EQUATION FOR WINDAGE LOSS OF AXIAL FLUX, A.C. 3 PHASE SYNCHRONOUS MOTOR

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EQUATION FOR WINDAGE LOSS OF AXIAL FLUX, A.C. 3 PHASE SYNCHRONOUS MOTOR. Submitted by – K.V.Krishna Murty.

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### EQUATION FOR WINDAGE LOSS OF AXIAL FLUX, A.C. 3 PHASE SYNCHRONOUS MOTOR

Submitted by –

K.V.Krishna Murty

Definition :Windage Loss: It is usually defined as the loss in power output in a component or a machine due to the movement of air that is present in and around the components of that system.
Various parameters and their values considered for calculations:  =absolute viscosity of air at 1700F = 2.081 X 10-5 kg/m.sec s = axial gap between the rotor and the stator = 0.015 in N =rotor rotational speed = 150,000 rpm R = radius of the rotor = 1.155 in r = radius of the shaft = 0.4 in s’ = axial gap between the rotor and the motor casing = 0.66 in t = thickness or width of the rotor = 0.25 ing = radial gap between the rotor circumferential surface and the motor casing = 1.3 in
Types of Windage losses associated with our motor:1) Loss in power due to movement of air that is present between the rotor circumferential surface and the motor casing  radial loss. 2) Loss in power output due to movement of air present between the rotor and the stator  axial loss.3) Loss in power due to movement of air between the rotor the motor casing  axial loss.
Calculationfor Windage loss - I : V=Rω Frictional force per area = f = V/g  Windage Loss in Watts = f * V * a where a = 2πR * t and t is the thickness of the rotor disk.
Windage Loss - I : Equation : W1 = 2πω2R3t/g considering a laminar flow with Couette velocity distribution profile,where, g=gap between the rotor circumferential edge surface and the casing inner surface. W1= 0.157 W
Calculationfor Windage losses - II & III:
• T = Shearing stress due to drag force at a distance x from the axis of the rotor = xω/s(s’ )
• M = Moment produced due to the frictional force = ∫rR (Tx) (2πx) dx
• Windage Loss in Watts = M * ω
Windage Loss - II : Equation : W2 = πω2(R4-r4)/2sconsidering a laminar flow with Couette velocity distribution profile and W2ี = 15.455 W where s = axial gap between the rotor and the stator. The Drag Force along the walls can be neglected because s << R in higher order terms.
Windage Loss - III : Equation : W3 =πω2(R4-r4)/2s’considering a laminar flow with Couette velocity distribution profile, where s’ = the axial gap between rotor and the casing = 0.66 in.W3 = 0.351 W
Analysis of W2: W2 is proportional to ‘ω2’, ‘ R4 - r4’ and is inversely proportional to ‘s’ where,ω is the angular velocity of the rotor, R is the rotor radius, r is the shaft radius and s is the axial gap between the rotor and the stator.
To lower W2  any one or more of the below are suggested according to the suitability of the system and whichever is feasible --
• decrease the angular velocity of rotation of the rotor.
• reduce the rotor size and/or increase the shaft size.
• increase the axial gap between the rotor and the stator.
Figures :

2) Hydro-dynamic configuration of the motor :

References : 1) Hydro-dynamic Resistance and the Heat Loss of Rotating Solids  L . A . Dorfman, Oliver and Boyd Ltd., 1963.2) Fundamentals of Fluid Film Lubrication  Bernard J. Hamrock, McGraw-Hill, Inc., 1994.3) Windage Loss calculation at Wright Patterson Air Force Base, U.S.  source Dr.Jay Vaidya4) A.C. Motor Design  H.C.J. deJong, 1989.