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Fig.1: End-Collar: FEM Model
Analyst: Rudy Alforque, 12/9/96
E-Mail: rudy@bnl.gov
The coil pack of the LHC superconducting magnet that will be built here at BNL will be a collared construction as in the old SSC magnets, and the Rhic DX magnets. Difficulties in assembly, however, require an end collar design that is slightly different from the central collar in order to bring out the conductors. A structural study was made of the end-collar design that was agreed upon during a meeting attended by Erich Willen, Ramesh Gupta, Mike Anerella, Gene Kelly, and Rudy Alforque.
II. FEM Model:
A linear, static 2-D finite element structural analysis of the end collar was performed using ANSYS REV5.2. The LHC end collar has the following geometry: Inner Radius, 2.5 in., and 20mm radial thickness. Stainless steel spacers will be placed between the outer surface of the coil and the inner surface of the end-collar. For modelling purposes, these spacers were assumed to be uniform as shown in Fig. 1. In the actual case, they will be spaced with enough clearance such that the superconductor can be routed out through the ends of the assembly. In the model, a space was provided between the outer surface of the spacers and the inner surface of the end-collar. The nodal points along this interface have one-to-one correspondence but non-coincident; Radial constraints imposed on corresponding nodes allow the transmission of pressure from the coil to the end-collar.
The relevant material properties used in the model, for both the collar and the spacers, were as follow: Young's Modulus, 28.8x106 psi, and Poisson's ratio, 0.29. The thickness of the coil pack was also given to be 10 mm.
A model, Fig. 1, was generated with quadrilateral, 4-node plane stress elements (Plane42). The applied loads and boundary conditions are described below.
III. Loads:
The pressure load on the inner surface of the spacer was 2400 psi which corresponds to a coil compression of 12,000 psi. This is derived from the assumption that the coil pack is fully circular and obeys the simple hoop stress equation for thin cylinders, S = PR/t, where S is the prescribed compressive stress on the coil pack, R is outer radius of the coil, 50 mm, and t = coil thickness, 10 mm. An azimuthal pressure of 12,000 psi was also applied to the sides of the pole spacers.
IV. Boundary conditions:
For this model, it is assumed that the surface of the plate that rests on the key are restrained vertically since the neighboring plate actually exerts that reactive force, keeping the key restrained in the y-direction.
Furthermore, the corresponding nodes at the ends of the plates that push against each other are related by constraint equations along the x-axis. Similarly, the nodes at the tack welds are also related by constraint equations.
V. Graphical Display of the Model:
Note: A 2nd model, Case II, was also run with a portion of the spacers removed.
VI. Structural Analysis: Results
Case I model was re-run with the keys already included in order to get a rough idea of the stress levels around that region. No further work was done for Case II; it was done only for purposes of comparison.
Please note that the following graphics for Case I were generated with the results coordinate system set to cylindrical (Rsys=1). Hence, the displacements, Ux, refer to radial deformations, whereas Case II was set at cartesian (Rsys=0).
Figs. 2a-2c below show the radial displacements for Case I, and Figs. 3a-2c show the Stress Intensity. All elements are shown here, including the keys, hence the peak value indicates a pretty conservative localized stress level. In addition, from the nodal reaction results, the resultant shearing force at the tack welds was about 250 lbs.
Fig.2a: End-Collar: Case I, Radial Displacements with elements shown
Fig.2b: End-Collar: Case I, Radial Displacements (Alternate Display)
Fig.3a: End-Collar: Case I, Stress Intensity with elements shown
Fig.3b: End-Collar: Case I, Stress Intensity (Alternate Display)
Fig.3c: End-Collar: Case I, Stress Intensity with Loads, Boundary conditions, and Reactions shown
Fig.4a: End-Collar: Case II, Ux
Fig.4b: End-Collar: Case II, Uy
