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Mechanical Power of Synchronous Motor Formula

GoMechanical Power of Synchronous Motor given Gross Torque Formula

GoMechanical Power of Synchronous Motor given Input Power Formula

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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. Check FAQs

P m = E b \cdot I a \cdot \cos (α - Φ s)

P_m - Mechanical Power?E_b - Back EMF?I_a - Armature Current?α - Load Angle?Φ_s - Phase Difference?

Mechanical Power of Synchronous Motor Example

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Here is how the Mechanical Power of Synchronous Motor equation looks like with Values.

Here is how the Mechanical Power of Synchronous Motor equation looks like with Units.

Here is how the Mechanical Power of Synchronous Motor equation looks like.

593.4103 = 180 \cdot 3.7 \cdot \cos (57 - 30)

593.4103W = 180V \cdot 3.7A \cdot \cos (57° - 30°)

593.4103 = 180 \cdot 3.7 \cdot \cos (57 - 30)

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Mechanical Power of Synchronous Motor Solution

Follow our step by step solution on how to calculate Mechanical Power of Synchronous Motor?

FIRST Step Consider the formula

P m = E b \cdot I a \cdot \cos (α - Φ s)

Next Step Substitute values of Variables

∴

P m = 180V \cdot 3.7A \cdot \cos (57° - 30°)

Next Step Convert Units

∴

P m = 180V \cdot 3.7A \cdot \cos (0.9948rad - 0.5236rad)

Next Step Prepare to Evaluate

∴

P m = 180 \cdot 3.7 \cdot \cos (0.9948 - 0.5236)

Next Step Evaluate

∴

P m = 593.41034510948W

LAST Step Rounding Answer

∴

P m = 593.4103W

Mechanical Power of Synchronous Motor Formula Elements

Variables

Functions

Mechanical Power

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.

Symbol: P_m

Measurement: PowerUnit: W

Note: Value can be positive or negative.

Formulas to find Mechanical Power

Back EMF

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.

Symbol: E_b

Measurement: Electric PotentialUnit: V

Note: Value can be positive or negative.

Formulas to find Back EMF

Armature Current

Armature Current Motor is defined as the armature current developed in an synchronous motor due to the rotation of rotor.

Symbol: I_a

Measurement: Electric CurrentUnit: A

Note: Value can be positive or negative.

Formulas to find Armature Current

Load Angle

Load Angle is defined as the difference between the phasors of back emf and source voltage or terminal voltage.

Symbol: α

Measurement: AngleUnit: °

Note: Value can be positive or negative.

Formulas to find Load Angle

Phase Difference

Phase Difference in Synchronous Motor is defined as the difference in the phase angle of Voltage and Armature current of a synchronous motor.

Symbol: Φ_s

Measurement: AngleUnit: °

Note: Value should be greater than 0.

Formulas to find Phase Difference

cos

Cosine of an angle is the ratio of the side adjacent to the angle to the hypotenuse of the triangle.

Syntax: cos(Angle)

Other Formulas to find Mechanical Power

Go Mechanical Power of Synchronous Motor given Gross Torque

P m = τ g \cdot N s

Go Mechanical Power of Synchronous Motor given Input Power

P m = P in - {I a}^{2} \cdot R a

Other formulas in Power category

Go Armature Current of Synchronous Motor given 3 Phase Mechanical Power

I a = \sqrt{\frac{P in(3Φ) - P me(3Φ)}{3 \cdot R a}}

Go Armature Current of Synchronous Motor given Input Power

I a = \frac{P in}{\cos (Φ s) \cdot V}

Go Armature Current of Synchronous Motor given Mechanical Power

I a = \sqrt{\frac{P in - P m}{R a}}

Go Load Current of Synchronous Motor given 3 Phase Mechanical Power

I L = \frac{P me(3Φ) + 3 \cdot {I a}^{2} \cdot R a}{\sqrt{3} \cdot V L \cdot \cos (Φ s)}

How to Evaluate Mechanical Power of Synchronous Motor?

Mechanical Power of Synchronous Motor evaluator uses Mechanical Power = Back EMF*Armature Current*cos(Load Angle-Phase Difference) to evaluate 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 evaluate Mechanical Power of Synchronous Motor using this online evaluator? To use this online evaluator 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.

FAQs on Mechanical Power of Synchronous Motor

What is the formula to find Mechanical Power of Synchronous Motor?

The formula of Mechanical Power of Synchronous Motor is expressed as Mechanical Power = Back EMF*Armature Current*cos(Load Angle-Phase Difference). Here is an example- 593.4103 = 180*3.7*cos(0.994837673636581-0.5235987755982).

How to calculate Mechanical Power of Synchronous Motor?

With Back EMF (E_b), Armature Current (I_a), Load Angle (α) & Phase Difference (Φ_s) we can find Mechanical Power of Synchronous Motor using the formula - Mechanical Power = Back EMF*Armature Current*cos(Load Angle-Phase Difference). This formula also uses Cosine (cos) function(s).

What are the other ways to Calculate Mechanical Power?

Here are the different ways to Calculate Mechanical Power-

Mechanical Power=Gross Torque*Synchronous Speed
Mechanical Power=Input Power-Armature Current^2*Armature Resistance

Can the Mechanical Power of Synchronous Motor be negative?

Yes, the Mechanical Power of Synchronous Motor, measured in Power can be negative.

Which unit is used to measure Mechanical Power of Synchronous Motor?

Mechanical Power of Synchronous Motor is usually measured using the Watt[W] for Power. Kilowatt[W], Milliwatt[W], Microwatt[W] are the few other units in which Mechanical Power of Synchronous Motor can be measured.

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Mechanical Power of Synchronous Motor Formula

​GoMechanical Power of Synchronous Motor given Gross Torque Formula

​GoMechanical Power of Synchronous Motor given Input Power Formula

Mechanical Power of Synchronous Motor Example

Mechanical Power of Synchronous Motor Solution

Mechanical Power of Synchronous Motor Formula Elements

Other Formulas to find Mechanical Power

Other formulas in Power category

How to Evaluate Mechanical Power of Synchronous Motor?

FAQs on Mechanical Power of Synchronous Motor

Variable Name

GoMechanical Power of Synchronous Motor given Gross Torque Formula

GoMechanical Power of Synchronous Motor given Input Power Formula