外轉(zhuǎn)子式直流發(fā)電機設(shè)計含7張CAD圖帶開題報告-獨家.zip
外轉(zhuǎn)子式直流發(fā)電機設(shè)計含7張CAD圖帶開題報告-獨家.zip,外轉(zhuǎn),直流發(fā)電機,設(shè)計,CAD,開題,報告,獨家
開題報告
學(xué)生姓名
學(xué)號
專業(yè)班級
指導(dǎo)教師
職稱
單 位
課題性質(zhì)
設(shè)計t 論文□
課題來源
科研t 教學(xué)□ 生產(chǎn)□ 其它□
畢業(yè)設(shè)計（論文）題目
外轉(zhuǎn)子式直流發(fā)電機設(shè)計
開題報告（闡述課題的目的、意義、研究現(xiàn)狀、研究內(nèi)容、研究方案、進度安排、預(yù)期結(jié)果、參考文獻等）
畢業(yè)設(shè)計（論文）的目的和意義：
時代進步和科技發(fā)展的同時，直流電機在生產(chǎn)、制造、運輸及日常的生活中所占的比重是越來越重。所以，對直流電機的研究是非常有必要也是非常有意義的。直流電動機在結(jié)構(gòu)上可以分為兩類：一是內(nèi)轉(zhuǎn)子直流電動機；二是外轉(zhuǎn)子直流電動機。外轉(zhuǎn)子直流電動機可以直接驅(qū)動電動機，從而省去了機械變速裝置，這樣提高了驅(qū)動效率。因此外轉(zhuǎn)子直流電動機在我國有相當(dāng)廣泛的應(yīng)用前景。
通過本次課題研究，我們將達到下面的目的：
1、培養(yǎng)綜合分析和解決本專業(yè)的一般工程技術(shù)問題的獨立工作能力，拓寬和深化學(xué)生的知識。
2、培養(yǎng)學(xué)生樹立正確的設(shè)計思想，設(shè)計構(gòu)思和創(chuàng)新思維，掌握工程設(shè)計的一般程序規(guī)范和方法。
3、培養(yǎng)學(xué)生樹立正確的設(shè)計思想和使用技術(shù)資料、國家標(biāo)準等手冊、圖冊工具書進行設(shè)計計算，數(shù)據(jù)處理，編寫技術(shù)文件等方面的工作能力。
4、培養(yǎng)學(xué)生進行調(diào)查研究，面向?qū)嶋H，面向生產(chǎn)，向工人和技術(shù)人員學(xué)習(xí)的基本工作態(tài)度，工作作風(fēng)和工作方法。
畢業(yè)設(shè)計（論文）的研究現(xiàn)狀：
外轉(zhuǎn)子直流電動機是一種用電子換向線路和轉(zhuǎn)子位置代替有刷直流電動機的電機，它具有運行可靠，維護方便，結(jié)構(gòu)簡單，無勵磁損耗且可方便地實現(xiàn)無級調(diào)速等優(yōu)點。永磁無刷直流電動機在結(jié)構(gòu)上可分為兩類：一是內(nèi)轉(zhuǎn)子永磁無刷直流電動機，即定子在外，永磁體在內(nèi)；另一類是外轉(zhuǎn)子永磁無刷直流電動機，即定子在內(nèi)，永磁本在外。
外轉(zhuǎn)子直流電動機是一種用電子換向線路和轉(zhuǎn)子位置代替有刷直流電動機的電機，它具有運行可靠，維護方便，結(jié)構(gòu)簡單，無勵磁損耗且可方便地實現(xiàn)無級調(diào)速等優(yōu)點。永磁無刷直流電動機在結(jié)構(gòu)上可分為兩類：一是內(nèi)轉(zhuǎn)子永磁無刷
直流電動機，即定子在外，永磁體在內(nèi)；另一類是外轉(zhuǎn)子永磁無刷直流電動機，即定子在內(nèi)，永磁本在外。
與感應(yīng)電動機相比，無刷直流電動機具有更大功率密度，更高的效率和更好的控制性能，主要表現(xiàn)在以下幾個方面：
1、由于采用高性能永磁性材料，，無刷直流電動機轉(zhuǎn)子體積得以減小，可以具有較低的慣性，更快的響應(yīng)速度，更高的轉(zhuǎn)矩慣量比。
2、由于沒有轉(zhuǎn)子損耗，也無需定子勵磁電流分量，所以無刷直流電動機具有較高的效率和功率密度。對于同等容量輸出，感應(yīng)電動機需要更大的功率整流器和逆變器。
3、由于沒有轉(zhuǎn)子發(fā)熱，無刷直流電動機也無需考慮轉(zhuǎn)子冷卻問題。
4、永磁無刷直流電動機將感應(yīng)電動機非線性本質(zhì)和復(fù)雜的控制系統(tǒng)簡化為離散六狀態(tài)的轉(zhuǎn)子位置控制，無需坐標(biāo)變換。
畢業(yè)設(shè)計（論文）主要內(nèi)容和要求：
本次畢業(yè)設(shè)計的主要內(nèi)容是完成外轉(zhuǎn)子式直流發(fā)電機設(shè)計。其技術(shù)要求為：a、額定功率：500W；b、額定電壓：24V； c、工作溫度：-20-40℃。
確定外轉(zhuǎn)子式直流發(fā)電機裝置；完成對傳動軸的設(shè)計、定子的設(shè)計、轉(zhuǎn)子的設(shè)計；傳動軸上面鍵槽的選用。通過上面的設(shè)計、相應(yīng)的校核及分析，對設(shè)計的方案進行分析，繪制外轉(zhuǎn)子式直流發(fā)電機的圖紙；編寫不少于5000字的設(shè)計計算說明書。
畢業(yè)設(shè)計（論文）應(yīng)完成的主要工作：
通過圖書館、網(wǎng)絡(luò)等獲取知識的途徑，充分了解國內(nèi)外外轉(zhuǎn)子式直流發(fā)電機的研究現(xiàn)狀及發(fā)展趨勢，掌握外轉(zhuǎn)子式直流發(fā)電機的組成、分類、工作原理及工作特點。依據(jù)現(xiàn)有的知識設(shè)計出一種額定功率為500W；額定電壓為24V；工作溫度在-20-40℃外轉(zhuǎn)子式直流發(fā)電機。對其結(jié)構(gòu)裝置及主要零部件進行詳細的設(shè)計、相應(yīng)的校核及分析，對設(shè)計的方案進行分析，繪制裝配圖及相應(yīng)的零件圖，完成設(shè)計說明書的撰寫。
畢業(yè)設(shè)計（論文）的研究方案：
1、查閱國內(nèi)外關(guān)于外轉(zhuǎn)子式直流發(fā)電機的相關(guān)資料。
2、了解外轉(zhuǎn)子式直流發(fā)電機的分類、工作原理和組成。
3、根據(jù)任務(wù)書給定的數(shù)據(jù)，對其結(jié)構(gòu)裝置及主要零部件進行詳細的設(shè)計、相應(yīng)的校核及分析。
4、通過電腦繪圖零件Autocad將所設(shè)計的參數(shù)通過電腦展示出來。并對某些部分加以受力分析，驗證其合理性。
畢業(yè)設(shè)計（論文）進度安排：
1-4周 完成開題報告、文獻綜述等
5-8周 完成方案設(shè)計
9-13周完成全部設(shè)計任務(wù) 準備答辯
畢業(yè)設(shè)計（論文）主要參考資料：
1、葉金虎，無刷直流電動機，科學(xué)出版社，1982
2、張深，直流無刷電動機原理及應(yīng)用，機械工業(yè)出版社，1996
3、沈建新，永磁無刷直流電動機特殊繞組結(jié)構(gòu)及無位置傳感器控制的研究，浙江大學(xué)博士論文，1997
4、林友仰、葉云岳，電機優(yōu)化技術(shù)，浙江大學(xué)出版社，1989
5、李燁等，永磁無刷直流電機技術(shù)發(fā)展水平與應(yīng)用前景，微電機，2001
6、胡虔生等，電機學(xué)，水利電力出版社，2001
7、盛劍霓，工程電磁場數(shù)值分析，西安交通大學(xué)出版社，1991
8、王沖權(quán)，電機的計算機輔助設(shè)計與優(yōu)化技術(shù)，上海交通大學(xué)出版社，1989
9、陳世坤，電機設(shè)計(上、下)，機械工業(yè)出版社，1997
10、顧興寶，高功率密度永磁無刷直流電動機，微特電機，2000
11、王秀和，永磁電機漏磁系數(shù)的確定，微特電機，1999
12、竇曉霞，永磁電機氣隙磁場分析與磁鋼選擇，微電機，2000
13、劉瑞芳，胡敏強等，永磁電機中永磁體數(shù)學(xué)模型的分析，微電機，2000
14、方瑞明、胡虔生，異步電機設(shè)計混合型專家系統(tǒng)，中小型電機，2000
15、方瑞明，永磁直流無刷電機設(shè)計混合型專家系統(tǒng)的研究，微電機，2001
16、鄭柒拾、王風(fēng)翔，永磁無刷直流電機的繞組參數(shù)計算，沈陽S業(yè)大學(xué)學(xué)報，2000
17、洪文治，直流永磁電機計算程序及電樞反應(yīng)研究，微特電機，2000
18、韓光寒等，無刷直流電動機電樞等效電阻的實例研究，微電機，2002
19、鞠立華、蔣書運 稀土永磁無刷直流電動機電磁場有限元分析,東南大學(xué)機械工程系碩士論文,2005
20、王淑紅,劉會飛,熊光煜,永磁無刷直流電動機的靜動態(tài)特性分析,太原理工大學(xué)電氣動力學(xué)院碩士論文,2005
21、鮑曉華，劉根，張敬華, 永磁無刷直流電動機運行特性的研究,合肥工業(yè)大學(xué)碩士論文,2002
22、徐惠明,外轉(zhuǎn)子永磁無刷直流電動機的結(jié)構(gòu)設(shè)計,中國船舶工業(yè)總公司第七一二研究所期刊,1998第一期
指導(dǎo)教師意見：
指導(dǎo)教師簽名：
年 月 日
教研室意見：
審查結(jié)果： 同 意□ 不 同 意□
教研室主任簽名：
年 月 日
英文原文
Introduction to D.C. Machines
D.C. machines are characterized by their versatility. By means of various combinations of shunt-, series-, and separately excited field windings they can be designed to display a wide variety of volt-ampere or speed-torque characteristics for both dynamic and steady state operation. Because of the ease with which they can be controlled, systems of D.C. machines are often used in applications requiring a wide range of motor speeds or precise control of motor output.
The essential features of a D.C. machine are shown schematically. The stator has salient poles and is excited by one or more field coils. The air-gap flux distribution created by the field winding is symmetrical about the centerline of the field poles. This is called the field axis or direct axis.
As we know, the A.C. voltage generated in each rotating armature coil is converted to D.C. in the external armature terminals by means of a rotating commutator and stationary brushes to which the armature leads are connected. The commutator-brush combination forms a mechanical rectifier, resulting in a D.C. armature voltage as well as an armature m.m.f. Wave then is 90 electrical degrees from the axis of the field poles, i.e. in the quadrature axis. In the schematic representation the brushes are shown in quadrature axis because this is the position of the coils to which they are connected. The armature m.m.f. Wave then is along the brush axis as shown. (The geometrical position of the brushes in an actual machine is approximately 90 electrical degrees from their position in the schematic diagram because of the shape of the end connections to the commutator.)
The magnetic torque and the speed voltage appearing at the brushes are independent of the spatial waveform of the flux distribution; for convenience we shall continue to assume a sinusoidal flux-density wave in the air gap. The torque can then be found from the magnetic field viewpoint.
The torque can be expressed in terms of the interaction of the direct-axis air-gap flux per pole and space-fundamental component of the armature m.m.f.wave. With the brushes in the quadrature axis the angle between these fields is 90 electrical degrees, and its sine equals unity. For a pole machine
（1-1）
In which the minus sign gas been dropped because the positive direction of the torque can be determined from physical reasoning. The space fundamental of the sawtooth armature m.m.f.wave is times its peak. Substitution in above equation then gives
（1-2）
Where, =current in external armature circuit;
=total number of conductors in armature winding;
=number of parallel paths through winding.
And
（1-3）
is a constant fixed by the design of the winding.
The rectified voltage generated in the armature has already been discussed before for an elementary single-coil armature. The effect of distributing the winding in several slots is shown in figure. In which each of the rectified sine wave is the voltage generated in one of the coils, commutation taking place at the moment when the coil sides are in the neutral zone. The generated voltage as observed from the brushes and is the sum of the rectified voltages of all the coils in series between brushes and is shown by the rippling line labeled in figure. With a dozen or so commutator segments per pole, the ripple becomes very small and the average generated voltage observed from the brushes equals the sum of the average values of the rectified coil voltages. The rectified voltage between brushes, Known also as the speed voltage, is
（1-4）
where is the design constant. The rectified voltage of a distributed winding has the same average value as that of a concentrated coil. The difference is that the ripple is greatly reduced.
From the above equations, with all variable expressed in SI units,
（1-5）
This equation simply says that the instantaneous power associated with the speed voltage equals the instantaneous mechanical power with the magnetic torque. The direction of power flow being determined by whether the machine is acting as a motor or generator.
The direct-axis air-gap flux is produced by the combined m.m.f. of the field windings. The flux-m.m.f. Characteristic being the magnetization curve for the particular iron geometry of the machine. In the magnetization curve, it is assumed that the armature –m.m.f. Wave is perpendicular to the field axis. It will be necessary to reexamine this assumption later in this chapter, where the effects of saturation are investigated more thoroughly. Because the armature e.m.f. is proportional to flux times speed, it is usually more convenient to express the magnetization curve in terms of the armature e.m.f. at a constant speed . The voltage for a given flux at any other speed is proportional to the speed, i.e.
（1-6）
There is the magnetization curve with only one field winding excited. This curve can easily be obtained by test methods, no knowledge of any design details being required.
Over a fairly wide range of excitation the reluctance of the iron is negligible compared with that of the air gap. In this region the flux is linearly proportional to the total m.m.f. of the field windings, the constant of proportionality being the direct-axis air-gap permeance.
The outstanding advantages of D.C. machines arise from the wide variety of operating characteristics that can be obtained by selection of the method of excitation of the field windings. The field windings may be separately excited from an external D.C. source, or they may be self-excited; i.e. the machine may supply its own excitation. The method of excitation profoundly influences not only the steady-state characteristics, but also the dynamic behavior of the machine in control systems.
The connection diagram of a separately excited generator is given. The required field current is a very small fraction of the rated armature current. A small amount of power in the field circuit may control a relatively large amount of power in the armature circuit; i.e. the generator is a power amplifier. Separately excited generators are often used in feedback control systems when control of the armature voltage over a wide range is required. The field windings of self-excited generators may be supplied in three different ways. The field may be connected in series with the armature, resulting in a series generator. The field may be connected in shunt with the armature, resulting in a shunt generator, or the field may be in two sections, one of which is connected in series and the other in shunt with the armature, resulting in a compound generator. With self-excited generators residual magnetism must be present in the machine iron to get the self-excitation process started.
In the typical steady-state volt-ampere characteristics, constant-speed prime movers being assumed. The relation between the steady state generated e.m.f. and the terminal voltage is
（1-7）
where is the armature current output and is the armature circuit resistance. In a generator, is larger than and the electromagnetic torque is a counter torque opposing rotation.
The terminal voltage of a separately excited generator decreases slightly with increase in the load current, principally because of the voltage drop in the armature resistance. The field current of a series generator is the same as the load current, so that the air-gap flux and hence the voltage vary widely with load. As a consequence, series generators are normally connected so that the m.m.f. of the series winding aids that of the shunt winding. The advantage is that through the action of the series winding the flux per pole can increase with load, resulting in a voltage output that is nearly usually contains many turns of relatively small wire. The series winding, wound on the outside, consists of a few turns of comparatively heavy conductor because it must carry the full armature current of the machine. The voltage of both shunt and compound generators can be controlled over reasonable limits by means of rheostats in the shunt field.
Any of the methods of excitation used for generators can also be used for motors. In the typical steady-state speed-torque characteristics, it is assumed that motor terminals are supplied from a constant-voltage source. In a motor the relation between the e.m.f. generated in the armature and terminal voltage is
（1-8）
where is now the armature current input. The generated e.m.f. is now smaller than the terminal voltage , the armature current is in the opposite direction to that in a generator, and the electron magnetic torque is in the direction to sustain rotation of the armature.
In shunt and separately excited motors the field flux is nearly constant. Consequently increased torque must be accompanied by a very nearly proportional increase in armature current and hence by a small decrease in counter e.m.f. to allow this increased current through the small armature resistance. Since counter e.m.f. is determined by flux and speed, the speed must drop slightly. Like the squirrel-cage induction motor, the shunt motor is substantially a constant-speed motor having about 5% drop in speed from no load to full load. Starting torque and maximum torque are limited by the armature current that can be commutated successfully.
An outstanding advantage of the shunt motor is case of speed control. With a rheostat in the shunt-field circuit, the field current and flux per pole can be varied at will, and variation of flux causes the inverse variation of speed to maintain counter e.m.f. approximately equal to the impressed terminal voltage. A maximum speed range of about 4 or 5 to I can be obtained by this method. The limitation again being commutating conditions. By variation of the impressed armature voltage, very speed ranges can be obtained.
In the series motor, increase in load is accompanied by increase in the armature current and m.m.f. and the stator field flux (provided the iron is not completely saturated). Because flux increase with load, speed must drop in order to maintain the balance between impressed voltage and counter e.m.f. Moreover, the increased in armature current caused by increased torque is varying-speed motor with a markedly drooping speed-load characteristic. For applications requiring heavy torque overloads, this characteristic is particularly advantageous because the corresponding power overloads are held to more reasonable values by the associated speed drops. Very favorable starting characteristics also result from the increase flux with increased armature current.
In the compound motor the series field may be connected either cumulatively, so that its m.m.f. adds to that of the shunt field, or differentially, so that it opposes. The differential connection is very rarely used. A cumulatively compounded motor has speed-load characteristic intermediate between those of a shunt and a series motor, the drop of speed with load depending on the relative number of ampere-turns in the shunt and series fields. It does not have disadvantage of very high light-load speed associated with a series motor, but it retains to a considerable degree the advantages of series excitation.
The application advantages of D.C. machines lie in the variety of performance characteristics offered by the possibilities of shunt, series and compound excitation. Some of these characteristics have been touched upon briefly in this article. Still greater possibilities exist if additional sets of brushes are added so that other voltages can be obtained from the commutator. Thus the versatility of D.C. machine system and their adaptability to control, both manual and automatic, are their outstanding features.
A D.C machines is made up of two basic components:
－The stator which is the stationary part of the machine. It consists of the following elements: a yoke inside a frame; excitation poles and winding; commutating poles (composes) and winding; end shield with ball or sliding bearings; brushes and brush holders; the terminal box.
－The rotor which is the moving part of the machine. It is made up of a core mounted on the machine shaft. This core has uniformly spaced slots into which the armature winding is fitted. A commutator, and often a fan, is also located on the machine shaft.
The frame is fixed to the floor by means of a bedplate and bolts. On low power machines the frame and yoke are one and the same components, through which the magnetic flux produced by the excitation poles closes. The frame and yoke are built of cast iron or cast steel or sometimes from welded steel plates.
In low-power and controlled rectifier-supplied machines the yoke is built up of thin (0.5～1mm) laminated iron sheets. The yoke is usually mounted inside a non-ferromagnetic frame (usually made of aluminum alloys, to keep down the weight). To either side of the frame there are bolted two end shields, which contain the ball or sliding bearings.
The (main)excitation poles are built from 0.5～1mm iron sheets held together by riveted bolts. The poles are fixed into the frame by means of bolts. They support the windings carrying the excitation current.
On the rotor side, at the end of the pole core is the so-called pole-shoe that is meant to facilitate a given distribution of the magnetic flux through the air gap. The winding is placed inside an insulated frame mounted on the core, and secured by the pole-shoe.
The excitation windings are made of insulated round or rectangular conductors, and are connected either in series or in parallel. The windings are liked in such a way that the magnetic flux of one pole crossing the air gap is directed from the pole-shoe towards the armature (North Pole), which the flux of the next pole is directed from the armature to the pole-shoe (South Pole).
The commutating poles, like the main poles, consist of a core ending in the pole-shoe and a winding wound round the core. They are located on the symmetry (neutral) axis between two main poles, and bolted on the yoke. Commutating poles are built either of cast-iron or iron sheets.
The windings of the commutating poles are also made from insulated round or rectangular conductors. They are connected either in series or in parallel and carry the machine's main current.
The rotor core is built of 0.5～1mm silicon-alloy sheets. The sheets are insulated from one another by a thin film of varnish or by an oxide coating. Both some 0.03～0.05mm thick. The purpose is to ensure a reduction of the eddy currents that arise in the core when it rotates inside the magnetic field. These currents cause energy losses that turn into heat. In solid cores, these losses could become very high, reducing machine efficiency and producing intense heating.
The rotor core consists of a few packets of metal sheet. Redial or axial cooling ducts (8～10mm inside) are inserted between the packets to give better cooling. Pressure is exerted to both side of the core by pressing devices foxed on to the shaft. The length of the rotor usually exceeds that of the poles by 2～5mm on either side－the effect being to minimize the variations in magnetic permeability caused by axial armature displacement. The periphery of the rotor is provided with teeth and slots into which the armature winding is inserted.
The rotor winding consists either of coils wound directly in the rotor slots by means of specially designed machines or coils already formed. The winding is carefully insulated, and it secured within the slots by means of wedges made of wood or other insulating material.
The winding overcharge are bent over and tied to one another with steel wire in order to resist the deformation that could be caused by the centrifugal force.
The coil-junctions of the rotor winding are connected to the commutator mounted on the armature shaft. The commutator is cylinder made of small copper. Segments insulated from one another, and also from the clamping elements by a layer of minacity. The ends of the rotor coil are soldered to each segment.
On low-power machines, the commutator segments form a single unit, insulated from one another by means of a synthetic resin such as Bakelite.
To link the armature winding to fixed machine terminals, a set of carbon brushes slide on the commutator surface by means of brush holders. The brushes contact the commutator segments with a constant pressure ensured by a spring and lever. Clamps mounted on the end shields support the brush holders.
The brushes are connected electrically－with the odd-numbered brushes connected to one terminal of the machine and the even-numbered brushes to the other. The brushes are equally spaced round the periphery of the commutator－the number of rows of brushes being equal to the number of excitation poles.
15
中文翻譯
直流電機的介紹
直流電機的特點是他們的多功用性。依靠不同的并勵、串勵和他勵勵磁繞組的組合，他們可以被設(shè)計為動態(tài)的和靜態(tài)的運轉(zhuǎn)方式從而呈現(xiàn)出寬廣范圍變化的伏安、－特性或速度－轉(zhuǎn)矩特性。因為它簡單的可操縱性，直流系統(tǒng)經(jīng)常被用于需要大范圍發(fā)動機轉(zhuǎn)速或精確控制發(fā)動機的輸出量的場合。
直流電機的總貌如圖所示。定子上有凸極，而且由一個或幾個勵磁線圈勵磁。氣隙磁通量以磁極中心線為軸線對稱分布。這條軸線叫做磁場軸線或直軸。
我們都知道，在每個旋轉(zhuǎn)電樞線圈中產(chǎn)生的交流電壓，經(jīng)由一與電樞聯(lián)接的旋轉(zhuǎn)的換向器和靜止的電刷，在電樞線圈出線端轉(zhuǎn)換成直流電壓。換向器－電刷組合構(gòu)成了一個機械整流器，它形成了一個直流電樞電壓和一個被固定在空間中的電樞磁勢波形。電刷的位置應(yīng)使換向線圈也處于磁極中性區(qū)，即兩磁極之間。這樣，電樞磁勢波的軸線與磁極軸線相差90度,也就是在交軸上。在示意圖中，電刷位于交軸上，因為這是線圈和電刷相連的位置。這樣，電樞磁勢波的軸線也是沿著電刷軸線的（在實際電機中，電刷的幾何位置大約偏移圖例中所示位置90度，這是因為元件的末端形狀構(gòu)成圖示結(jié)果與換向器相連。）。電刷上的電磁轉(zhuǎn)矩和旋轉(zhuǎn)電勢與磁通分布的空間波形無關(guān)；為了方便我們可以假設(shè)在氣隙中有一個正弦的磁通密度波形。轉(zhuǎn)矩可以從磁場的觀點分析得到。
轉(zhuǎn)矩可以用每個磁極的直軸氣隙磁通和電樞磁勢波的空間基波分量相互作用的結(jié)果來表示。在交軸上的電刷和這個磁場的夾角為90度，其正弦值等于1，對于一臺極電機
（1-1）
式中帶負號被去掉因為轉(zhuǎn)矩的正方向可以由物理的推論測定出來。鋸齒電樞磁勢波的空間基波是它最大值的。代替上面的等式可以給出：
（1-2）
其中：=電樞外部點路中的電流；
=電樞繞組中總導(dǎo)體數(shù)；
=通過繞組的并聯(lián)支路數(shù)；
及 （1-3）
其為一個由繞組設(shè)計而確定的常數(shù)。
簡單的單個線圈的電樞中的整流電壓前在面已被討論過。將繞組分散在幾個槽中的效果可用圖形表示，在圖示中每一個整流的正弦波是在線圈中產(chǎn)生的電壓,換向線圈邊處于磁中性區(qū)。從電刷觀察到的電壓是電刷間所有串聯(lián)線圈中整流電壓的總和，在圖中標(biāo)以的文波表示。每個磁極用12個或更多換向片,可以使波動變得很小。從電刷中觀測到平均產(chǎn)生的電壓等于整流線圈電壓的平均值的總和。電刷之間整流電壓，即旋轉(zhuǎn)電勢為
（1-4）
為常數(shù)。分布繞組的整流電壓與集中繞組有相同的平均值，不同的是波動大大減低了。
在上面的等式中，所有的變量都是標(biāo)準國際單位制。
（1-5）
這個等式清楚地說明，與旋轉(zhuǎn)電勢相關(guān)的瞬間功率等于與磁場轉(zhuǎn)矩有關(guān)的瞬時機械功率，能量的流向是由設(shè)備的確定，是發(fā)動機還是發(fā)電機。
直軸氣隙磁量由勵磁繞組的合成磁勢產(chǎn)生，其磁通—磁勢曲線就是電機的具體鐵磁材料的幾何尺寸決定的磁化曲線。在磁化曲線中, 假設(shè)電樞磁勢波的軸線與磁場軸垂直，因此假定電樞磁勢對直軸磁通不產(chǎn)生作用。在本文的后面有必要重新檢驗這一假設(shè)，飽和效應(yīng)會深入研究。因為電樞電勢是與磁通、時間、速度成比例，所以通常用恒定轉(zhuǎn)速下的電樞電勢來表示磁化曲線更為方便。任意轉(zhuǎn)速電壓時，任一給定磁通下的電壓與轉(zhuǎn)速成正比，也就是說
（1-6）
圖中磁化曲線只有一個勵磁繞組勵磁的，這種曲線可以通過測試的方法輕松獲得，不需要任何設(shè)計步驟的知識。
大范圍勵磁下的鐵磁阻與空氣氣隙相比可以忽略不計，在這種情況下磁通與勵磁繞組的總磁勢成線性比例關(guān)系，比例常數(shù)就是直軸的氣隙導(dǎo)磁性。
直流電機的顯著優(yōu)勢源自于通過選擇勵磁繞組的勵磁方式而獲得不同的運轉(zhuǎn)方式。勵磁繞組可以從外部直流電源以他勵的方式勵磁，也可以以自勵的方式勵磁。換句話，直流電機可以提供自身勵磁。勵磁方式不僅極大地影響它的靜態(tài)特性，而且極大地影響在控制系統(tǒng)中電機的動態(tài)性能。
他勵發(fā)電機的聯(lián)接圖解已經(jīng)給出的。所需的勵磁電流只是電樞電流中的一小部分。在勵磁電路中少量的功率可以控制相對一大部分電樞電路的功率。換句話說，發(fā)電機是一個功率放大器，當(dāng)需要在大范圍控制電樞電壓時，他勵發(fā)電機通常在反饋控制系統(tǒng)中使用。自勵發(fā)電機的勵磁繞組可以有三種不同的供電方式。勵磁線圈可以與電樞串聯(lián)起來，這便是串勵發(fā)電機；勵磁繞組可以與電樞并聯(lián)在一起，這便是并勵發(fā)電機。也可以同時以兩種方式相連接組成一個復(fù)勵發(fā)電機。為了引起自勵過程，在自勵發(fā)電機中必須存在剩磁。
在典型的靜態(tài)伏-安特性中，假定原動機速度恒定，穩(wěn)態(tài)電動勢與端電壓之間的關(guān)系為
（1-7）
其中是電樞輸出電流，是電樞回路電阻。在發(fā)動機中，大于。電磁轉(zhuǎn)矩是一個反轉(zhuǎn)矩。
他勵發(fā)電機的端電壓隨著負載電流的增大而輕微的減小，主要是因為電壓在電樞電阻上的壓降。串勵發(fā)電機中的勵磁電流與負載電流相同，所以氣隙磁通和電壓隨負載變化很大，因此很少采用串勵發(fā)電機。并勵發(fā)電機電壓隨負載增加會有所下降，但在許多應(yīng)用場合，這并不妨礙使用。復(fù)勵發(fā)電機的連接通常使串勵繞組的磁勢與并勵繞組磁勢相加，其優(yōu)點是通過串勵繞組作用，每極磁通隨著負載增加，從而產(chǎn)生一個隨負載增加近似為常數(shù)的輸出電壓。通常，并勵繞組匝數(shù)多，導(dǎo)線細；而繞在外部的串勵繞組由于它必須承載電機的整個電樞電流，所以其構(gòu)成的導(dǎo)線相對較粗。不論是并勵還是復(fù)勵發(fā)電機的電壓都可借助并勵磁場中的變阻器在適度的范圍內(nèi)得到調(diào)節(jié)。
所有勵磁的方法在電動機上同樣適用。在電動機典型的靜態(tài)轉(zhuǎn)速—轉(zhuǎn)矩特性中，電機端電壓假設(shè)由恒壓源供電，在電動機中感應(yīng)的電勢與路端電壓間關(guān)系是
（1-8）
是電樞輸入電流。電勢小于端電壓。電樞電流與發(fā)電機中的方向相反，且電磁轉(zhuǎn)矩與電樞旋轉(zhuǎn)方向相同。
對于并勵與他勵電動機來說，磁場磁通基本近似為常數(shù)，因此轉(zhuǎn)矩的增加必須要求電樞電流近似成比例增大，同時為允許增大的電流通過小的電樞電阻，要求反電勢稍有減少。由于反電勢決定于磁通和轉(zhuǎn)速，因此，轉(zhuǎn)速必須稍稍降低。與鼠籠式感應(yīng)電動機類似，并勵電動機實際是一種從空載到滿負荷的速度基本上只有5%的下降的恒速電動機。從起動轉(zhuǎn)矩到達到最大轉(zhuǎn)矩之間一直是被電樞電流所控制可以正常交替進行。
并勵電動機的一個顯著優(yōu)點是速度控制，通過在并勵繞組回路裝上內(nèi)部變阻器，勵磁電流和每極磁通都可任意改變。而磁通的變化導(dǎo)致轉(zhuǎn)速相反的變化以維持反電勢大致等于外施加端電壓。用這種方法我們可以獲得最大調(diào)速范圍為4或5比1，最高轉(zhuǎn)速同樣受到換向條件的限制。通過改變外施加電樞電壓，可以獲得很寬的調(diào)速范圍。
對于串勵電動機來說，電樞電流、電樞磁勢波以及定子磁場磁通隨負載增長而增長。因為由于負載增大而造成的磁通增大，速度必須降低，這樣才可以維持反電勢與外加電壓之間的平衡。此外，由于磁通增加，所以轉(zhuǎn)矩增大所引起電樞電流的增大比并勵電動機中的要小。因此串勵電動機是一種具有明顯下降的轉(zhuǎn)
收藏