토크가 일정하게 유지할 수 있다.
이 사이트에 자세히 나와있다.
http://www.instructables.com/id/Make-Your-Own-Miniature-Electric-Hub-Motor/step2/The-Brushless-DC-Motor/
위 사이트 자료는 아래에.
Step 2: The Brushless DC Motor
At the heart of most hub motors is a brushless DC motor. To build a hub motor right, you need to understand some basics of brushless DC motors. To understand brushless DC motors, you should understand brushed DC motors. If you've taken a controls class, chances are that you've used brushed DC motors as a "plant" to test your controls on.
I've highlighted and bolded the juicy stuff that you'll need, but for the sake of continuity it's probably good to grunge through all of it anyway.
Brushed DC Motor Physics
Perhaps the best DC motor primer I have seen (I'm not biased at all, I promise guys! Pinky promise! ) is the MIT OpenCourseware notes for 2.004: Dynamics and Control II. Take a read through it at your own leisure, but the basic rundown is that a brushed DC motor is a bidirectional transducer between electrical power and mechanical power that is characterized by a motor constant Km , and an internal resistance Rm. For simplicity, motor inductance L will not be considered. Essentially if you know Km and Rm, and a few details about your power source, you can more or less characterize your entire motor.\
Update 10/06/2010: The original 2.004 document link is dead, but here's onethat's roughly the same content-wise. Also from MIT OCW.
The motor constant Km contains information about how much torque your motor will produce per ampere of current draw (Nm / A) as well as how many voltsyour motor will generate across its terminals per unit speed that you spin it at (V / rad / s, or Vs / rad, or simply V*s). This "back-EMF constant" is numerically equal to Km, but some times called Kv.
In a DC motor, Km is given by the expression
Km = 2 * N * B * L * R
where N is the number of complete loops of wire interacting with your permanent magnetic field of strength B (measured in Tesla). This interaction occurs across a certain length L which is generally the length of your magnets, and a radius Rwhich is the radius of your motor armature. The 2 comes from the fact that your loop of wire must go across then back across the area of magnetic influence in order to close on itself. This R has nothing to do with Rm, by the way.
As an aside, I will be using only SI (metric!!!!!) units here because they are just so much easier to work with for physics.
Let's look at the expression for Km again. We know from the last page that
Pe = V * I and Pm = T * ω
In the ideal motor of 100% efficiency (the perfect transducer), Pe = Pm, because power in equals power out. So
V * I = T * ω
Where have we seen this before? Swap some values:
V / ω = T / I
Kv = Km
Oh snap.
The takeaway fact of this is that knowing a few key dimensions of your motor: The magnetic field strength, the length of the magnetic interaction, the number of turns, and the radius of the armature, you can actually ballpark your motor performance figures usually to within a factor of 2.
Now it's time for...
The Brushless DC Motor
BLDC motors lie in the Awkward Gray Zone between DC motor and AC motors. There is substantial disagreement in the EE and motor engineering community about how a machine which relies on three phase alternating current can be called a DC motor. The differentiating factor for me personally is:
In a brushless DC motor, electronic switches replace the mechanical brush-and-copper switch that route current to the correct windings at the correct time to generate a rotating magnetic field. The only duty of the electronics is to emulate the commutator as if the machine were a DC motor. No attempt is made to use AC motor control methods to compensate for the AC characteristics of the machine.
This gives me an excuse to use DC motor analysis methods to rudimentarily design BLDC motors.
I will admit that I do not have in depth knowledge of BLDC or AC machines. In another daring act of outsourcing, I will encourage you to peruse James Mevey's Incredible 350-something-page Thesis about Anything and Everything you Ever Wanted to Know about Brushless Motors Ever. Like, Seriously Ever.
There's alot of things you don't need to know in that, though, such as how field-oriented control works. What is extremely helpful in understand BLDC motors is the derivation of their torque characteristics from pages 37 to 46. The short rundown of how things work in a BLDC motor is that an electronic controller sends current through two out of three phases of the motor in an order that generates a rotating magnetic field, a really trippy-ass thing that looks like this.
The reason that we consider two out of three phases is because a 3 phase motor has, fundemantally, 3 connections, two of which are used at any one time. Here's a good illustration of the possible configurations of 3 phase wiring. Current must come in one connection, and out the other.
In Mevey 38, equation 2.30, the torque of one BLDC motor phase is given by
T = 2 * N * B * Y * i * D/2
where Y has replaced L in my previous DC motor equation and D/2 (half the rotor diameter) replaces R.
If you do it my way, it becomes
T = 2 * N * B * L * R * i , replacing D/2 with R.
Remember now that two phases of the motor has current i flowing in it. Hence,
T = 4 * N * B * L * R * i
This is the Equations to Know for simple estimation of BLDC torque. Peak torque production is (modestly) equal to 4 times the:
� number of turns per phase
� strength of the permanent magnetic field
� length of the stator / core (or the magnet too, if they are equal)
� radius of the stator
� current in the motor windings
As expected, this scales linearly with current. In real life, this will probably get you within a factor of two. That is, your actual torque production might be between this theoretical T and T/2
Wait, 4? Does that mean if I turn my brushed DC motor into a brushless motor, it will suddenly have twice the torque? Not necessarily. This is a mathematical construct - a DC motor's windings are considered in a different fashion which causes the definition of N and L to change.
Next, we will see how to use this equation to size your motor.
28 July 2010 Update to the definition of T
In the equation T = 4* N * L * B * R i, the constant 4 comes from the derivation of a motor with only one tooth per phase, assuming N is the number of turns of wire per tooth on the stator.
The full derivation of this constant involves each loop of wire actually being twosections of wire, each of length L. This is due the fact that a loop involves going across the stator, then back again. Next, in a BLDC motor, two phases are always powered, therefore contributing torque.
We can observe that in a motor with only 1 tooth per phase (a 3-toothed stator), there are no more multiplicative factors. However, for each tooth you add per phase (2 teeth per phase in a 6-tooth stator, 3 teeth per phase in a 9-tooth stator, etc.) the above constant must be multiplied accordingly. The constant in front of the equation essentially accounts for the number of active passes of wire, which is 2 passes per loop times 2 phases active times number of teeth per phase.
So, what I actually mean is that T = 4 * m * N * B * L * R * i where
m = the newly defined teeth per phase count.
As the windings themselves have yet to be introduced, keep in mind the number of teeth per phase in the dLRK winding is 4.
I've highlighted and bolded the juicy stuff that you'll need, but for the sake of continuity it's probably good to grunge through all of it anyway.
Brushed DC Motor Physics
Perhaps the best DC motor primer I have seen (I'm not biased at all, I promise guys! Pinky promise! ) is the MIT OpenCourseware notes for 2.004: Dynamics and Control II. Take a read through it at your own leisure, but the basic rundown is that a brushed DC motor is a bidirectional transducer between electrical power and mechanical power that is characterized by a motor constant Km , and an internal resistance Rm. For simplicity, motor inductance L will not be considered. Essentially if you know Km and Rm, and a few details about your power source, you can more or less characterize your entire motor.\
Update 10/06/2010: The original 2.004 document link is dead, but here's onethat's roughly the same content-wise. Also from MIT OCW.
The motor constant Km contains information about how much torque your motor will produce per ampere of current draw (Nm / A) as well as how many voltsyour motor will generate across its terminals per unit speed that you spin it at (V / rad / s, or Vs / rad, or simply V*s). This "back-EMF constant" is numerically equal to Km, but some times called Kv.
In a DC motor, Km is given by the expression
Km = 2 * N * B * L * R
where N is the number of complete loops of wire interacting with your permanent magnetic field of strength B (measured in Tesla). This interaction occurs across a certain length L which is generally the length of your magnets, and a radius Rwhich is the radius of your motor armature. The 2 comes from the fact that your loop of wire must go across then back across the area of magnetic influence in order to close on itself. This R has nothing to do with Rm, by the way.
As an aside, I will be using only SI (metric!!!!!) units here because they are just so much easier to work with for physics.
Let's look at the expression for Km again. We know from the last page that
Pe = V * I and Pm = T * ω
In the ideal motor of 100% efficiency (the perfect transducer), Pe = Pm, because power in equals power out. So
V * I = T * ω
Where have we seen this before? Swap some values:
V / ω = T / I
Kv = Km
Oh snap.
The takeaway fact of this is that knowing a few key dimensions of your motor: The magnetic field strength, the length of the magnetic interaction, the number of turns, and the radius of the armature, you can actually ballpark your motor performance figures usually to within a factor of 2.
Now it's time for...
The Brushless DC Motor
BLDC motors lie in the Awkward Gray Zone between DC motor and AC motors. There is substantial disagreement in the EE and motor engineering community about how a machine which relies on three phase alternating current can be called a DC motor. The differentiating factor for me personally is:
In a brushless DC motor, electronic switches replace the mechanical brush-and-copper switch that route current to the correct windings at the correct time to generate a rotating magnetic field. The only duty of the electronics is to emulate the commutator as if the machine were a DC motor. No attempt is made to use AC motor control methods to compensate for the AC characteristics of the machine.
This gives me an excuse to use DC motor analysis methods to rudimentarily design BLDC motors.
I will admit that I do not have in depth knowledge of BLDC or AC machines. In another daring act of outsourcing, I will encourage you to peruse James Mevey's Incredible 350-something-page Thesis about Anything and Everything you Ever Wanted to Know about Brushless Motors Ever. Like, Seriously Ever.
There's alot of things you don't need to know in that, though, such as how field-oriented control works. What is extremely helpful in understand BLDC motors is the derivation of their torque characteristics from pages 37 to 46. The short rundown of how things work in a BLDC motor is that an electronic controller sends current through two out of three phases of the motor in an order that generates a rotating magnetic field, a really trippy-ass thing that looks like this.
The reason that we consider two out of three phases is because a 3 phase motor has, fundemantally, 3 connections, two of which are used at any one time. Here's a good illustration of the possible configurations of 3 phase wiring. Current must come in one connection, and out the other.
In Mevey 38, equation 2.30, the torque of one BLDC motor phase is given by
T = 2 * N * B * Y * i * D/2
where Y has replaced L in my previous DC motor equation and D/2 (half the rotor diameter) replaces R.
If you do it my way, it becomes
T = 2 * N * B * L * R * i , replacing D/2 with R.
Remember now that two phases of the motor has current i flowing in it. Hence,
T = 4 * N * B * L * R * i
This is the Equations to Know for simple estimation of BLDC torque. Peak torque production is (modestly) equal to 4 times the:
� number of turns per phase
� strength of the permanent magnetic field
� length of the stator / core (or the magnet too, if they are equal)
� radius of the stator
� current in the motor windings
As expected, this scales linearly with current. In real life, this will probably get you within a factor of two. That is, your actual torque production might be between this theoretical T and T/2
Wait, 4? Does that mean if I turn my brushed DC motor into a brushless motor, it will suddenly have twice the torque? Not necessarily. This is a mathematical construct - a DC motor's windings are considered in a different fashion which causes the definition of N and L to change.
Next, we will see how to use this equation to size your motor.
28 July 2010 Update to the definition of T
In the equation T = 4* N * L * B * R i, the constant 4 comes from the derivation of a motor with only one tooth per phase, assuming N is the number of turns of wire per tooth on the stator.
The full derivation of this constant involves each loop of wire actually being twosections of wire, each of length L. This is due the fact that a loop involves going across the stator, then back again. Next, in a BLDC motor, two phases are always powered, therefore contributing torque.
We can observe that in a motor with only 1 tooth per phase (a 3-toothed stator), there are no more multiplicative factors. However, for each tooth you add per phase (2 teeth per phase in a 6-tooth stator, 3 teeth per phase in a 9-tooth stator, etc.) the above constant must be multiplied accordingly. The constant in front of the equation essentially accounts for the number of active passes of wire, which is 2 passes per loop times 2 phases active times number of teeth per phase.
So, what I actually mean is that T = 4 * m * N * B * L * R * i where
m = the newly defined teeth per phase count.
As the windings themselves have yet to be introduced, keep in mind the number of teeth per phase in the dLRK winding is 4.
Step 3: The Brushless DC Motor and You
So how does
T = 4 * m * N * B * L * R * i , otherwise known as T = Km * i
affect your motor design, and why am I viciously pounding on torque so much? Because torque is ultimately what hauls you around, and is one of the components of mechanical power Pm. Once you determine roughly how much mechanical power you will need, you can size wires and components appropriately.
Notice some key characteristics of the equation and how they affect motor performance:
� Torque increases with number of turns N
� ...and radius of the stator R
� ...and strength of the magnetic field B
� ...and length of the stator L
� ...and winding current i.
What we observe here is that to a degree, you can linear scale motor characteristics to estimate the performance of another motor.
This is "R/C Hobby Industry Hand Wave" number one. The concept of turns and motor sizes.
A 100mm diameter motor will, all else being equal, produce twice as much torque as a 50mm diameter motor.
A motor with 1.2T permanent magnetic field will likely be 20% more torquey than a 1T motor. And so on.
This has its limits - you cannot reasonably assume that you can quintuple your windings and get 5 times the torque - other magnetic characteristics of motors, such as saturation come into play. But, as will be shown, it is not unreasonable to extrapolate the performance of a 25 turn-per-stator-tooth motor from a 20 turn one, and such.
The LRK Winding
At the bottom of it all, what I am designing and making is a fractional-slot permanent magnet three phase motor. What the frunk does that mean? The fractional slot just means that (magnet pole pairs * phases) / (number of teeth on the stator) is not an integer. If you understood that, you know it more than I do.
A brief explanation is that the ratio of "number of stator teeth" to "number of magnet pairs" strongly affects the physical characteristics of the motor. A "magnet pole pair" is defined as two magnets, one with the North pole facing radially inwards, the other with the N pole facing outwards.
This ratio, commonly called T : 2P (for teeth to 2 * total poles), affects the cogging of the motor, i.e. its smoothness.
Get a DC brush motor and twirl the shaft - there is a minimum amount of torque required to 'click' it over to the next stable position. This is cogging. It causes undesirable vibrations and high-order electrical system effects, and we don't like it.
A type of motor winding with T : 2P close to 1 (but not 1 exactly - that results in a motor which doesn't want to move) substantially reduces cogging (to near zero) and is the most popular "small BLDC motor" winding around. It is called the LRK winding, after Messrs. Lucas, Retzbach, and Kuhlfuss, who documented the use of this winding for model airplane builders in 2001. Not only does it offer low cogging, but also ease of winding and scalability.
Here are figures of the basic LRK winding and a variant called the DLRK (Distributed LRK).
The takeaway here is that using a stator with 12 teeth (or slots, the area between the teeth) and 14 magnets (that is, 7 pole pairs) will give you a pretty decent motor to start with and use in your fledgling motor engineering career.
The difference between the two winding styles is subtle. The distributed LRK winding has a smaller end-turn effect. An end turn is the wire that has to wrap around outside of the magnetic field in order to close the loop. It contributes notorque, but does have a resistance (all wires have nonzero resistance - we're not talking superconductors here). The dLRK avoids bunching the end turns up excessively, which results in a slightly more efficient motor. Slightly as in one or two percentage points - nothing to win a Nobel Prize over.
Below is a picture of Razer's motor core with a full dLRK winding.
T = 4 * m * N * B * L * R * i , otherwise known as T = Km * i
affect your motor design, and why am I viciously pounding on torque so much? Because torque is ultimately what hauls you around, and is one of the components of mechanical power Pm. Once you determine roughly how much mechanical power you will need, you can size wires and components appropriately.
Notice some key characteristics of the equation and how they affect motor performance:
� Torque increases with number of turns N
� ...and radius of the stator R
� ...and strength of the magnetic field B
� ...and length of the stator L
� ...and winding current i.
What we observe here is that to a degree, you can linear scale motor characteristics to estimate the performance of another motor.
This is "R/C Hobby Industry Hand Wave" number one. The concept of turns and motor sizes.
A 100mm diameter motor will, all else being equal, produce twice as much torque as a 50mm diameter motor.
A motor with 1.2T permanent magnetic field will likely be 20% more torquey than a 1T motor. And so on.
This has its limits - you cannot reasonably assume that you can quintuple your windings and get 5 times the torque - other magnetic characteristics of motors, such as saturation come into play. But, as will be shown, it is not unreasonable to extrapolate the performance of a 25 turn-per-stator-tooth motor from a 20 turn one, and such.
The LRK Winding
At the bottom of it all, what I am designing and making is a fractional-slot permanent magnet three phase motor. What the frunk does that mean? The fractional slot just means that (magnet pole pairs * phases) / (number of teeth on the stator) is not an integer. If you understood that, you know it more than I do.
A brief explanation is that the ratio of "number of stator teeth" to "number of magnet pairs" strongly affects the physical characteristics of the motor. A "magnet pole pair" is defined as two magnets, one with the North pole facing radially inwards, the other with the N pole facing outwards.
This ratio, commonly called T : 2P (for teeth to 2 * total poles), affects the cogging of the motor, i.e. its smoothness.
Get a DC brush motor and twirl the shaft - there is a minimum amount of torque required to 'click' it over to the next stable position. This is cogging. It causes undesirable vibrations and high-order electrical system effects, and we don't like it.
A type of motor winding with T : 2P close to 1 (but not 1 exactly - that results in a motor which doesn't want to move) substantially reduces cogging (to near zero) and is the most popular "small BLDC motor" winding around. It is called the LRK winding, after Messrs. Lucas, Retzbach, and Kuhlfuss, who documented the use of this winding for model airplane builders in 2001. Not only does it offer low cogging, but also ease of winding and scalability.
Here are figures of the basic LRK winding and a variant called the DLRK (Distributed LRK).
The takeaway here is that using a stator with 12 teeth (or slots, the area between the teeth) and 14 magnets (that is, 7 pole pairs) will give you a pretty decent motor to start with and use in your fledgling motor engineering career.
The difference between the two winding styles is subtle. The distributed LRK winding has a smaller end-turn effect. An end turn is the wire that has to wrap around outside of the magnetic field in order to close the loop. It contributes notorque, but does have a resistance (all wires have nonzero resistance - we're not talking superconductors here). The dLRK avoids bunching the end turns up excessively, which results in a slightly more efficient motor. Slightly as in one or two percentage points - nothing to win a Nobel Prize over.
Below is a picture of Razer's motor core with a full dLRK winding.
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