Repulsion Motor

Design of Repulsion Motor

The repulsion motor is the first single-phase AC motor in which the armature field builds up as a consequence of the voltage induced in the rotor. The rotor has the same design as the one in the universal motor – laminated sheet steel with an armature winding inserted into grooves, whose coil ends are connected to the collector segments. The carbon brushes no longer serve to feed current – they are attached on a moveable mount and short-circuited. The stator has no salient pole pieces – the exciter winding is inserted into the grooves of the dynamo steel core.

How the motor works

 

As was the case in the transformer the current carrying exciter winding induces a voltage in the coils of the armature winding. The position of the short-circuited brushes determines the current flow in the armature winding. If the brushes are aligned with the magnetic poles, the total current is equal to 0 – no magnetic field can build up in the rotor. The maximum current flows through the armature winding when the brushes are rotated by 90° from this alignment. A magnetic field arises whose direction coincides with the direction of the magnetic field in the stator. These brush positions are correspondingly defined as the "soft" and "hard" neutral positions.

Torque, speed and back emf

In order for torque to be exerted on the rotor, the brushes are turned by 15° out of the "hard" neutral position. Now the north pole of the rotor is repelled by the north pole of the stator. If the brushes are turned by 15° in the opposite direction, the rotation direction of the motor is reversed. At approx. 75% of the rated speed all of the collector segments are short-circuited with a ring and the brushes are lifted – their position no longer determines the amplitude of the armature current. Only the induced back emf is responsible for the armature current in the short-circuited rotor.

Short-circuit voltage and current

 

The output voltage of the transformer depends on the type of load and on the load current. One measure for voltage change is the short-circuit voltage, which is the voltage that must be applied to the input winding so that it consumes the rated current when the output winding is short-circuited. In transformers with low internal resistance the output voltage only drops off slightly under load. This kind of transformer has a rigid voltage characteristic. Transformers with high short-circuit voltage are called voltage compliant or flexible. Critical for the short-circuit response is the dispersion which differs for various winding arrangements.

Power dissipation and efficiency

 

The efficiency of transformers is specified as the ratio between active power output and absorbed active power. Transformation of electrical energy in real transformers involves power loss. This includes the load-dependent losses in the winding impedance, as well as the voltage and frequency dependent magnetic and eddy current losses arising in the magnetic circuit. The power loss is converted into thermal energy. The iron losses are measured in no-load operation whereas the winding losses are measured in short-circuit experiments.

Operation at no-load and under load

 

Without load the transformer responds like a coil of large inductance. The current consumed by the input winding is the no-load current. The no-load voltage induced at the output is computed according to the primary transformer equation. When operating at no-load almost all of the magnetic flux is concentrated in the iron core. When a load is connected, the load current weakens the input current in accordance with Lenz's law. Some of the lines of flux are then distributed outside the core and this is called leakage flux.

Transformation ratios

 

In an ideal transformer which achieves 100% power coupling (loss-free) the same magnetic flux permeates both windings. Without load the voltages respond in line with the number of winding turns. The higher to lower voltage ratio is called the transformation ratio. When the transformer is coupled the currents under load respond in inverse ratio to the number of turns. The impedances are carried forward in the square of the transformation ratio. Due to the power losses arising in real transformers these transformation ratios are only approximately correct.

Types of Inductors

 

An inductor is basically a coil of wire. The material around which the coil is formed is called the core. Both fixed and variable inductors are classified according to the type of core material used. Three common types are: the air core, the iron core, and the ferrite core. Each has a unique symbol, shown above. Inductors are made in a variety of shapes and sizes. Some are shown above. Small fixed inductors are encapsulated in an insulating material and have the appearance of a small resistor. Variable inductors usually have a screw type adjustment, to allow inductance to be changed. 

Series and Parallel Inductors

When inductors are connected in series, the total inductance, L_T, is the sum of the individual inductors. The formula is similar to total resistance in series and total capacitance in parallel.

 

When inductors are connected in parallel the total inductance is less than the smallest inductance. The reciprocal of the total inductance is equal to the sum of the reciprocals of the individual inductances. The formula is similar to the formula for total parallel resistance and total series capacitance.

Lenz's Law

 

When the current through a coil changes, a voltage is induced. Lenz's Law states that the polarity of the induced voltage always opposes the change in current that caused it. The diagram above illustrates this law. When the switch closes, the current tries to increase, and the magnetic field starts expanding. The expanding magnetic field induces a voltage, which opposes an increase in current. So, at the instant of switching, the current remains the same. When the rate of expansion decreases, the induced voltage decreases, allowing the current to increase. As the current reaches a constant value, there is no induced voltage.  

The diagram illustrates the direction of induced voltage when the current is switched off. In a steady-state condition, the current has a constant value. There is no induced voltage because the magnetic field is unchanging. If the switch is opened, the current tries to reduce, and the magnetic field begins to collapse. At the time of switching, the induced voltage has a direction that prevents any decrease in current. The current remains the same as prior to the switch opening. When the rate of collapse decreases, induced voltage decreases, allowing current to decrease to zero value. 

Inductor

Faraday's Law

A permanent magnet has a magnetic field around it, which consists of lines of force, or flux lines Φ, going from the north pole (N) to the south pole (S). Moving a magnet relative to a coil of wire and thus cutting across the flux lines induces a current through the coil.

 

Faraday's Law states: The induced voltage u_ind is directly proportional to the rate of change of the magnetic field with respect to the coil and the number of turns in the coil. A coil with more turns (loops), produces a greater voltage. The faster the magnet is moved, the greater the induced voltage.

Basic Inductor

 

A coil of wire forms a basic inductor. Current through the coil produces an electromagnetic field, which creates a north (N) and a south (S) pole. The more lines of force, the greater the flux, and the stronger the magnetic field.
Constant current has an associated constant magnetic field and there is no induced voltage. An increase in current expands the field. A decrease in current reduces it. As the field expands and collapses with current change, the flux Φ is effectively in motion. Hence, a varying current can produce induced voltage without magnetic motion.

Inductance

 

Inductance is the ability of a conductor to produce induced voltage when the current varies. Conductors that introduce a definite inductance into the circuit are called inductors or coils. The symbol for inductance is L, and the unit is the Henry (H). The inductance is one Henry when the current, changing at the rate of 1A per second, induces 1V across the coil.

An inductor stores energy in the magnetic field created by the current. The energy stored is proportional to the inductance and the square of the current. The energy is supplied by the voltage source that produces the current.

More Detail about Inductor

RC Circuit

Series RC Circuit

In a series RC circuit, the current is the same through both the resistor and capacitor. Thus, the resistor voltage (U_R) is in phase with the current (I), and the capacitor voltage (U_C) lags the current by 90^o. Therefore, there is a phase difference of 90^o between U_R and U_C as shown above. From Kirchoff's voltage law, the sum of the voltage drops must equal the source voltage, U_s. Since U_R and U_C are 90^o out of phase, the magnitude of the source voltage can be expressed by using the Pythagorean theorem, as shown in the diagram.

Capacitive Impedance

The impedance Z of an RC circuit is the complete opposite to sinusoidal current. Its unit is the ohm. The phase angle is the phase difference between the total current and the source voltage. In a purely resistive circuit, the impedance is equal to total resistance. The phase angle is zero. In a purely capacitive circuit, the impedance is the total capacitive reactance. The phase angle is 90^o, with the current leading the voltage. The impedance, Z, of a series RC circuit, depends on both the R and the C reactance values. It is determined by the impedance triangle shown. The phase angle is between zero and 90^o.

Z_C Frequency Dependence

 

Capacitance reactance X_c varies inversely with frequency. Impedance Z changes in the same way as X_c. Therefore, in RC circuits, Z is inversely related to frequency. The diagram illustrates how Z and X_c change with frequency, with the source voltage held at a constant value. As the frequency increases, X_c decreases. Less voltage is dropped across the capacitor since U_c = I X_c. Also, Z decreases as X_c decreases, causing the current to increase. An increase in I causes more voltage across R as U_R = IR