Data-Driven Update of B(H) Curves of Iron Yokes in Normal Conducting Accelerator Magnets

Constitutive equations are used in electromagnetic field simulations to model a material response to applied fields or forces. The $B(H)$ characteristic of iron laminations depends on thermal and mechanical stresses that may have occurred during the manufacturing process. Data-driven modelling and updating of the $B(H)$ characteristic are therefore well known necessities. In this work the $B(H)$ curve of an iron yoke of an accelerator magnet is updated based on observed magnetic flux density data by solving a non-linear inverse problem. The inverse problem is regularized by restricting the solution to the function space that is spanned by the truncated Karhunen Loeve expansion of a stochastic $B(H)$-curve model based on material measurements. It is shown that this method is able to retrieve a previously selected ground truth $B(H)$-curve. With the update of the $B(H)$ characteristic, the numerical model gains predictive capacities for excitation currents that were not included in the data

An Automated Parametric Surface Patch-Based Construction Method for Smooth Lattice Structures with Irregular Topologies

Additive manufacturing enables the realization of complex component designs that cannot be achieved with conventional processes, such as the integration of cellular structures, such as lattice structures, for weight reduction. To include lattice structures in component designs, an automated algorithm compatible with conventional CAD that is able to handle various lattice topologies as well as variable local shape parameters such as strut radii is required. Smooth node transitions are desired due to their advantages in terms of reduced stress concentrations and improved fatigue performance. The surface patch-based algorithm developed in this work is able to solidify given lattice frames to smooth lattice structures without manual construction steps. The algorithm requires only a few seconds of sketching time for each node and favours parallelisation. Automated special-case workarounds as well as fallback mechanisms are considered for non-standard inputs. The algorithm is demonstrated on irregular lattice topologies and applied for the construction of a lattice infill of an aircraft component that was additively manufactured

Vertical Shape determination of a stretched wire from oscillation measurements

The Geodetic Metrology group at CERN uses stretched wires as a reference for the position monitoring and alignment of accelerator components. Until now, stretched wires find in particular use as horizontal offset measure- ment references, since their vertical projection is a line. However, the wire positioning system is able to measure not only the horizontal but also the vertical wire position. In order to use this data as vertical reference of the alignment system, a framework to describe the vertical wire shape is required. This work re-conceptualises a previously proposed optimization based algorithm, that calculates the vertical wire shape via its fundamental frequency from oscillation measurements. As a result, the determination of the vertical shape with respect to a static parabola fitting model was improved one order of magnitude compared to the previously available oscillation-based algorithm. Now, it is possible to determine the wire position with respect to static wire measurements with a precision of the same order of magnitude as the static parabolic fitting model for wires of up to 140 m length. Furthermore, the study of wire oscillations revealed methods to localize restrictions of the wire. With these means, an alternative evaluation method to the static parabolic fitting model is provided that adds information to already existing alignment systems and offers new sensor configuration possibilities for future alignment systems

Combination of Measurement Data and Domain Knowledge for Simulation of Halbach Arrays with Bayesian Inference

Accelerator magnets made from blocks of permanent magnets in a zero-clearance configuration are known as Halbach arrays. The objective of this work is the fusion of knowledge from different measurement sources (material and field) and domain knowledge (magnetostatics) to obtain an updated magnet model of a Halbach array. From Helmholtz-coil measurements of the magnetized blocks, a prior distribution of the magnetization is estimated. Measurements of the magnetic flux density are used to derive, by means of Bayesian inference, a posterior distribution. The method is validated on simulated data and applied to measurements of a dipole of the FASER detector. The updated magnet model of the FASER dipole describes the magnetic flux density one order of magnitude better than the prior magnet model

Combination of Measurement Data and Domain Knowledge for Simulation of Halbach Arrays With Bayesian Inference

Accelerator magnets made from blocks of permanent magnets (PMs) in a zero-clearance configuration are known as Halbach arrays. The objective of this article is the fusion of knowledge from the magnetic field and material measurements and domain knowledge (magnetostatics) to obtain an updated magnet model of a Halbach array. From Helmholtz coil measurements of the magnetized blocks, a prior distribution of the magnetization is estimated. Measurements of the magnetic flux density are used to derive a posterior distribution by means of Bayesian inference. The method is validated on simulated data and applied to measurements of a dipole of the FASER detector. The updated magnet model of the FASER dipole describes the magnetic flux density one order of magnitude better than the prior magnet model

A parametric mesostructural approach for robust design of additive manufacturing parts

Additive Manufacturing (AM) allows for production of potentially complex design solutions and motivates the use of Structural Optimization tools in product development to chase the structural limit of a design problem and its solution concept. Scratching on the limits of the material strength, design solutions can lack robustness concerning simplifications in model assumptions and uncertainties. However, the design freedom with AM can also actively be used to enhance robustness and reliability of solutions. To this end, an approach is presented that introduces Parametric Mesostructures into selective areas of the Additive Design. Structural members and coherent mechanical characteristics of these mesostructures can significantly reduce local stress peaks and can account for uncertainties, e.g. direction of load application. Their design is motivated by Structural Optimization and analysis results. Implementation of the approach is demonstrated and discussed on the example of a structural aircraft component