4电磁理论及磁路.doc

Words and Expressionselectromagnetism 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 permeability 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demagnetization 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 area 横截面proportional to 与成正比inversely proportional to 与成反比Unit 7 Magnetic Theory and CircuitsAn 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 home. 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 mechanical 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 distribution 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 salient 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 law 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 established, 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 long conductor carrying a constant-magnitude current and an elemental conductor of length l carrying a constant-magnitude current in a direction opposite to. 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 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 （4.1） Where （4.2）B is in fact a flux density, it has the units of flux per 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 （4.3）Permeability is expressed in units of henrys/meter.If the surrounding medium is other than free space, the absolute permeabilityis again readily found from Eq.(4.1). A comparison with the result obtained for free space then leads to a quantity called relative permeability,. Expressed mathematically we have （4.4）Equation (4.4) clearly indicates that 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 can exceed one hundred thousand. Most ferromagnetic materials, however, have values of in 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 the normal component of the vector magnetic field B. Expressed mathematically we have （4.5）where s stands for surface integral, A represents the area of the coil, and is the normal component of B to the coil area. It has the units of weber.Magnetic Field Intensity H. Often in magnetic circuit 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, including air. Accordingly, magnetic field intensity is defined as （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 magnetic 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 （4.7）Equation (4.7) states that the closed line integral of the 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 （4.8）where F denotes the ampere-turns enclosed by the assumed closed flux line path. The quantity 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 revealed when the field intensity, having been increased to some value, say 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. Furthermore, 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 intensity 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 engineering 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 always 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 density 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 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 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 energy 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 and 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 will 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 circuit. 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 flux 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 the magnetomotive force driving flux through two series connected reluctances-, the reluctance of the iron, and , the reluctance of the air.Fig.4.1 Typical hysteresis loops and normal magnetization curveFig. 4.2 Typical magnetic circuitFig. 4.3 Single-line equivalentinvolving iron and air circuit of Fig. 4. 2If 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 （4.9）Now in those situations where B is a constant and penetrates a fixed, known area A, the corresponding magnetic flux may be written as （4.10）Inserting Eq.(4.10) into Eq. (4.9) yields （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 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 A. However, this flux is limited in value by what is called the reluctance of the magnetic circuit, which is defined as （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 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 （4.13）which is often referred to as 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通以定常电流的长导线和一个通以定常电流的长度为的导线（导体），使电流方向与电流方向相反，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： 其中：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： 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相比，可得相对磁导率。表示为：。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： 其中s表示积分面积；A表示线圈面积；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：。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