinery 电机 ampere-turns/meter 安培 圈 /米 Amperes circuit law 安培回路定律 magnetomotive force 磁势 magnetization curve 磁化曲线 de
4、magnetization n. 退磁 residual flux density 剩余磁通密度 剩磁 retentivity 记忆力 saturation 饱和 hysteresis 磁滞现象 hysteresis loop 磁滞环 coercive force 矫顽磁力 coercivity 矫顽力 矫顽性 magnetic circuit 磁路 mask v. 补偿 clearance n. 间隙，空隙 equivalent circuit 等效电路 reluctance n. 磁阻 examination n. 观察 dimension n. 量纲 cross-sectional ar
5、ea 横截面 proportional to 与 成正比 inversely proportional to 与 成反比 Unit 7 Magnetic Theory and Circuits An understanding of electromagnetism is essential to the study of electrical engineering because it is the key to the operation of a great part of the electrical apparatus found in industry as well as ho
6、me. All electric motors and generators, ranging in size from the fractional horsepower units found in home appliances to the 25, 000-hp giants used in some industries, depend upon the electromagnetic field as the coupling device permitting interchange of energy between an electrical system and a mec
7、hanical system and vise versa. Similarly, static transformers provide the means for converting energy from one electrical system to another through the medium of a magnetic field. Transformers are to be found in such varied applications as radio and television receivers and electrical power distribu
8、tion circuits. Other important devices-for example, circuit breakers, automatic switches and relays require the presence of a confined magnetic field for their proper operation. It is the purpose of this unit to provide the reader with background so that he can identify a magnetic field and its sali
9、ent characteristics and more readily understand the function of the magnetic field in electrical equipment. As has been previously pointed out, the science of electrical engineering is founded on a few fundamental laws derived from basic experiments. In this area of electromagnetism it is Amperes la
10、w that concerns us, and, in fact, serves as the starting point of our treatment. On the basis of the results obtained by Ampere in 1820, in his experiments on the forces existing between two current-carrying conductors, such quantities as magnetic flux are readily defined. Once this base is establis
11、hed, attention is then directed to a discussion of the magnetic properties of certain useful engineering materials as well as to the idea of a “magnetic circuit“ to help simplify the computations involved in analyzing magnetic devices. Amperes Circuital Law. Amperes experiment consists of a very lon
12、g conductor carrying a constant-magnitude current 1I and an elemental conductor of length l carrying a constant-magnitude current 2I in a direction opposite to 1I . It is assumed that conductor 1 and 2 lie in the same horizontal plane and are parallel to each other. In accordance with Amperes law it
13、 is found that there exist a force on the elemental conductor (The direction of the force can be indicated by the right-hand rule). The magnitude of this force can be shown to be given by n ew t o n slBIlIrIF 2212 （ 4.1） Where rIB 2 1 （ 4.2） B is in fact a flux density, it has the units of flux per
14、square meter or teslas. Permeability. It is a characteristic of the surrounding medium, which increase or decrease the magnetic flux density for a specified current. The permeability of the vacuum (free space) can be expressed 70 104 （ 4.3） Permeability is expressed in units of henrys/meter. If the
15、surrounding medium is other than free space, the absolute permeability is again readily found from Eq.(4.1). A comparison with the result obtained for free space then leads to a quantity called relative permeability, r . Expressed mathematically we have 0r （ 4.4） Equation (4.4) clearly indicates tha
16、t relative permeability is simply a numeric which expresses the degree to which the magnetic flux density is increased or decreased over that of free space. For some materials, such as Deltamax, the value of r can exceed one hundred thousand. Most ferromagnetic materials, however, have values of r i
17、n the hundreds of thousands. Magnetic Flux . It is reasonable to expect that since B denotes magnetic flux density, multiplication by the effective area that B penetrates should yield the total magnetic flux. The magnetic flux through any surface is more rigorously defined as the surface integral of
18、 the normal component of the vector magnetic field B. Expressed mathematically we have s ndAB（ 4.5） where s stands for surface integral, A represents the area of the coil, and nB is the normal component of B to the coil area. It has the units of weber. Magnetic Field Intensity H. Often in magnetic c
19、ircuit computations it is helpful to work with a quantity representing the magnetic field which is independent of the medium in which the magnetic flux exists. This is especially true in situations such as are found in electrical machinery where a common flux penetrates several different materials,
20、including air. Accordingly, magnetic field intensity is defined as BH（ 4.6） More generally the units for H are ampere-turns/meter rather than amperes/meter. This is apparent whenever the field winding is made up of more than just a single conductor. Amperes Circuit Law. Now that the fundamental magn
21、etic quantities-flux density B, flux , field intensity H and permeability have been defined, we shall develop a very useful relationship. A line integration of H along any given closed circular path proves interesting. Thus a m piH d l （ 4.7） Equation (4.7) states that the closed line integral of th
22、e magnetic field intensity is equal to the enclosed current (or ampere-turns) that produces the magnetic field lines. This relationship is called Amperes circuit law and is more generally written as FHdl （ 4.8） where F denotes the ampere-turns enclosed by the assumed closed flux line path. The quant
23、ity F is also knows the magnetomotive force and frequently abbreviated as mmf. This relationship is useful in the study of electromagnetic devices and is referred to in subsequent chapters. Magnetization Curves of Ferromagnetic Materials. An interesting characteristic of ferromagnetic material is re
24、vealed when the field intensity, having been increased to some value, say aH is subsequently decreased. It is found that the material opposes demagnetization and, accordingly, does not retrace along the magnetizing curve Oa but rather along a curve located above Oa. See curve ab in Fig.4.1. Furtherm
25、ore, it is seen that when the field intensity is returned to zero, the flux density is no longer zero as was the case with the virgin sample. This happens because some of the domains remain oriented in the direction of the originally applied field. The value of B that remains after the filed intensi
26、ty H is removed is called residual flux density. Moreover, its value varies with the extent to which the material is magnetized. The maximum possible value of the residual flux density is called retentivity and results whenever values of H are used that cause complete saturation. Frequently, in engi
27、neering applications of ferromagnetic materials, the steel is subjected to cyclically varying values of H having the same positive and negative limits. As H varies through many identical cycles, the graph of B versus H gradually approaches a fixed closed curve as depicted in Fig.4.1. The loop is alw
28、ays traversed in the direction indicated by the arrows. Since time is implicit variable for these loops, note that B is always lagging behind H. Thus, when H is zero, B is finite and positive, as at point b, and when B is zero, as at c, H is finite and negative, and so forth. This tendency of flux d
29、ensity to lag behind the field intensity when the ferromagnetic material is in a symmetrically cyclically magnetized condition is called hysteresis and the closed curve abcdea is called a hysteresis loop. Moreover, when the material is in this cyclic condition the amount of magnetic field intensity
30、required to reduce the residual flux density to zero is called the coercive force. Usually, the maximum value of the coercive force is called the coercivity. The Magnetic Circuit. In general, problems involving magnetic devices are basically field problems because they are concerned with quantities
31、such as and B which occupy three-dimensional space. Fortunately, however, in most instances the bulk of the space of interest to the engineer is occupied by ferromagnetic materials except for small air gaps which are present either by intention or by necessity. For example, in electromechanical ener
32、gy conversion devices the magnetic flux must permeate a stationary as well as a rotating mass of ferromagnetic material, thus making an air gap indispensable. On the other hand, in other devices an air gap may be intentionally inserted in order to mask the nonlinear relationship existing between B a
33、nd H. But in spite of the presence of air gaps it happens that the space occupied by the magnetic field and the space occupied by the ferromagnetic material are practically the same. Usually this is because air gaps are made as small as mechanical clearance between rotating and stationary members wi
34、ll allow and also because the iron by virtue of its high permeability confines the flux to itself as copper wire confines electric current or a pipe restricts water. On this basis the three-dimensional field problem becomes a one-dimensional circuit problem and leads to the idea of a magnetic circui
35、t. Thus we can look upon the magnetic circuit as consisting predominantly of iron paths of specified geometry which serves to confine the flux, air gaps may be included. Figure 4.2 shows a typical magnetic circuit consisting chiefly of iron. Note that the magnetomotive force of the coil produces a f
36、lux which is confined to the iron and to that part of the air having effectively the same cross-sectional area as the iron. Furthermore, a little thought reveals that this magnetic circuit may be replaced by a single-line equivalent circuit as depicted in Fig.4.3. The equivalent circuit consists of
37、the magnetomotive force driving flux through two series connected reluctances- iR , the reluctance of the iron, and aR , the reluctance of the air. Fig.4.1 Typical hysteresis loops and normal magnetization curve Fig. 4.2 Typical magnetic circuit Fig. 4.3 Single-line equivalent involving iron and air
38、 circuit of Fig. 4. 2 If the total path length of a flux line is assumed to be L, then the total magnetomotive force associated with the specified flux line is LBHLF （ 4.9） Now in those situations where B is a constant and penetrates a fixed, known area A, the corresponding magnetic flux may be writ
39、ten as BA （ 4.10） Inserting Eq.(4.10) into Eq. (4.9) yields ALHLF （ 4.11） The quantity in parentheses in this last expression is interesting because it bears a very strong resemblance to the definition of resistance in an electric circuit. Recall that the resistance in an electric circuit represents
40、 an impediment to the flow of current under the influence of a driving voltage. An examination of Eq.(4.11) provides a similar interpretation for the magnetic circuit. We are already aware that F is the driving magnetomotive force which creates the flux penetrating the specified cross-sectional area
41、 A. However, this flux is limited in value by what is called the reluctance of the magnetic circuit, which is defined as ALR （ 4.12） No specific name is given to the dimension of reluctance except to refer to it as so many units of reluctance. Equation (4.12) reveals that the impediment to the flow
42、of flux which a magnetic circuit presents is directly proportional to the length and inversely proportional to the permeability and cross-sectional area-results which are entirely consistent with physical reasoning. Inserting Eq. (4.12) into Eq. (4.11) yields RF （ 4.13） which is often referred to as
43、 the Ohms law of the magnetic circuit. It is important to keep in mind, however, that these manipulations in the forms shown are permissible as long as B and A are fixed quantities. 电磁理论及磁路 了解电磁学是对电气工程研究的基础，因为电磁学是工业及家用电器操作的关键问题。所有的从小到零点几马力的家用至大到 25000马力的工业用电动机及发电机都依靠电磁场作为耦合装置来实现电系统和机械系统之间的能量转换。类似地，静
44、态变压器以电磁场为媒介实现电系统之间能量的转换。变压器大量用于无线电、电视接收器及送变电电路中。其他的设备，如：断路器、自动闸及继电器的使用要求一定的磁场效应。这一单元的目的是为读者提供电磁学的背景，以使读者能 够识别电磁场，了解电磁场的特性及更好地理解电磁场在电气设备中的应用。 如前所述，电气工程学是基于试验得出的几个基本定律建立的。电磁学的这一领域中，安培定律是我们介绍的出发点。基于 1820 年安培得到的结论，根据实验中两个通电导线之间力的作用，可以容易地定义磁通。有了此基础后，我们将讨论特定工程材料的磁特性以及磁路的概念以便对磁设备进行分析 估算 。 安培环路定律： 安培的试验使用一根
45、通以定常电流 1I 的长导线和一个通以定常电流 2I 的长度为 l 的导线（导体），使电流 2I 方向与电流 1I 方向相反，导线 1 和导线 2 放置在同一水平面内，并且保持平行。根据安培定律可得：导线之间存在力的作用（力的方向由右手螺旋定则确定），力的大小如下给出：牛顿lBIlIrIF 2212 其中： rIB 2 1 为磁通密度，磁通密度的单位是：磁通 /平方米或特斯拉。 磁导率：它是描述在 周围媒介中通以一定电流时，磁通密度增加或减小的特性的。真空磁导率为：70 104 磁导率的单位是亨利 /米。 如果周围介质不为真空，由公式（ 4.1）可见为： 。将绝对磁导率与真空时的磁导率 0 相
46、比，可得相对磁导率 r 。表示为：0r 。由公式（ 4.4）可见，相对磁导率是一个简单的数值，它表示相对于真空时的 磁通密度的增加或减小的程度。对于 克镍铁磁性合金，相对磁导率可能高达十万；对于大多数铁磁性材料，相对磁导率为几十万。 磁通 ：用磁通密度 B乘以磁通所穿透的有效面积可以得到总的磁通。 任意平面的磁通严格地定义为；磁通密度向量法线分量的面积积分。数学表达式如下： s ndAB 其中 s 表示积分面积； A表示线圈面积； nB 表示 B 在线圈面积法线方向的分量。磁通的单位为韦伯。 磁场强度 H：在磁回路 计算中，用一个参量定量地表示磁场，并且保证该量与周围的介质无关是很有必要的。这
47、一描述尤其适用于电机中共有磁通穿过不同介质（包括空气）的情况。因此，磁场强度定义为：BH。磁场强度的单位常用安培 圈 /米而不用安培 /米。这一单位适用于磁场是由线圈缠绕产生而不是由单个导体产生的情况。 安培环路定律：在定义了基本的磁通密度 B、磁通 、磁场强度 H及磁导率 的前提下，我们将推导出如下关 系。我们感兴趣的是磁场强度 H 沿任意给定闭合环路的线积分，a m piH d l 公式（ 4.7）说明，磁场强度的闭合环路线积分等于产生磁场的线圈中的电流和。这一关系称为安培环路定律，可以写成如下一般形式： FHdl 其中： F 表示由闭合磁通线回路所包含的电流安培乘以圈数。参量 F 称为磁势，缩写为 mmf。这一关系对研究电磁设备非常有用，将在后续章节中被引用。 铁磁性介质的磁化曲线：将铁磁性介质的磁场强度先增加到 aH ，然后再减小，可以看出铁磁性介质的相关特性。我们将发现介质具有抗退磁性，即不是沿磁化曲线 Oa折回，而是沿 Oa上方一曲线返回，如图 4.1中 ab。另外，当磁场强度返回零时，磁通密度不再为初始情况下的零。这是因为某些区域仍然保
