Calculating Smeared Material Properties for a SMES Magnet Coil

Timothy A. Brandsberg, PE BWX Technologies, Inc.

Abstract This paper documents a method for using ANSYS to calculate the smeared material properties associated with the coil structure of a Superconducting Magnetic Energy Storage System (SMES). This SMES has been designed to stabilize electric utility grid oscillations, such as was experienced in the Northeast in August of 2003.

The coil structure is very large (12 feet OD) with many small turns of wire, stainless steel conduit, tapes and epoxy to form a very non-homogeneous composite structure. To evaluate the general magnet performance, it is necessary to substitute the details of the coil winding with a smeared, orthotropic material. The method described involves creating a detailed model of a small cell that embodies the structural details of the various coil pack components, and applying unit deflections to produce reaction forces and moments. These reactions are then used to calculate the various terms of the anisotropic material property matrix.

Introduction

BWX Technologies, Inc. (BWXT) has completed construction of a number of electromagnetic coil modules for use in a demonstration of a Superconducting Magnetic Energy Storage System (SMES). The SMES system design and manufacturing work was supported under a grant from the DOE to demonstrate and commercialize the SMES technology. The final demonstration phase of the SMES system will be completed by the Center for Advanced Power Systems at Florida State University. The objective of this final phase is to demonstrate the ability of this technology to help stabilize a portion of a utility power grid during load swing and load shedding transients. This magnet will store up to 70 mega-joules of energy (i.e., 70 seconds at one megawatt or 0.1 second at 70 megawatts) that will be instantly available to the grid to make up for mismatches in generation and load that might cause deterioration of the local power quality, or even a shutdown of the grid.

The magnet consists of a solenoid coil structure with a conductor pack OD of 12 feet and ID of 10 feet. The coil structure is formed from a series of coil modules to allow scalability of magnet size for various applications. The demonstration coil will use 7 of the coil modules, resulting in a finished solenoid assembly height of about 3.5 feet tall. The completed coil will operate at a temperature of 4.5K while located inside of a 14-foot diameter thermally insulated vacuum vessel, conceptually shown as an exploded view in figure 1.

Figure 1. SMES Solenoid Magnet & Vacuum Vessel

The conductor being used consists of hair-like strands of superconducting Niobium-Titanium alloy that has been co-extruded with copper to form a wire. Lengths of this wire were twisted to form cables that are further encased in a stainless steel tube. The tubing provides a pressure boundary for the liquid helium coolant needed to maintain the conductor in a superconducting state. To facilitate a tightly packed winding, the tubing was swaged to form a rectangular shape as shown in figure 2. This configuration is called CICC for Cable-In-Conduit-Conductor.

Figure 2. CICC with Conductor Cables Exposed

The coil was created by wrapping a quarter-mile length of this CICC around a 10-foot diameter fiberglass ring to form a double pancake configuration as shown in figure 3. The winding machine automatically wrapped the CICC with KAPTON (non-adhesive) and woven glass fiber tapes for electrical insulation. After winding four (4) double pancakes, an outer fiberglass ring was assembled to form the outer diameter of the winding pack. This was followed by sealing the pack to allow impregnation of the winding pack with epoxy to provide structural integrity to the overall structure. Figure 4A shows a finished coil module ready for stacking and bonding to form the overall magnet. Figure 4B shows a cross section sample of a test module with an epoxy impregnated array of CICC which was used for potting system verification.

Since this magnet is a composite structure consisting of many materials with varying orthotropic material properties and orientations, the structural and especially the thermal stress analysis becomes quite complex. Although ANSYS provides the ability to model the these properties to virtually any extent that the analyst can define them, a coil model representing more than a thousand turns can be massive. To reduce the model size for evaluation of the overall magnet performance, the coil pack was modeled as a monolithic orthotropic material with homogeneous properties based on the smeared performance of the detailed CICC and insulation system.

Figure 3 - Example Double Pancake Winding

Figure 4A – One of Seven Potted Modules Fabricated for the SMES Magnet

Figure 4B – Test Module Cross Section

Method of Smearing the Properties

ANSYS was used to calculate the smeared properties by modeling a small section of the winding pack in detail, as shown in Figure 5. Various unit displacements were applied to this model and the reaction forces on the constrained faces were calculated. Using the input displacements and output reaction forces, the various orthotropic material properties could then be calculated. These calculations are based on methods reported by L. Myatt in Reference 1.

Figure 5 - ANSYS Model for Smeared Property Calculations Since the KAPTON tape is not bonded to the stainless steel conduit, the elastic modulus of this structure under lateral compression is quite different from that under lateral tension. In the first case, the stiffness is dominated by the stainless steel conduit. However, in the second case, the stiffness is dominated by the glass reinforced epoxy since the Kapton can separate from the conduit (as shown in Figure 6). This means that the smeared radial and axial properties have different values for tension and compression loading. Fortunately, the overall loading of the magnet is compressive in the radial and axial directions, and need not be considered in the model of the whole structure.

Figure 6 - Tensile Loading Across Pack Can Open Gaps Resulting in Low Elastic Modulus For each orthotropic property to be calculated there is a set of constraints and unit displacements to be applied. Additionally, the boundaries that move are coupled to move as a plane for symmetry. Table 1 lists the constraints applied for each parameter to be calculated. Table 2 lists the formulae for calculating the property values from the model results data. Figure 7 shows several of the deformed model shapes for certain of these cases.

One factor that became obvious during the development of this process is that an analyst must be careful about the use and input of the value for Poisson’s Ratio. In typical mechanics of materials textbooks, Poisson’s Ratio is the ratio of the strain in one orthogonal direction as a result of stress-induced strain in another. Typically, this is obtained in a tensile test by measuring the strain in the direction of the stress and the strain perpendicular to the stress, and taking their ratio. This value (obtained as the ratio of strains) should be input to ANSYS as PRxy, PRxz, and PRyz. The values for NUxy, NUxz, and NUyz are different by the ratio of the modulus of elasticity in the orthogonal directions. In composite material structures, this can make a very significant difference in the results generated. In an isotropic material, there is no difference since the elastic modulus is the same in each orthogonal direction.

Figure 7 - Several Smear Calculation Mode Shapes

Verification of the Calculation Process

One method used to check the validity of the results involves the use of a single orthotropic material for the whole model and verifying that the resulting calculated smeared properties were the same as input. Table 3 compares the results of this method when applied to a structure consisting of a single orthotropic material. Obviously, the method produces output that matches the input material properties.

A second test of the validity of this modeling method took advantage of measured CICC coil pack modulus data reported by Reference 2. This reference reported on measurements of a segment of the coil pack material being considered for use in the Japanese LHD Fusion Reactor experiment. The elastic modulus measured in this experiment was 22.7 GPa in the axial direction and 16.0 GPa in the radial direction. Using the methods described in this paper, the calculated modulus of elasticity for this structure was 22.1 and 15.4 GPa respectively. This result was closer to the test data (and thus is assumed to be more accurate) than the methods described in the paper that included a curved beam analysis and a simple finite element analysis.

Use of the Smeared Properties

The resulting smeared properties were used in an axi-symmetric model of the overall magnet to evaluate the distribution of the magnetic forces in the winding pack and the interaction of the coil pack and the outer insulation when cooling down to the operating temperature. Figure 8 shows the hoop, radial and axial stress distribution within the winding pack due to the magnetic forces.

Figure 8 - Magnetic Stress Distribution within the Winding Pack To evaluate the structural stresses in the CICC walls, the peak stresses calculated with the smeared model are applied to the exterior faces of a detailed sub-model of several CICC and the adjacent glass reinforced epoxy. A typical sub-model is shown in Figure 9. The insulation around each conduit is modeled with its

element coordinate system aligned parallel to the exterior face of the CICC. This allows the Z-direction to represent the thru-thickness direction for the glass cloth tape. The X- and the Y-directions represent the warp and weave (orthogonal, in-plane) directions. Each direction has unique orthotropic properties and strength values which must be considered when evaluating the results.

Figure 9 - Typical Sub-Model of CICC Pack Figure 10 shows a displacement plot of the detailed sub-model with the magnetic loads applied. Note that the top surface of the CICC tends to bow inwards due to the moment introduced by transferring the vertical load around the corners. On some high performance magnet systems such as in a fusion reactor, this tends to put the epoxy into a tensile load through the thickness of the insulation – which is the weakest direction. Where the KAPTON is not bonded to the CICC, no through-thickness tensile stress would develop since the KAPTON would pull away from the CICC wall.

Figure 10 - Displacement Plot of CICC Pack Sub-Model with Magnetic Loads

Table 1 Constraints on External Faces of the Unit Cell Model

Face at => x=0 y=0 z=0 x=1 y=1 z=1

Load Step

1 - Exx ux=0 uy=0 uz=0 ux=1 uy=cp* uz=cp*

2 - Eyy ux=0 uy=0 uz=0 ux=cp* uy=1 uz=cp*

3 - Ezz ux=0 uy=0 uz=0 ux=cp* uy=cp* uz=1

4 - Gxy uy,uz=0 ux,uy,uz=0 uy,uz=0 uy,uz=0 uy,uz=0, ux=1 uy,uz=0

5 - Gxz uy,uz=0 uy,uz=0 ux,uy,uz=0 uy,uz=0 uy,yz=0 uy,uz=0, ux=1

6 - Gyz ux,uz=0 ux,uz=0 ux,uy,uz=0 ux,uz=0 ux,uz=0 ux,uz=0, uy=1

7 - Alpha ** ux=0 uy=0 uz=0 ux=cp* uy=cp* uz=cp*

* = cp means that all nodes on this plane are coupled for motion in the direction specified

** A uniform temperature is applied to cause thermal contraction/expansion

Table 2 To Calculate the Smeared Material Properties

1. Obtain the sum of the nodal reaction force component (i.e., Fx, Fy or Fz) acting on the appropriate fixed plane (i.e., x=0, y=0, or z=0).

2. Obtain the “unit deflection” applied in the appropriate load step (i.e., Ux, Uy, Uz) at the non-fixed faces of the cell (i.e., x=1,y=1, or z=1)

3. Obtain the cell dimension parallel to the unit dimension (i.e., DIMx, DIMy, DIMz)

4. Then:

To Calculate Smeared Property

value for:

Use Load Step No.

Exx 1 Exx = { DIMx * Fx(x=0) } / Ux(x=1)

Eyy 2 Eyy = { DIMy * Fy(y=0) } / Uy(y=1)

Ezz 3 Ezz = { DIMz * Fz(z=0) } / Uz(z=1)

Gxy 4 Gxy = { DIMy * Fx(y=0) } / { DIMx * DIMz * Ux(y=1) }

Gxz 5 Gxz = { DIMz * Fx(z=0) } / { DIMx * DIMy * Ux(z=1) }

Gyz 6 Gyz = { DIMz * Fy(z=0) } / { DIMx * DIMy * Uy(z=1) }

PRxy 1 PRxy = {Uy(y=1) / DIMy } / { Ux(x=1) / DIMx }

PRxz 1 PRxz = { Uz(z=1) / DIMz } / { Ux(x=1) / DIMx }

PRyz 2 PRyz = { Uz(z=1) / DIMz } / { Uy(y=1) / DIMy }

ALPHAx 7 ALPHAx = { Ux(x=1) / DIMx } / TempDiff

ALPHAy 7 ALPHAy = { Uy(y=1) / DIMy } / TempDiff

ALPHAz 7 ALPHAz = { Uz(z=1) / DIMz } / TempDiff

Table 3 Test of Smearing Model Method

With Uniform Orthotropic Material Properties as Input

Input Property Value Output Property Value

Exx 20 GPa 20.00 GPa

Eyy 30 GPa 30.00 GPa

Ezz 32 GPa 32.00 GPa

Gxy 7.6 GPa 7.60 GPa

Gxz 7.6 GPa 7.60 GPa

Gyz 10.7 GPa 10.70 GPa

Alpha-x 20 e-6 20.00 e-6

Alpha-y 10 e-6 10.00 e-6

Alpha-z 12e-6 12.00 e-6

PRxy .26 .26

PRyz .27 .27

PRxz .28 .28

Conclusion In this effort, a method has been documented that allows a complex composite structure to be simplified for overall structural performance. A test of this method has demonstrated that the calculated smeared elastic modulus properties compared very well with previously documented measurements of actual magnet hardware.

References 1) R.L. Myatt, Finite-Element Analysis Of The TPX Toroidal Field-Coil System, IEEE Transactions

On Magnetics, Part 2 JUL 1994

2) H. Nishimura, H. Tamura, S. Imagawa, T.Mito, K. Takahata, J. Yamamoto, S. Mizumaki, H. Ogata, and H. Takano, Experimental Rigidity Evaluation of Conduit Pack for Forced-Flow Superconducting Coil, Adv. In Cryogenic Engineering, Vol. 40, 1994.