Torque Induced in Synchronous Motor Calculator

✖Terminal Voltage is defined as the voltage developed at the terminal of the phase of a synchronous machine.ⓘ Terminal Voltage [V_Φ]			+10% -10%
✖Internal Generated Voltage is defined as the voltage which is generated internally in any synchronous machine and does not appear at the terminal of the machine.ⓘ Internal Generated Voltage [E_a]			+10% -10%
✖Torque Angle is defined as the angle between the rotor and the net magnetic field.ⓘ Torque Angle [δ]			+10% -10%
✖Motor Speed is defined as the speed at which the rotor of a motor rotates.ⓘ Motor Speed [N_m]			+10% -10%
✖Synchronous Reactance is defined as the sum of Armature Reactance and the Leakage Reactance of a synchronous machine.ⓘ Synchronous Reactance [X_s]			+10% -10%

✖Torque is defined as the measure of the force that can cause an object to rotate about an axis. It is induced due to the interaction of rotor and stator magnetic field.ⓘ Torque Induced in Synchronous Motor [τ]

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Torque Induced in Synchronous Motor Solution

STEP 0: Pre-Calculation Summary

Formula Used

Torque = (3*Terminal Voltage*Internal Generated Voltage*sin(Torque Angle))/(9.55*Motor Speed*Synchronous Reactance)
τ = (3*V_Φ*E_a*sin(δ))/(9.55*N_m*X_s)
This formula uses 1 Functions, 6 Variables

Functions Used

sin - Sine is a trigonometric function that describes the ratio of the length of the opposite side of a right triangle to the length of the hypotenuse., sin(Angle)

Variables Used

Torque - (Measured in Newton Meter) - Torque is defined as the measure of the force that can cause an object to rotate about an axis. It is induced due to the interaction of rotor and stator magnetic field.
Terminal Voltage - (Measured in Volt) - Terminal Voltage is defined as the voltage developed at the terminal of the phase of a synchronous machine.
Internal Generated Voltage - (Measured in Volt) - Internal Generated Voltage is defined as the voltage which is generated internally in any synchronous machine and does not appear at the terminal of the machine.
Torque Angle - (Measured in Radian) - Torque Angle is defined as the angle between the rotor and the net magnetic field.
Motor Speed - (Measured in Radian per Second) - Motor Speed is defined as the speed at which the rotor of a motor rotates.
Synchronous Reactance - (Measured in Ohm) - Synchronous Reactance is defined as the sum of Armature Reactance and the Leakage Reactance of a synchronous machine.

STEP 1: Convert Input(s) to Base Unit

Terminal Voltage: 28.75 Volt --> 28.75 Volt No Conversion Required
Internal Generated Voltage: 25.55 Volt --> 25.55 Volt No Conversion Required
Torque Angle: 75 Degree --> 1.3089969389955 Radian (Check conversion here)
Motor Speed: 13560 Revolution per Minute --> 1419.99987935028 Radian per Second (Check conversion here)
Synchronous Reactance: 4.7 Ohm --> 4.7 Ohm No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

τ = (3*V_Φ*E_a*sin(δ))/(9.55*N_m*X_s) --> (3*28.75*25.55*sin(1.3089969389955))/(9.55*1419.99987935028*4.7)

Evaluating ... ...

τ = 0.0333967533646358

STEP 3: Convert Result to Output's Unit

0.0333967533646358 Newton Meter --> No Conversion Required

FINAL ANSWER

0.0333967533646358 ≈ 0.033397 Newton Meter <-- Torque

(Calculation completed in 00.020 seconds)

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Created by Parminder Singh

Chandigarh University (CU), Punjab

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GURU TEGH BAHADUR INSTITUTE OF TECHNOLOGY (GTBIT), NEW DELHI

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< Torque Calculators

Torque Induced in Synchronous Motor

LaTeX Go Torque = (3*Terminal Voltage*Internal Generated Voltage*sin(Torque Angle))/(9.55*Motor Speed*Synchronous Reactance)

Pull Out Torque in Synchronous Motor

LaTeX Go Torque = (3*Terminal Voltage*Internal Generated Voltage)/(9.55*Motor Speed*Synchronous Reactance)

< Synchronous Motor Circuit Calculators

Load Current of Synchronous Motor given 3 Phase Mechanical Power

LaTeX Go Load Current = (Three Phase Mechanical Power+3*Armature Current^2*Armature Resistance)/(sqrt(3)*Load Voltage*cos(Phase Difference))

Armature Current of Synchronous Motor given 3 Phase Mechanical Power

LaTeX Go Armature Current = sqrt((Three Phase Input Power-Three Phase Mechanical Power)/(3*Armature Resistance))

Armature Current of Synchronous Motor given Mechanical Power

LaTeX Go Armature Current = sqrt((Input Power-Mechanical Power)/Armature Resistance)

Armature Current of Synchronous Motor given Input Power

LaTeX Go Armature Current = Input Power/(cos(Phase Difference)*Voltage)

Torque Induced in Synchronous Motor Formula

LaTeX Go

Torque = (3*Terminal Voltage*Internal Generated Voltage*sin(Torque Angle))/(9.55*Motor Speed*Synchronous Reactance)
τ = (3*V_Φ*E_a*sin(δ))/(9.55*N_m*X_s)

How does a synchronous motor work?

Typically, the synchronous motor has a stator with a winding similar to that of an induction motor. Its rotor produces a constant magnetic field, either from a direct current in its windings or by use of permanent magnets. The rotor’s magnetic field tends to align with the rotating field produced by the three-phase alternating currents in the stator.

How to Calculate Torque Induced in Synchronous Motor?

Torque Induced in Synchronous Motor calculator uses Torque = (3*Terminal Voltage*Internal Generated Voltage*sin(Torque Angle))/(9.55*Motor Speed*Synchronous Reactance) to calculate the Torque, The Torque Induced in Synchronous Motor formula is defined as the measure of the force that can cause an object to rotate about an axis. It is induced due to the interaction of rotor and stator magnetic field. Torque is denoted by τ symbol.

How to calculate Torque Induced in Synchronous Motor using this online calculator? To use this online calculator for Torque Induced in Synchronous Motor, enter Terminal Voltage (V_Φ), Internal Generated Voltage (E_a), Torque Angle (δ), Motor Speed (N_m) & Synchronous Reactance (X_s) and hit the calculate button. Here is how the Torque Induced in Synchronous Motor calculation can be explained with given input values -> 0.033397 = (3*28.75*25.55*sin(1.3089969389955))/(9.55*1419.99987935028*4.7).

FAQ

What is Torque Induced in Synchronous Motor?

The Torque Induced in Synchronous Motor formula is defined as the measure of the force that can cause an object to rotate about an axis. It is induced due to the interaction of rotor and stator magnetic field and is represented as τ = (3*V_Φ*E_a*sin(δ))/(9.55*N_m*X_s) or Torque = (3*Terminal Voltage*Internal Generated Voltage*sin(Torque Angle))/(9.55*Motor Speed*Synchronous Reactance). Terminal Voltage is defined as the voltage developed at the terminal of the phase of a synchronous machine, Internal Generated Voltage is defined as the voltage which is generated internally in any synchronous machine and does not appear at the terminal of the machine, Torque Angle is defined as the angle between the rotor and the net magnetic field, Motor Speed is defined as the speed at which the rotor of a motor rotates & Synchronous Reactance is defined as the sum of Armature Reactance and the Leakage Reactance of a synchronous machine.

How to calculate Torque Induced in Synchronous Motor?

The Torque Induced in Synchronous Motor formula is defined as the measure of the force that can cause an object to rotate about an axis. It is induced due to the interaction of rotor and stator magnetic field is calculated using Torque = (3*Terminal Voltage*Internal Generated Voltage*sin(Torque Angle))/(9.55*Motor Speed*Synchronous Reactance). To calculate Torque Induced in Synchronous Motor, you need Terminal Voltage (V_Φ), Internal Generated Voltage (E_a), Torque Angle (δ), Motor Speed (N_m) & Synchronous Reactance (X_s). With our tool, you need to enter the respective value for Terminal Voltage, Internal Generated Voltage, Torque Angle, Motor Speed & Synchronous Reactance and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

How many ways are there to calculate Torque?

In this formula, Torque uses Terminal Voltage, Internal Generated Voltage, Torque Angle, Motor Speed & Synchronous Reactance. We can use 2 other way(s) to calculate the same, which is/are as follows -

Torque = (3*Terminal Voltage*Internal Generated Voltage)/(9.55*Motor Speed*Synchronous Reactance)
Torque = (3*Terminal Voltage*Internal Generated Voltage)/(9.55*Motor Speed*Synchronous Reactance)

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