Maximum Running Torque Calculator

✖EMF is defined as the electro motive force which is needed to move the electrons within an electrical conductor to generate flow of current through the conductor.ⓘ EMF [E]			+10% -10%
✖Synchronous speed is a definite speed for an alternating-current machine that is dependent on the frequency of the supply circuit.ⓘ Synchronous Speed [N_s]			+10% -10%
✖Reactance is defined as the opposition to the flow of current from a circuit element due to its inductance and capacitance.ⓘ Reactance [X]			+10% -10%

✖Running Torque is maximum at the value of slip (s) which makes rotor reactance per phase equal to rotor resistance per phase.ⓘ Maximum Running Torque [τ_run]

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Formula

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Maximum Running Torque

Formula

`"τ"_{"run"} = (3*"E"^2)/(4*pi*"N"_{"s"}*"X")`

Example

`"0.181512N*m"=(3*("305.8V")^2)/(4*pi*"15660rev/min"*"75Ω")`

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Maximum Running Torque Solution

STEP 0: Pre-Calculation Summary

Formula Used

Running Torque = (3*EMF^2)/(4*pi*Synchronous Speed*Reactance)
τ_run = (3*E^2)/(4*pi*N_s*X)
This formula uses 1 Constants, 4 Variables

Constants Used

pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288

Variables Used

Running Torque - (Measured in Newton Meter) - Running Torque is maximum at the value of slip (s) which makes rotor reactance per phase equal to rotor resistance per phase.
EMF - (Measured in Volt) - EMF is defined as the electro motive force which is needed to move the electrons within an electrical conductor to generate flow of current through the conductor.
Synchronous Speed - (Measured in Radian per Second) - Synchronous speed is a definite speed for an alternating-current machine that is dependent on the frequency of the supply circuit.
Reactance - (Measured in Ohm) - Reactance is defined as the opposition to the flow of current from a circuit element due to its inductance and capacitance.

STEP 1: Convert Input(s) to Base Unit

EMF: 305.8 Volt --> 305.8 Volt No Conversion Required
Synchronous Speed: 15660 Revolution per Minute --> 1639.91136509036 Radian per Second (Check conversion here)
Reactance: 75 Ohm --> 75 Ohm No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

τ_run = (3*E^2)/(4*pi*N_s*X) --> (3*305.8^2)/(4*pi*1639.91136509036*75)

Evaluating ... ...

τ_run = 0.181511737394367

STEP 3: Convert Result to Output's Unit

0.181511737394367 Newton Meter --> No Conversion Required

FINAL ANSWER

0.181511737394367 ≈ 0.181512 Newton Meter <-- Running Torque

(Calculation completed in 00.020 seconds)

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Created by Urvi Rathod

Vishwakarma Government Engineering College (VGEC), Ahmedabad

Urvi Rathod has created this Calculator and 1500+ more calculators!

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< 6 Torque & Efficiency Calculators

Torque of Induction Motor under Running Condition

Go Torque = (3*Slip*EMF^2*Resistance)/(2*pi*Synchronous Speed*(Resistance^2+(Reactance^2*Slip)))

Starting Torque of Induction Motor

Go Torque = (3*EMF^2*Resistance)/(2*pi*Synchronous Speed*(Resistance^2+Reactance^2))

Induced Torque given Magnetic Field Density

Go Torque = (Machine Construction Constant/Magnetic Permeability)*Rotor Magnetic Flux Density*Stator Magnetic Flux Density

Maximum Running Torque

Go Running Torque = (3*EMF^2)/(4*pi*Synchronous Speed*Reactance)

Rotor Efficiency in Induction Motor

Go Efficiency = (Motor Speed)/(Synchronous Speed)

Gross Torque Developed per Phase

Go Gross Torque = Mechanical Power/Motor Speed

< 25 Induction Motor Circuit Calculators

Torque of Induction Motor under Running Condition

Go Torque = (3*Slip*EMF^2*Resistance)/(2*pi*Synchronous Speed*(Resistance^2+(Reactance^2*Slip)))

Rotor Current in Induction Motor

Go Rotor Current = (Slip*Induced EMF)/sqrt(Rotor Resistance per Phase^2+(Slip*Rotor Reactance per Phase)^2)

Starting Torque of Induction Motor

Go Torque = (3*EMF^2*Resistance)/(2*pi*Synchronous Speed*(Resistance^2+Reactance^2))

Maximum Running Torque

Go Running Torque = (3*EMF^2)/(4*pi*Synchronous Speed*Reactance)

Linear Synchronous Speed

Go Linear Synchronous Speed = 2*Pole Pitch Width*Line Frequency

Stator Copper Loss in Induction Motor

Go Stator Copper Loss = 3*Stator Current^2*Stator Resistance

Rotor Copper Loss in Induction Motor

Go Rotor Copper Loss = 3*Rotor Current^2*Rotor Resistance

Synchronous Speed in Induction Motor

Go Synchronous Speed = (120*Frequency)/(Number of Poles)

Frequency given Number of Poles in Induction Motor

Go Frequency = (Number of Poles*Synchronous Speed)/120

Armature Current given Power in Induction Motor

Go Armature Current = Output Power/Armature Voltage

Synchronous Speed of Induction Motor given Efficiency

Go Synchronous Speed = (Motor Speed)/(Efficiency)

Rotor Efficiency in Induction Motor

Go Efficiency = (Motor Speed)/(Synchronous Speed)

Field Current using Load Current in Induction Motor

Go Field Current = Armature Current-Load Current

Rotor Input Power in Induction Motor

Go Rotor Input Power = Input Power-Stator Losses

Load Current in Induction Motor

Go Load Current = Armature Current-Field Current

Force by Linear Induction Motor

Go Force = Input Power/Linear Synchronous Speed

Motor Speed given Efficiency in Induction Motor

Go Motor Speed = Efficiency*Synchronous Speed

Rotor Copper Loss given Input Rotor Power

Go Rotor Copper Loss = Slip*Rotor Input Power

Pitch Factor in Induction Motor

Go Pitch Factor = cos(Short Pitched Angle/2)

Gross Mechanical Power in Induction Motor

Go Mechanical Power = (1-Slip)*Input Power

Rotor Frequency given Supply Frequency

Go Rotor Frequency = Slip*Frequency

Resistance given Slip at Maximum Torque

Go Resistance = Slip*Reactance

Reactance given Slip at Maximum Torque

Go Reactance = Resistance/Slip

Breakdown Slip of Induction Motor

Go Slip = Resistance/Reactance

Slip given Efficiency in Induction Motor

Go Slip = 1-Efficiency

Maximum Running Torque Formula

Running Torque = (3*EMF^2)/(4*pi*Synchronous Speed*Reactance)
τ_run = (3*E^2)/(4*pi*N_s*X)

what is the synchronous speed?

Synchronous Speed is the speed of the stator magnetic field in the three-phase induction motor. The synchronous speed is given by
Ns = 120f / p
Where
Ns = Synchronous speed in RPM
f = Supply frequency and
p = Number of poles
The standard frequency in India is 50 Hz therefore the synchronous speed for different pole condition is

How to Calculate Maximum Running Torque?

Maximum Running Torque calculator uses Running Torque = (3*EMF^2)/(4*pi*Synchronous Speed*Reactance) to calculate the Running Torque, The Maximum running torque is when the rotor rotates at its maximum speed which makes rotor reactance per phase equal to rotor resistance per phase. Running Torque is denoted by τ_run symbol.

How to calculate Maximum Running Torque using this online calculator? To use this online calculator for Maximum Running Torque, enter EMF (E), Synchronous Speed (N_s) & Reactance (X) and hit the calculate button. Here is how the Maximum Running Torque calculation can be explained with given input values -> 0.181512 = (3*305.8^2)/(4*pi*1639.91136509036*75).

FAQ

What is Maximum Running Torque?

The Maximum running torque is when the rotor rotates at its maximum speed which makes rotor reactance per phase equal to rotor resistance per phase and is represented as τ_run = (3*E^2)/(4*pi*N_s*X) or Running Torque = (3*EMF^2)/(4*pi*Synchronous Speed*Reactance). EMF is defined as the electro motive force which is needed to move the electrons within an electrical conductor to generate flow of current through the conductor, Synchronous speed is a definite speed for an alternating-current machine that is dependent on the frequency of the supply circuit & Reactance is defined as the opposition to the flow of current from a circuit element due to its inductance and capacitance.

How to calculate Maximum Running Torque?

The Maximum running torque is when the rotor rotates at its maximum speed which makes rotor reactance per phase equal to rotor resistance per phase is calculated using Running Torque = (3*EMF^2)/(4*pi*Synchronous Speed*Reactance). To calculate Maximum Running Torque, you need EMF (E), Synchronous Speed (N_s) & Reactance (X). With our tool, you need to enter the respective value for EMF, Synchronous Speed & Reactance and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

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