# Static Tactile Sensing for a Robotic Electronic Skin via an Electromechanical Impedance-Based Approach

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## Abstract

**:**

## 1. Introduction

## 2. Problem Statement

## 3. Method of Approach

## 4. Experiment and Results

#### 4.1. Smart Skin Sample Development

#### 4.2. Test Procedure

#### 4.3. Results of Impedance Response to Static Pressure Loads

_{ℎ}(𝜔

_{𝑖}) denotes the baseline impedance; 𝑍

_{u}(𝜔

_{𝑖}) is added weight impedance; and 𝜔

_{𝑖}denotes frequency interval.

## 5. Finite Element Simulation Study

#### 5.1. Hyperelastic Material Property of Silicone Rubber

#### 5.2. Dynamic Compressive Behavior of Silicone Rubber Material

^{6}Hz. Again, the objective of this simulation study was to obtain qualitative insights into the impedance behavior of the embedded PZT sensor. Therefore, by amplifying seven times, the stiffness was good enough to capture the change of the impedance behavior.

#### 5.3. A Direct Steady-State Dynamic Analysis for Simulating Impedance Behavior

#### 5.4. The Effect of the Silicone Rubber Stiffness to the Impedance Response

## 6. Discussions Based on the Theoretical Model

#### 6.1. Analytical Model: Dynamic Interaction between the PZT Sensor and Structure

_{31}is the piezoelectric strain coefficient; ε

_{33}is the dielectric permittivity; and Y

^{E}is the Young’s Modulus of the PZT sensor. The structural mechanical impedance Z

_{S}is shown in Equation (8), where c is the damping coefficient and the mechanical impedance of the PZT sensor Za is represented in Equation (9)

#### 6.2. The Effect of Stress on PZT Material Properties to Impedance Response

_{3}, with the increase of T

_{3}from 0 MPa to 75 MPa, the piezoelectric strain coefficient d

_{31}increased proportionally by around 50%, and the dielectric permittivity ε

_{33}also increased almost linearly by 60%. However, considering that the compressive stress level in our study is in the order of 10

^{−2}MPa, the stress effect to the coefficient of d

_{31}and ε

_{33}is negligible. In addition, in both studies of Zhang et al. [24] and Safour et al. [15], the Young’s Modulus Y

^{E}has even less change under the uniaxial compressive stress compared with d

_{31}and ε

_{33}, so that its change can also be ignorable. Therefore, in this study, the effect of stress on PZT material properties to impedance response is insignificant.

#### 6.3. The Effect of Stress on PZT Geometry Change to Impedance Response

^{−11}m. For the width and length direction, the maximum displacements are 1.621 × 10

^{−11}m and 1.885 × 10

^{−11}m, respectively. By plugging these changes into Equation (7), we found that the overall changes to the impedance response are at the level of 0.0002%. This change is essentially extremely small compared with the experiment results, which have a change of 5% in the amplitude decrease. Therefore, in this study, the effect of stress on PZT geometry changes to impedance response can be neglected.

## 7. Conclusions and Future Work

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 2.**The framework of using the EMI-based method to detect static pressure loads for application on smart skin with an embedded PZT sensor.

**Figure 3.**(

**a**) Schematic of smart skin sample with a PZT sensor embedded in soft silicone; (

**b**) the real sample with wiring and connectors.

**Figure 5.**The electromechanical impedance behavior from the PZT sensor at zero static pressure load.

**Figure 6.**(

**a**) Real part of the impedance response under different static pressure load; (

**b**) maximum impedance amplitude change at each static load with respect to the value at 0.5 N.

**Figure 7.**(

**a**) Real part of the impedance response under different static pressure loads, including baseline data; (

**b**) tactile index at different static loads.

**Figure 9.**Nonlinear stress-strain relationship for Smooth-On Ecoflex 00-30 under static compressive load.

**Figure 10.**Simulation result of the nodal electric charge at one node at the top surface of the PZT sensor.

**Figure 11.**Comparison of the experiment and simulation results on the impedance behavior of a PZT sensor embedded in the silicone rubber: (

**a**) real part; (

**b**) imaginary part.

**Figure 12.**(

**a**) Simulation results of the static normal pressure load effect to the smart skin sample with a PZT sensor embedded in the silicone rubber; (

**b**) simulated maximum amplitude change at each static load, with respect to the value at 0.5 N.

**Figure 14.**Displacement distribution of a PZT sensor in thickness direction under a static pressure load of 6.29 kPa. (U and U3 are displacement in m.).

Density | Young’s Modulus E_{11} | Young’s Modulus E_{33} | Relative Dielectric Constant K_{T} | Piezo Charge Constant d_{33} | Piezo Voltage Constant g_{33} |
---|---|---|---|---|---|

7.6 g/cm^{3} | 63 GPa | 54 GPa | 1700 | 400 pC/N | 24.8 mV-m/N |

Property | Unit | Piezo PZT-5A |
---|---|---|

E_{11} | GPa | 60.97 |

E_{22} | GPa | 60.97 |

E_{33} | GPa | 53.19 |

G_{23} | GPa | 21.05 |

G_{31} | GPa | 21.05 |

G_{12} | GPa | 22.57 |

v_{23} | 0.4402 | |

v_{13} | 0.4402 | |

v_{12} | 0.3500 | |

ρ | kg/m^{3} | 7750 |

Static Load (N) | Stress (kPa) | Strain | Stiffness (kPa) |
---|---|---|---|

0.5 | 1.2875 | 0.01563 | 61.757 |

1.0 | 2.5375 | 0.03498 | 67.473 |

1.5 | 3.7875 | 0.05281 | 72.740 |

2.0 | 5.0375 | 0.06943 | 77.650 |

2.5 | 6.2875 | 0.08506 | 82.267 |

Static Load (N) | Dynamic Stiffness (kPa) |
---|---|

0.5 | 431.27 |

1.0 | 472.25 |

1.5 | 509.12 |

2.0 | 543.46 |

2.5 | 575.78 |

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**MDPI and ACS Style**

Liu, C.; Zhuang, Y.; Nasrollahi, A.; Lu, L.; Haider, M.F.; Chang, F.-K.
Static Tactile Sensing for a Robotic Electronic Skin via an Electromechanical Impedance-Based Approach. *Sensors* **2020**, *20*, 2830.
https://doi.org/10.3390/s20102830

**AMA Style**

Liu C, Zhuang Y, Nasrollahi A, Lu L, Haider MF, Chang F-K.
Static Tactile Sensing for a Robotic Electronic Skin via an Electromechanical Impedance-Based Approach. *Sensors*. 2020; 20(10):2830.
https://doi.org/10.3390/s20102830

**Chicago/Turabian Style**

Liu, Cheng, Yitao Zhuang, Amir Nasrollahi, Lingling Lu, Mohammad Faisal Haider, and Fu-Kuo Chang.
2020. "Static Tactile Sensing for a Robotic Electronic Skin via an Electromechanical Impedance-Based Approach" *Sensors* 20, no. 10: 2830.
https://doi.org/10.3390/s20102830