## 2 Materials and Methods
### Measurement Methods  
The main aim of the experimental measurements was to evaluate the behavior of the magnet holder under external load and determine the possibilities and the range of positioning and calibrating the magnet. The measurements of the magnet holder were made on the experimental test stand shown in Figure 9. Due to the safety requirements, during measurements, the magnet was replaced by a non-magnetized element with the same geometry and comparable stiffness. The direction of the force caused by the magnetic field of the Halbach array depends on the direction of the magnet's magnetization. Two cases were considered in which the magnetic force pushes the block into the holder or pulls out the block outside the holder. Both cases were considered during measurements (see Figure 9a and Figure 9b, respectively). The external force (simulating magnetic force) was simulated using concrete and steel weights suspended on a steel rope with a diameter of 10 mm. The rope was attached to the central part of the dummy magnet. The support frame (yellow color) was made of steel profiles ensuring high stiffness. Such high stiffness was required due to the reliability of the measurements within the range of 0-300 \(\upmu\)m. To apply loading, the magnet holder was mounted on the steel C-cross-section profile. The magnet holder was loaded by static force within the range of \(F\) = 1-2.8 kN for both configurations with load increments equal to 0.05 kN, 0.1 kN, or 0.25 kN.  
The preliminary measurements were conducted using dial indicators (Article No 119110104, Limit, Alingsas, Sweden) with a measurement range of 0-10 mm and with a measuring scale graduation equal to 0.01 mm. Dial indicators were mounted on a Limit stand (Article No 119081008, Limit, Alingsas, Sweden). The screws were tightened and adjusted using the adjustable torque wrench Yato model 1-10/0.1 Nm (Yato, Shanghai, China). The  
Figure 8: Pretensioning of bolts using “Bolt Pretension” function.  
Figure 9: Experimental test stand for measurement of magnet holder: (**a**) with simulation of the “push-in” conditions and (**b**) simulation of the “pull-out” conditions.  
measurements of the magnet's displacement were conducted directly on the magnet's upper working face, at the points indicated in Figure 10.  
Finally, the mechanical behavior of the structure was analyzed with the use of the Digital Image Correlation (DIC). Due to the planar deformation of the magnet grips, one high-resolution camera (Nikon D-90 and an AF-S NIKKOR 50 mm f/1.8 G lens; Nikon Imaging Japan Inc., Tokyo, Japan) was used for collecting the images. The resolution of captured images was equal to 4288 \(\times\) 2848 pixels. The measured structure (surface) was illuminated by the external LED light. Before each new test series, a new reference image was made. All DIC tests were made with the same settings. The post-processing analyses were performed in GOM Correlate Software ver. 2018 Hotfix 1 [42]. The calculations were made for the subset size equal to 50 \(\times\) 50 pixels and the point distance equal to 20 pixels. The accuracy of the applied DIC system was determined and verified based on FEM calculations and presented in Ref. [43].  
All measurements were conducted using the same procedure and mounting sequence. The inner frame-fixing screws were tightened with the same torque \(M_{m}\) = 10 Nm in all tested cases. Only the clamp mountings screws (with torque \(M_{c}\)) and adjustment screws (with torque \(M_{r}\)) were tightened and loosened in the range of 0-10 Nm. The bolts were tightened in the same order (each time to the opposite screw or diagonally--from the left-front screw visible in the photographs) with small increments of the torque.