Induction Motor & Linear Induction Motors Formulas & Equations

Formulas and Equations for Linear and Induction Motors

The following equations and formulas related to linear and induction motors can be used to calculate the basic parameters while analyzing and designing a single phase and three phase induction motor.

Formula and Equations for Induction Motor:

Induced EMF:

e_ind = vBl

where

• e_ind = induced EMF
• v = velocity of the rotor
• B = magnetic flux density
• l = length of conductors inside magnetic field

Rotor Current:

The rotor current is given by:

Torque Induced:

Terms used in Motor Torque Equations and formulas.

• N_s = Synchronous speed
• s = slip of the motor
• s_b = breakdown or pull-out slip
• E₁ = stator voltage or input voltage
• E₂ = Rotor EMF per phase at a standstill
• R₂ = Rotor Resistance Per Phase
• X₂ = Rotor Reactance Per Phase
• V = supply voltage
• K = rotor/stator turn ration per Phase

Starting Torque

• Maximum Starting Torque Condition

R₂ = X₂

• Starting Torque Relation With Supply Voltage

T_st  α  V²

• Torque In Running Condition

• Gross Torque

• Maximum Running Torque Condition

R₂ = sX₂

• Maximum Running Torque

• Breakdown Slip

• Torque Relation With Max Torque

Slip Speed & Slip of Induction Motor:

Slip speed is the difference between synchronous speed and rotor speed;

• N_slip = N­_s – N­                         (Speed in RPM)
• ω_slip = ω_s – ω­                        (Angular speed in Rad/sec)

Where

• N­­_slip = Slip speed
• N_{s ­}= Synchronous speed = 120f/P
• N­­ = Rotor speed of motor

The slip of induction motor is a relative term expressed in percentage. It is given by:

Where

• S is the slip of induction motor

Rotor Speed:

The rotor speed of induction motor is given by

• N = (1-s)N_s                (Speed in RPM)
• ω = (1-s) ω _s             (Angular speed in Rad/sec)

Electrical Frequency on the Rotor: 

Where

• f_r  = Rotor Frequency
• f  = Line Frequency
• P = Number of Poles

Power of Induction Motor:

Related terms used in Motor Power Formulas and Equation.

• P₁ = Stator input Power
• P₂ = Rotor Input power
• P_m = Rotor Gross Output Power
• P_out = Output Power
• T_g = gross torque
• T_sh = shaft torque

Rotor Input Power:

P₂ = T_gω_s

• Rotor Gross Output Power:

P_m = T_gω

• Output Power:

P_out = T_shω

P1 = P2 + stator Losses = P_m + Rotor Copper Losses = P_out + Windage & friction Losses

Rotor Input Power: Output Mechanical Power: Rotor Cu loss ratio:

Where

• P_cr = I²R = rotor Copper loss

Synchronous Watt:

The torque at which the machine at synchronous speed will generate one watt;

Efficiency of Induction Motor:

• Rotor Efficiency:

• Overall Efficiency

Formula & Equations for Linear Induction Motor:

Synchronous Speed:

Where

• v_s  = linear synchronous speed
• w = width of one pole-pitch
• f = line frequency

Slip:

Where

• v_s = linear synchronous speed
• v = Actual speed

Thrust or Force:

Where

P₂ = Rotor input Power

Rotor Cu Loss:

Gross Mechanical Power:

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