محرك حثي

"Tesla motor" redirects here. For the electric car company, see Tesla, Inc.

Three-phase totally-enclosed fan-cooled (TEFC) induction motor with end cover on the left, and without end cover to show cooling fan on the right. In TEFC motors, interior heat losses are dissipated indirectly through enclosure fins, mostly by forced air convection.

Cutaway view through stator of TEFC induction motor, showing rotor with internal air circulation vanes. Many such motors have a symmetric armature, and the frame may be reversed to place the electrical connection box (not shown) on the opposite side.

المحرك الحثي هو محرك تيار متردد يقوم بتحويل الطاقة الكهربائية إلى طاقة حركية وهو أحد تطبيقات قانون فارادي للحث فهو يعمل فقط في أنظمة التيار المتناوب

induction motor or asynchronous motor is an AC electric motor in which the electric current in the rotor needed to produce torque is obtained by electromagnetic induction from the magnetic field of the stator winding. An induction motor can therefore be made without electrical connections to the rotor. An induction motor's rotor can be either wound type or squirrel-cage type.

Three-phase squirrel-cage induction motors are widely used as industrial drives because they are self-starting, reliable, and economical. Single-phase induction motors are used extensively for smaller loads, such as garbage disposals and stationary power tools. Although traditionally only used for one-speed service, single- and three-phase induction motors are increasingly being installed in variable-speed applications using variable-frequency drives (VFD). VFDs offer especially important energy savings opportunities for existing and prospective induction motors in applications like fans, pumps and compressors that have a variable load.

المحرك الحثي

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 تاريخ

A model of Nikola Tesla's first induction motor at the Tesla Museum in Belgrade, Serbia

Squirrel-cage rotor construction, showing only the center three laminations

In 1824, the French physicist François Arago formulated the existence of rotating magnetic fields, termed Arago's rotations. By manually turning switches on and off, Walter Baily demonstrated this in 1879, effectively the first primitive induction motor.

The first commutator-free single-phase AC induction motor was invented by Hungarian engineer Ottó Bláthy; he used the single-phase motor to propel his invention, the electricity meter.

The first AC commutator-free polyphase induction motors were 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 US patents in October and November 1887 and was granted some of these patents in May 1888. In April 1888, the Royal Academy of Science of Turin published Ferraris's research on his AC polyphase motor detailing the foundations of motor operation. In May 1888 Tesla presented the technical paper A New System for Alternating Current Motors and Transformers to the American Institute of Electrical Engineers (AIEE) describing three four-stator-pole motor types: one having 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 a separately excited DC supply to the rotor winding.

George Westinghouse, who was developing an alternating current power system at that time, licensed Tesla's patents in 1888 and purchased a US patent option on Ferraris' induction motor concept. Tesla was also employed for one year as a consultant. Westinghouse employee C. F. Scott was assigned to assist Tesla and later took over development of the induction motor at Westinghouse. Steadfast in his promotion of three-phase development, Mikhail Dolivo-Dobrovolsky invented the cage-rotor induction motor in 1889 and the three-limb transformer in 1890. Furthermore, 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. Arthur E. Kennelly was the first to bring out the full significance of complex numbers (using j to represent the square root of minus one) to designate the 90º rotation operator in analysis of AC problems. GE's Charles Proteus Steinmetz greatly developed application of AC complex quantities including an analysis model now commonly known as the induction motor 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.

 مبدأ عمله

يسير تيار متردد من جهة الطرف الثابت المربوط في مصدر جهد متردد ويمر التيار في ملفات الساكن التي تختلف في عدد الأقطاب من محرك لآخر و عند مرور التيار المتردد في ملف ينشأ فيض مغناطيسي متردد كذلك طبقا لقانون فرداي و يجري هذا الفيض في الدائرة المغناطيسية التي تتكون بين الساكن و الدوار - حيث لا يوجد أي ربط كهربي بين الساكن و الدوار - وعندما يمر فيض مغناطيسي في ملفات الطرف الدوار يستحث تيار كهربائي في دائرة الدوار الكهربية طبقا كذلك لقانون فرداي فينتج عن حركة التيار و الفيض مجال مغناطيسي دوار يقوم بتدوير الطرف الثانوي .

 مكونات المحرك

يتكون المحرك من طرفين أحدهما ساكنويسمى(stator)والآخر دوارويسمى(rotor)وترتبط سرعة الدوران بقيمة تردد التيار في الدائرة والمحرك الحثي هو المحرك الأكثر استعمالا في المصانع والآلات, ويتكون دوار من شرائح لتقليل تيار الفقد (eddy current loss) و زيادة الكفاءة

وما بين الدوار و الساكن مسافة من الهواء تسمى الثغرة الهوائية(air gap) و كلما قلت المسافة بين الدوار و الساكن قلت قيمة مقاومة الهواء .

 أنواع المحرك

للمحرك ذو التيار المتردد نوعان :

• المحرك ذو القفص السنجابي
• المحرك انزلق

كائية تصية

 الإنشاء

Typical winding pattern for a three-phase (U, W, V), 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, 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. Induction motors using a squirrel-cage rotor winding may have the rotor bars skewed slightly to smooth out torque in each revolution.

Standardized NEMA & IEC motor frame sizes throughout the industry result in interchangeable dimensions for shaft, foot mounting, general aspects as well as certain motor flange aspect. Since an open, drip proof (ODP) motor design allows a free air exchange from outside to the inner stator windings, this style of motor tends to be slightly more efficient because the windings are cooler. At a given power rating, lower speed requires a larger frame.

 الكفاءة

انظر أيضاً: Variable-frequency drive § Energy savings

Full-load motor efficiency is around 85–97%, 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%.

For an electric motor, the efficiency, represented by the Greek letter Eta, is defined as the quotient of the output mechanical power and the input electric power, and calculated using this formula:

$\eta =OutputMechanicalPower\div InputElectricalPower$

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.

 دائرة ستاينمتس المكافئة

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 $V_{\text{s}}/X$, with LRC typically ranging between 6 and 7 times rated current for standard Design B motors.
• Breakdown torque $T_{\text{max}}$ happens when $s\approx R_{\text{r}}'/X$ and $I_{\text{s}}\approx 0.7\;LRC$ such that $T_{\text{max}}\approx KV_{\text{s}}^{2}/2X$ 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

  ${\frac {X_{\text{s}}}{X_{\text{r}}'}}\approx {\frac {0.4}{0.6}}$.

• Neglecting stator resistance, an induction motor's torque curve reduces to the Kloss equation

  $T_{\text{em}}\approx {\frac {2T_{\text{max}}}{{\frac {s}{s_{\text{max}}}}+{\frac {s_{\text{max}}}{s}}}}$, where $s_{\text{max}}$ is slip at $T_{\text{max}}$.

Circuit parameter definitions
		الوحدات
$f$	stator source frequency	Hz
$f_{\text{s}}$	stator synchronous frequency	Hz
$n_{\text{r}}$	rotor speed in revolutions per minute	rpm
$n_{\text{s}}$	synchronous speed in revolutions per minute	rpm
$I_{\text{s}}$	stator or primary current	A
$I_{\text{r}}'$	rotor or secondary current referred to stator side	A
$I_{\text{m}}$	magnetizing current	A
$j={\sqrt {-1}}$	imaginary number, or 90° rotation, operator
$K_{\text{TE}}$	$=X_{m}/\left(X_{s}+X_{m}\right)$ Thévenin reactance factor
$m$	number of motor phases
$p$	number of motor poles
$P_{\text{em}}$	electromechanical power	W or hp
$P_{\text{gap}}$	air gap power	W
$P_{\text{r}}$	rotor copper losses	W
$P_{\text{o}}$	input power	W
$P_{\text{h}}$	core loss	W
$P_{\text{f}}$	friction and windage loss	W
$P_{\text{rl}}$	running light watts input	W
$P_{\text{sl}}$	stray-load loss	W
$R_{\text{s}},X_{\text{s}}$	stator or primary resistance and leakage reactance	Ω
$R_{\text{r}}',X_{\text{r}}'$	rotor or secondary resistance & leakage reactance referred to the stator side	Ω
$R_{\text{o}},X_{\text{o}}$	resistance & leakage reactance at motor input	Ω
$R_{\text{TE}},X_{\text{TE}}$	Thévenin equivalent resistance & leakage reactance combining $R_{\text{s}},X_{\text{s}}$ and $X_{m}$	Ω
$s$	slip
$T_{\text{em}}$	electromagnetic torque	Nm or ft-lb
$T_{\text{max}}$	breakdown torque	Nm or ft-lb
$V_{\text{s}}$	impressed stator phase voltage	V
$X_{\text{m}}$	magnetizing reactance	Ω
$X$	$X_{s}+X_{r}'$	Ω
$Z_{\text{s}}$	stator or primary impedance	Ω
$Z_{\text{r}}'$	rotor or secondary impedance referred to the primary	Ω
$Z_{\text{o}}$	impedance at motor stator or primary input	Ω
$Z$	combined rotor or secondary and magnetizing impedance	Ω
$Z_{\text{TE}}$	Thévenin equivalent circuit impedance, $R_{\text{TE}}+X_{\text{TE}}$	Ω
$\omega _{\text{r}}$	rotor speed	rad/s
$\omega _{\text{s}}$	synchronous speed	rad/s
$Y$	$=G+jB={\frac {1}{Z}}={\frac {1}{R+jX}}={\frac {R}{Z^{2}}}-{\frac {jX}{Z^{2}}}$	S or Ʊ
$\left\vert Z\right\vert$	${\sqrt {R^{2}+X^{2}}}$	Ω

Basic electrical equations

$\omega _{\text{s}}={\frac {2\pi n_{\text{s}}}{60}}=2\pi f_{\text{s}}={\frac {4\pi f}{p}}$ Motor input equivalent impedance $Z_{\text{m}}=R_{\text{s}}+jX_{\text{s}}+{\frac {\left({\frac {1}{s}}R_{\text{r}}'+jX_{r}'\right)(jX_{\text{m}})}{{\frac {1}{s}}R_{\text{r}}'+j\left(X_{\text{r}}'+X_{\text{m}}\right)}}$ Stator current $I_{\text{s}}=V_{\text{s}}/Z_{\text{m}}=V_{\text{s}}/\left(R_{\text{s}}+jX_{\text{s}}+{\frac {\left({\frac {1}{s}}R_{\text{r}}'+jX_{\text{r}}'\right)(jX_{\text{m}})}{{\frac {1}{s}}R_{\text{r}}'+j\left(X_{\text{r}}'+X_{m}\right)}}\right)$ Rotor current referred to the stator side in terms of stator current $I_{\text{r}}'={\frac {jX_{m}}{{\frac {1}{s}}R_{\text{r}}'+j\left(X_{\text{r}}'+X_{\text{m}}\right)}}I_{\text{s}}$

Power equations

From Steinmetz equivalent circuit, we have ${\frac {1}{s}}R_{\text{r}}'=R_{\text{r}}'{\frac {1-s}{s}}+R_{\text{r}}'$ That is, air gap power is equal to electromechanical power output plus rotor copper losses ${\begin{aligned}P_{\text{gap}}&=P_{\text{em}}+P_{r}\\P_{r}&=3R_{\text{r}}'I_{\text{r}}^{\prime 2}\\P_{\text{gap}}&={\frac {3R_{\text{r}}'I_{\text{r}}^{\prime 2}}{s}}\\P_{\text{em}}&=3R_{\text{r}}'I_{\text{r}}^{\prime 2}{\frac {1-s}{s}}\\P_{\text{em}}&=P_{\text{gap}}(1-s)\end{aligned}}$ Expressing electromechanical power output in terms of rotor speed $P_{\text{em}}={\frac {3R_{\text{r}}'I_{\text{r}}^{\prime 2}n_{\text{r}}}{sn_{\text{s}}}}$ (watts) $P_{\text{em}}={\frac {3R_{\text{r}}'I_{\text{r}}^{\prime 2}n_{\text{r}}}{746\;sn_{\text{s}}}}$ (hp) Expressing $T_{\text{em}}$ in ft-lb: $P_{\text{em}}={\frac {T_{\text{em}}n_{\text{r}}}{5252}}$ (hp)

Torque equations

$T_{\text{em}}={\frac {P_{\text{em}}}{\omega _{r}}}={\frac {\frac {P_{\text{r}}}{s}}{\omega _{s}}}={\frac {3I_{\text{r}}^{\prime 2}R_{\text{r}}'}{\omega _{\text{s}}s}}$ (newton-meters) In order to be able to express $T_{\text{em}}$ directly in terms of $s$, IEEE recommends that $R_{\text{s}},X_{\text{s}}$ and $X_{\text{m}}$ be converted to the Thévenin equivalent circuit IEEE recommended Thévenin equivalent circuit حيث $V_{\text{TE}}={\frac {X_{\text{m}}}{\sqrt {R_{\text{s}}^{2}+(X_{\text{s}}+X_{\text{m}})^{2}}}}V_{\text{s}}$ $Z_{\text{TE}}=R_{\text{TE}}+jX_{\text{TE}}={\frac {jX_{\text{m}}\left(R_{\text{s}}+jX_{\text{s}}\right)}{R_{\text{s}}+j\left(X_{\text{s}}+X_{\text{m}}\right)}}$ Since $R_{\text{s}}^{2}\gg {\left(X_{\text{s}}+X_{\text{m}}\right)^{2}}$ and $X_{\text{s}}\ll X_{\text{m}}$, and letting $K_{\text{TE}}={\frac {X_{\text{m}}}{X_{\text{s}}+X_{\text{m}}}}$ $V_{\text{TE}}\approx Z_{\text{TE}}V_{\text{s}}$ and $Z_{\text{TE}}\approx K_{\text{TE}}^{2}R_{\text{s}}+jX_{\text{s}}$ $T_{\text{em}}={\frac {3V_{\text{TE}}^{2}}{\left(R_{\text{TE}}+{\frac {1}{s}}R_{\text{r}}'\right)^{2}+\left(X_{\text{TE}}+X_{r}'\right)^{2}}}\cdot {\frac {1}{s}}R_{\text{r}}'\cdot {\frac {1}{\omega _{\text{s}}}}$ (N·m) For low values of slip: Since $R_{\text{TE}}+R_{\text{r}}'\gg R_{\text{TE}}+X_{\text{r}}'$ and $R_{\text{r}}'\gg R_{\text{TE}}$ $T_{\text{em}}\approx {\frac {1}{\omega _{\text{s}}}}\cdot {\frac {3V_{\text{TE}}^{2}}{R_{\text{r}}'}}s$ (N·m) For high values of slip Since $R_{\text{TE}}+R_{r}'\ll R_{\text{TE}}+X_{r}'$ $T_{\text{em}}\approx {\frac {1}{\omega _{\text{s}}}}\cdot {\frac {3V_{\text{TE}}^{2}}{\left(X_{\text{s}}+X_{\text{r}}'\right)^{2}}}\cdot {\frac {R_{\text{r}}^{\prime 2}}{s}}$ (N·m) For maximum or breakdown torque, which is independent of rotor resistance $T_{\text{max}}={\frac {1}{2\omega _{s}}}\cdot {\frac {3V_{\text{TE}}^{2}}{R_{\text{TE}}+{\sqrt {R_{\text{TE}}^{2}+(X_{\text{TE}}+X_{\text{r}}')^{2}}}}}$ (N·m) Corresponding slip at maximum or breakdown torque is $s={\frac {R_{\text{r}}'}{\sqrt {R_{\text{TE}}^{2}+\left(X_{\text{TE}}+X_{\text{r}}'\right)^{2}}}}$ In foot-pound units $T_{\text{em}}={\frac {21.21\;I_{r}^{\prime 2}R_{\text{r}}'}{n_{\text{r}}s}}$ (ft-lb) $T_{\text{em}}={\frac {7.04\;P_{\text{gap}}}{n_{\text{s}}}}$ (ft-lb)

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 محرك حثي خطي

المقالة الرئيسية: Linear induction motor

Linear induction motors, which work on the same general principles as rotary induction motors (frequently three-phase), are designed to produce straight line motion. Uses include magnetic levitation, linear propulsion, linear actuators, and liquid metal pumping.

 انظر أيضاً

• AC motor
• Circle diagram
• Induction generator
• Premium efficiency
• Variable refrigerant flow

 المصادر التقليدية

• Bailey, Benjamin Franklin (1911). The Induction Motor. McGraw-Hill. induction motor.
• 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.

 وصلات خارجية

• Who Invented the Polyphase Electric Motor?
• Silvanus Phillips Thompson: Polyphase electric currents and alternate current motors
• Induction motor topics from Hyperphysics website hosted by C.R. Nave, GSU Physics and Astronomy Dept.
• Cowern Papers