Finite Element Analysis of the18 Turn Beam H. F. Fan November 5, 2004

18 Turn Beam FEA Model Nodes couples in Dy 1000 lb Dx=0 Dz=0 Dy=0 at support Beam is 42” long and 40” in span ¼ of beam was modeled (half width & half length) Conductor is x inches Turn insulation is 0.03 inches Ground wrap is 0.03 inches E of conductor is 9.5E6 psi E of turn insulation is 1.5E6 psi E of ground wrap is 1.5E6 psi Poissons’ ratio is 0.31 Boundary conditions and loading: Dz = 0 on mid-span surface Dx = 0 on mid-width surface Dy = 0 at support Nodes on top surface within 0.5” of mid-span are coupled in Dy for a vertical force of lb

Vertical Displacement Uy for 4000 lb Load Undeformed shape Whole model Conductor only

Von Mises Stress and Axial Stress of Conductor

Axial Stress of Turn Insulation and Ground Wrap

Simple Beam Pure Bending Stress Calculations Calculate equivalent Ie: Ratio of E i /E c = 1.5E6/9.5E6 = Width of turn insulation and ground wrap is multiplied by the factor of A c of a conductor = in^2 I c of a conductor = in^4 I 1 = 18xI c + 4*  A c *(i*0.56)^2 where i=1,2,3,4 = in^4 A i1 = 0.625*0.06 = in^2 I i1 = 0.625*0.06^3/12 = 1.125E-5 in^4 I i2 = 0.06*5.1^3/12 = in^4 I 2 = 0.158*[3*I i2 + 20xI i1 + 4*  A i1 *(i*0.28)^2] where i=1,3,5,7,9 = 0.62 in^4 I e = I 1 + I 2 = in^4 Bending Moment M = 4000*40/4 = in-lb Distance from neutral axis y = 2.49 in Max. bending stress = My/I e = 7969 psi 5.1” 1.43”

Vertical Displacement Calculations Max. displacement produced by the bending moment: dmax = 4000*40^3/(48*E*Ie) = in Max. displacement produced by the shear force: dmax =  *4000*L/(4*A*G) Assuming a = 3/2 A = (neglecting insulation) G = 3.0E6 then dmax = (3/2)*4000*40/(4*5.625*3.0E6) = in Total maximum displacement = in

Discussions: The calculated maximum bending stress is 7969 psi If we consider the applied load is uniformly distributed in 1”, then the maximum bending moment become: Max. bending moment = 4000*40/ *0.5/2 = lb-in, and Maximum bending stress = 7870 psi The FEA maximum stress occurs at the corner of the upper conductor The peak FEA axial stress on the conductor are psi and 7843 psi Higher stress in the compression side is due to the Poisson’s effect from the applied loading The calculated bending stress assumed the neutral axis is at the mid-height The calculated maximum vertical displacement is inches, which is the superposition of the bending and shear effects. The vertical displacement produced by the shear force depend on the assumed values of parameters , A, and G. The values are approximate numbers. However, the contribution of the shear displacement is much less then the bending displacement in this case. The maximum displacement from FEA is inches