# Analysis of the Electrical Impedance of Graphite and Silver Graphite Carbon Brushes for Use in the Impedance Measurement of Sensory Utilizable Machine Elements

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## Abstract

**:**

## 1. Introduction

- How is the sensory function supplied with energy?
- How is the sensor signal transmitted out of the rotating system to the evaluation unit?

## 2. Materials and Methods

## 3. Results

#### 3.1. Overview of Experimental Results

#### 3.2. Identification and Evaluation of Significant Effects on the Electrical Impedance

#### 3.2.1. Effect and Significance of Material

#### 3.2.2. Effect and Significance of Contacting Position

#### 3.2.3. Effect and Significance of Rotational Speed

#### 3.3. Influence of Runtime and Carrier Frequency on the Electrical Impedance

## 4. Discussion

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## Appendix A

Sum of Squares | DF | Mean Squares | F | p-Value | |
---|---|---|---|---|---|

Material | 92,878 | 1 | 92,878 | 0.13629 | 0.71684 |

Position | 4.9085 × 10^{6} | 1 | 4.9085 × 10^{6} | 7.2027 | 0.016304 |

Speed | 76,586 | 1 | 76,586 | 0.11238 | 0.74181 |

Material and Position | 2.4528 × 10^{5} | 1 | 2.4528 × 10^{5} | 0.35992 | 0.55695 |

Material and Speed | 3.0215 × 10^{6} | 1 | 3.0215 × 10^{6} | 4.4337 | 0.051384 |

Position and Speed | 9760 | 1 | 9760 | 0.014322 | 0.90623 |

Material and Position and Speed | 2.4408 × 10^{6} | 1 | 2.4408 × 10^{6} | 3.5816 | 0.07666 |

Error | 1.0904 × 10^{7} | 16 | 6.8149 × 10^{5} | ||

Total | 2.1699 × 10^{7} | 23 |

Sum of Squares | DF | Mean Squares | F | p-Value | |
---|---|---|---|---|---|

Material | 1.0989 | 1 | 1.0989 | 8.9809 | 0.008536 |

Position | 5.0624 | 1 | 5.0624 | 41.372 | 8.2897 × 10^{−6} |

Speed | 0.22537 | 1 | 0.22537 | 1.8418 | 0.19358 |

Material and Position | 1.2338 | 1 | 1.2338 | 10.083 | 0.0058736 |

Material and Speed | 0.0051747 | 1 | 0.0051747 | 0.04229 | 0.83966 |

Position and Speed | 0.6561 | 1 | 0.6561 | 5.3619 | 0.034181 |

Material and Position and Speed | 0.14021 | 1 | 0.14021 | 1.1458 | 0.30031 |

Error | 1.9578 | 16 | 0.12236 | ||

Total | 10.38 | 23 |

Sum of Squares | DF | Mean Squares | F | p-Value | |
---|---|---|---|---|---|

Material | 3.3866 × 10^{5} | 1 | 3.3866 × 10^{5} | 5.5927 | 0.031008 |

Position | 26062 | 1 | 26062 | 0.43039 | 0.52112 |

Speed | 1.1842 × 10^{5} | 1 | 1.1842 × 10^{5} | 1.9557 | 0.18106 |

Material and Position | 28,688 | 1 | 28,688 | 0.47376 | 0.50112 |

Material and Speed | 1.7643 × 10^{5} | 1 | 1.7643 × 10^{5} | 2.9136 | 0.10716 |

Position and Speed | 28,798 | 1 | 28,798 | 0.47558 | 0.50031 |

Material and Position and Speed | 60,409 | 1 | 60,409 | 0.99762 | 0.33275 |

Error | 9.6885 × 10^{5} | 16 | 60,553 | ||

Total | 1.7463 × 10^{6} | 23 |

Sum of Squares | DF | Mean Squares | F | p-Value | |
---|---|---|---|---|---|

Material | 19,636 | 1 | 19,636 | 0.034968 | 0.85401 |

Position | 5.1165 × 10^{6} | 1 | 5.1165 × 10^{6} | 9.1115 | 0.0081578 |

Speed | 567.66 | 1 | 567.66 | 0.0010109 | 0.97503 |

Material and Position | 1.4106 × 10^{6} | 1 | 1.4106 × 10^{6} | 0.25121 | 0.62305 |

Material and Speed | 2.3054 × 10^{6} | 1 | 2.3054 × 10^{6} | 4.1055 | 0.059752 |

Position and Speed | 633.49 | 1 | 633.49 | 0.0011281 | 0.97362 |

Material and Position and Speed | 2.1593 × 10^{6} | 1 | 2.1593 × 10^{6} | 3.8452 | 0.067534 |

Error | 8.9846 × 10^{6} | 16 | 5.6154 × 10^{5} | ||

Total | 1.8728 × 10^{7} | 23 |

Sum of Squares | DF | Mean Squares | F | p-Value | |
---|---|---|---|---|---|

Material | 4.5254 × 10^{7} | 1 | 4.5254 × 10^{7} | 0.073189 | 0.79021 |

Position | 4.2856 × 10^{9} | 1 | 4.2856 × 10^{9} | 6.9311 | 0.018096 |

Speed | 2.3858 × 10^{8} | 1 | 2.3858 × 10^{8} | 0.38585 | 0.54324 |

Material and Position | 3.4512 × 10^{7} | 1 | 3.4512 × 10^{7} | 0.055816 | 0.081623 |

Material and Speed | 2.6144 × 10^{9} | 1 | 2.6144 × 10^{9} | 4.2282 | 0.05645 |

Position and Speed | 2.3297 × 10^{8} | 1 | 2.3297 × 10^{8} | 0.37678 | 0.54796 |

Material and Position and Speed | 2.5973 × 10^{9} | 1 | 2.5973 × 10^{9} | 4.2005 | 0.057175 |

Error | 9.8931 × 10^{9} | 16 | 6.1832 × 10^{8} | ||

Total | 1.9942 × 10^{10} | 23 |

Sum of Squares | DF | Mean Squares | F | p-Value | |
---|---|---|---|---|---|

Material | 3.9386 × 10^{−11} | 1 | 3.9386 × 10^{−11} | 40.281 | 9.6967 × 10^{−6} |

Position | 3.7262 × 10^{−11} | 1 | 3.7262 × 10^{−11} | 38.108 | 1.3379 × 10^{−5} |

Speed | 1.2844 × 10^{−12} | 1 | 1.2844 × 10^{−12} | 1.3136 | 0.2686 |

Material and Position | 3.7566 × 10^{−11} | 1 | 3.7566 × 10^{−11} | 38.42 | 1.2766 × 10^{−5} |

Material and Speed | 1.2531 × 10^{−12} | 1 | 1.2531 × 10^{−12} | 1.2816 | 0.27429 |

Position and Speed | 1.5714 × 10^{−12} | 1 | 1.5714 × 10^{−12} | 1.6071 | 0.22304 |

Material and Position and Speed | 1.6058 × 10^{−12} | 1 | 1.6058 × 10^{−12} | 1.6422 | 0.21828 |

Error | 1.5645 × 10^{−11} | 16 | 9.7778 × 10^{−13} | ||

Total | 1.3557 × 10^{−10} | 23 |

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**Figure 1.**Measurement path from contact point 1 to contact point 2 for the sensory utilization of a rolling element bearing via impedance measurement. The impedance of the sliding contact ${Z}_{SC}$ is connected in series with the impedance of the rolling element bearing ${Z}_{DUT}$.

**Figure 2.**Experimental setup: (1) Steel shaft; (2) Reference contact in axial position (silver graphite); (3.1) Axial contact; (3.2) Radial contact; (4) Insulated main shaft; (5) Electric motor; (6) Pillow block bearings; (7) Flange connection; (8) Connection of reference contact to ground (yellow cable); (9) Connection of axial or radial contact (red cable).

**Figure 3.**Impedance data over 2 s for silver graphite carbon brushes at a constant rotational speed of 500 rpm and 100 kHz carrier frequency for three individual measurement runs: (

**a**) the axial contact shows a smaller but noisier impedance; (

**b**) the radial contact shows a larger but less noisy impedance.

**Figure 4.**Main effect diagrams of the factor material for different features. Effects significant according to ANOVA (see Table 3) are outlined: (

**a**) No significant effect on $\left|Z\right|$; (

**b**) Significant effect on $Re\left(Z\right)$, silver graphite decreases real part; (

**c**) No significant effect on $R$; (

**d**) Significant effect on $\phi \left(Z\right)$, silver graphite increases phase to 0°; (

**e**) No significant effect on $Im\left(Z\right)$; (

**f**) Significant effect on $C$, silver graphite increases capacitance.

**Figure 5.**Main effect diagrams of the factor position for different features. Effects significant according to ANOVA (see Table 4) are outlined: (

**a**) Significant effect on $\left|Z\right|$, radial contact increases absolute value; (

**b**) No significant effect on $Re\left(Z\right)$; (

**c**) Significant effect on $R$, radial contact increases resistance; (

**d**) Significant effect on $\phi \left(Z\right)$, radial contact decreases phase; (

**e**) Significant effect on $Im\left(Z\right)$, radial contact decreases imaginary part; (

**f**) Significant effect on $C$, radial contact decreases capacitance.

**Figure 6.**Main effect diagrams of the factor rotational speed for different features: (

**a**) No significant effect on $\left|Z\right|$; (

**b**) No significant effect on $Re\left(Z\right)$; (

**c**) No significant effect on $R$; (

**d**) No significant effect on $\phi \left(Z\right)$; (

**e**) No significant effect on $Im\left(Z\right)$; (

**f**) No significant effect on $C$.

**Figure 7.**Periodical frequency sweeps (1 kHz to 1 MHz) for a silver graphite carbon brush at 500 rpm in axial contact over a period of 120 min: (

**a**) Frequency behavior of $\left|Z\right|$; (

**b**) Frequency behavior of $\phi \left(Z\right)$.

**Figure 8.**(

**a**) Mean of $\left|Z\right|$ for the entire frequency sweep (1 kHz to 1 MHz) over a period of 120 min; (

**b**) Mean of $\phi \left(Z\right)$ for the entire frequency sweep (1 kHz to 1 MHz) over a period of 120 min.

Factor | $\mathbf{Level}-$ | $\mathbf{Level}+$ |
---|---|---|

Material | Graphite ^{1} | Silver graphite ^{1} |

Rotational speed | 500 rpm | 2000 rpm |

Sliding speed for ${r}_{a}=10.5\mathrm{m}\mathrm{m}$ | 0.55 m/s | 2.2 m/s |

Sliding speed for ${r}_{r}=15\mathrm{m}\mathrm{m}$ | 0.79 m/s | 3.1 m/s |

Position | Axial | Radial |

^{1}Exact material mixture unknown, as it was not specified by manufacturer.

**Table 2.**Two-stage full factorial experimental design with blocks for axial and radial contacting and randomization inside both blocks.

Material | Rotational Speed | Position | Repetition | Test Number (Randomized) |
---|---|---|---|---|

Silver graphite | 500 rpm | Axial | 1 | 5 |

Silver graphite | 2000 rpm | Axial | 1 | 7 |

Graphite | 500 rpm | Axial | 1 | 10 |

Graphite | 2000 rpm | Axial | 1 | 2 |

Silver graphite | 500 rpm | Axial | 2 | 3 |

Silver graphite | 2000 rpm | Axial | 2 | 8 |

Graphite | 500 rpm | Axial | 2 | 1 |

Graphite | 2000 rpm | Axial | 2 | 9 |

Silver graphite | 500 rpm | Axial | 3 | 6 |

Silver graphite | 2000 rpm | Axial | 3 | 4 |

Graphite | 500 rpm | Axial | 3 | 12 |

Graphite | 2000 rpm | Axial | 3 | 11 |

Silver graphite | 500 rpm | Radial | 1 | 24 |

Silver graphite | 2000 rpm | Radial | 1 | 19 |

Graphite | 500 rpm | Radial | 1 | 14 |

Graphite | 2000 rpm | Radial | 1 | 21 |

Silver graphite | 500 rpm | Radial | 2 | 20 |

Silver graphite | 2000 rpm | Radial | 2 | 22 |

Graphite | 500 rpm | Radial | 2 | 13 |

Graphite | 2000 rpm | Radial | 2 | 23 |

Silver graphite | 500 rpm | Radial | 3 | 18 |

Silver graphite | 2000 rpm | Radial | 3 | 15 |

Graphite | 500 rpm | Radial | 3 | 16 |

Graphite | 2000 rpm | Radial | 3 | 17 |

Feature | Symbol | p-Value | Significance ^{2} |
---|---|---|---|

Absolute value | $\left|Z\right|$ | 0.71684 | |

Phase | $\phi \left(Z\right)$ | 0.00854 | X |

Real part | $Re\left(Z\right)$ | 0.03101 | X |

Imaginary part | $Im\left(Z\right)$ | 0.85401 | |

Resistance | $R$ | 0.79021 | |

Capacitance | $C$ | ~0.00001 | X |

^{2}Significant when p-value < 0.05.

Feature | Symbol | p-Value | Significance ^{3} |
---|---|---|---|

Absolute value | $\left|Z\right|$ | 0.01630 | X |

Phase | $\phi \left(Z\right)$ | ~0.00001 | X |

Real part | $Re\left(Z\right)$ | 0.52112 | |

Imaginary part | $Im\left(Z\right)$ | 0.00816 | X |

Resistance | $R$ | 0.01810 | X |

Capacitance | $C$ | ~0.00001 | X |

^{3}Significant when p-value < 0.05.

Feature | Symbol | p-Value | Significance ^{4} |
---|---|---|---|

Absolute value | $\left|Z\right|$ | 0.74181 | |

Phase | $\phi \left(Z\right)$ | 0.52112 | |

Real part | $Re\left(Z\right)$ | 0.18106 | |

Imaginary part | $Im\left(Z\right)$ | 0.97503 | |

Resistance | $R$ | 0.54324 | |

Capacitance | $C$ | 0.26860 |

^{4}Significant when p-value < 0.05.

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## Share and Cite

**MDPI and ACS Style**

Hausmann, M.; Schirra, T.; Kirchner, E.
Analysis of the Electrical Impedance of Graphite and Silver Graphite Carbon Brushes for Use in the Impedance Measurement of Sensory Utilizable Machine Elements. *Machines* **2023**, *11*, 1009.
https://doi.org/10.3390/machines11111009

**AMA Style**

Hausmann M, Schirra T, Kirchner E.
Analysis of the Electrical Impedance of Graphite and Silver Graphite Carbon Brushes for Use in the Impedance Measurement of Sensory Utilizable Machine Elements. *Machines*. 2023; 11(11):1009.
https://doi.org/10.3390/machines11111009

**Chicago/Turabian Style**

Hausmann, Maximilian, Tobias Schirra, and Eckhard Kirchner.
2023. "Analysis of the Electrical Impedance of Graphite and Silver Graphite Carbon Brushes for Use in the Impedance Measurement of Sensory Utilizable Machine Elements" *Machines* 11, no. 11: 1009.
https://doi.org/10.3390/machines11111009