A do-it-yourself approach for developing a magnetic field mapping setup using a 3D printer

A DIY kit of a 3D printer, Anet A8 (CTC A8 W5), with an A1284-base mainboard, was used as a base for position control. The kit was purchased from an online store, where different analog kits are available at about one hundred euros [18]. As declared by the manufacturer, the position accuracy is 0.012 mm for the x,y-axes and 0.004 mm for the z-axis. The working area is 220 mm × 220 mm × 240 mm.

For the magnetic induction (B) measurements, we used a Lake Shore gaussmeter model 475 DSP coupled with an axial Lake Shore 400 HSE Hall probe (Lake Shore Cryotronics Inc., USA). Thus, the instrument gives the measurement of the axial component (${B_z}$) of the induction field ${\boldsymbol{B}}$ vector. The probe's sensitivity was lower than 5 milligauss (mG), while the magnetic induction range was up to 35 kG. As reported by the manufacturer, the nominal active area of the sensing element is about 1 mm in diameter. The stem for the Hall probe is made from fiberglass epoxy and has a diameter of 5 mm. It should be noted that the center of the active area of the Hall probe is inside the stem at a distance of 1.9 mm. Therefore, the position of the active area is at a distance of z_active = z + 1.9 mm, where z is the position of the surface of the Hall probe stem. The stem was therefore fixed perpendicularly to the magnet plane. The LabView 8.2 (National Instruments, USA) development environment was used as an interface to control both the 3D printer and the gaussmeter.

The magnetic mapping setup consists of three components (figures 1(a) and (b)): (i) a personal computer (PC); (ii) a Hall probe connected to the gaussmeter; and (iii) a modified 3D printer (PC-controlled) to drive the probe movements. Serial commands achieve communication with the printer via USB. A Hall probe holder (figure 1(c)) fabricated with the 3D printer replaces the original extruder in which the probe is vertically inserted. Data obtained by the gaussmeter and, simultaneously, the spatial position of the probe, are collected and stored in the PC.

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The software program for 3D printer movement control and data acquisition was operated using the LabView platform. The software solution provides a user interface consisting of several blocs (figure 2): (i) settings and checkout of the system; (ii) control of the position of the probe; (iii) the settings of the sequence of the measurement; and (iv) a real-time plot of the result.

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The commands for position control are specified using the numerical control code (G-code) [19]. An example of the G-code, setting the relative position of the probe, and moving the probe along the x-axis, is:

G91; set to relative positioning

G1 X1; move 1 mm along the x-axis

Similarly, one can control the position for the y- and z-axes by replacing 'X1' with 'Y1' and 'Z1', respectively. The step size can be selected, and additional parameters, such as the speed, can be controlled by the command 'Fxxx' that sets it to xxx mm/time unit (the time unit may depend on the printer's firmware, mm/min for Marlin). The movement achievable by a standard commercial printer is about 3000 mm min⁻¹ (usually, at speeds above, the printer starts to shake).

A 'VISA Instrument I/O' interface in LabView sends such commands to the device. The feedback signal is received from a gaussmeter connected to a PC via an IEEE-488.2 GPIB interface for USB (National Instruments). The program solution was obtained using 'LabView Instrument Driver Export Wizard', after installing appropriated drivers provided by LakeShore [20].

Briefly, the software solution consisted of three stacked control statement structures ('for' loop). Each loop defines the position of the probe in one of the planes in the Cartesian coordinate system. Accordingly, the number of iterations and the increment allow one to control the scanning area. At each point, after a delay time (t_d), required for system stabilization to prevent the effects of both mechanical vibrations (induced by movement) and instrumental time delay, due to the gaussmeter time constant, the data are collected from the gaussmeter. Data collection occurs through an addition 'for' loop. This structure collects the desired number N of values of B from the gaussmeter to average them. The standard deviation (σ) over the N points is also calculated.

It should be noted that the magnetic induction B is a vector with three projections (B_x, B_y, B_z ), and the Hall probe is only sensitive to one of those projections if it is not a 3-axis probe. There are three basic configurations of probes (figure 3):

• Axial—usually has a cylindrical shape and measures the axial component of B;
• Transverse—usually has a rectangular shape and measures perpendicular to the plane component of B ;
• 3-axis probe—allows measurement of all three components of the magnetic field.

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We used an N35-grade test-magnet (HKCM Engineering e.K., Germany) with a block shape of 20 mm × 40 mm × 5 mm coated with Ni and well-known polarity to calibrate and test the system. The magnet was placed on the surface of the printing bed below the sensor (figure 1(c)). Using both axial and transverse probes in two perpendicular orientations, the three components of magnetic flux density, B_x, B_y, and B_z , were collected at 4 mm from the magnet surface. Ten measurements of the signal (N = 10) were collected every 100 ms; then, the signal was averaged, and the standard deviation σ was calculated at each point every 2 mm over a rectangular area of 40 mm × 50 mm. The first parameter to optimize was the delay time t_d between measurements: this parameter was chosen to be equal to 0.1, 2, 5, and 10 s. All the measured B_x, B_y , and B_z signals are reported in figure 4(a). All the obtained maps depict physically reasonable profiles expected for the axially magnetized magnet, with the maximum value of the B_z component of the magnetic induction of about 1.4 kG under the magnet's edges. A more precise evaluation was achieved by comparison of standard deviation values (figure 4(b)). According to our experiments, for t_d ⩽ 5 s, σ increases to its maximum, reaching 3%, associated with residual vibrations after the mechanical movement of the probe and a significant time delay in the response of the probe.

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The next parameter of the experimental protocol, fixing t_d = 5 s, is the step size for mapping (figure 5). At first glance, the smaller step size provides a better resolution; however, it dramatically increases the measurement time. For the test-magnet sample (figure 5), a single measurement took around 7, 40, and 170 min for a step size of 5, 2, and 1 mm, respectively. Therefore, this parameter and t_d should be selected based on the task required and the size of the investigated object. The accuracy of the positioner setup (>0.012 mm for the x,y-axes) and the sensor's active-area size limit the lower spatial resolution. The sensor used in this study was 1 mm² in size, which provides sub-millimeter resolution. However, qualitative analysis with lower resolution is also possible. In this case, the magnetic flux at each point presents an average value over a region larger than the step size. In section 3.2, we show the mapping with a step size of 0.1 mm.

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By considering a step size = 2 mm, t_d = 5 s, and N = 10 s as optimal parameters, we measured the induction B of the HKCM test-magnet at different heights over the magnet (z = 1.9, 5.9, and 9.9 mm). As reported in figures 6(a)–(c), vector B is composed by the three independently measured values of projections B_x, B_y , and B_z utilizing the axial and transversal probes in two perpendicular orientations. In this case, the magnitude of $B$ is proportional to the length of the arrows because the dimension of the axes is mm (length). The vectors start from the point of measurement in the space ($x,{\text{ }}y,{\text{ }}z$) and the coordinates of the ends of the arrows are (x+ B_x/k, y+ B_y/k, z+ B_z/k), where k is a scale factor (converting Gauss units into millimeters for visual rendering). Thus, the orientation of arrows shows the orientation of B , and their magnitude is proportional to the intensity of B .

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To demonstrate this approach's applicability to mapping the magnetic field of different objects, we selected a smartphone, a flexible refrigerator (fridge) magnet, and a 5¼ inch floppy disk media. All the samples show a particular magnetic field texture with different magnetic fields and size ranges. We performed all scans at the minimal possible distance (<0.1 mm) above the objects' surface. The most intense component of the magnetic field for this configuration, ${{\text{B}}_{\text{z}}}$, was measured with an axial Hall probe.

The magnetic field of the smartphone is mainly produced by the loudspeakers and vibration mode motor, placed on the upper central and downright part of the device. To overcome the significant difference in the magnitude of signals from different parts, the smartphone magnetic map is presented on a logarithmic scale (figure 7). This example demonstrates the potential of the device for mapping sophisticated macroscopic objects. The maximal scanning area of our device is 220 mm × 220 mm × 240 mm. This area can be increased by extending the frame of the positioner setup (replacing guides with longer ones).

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To define the device's spatial resolution, the magnetic field of a flexible fridge magnet was measured (figure 8(a)). Typically, this material consists of magnetic ferrite particles embedded into resin [21, 22]. The magnetic structure of the fridge magnet presents planar Halbach arrays that allow increasing magnetic flux from one side of this array [23–25]. Figure 8(a) shows a magnetic map of a 10 × 3 mm² part of the strong side of the Halbach planar array, performed with a step size of 0.1 mm along the x-axis. The upper part presents an average among all y-axis measurements of the field profile along the x-axis for one period of the structure. The signal has a sinusoidal shape with a period of 3.2 ± 0.1 mm and a magnitude of 204 ± 5 G. The corresponding width of one stripe ∼1.6 mm is in the range of 1–2 mm, known for standard flexible-sheet refrigerator magnets [21]. Measurement of this sample with a step size of 0.1 mm gives a reasonable result. The bottom part of figure 8(b) represents a domain structure of a single segment of a standard refrigerator magnet [22]. The magnetic induction vector gradually changes its local orientation along the x-axis [24, 26]. The measured B_z component was fitted with a sinusoidal function, which describes the behavior of the rotating vector of the magnetic induction well.

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To demonstrate the possibility of further scaling of the system to measure at lower dimensions, a 10 mm × 10 mm area of the 5¼ inch floppy was mapped with a resolution of 0.1 mm (figure 9). The size of magnetic domains representing bits of information is of the order of tens of micrometers [27], which is lower than the sensor's resolution. However, the map shows distinguished areas with periodicity, probably resulting from several bits of information. Moreover, a clear stripe with a thickness around 0.4 mm was detected, presumably corresponding to a sector on the disk. The amplitude of the magnetic field was about 0.3 G; that is, the order of magnitude of the ambient magnetic field, which was subtracted. To accurately measure magnetic fields below ∼1 G in the position controller, it is necessary to replace metallic parts made of magnetic materials (e.g. steel) with non-magnetic materials and insulate the environment's magnetic fields.

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