Flashcards in 2nd Half Deck (41):
For a rotor with N teeth, how many steps per revolution is there if there are 4 poles on the stator
How do we approximate the torque vs rotor position characteristic in stepper motors
As a sinusoid, with zero crossings every half a rotor tooth pitch (as it starts getting attracted to the next tooth along), with peak static torque when current is at the rated value. Peak static torque is proportional to rotor current.
Equation for the restoring torque produced by a stepper Motor when you have number of teeth, peak static torque and angular displacement from centre
T = Tmax x sin (Nt x Angle)
Equation for natural frequency of stepper motor and why it needs to be avoided
w = (k/J)^-1/2
K torsional stiffness
J moment of Inertia
if you excite this then there is the
possibility of increasingly large oscillations. Ultimately this can result in the motor missing steps and becoming uncontrollable.
k = Nt x Tpeak
How much rotor movement corresponds to one pulse?
The rotor moves one step
Equation to find torsional stiffness
Differentiate restoring torque equation wrt angle theta.
When operating at speed, what type of motor does a stepper motor behave like but what change do you make
Sinusoidal BLDCM, but we take the winding resistance as significant thus include the IR term with the excitation. (Phasor diagram has sides E + IR, V, wLI
Best method for finding the torque from a phasor diagram
Find the power out as you know this is equal to Tw and Pin - Ploss
Pin = 2VI cos phi (2 phase Motor)
Ploss = 2I^2 R
How do you find I rms from current-Time graph
By squaring th current t values, integrating over time and then finding the square root
How is microstepping achieved
by exciting pairs of phases with different proportions of current.
How to adapt data book torque equation for sinusoidal BLDCM power out
Change ws to w and Xs to Ls
For an Induction Motor what are the terms in the Pout = Pin - Ploss equation
Pout = Pin - Ploss
Twr = Tws- 3 I2^2 R2
How to find referred rotor current for induction motor equivalent circuit
Make the circuit all series by using thevenin equivalent
When does max torque occur for an Induction Motor
Then R2/s = X2
(Max power transfer theorem)
For Induction Motor, how do we adapt EC for no load case
No referred branch, as R2 becomes very large.
When an Induction Motor is operating under VVVF, what relationship holds
Constant V/f control.
What is base speed
The speed in rads-1 of the motor as inferred from the name-plate of the max speed at which rated flux can be maintained.
K rated equation
Base voltage / base speed (v/f control)
What does V-f cube look like for Induction Motor up until and after base voltage is reached
Below Vb, V/f is constant at K rated and flux is constant. Above, power is constant, but to operate at higher speed a lower flux is needed (field weakening)
Can also have flat line at start at Vboost
Advantages of single phase induction motors
Cheap to manufacture
Operate from a single phase as pc supply which is typically available in domestic environment
Example: pump motor in dishwasher.
PM brushed dc Motor vs field wound. 2a, 1d
A: no I^2 pR field winding losses
Greater torque and hence power density
D: field can’t be altered, hence field weakening can’t be used to extend speed range
What’s quadrant drive control
Represented by the graph of T-speed with the different quadrants showing combinations of Forward, reverse, motoring and generating
Benefit of distributing the stator windings in 3 phase Induction Motors
Conductors are distributed in many slots around the stator periphery: better use of space and reduced the harmonic content of the air gap flux density
Benefit of short pitching the stator windings in 3 phase Induction Motors,
Reduced the harmonic content of the air gap flux density, menacing smoother torque production, and reducing elimination of cogging torque.
Reduces the length of the windings therefore deducting coil resistance losses.
Constructional differences between sinusoidal and trapezoidal BLDCM
Rotors are similar: both with a set of radially magnetised permanent magnets so that poles alternate NSNS
Stator are different:
Trap has multiple poles, different to number of rotor poles (avoid cogging). Stator coils are then rapped around stator poles to give concentrated stator winding.
Sin is wound as for conventional synchronous machine ie distributed winding of same pole number as the rotor.
Why are the two rotors in a stepper motor are offset by half a tooth pitch
So that the teeth on the North Pole rotor wheel and the teeth on the South Pole rotor wheel will align with opposite poles, which is needed for the correct ordering of pole excitation to move the rotor by 1/4 of a tooth pitch each time.
How to find gearbox ratio to give max angular position ratio
The max angular position error occurs when load torque is equal to restoring torque, and is equal to 1/4 tooth which is SAME as step angle of stepper motor. Therefore the gear ratio is used to change this system angle to be the max angular displacement.
How does gearing affect the moment of Inertia of the load seen by the stepper motor
Reduces By a factor of 1/(gear ratio)^2
When an Induction Motor is fully fluxed, what operating mode is it in
When is V/f (constant flux operation) control no longer viable
Above the max output voltage from inverter (base voltage)
What happens to the flux in the field weakening regime for an Induction Motor?
The flux falls in inverse proportion to frequency
Simplified formula for torque in induction motor and assumptions made to derive it
T = (3 V1^2 s)/ ws R2’
Stator impedance (R1 and X1) can be neglected so terminal voltage appears across magnetising branch .
X2’ can be neglected in comparison with R2’/s at small slip values and up to frequency values beyond the normal operating range
How to find max speed at which rated torque can be delivered in Induction Motor
Rearrange slip equation for wr
What’s the max speed in reverse for an Induction Motor and how it it achieved
It’s the same as in the forward direction and is achieved by just applying negative frequency (reverse phase sequence)
What is the desirable part of the torque speed characteristic of an Induction Motor
The steep negative slope
Where is slip zero
At synchronous speed
Why is VVVF desirable for induction machines
An inverted which generates a VVVF output can taminto the desirable range of the torque speed characteristic (the steep negative slope) and translate it into a wide range of actual speeds. To maintain it in this region, the applied voltage needs to vary with frequency, fixed V/f operation.
Why do sinusoidal BLDCM have same number of stator and rotor poles?
As they work on the interaction of nice sine waves of current and flux, and to obtain useful torque and smooth performance they must have the Sam people numbers.
For magnetic circuits, equation that allows you to construct an equivalent magnetic circuit
NI = the reluctance of the different sections x the flux there
Flux is analogous to current
Coil amp turns is voltage
Reluctance is resistance
Equation for reluctance
For a given section
Reluctance = l / muo mur A