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Posted on Aug 4, 2021 in Electronics

Magnetomotive Force

 = magnetomotive force (mmf) in (A-t)

N = number of turns in coil (t)

I = current in coil (A)

Magnetic Field Intensity

H = magnetic field intensity

 = mmf (A-t)

N = number of turns in coil (t)

I = current in coil (A)

 = mean length of magnetic circuit, or section (m)

Flux Density: 

B = flux density (Wb/m²) or (T)

 = magnetic flux (Wb)

A = cross-sectional area (m²)

Magnetic Circuit Equation:

 = magnetic flux (Wb)

 = magnetomotive force (mmf) in (A-t)

 = reluctance of magnetic circuit (A-t/Wb)

Magnetic Permeability: 

B = flux density (Wb/m²) or (T)

H = magnetic field intensity

 = mean length of magnetic circuit, or section (m)

A = cross-sectional area (m²)

 = permeability of material (Wb/A-t * m)

Relative permeability

 = relative permeability, dimensionless constant

 = permeability of free space (air gaps) = 4π10^-7 (Wb/A-t *m)

 = permeability of material (Wb/A-t * m)

Analogies Between Electric and Magnetic Circuits

 corresponds to I

 corresponds to E

 corresponds to R

Magnetic Hysteresis Loss:

 = hysteresis loss (W/unit mass of core)

 = frequency of flux wave (Hz)

 = maximum value of flux density wave (T)

 = constant (dependent on magnetic characteristics of the material, its density, and units used)

n = Steinmetz exponent (avg. of 1.6 for silicone steel sheets)

1.8          Interaction of Magnetic Fields (Motor Action)

• When two or more sources of magnetic fields are arranged so their fluxes, or a component of their fluxes are parallel within a common region, a mechanical force will be produced that tends to either force the sources of flux together or apart.
• Flux bunching: a net increase in flux in the common region when a force of repulsion is created when two magnetic sources have flux parallel and in the same direction.
  1. Parallel conductors with current in opposite directions
• A net subtraction of flux occurs in the common region when a force of attraction is created when two magnetic sources have flux parallel and in opposite directions
  1. Parallel conductors with current in the same direction

1.9          Elementary Two-Pole Motor

• Rotor core containing two insulated conductors in rotor slots, centered between poles of stationary magnets (stator). Current in conductors are in opposite directions. Assuming rotor and stator were energized at different times, the resultant fluxes produce a counterclockwise moment or torque, called motor action (assuming stators and conductors match Figure 1.10).

1.10        Magnitude of the Mechanical Force Exerted on a Current-Carrying Conductor Situated in a Magnetic Field (BLI)

• Magnitude of mechanical force exerted on a straight conductor that is carrying an electric current and situated within and perpendicular to a magnetic field.
• Mechanical force direction is determined by the direction of flux bunching

F = mechanical force (N)

B = flux density (Wb/m²) or (T)

 = effective length of rotor conductor (normal to field) (m)

I = current in rotor conductor (A)

 = effective length of rotor conductor (normal to field) (m)

 = total length of conductor immersed in magnetic field

 = skewing angle, ranging from 0 to 30 degrees

• Developed Torque: direction of developed torque on the shaft is determined from the end fiew of the conductors and magent poles. Figure 1.12(b) shows that torque is in the CCW direction, and the magnitude is equal to:

Or

 = developed torque (N * m)

F = mechanical force (N)

d = distance between center of shaft and center of a conductor (m)

B = flux density (Wb/m²) or (T)

 = effective length of rotor conductor (normal to field) (m)

I = current in rotor conductor (A)

1.11        Electromagnetically Induced Voltages (Generator Action)

• Generated by relative motion or transformer action. Voltages generated by transformer action are due to flux varying with time through the window of a stationary coil. Voltages generated by relative motion involve a moving coil and stationary magnet or moving magnet and stationary coil.
• Faraday’s Law: magnitude of the voltage induced in a coil by electromagnetic induction is proportional to the number of series-connected turns in the coil, and the rate of change of flux through its window. See Figure 1.13

 = induced voltage (electromotive force, emf) (V)

N = number of series-connected turns

 = rate of change of flux through window (Wb/s)

• Voltage, current, and flux generated by transformer action or relative motion will always be induced in a direction opposite the action that caused it.
• Speed Voltage: voltage caused by relative motion, also called “flux cutting” voltages. Two parallel conductors are placed on perpendicular conducting rails, in a magnetic field perpendicular to the window the conductors create. If a conductor physically moves through, or “cuts” a flux line, a voltage is generated.

 = induced voltage (electromotive force, emf) (V)

B = flux density (Wb/m²) or (T)

 = effective length of rotor conductor (normal to field) (m)

v = velocity of conductor (m/s)

• If one conductor is fixed, and one moves away, an emf is generated in the moving conductor. If both move away from each other, a doubled net emf is produced. If both move in the same direction, no net emf is produced.

1.12        Elementary Two-Pole Generator

Summary of Terms and Equations:

Questions:

• Difference between B, H, and φ?
• How to determine the direction of mechanical force produced by flux bunching in a two-pole motor. Flux bunching occurs between the conductors induced magnetic field, and due to the magnet.
  1. Are the magnetic fields between conductors isolated in the rotor?
• Lenz’s Law?