# Single phase induction motor

SINGLE PHASE INDUCTION MOTOR
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In this case, we are going to look at the behaviour of the single-phase induction motor of a fan coil for air conditioning a hotel room, and what happens when the motor is connected to a voltage and electrical frequency different from that of its manufacture.

### Technical characteristics

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As we can see on the motor’s nameplate, it has been manufactured to work at a voltage of 115v and 60Hz. The reality is very different since this motor has been connected to a voltage of 127v and 50Hz.

### Relationship between Voltage and Frequency

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The relationship between voltage and frequency is a constant, U / F = Cte

#### Introduction

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The operation of induction motors is due to the fact that a mechanical torque (motor torque) is produced inside them due to the interaction of a magnetic field (magnetic flux), which circulates through its magnetic circuit and the electric currents that circulate through the conductors of the same system.

Induction motors (IM) can operate with supply voltage values higher than the nominal one (which is the one shown on the rating plate, (115v) of up to approximately 10%. But so as not to produce higher heating to those allowed by the materials with which the motor has been built (magnetic plate), (Fe iron), conductors (Cu copper), casing, shaft, bearings, etc.)

The power supply frequency of the motor must vary proportionally to the variation of the supply voltage; that is, the relationship between the supply voltage U and the frequency (f) must be constant, U / f = constant.
With the above it is achieved that the magnetic flux (Φ) and the motor supply current (I) do not vary appreciably . Both magnitudes (Φ, I) are the cause of the loss of energy in the form of heat due to the Joule effect inside the motor.
If both magnitudes do not vary, the dissipation of thermal energy in the motor will not vary and therefore will cause temperature increases in parts of the motor.
The variation of the supply frequency (f) produces variation of the motor speed which is approximately proportional to frequency variation.
Es conocido que si un motor IM de cuatro polos es alimentado a 50Hz, su velocidad de sincronismo es de  ns = 1500 r.p.m. (revolutions per minute).

Its actual speed is somewhat less than 1500 rpm. If it is fed at 60Hz, ns = 1800 rpm and the engine cools to a somewhat better level.

#### Analysis

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In the case of the exact motor being analysed in this case study, the electrical supply in question is 125V, 50Hz. In other words, the supply voltage has been increased by approximately 8.7% and the frequency has been decreased by approximately 6.7%, which inevitably leads to an increase in energy losses both in the magnetic circuit (Fe) as in conductors (Cu); This causes an increase in temperature in these parts of the engine.
When the engine works in permanent regime, the temperatures in its different parts stabilise and a flow of heat is established from the inside of the engine to the outside of it.
This heat flow is transmitted to the outside through the motor housing and also through the shaft that is supported by the bearings, through which part of the thermal flux also passes, consequently also producing an increase in the temperature of the bearings.
Both the bearings and the grease that lubricates them are very sensitive to the increase in temperature, which can deteriorate them. If the grease deteriorates, it loses its lubricating property and the bearing stops working properly.
The qualitative analysis carried out can be deepened further using a simple equation that relates the electrical (U, I) and magnetic (Φ) magnitudes mentioned above.
When a motor is fed with a voltage (U), an electromotive force (E) is generated in the motor coils, such that U and E are approximately equal U ≅ E. Furthermore, E depends on the flux (Φ) and on the frequency (f), such that:

K is a constant value that depends on the construction characteristics of the motor. In other words, for a specific motor, K has a fixed value.

From here on, the values corresponding to those on the nameplate will be indicated with a subscript (1)

E1 ≅ U1 = 115V, f1 = 60Hz

The subscript (2) refers to the values corresponding to the supply conditions E2 ≅ U2 = 115V, f2 = 50Hz

That means that we get:

E1 = K x Φ1 x f1 ; E1 = K x Φ1 x f1

If it is divided it remains.

In other words, the magnetic flux (Φ2 ) in the actual operating conditions of the motor is approximately 30% higher than the magnetic flux ( Φ1 ) corresponding to the operating conditions for which the motor has been designed; indicated on its nameplate.

#### Consequences

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The consequences of this 30% increase in magnetic flux are as follows:

1. On the one hand, excessive heating of the magnetic plates of the motor, both in the moving part (rotor) and in the fixed part (stator).
2. At the same time, as the magnetic flux is generated by a part of the current absorbed by the motor (called magnetising current, (Iµ). Increasing the flux of 30% implies increasing the magnetising current (Iµ) by a value much higher than 30% as there is no proportionality between the increase in flux with that of the current, due to the saturation of certain parts of the motor’s magnetic circuit (see Figure).
graphic.

It is important to bear in mind that in order to ensure that the motors use the least possible material and therefore reduce their size and cost, they are built in such a way that some parts of the magnetic circuit, especially the grooves, work in the saturation zone.
Depending on the characteristics constructive of the motor, this increase in l can be up to 100% or more. This increase in lp leads to a significant increase in the current absorbed by the motor (I) .
The increase in current (I) produces an increase in losses in the conductors (Cu), which are proportional to the square of the current and therefore there is an excessive heating of the conductors of the motor windings, both in the rotor and in the stator. Note: The current absorbed by the motor (I) has two components:
Note: The current absorbed by the motor (I) has two components: (Ia) and (Iμ), such that:

To carry out this report, one of the damaged engines has been disposed of at the Secrets Wild Orchid and Secrets St. James hotels in Jamaica. The nameplate of this motor is shown in Figure 1.
From the visual observation of this motor the following conclusions can be drawn:
1. The grease in the bearings is deteriorated due to overheating, which means that it no longer performs its lubricating function correctly, affecting the proper functioning of the bearings, which can also be damaged. The figure clearly shows the deteriorated appearance of the fat.

1. In the figure below, you can see parts of the stator windings darker in color than the rest of the winding. This darker color is due to the current greater than the nominal one that has passed through the conductors.
3. This darker color is due to the current greater than the nominal one that has passed through the conductors.

4. In the figure of the side cover of the motor, next to the outside of the bearing, there are yellowish spots due to overheating.

The visual observations described indicate that the engine has been working with temperatures inside it that are higher than those allowed by its construction materials.

#### Conclusions

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The motors that are the object of this report have operated under supply conditions (125V, 50Hz) (as indicated by the applicant for this report) different from their nameplate (115V, 60Hz).
The supply conditions are inadequate for the proper functioning of the motor, since on the one hand the supply voltage is increased (from 115V to 125V) and on the other the frequency is lowered from (60Hz to 50Hz).
This results in significant increases both in the magnetic flux (Φ) common to the stator windings (coils) and the rotor groove conductors, as well as in the motor supply current (I).
The increase in flux (Φ) and current (I) produce excessive heating in the different parts of the motor; among them in the bearings, which affect the lubricating grease and the material of the bearing itself, which causes its progressive deterioration and consequent breakdown.
In summary, it can be concluded that the cause of the deterioration of the motors is due to the fact that their manufacturing characteristics indicated on the nameplate (115V, 60Hz) are not suitable to function under the conditions of the building’s electrical supply (125V, 60Hz).
All of the above is corroborated by observing the photographs of one of the affected engines, whose nameplate is that of Figure 1.

Engineering department.

We Resolve