Experimental and numerical investigation of the winding process of superconducting coils made of multi-strand Rutherford-type Nb3Sn cable

The High Luminosity-LHC (HL-LHC) project and the Future Circular Collider study (FCC) require higher magnetic fields than provided by the magnets presently installed in the Large Hadron Collider (LHC). In order to fulfill this requirement new dipole and quadrupole magnets are designed based on Nb3Sn superconductor. Due to the brittleness of Nb3Sn compound, the cable is wound into a coil in its pristine state. Subsequently, after the coil winding process a heat treatment cycle is carried out in order to form the superconducting intermetallic phases. This production sequence is also called wind-and-react technique. The cable used to produce these coils consists of 40-strands with a diameter of up to 1 mm. This Rutherford cable with its trapezoidal cross section was optimized to allow a tight azimuthal compaction in a cos-θ coil type. Due to the compact coil design the cable is subjected to a small bending radius in the coil-end regions, which can lead to mechanical instabilities (deformations) of the individual strands. These unwanted strand deformations can impact overall geometrical quality and electromagnetic performance of the coil. Manual corrections of such deformations might be acceptable for prototyping phases or small series production. However it is crucial to develop methods to minimize these phenomena especially in view of large series productions like foreseen for the production of the FCC magnet system. This thesis is therefore aiming to develop methods to define, quantify and compensate the observed strand deformations based on numerical computations and experimental campaigns. The experimental campaigns will require to develop a special testing machine and winding specimens, since one requirement is not to interfere ongoing series production. The ongoing winding process for prototype and series coil production was mainly of scientific input regarding the observed mechanical instabilities. It will be shown that the complex winding kinematics can be in a first iteration reduced to single Degree Of Freedom (DOF) on a small winding setup, which will allow to reproduce the observed cable deformation. This setup is used to carry out test campaigns with different Rutherford cables, which allow good comparison of winding performance of various cable designs. In order to quantify the observed deformation it is crucial to define an adequate measurement routine. This is addressed by the development of an optical scanning device, which allows to perform the metrological inspection of the winding samples. In parallel to these experimental campaigns numerical computations and X-ray absorption tomograms are carried out aiming to support the theoretical input in understanding the winding deformations. Mechanical tests improve the material definition for the numerical model will be carried out. The multi-body model will allow to generate deformation functions similar to the ones observed on the full-size winding machine and 1 DOF winding specimen. In addition, it is shown that the Nb3Sn cable insulation layers deteriorate the direct observation of the strand deformation. Therefore a non-destructive inspection method will be examined aiming to determine the strand location underneath those layers. It is important to underline that the analysis and contribution described in this thesis intends to provide the basis allowing to improve the quality and repeatability of obtained coil geometry. A potential further development is suggested that includes an enhanced monitoring of the coil geometry and development of winding machine kinematics, which can be applied for a future winding process. The doctoral thesis is composed of nine chapters. Chapter 1 is introductory and is subdivided in two parts. Part 1 describes CERN particle accelerator infrastructure and introduces the ongoing projects and studies. Part 2 describes the dipole and quadrupole superconducting magnet constituents, introduces the superconductivity phenomenon and utilized Rutherford-type cables. In addition, the dipole coil optimization performed at CERN with ROXIE software is introduced along with the main design parameters. Chapter 2 describes the winding process of superconducting coils based on the procedures and experience gathered at CERN Large Magnet Facility. First three subchapters describe the winding machine kinematics following the Denavit-Hartenberg notation, operations performed during the process and required manual manipulation. Afterwards, fourth subchapter includes the cable deformations observed during the prototype coil winding, i.e. the strand pop-out and protrusion. The Rutherford cable deformation is categorized based on the applied bending momentum in fifth subchapter. Chapter 3 determines main goals of presented thesis and states the hypothesis. Additionally, it includes the scope of a conducted research. Chapter 4 deals with the modelling with use of Finite Element Method. First subchapter investigates the stress distribution of the wound cable due to the tensioning force. The model includes a simplified cable geometry (i.e. rectangular cross-section stripe of homogeneous material), and the 11 T end-key is used as a support. Second subchapter describes the winding simulation of 10-strand Rutherford cable, and includes the plastic material property (i.e. the multilinear isotropic hardening). The material definition is derived from the performed tensile test. The Rutherford cable geometry is investigated based on the Computed Tomography of the cable specimen. The cable deformation functions are extracted using a developed algorithm, and the discussion is given in third subchapter. Chapter 5 introduces three tested techniques allowing digitizing the inspected specimen. First subchapter aims to locate the individual strands underneath the S-2 Glass and Mica insulation layers by use of the Active Thermography method. Second subchapter evaluates the spatial resolution of obtained scans by use of laser triangulation and structural light surface scanning techniques. Afterwards, the highest quality scans are used to validate a developed in-house scanner. Chapter 6 is subdivided on four parts and focuses on defining the winding experiment methodology. First part describes the winding frame used to wind specimens in controllable environment. Second part shows a developed specimen scanning device. The Winding Scanner allows obtaining high accuracy scan of specimen’s outer surface with use of three motorized DOF and laser measurement head. The obtained scan is analyzed following the method shown in third subchapter. The computed deformation indicators allow quantifying three observed deformation types, i.e. the envelope, the strand pop-out, and the protrusion. Fourth part shows the method used to measure the cable springback angle in order to estimate the amount of elastic deformation of a wound cable. Chapter 7 is divided into three subchapters and define the winding test campaigns conducted following the methodology described in chapter 6. First subchapter investigates cable deformation obtained by various winding tension and direction. Shown results include recommended parameters allowing obtaining the lowest amount of cable deformation for given criteria. Second subchapter investigates the influence of cable pre-torsion on the winding deformation. The presented results indicate that the additional Degree Of Freedom of the winding machine is beneficial for performance and repeatability of winding process. The additional tests performed with use of developed method are shown in third subchapter. These include the investigation of wound cable deformation due to the Reaction Heat Treatment in up to 650°C, as well as the wound cable volume digitization with use of the neutron tomography. Chapter 8 concentrates on the additional geometrical measurements performed during winding and curing of MQXFB CR107 quadrupole coil. In addition to the standard procedure of measuring the cable bottom position, the top position of the cable as well as the cable protrusion were measured. Proposed investigation contribute to understanding the geometry variations between consecutive coil production steps (i.e. winding and curing). In addition, the improved Quality Control (QC) procedure is applicable to the reaction and impregnation procedures, and may allow to control the repeatability of obtained coil geometry. Comprehensive summary is given in chapter 9. This includes the description of obtained objectives and a recommended outline of future studies aiming for automated superconducting coil winding.