Difference between revisions of "Brushed DC Motor Theory"
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[[Category:Motors]] |
[[Category:Motors]] |
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'''How does a motor work?''' |
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Let's consider a permanent magnet brushed motor. The piece connected to the ground is called the <I>stator</I> and the piece |
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connected to the |
connected to the output shaft is called the <I>rotor</I>. The inputs of the motor are connected to 2 wires and by applying a voltage |
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across them, the motor turns. |
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connected to the output shaft is called the <I>rotor</I>. The inputs |
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of the motor are connected to 2 wires and by applying a voltage |
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across them, the motor turns.</P> |
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The<I> torque </I>of a motor is generated by a current carrying conductor in a magnetic field. The<I> right hand rule </I>states that |
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if you point your right hand fingers along the direction of current, <math>I</math>, and curl them towards the direction of the magnetic flux, <math>B</math>, the direction of force is along the thumb. |
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conductor in a magnetic field. The<I> right hand rule </I>states that |
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if you point your right hand fingers along the direction of current, |
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I, and curl them towards the direction of the magnetic flux, B, the |
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direction of force is along the thumb.</P> |
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[[image:motor1.gif|580px]] |
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<P><IMG SRC="motor1.gif" WIDTH=580 HEIGHT=454 X-CLARIS-USEIMAGEWIDTH X-CLARIS-USEIMAGEHEIGHT ALIGN=bottom></P> |
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Now, imagine a loop of wire with some resistance is inserted between the two permanent magnets. The following diagrams show how |
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the motor turns: |
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between the two permanent magnets. The following diagrams show how |
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the motor turns:</P> |
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{| |
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<P><TABLE BORDER=1 WIDTH=900 HEIGHT=480> |
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|+ |
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<TR> |
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|[[image:motor2.jpg|480px|frame|Diagram showing how the motor works]] |
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|[[image:sine1.jpg|454px|framce|Relationship between the Torque and the angle the loop made with the magnet]] |
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|} |
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You might be able to notice that the direction of rotation is changing every half cycle. To keep it rotating in the same direction, |
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<TD WIDTH=440 HEIGHT=405> |
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we have to switch the current direction. The process of switching current is called commutation. To switch the direction of curent, we |
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<P><IMG SRC="motor2.gif" WIDTH=480 HEIGHT=473 X-CLARIS-USEIMAGEWIDTH X-CLARIS-USEIMAGEHEIGHT ALIGN=bottom></P> |
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have to use <I>brushes</I> and <I>commutators</I>. Commutation can also be done electronically (Brushless motors) and a brushless motor |
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usually has a longer life. The following diagram shows how brushes and commutators work. |
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<P>Diagram showing how the motor works</P> |
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</TD> |
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<TD WIDTH=454 HEIGHT=405> |
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<P><IMG SRC="sine1.jpg" WIDTH=454 HEIGHT=437 X-CLARIS-USEIMAGEWIDTH X-CLARIS-USEIMAGEHEIGHT ALIGN=bottom></P> |
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<P>Relationship between the Torque and the angle the loop |
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made with the magnet.</P> |
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</TD> |
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[[image:motor3.gif|550px]] |
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</TR> |
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</TABLE> |
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</P> |
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We could also have several commutators and loops. The total torque generated is the sum of all the torques from each of the loops |
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<P>You might be able to notice that the direction of rotation is |
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added. |
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changing every half cycle. To keep it rotating in the same direction, |
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we have to switch the current direction. The process of switching |
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current is called commutation. To switch the direction of curent, we |
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have to use <I>brushes</I> and <I>commutators</I>. Commutation can |
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also be done electronically (Brushless motors) and a brushless motor |
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usually has a longer life. The following diagram shows how brushes |
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and commutators work.</P> |
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{| |
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<P><IMG SRC="motor3.gif" WIDTH=550 HEIGHT=473 X-CLARIS-USEIMAGEWIDTH X-CLARIS-USEIMAGEHEIGHT ALIGN=bottom></P> |
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|+ |
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|[[image:brush.jpg|350px|frame|Motor with several commutators and loops]] |
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|[[image:torque1.jpg|300px]] |
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|[[image:torque2.jpg|300px]] |
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|} |
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So, the torque is proportional to the current through the windings, |
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<P>We could also have several commutators and loops. The total torque |
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generated is the sum of all the torques from each of the loops |
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added.</P> |
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<math>\Tau = k I</math>, |
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<P><TABLE BORDER=1 WIDTH=950 bordercolor="#000000" bordercolordark="#000000" bordercolorlight="#FFFFFF"> |
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<TR> |
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<TD WIDTH=350> |
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<P><IMG SRC="brush.jpg" WIDTH=350 HEIGHT=250 X-CLARIS-USEIMAGEWIDTH X-CLARIS-USEIMAGEHEIGHT ALIGN=bottom></P> |
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<P>Motor with several commutators and loops</P> |
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</TD> |
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<TD WIDTH=300> |
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<P><IMG SRC="torque1.jpg" WIDTH=300 HEIGHT=240 X-CLARIS-USEIMAGEWIDTH X-CLARIS-USEIMAGEHEIGHT ALIGN=bottom></P> |
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where <math>\Tau</math> is the torque, <math>I</math> is the current, and <math>k</math> is a constant. The wire coils have both a resistance, <math>R</math>, and an inductance, <math>L</math>. When the motor is turning, the current is switching, causing a |
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</TD> |
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voltage, |
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<TD WIDTH=300> |
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<P><IMG SRC="torque2.jpg" WIDTH=300 HEIGHT=240 X-CLARIS-USEIMAGEWIDTH X-CLARIS-USEIMAGEHEIGHT ALIGN=bottom></P> |
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</TD> |
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</TR> |
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</TABLE> |
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</P> |
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<math>V = L \frac{dI}{dt}</math> |
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<P>So, the torque is proportional to the current through the |
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windings,</P> |
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This voltage is known as the back-emf(electromotive force), <math>\epsilon</math>. If the angular velocuty of the motor is <math>\omega</math>, then |
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<BLOCKQUOTE>T = kI where T is the torque, I is the current, and k is |
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a constant</BLOCKQUOTE> |
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<math>\epsilon = k\omega</math>, |
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<P>The wire coils have both a resistance, R, and an inductance, L. |
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When the motor is turning, the current is switching, causing a |
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voltage,</P> |
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like a generator. This voltage, <math>\epsilon</math>, is working against the voltage we apply across the terminals, and so, |
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<P>V = L dI/dt</P> |
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<math>(V- k\omega) = IR</math>, |
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<P>This voltage is known as the back-emf(electromotive force), e.</P> |
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where |
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<P>If the angular velocuty of the motor is w, then e = k<I>w</I> |
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(like a generator)</P> |
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<math>I = \frac{\Tau}{R}</math> |
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<P>This voltage, e, is working against the voltage we apply across |
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the terminals, and so,</P> |
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which implies |
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<P>(V- k<I>w</I>) = IR where I =<I> T</I>/R</P> |
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< |
<math>(V-k\omega) = \frac{\Tau}{k}R</math>. |
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The maximum or stall torque is the torque at which <math>\omega = 0</math> or |
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<math>\Tau = \frac{kV}{R}</math>, |
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and the stall or starting current, |
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<math>I = \frac{V}{R}</math> |
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<P>The no load speed, <I>w</I> = V/k, is the maximum speed the motor |
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can run. Given a constant voltage, the motor will settle at a |
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constant speed, just like a terminal velocity.</P> |
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The no load speed, |
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<P>If we plot w = V/k - (<I>T</I>/k^2)R, we can get the speed-torque |
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<math>\omega = \frac{V}{k}</math>, |
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is the maximum speed the motor can run. Given a constant voltage, the motor will settle at a constant speed, just like a terminal velocity. If we plot w = V/k - (<I>T</I>/k^2)R, we can get the speed-torque |
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curve:</P> |
curve:</P> |
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Revision as of 13:17, 9 June 2006
How does a motor work?
Let's consider a permanent magnet brushed motor. The piece connected to the ground is called the stator and the piece connected to the output shaft is called the rotor. The inputs of the motor are connected to 2 wires and by applying a voltage across them, the motor turns.
The torque of a motor is generated by a current carrying conductor in a magnetic field. The right hand rule states that if you point your right hand fingers along the direction of current, , and curl them towards the direction of the magnetic flux, , the direction of force is along the thumb.
Now, imagine a loop of wire with some resistance is inserted between the two permanent magnets. The following diagrams show how the motor turns:
You might be able to notice that the direction of rotation is changing every half cycle. To keep it rotating in the same direction, we have to switch the current direction. The process of switching current is called commutation. To switch the direction of curent, we have to use brushes and commutators. Commutation can also be done electronically (Brushless motors) and a brushless motor usually has a longer life. The following diagram shows how brushes and commutators work.
We could also have several commutators and loops. The total torque generated is the sum of all the torques from each of the loops added.
So, the torque is proportional to the current through the windings,
,
where is the torque, is the current, and is a constant. The wire coils have both a resistance, , and an inductance, . When the motor is turning, the current is switching, causing a voltage,
This voltage is known as the back-emf(electromotive force), . If the angular velocuty of the motor is , then
,
like a generator. This voltage, , is working against the voltage we apply across the terminals, and so,
,
where
which implies
.
The maximum or stall torque is the torque at which or
,
and the stall or starting current,
The no load speed,
,
is the maximum speed the motor can run. Given a constant voltage, the motor will settle at a constant speed, just like a terminal velocity. If we plot w = V/k - (T/k^2)R, we can get the speed-torque
curve:
<IMG SRC="graph.jpg" WIDTH=320 HEIGHT=230 X-CLARIS-USEIMAGEWIDTH X-CLARIS-USEIMAGEHEIGHT ALIGN=bottom>
Units
Here are the different units for the torque, current and voltage
Torque: oz.in., Nm (=kgm/s^2*m), kgfm(=9.8 times Nm), gfcm, mNm, etc.
Current: Amperes(Amps), mA
Voltage: Volts
mechanical power = T*w(Nm/sec) = 1 watt
electrical power = VI = 1 volt * amp = 1watt