2 Magnet Selection

Impact of Magnet Parameters

When selecting a magnet for a linear mover, consider temperature, magnetic material, magnet grade, magnet geometry, and general mechanical constraints. These system variables all have an impact on the overall function and reliability of the system.

As an example study, an axially magnetized cylinder magnet with a remanence (B_r ) of 850 mT was simulated traveling above a sensor with an incrementally increased air gap.

Figure 2-1 Slide-By Linear Magnetic Position Sensing

The magnet had an outer diameter of 16 mm and a thickness of 6 mm. Each horizontal line represents the magnitude of the vertical component (B_z) of the observable magnetic flux density. Plotted together, a 3D heat map is produced that shows how this one field component varies in the region below the magnet. In this case, the horizontal displacement is swept from –40 mm to +40 mm, and the vertical air gap between the sensor and magnet ranges from 2 mm to 15 mm.

Figure 2-2 B-Field Z Component Versus Linear Position

In the case of TMAG5170, the device offers two variants, each with three user programmable input ranges that vary from ±25 mT to ±300 mT. Any inputs above the maximum range are not useful. Alternatively, the TMAG5170D-Q1 is a dual-die version of the TMAG5170 that can be used if redudency in the system is required.

When examining these results closely, when the air gap distance between the sensor element and magnet is very small, there is distortion near the peak of the bell-shaped input curve as the curve begins to flatten. At very close ranges, bad peaking results from the corner effects of the magnet body concentrating on the magnetic field.

For comparison, consider how a change in the magnet geometry can impact overall function. For instance, if the magnet had an outer diameter of 8 mm while all other parameters were the same, you can note several different changes in behavior.

Figure 2-3 Linear Position Sweep With Reduced Magnet Diameter

One noted change is that the useful width of the input range dramatically reduced. The Calibration Method section explains that the maximum sensing range is typically at least 2x the diameter of the magnet.

Additionally, the corner effects observed at very close proximity are dramatically reduced when using a narrower magnet. The peak amplitude drops quickly when the air gap range increases. Intuitively, the sensing range for a smaller magnet is not as large as the sensing range of the original. What makes things even more difficult is that reducing the signal-to-noise ratio (SNR) increases uncertainty in any measurement. Therefore, target a peak input value nearly the full scale input range of the sensor selected.

Assuming then that the larger diameter is more desirable for the increased sensing range, another study of the impact of the magnet thickness can be informative. Consider next, the impact of increasing the thickness from 6 mm to 12 mm.

Figure 2-4 Linear Position Sweep With Increased Magnet Thickness

Similar to reducing the diameter of the magnet, increasing the thickness reduced the cornering effect, although visible distortion still occurs at very close proximity. From here, we can deduce that the ratio of the thickness to the diameter can impact the closest sensing range possible for this motion. Unsurprisingly, the peak B-field magnitude also increased when a magnet with larger mass was used.

Beyond just the considerations for magnet size, the material and grade of the magnet can impact field strength and cost to build the system. For example, magnetic materials can weaken as temperatures rise. Table 2-1 shows the typical values for this behavior.

If the working environment experiences large temperature variations, consider selecting a Samarium Cobalt (SmCo) magnet to reduce the effects of temperature drift.

Consider the approximate working air gap range for the sensor. The magnetic flux density observed by the sensor is inversely proportional to the square of the distance. That is, as the range increases, expect to see exponential decay in the strength of the field.

Figure 2-5 Magnetic Flux Density Versus Air Gap Range for Various Magnet Materials

For any magnetic material, there are often several different grades of magnets which are usually distinguished by the B_r of the material. This value is well defined for any particular material, regardless of the size of the magnet. As B_r decreases, the B-field for any specific shape magnet can weaken. Neodymium type magnets, such as N35 and N52, tend to be the strongest commercially available option and inexpensive ferrite materials such as FRM-12 tend to be the weakest.

Calibration Method

For any particular magnet selected, the position of the magnet can be calculated by deriving the mechanical angle using the arc-tangent of the outputs of the Hall-effect sensor.

For example, the input field produced by Figure 2-6 with a remanence of 850 mT is shown in the following plot.

Figure 2-6 Magnet (10 mm ⌀ × 4 mm) at 10-mm Vertical Air Gap

Calculations of angle using these inputs directly can be compared to the real mechanical angle.

Figure 2-7 Mechanical Angle Versus Calculated Arctangent

Notice that the form is similar but is distorted somewhat in shape and extent. This distortion can be corrected using the following form:

In Equation 1, four specific correction factors are required to obtain linearity. α specifies the amplitude correction applied to the Z axis input, β specifies a fixed offset which must be applied to the Z axis input. γ is a scalar correction for the magnetic angle, and φ is a scalar factor of the Y axis input which corrects some non-linearity in the final result.

In this case, setting the following empirically derived values for each factor produce a final position accuracy shown in Figure 2-8.

α = 0.791 ; β = 16.3 ; γ = 0.4104 ; φ = 0.448

Figure 2-8 Calibrated Position Error Versus Absolute Position

This same method was applied in the following figures to obtain similar accuracy. In each case, the position error is minimized over a region approximately 2x the diameter of the magnet.

α = 0.833 ; β = 4.85 ; γ = 0.397 ; φ = 1.07

Figure 2-9 Position Error for Magnet (5 mm ⌀ × 4 mm) at 10-mm Air Gap

α = 0.739 ; β = 24.12 ; γ = 0.4215 ; φ = 0.4617

Figure 2-10 Position Error for Magnet (14 mm ⌀ × 4 mm) at 10-mm Air Gap

The quality of each calibration varies with the exactness of the correction factors applied. In the case of the largest diameter magnet, peak error in the sensing range is approximately 10 um.

Of similar note, the ratio of the potential sensing range to the magnet diameter is largest for the smaller (and weakest) magnet.

Similarly, varying the air gap distance is possible to demonstrate impact on the expected sensing range of the sensor. Consider the following plots based on the 14 mm ⌀ x 4 mm magnet at air gaps of 5 mm and 20 mm.

α = 0.79 ; β = 58.9 ; γ = 0.297 ; φ = 0.049

Figure 2-11 Position Error for Magnet (14 mm ⌀ × 4 mm) at 5-mm Air Gap

α = 0.775 ; β = 4.95 ; γ = 0.436 ; φ = 1.54

Figure 2-12 Position Error for Magnet (14 mm ⌀ × 4 mm) at 20-mm Air Gap

In both cases, the maximum sensing range for the magnet was reduced. In the case of the 5-mm air gap, the input field was limited by distortion. In the case of the 20-mm air gap, the sensing range is limited by the strength of the magnetic field. The design goal, therefore, is to target a strong magnetic field that neither saturates the input of the sensor nor becomes distorted due to close range of the magnet.

In some cases, using a bar-shaped magnet can be advantageous for ease of assembly. This calibration method is not limited to cylindrical magnets. Similar to the previous cases, implementing the same calibration method for a square-faced magnet traveling over the sensor can produce excellent linearity (see Figure 2-13).

α = 0.75 ; β = 53.7 ; γ = 0.3815 ; φ = 0.089

Figure 2-13 Position Error for Magnet (10 mm × 10 mm × 4 mm) at 5-mm Air Gap