Mechanical Power of Synchronous Motor Calculator

✖Back EMF is a voltage that is generated in a motor or generator due to the motion of the armature or rotor. It is called "back" EMF as its polarity opposes the voltage applied.ⓘ Back EMF [E_b]			+10% -10%
✖Armature Current Motor is defined as the armature current developed in an synchronous motor due to the rotation of rotor.ⓘ Armature Current [I_a]			+10% -10%
✖Load Angle is defined as the difference between the phasors of back emf and source voltage or terminal voltage.ⓘ Load Angle [α]			+10% -10%
✖Phase Difference in Synchronous Motor is defined as the difference in the phase angle of Voltage and Armature current of a synchronous motor.ⓘ Phase Difference [Φ_s]			+10% -10%

✖Mechanical Power power is the product of a force on an object and the object's velocity or the product of torque on a shaft and the shaft's angular velocity.ⓘ Mechanical Power of Synchronous Motor [P_m]

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Mechanical Power of Synchronous Motor

Formula

`"P"_{"m"} = "E"_{"b"}*"I"_{"a"}*cos("α"-"Φ"_{"s"})`

Example

`"593.4103W"="180V"*"3.70A"*cos("57°"-"30°")`

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Mechanical Power of Synchronous Motor Solution

STEP 0: Pre-Calculation Summary

Formula Used

Mechanical Power = Back EMF*Armature Current*cos(Load Angle-Phase Difference)
P_m = E_b*I_a*cos(α-Φ_s)
This formula uses 1 Functions, 5 Variables

Functions Used

cos - Cosine of an angle is the ratio of the side adjacent to the angle to the hypotenuse of the triangle., cos(Angle)

Variables Used

Mechanical Power - (Measured in Watt) - Mechanical Power power is the product of a force on an object and the object's velocity or the product of torque on a shaft and the shaft's angular velocity.
Back EMF - (Measured in Volt) - Back EMF is a voltage that is generated in a motor or generator due to the motion of the armature or rotor. It is called "back" EMF as its polarity opposes the voltage applied.
Armature Current - (Measured in Ampere) - Armature Current Motor is defined as the armature current developed in an synchronous motor due to the rotation of rotor.
Load Angle - (Measured in Radian) - Load Angle is defined as the difference between the phasors of back emf and source voltage or terminal voltage.
Phase Difference - (Measured in Radian) - Phase Difference in Synchronous Motor is defined as the difference in the phase angle of Voltage and Armature current of a synchronous motor.

STEP 1: Convert Input(s) to Base Unit

Back EMF: 180 Volt --> 180 Volt No Conversion Required
Armature Current: 3.7 Ampere --> 3.7 Ampere No Conversion Required
Load Angle: 57 Degree --> 0.994837673636581 Radian (Check conversion here)
Phase Difference: 30 Degree --> 0.5235987755982 Radian (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

P_m = E_b*I_a*cos(α-Φ_s) --> 180*3.7*cos(0.994837673636581-0.5235987755982)

Evaluating ... ...

P_m = 593.41034510948

STEP 3: Convert Result to Output's Unit

593.41034510948 Watt --> No Conversion Required

FINAL ANSWER

593.41034510948 ≈ 593.4103 Watt <-- Mechanical Power

(Calculation completed in 00.004 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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Osmania University (OU), Hyderabad

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< 8 Power Calculators

Mechanical Power Developed by Synchronous Motor

Go Mechanical Power = ((Back EMF*Voltage)/Synchronous Impedance)*cos(Phase Difference-Load Angle)-(Back EMF^2/Synchronous Impedance)*cos(Phase Difference)

3 Phase Input Power of Synchronous Motor

Go Three Phase Input Power = sqrt(3)*Load Voltage*Load Current*cos(Phase Difference)

Mechanical Power of Synchronous Motor

Go Mechanical Power = Back EMF*Armature Current*cos(Load Angle-Phase Difference)

3 Phase Mechanical Power of Synchronous Motor

Go Three Phase Mechanical Power = Three Phase Input Power-3*Armature Current^2*Armature Resistance

Input Power of Synchronous Motor

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

Mechanical Power of Synchronous Motor given Input Power

Go Mechanical Power = Input Power-Armature Current^2*Armature Resistance

Output Power for Synchronous Motor

Go Output Power = Armature Current^2*Armature Resistance

Mechanical Power of Synchronous Motor given Gross Torque

Go Mechanical Power = Gross Torque*Synchronous Speed

< 25 Synchronous Motor Circuit Calculators

Load Current of Synchronous Motor given 3 Phase Mechanical Power

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

Power Factor of Synchronous Motor given 3 Phase Mechanical Power

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

Distribution Factor in Synchronous Motor

Go Distribution Factor = (sin((Number of Slots*Angular Slot Pitch)/2))/(Number of Slots*sin(Angular Slot Pitch/2))

Load Current of Synchronous Motor using 3 Phase Input Power

Go Load Current = Three Phase Input Power/(sqrt(3)*Load Voltage*cos(Phase Difference))

3 Phase Input Power of Synchronous Motor

Go Three Phase Input Power = sqrt(3)*Load Voltage*Load Current*cos(Phase Difference)

Mechanical Power of Synchronous Motor

Go Mechanical Power = Back EMF*Armature Current*cos(Load Angle-Phase Difference)

Armature Current of Synchronous Motor given 3 Phase Mechanical Power

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

Armature Current of Synchronous Motor given Mechanical Power

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

Power Factor of Synchronous Motor using 3 Phase Input Power

Go Power Factor = Three Phase Input Power/(sqrt(3)*Load Voltage*Load Current)

Armature Resistance of Synchronous Motor given 3 Phase Mechanical Power

Go Armature Resistance = (Three Phase Input Power-Three Phase Mechanical Power)/(3*Armature Current^2)

3 Phase Mechanical Power of Synchronous Motor

Go Three Phase Mechanical Power = Three Phase Input Power-3*Armature Current^2*Armature Resistance

Phase Angle between Voltage and Armature Current given Input Power

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

Armature Current of Synchronous Motor given Input Power

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

Input Power of Synchronous Motor

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

Armature Resistance of Synchronous Motor given Input Power

Go Armature Resistance = (Input Power-Mechanical Power)/(Armature Current^2)

Magnetic Flux of Synchronous Motor given Back EMF

Go Magnetic Flux = Back EMF/(Armature Winding Constant*Synchronous Speed)

Armature Winding Constant of Synchronous Motor

Go Armature Winding Constant = Back EMF/(Magnetic Flux*Synchronous Speed)

Mechanical Power of Synchronous Motor given Input Power

Go Mechanical Power = Input Power-Armature Current^2*Armature Resistance

Power Factor of Synchronous Motor given Input Power

Go Power Factor = Input Power/(Voltage*Armature Current)

Angular Slot Pitch in Synchronous Motor

Go Angular Slot Pitch = (Number of Poles*180)/(Number of Slots*2)

Output Power for Synchronous Motor

Go Output Power = Armature Current^2*Armature Resistance

Number of Poles given Synchronous Speed in Synchronous Motor

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

Synchronous Speed of Synchronous Motor

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

Synchronous Speed of Synchronous Motor given Mechanical Power

Go Synchronous Speed = Mechanical Power/Gross Torque

Mechanical Power of Synchronous Motor given Gross Torque

Go Mechanical Power = Gross Torque*Synchronous Speed

Mechanical Power of Synchronous Motor Formula

Mechanical Power = Back EMF*Armature Current*cos(Load Angle-Phase Difference)
P_m = E_b*I_a*cos(α-Φ_s)

What are the characteristics of a synchronous motor?

Synchronous motors operate at a constant speed determined by the frequency of the power supply and the number of poles in the motor. They have a high power factor, precise speed control, require DC excitation for the rotor, and offer high efficiency and starting torque, making them suitable for heavy loads.

How to Calculate Mechanical Power of Synchronous Motor?

Mechanical Power of Synchronous Motor calculator uses Mechanical Power = Back EMF*Armature Current*cos(Load Angle-Phase Difference) to calculate the Mechanical Power, The Mechanical Power of Synchronous Motor formula is defined as any energy derived from steam, water, wind, electricity, compressed air or gas, or the combustion of fuel or explosive, which is used to drive or work any machinery. Mechanical Power is denoted by P_m symbol.

How to calculate Mechanical Power of Synchronous Motor using this online calculator? To use this online calculator for Mechanical Power of Synchronous Motor, enter Back EMF (E_b), Armature Current (I_a), Load Angle (α) & Phase Difference (Φ_s) and hit the calculate button. Here is how the Mechanical Power of Synchronous Motor calculation can be explained with given input values -> 593.4103 = 180*3.7*cos(0.994837673636581-0.5235987755982).

FAQ

What is Mechanical Power of Synchronous Motor?

The Mechanical Power of Synchronous Motor formula is defined as any energy derived from steam, water, wind, electricity, compressed air or gas, or the combustion of fuel or explosive, which is used to drive or work any machinery and is represented as P_m = E_b*I_a*cos(α-Φ_s) or Mechanical Power = Back EMF*Armature Current*cos(Load Angle-Phase Difference). Back EMF is a voltage that is generated in a motor or generator due to the motion of the armature or rotor. It is called "back" EMF as its polarity opposes the voltage applied, Armature Current Motor is defined as the armature current developed in an synchronous motor due to the rotation of rotor, Load Angle is defined as the difference between the phasors of back emf and source voltage or terminal voltage & Phase Difference in Synchronous Motor is defined as the difference in the phase angle of Voltage and Armature current of a synchronous motor.

How to calculate Mechanical Power of Synchronous Motor?

The Mechanical Power of Synchronous Motor formula is defined as any energy derived from steam, water, wind, electricity, compressed air or gas, or the combustion of fuel or explosive, which is used to drive or work any machinery is calculated using Mechanical Power = Back EMF*Armature Current*cos(Load Angle-Phase Difference). To calculate Mechanical Power of Synchronous Motor, you need Back EMF (E_b), Armature Current (I_a), Load Angle (α) & Phase Difference (Φ_s). With our tool, you need to enter the respective value for Back EMF, Armature Current, Load Angle & Phase Difference 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 Mechanical Power?

In this formula, Mechanical Power uses Back EMF, Armature Current, Load Angle & Phase Difference. We can use 5 other way(s) to calculate the same, which is/are as follows -

Mechanical Power = Input Power-Armature Current^2*Armature Resistance
Mechanical Power = Gross Torque*Synchronous Speed
Mechanical Power = ((Back EMF*Voltage)/Synchronous Impedance)*cos(Phase Difference-Load Angle)-(Back EMF^2/Synchronous Impedance)*cos(Phase Difference)
Mechanical Power = Gross Torque*Synchronous Speed
Mechanical Power = Input Power-Armature Current^2*Armature Resistance

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