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

MOTORSubmitted 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.

Motor 3-D representation:

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.

Calculation for 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 = 2πω2R3tg 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

Calculation for 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 = ∫r

R (Tx) (2πx) dx

Windage Loss in Watts = M * ω

Windage Loss - II : Equation : W2 = πω2Rrs considering a laminar flow with Couette velocity distribution profile and W2 ี= 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 = πω2Rrs’ 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

Total Windage Loss

= 0.157 + 15.455 + 0.351 = 15.963 W with W2 as the major loss.

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 :

1) Couette Velocity Profile :

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.

Reference for values : Motor AUTO-CAD representation by William Funk.