Cogging And Crawling of Induction Motor

Induction Motor
Photo Credit - www.wikipedia.com

Crawling

 It has been found that induction motor practically this squirrel cage type ,sometimes exhibit,a tendency to run stable at speeds as low as ¹/₇th of their synchronous speed .This is known as crawling of induction motor. This action is due to ,the fact that the AC winding of the stator produces a flux wave which is not pure sine wave .It is a complex wave consisting of a fundamental wave which revolves synchronously and odd harmonics like 3^rd,5^th,7^th etc. which rotate either in the forward or backward direction at ^Ns/₃, ^Ns/₅, ^Ns/₇ speed respectively. As a result in addition to the fundamental torque ,harmonics torques also developed whose synchronous speed for fundamental torque. For Example Ns/n, where N is the order of harmonics torque. Since the 3^rd harmonics current are absent in a balanced three phase system ,they produce  no torque .Hence total motor torque has there components.

1. The fundamental torque rotating with synchronous speed 
2. Fifth harmonics torque rotating at ^Ns/₅ 
3. Seventh harmonics torque having a speed of ^Ns/₇

If we neglect all the higher  harmonics, the resultant torque can be taken as equal to the sum of the fundamental torque and the seventh harmonics torque. When this happen the motor will not accelerate  up-to its normal speed  but will remain running at a speed which is nearly equal to ¹/₇th of its full speed. This is referred as a crawling and  motor starts running with unwanted sound .

Cogging

The rotor of particularly squirrel cage  induction motor sometimes refuse to start at all particularly a  when the voltage is low. This happens of stator teeth is equal to the  number of  rotor teeth ,and therefore  due to the magnetic locking or cogging .It is found that the reluctance of magnetic paths  is minimum  when the stator and rotor teeth comes in front of each other, it is in such position of maximum reluctance that the stator tends to remain fixed thus causes serious trouble during starting.

This can be easily overcome by making number of rotor slots more than the number of stator slots and by giving slightly skew to the rotor slots (skewed).What is meant is to arrange the stack of rotor laminations so that the rotor slots are "skewed" or angled with respect to the axis of rotation. Constructing the rotor with skewed slots and providing more (or fewer) rotor slots than stator slots is the remedy for both cogging and crawling.

Analog Circuits

465 Tektronics Oscilloscope

 

 

A system can be analog or digital. Electronic system/circuits comprises of digital and analog circuits.
So what is this analog circuits?
Analog circuits are those in which voltage and current vary continuously through the given range of time. Analog circuit uses continued value analog signals (continuous valued signals). They can take on infinite values within the specified range. This circuits are usually complex combinations of Op-Amps, resistors, capacitors and other basic electronic components (electronic circuit elements). This circuits can be designed to amplify, attenuate, isolate, distort or modify the applied signal in some way. Analog circuits can be very difficult or complex to design due to the involvement of various connection of circuit elements or they can be simple like combining two resistor to make a voltage divider. Analog circuits are much more sensitive to noise (undesired voltage, harmonics). But sometimes this sensitivity of analog circuit to noise is used as an advantage(This point will be explained in more details where an example of this, is encountered).

Class B Push Pull Amplifeir

The devices which uses analog circuits to process the signals are called analog devices. Examples of analog devices include signal generators, radio frequency transmitter/receiver, electric motors and speed controllers.

Basic Circuit Element - Inductor

Chip Inductor
Image Courtesy - www.directindustry.com  

Inductors are also called as storage element because they store energy in their magnetic field. In electric circuits the inductor shown is an idealization of the physical inductor. The practical inductance or inductor or a two terminal element will be called an inductor if at any time t its flux φ(t) and its current i(t) satisfy the relation defined by a curve in the iφ plane. This curve is called the characteristic of the inductor at time t.
An inductor is represented symbolically as shown in figure below,

Inductor Symbol

In circuit theory, the fundamental characterization of a two terminal element is in terms of voltage and current. The voltage across the inductor is given by Faraday's Law as ,

v = ^dφ/_dt    ..............(1)

where v is in Volts and φ is in Webers (Wb).
But we know that

φ(t)= Li(t) ................(2)

where L is constant and is called inductance. The SI unit of Inductor is "Henry" and it is shown by capital letter H.

Therefore equation (1) will become,

v = L^d/_dt i(t)...............(3)

Now integrating both sides,

v ^i(t)/_L = ^d/_dti(t)

where i(0) is called inductor current at t=0.

Let us verify this relation between voltage and current that above all equation agrees with Lenz's law; which states that "the electromotive force(emf) induced by a rate of change of flux will have a polarity such that it will oppose the cause of such rate of change of flux."

From equation (1), (2) and (3) we can conclude that

1. When the current i(t) increases; that is  ^d/_dt i(t) > 0, the flux φ also increases; that is ^dφ/_dt  >0.
2. Inductors opposes the instantaneous change in current through it.
3. Inductors have memory that it shows the property of causality.

Torque Speed Characteristics Of Double Cage Induction Motor

Torque speed characteristics of Double cage induction motor

The main disadvantage of squirrel cage motor is poor starting torque  because of low rotor resistance .The starting torque could be increased by having a cage of  high resistance but then the motor will have poor efficiency under normal running conditions.The difficulty with squirrel cage induction  motor is that its cage is permanently short circuited ,so no external resistance can be introduced . Many efforts have been made to build a squirrel motor with high starting torque without scarifying its electrical efficiency under normal running conditions ,which cannot be possible easily .Two  independent cages on the rotor was tried and a motor called as double cage motor is invented .The outer cage consist of bare of high resistance where as the inner cage has low resistance .Hence outer cage has high resistance and low ratio reactance to reactance where as the inner cage has low resistance but being situated at deep in the rotor .has large ratio of reactance to reactance .Hence the outer cage develops maximum torque at starting while the inner cage about 15%  slip .At starting and at large slip values ,frequency of induced emf in the rotor is high ,so the reactance of inner cage and therefore its impedance are both high .Hence very little current flows in it . Most of starting current is confused to outer cage ,despite its high resistance .Hence the motor develops high starting torque due to high resistance outer cage .
                                               As the speed increase the frequency of rotor emf decreases ,so that the reactance and hence the impedance of inner cage decreases and becomes very small under normal running conditions . Most of the current then flows through it and hence it develops the grater part of the motor torque .When speed is normal ,frequency of the rotor emf is so small that the reactance of both cages is practically negligible .The current is carried by two cages in parallel giving a low combined resistance .Hence it has been made possible to construct a  single machine which has a good starting torque with reasonable starting current and which maintain high efficiency with good speed regulation under operating conditions.      

Basic Circuit Element-Capacitor

Different types of Capacitor
Photo Credit - www.wikipedia.org

A capacitor stores electrical energy by electrostatic stress in the dielectric.it consist of two conducting surfaces separated by a layer of an insulating medium which is called dielectric.the conducting surface may be in form of either circular plates or be of spherical or cylindrical shape.
Capacitance - Capacitance is the property of capacitor to store electricity.the capacitance of a capacitor is defined as the amount of charge required to create a unit potential difference between its plates.due its property of storing electricity (charge),capacitor is called a storing element.If a charge of Q coulomb is given to one of the two plate of capacitor and if a potential difference of V volts is established between the two ,then its capacitance is

C = ^Q/_V = ^Charge/_{Potential difference}

Capacitance is the charge required per unit potential difference. The unit of capacitance is coulomb/volt which is also called farad.

1 farad =1 coulomb/volt 

One farad is defined as the capacitance of a capacitor which required a charge of one coulomb to establish a potential difference of one volt between its poles.
The characteristic of nearly all physical capacitors is monotonically increasing that, as v increases Q increases.

Characteristic of physical capacitor

In the circuit diagrams a capacitor is represented symbolically as shown in figure below,

Symbol of capacitor

When i(t) is positive, positive charges are brought (at time t) to the top plate whose charge is Q. The rate of change of Q is also positive. Thus we have,

i(t) = ^dQ/_dt

Current - voltage relationship in capacitor

The charge on a capacitor is given by the expression 

Q = Cv

Putting this value in the above equation of i(t) we get,

From the above equation following important parameters are found:

1. Since Q = Cv, the voltage across a capacitor is directly proportional to charge Q where C is capacitance/proportionality constant.
2. A capacitor has the property of causality.
3. Current in the capacitor is present only when voltage on it changes with time that is, AC Voltage. When its voltage is constant or DC voltage, i(t) = 0. Hence the capacitor behaves like open circuit.
4. Rate of change in voltage of a capacitor is inversely proportional to its capacitance.
   
5. Rate of change in capacitor voltage is slower when the value of capacitance C is high. Also the capacitor does not accommodate the change in current instantaneously.

In this way the introduction of capacitor is given briefly. We will also update more details of capacitor including its charging, discharging, types etc in upcoming posts.

Block Diagram Algebra

The transfer function for the input output behaviour of a linear system or element of a linear system is given by

G(s) = ^C(s)/_R(s)

where R(S )-Laplace transform  of the input variable  and 

C(S)-Laplace transform of  the  output variable 

A control system may have many number of components  connected to each  other  and each components have its own transfer function .To show this different transfer function of each component a block diagram is generally referred .
block diagram of  a system is pictorial representation or convenient graphical representation of the input -output behaviour i.e. transfer function of each component and of the flow signals . The block diagram depicts the interrelationship  between different system components .The block diagram  representation is more advantageous than mathematical representation as it identical the flow of signal of the actual system more realistically .
The block itself shows transfer function and it is a system of mathematical  operation on the input signal to the block that produces output signal .The flow  of information is unidirectional from input to the output with the output being equal to the result of product of input and output transfer function. The blocks are connected by lines with arrows indicating the unidirectional flow of information. The arrowhead which points toward the block designates the input and the arrowhead coming out of the block that is leading away from the block represents the output. Such arrows are referred to as signal.

Block Diagram Algebra - Figure

The above figure shows that the signal into the block represents the input R(s) and the signal leading away from the block represents the output C(s), while the block itself represents the transfer function.

Summing Point

Summing Point :- The figure (b) shows the summing operation. The plus indicated that the signal a and b are to be added. The quantities being added have the same dimension and units. Figure (a) shows the differencing operation. The plus and minus sign indicates that the two signals a and b are to be subtracted. If the circle with cross symbol is not shown with any sign convention, by default the two signals are added.
Branch Point :- It is a point from which the signal from block goes concurrently to other block.