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Mechanical Power Developed by Synchronous Motor Formula

GoMechanical Power of Synchronous Motor 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 = (\frac{E b \cdot V}{Z S}) \cdot \cos (Φ s - α) - (\frac{{E b}^{2}}{Z S}) \cdot \cos (Φ s)

P_m - Mechanical Power?E_b - Back EMF?V - Voltage?Z_S - Synchronous Impedance?Φ_s - Phase Difference?α - Load Angle?

Mechanical Power Developed by Synchronous Motor Example

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

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

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

587.7329 = (\frac{180 \cdot 240}{17.75}) \cdot \cos (30 - 57) - (\frac{180^{2}}{17.75}) \cdot \cos (30)

587.7329W = (\frac{180V \cdot 240V}{17.75Ω}) \cdot \cos (30° - 57°) - (\frac{{180V}^{2}}{17.75Ω}) \cdot \cos (30°)

587.7329 = (\frac{180 \cdot 240}{17.75}) \cdot \cos (30 - 57) - (\frac{180^{2}}{17.75}) \cdot \cos (30)

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Mechanical Power Developed by Synchronous Motor Solution

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

FIRST Step Consider the formula

P m = (\frac{E b \cdot V}{Z S}) \cdot \cos (Φ s - α) - (\frac{{E b}^{2}}{Z S}) \cdot \cos (Φ s)

Next Step Substitute values of Variables

∴

P m = (\frac{180V \cdot 240V}{17.75Ω}) \cdot \cos (30° - 57°) - (\frac{{180V}^{2}}{17.75Ω}) \cdot \cos (30°)

Next Step Convert Units

∴

P m = (\frac{180V \cdot 240V}{17.75Ω}) \cdot \cos (0.5236rad - 0.9948rad) - (\frac{{180V}^{2}}{17.75Ω}) \cdot \cos (0.5236rad)

Next Step Prepare to Evaluate

∴

P m = (\frac{180 \cdot 240}{17.75}) \cdot \cos (0.5236 - 0.9948) - (\frac{180^{2}}{17.75}) \cdot \cos (0.5236)

Next Step Evaluate

∴

P m = 587.73288801822W

LAST Step Rounding Answer

∴

P m = 587.7329W

Mechanical Power Developed by 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

Voltage

Voltage, electric pressure or electric tension is the difference in electric potential between two points in electrical machines.

Symbol: V

Measurement: Electric PotentialUnit: V

Note: Value should be greater than 0.

Formulas to find Voltage

Synchronous Impedance

The synchronous impedance (Z_S ) is an imaginary impedance employed to account for the voltage effects in the armature circuit of the alternator.

Symbol: Z_S

Measurement: Electric ResistanceUnit: Ω

Note: Value can be positive or negative.

Formulas to find Synchronous Impedance

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

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

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

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

Go Mechanical Power of Synchronous Motor given Input Power

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

Go Mechanical Power of Synchronous Motor given Gross Torque

P m = τ g \cdot N s

Other formulas in Power category

Go Input Power of Synchronous Motor

P in = I a \cdot V \cdot \cos (Φ s)

Go 3 Phase Input Power of Synchronous Motor

P in(3Φ) = \sqrt{3} \cdot V L \cdot I L \cdot \cos (Φ s)

Go 3 Phase Mechanical Power of Synchronous Motor

P me(3Φ) = P in(3Φ) - 3 \cdot {I a}^{2} \cdot R a

Go Output Power for Synchronous Motor

P out = {I a}^{2} \cdot R a

How to Evaluate Mechanical Power Developed by Synchronous Motor?

Mechanical Power Developed by Synchronous Motor evaluator uses Mechanical Power = ((Back EMF*Voltage)/Synchronous Impedance)*cos(Phase Difference-Load Angle)-(Back EMF^2/Synchronous Impedance)*cos(Phase Difference) to evaluate the Mechanical Power, The Mechanical Power Developed by Synchronous Motor formula is defined as the expression for net power developed by the synchronous motor by which Mechanical power developed. Mechanical Power is denoted by P_m symbol.

How to evaluate Mechanical Power Developed by Synchronous Motor using this online evaluator? To use this online evaluator for Mechanical Power Developed by Synchronous Motor, enter Back EMF (E_b), Voltage (V), Synchronous Impedance (Z_S), Phase Difference (Φ_s) & Load Angle (α) and hit the calculate button.

FAQs on Mechanical Power Developed by Synchronous Motor

What is the formula to find Mechanical Power Developed by Synchronous Motor?

The formula of Mechanical Power Developed by Synchronous Motor is expressed as Mechanical Power = ((Back EMF*Voltage)/Synchronous Impedance)*cos(Phase Difference-Load Angle)-(Back EMF^2/Synchronous Impedance)*cos(Phase Difference). Here is an example- 587.7329 = ((180*240)/17.75)*cos(0.5235987755982-0.994837673636581)-(180^2/17.75)*cos(0.5235987755982).

How to calculate Mechanical Power Developed by Synchronous Motor?

With Back EMF (E_b), Voltage (V), Synchronous Impedance (Z_S), Phase Difference (Φ_s) & Load Angle (α) we can find Mechanical Power Developed by Synchronous Motor using the formula - Mechanical Power = ((Back EMF*Voltage)/Synchronous Impedance)*cos(Phase Difference-Load Angle)-(Back EMF^2/Synchronous Impedance)*cos(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=Back EMF*Armature Current*cos(Load Angle-Phase Difference)
Mechanical Power=Input Power-Armature Current^2*Armature Resistance
Mechanical Power=Gross Torque*Synchronous Speed

Can the Mechanical Power Developed by Synchronous Motor be negative?

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

Which unit is used to measure Mechanical Power Developed by Synchronous Motor?

Mechanical Power Developed by 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 Developed by Synchronous Motor can be measured.

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Mechanical Power Developed by Synchronous Motor Formula

​GoMechanical Power of Synchronous Motor Formula

​GoMechanical Power of Synchronous Motor given Input Power Formula

Mechanical Power Developed by Synchronous Motor Example

Mechanical Power Developed by Synchronous Motor Solution

Mechanical Power Developed by Synchronous Motor Formula Elements

Other Formulas to find Mechanical Power

Other formulas in Power category

How to Evaluate Mechanical Power Developed by Synchronous Motor?

FAQs on Mechanical Power Developed by Synchronous Motor

Variable Name

GoMechanical Power of Synchronous Motor Formula

GoMechanical Power of Synchronous Motor given Input Power Formula