# Study on Wavelet Packet Energy Characteristics on Friction Signal of Lapping with the Fixed Abrasive Pad

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## Abstract

**:**

## 1. Introduction

## 2. Basic Principles

## 3. Experimental Part

#### 3.1. Experimental Design

#### 3.2. Measurement and Characterization

#### 3.2.1. Material Removal Rate

^{3}; s is the workpiece area, cm

^{2}; and t is the processing time, min.

#### 3.2.2. Observation of Surface Roughness and Three-Dimensional Morphology

## 4. Results and Discussion

#### 4.1. Relationship between the MRR and Energy Proportion of Wavelet Packet

#### 4.2. Relationship between Surface Roughness of the FAP and Energy Proportion of Wavelet Packet

#### 4.3. Relationship between Surface Roughness of Workpiece after Wear and the Energy Proportion of Wavelet Packet

#### 4.4. Discussion

## 5. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 3.**The experimental equipment and partial enlarged view. Note: (

**a**) FAP sample; (

**b**) local amplification; (

**c**) experimental equipment.

**Figure 5.**Proportion of wavelet packet energy in each processing stage of the FAP. Note: (

**a**) Lapping time 0–30 min; (

**b**) lapping time 30–60 min; (

**c**) lapping time 60–90 min; (

**d**) lapping time 90–120 min; (

**e**) lapping time 120–150 min; (

**f**) lapping time 150–180 min.

**Figure 8.**Relationship between surface roughness of the FAP and energy proportion of frequency bands 7 and 8.

**Figure 9.**Three-dimensional surface morphology of the FAP in different processing stages. Note: (

**a**) Lapping time 0–30 min; (

**b**) lapping time 30–60 min; (

**c**) lapping time 60–90 min; (

**d**) lapping time 90–120 min; (

**e**) lapping time 120–150 min; (

**f**) lapping time 150–180 min.

**Figure 10.**Relationship between workpiece surface roughness and energy proportion of frequency bands 7 and 8.

**Figure 11.**The three-dimensional morphology of quartz glass workpiece lapping by FAP samples at different processing stages. Note: (

**a**) The FAP samples (0–30 min) lapping quartz glass workpiece; (

**b**)the FAP samples (30–60 min) lapping quartz glass workpiece; (

**c**) the FAP samples (60–90 min) lapping quartz glass workpiece; (

**d**) the FAP samples (90–120 min) lapping quartz glass workpiece; (

**e**) the FAP samples (120–150 min) lapping quartz glass workpiece; (

**f**) the FAP samples (150–180 min) lapping quartz glass workpiece.

**Figure 12.**Machining wear principle of the FAP. Note: (

**a**) Lapping time 0–30 min; (

**b**) lapping time 30–60 min; (

**c**) lapping time 60–90 min; (

**d**) lapping time 90–120 min; (

**e**) lapping time 120–150 min; (

**f**) lapping time 150–180 min.

Parameter | Condition |
---|---|

Lapping fluid | Deionized water |

Lapping pressure | 26.7 kPa |

Slurry flow rate Speed | 50 mL/min 100 rpm |

Parameter | Condition |
---|---|

Spindle speed | 150 r/min (100 rpm) |

Pressure | 26.7 kPa |

Wear time | 1 min |

Serial Number | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 |
---|---|---|---|---|---|---|---|---|

Node | (3,1) | (3,2) | (3,3) | (3,4) | (3,5) | (3,6) | (3,7) | (3,8) |

Frequency band (Hz) | 0–0.625 | 0.625–1.25 | 1.25–1.875 | 1.875–2.5 | 2.5–3.125 | 3.125–3.75 | 3.75–4.375 | 4.375–5 |

**Table 4.**Surface roughness and three-dimensional surface parameters of the FAP in each processing stage.

Lapping Time | Sa/nm | Sp/nm | Sq/nm |
---|---|---|---|

30 min | 1294.08 | 7855.92 | 1713.72 |

60 min | 966.01 | 6186.56 | 1372.41 |

90 min | 940.32 | 5778.66 | 1343.55 |

120 min | 873.51 | 5018.38 | 1251.19 |

150 min | 830.26 | 4629.98 | 1190.13 |

180 min | 782.09 | 3626.41 | 1100.47 |

Lapping Time | Sa/nm |
---|---|

30 min | 1028.838 |

60 min | 787.058 |

90 min | 697.936 |

120 min | 657.071 |

150 min | 577.03 |

180 min | 541.184 |

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**MDPI and ACS Style**

Wang, Z.; Zhang, Z.; Wang, S.; Pang, M.; Ma, L.; Su, J.
Study on Wavelet Packet Energy Characteristics on Friction Signal of Lapping with the Fixed Abrasive Pad. *Micromachines* **2022**, *13*, 981.
https://doi.org/10.3390/mi13070981

**AMA Style**

Wang Z, Zhang Z, Wang S, Pang M, Ma L, Su J.
Study on Wavelet Packet Energy Characteristics on Friction Signal of Lapping with the Fixed Abrasive Pad. *Micromachines*. 2022; 13(7):981.
https://doi.org/10.3390/mi13070981

**Chicago/Turabian Style**

Wang, Zhankui, Zhao Zhang, Shiwei Wang, Minghua Pang, Lijie Ma, and Jianxiu Su.
2022. "Study on Wavelet Packet Energy Characteristics on Friction Signal of Lapping with the Fixed Abrasive Pad" *Micromachines* 13, no. 7: 981.
https://doi.org/10.3390/mi13070981