# Tactile Sensing Using Magnetic Foam

^{1}

^{2}

^{3}

^{4}

^{5}

^{*}

## Abstract

**:**

## 1. Introduction

_{v}of the composite [3], defined as the ratio of the filler volume divided by the sample volume, and beyond the percolation threshold ϕ

_{c}the composite conductivity increases drastically. By compressing the composite, the electric conductivity then increases [4]. The largest electrical conductivity increase is found in a small compression range window: close to the percolation threshold.

^{2}surface, the device can detect the point of pressure application; hence, it can mimic the tactile sense of the skin. Deformation up to 50% was recorded and successfully localized. The equivalent force range detected was up to 4.5 N with a resolution of 0.29 N.

## 2. Materials and Methods

#### 2.1. Magnetic Foam Composite Preparation

_{m}= m

_{Fe}/m

_{tot}= 70%; m

_{Fe}and m

_{tot}are the particles’ mass and the total mass, respectively. Particles were first mixed with the solution and hand-stirred for 5 min; then the curing agent was added. The mixture was molded as a membrane with a controlled thickness, a 3.1 mm thick sample. The curing time was about 20 min at room temperature. Once cured, the membrane was cut into 20 × 20 mm

^{2}. Figure 2 presents the internal pore structure of the obtained sample. The remaining parts were used for characterizing the mechanical and magnetic properties.

#### 2.2. Sensing Device

^{2}, as seen in Figure 3a. Taxtel size is 20/3~6.7 mm, which is smaller than 7.5 mm in [6] or 30 mm [7]. The array was glued onto a PCB to fix this device to connectors. Each coil was then labeled L1 to L9 for tracking the deformation by the measurement of the change of inductance (Figure 3b). Finally, the foam was placed above the array (Figure 3c).

#### 2.3. Mechanical Testing

_{0}= 3.55 mm

^{2}) as [8,19]:

_{0}= 3.1 mm) as [8,19]:

#### 2.4. Magnetic Characterization

## 3. Results

#### 3.1. FTIR

#### 3.2. Mechanical Test

#### 3.3. Magnetization Loop

_{v}. The filling factor is defined as the volume represented by all the CIPs (n*V

_{p}, with n the particle number with individual volume V

_{p}) inside the sample volume (V

_{tot}) as:

_{v}= 1.35%. Sample magnetization was also recorded at a different level of compression ε defined according to Equation (2).

_{r}is then obtained from the slope dM/dH around H = 0, which traditionally refers to the magnetic susceptibility χ of the material. The relationship between susceptibility and relative permeability is µ

_{r}= χ + 1. The different relative permeabilities for different compression levels are plotted in Figure 7.

_{v}= 1.35%. It can be observed in Figure 7 that the relative permeability is increasing with the compression ε. The change is, however, relatively small; the initial permeability was µ

_{r}= 1.06 and the largest permeability was µ

_{r}= 1.11 for deformation of −50%, and the increase in permeability was Δµ

_{r}= 0.05. This kind of increase in permeability with compression was also observed by using a permeability meter [15] and similar changes of values were measured. For an isotropic composite with this low filling factor, the Maxwell Garnett approximation [24], is:

_{r}(ϕ

_{v}, ε) with deformation, assuming a large compressibility of the matrix, can be expressed by [15]:

_{r}(ϕ

_{v}) = 1.04 and Equation (5), assuming a compression of ε = −0.5, provides Δµ

_{r}(ϕ

_{v}, ε) = 0.04. These values are relatively close to the values in Figure 7.

#### 3.4. Sensing Array

_{i}(ε = 0), where i = 1–9, were slightly different for each coil; this can arise from connections but it is also important to point out that these were all within the measurement uncertainty. More important are the trends of these curves: some have a positive slope, whereas others exhibit a negative slope.

## 4. Discussion

_{1}(ε ≠ 0) > L

_{1}(ε = 0). This curve behaved as a line in a first approximation, and a linear coefficient α

_{i}can be defined as:

_{1}was negative. In Figure 7, the compression was inducing an increase in magnetic permeability. The inductance of a coil is proportional to the magnetic flux detected, so it is proportional to the magnetic permeability of the nearby magnetic layer. The composite increased its permeability as it was compressed, so the inductance coil placed below the compressed magnetic layer increased as well. This is coherent with the negative coefficient α

_{1}. The negative value of coefficient α

_{i}implies a compression.

_{1}, α

_{2}, α

_{3}, and α

_{4}have amplitudes as |α

_{1}| >|α

_{2}| ~ |α

_{4}| >|α

_{5}|. When looking at the disposition of the coils, coil L1 was placed directly under the applied compression, coils L2 and L4 were equidistant to L1, and coil L5 was located a little farther. As the deformation was applied at point A, it is natural that the deformation was the largest at point A and decreased its amplitude with an increasing distance. This means that the α

_{i}were actually mapping the local deformation amplitude.

_{i}coefficients was then interpolated into an α(x,y) map, and this α(x,y) map is shown in Figure 9d.

_{r}= 1, so the coil detected a lower effective permeability in its neighborhood. This gap then increased as the deformation grew stronger, making the measured coefficient α(x,y) > 0 on this area. In this presented experiment, the positive α was not necessarily because of the dilatation of the material. This issue can be solved by gluing the magnetic layer onto the coil surface. This was not performed in these experiments because other samples might be tested in future experiments.

^{2}/4), the local force can be calculated. The inductance behavior of L1 with the deformation, extracted from Figure 8, is then plotted as a function of the local force in Figure 11.

## 5. Conclusions

^{3}layer. As it experienced uniaxial compression, its magnetic permeabilities were increased, especially the permeability. This change in permeability was successfully detected by a coil array. The stress versus strain curve in compression was recorded, and Young’s modulus was measured. The applied deformation could be converted into applied force. A deformation was locally applied to the magnetic layer. The amplitude of deformation was recorded up to 50% in compression. A map of the inductance change was constructed, giving information on the surface affected by an applied deformation or force.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 2.**Sample cross-section (

**a**), threshold processed picture (

**b**), picture analysis selection (yellow square), color inversion of the selected area (

**c**), and the result of the picture analysis with the number tag corresponding to the black area on the picture (

**d**).

**Figure 3.**Coils array device fabrication: (

**a**) 3 × 3 coils, (

**b**) array glued on the PCB, and (

**c**) with a 20 × 20 mm

^{2}sample. Here the inductance L9 is connected to the impedance meter for measurement.

**Figure 6.**Magnetization versus applied field for different compression. Bold line and dotted lines highlight the magnetic permeability and saturation of the non-deformed composite, respectively.

**Figure 9.**Applied compressive displacement localization (

**a**–

**c**) and the resulting α(x,y) map (

**d**–

**f)**: blue and green refer to negative coefficient values (compression), whereas yellow and red refer to positive coefficient values.

**Figure 10.**Application of the deformation for the case presented in Figure 7; (

**a**) before the application of the deformation and (

**b**) after the application of the deformation.

**Figure 11.**Inductance versus applied force on L1. Broken line is a linear approximation with the parameters shown in the inset.

Wavenumber (cm^{−1}) | Vibration Group | Vibration Type |
---|---|---|

3440 | Free N-H | Stretching ^{1,2} |

3330 | H-bonded N-H | Stretching ^{1,2} |

2890 | CH_{2} | Asymmetry stretching ^{2} |

2850 | CH_{2} | Symmetry stretching ^{2} |

1709 | Free C=O | Stretching ^{1} |

1728 | H-bonded C=O | Stretching ^{1} |

1597 | Benzene ring | Framework vibration ^{2} |

1537 | N-H | Bending ^{2} |

1412 | CH_{2} | Bending ^{2,3} |

1373 | CN | Stretching ^{3} |

1225 | CO | Stretching ^{2} |

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**MDPI and ACS Style**

Diguet, G.; Froemel, J.; Muroyama, M.; Ohtaka, K.
Tactile Sensing Using Magnetic Foam. *Polymers* **2022**, *14*, 834.
https://doi.org/10.3390/polym14040834

**AMA Style**

Diguet G, Froemel J, Muroyama M, Ohtaka K.
Tactile Sensing Using Magnetic Foam. *Polymers*. 2022; 14(4):834.
https://doi.org/10.3390/polym14040834

**Chicago/Turabian Style**

Diguet, Gildas, Joerg Froemel, Masanori Muroyama, and Koichi Ohtaka.
2022. "Tactile Sensing Using Magnetic Foam" *Polymers* 14, no. 4: 834.
https://doi.org/10.3390/polym14040834