DC machine Torque Equation
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| DC machine single and double layer winding torque equation[figure 1] |
Introduction
In DC machine two type layer winding is used according to its torque.We are trying to make understand with some equations the DC machine torque of both layer winding are equal or not .Or in other words, how can that level effect the torque equation.
Let's see.
DC machine single layer windings torque equation
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| DC machine single and double layer winding torque equation[figure 2] |
r=armature radius
l=each conductor length
Z=Total number of armature conductor
nc=number of conductor
i=current in each conductor
a= number of parallel paths
B=flux density
φ=flux per pole
P=number of poles
∆F= instantaneous of force
∆T= instantaneous of torque
Forces in each conductor (F)=B.i.l newton
Torque=fource×distance
Torque in one conductor =F.r newton-meter
Total armature torque=Z.F.r newton-meter
Ta=Z(Bil)r
Ta=ZBilr
Ta=Z(φp/a)(Ia/A)lr [.'.B=φp/a, i=Ia/A]
Ta=Z(φp/(2πrl/P))(Ia/A)lr [.'. a=2πrl/P]
Ta=Z(φp/(2π/P))(Ia/A)
Ta=0.159ZφpIa P/A
Ta ∝ φpIa
Ta ∝ kφpIa
This contain show Torque equation of single layer winding
Torque Equation Of Double Layer Winding in Dc machine
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| DC machine single and double layer winding torque equation[figure 3] |
∆F=2ncBlIc
∆F=2ncBl Ia/a [.'. Ic=Ia/a ]
∆T=2r(∆F)
∆T=4nc Brl Ia/a
So, dT=4(Z/4π)Brl Ia/a dθ [.'. nc=z/4π) ]
Total torque between two brushes.[0-> 2Ï€/p]
So, Ta =Z/Ï€ Ia/a ∫0(2Ï€/p) Brl dθ [.'.
φp = ∫0(2Ï€/p) Brl dθ]
Total armature torque ,
Ta =z/Ï€ Ia/a P/2 ∫0(2Ï€/p) Brl dθ [ p/2= is for torque of one complete rotation of armature]
Ta=ZIaP/2Ï€a =Z/2Ï€ P/a
=Z/2π P/a φp Ia
=0.159 ZP/a φp Ia
Ta ∝ φpIa
Ta ∝ kφpIa
The Torque equation of both types of layer of machine is the same but if their different constant values so the actual torque depends upon their content values.
Conclusion
In this equation states that the constant value changes with the torque. In this equation helps to find out the application wise required torque wish choose the single layer and double layer winding.
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