# Voltage-Induced Friction with Application to Electrovibration

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Theory

#### 2.1. Contact Mechanics Approach

#### 2.2. Electrostatic Approach and Coupling to Contact Mechanics

## 3. Comparison with Experimental Data

#### 3.1. Friction Force as a Function of Time during Sinusoidal Excitation

#### 3.2. Friction Force as a Function of Externally Applied Normal Force

#### 3.3. Electrostatic Force as a Function of Applied Voltage Amplitude

## 4. Summary and Discussion

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**Schematic representation of the electromechanical frictional contact between the index fingertip and touchscreen.

**Figure 2.**Qualitative representation of the adhesive tangential contact between an elastic sphere and a rigid plane; the distribution of the elastic normal stresses at the surface according to Maugis’ theory is included.

**Figure 3.**Normalized representation of the elastic normal stresses and normal surface displacements in a contact between a rigid parabolic indenter and an elastic half-space: (

**a**) Non-adhesive contact according to Hertz; (

**b**) Adhesive contact according to Johnson, Kendall and Roberts.

**Figure 4.**Parallel-plate capacitor for modeling the contact between the fingertip and touchscreen from an electrostatic point of view.

**Figure 5.**External applied force (green) and friction force under both conditions: electrovibration is turned on (red) and turned off (blue).

**Figure 6.**Friction force as a function of externally applied force under both conditions: electrostatic forces due to an applied high-frequency square wave voltage are turned off (green) and on (orange).

**Figure 7.**Percentage increase of the apparent contact area as a function of the applied voltage amplitude for three different externally applied normal forces: 0.1 N, 0.5 N and 2.0 N.

Symbol | Parameter Name | Value and Unit |
---|---|---|

$\mu $ | Friction coefficient | 0.5 (0.3) |

$R$ | Radius of fingertip | 1 cm |

${E}^{*}$ | Equivalent effective elastic modulus | 40 kPa |

${\epsilon}_{r,sc}$ | Relative permittivity of stratum corneum | $1650$ |

${\epsilon}_{r,i}$ | Relative permittivity of insulating layer | $3.35$ |

${\epsilon}_{0}$ | Permittivity of free space | $8.854\xb7{10}^{-12}\frac{As}{Vm}$ |

${h}_{sc}$ | Thickness of stratum corneum | 300 µm |

${h}_{i}$ | Thickness of insulating layer | 1 µm |

${h}_{L}$ | Thickness of equivalent air gap | 5 µm |

${F}_{\mathrm{ext}}$ | External applied normal force | 0.5 N |

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**MDPI and ACS Style**

Heß, M.; Popov, V.L. Voltage-Induced Friction with Application to Electrovibration. *Lubricants* **2019**, *7*, 102.
https://doi.org/10.3390/lubricants7120102

**AMA Style**

Heß M, Popov VL. Voltage-Induced Friction with Application to Electrovibration. *Lubricants*. 2019; 7(12):102.
https://doi.org/10.3390/lubricants7120102

**Chicago/Turabian Style**

Heß, Markus, and Valentin L. Popov. 2019. "Voltage-Induced Friction with Application to Electrovibration" *Lubricants* 7, no. 12: 102.
https://doi.org/10.3390/lubricants7120102