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Fig.1:
End-Collar: FEM Model
Analyst: Rudy Alforque, 2/13/97
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 25.4 mm 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, the corresponding nodes on the surface of the plate and those on the key are related by constraint equations while the more interior nodes on the keys are 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:
VI. Structural Analysis: Results
Please note that in the following graphics the results coordinate system was set to cylindrical (Rsys=1). Hence, the displacements, Ux, refer to radial deformations.
All elements are shown here, including the keys, hence the peak stress 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. 2:
End-Collar: Radial Displacements with elements shown
Fig.3:
End-Collar: Stress Intensity
