**deep bar double cage induction motor**is used for the applications which demands higher starting torque.

_{s}[(sE

_{2}

^{2}R

_{2}/(R

_{2}

^{2}+sX

_{2}

^{2})]

**T**

_{st}= K [(E_{2}^{2}R_{2}/(R_{2}^{2}+X_{2}^{2}**)]**—–(1)

_{s}

_{2}= Rotor Resistance

_{2}= Rotor Reactance

_{2}= Rotor Induced Voltage

_{2 }and inversely proportional to the rotor reactance(X

_{2}). The rotor resistance of squirrel cage induction motor is kept low to increase the efficiency of the motor by reducing the copper loss.

At start the slip of the motor is unity and the rotor supply frequency is;

*fr = s fs*

*fr = 1 x fs*

*fr = fs*

*The rotor reactance is slip dependent and at start the rotor reactance is;*

*X*

_{2}= 2∏ s f_{s }L_{2}

*X _{2} = 2∏ f_{s }L_{2}*

At start, the rotor reactance is very high because slip=1.

Therefore, the starting torque of the squirrel cage induction motor is low because at start the motor has high rotor reactance. The rotor resistance of the squirrel cage induction motor is low throughout its speed range. Because of these reasons, the squirrel cage induction motor has low starting torque.

To increase the starting torque of squirrel cage induction motor, the rotor resistance of a squirrel cage induction is increased by incorporating double bar double cage in the rotor circuit. **Construction of Deep Bar Double Cage Induction Motor**

The construction of double cage induction motor is as shown below.

The double cage induction motor has two cages in the rotor circuit used for increasing the starting torque.The rotor of the squirrel cage induction motor has two winding in the rotor. The outer cage has the rotor bars of high resistance and low reactance. The inner cage has rotor bars of low resistance and high reactance. Each rotor bars are short circuited by the end rings.

The outer cage bars are made high resistivity materials like aluminum, brass or bronze etc. The cross section area of outer cage bars is less as compared to the cross section area of the inner cage bars. Therefore, the outer cage bars have more resistance than the innner cage bars. The resistance of the outer cage bars is about 5-6 times of the resistance of the inner cage bars.Therefore, the deep bar double cage induction motor produce more starting torque.

The leakage flux linking to the outer and inner cage bars depend on the **dimension of the air constriction**. The air constriction plays a vital role in the flux linking to outer and inner cage bars. In case of air constriction absence, the flux finds its path through the iron part of the rotor and would not reach at the inner cage bars of the motor and the inner cage bars will not contribute in torque production. **Operational principle of Deep Bar Double Cage Induction Motor**

At start, the frequency of the rotor induced voltage is equal to the stator frequency*(fr=fs as slip=1 at start)*.The high frequency rotor current tends to flow through the outer cage bars due to skin effect and due to low leakage rectance . The inner cage bars have more reactance than the outer cage bars reactance. The conductor arrangement in inner and outer cage of the rotor is as shown below.

Thus the inner cage impedes the rotor current when the rotor frequency is more. so, most of the current will find its path through the low impedance outer cage bars.

The resistance of the outer cage bars are more,** therefore Deep Bar Double Cage Induction Motor develops high starting torque.**

The rotor frequency gets decreased with an acceleration of the motor towards its base speed. The frequency of rotor induced voltage and current depend on the slip of the motor. The slip gets decreased with an increase of the motor speed. The slip at start is equal to unity and the slip becomes very less at normal running of the motor.*fr = s fs*The relationship of the rotor frequency and the slip is as shown in below given graph.

The impedance of the inner cage bars gets reduced when motor attains its full speed. At start the most of the rotor current flows through the outer cage bars. When motor accelerates the current starts shifting from the outer cage bars to the inner cage bars. When the motor attains the full speed, the maximum current flows through the inner cage bars. **Speed Torque Characteristics of Double Cage Induction Motor**The speed torque characteristics of double cage induction motor is as shown below.

When an double cage induction motor is switched on, the most of the current flows through the outer cage bars and as the outer cage bars offers low impedance the torque of the motor improves. At start, the outer cage bars produce more torque than the inner cage bars.If the torque produced by inner and outer cage bars are added , the total torque produced by double cage motor is much more than the torque produced by single cage motor.

With an acceleration of the motor the impedance of the inner cage bars starts decreasing and the motor current starts shifting from outer cage bars to inner cage bars. The division of the current in the outer cage and inner cage bars is inversely proportional to their leakage impedance. The motor almost behaves as a single cage motor when motor attains its full rated speed.

The equivalent circuit of the **deep bar double cage induction motor **is as given below.

**Comparison between Single Cage and Double Cage Induction Motor**