Armature Winding Constant 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%
✖Magnetic flux (Φ) is the number of magnetic field lines passing through the magnetic core of an electrical dc motor.ⓘ Magnetic Flux [Φ]			+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%

✖Armature Winding Constant is defined as the ratio of the voltage applied to the motor terminals to the speed of the motor under no-load conditions.ⓘ Armature Winding Constant of Synchronous Motor [K_a]

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Formula

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Armature Winding Constant of Synchronous Motor

Formula

`"K"_{"a"} = "E"_{"b"}/("Φ"*"N"_{"s"})`

Example

`"0.614762"="180V"/("0.12Wb"*"23300rev/min")`

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Armature Winding Constant of Synchronous Motor Solution

STEP 0: Pre-Calculation Summary

Formula Used

Armature Winding Constant = Back EMF/(Magnetic Flux*Synchronous Speed)
K_a = E_b/(Φ*N_s)
This formula uses 4 Variables

Variables Used

Armature Winding Constant - Armature Winding Constant is defined as the ratio of the voltage applied to the motor terminals to the speed of the motor under no-load conditions.
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.
Magnetic Flux - (Measured in Weber) - Magnetic flux (Φ) is the number of magnetic field lines passing through the magnetic core of an electrical dc motor.
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.

STEP 1: Convert Input(s) to Base Unit

Back EMF: 180 Volt --> 180 Volt No Conversion Required
Magnetic Flux: 0.12 Weber --> 0.12 Weber No Conversion Required
Synchronous Speed: 23300 Revolution per Minute --> 2439.97029416382 Radian per Second (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

K_a = E_b/(Φ*N_s) --> 180/(0.12*2439.97029416382)

Evaluating ... ...

K_a = 0.6147615827897

STEP 3: Convert Result to Output's Unit

0.6147615827897 --> No Conversion Required

FINAL ANSWER

0.6147615827897 ≈ 0.614762 <-- Armature Winding Constant

(Calculation completed in 00.004 seconds)

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Home » Engineering » Electrical » Machine » AC Machines » Synchronous Motor » Mechanical Specification » Armature Winding Constant of Synchronous Motor

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Vishwakarma Government Engineering College (VGEC), Ahmedabad

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< 5 Mechanical Specification Calculators

Distribution Factor in Synchronous Motor

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

Angular Slot Pitch in Synchronous Motor

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

Number of Poles given Synchronous Speed in Synchronous Motor

Go Number of Poles = (Frequency*120)/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

Armature Winding Constant of Synchronous Motor Formula

Armature Winding Constant = Back EMF/(Magnetic Flux*Synchronous Speed)
K_a = E_b/(Φ*N_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 Armature Winding Constant of Synchronous Motor?

Armature Winding Constant of Synchronous Motor calculator uses Armature Winding Constant = Back EMF/(Magnetic Flux*Synchronous Speed) to calculate the Armature Winding Constant, The Armature Winding Constant of Synchronous Motor given Back Emf formula is defined as the constant of the armature winding that is used for finding many quantities of synchronous motor. Armature Winding Constant is denoted by K_a symbol.

How to calculate Armature Winding Constant of Synchronous Motor using this online calculator? To use this online calculator for Armature Winding Constant of Synchronous Motor, enter Back EMF (E_b), Magnetic Flux (Φ) & Synchronous Speed (N_s) and hit the calculate button. Here is how the Armature Winding Constant of Synchronous Motor calculation can be explained with given input values -> 0.614762 = 180/(0.12*2439.97029416382).

FAQ

What is Armature Winding Constant of Synchronous Motor?

The Armature Winding Constant of Synchronous Motor given Back Emf formula is defined as the constant of the armature winding that is used for finding many quantities of synchronous motor and is represented as K_a = E_b/(Φ*N_s) or Armature Winding Constant = Back EMF/(Magnetic Flux*Synchronous Speed). 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, Magnetic flux (Φ) is the number of magnetic field lines passing through the magnetic core of an electrical dc motor & Synchronous speed is a definite speed for an alternating-current machine that is dependent on the frequency of the supply circuit.

How to calculate Armature Winding Constant of Synchronous Motor?

The Armature Winding Constant of Synchronous Motor given Back Emf formula is defined as the constant of the armature winding that is used for finding many quantities of synchronous motor is calculated using Armature Winding Constant = Back EMF/(Magnetic Flux*Synchronous Speed). To calculate Armature Winding Constant of Synchronous Motor, you need Back EMF (E_b), Magnetic Flux (Φ) & Synchronous Speed (N_s). With our tool, you need to enter the respective value for Back EMF, Magnetic Flux & Synchronous Speed 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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