موتور القایی

فارسی

English

موتورهای القایی روتور سه‌فاز روند عملکرد یک موتور القایی روتور قفسی موتور القایی نوعی از موتور جریان متناوب موتور AC آسنکرون (غیرهمزمان) است که توان مورد نیاز در قسمت متحرک آن از طریق القای الکترومغناطیسی تامین می‌شود. نام دیگر این موتور، موتور قفس‌سنجابی است، چون میله‌های روتور شبیه قفس همستر (سنجاب) است که در دو انتها اتصال کوتاه شده‌است. یک موتور الکتریکی در روتور خود انرژی الکتریکی را به انرژی مکانیکی تبدیل می‌کند. برای تامین توان مورد نیاز روتور راه‌های مختلفی وجود دارد. در یک موتور DC توان آرمیچر مستقیما به وسیله یک منبع جریان مستقیم تامین می‌شود در حالی که در یک موتور القایی این توان از طریق استاتور در روتور القا می‌شود. موتورهای القایی را به علت شباهت بسیار زیاد آنها به ترانسفورماتور ترانسفورماتور دوار نیز می‌نامند چرا که استاتور این موتورها از نظر عملکرد شباهت زیادی به سیم‌پیچ اولیه و روتور آنها به سیم‌پیچ ثانویه ترانس دارد. از موتورهای القایی به ویژه موتورهای القایی سه فاز به طور گسترده‌ای در صنعت استفاده می‌شود. قدرت بالا، ساختار ساده و عدم وجود جاروبک‌ها (که به تعمیر و نگه‌داری زیادی نیاز دارند) و قابلیت بالای موتورهای القایی برای کنترل سرعت از جمله دلایل استفاده از آنهاست. تاریخچه اولین موتور القایی در سال ۱۸۸۲ توسط نیکولا تسلا در فرانسه اختراع شد اما در سال ۱۸۸۸ و پس از نقل مکان تسلا به ایالات متحده به طور رسمی ثبت شد. اولین موتور القایی روتور قفسی یک سال بعد توسط میخاییل دولیوو دوبرولسکی در اروپا اختراع شد. پیشرفت‌های تکنیکی در زمینه تولید این موتورها تا جایی ادامه یافت که در سال ۱۹۷۶ موتوری القایی با قدرت خروجی ۱۰۰ اسب بخار با حجمی برابر موتور ۷٫۵ اسب بخاری سال ۱۸۹۷ ساخته شد. امروزه پرکاربردترین موتورهای القایی را موتورهای روتور قفس سنجابی تشکیل می‌دهند[نیازمند منبع]. اصول عملکرد و مقایسه با موتورهای سنکرون بزرگترین تفاوت بین یک موتور القایی AC و یک موتور سنکرون AC این است که در موتور سنکرون توان روتور به طور مستقیم از یک منبع خارجی تامین می‌شود. این جریان در روتور نیز خود میدان مغناطیسی تولید خواهد کرد و به دلیل اثر متقابل میدان‌های استاتور و روتور، روتور در جهت میدان دوار استاتور به حرکت در خواهد آمد. از طرفی برای القای جریان در روتور، اختلاف سرعتی بین سرعت میدان دوار و سرعت گردش روتور به وجود می آید. در غیر این صورت میدان دوار نسبت به روتور امکان حرکت نخواهد داشت و هادی‌های روتور شار میدان تولید شده توسط استاتور را قطع نکرده و در نتیجه ولتاژی در روتور القا نخواهد شد. این اختلاف سرعت بین سرعت میدان دوار و سرعت حرکت روتور در اصطلاح لغزش (Slip) نامیده می‌شود. لغزش یک مؤلفه بدون واحد است. از آنجا که در موتورهای القایی اختلاف سرعت شرط و ضرورت عملکرد آنهاست به این موتورهای موتورهای غیرهمزمان یا آسنکرون می‌گویند. انواع براساس تعداد فازها: موتور القایی سه‌فاز (خود راه انداز) موتور القایی تک‌فاز (غیر خود راه انداز) بر اساس نوع روتور: موتور القایی روتور قفسی موتورالقایی روتور سیم‌پیچی شده فرمول‌ها مهمترین رابطه در موتورهای القایی رابطه بین فرکانس منبع f، تعداد زوج قطب‌ها p و سرعت میدان دوار ns است: $f = \frac{pn_s}{60\ [\mbox{sec/min}]}$. و از این رابطه خواهیم داشت: $\mbox{Synchronous speed, }n_s = \frac{60\ [\mbox{sec/min}]f}{p}\quad[\mbox{rev/min}]$ و سرعت روتور برابر است با: $\mbox{Rotor speed, }n_r = n_s(1-s)\,\!$ و s نشان‌دهنده لغزش (Slip) است و از این رابطه به دست می‌آید: $s = \frac{n_s-n_r}{n_s}$ در موتورهای سنکرون سرعت روتور همیشه برابر سرعت میدان دوار است و از این رابطه $n_s = \tfrac{60f}{p}$ به دست می‌آید. ساختار استاتور: استاتور موتورهای القایی از قطب‌های سیم‌پیچی شده‌ای تشکیل شده که با عبور جریان از آنها با تولید میدان مغناطیسی در روتور ولتاژ القا می‌کنند. تعداد قطب‌ها با توجه به سرعت و گشتاور مورد نیاز می‌تواند مختلف باشد ولی تعداد آنها همواره یک عدد زوج است. روتور: روتور موتورهای القایی به دو صورت است: روتور قفسی روتور سیم‌پیچی شده به دلیل مزایای بالای روتورهای قفسی مانند سادگی، هزینه کمتر، نیاز کمتر به تعمیر و نگهداری و... رایج‌ترین روتورها در موتورهای القایی روتورهای قفسی هستند. این روتورها از میله‌هایی از جنس مس یا آلومینیوم تشکیل شده‌اند که یه صورت یک استوانه به همدیگر متصل شده‌اند و در دو طرف به وسیله دو حلقه اتصال کوتاه شده‌اند. روتورهای سیم‌پیچی شده در صنعت کاربردهای خاص خود را دارند و بیشتر در موتورهایی که نیاز به گشتاور راه‌اندازی بالایی دارند مورد استفاده قرار می‌گیرند. کنترل سرعت سرعت چرخش میدان دوار در موتورهای القایی تابع فرکانس منبع و تعداد قطب‌های استاتور است. پیش از پیشرفت المان‌های الکترونیک قدرت تغییر فرکانس موتورهای القایی به راحتی ممکن نبود و این کاربرد این نوع موتورها را محدود می‌کرد. روش‌ها مختلفی برای تغییر سرعت موتورهای القایی وجود دارد ولی رایج‌ترین روش استفاده از تکنیک PWM (Pulse Width Modulation) یا تلفیق پهنای فرکانس است، که در آن یک موج DC به طور مرتب و سرعتی قابل تنظیم قطع و وصل می‌شود. از این طریق می‌توان توان وروردی متوسط موتور را کنترل کرد. راه‌اندازی همانطور که گفته شد در موتورهای القایی رابطه‌ای مستقیم بین مقدار لغزش و مقدار جریان القایی در روتور وجود دارد. به این ترتیب بیشترین میزان جریان القایی در روتور در هنگام راه‌اندازی (لغزش ۱) به وجود می‌آید. در این حالت موتور مانند ترانسفورماتوری عمل خواهد کرد که سیم‌پیچ ثانویه آن اتصال کوتاه شده باشد‍؛ بالا بودن جریان القا شده در روتور موجب بالا رفتن جریان استاتور می‌شود و به همین دلیل میزان جریان راه‌اندازی در استاتور تقریبا بین ۵ تا ۹ برابر جریان در بار کامل است. جریان بالای موتور در لحظه راه‌اندازی می‌تواند باعث افت ولتاژ در بقیه مصرف کننده شود اما این جریان بالا در موتور زیاد ادامه پیدا نمی‌کند چون با راه افتادن موتور لغزش به تدریج کاهش یافته و میزان جریان استاتور نیز کاهش می‌یابد. در صورتی که بار موتور در لحظه راه‌اندازی به اندازه‌ای باشد که موتور قادر به چرخش نباشد جریان بالا موجب سوختن سیم‌پیچ استاتور خواهد شد. برای جلوگیری از افزایش بیش از حد جریان در موتور از راه‌اندازها برای کاهش ولتاژ راه‌اندازی و محدود سازی جریان راه‌اندازی استفاده می‌کنند این راه‌اندازها طوری طراحی شده‌اند که با رسیدن موتور به سرعت متوسط ولتاژ را افزایش دهند. سه فاز موتورهای سه فاز به علت استفاده از برق سه فاز دارای اختلاف الکتریکی ۱۲۰ درجه‌ای بین هر یک از سیم‌پیچ‌های فازها هستند. این اختلاف موجب چرخیدن موتور با توجه به جهت فازها در سیم‌پیچ‌ها می‌شود و نیاز به سیم‌پیچ راه انداز را از بین می‌برد. در این موتورها با جابه جایی دو فاز می‌توان جهت چرخش این موتورها را تغییر داد. تک فاز این موتورها به علت استفاده از یک فاز نمی‌توانند در لحظه اولیه موتور را به حرکت در آورند چون اختلاف بین هر قطب ۱۸۰ درجه‌است که موتور را در حالتی قفل شده نگه می‌دارد. برای رفع این مشکل از یک سیم‌پیچ دیگر به نام سیم‌پیچ کمکی استفاده می‌کنند. این سیم‌پیچ باید دارای اختلاف فاز با سیم‌پیچ اصلی موتور باشد و برای ایجاد این اختلاف فاز از مصرف کننده‌های رآکتیو مانند سلف یا خازن استفاده می‌کنند. اختلاف فاز اندک بین موجب متمایل شدن روتور شده و روتور به حرکت در خواهد آمد. پس از به حرکت در آمدن رتور به علت وجود اینرسی موتور در همان جهت به چرخش ادامه خواهد داد و نیازی به سیم‌پیچ راه‌انداز نخواهد بود و (در بیشتر موتورهای القایی) این سیم‌پیچ از مدار خارج می‌شود. برای تغییر جهت چرخش در این موتورها باید جهت حرکت جریان در یکی از سیم‌پیچ‌های اصلی یا راه‌انداز را برعکس کرد. جستارهای وابسته موتور الکتریکی موتور روتور قفسی جریان متناوب منابع مشارکت‌کنندگان ویکی‌پدیا، «Induction motor»، ویکی‌پدیای ، دانشنامهٔ آزاد (بازیابی در ۳۱ اکتبر ۲۰۰۸). در ویکی‌انبار پرونده‌هایی دربارهٔ موتور القایی موجود است.

Three-phase totally enclosed fan-cooled (TEFC) induction motor, with and, at right, without end cover to show cooling fan. In TEFC motor, interior losses are dissipated indirectly through enclosure fins mostly by forced air convection. An induction or asynchronous motor is an AC motor in which current is induced in the rotor winding by the magnetic field of the stator winding, by electromagnetic induction. Therefore they do not require the sliding electric contacts, such as a commutator or slip rings, which are needed to transfer current to the rotor winding in other types of motor such as the universal motor. Rotor windings consist of short-circuited loops of conductors and are made in two types: the wound rotor and the squirrel-cage rotor. Three-phase squirrel-cage induction motors are widely used in industrial drives because they are rugged, reliable and economical. Single-phase induction motors are used extensively for smaller loads, such as household appliances like fans. Although the simple induction motor is a fixed-speed device, they are increasingly being used with variable-frequency drive (VFD) systems, which allow the speed to be varied. VFDs offer especially important energy savings opportunities for existing and prospective induction motors in variable-torque centrifugal fan, pump and compressor load applications. Squirrel cage induction motors are very widely used in both fixed-speed and VFD applications. Cutaway view through stator of TEFC induction motor. Note rotor air circulation vanes. History Nikola Tesla Early squirrel cage rotor In 1824, the French physicist François Arago formulated the existence of rotating magnetic fields, termed Arago's rotations, which, by manually turning switches on and off, Walter Baily demonstrated in 1879 as in effect the first primitive induction motor. Practical alternating current induction motors seem to have been independently invented by Galileo Ferraris and Nikola Tesla, a working motor model having been demonstrated by the former in 1885 and by the latter in 1887. Tesla applied for U.S. patents in October and November 1887 and was granted some of these patents in May 1888. He presented his technical paper A New System for Alternating Current Motors and Transformers to the American Institute of Electrical Engineers (AIEE) soon after that year. Tesla's paper described three four-stator-pole motor types: one with a four-pole rotor forming a non-self-starting reluctance motor, another with a wound rotor forming a self-starting induction motor, and the third a true synchronous motor with separately-excited DC supply to rotor winding. Tesla's U.S. Patent 382,279, filed in November 1887, however, described a shorted-winding-rotor induction motor. George Westinghouse promptly licensed Tesla’s patents and employed Tesla for one year as a consultant to develop them. Westinghouse employee C. F. Scott was assigned to assist Tesla and later took over development of the induction motor at Westinghouse. In 1888, the Royal Academy of Science of Turin published Ferraris's research detailing the foundations of motor operation while however concluding that "the apparatus based on that principle could not be of any commercial importance as motor." Steadfast in his promotion of three-phase development, Mikhail Dolivo-Dobrovolsky's invented the cage-rotor induction motor in 1889 and the three-limb transformer in 1890. However, he claimed that Tesla's motor was not practical because of two-phase pulsations, which prompted him to persist in his three-phase work. Although Westinghouse achieved its first practical induction motor in 1892 and developed a line of polyphase 60 hertz induction motors in 1893, these early Westinghouse motors were two-phase motors with wound rotors until B. G. Lamme developed a rotating bar winding rotor. The General Electric Company (GE) began developing three-phase induction motors in 1891. By 1896, General Electric and Westinghouse signed a cross-licensing agreement for the bar-winding-rotor design, later called the squirrel-cage rotor. GE's Charles Proteus Steinmetz was the first to make use of the letter "j" (the square root of negative one) to designate the 90 degree rotation operator in electrical mathematical expressions, and to thus be able to describe the induction motor in terms now commonly known as the Steinmetz equivalent circuit. Induction motor improvements flowing from these inventions and innovations were such that a 100 horsepower induction motor currently has the same mounting dimensions as a 7.5 horsepower motor in 1897. Principle of operation A three-phase power supply provides a rotating magnetic field in an induction motor. In both induction and synchronous motors, the AC power supplied to the motor's stator creates a magnetic field that rotates in time with the AC oscillations. Whereas a synchronous motor's rotor turns at the same rate as the stator field, an induction motor's rotor rotates at a slower speed than the stator field. The induction motor stator's magnetic field is therefore changing or rotating relative to the rotor. This induces an opposing current in the induction motor's rotor, in effect the motor's secondary winding, when the latter is short-circuited or closed through an external impedance. The rotating magnetic flux induces currents in the windings of the rotor; in a manner similar to currents induced in transformer's secondary windings. These currents in turn create magnetic fields in the rotor that react against the stator field. Due to Lenz's Law, the direction of the magnetic field created will be such as to oppose the change in current through the windings. The cause of induced current in the rotor is the rotating stator magnetic field, so to oppose this the rotor will start to rotate in the direction of the rotating stator magnetic field. The rotor accelerates until the magnitude of induced rotor current and torque balances the applied load. Since rotation at synchronous speed would result in no induced rotor current, an induction motor always operates slower than synchronous speed. The difference between actual and synchronous speed or slip varies from about 0.5 to 5% for standard Design B torque curve induction motors. The induction machine's essential character is that it is created solely by induction instead of being separately excited as in synchronous or DC machines or being self-magnetized as in permanent magnet motors. For these currents to be induced, the speed of the physical rotor must be lower than that of the stator's rotating magnetic field ($n_s$), or the magnetic field would not be moving relative to the rotor conductors and no currents would be induced. As the speed of the rotor drops below synchronous speed, the rotation rate of the magnetic field in the rotor increases, inducing more current in the windings and creating more torque. The ratio between the rotation rate of the magnetic field as seen by the rotor (slip speed) and the rotation rate of the stator's rotating field is called slip. Under load, the speed drops and the slip increases enough to create sufficient torque to turn the load. For this reason, induction motors are sometimes referred to as asynchronous motors. An induction motor can be used as an induction generator, or it can be unrolled to form the linear induction motor which can directly generate linear motion. Synchronous speed An AC motor's synchronous speed, $n_s$, is the rotation rate of the stator's magnetic field, which is expressed in revolutions per minute as $n_s={120\times{f}\over{p}}$ (RPM), where $f$ is the motor supply's frequency in Hertz and $p$ is the number of magnetic poles. That is, for a six-pole three-phase motor with three pole-pairs set 120° apart, $p$ equals 6 and $n_s$ equals 1,000 RPM and 1,200 RPM respectively for 50 Hz and 60 Hz supply systems. Slip Typical torque curve as a function of slip, represented as 'g' here. Slip, $s$, is defined as the difference between synchronous speed and operating speed, at the same frequency, expressed in rpm or in percent or ratio of synchronous speed. Thus $s = \frac{n_s-n_r}{n_s}\,$ where $n_s$ is stator electrical speed, $n_r$ is rotor mechanical speed. Slip, which varies from zero at synchronous speed and 1 when the rotor is at rest, determines the motor's torque. Since the short-circuited rotor windings have small resistance, a small slip induces a large current in the rotor and produces large torque. At full rated load, slip varies from more than 5% for small or special purpose motors to less that 1% for large motors. These speed variations can cause load-sharing problems when differently sized motors are mechanically connected. Various methods are available to reduce slip, VFDs often offering the best solution. Torque See also: Fleming's left-hand rule for motors Standard torque Speed-torque curves for four induction motor types: A) Single-phase, B) Polyphase cage, C) Polyphase cage deep bar, D) Polyphase double cage Typical speed-torque curve for NEMA Design B Motor The typical speed-torque relationship of a standard NEMA Design B polyphase induction motor is as shown in the curve at right. Suitable for most low performance loads such as centrifugal pumps and fans, Design B motors are constrained by the following typical torque ranges: Breakdown torque, 175-300 percent of rated torque Locked-rotor torque, 75-275 percent of rated torque Pull-up torque, 65-190 percent of rated torque. Over a motor's normal load range, the torque's slope is approximately linear or proportional to slip because the value of rotor resistance divided by slip, $R_r^'/s$, dominates torque in linear manner. As load increases above rated load, stator and rotor leakage reactance factors gradually become more significant in relation to $R_r^'/s$ such that torque gradually curves towards breakdown torque. As torque increases beyond breadown torque motor stalls. Although polyphase motors are inherently self-starting, their starting and pull-up torque design limits must be high enough to overcome actual load conditions. In two-pole single-phase motors, the torque goes to zero at 100% slip (zero speed), so these require alterations to the stator such as shaded-poles to provide starting torque. Starting Main article: Motor controller There are five basic types of competing small induction motor: single-phase capacitor-start, capacitor-run, split-phase and shaded-pole types, and small polyphase induction motors. A single-phase induction motor requires separate starting circuitry to provide a rotating field to the motor. The normal running windings within such a single-phase motor can cause the rotor to turn in either direction, so the starting circuit determines the operating direction. In certain smaller single-phase motors, starting is done by mean of a shaded pole with a copper wire turn around part of the pole. The current induced in this turn lags behind the supply current, creating a delayed magnetic field around the shaded part of the pole face. This imparts sufficient rotational field energy to start the motor. These motors are typically used in applications such as desk fans and record players, as the required starting torque is low, and the low efficiency is tolerable relative to the reduced cost of the motor and starting method compared to other AC motor designs. Larger single phase motors have a second stator winding fed with out-of-phase current; such currents may be created by feeding the winding through a capacitor or having it receive different values of inductance and resistance from the main winding. In some designs, the second winding is disconnected once the motor is up to speed, usually either by a centrifugal switch acting on weights on the motor shaft or a thermistor which heats up and increases its resistance, reducing the current through the second winding to an insignificant level. Other designs keep the second winding on when running, improving torque. Self-starting polyphase induction motors produce torque even at standstill. Available cage induction motor starting methods include direct-on-line starting, reduced-voltage reactor or auto-transformer starting, star-delta starting or, increasingly, new solid-state soft assemblies and, of course, VFDs. Polyphase motors have rotor bars shaped to give different speed-torque characteristics. The current distribution within the rotor bars varies depending on the frequency of the induced current. At standstill, the rotor current is the same frequency as the stator current, and tends to travel at the outermost parts of the cage rotor bars (by skin effect). The different bar shapes can give usefully different speed-torque characteristics as well as some control over the inrush current at startup. In wound rotor motors, rotor circuit connection through slip rings to external resistances allows change of speed-torque characteristics for acceleration control and speed control purposes. Speed control Typical speed-torque curves for different motor input frequencies as for example used with variable-frequency drives. Before the development of semiconductor power electronics, it was difficult to vary the frequency, and cage induction motors were mainly used in fixed speed applications. Applications such as electric overhead cranes used DC drives or wound rotor motors (WRIM) with slip rings for rotor circuit connection to variable external resistance allowing considerable range of speed control. However, resistor losses associated with low speed operation of WRIMs is a major cost disadvantage, especially for constant loads. Large slip ring motor drives, termed slip energy recovery systems, some still in use, recover energy from the rotor circuit, rectify it, and return it to the power system using a VFD. In many industrial variable-speed applications, DC and WRIM drives are being displaced by VFD-fed cage induction motors. The most common efficient way to control asynchronous motor speed of many loads is with VFDs. Barriers to adoption of VFDs due to cost and reliability considerations have been reduced considerably over the past three decades such that it is estimated that drive technology is adopted in as many as 30-40% of all newly installed motors. Construction Typical winding pattern for a three-phase (U, V, W), four-pole motor. Note the interleaving of the pole windings and the resulting quadrupole field. The stator of an induction motor consists of poles carrying supply current to induce a magnetic field that penetrates the rotor. To optimize the distribution of the magnetic field, the windings are distributed in slots around the stator, with the magnetic field having the same number of north and south poles. Induction motors are most commonly run on single-phase or three-phase power, but two-phase motors exist; in theory, induction motors can have any number of phases. Many single-phase motors having two windings can be viewed as two-phase motors, since a capacitor is used to generate a second power phase 90° from the single-phase supply and feeds it to the second motor winding. Single-phase motors require some mechanism to produce a rotating field on startup. Cage induction motor rotor's conductor bars are typically skewed to reduce noise. Rotation reversal The method of changing the direction of rotation of an induction motor depends on whether it is a three-phase or single-phase machine. In the case of three phase, reversal is carried out by swapping connection of any two phase conductors. In the case of a single-phase motor it is usually achieved by changing the connection of a starting capacitor from one section of a motor winding to the other. In this latter case both motor windings are usually similar (e.g. in washing machines). Power factor The power factor of induction motors varies with load, typically from around 0.85 or 0.90 at full load to as low as 0.35 at no-load, due to stator and rotor leakage and magnetizing reactances. Power factor can be improved by connecting capacitors either on an individual motor basis or, by preference, on a common bus covering several motors. For economic and other considerations power systems are rarely power factor corrected to unity power factor. Power capacitors application with harmonic currents requires power system analysis to avoid harmonic resonance between capacitors and transformer and circuit reactances. Common bus power factor correction is recommended to minimize resonant risk and to simplify power system analysis. Efficiency (See also Energy savings) Full load motor efficiency varies from about 85 to 97%, related motor losses being broken down roughly as follows: Friction and windage, 5% – 15% Iron or core losses, 15% – 25% Stator losses, 25% – 40% Rotor losses, 15% – 25% Stray load losses, 10% – 20%. Various regulatory authorities in many countries have introduced and implemented legislation to encourage the manufacture and use of higher efficiency electric motors. There is existing and forthcoming legislation regarding the future mandatory use of premium-efficiency induction-type motors in defined equipment. For more information, see: Premium efficiency and Copper in energy efficient motors. Steinmetz equivalent circuit (See also Equivalent circuit, Blocked rotor test, Open circuit test) Many useful motor relationships between time, current, voltage, speed, power factor and torque can be obtained from analysis of the Steinmetz equivalent circuit (also termed T-equivalent circuit or IEEE recommended equivalent circuit), a mathematical model used to describe how an induction motor's electrical input is transformed into useful mechanical energy output. The equivalent circuit is a single-phase representation of a multiphase induction motor that is valid in steady-state balanced-load conditions. The Steinmetz equivalent circuit is expressed simply in terms of the following components: Stator resistance and leakage reactance ($R_s$, $X_s$). Rotor resistance, leakage reactance, and slip ($R_r$, $X_r$ or $R_r^'$, $X_r^'$, and $s$). Magnetizing reactance ($X_m$). Paraphrasing from Alger in Knowlton, an induction motor is simply an electrical transformer the magnetic circuit of which is separated by an air gap between the stator winding and the moving rotor winding. The equivalent circuit can accordingly be shown either with equivalent circuit components of respective windings separated by an ideal transformer or with rotor components referred to the stator side as shown in the following circuit and associated equation and parameter definition tables. Steinmetz equivalent circuit The following rule-of-thumb approximations apply to the circuit: Maximum current happens under locked rotor current (LRC) conditions and is somewhat less than ${V_s}/X$, with LRC typically ranging between 6 and 7 times rated current for standard Design B motors. Breakdown torque $T_{max}$ happens when $s\approx{R_r^'/X}$ and $I_s\approx{0.7}LRC$ such that $T_{max}\approx{K*V_s^2}/(2X)$ and thus, with constant voltage input, a low-slip induction motor's percent-rated maximum torque is about half its percent-rated LRC. The relative stator to rotor leakage reactance of standard Design B cage induction motors is $\frac{X_s}{X_r^'}\approx\frac{0.4}{0.6}$. Neglecting stator resistance, an induction motor's torque curve reduces to the Kloss equation $T_{em}\approx\frac{2T_{max}}{\frac{s}{s_{max}}+\frac{s_{max}}{s}}$, where $s_{max}$ is slip at $T_{max}$. Linear induction motor Main article: linear induction motor Linear induction motors, that work on same general principles as rotary induction motors and are frequently three-phase, are designed to produce straight line motion. Uses include magnetic levitation, linear propulsion, linear actuators, and liquid metal pumping. See also Circle diagram Induction generator Premium efficiency Copper in energy efficient motors Notes References Classical sources Bailey, Benjamin Franklin (1911). The Induction Motor. McGraw-Hill.  Behrend, Bernhard Arthur (1901). The Induction Motor: A Short Treatise on its Theory and Design, With Numerous Experimental Data and Diagrams. McGraw Publishing Company / Electrical World and Engineer.  Boy de la Tour, Henri (1906). The Induction Motor: Its Theory and Design, Set Forth By a Practical Method of Calculation. Translated Cyprien Odilon Mailloux. McGraw Pub. Co.  External links An induction motor drawing Rotating magnetic fields: interactive, (Italian) Construct your squirrel cage induction motor, using povray Induction motor topics from Hyperphysics website hosted by C.R. Nave, GSU Physics and Astronomy Dept. Three-Phase Induction Machines hosted by University of Alberta's Andy Knight