Distribution Factor in Synchronous Motor Calculator

✖The number of slots per pole per phase determines how the winding layout is arranged. It is also disclosing information about the winding factor and its harmonics.ⓘ Number of Slots [n_s]			+10% -10%
✖Angular Slot Pitch is angle between two consecutive slots in the rotor of a Synchronous Motor.ⓘ Angular Slot Pitch [Y]			+10% -10%

✖Distribution Factor is defined as the ratio of the emf induced in a single coil to the total emf induced in all the coils in the armature. It is also called Coil Pitch Factor.ⓘ Distribution Factor in Synchronous Motor [K_d]

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Formula

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Distribution Factor in Synchronous Motor

Formula

`"K"_{"d"} = (sin(("n"_{"s"}*"Y")/2))/("n"_{"s"}*sin("Y"/2))`

Example

`"0.001297"=(sin(("95"*"162.8°")/2))/("95"*sin("162.8°"/2))`

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Distribution Factor in Synchronous Motor Solution

STEP 0: Pre-Calculation Summary

Formula Used

Distribution Factor = (sin((Number of Slots*Angular Slot Pitch)/2))/(Number of Slots*sin(Angular Slot Pitch/2))
K_d = (sin((n_s*Y)/2))/(n_s*sin(Y/2))
This formula uses 1 Functions, 3 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

Distribution Factor - Distribution Factor is defined as the ratio of the emf induced in a single coil to the total emf induced in all the coils in the armature. It is also called Coil Pitch Factor.
Number of Slots - The number of slots per pole per phase determines how the winding layout is arranged. It is also disclosing information about the winding factor and its harmonics.
Angular Slot Pitch - (Measured in Radian) - Angular Slot Pitch is angle between two consecutive slots in the rotor of a Synchronous Motor.

STEP 1: Convert Input(s) to Base Unit

Number of Slots: 95 --> No Conversion Required
Angular Slot Pitch: 162.8 Degree --> 2.84139602224623 Radian (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

K_d = (sin((n_s*Y)/2))/(n_s*sin(Y/2)) --> (sin((95*2.84139602224623)/2))/(95*sin(2.84139602224623/2))

Evaluating ... ...

K_d = 0.00129742292297276

STEP 3: Convert Result to Output's Unit

0.00129742292297276 --> No Conversion Required

FINAL ANSWER

0.00129742292297276 ≈ 0.001297 <-- Distribution Factor

(Calculation completed in 00.004 seconds)

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Home » Engineering » Electrical » Machine » AC Machines » Synchronous Motor » Mechanical Specification » Distribution Factor in Synchronous Motor

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Created by Aman Dhussawat

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

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Verified by Parminder Singh

Chandigarh University (CU), Punjab

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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

Distribution Factor in Synchronous Motor Formula

Distribution Factor = (sin((Number of Slots*Angular Slot Pitch)/2))/(Number of Slots*sin(Angular Slot Pitch/2))
K_d = (sin((n_s*Y)/2))/(n_s*sin(Y/2))

What is distribution factor and pitch factor?

We express it as the ratio of the phasor sum of the emfs induced in all the coils distributed in some slots under one pole to the arithmetic sum of the emfs induced. Distribution factor is, As pitch factor, distribution factor is also always less than unity. Let the number of slots per pole is n.

How to Calculate Distribution Factor in Synchronous Motor?

Distribution Factor in Synchronous Motor calculator uses Distribution Factor = (sin((Number of Slots*Angular Slot Pitch)/2))/(Number of Slots*sin(Angular Slot Pitch/2)) to calculate the Distribution Factor, The Distribution Factor in Synchronous Motor formula is defined as the ratio of phasor sum of coil emfs to the arithmetic sum of coil emfs. It is also known as Belt or Breadth factor and denoted by kd. Distribution Factor is denoted by K_d symbol.

How to calculate Distribution Factor in Synchronous Motor using this online calculator? To use this online calculator for Distribution Factor in Synchronous Motor, enter Number of Slots (n_s) & Angular Slot Pitch (Y) and hit the calculate button. Here is how the Distribution Factor in Synchronous Motor calculation can be explained with given input values -> 0.001297 = (sin((95*2.84139602224623)/2))/(95*sin(2.84139602224623/2)).

FAQ

What is Distribution Factor in Synchronous Motor?

The Distribution Factor in Synchronous Motor formula is defined as the ratio of phasor sum of coil emfs to the arithmetic sum of coil emfs. It is also known as Belt or Breadth factor and denoted by kd and is represented as K_d = (sin((n_s*Y)/2))/(n_s*sin(Y/2)) or Distribution Factor = (sin((Number of Slots*Angular Slot Pitch)/2))/(Number of Slots*sin(Angular Slot Pitch/2)). The number of slots per pole per phase determines how the winding layout is arranged. It is also disclosing information about the winding factor and its harmonics & Angular Slot Pitch is angle between two consecutive slots in the rotor of a Synchronous Motor.

How to calculate Distribution Factor in Synchronous Motor?

The Distribution Factor in Synchronous Motor formula is defined as the ratio of phasor sum of coil emfs to the arithmetic sum of coil emfs. It is also known as Belt or Breadth factor and denoted by kd is calculated using Distribution Factor = (sin((Number of Slots*Angular Slot Pitch)/2))/(Number of Slots*sin(Angular Slot Pitch/2)). To calculate Distribution Factor in Synchronous Motor, you need Number of Slots (n_s) & Angular Slot Pitch (Y). With our tool, you need to enter the respective value for Number of Slots & Angular Slot Pitch 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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