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Distribution Factor in Synchronous Motor Formula

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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. Check FAQs

K d = \frac{\sin (\frac{n s \cdot Y}{2})}{n s \cdot \sin (\frac{Y}{2})}

K_d - Distribution Factor?n_s - Number of Slots?Y - Angular Slot Pitch?

Distribution Factor in Synchronous Motor Example

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Here is how the Distribution Factor in Synchronous Motor equation looks like with Values.

Here is how the Distribution Factor in Synchronous Motor equation looks like with Units.

Here is how the Distribution Factor in Synchronous Motor equation looks like.

0.0013 = \frac{\sin (\frac{95 \cdot 162.8}{2})}{95 \cdot \sin (\frac{162.8}{2})}

0.0013 = \frac{\sin (\frac{95 \cdot 162.8°}{2})}{95 \cdot \sin (\frac{162.8°}{2})}

0.0013 = \frac{\sin (\frac{95 \cdot 162.8}{2})}{95 \cdot \sin (\frac{162.8}{2})}

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Distribution Factor in Synchronous Motor Solution

Follow our step by step solution on how to calculate Distribution Factor in Synchronous Motor?

FIRST Step Consider the formula

K d = \frac{\sin (\frac{n s \cdot Y}{2})}{n s \cdot \sin (\frac{Y}{2})}

Next Step Substitute values of Variables

∴

K d = \frac{\sin (\frac{95 \cdot 162.8°}{2})}{95 \cdot \sin (\frac{162.8°}{2})}

Next Step Convert Units

∴

K d = \frac{\sin (\frac{95 \cdot 2.8414rad}{2})}{95 \cdot \sin (\frac{2.8414rad}{2})}

Next Step Prepare to Evaluate

∴

K d = \frac{\sin (\frac{95 \cdot 2.8414}{2})}{95 \cdot \sin (\frac{2.8414}{2})}

Next Step Evaluate

∴

K d = 0.00129742292297276

LAST Step Rounding Answer

∴

K d = 0.0013

Distribution Factor in Synchronous Motor Formula Elements

Variables

Functions

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.

Symbol: K_d

Measurement: NAUnit: Unitless

Note: Value can be positive or negative.

Formulas to find Distribution 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.

Symbol: n_s

Measurement: NAUnit: Unitless

Note: Value should be greater than 0.

Formulas to find Number of Slots

Angular Slot Pitch

Angular Slot Pitch is angle between two consecutive slots in the rotor of a Synchronous Motor.

Symbol: Y

Measurement: AngleUnit: °

Note: Value should be greater than 0.

Formulas to find Angular Slot Pitch

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.

Syntax: sin(Angle)

Other formulas in Mechanical Specification 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 Distribution Factor in Synchronous Motor?

Distribution Factor in Synchronous Motor evaluator uses Distribution Factor = (sin((Number of Slots*Angular Slot Pitch)/2))/(Number of Slots*sin(Angular Slot Pitch/2)) to evaluate 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 evaluate Distribution Factor in Synchronous Motor using this online evaluator? To use this online evaluator for Distribution Factor in Synchronous Motor, enter Number of Slots (n_s) & Angular Slot Pitch (Y) and hit the calculate button.

FAQs on Distribution Factor in Synchronous Motor

What is the formula to find Distribution Factor in Synchronous Motor?

The formula of Distribution Factor in Synchronous Motor is expressed as Distribution Factor = (sin((Number of Slots*Angular Slot Pitch)/2))/(Number of Slots*sin(Angular Slot Pitch/2)). Here is an example- 0.001297 = (sin((95*2.84139602224623)/2))/(95*sin(2.84139602224623/2)).

How to calculate Distribution Factor in Synchronous Motor?

With Number of Slots (n_s) & Angular Slot Pitch (Y) we can find Distribution Factor in Synchronous Motor using the formula - Distribution Factor = (sin((Number of Slots*Angular Slot Pitch)/2))/(Number of Slots*sin(Angular Slot Pitch/2)). This formula also uses Sine (sin) function(s).

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