# Conical Grinding Wheel Ultrasonic-Assisted Grinding Micro-Texture Surface Formation Mechanism

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## Abstract

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## 1. Introduction

_{2}engineering ceramics with a new type of ultrasonic honing machine [4,5]. Tawakoli adopted ultrasonic assisted technology in dry grinding [6]. The results obtained showed that grinding forces decreased significantly. Mohsen Ghahramani Nik et al. proved the effect of ultrasonic vibration on the grinding of Ti6Al4V alloy [7]. W. M. Zeng et al. studied RUAG of advanced ceramics and discussed tool wear and cutting forces [8]. The Wu team [9,10,11] investigated elliptical ultrasonic-assisted grinding (EUAG) technologies. Most of the experiment results showed the feasibility of UAG in improving surface properties. Since 2014, the field of hard and brittle materials has found the application of UAG technologies [12,13] and carbon fiber-reinforced plastic [14], among others, other than special alloys. Research methods were transferred from qualitative to quantitative analyses. Past research has established mathematical models of cutting force [15,16], material removal rate [17,18], roughness [19], morphology [20], and cavitation bubble [21]; and further discussed the relationship between grinding parameters and ground surface.

_{2}-based ceramic material [22]. Guo et al. investigated the influences of ultrasonic vibration parameters and tilt angle on the ground quality of micro-structured surfaces [23]. Zheng et al. built surface micro-texture models based on multi-grains motion equations [24]. Wen et al. proposed an improved model of a rough surface profile to find the microscopic feature parameters, such as the curvature radius of the grain, which are suitable for contact analysis and calculation [25,26]. One-dimensional longitudinal vibration often adopts a slender horn with a small tool head. Longitudinal ultrasonic vibration produces sinusoidal micro-texture, which changes the linear micro-texture of CG. Interference action of multiple abrasive grains subdivides the surface further. Compared with CG, micro-texture reduces surface roughness and thermal damage and improves lubrication characteristics.

## 2. RUAG Kinematic Model

#### 2.1. Experimental Setup

#### 2.2. Theoretical Kinematic Model

## 3. Micro-Texture Feature Models

#### 3.1. Pit Model

#### 3.2. Grinding Depth Equation

#### 3.2.1. Effective Abrasive Gains Number

#### 3.2.2. Calculation of Grinding Depth

#### 3.3. Calculation of Texture Spacing

#### 3.4. RSA of the Theoretical Model

#### 3.4.1. Experimental Design and Result

#### 3.4.2. Discussion of RSA

## 4. RUAG Progress Simulation

#### 4.1. Finite Element Simulation Preprocessing

#### 4.2. Micro-Texture Characteristic Analysis

## 5. Experiment Results and Discussion

#### 5.1. Influence of Amplitude

#### 5.2. Influence of Feed and Rotational Speed

## 6. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 2.**RUAG kinematic models: (

**a**) grinding wheel model, (

**b**) abrasive grain’s trajectory, (

**c**) abrasive grain model, and (

**d**) micro-pit model.

**Figure 3.**RSA of the relative parameters: (

**a**) ${V}_{s}-n-{h}_{p}$, (

**b**) ${V}_{s}-A-{h}_{p}$, (

**c**) $n-A-{h}_{p}$, (

**d**) ${V}_{s}-A-{l}_{\mathrm{s}}$, (

**e**) ${V}_{s}-A-\u2206d$, and (

**f**) ${V}_{s}-A-{A}_{p}$.

**Figure 5.**Simulated micro-pit of group 1: (

**a**) A = 0, (

**b**) A = 8 μm, (

**c**) A = 10 μm, and (

**d**) A = 12 μm.

**Figure 6.**Simulation result comparisons of groups 2 and 3: (

**a**) $n=2000\mathrm{R}\mathrm{P}\mathrm{M}$, ${V}_{s}=1\mathsf{\mu}\mathrm{m}/\mathrm{s}$, (

**b**) $n=3000\mathrm{R}\mathrm{P}\mathrm{M}$, ${V}_{s}=1\mathsf{\mu}\mathrm{m}/\mathrm{s}$, (

**c**) $n=2000\mathrm{R}\mathrm{P}\mathrm{M}$, ${V}_{s}=10\mathsf{\mu}\mathrm{m}/\mathrm{s}$, (

**d**) $n=3000\mathrm{R}\mathrm{P}\mathrm{M}$, ${V}_{s}=10\mathsf{\mu}\mathrm{m}/\mathrm{s}$, (

**e**) $n=2000\mathrm{R}\mathrm{P}\mathrm{M}$, ${V}_{s}=20\mathsf{\mu}\mathrm{m}/\mathrm{s}$, (

**f**) $n=3000\mathrm{R}\mathrm{P}\mathrm{M}$, ${V}_{s}=20\mathsf{\mu}\mathrm{m}/\mathrm{s}$, (

**g**) $n=2000\mathrm{R}\mathrm{P}\mathrm{M}$, ${V}_{s}=30\mathsf{\mu}\mathrm{m}/\mathrm{s}$ and (

**h**) $n=3000\mathrm{R}\mathrm{P}\mathrm{M}$, ${V}_{s}=30\mathsf{\mu}\mathrm{m}/\mathrm{s}$.

**Figure 7.**Surface texture comparison of group 1: (

**a**) $A=0$, (

**b**) $A=8\mathsf{\mu}\mathrm{m}$, (

**c**) $A=10\mathsf{\mu}\mathrm{m}$, and (

**d**) $A=12\mathsf{\mu}\mathrm{m}$.

**Figure 8.**Micro-texture comparison of group 1: (

**a**) A = 0, (

**b**) A = 8 μm, (

**c**) A = 10 μm, and (

**d**) A = 12 μm.

**Figure 9.**Micro-texture comparisons of groups 1 and 2: (

**a**) $A-{R}_{a}-{A}_{p}$ of group 1, (

**b**) $A-{l}_{s}$ of group 1, (

**c**) ${V}_{s}-{R}_{a}-{A}_{p}$ of group 2, and (

**d**) ${V}_{s}-{l}_{s}$ of group 2.

**Figure 10.**Experimental micro-pit comparisons: (

**a**) $n=2000\mathrm{R}\mathrm{P}\mathrm{M}$, ${V}_{s}=10\mathsf{\mu}\mathrm{m}/\mathrm{s}$, (

**b**) $n=2000\mathrm{R}\mathrm{P}\mathrm{M}$, ${V}_{s}=20\mathsf{\mu}\mathrm{m}/\mathrm{s}$, (

**c**) $n=2000\mathrm{R}\mathrm{P}\mathrm{M}$, ${V}_{s}=30\mathsf{\mu}\mathrm{m}/\mathrm{s}$, (

**d**) $n=3000\mathrm{R}\mathrm{P}\mathrm{M}$, ${V}_{s}=10\mathsf{\mu}\mathrm{m}/\mathrm{s}$, (

**e**) $n=3000\mathrm{R}\mathrm{P}\mathrm{M}$, ${V}_{s}=20\mathsf{\mu}\mathrm{m}/\mathrm{s}$, and (

**f**) $n=2000\mathrm{R}\mathrm{P}\mathrm{M}$,${V}_{s}=10\mathsf{\mu}\mathrm{m}/\mathrm{s}$, convex.

Parameters | Values |
---|---|

Wheel diameter (mm) | 60.00 |

Outside pressure angle (°) | 17.92 |

Inside pressure angle (°) | 22.08 |

Point width (mm) | 0.73 |

Outside edge radius (mm) | 0.50 |

Inside edge radius (mm) | 0.50 |

Mean radius (mm) | 23.14 |

Material Properties | Workpiece (45# Steel) | Grain (CBN) |
---|---|---|

Density ($\mathrm{k}\mathrm{g}/{\mathrm{m}}^{3}$) | 7850 | 15,700 |

Elastic modulus (GPa) | 210 | 705 |

Poisson’s ratio | 0.33 | 0.23 |

Specific heat capacity ($\mathrm{J}/(\mathrm{k}\mathrm{g}\xb7\xb0\mathrm{C})$) | 526.3 | 178 |

Thermal conductivity ($\mathrm{w}/(\mathrm{m}\xb7\xb0\mathrm{C})$) | 6.7 | 24 |

Linear expansion coefficient (${10}^{-6}/\xb0\mathrm{C}$) | 9 | 5 |

Groups | Amplitude $\left(\mathsf{\mu}\mathbf{m}\right)$ | Feed Speed $(\mathsf{\mu}\mathbf{m}/\mathbf{s})$ | Rotational Speed (rpm) |
---|---|---|---|

1 | 0/8/10/12 | 1 | 3000 |

2 | 8 | 1/10/20/30 | 2000 |

3 | 8 | 1/10/20/30 | 3000 |

Amplitude A $\left(\mathsf{\mu}\mathbf{m}\right)$ | Theoretical Length ${\mathit{l}}_{\mathbf{s}}$$\left(\mathsf{\mu}\mathbf{m}\right)$ | Theoretical Depth
${\mathit{A}}_{\mathit{p}}$ $\left(\mathsf{\mu}\mathbf{m}\right)$ | Theoretical Spacing
$\u2206\mathit{d}$ $\left(\mathsf{\mu}\mathbf{m}\right)$ | Simulated Length
${\mathit{l}}_{\mathbf{s}}$ $\left(\mathsf{\mu}\mathbf{m}\right)$ | Grinding Depth
${\mathit{h}}_{\mathit{p}}$ $\left(\mathsf{\mu}\mathbf{m}\right)$ |
---|---|---|---|---|---|

0 | - | 0.006 | 31.787 | - | 0.006 |

8 | 35.215 | 0.098 | 31.359 | 39.51 | −2.363 |

10 | 32.663 | 0.106 | 31.325 | 36.153 | −2.971 |

12 | 30.717 | 0.112 | 31.296 | 33.186 | −3.580 |

Feed Speed ${\mathit{V}}_{\mathit{s}}$ $(\mathsf{\mu}\mathbf{m}/\mathbf{s})$ | Theoretical Length ${\mathit{l}}_{\mathbf{s}}$$\left(\mathsf{\mu}\mathbf{m}\right)$ | Theoretical Depth
${\mathit{A}}_{\mathit{p}}$ $\left(\mathsf{\mu}\mathbf{m}\right)$ | Theoretical Spacing
$\u2206\mathit{d}$ $\left(\mathsf{\mu}\mathbf{m}\right)$ | Simulated Length
${\mathit{l}}_{\mathbf{s}}$ $\left(\mathsf{\mu}\mathbf{m}\right)$ | Grinding Depth
${\mathit{h}}_{\mathit{p}}$ $\left(\mathsf{\mu}\mathbf{m}\right)$ |
---|---|---|---|---|---|

1 | 26.850 | 0.128 | 31.224 | 32.260 | −2.333 |

10 | 57.038 | 0.559 | 29.275 | 62.500 | −1.902 |

20 | 71.307 | 0.853 | 27.949 | 78.620 | −1.609 |

30 | 81.210 | 1.084 | 26.904 | 85.680 | −1.378 |

Feed Speed ${\mathit{V}}_{\mathit{s}}$ $(\mathsf{\mu}\mathbf{m}/\mathbf{s})$ | Theoretical Length ${\mathit{l}}_{\mathbf{s}}$$\left(\mathsf{\mu}\mathbf{m}\right)$ | Theoretical Depth
${\mathit{A}}_{\mathit{p}}$ $\left(\mathsf{\mu}\mathbf{m}\right)$ | Theoretical Spacing
$\u2206\mathit{d}$ $\left(\mathsf{\mu}\mathbf{m}\right)$ | Simulated Length
${\mathit{l}}_{\mathbf{s}}$ $\left(\mathsf{\mu}\mathbf{m}\right)$ | Grinding Depth
${\mathit{h}}_{\mathit{p}}$ $\left(\mathsf{\mu}\mathbf{m}\right)$ |
---|---|---|---|---|---|

1 | 35.215 | 0.098 | 46.660 | 46.660 | −2.363 |

10 | 74.951 | 0.435 | 82.060 | 82.060 | −2.027 |

20 | 93.371 | 0.668 | 100.790 | 100.790 | −1.794 |

30 | 106.772 | 0.854 | 114.170 | 114.170 | −1.608 |

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## Share and Cite

**MDPI and ACS Style**

Han, J.; Jiang, Y.; Li, X.; Li, Q.
Conical Grinding Wheel Ultrasonic-Assisted Grinding Micro-Texture Surface Formation Mechanism. *Machines* **2023**, *11*, 428.
https://doi.org/10.3390/machines11040428

**AMA Style**

Han J, Jiang Y, Li X, Li Q.
Conical Grinding Wheel Ultrasonic-Assisted Grinding Micro-Texture Surface Formation Mechanism. *Machines*. 2023; 11(4):428.
https://doi.org/10.3390/machines11040428

**Chicago/Turabian Style**

Han, Jiaying, Yiqi Jiang, Xinrui Li, and Qing Li.
2023. "Conical Grinding Wheel Ultrasonic-Assisted Grinding Micro-Texture Surface Formation Mechanism" *Machines* 11, no. 4: 428.
https://doi.org/10.3390/machines11040428