# A Magnet Splicing Method for Constructing a Three-Dimensional Self-Decoupled Magnetic Tactile Sensor

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## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Structure and Mechanism

_{0}is the maximum magnitude of each component.

_{x}, B

_{y}, B

_{z}):

_{x}, R

_{y}, and S

_{z}) that are linearly related to the displacements to calculate the triaxial displacement of the magnetic film, respectively:

_{x}, γ

_{y}, ε, G, E, and h are the shear strain in the x direction, the shear strain in the y direction, normal strain, shear modulus, elastic modulus, and thickness of the elastomer substrate, respectively. For the isotropic silicone elastomer, $G=E/(2\left(1+v\right))$, where v is the Poisson’s ratio of the material. According to Equation (14), and by introducing six compensation coefficients, we can obtain

_{1}, a

_{2,}and a

_{3}are compensation coefficients for elastic modulus and shear modulus, respectively, because the shear modulus and elastic modulus are affected by the combination of magnetic films, silicon elastomer, and adhesive. Meanwhile, there may be manufacturing defects in them. b

_{1}, b

_{2}, and b

_{3}are used to compensate for the calibration deviation under different installation conditions. These compensation coefficients can be determined by force–displacement calibration.

#### 2.2. Materials and Fabrication

_{m}) to obtain the magnetization direction along the film’s plane, ensuring they had exactly the same magnetization strength and direction.

## 3. Results and Discussion

#### 3.1. Simulation and Verification of the Spliced Magnetic Film

_{x}is independent of the displacements in the y- and z-directions but only related to the displacement in the x-direction. Similar conclusions can be drawn for the decoupling parameters R

_{y}(Figure 7b) and S

_{z}(Figure 7c), which show that the spliced magnetic film has great decoupling performance.

#### 3.2. Decoupling Performance in Experiment

_{x}, R

_{y,}and S

_{z}) in 3D space can be calculated in the practical experiment, as shown in Figure 8.

_{x}is independently related to the displacement in the x-direction; that is, it changes with the displacement in the x-direction but remains constant when the displacement in the y- or z-direction changes (Figure 8a). ∆R

_{y}(Figure 8b) and ∆S

_{z}(Figure 8c) are also independently related to the displacement in the y-direction and the displacement in the z-direction, respectively, and remain constant as the displacements in the other two directions vary. For isotropic materials, the stresses in the three directions are independent of each other, so the displacement in any single direction can be directly linked to the force in that direction. Therefore, the relationships between the decoupling parameters and the external forces applied to the tactile sensor can be obtained directly from their relationships to the 3D displacements, which are much easier to clearly present. Moreover, in the process of splicing, part of the magnetic films is prone to position deviation, resulting in errors in the spatial distribution of decoupling parameters. The average root-mean-square errors (RMSEs) of ∆R

_{x}, ∆R

_{y}, and ∆S

_{z}are 0.058, 0.066, and 0.044, respectively, indicating that the magnetic tactile sensor with the spliced film has good 3D decoupling performance over the shown operating range. In addition, the displacement resolution of the sensor can be obtained here: 0.015 mm in both shear and normal directions, which is mainly limited by the resolution of the 3D Hall sensor to perceive the magnetic flux density. Therefore, the improved performance of 3D Hall sensors will lead to enhanced force sensing performance of our sensors.

#### 3.3. Force Sensing Experiment of the Tactile Sensor

_{y}(or S

_{z}) changed, while the other decoupling parameters remained constant. The readings of the forcemeters could be recorded to obtain the perception curves of the sensor to shear forces (Figure 9d) and normal forces (Figure 9h). Combined with the distribution of decoupling parameters in 3D space and the force perception curves of the tactile sensor, any force with an arbitrary direction and magnitude within the working range could be accurately sensed.

## 4. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 3.**Diagram of the 3D configuration of magnetic flux density vectors below the magnetic film with the ideal centripetal magnetization. (

**a**) Magnetic flux density vectors between the Hall sensor and the magnetic film (the arrows’ lengths are calculated logarithmically). (

**b**) Top view of the magnetic flux density vector distribution (the arrows’ lengths are calculated logarithmically). (

**c**) Side view of the magnetic flux density vector distribution (the arrows’ lengths are calculated logarithmically).

**Figure 4.**Preparation method of magnetic films. (

**a**) Scrape the magnetic paste into the mold through a scraper blade. (

**b**) Cure the formed magnetic paste at 120 °C. (

**c**) Magnetize the cured films in a magnetizing coil.

**Figure 6.**Comparison of the magnetic flux density distribution obtained from the simulation of the splicing model and the calculation of the ideal model. (

**a**) B

_{x}, (

**b**) B

_{y}, and (

**c**) B

_{z}obtained by the simulation of the splicing model. (

**d**) B

_{x}, (

**e**) B

_{y}, and (

**f**) B

_{z}obtained by the calculation of the ideal model.

**Figure 7.**The decoupling parameter distribution obtained by the simulation of the splicing model. (

**a**) The simulation distribution of R

_{x}under the splicing model. (

**b**) The simulation distribution of R

_{y}under the splicing model. (

**c**) The simulation distribution of S

_{z}under the splicing model.

**Figure 8.**Spatial distribution of decoupling parameters. (

**a**) Decoupling parameter ∆R

_{x}under the triaxial displacement of the spliced magnetic film. (

**b**) Decoupling parameter ∆R

_{y}under the triaxial displacement of the spliced magnetic film. (

**c**) Decoupling parameter ∆S

_{z}under the triaxial displacement of the spliced magnetic film.

**Figure 9.**Force sensing experiment of the tactile sensor. (

**a**) Illustration of applying shear forces. (

**b**) Three-dimensional magnetic flux density signals during the application of shear forces. (

**c**) Changes in decoupling parameters during the application of shear forces. (

**d**) Relationships between the shear force and decoupling parameter ∆R

_{y}(or ∆R

_{x}) of the sensor. (

**e**) Illustration of applying normal forces. (

**f**) Three-dimensional magnetic flux density signals during the application of normal forces. (

**g**) Changes in decoupling parameters during the application of normal forces. (

**h**) Relationships between the normal force and decoupling parameter ∆S

_{z}of the sensor.

**Table 1.**Parameters of magnetism for magnetic films and the range of study in simulation and calculation.

Parameter | Splicing Model | Ideal Model |
---|---|---|

Remanence (${m}_{0}$) | 0.12 (T) | 0.12 (T) |

Wavelength ($\lambda $) | 10 (mm) | 10 (mm) |

Film size | 20 × 20 (mm) | Infinite |

Thickness (d) | 1 (mm) | 1 (mm) |

Range of study | x: −2~2, y: −2~2, z: −5~−3 (mm) | x: −2~2, y: −2~2, z: −5~−3 (mm) |

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## Share and Cite

**MDPI and ACS Style**

Dai, H.; Wu, Z.; Meng, C.; Zhang, C.; Zhao, P.
A Magnet Splicing Method for Constructing a Three-Dimensional Self-Decoupled Magnetic Tactile Sensor. *Magnetochemistry* **2024**, *10*, 6.
https://doi.org/10.3390/magnetochemistry10010006

**AMA Style**

Dai H, Wu Z, Meng C, Zhang C, Zhao P.
A Magnet Splicing Method for Constructing a Three-Dimensional Self-Decoupled Magnetic Tactile Sensor. *Magnetochemistry*. 2024; 10(1):6.
https://doi.org/10.3390/magnetochemistry10010006

**Chicago/Turabian Style**

Dai, Huangzhe, Zheyan Wu, Chenxian Meng, Chengqian Zhang, and Peng Zhao.
2024. "A Magnet Splicing Method for Constructing a Three-Dimensional Self-Decoupled Magnetic Tactile Sensor" *Magnetochemistry* 10, no. 1: 6.
https://doi.org/10.3390/magnetochemistry10010006