# Study on the CBN Wheel Wear Mechanism of Longitudinal-Torsional Ultrasonic-Assisted Grinding Applied to TC4 Titanium Alloy

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## Abstract

**:**

## 1. Introduction

## 2. Establishment of a Wheel Wear Model of TC4 Titanium Alloy in LTUAG

#### 2.1. Analysis of Kinematics Characteristics of TC4 Titanium Alloy in LTUAG

_{w}, the motion work in the xoy plane includes rotational motion around the z-axis with a rotational speed of n, a torsional ultrasonic vibration with an amplitude of b, and a longitudinal ultrasonic vibration with an amplitude of a along the z-axis.

_{w}is the workpiece feed speed, R is the grinding wheel radius, ω is the grinding wheel angular speed, b is the torsional ultrasonic vibration amplitude, a is the longitudinal ultrasonic vibration amplitude, f

_{b}is the torsional-ultrasonic vibration frequency, f

_{a}is the longitudinal ultrasonic vibration frequency, and φ is the phase difference between longitudinal and torsional vibration.

_{c}, of a single abrasive particle in LTUAG in one vibration cycle can be obtained as:

_{p}, of a single abrasive particle can be expressed as:

_{a}is the rotational speed of the grinding wheel. According to Figure 2 and Equation (4), the removal volume, V

_{p}, of a single abrasive grain material during ordinary grinding can be obtained as:

_{p}is the cross-sectional area of ordinary grinding chips.

#### 2.2. Establishment of a Grinding Force Model for Titanium Alloy in LTUAG

_{gt}, and the radial grinding force, F

_{gr}, of a single abrasive particle in LTUAG can be expressed as:

_{gt}

_{c}is the tangential deformation force for wear debris of a single abrasive particle, F

_{gtf}is the tangential friction of a single abrasive particle, F

_{grc}is the radial deformation force for wear debris of a single abrasive particle, and F

_{grf}is the radial friction of a single abrasive particle. According to the research of Yan et al. [13], the tangential grinding force, F

_{gt}, and radial grinding force, F

_{gr}, of a single abrasive particle in LTUAG can be expressed as:

_{p}, grinding linear speed, v

_{s}, feed speed, v

_{w}, longitudinal ultrasonic amplitude, a, torsional ultrasonic amplitude, b, and longitudinal-torsional ultrasonic vibration frequency, f. During LTUAG, the grinding force increases with the increase of the grinding depth and the feed rate and decreases with the increase of ultrasonic amplitude, grinding linear velocity, and longitudinal-torsional ultrasonic vibration frequency. According to Equations (3) and (4), the grinding arc length of a single abrasive particle in LTUAG is longer than that of a single abrasive particle in ordinary grinding. The grinding force in LTUAG is smaller than that in ordinary grinding under the same grinding conditions.

#### 2.3. Establishment of an Abrasive Particle Surface Temperature Model for TC4 Titanium Alloy in LTUAG

_{t}is the tool’s thermal conductivity, q

_{m}is the heat source density, L

^{t}is the fixed heat source’s length, $B(s)$ is the proportionality coefficient of grinding heat transfer into the grinding grain generated during grinding, w is the unit cutting width, R

_{ts}is the distance from the fixed heat source to a point inside the tool, and R

_{ts}′ is the distance from the mirror image heat source to a point inside the tool.

_{c}, and the length of the contact surface between abrasive particles and chips, l

_{AD}, can be expressed as:

_{s}is the grinding line speed, ϕ is the shear angle, a

_{p}is the grinding depth, and η is the friction angle.

_{f}

_{1}, q

_{f}

_{2}) as:

_{1}is the friction force between the rake face of the abrasive particle and the chip interface, f

_{2}is the friction force between the flank face of the abrasive particle and the workpiece surface, w is the unit cutting width, l

_{AG}is the length of the flank face of the abrasive grain, l

_{AG}= u, and F

_{gt}and F

_{gr}are the tangential grinding force and radial grinding force of a single abrasive particle in LTUAG.

_{gt}, the radial grinding force, F

_{gr}, the grinding linear speed, v

_{s}, and the grinding depth, a

_{p}. The friction heat source density on the rake face of the abrasive grain in LTUAG increases with the increase of the tangential grinding force, F

_{gt}, radial grinding force, F

_{gr}, and grinding linear velocity, v

_{s}, and decreases with the increase of grinding depth, a

_{p}. The friction heat source density of the abrasive flank face increases with the increase of radial grinding force, F

_{gr}, and grinding linear velocity, v

_{s}, in LTUAG of a single abrasive particle.

_{total}is the average temperature inside the abrasive grain, T

_{f}

_{1}is the temperature rise caused by the friction heat source of the abrasive grain’s rake face, T

_{f}

_{2}is the temperature rise caused by the friction heat source of the abrasive grain’s flank face, and T

_{room}is the room temperature.

_{s}, and the friction heat source density of the abrasive grain rake face and flank face (q

_{f}

_{1}, q

_{f}

_{2}). During the grinding process, the surface temperature of the abrasive grains increases with the increase of the grinding linear velocity, v

_{s}, and the friction heat source density on the rake face and the flank face of the abrasive grains. In addition, according to Equations (7) and (10), the introduction of longitudinal-torsional ultrasonic vibration makes the tangential grinding force and the radial grinding force of a single abrasive particle (F

_{gt}, F

_{gr}), and the friction heat source of the density of the rake face and flank face of the abrasive grain (q

_{f}

_{1}, q

_{f}

_{2}), decrease. To a certain extent, the surface temperature of the abrasive grains is reduced, thereby reducing the influence of the temperature field of the abrasive grain surface on the fatigue wear of the abrasive grains and improving the durability of the grinding wheel.

#### 2.4. Establishment of a Grinding Wheel Wear Model in LTUAG for TC4 Titanium Alloy

_{r}is the workpiece feed rate during cutting.

_{w}and B

_{w}are the characteristic correlation coefficients of adhesive wear of CBN, V

_{n}is the relative sliding velocity of the chip contact surface, P

_{n}is the positive pressure of the contact surface between the tool and the workpiece, and T

_{m}is the tool surface temperature during cutting.

_{N}, of the abrasive particle face during LTUAG can be expressed as:

_{wheel}(t), of the stable wear stage in LTUAG can be expressed as:

_{w}, the grinding linear speed, v

_{s}, and the tangential grinding force and the radial grinding force of a single abrasive particle in LTUAG (F

_{gt}, F

_{gr}). The abrasive rake face temperature, T

_{f}

_{1}, and the abrasive flank temperature, T

_{f}

_{2}, are also related. It can be seen from Equations (7) and (12) that the grinding force of LTUAG and the surface temperature of abrasive grains increase with the increase of grinding depth and decrease with the increase of ultrasonic amplitude. Therefore, the grinding wheel wear rate of TC4 titanium alloy in LTUAG increases with the increase of the grinding depth and the workpiece feed rate and decreases with the increase of the grinding linear speed and the ultrasonic amplitude.

## 3. Verification and Analysis of the Grinding Wheel Wear Test of TC4 Titanium Alloy in LTUAG

#### 3.1. Test Conditions and Program

#### 3.2. Test Results and Analysis

#### 3.2.1. Influence of Process Parameters on Grinding Force in LTUAG

#### 3.2.2. Effect of Process Parameters on Grinding Temperature of LTUAG

#### 3.2.3. The Effect of Process Parameters on the Wear Rate of Grinding Wheels in LTUAG

## 4. Conclusions

- The grinding force model and the grinding abrasive surface temperature model of LTUAG were established based on the single-grain grinding arc length model in LTUAG, and on this basis, the grinding wheel wear model of LTUAG was established by combining the wear model and the bond wear model. The theoretical analysis results showed that the grinding wheel wear rate of LTUAG increased as the grinding depth and workpiece feed rate increased and decreased as the grinding linear speed and ultrasonic amplitude decreased.
- The single-factor test of LTUAG of TC4 titanium alloy showed that the grinding force and grinding temperature increased as the grinding depth and workpiece feed rate increased and decreased as the longitudinal amplitude increased. The grinding force gradually decreased as the grinding wheel speed increased, and the grinding temperature gradually increased as the grinding wheel speed increased. In addition, the variation trend of the experimental results of the grinding force and grinding temperature under different process parameters was consistent with the theoretical prediction results, which verified the accuracy of the established grinding force model and grinding temperature model in LTUAG.
- The single-factor test results of the grinding wheel wear rate of TC4 titanium alloy in LTUAG showed that the use of longitudinal-torsional ultrasonic vibration reduced the wear rate of the grinding wheel by 25.2%, thereby increasing the service life of the grinding wheel and improving the machining efficiency of TC4 titanium alloy. The experimental results of the grinding wheel wear rate were consistent with the theoretical prediction results during LTUAG, which verified the accuracy of the grinding wheel wear model in LTUAG established in this study.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 1.**Schematic diagram of the longitudinal-torsional ultrasonic-assisted grinding (LTUAG) system and its motion model. (

**a**) Schematic diagram of the grinding system in LTUAG. (

**b**) Schematic diagram of the motion model in LTUAG.

**Figure 2.**Grinding force model of a single CBN abrasive particle in LTUAG. (In the figure: v

_{s}is the grinding linear speed, a

_{p}is the grinding depth of a single abrasive particle in LTUAG, F

_{gt}

_{c}is the tangential deformation force for wear debris of a single abrasive particle, F

_{gtf}is the tangential friction of a single abrasive particle, F

_{grc}is the radial deformation force for wear debris of a single abrasive particle, F

_{grf}is the radial friction of a single abrasive particle.).

**Figure 5.**Workpieces, grinding wheels, and temperature test pieces used in the test. (

**a**) TC4 workpiece. (

**b**) Ceramic base CBN grinding wheel. (

**c**) Temperature test piece.

**Figure 7.**Influence of process parameters on the grinding force of LTUAG. (

**a**) Depth of grinding. (

**b**) Speed of the grinding wheel. (

**c**) Feed rate. (

**d**) Lengthening amplitude.

**Figure 8.**The influence of process parameters on the grinding temperature of LTUAG. (

**a**) Depth of grinding. (

**b**) Speed of the grinding wheel. (

**c**) Feed rate. (

**d**) Longitudinal amplitude.

**Figure 9.**Influence of process parameters on grinding wheel wear rate in LTUAG. (

**a**) Depth of grinding. (

**b**) Speed of the grinding wheel. (

**c**) Feed rate. (

**d**) Lengthening amplitude.

Project | Parameter |
---|---|

The maximum travel of the table (x-axis) | 850 mm |

The maximum travel of the table (y-axis) | 500 mm |

Maximum stroke of spindle (z-axis) | 540 mm |

Range of rotation | 50~8000 r/min |

Maximum spindle power | 11 kW |

Maximum output torque | 35.8 N∙m |

Positioning accuracy | 0.005 mm |

Project | Parameter |
---|---|

Input voltage | AC voltage 220 V |

Frequency | 50 Hz |

Output power | Greater than 250 W |

Frequency adjustable range | 18–23 KHz |

Project | Parameter |
---|---|

Grinding wheel model | 1A1W-type ceramic base CBN flat grinding wheel |

Manufacturer | Zhengzhou Abrasives Grinding Research Institute Co., Ltd. |

Grinding wheel length/mm | 10 |

Wheel diameter/mm | 15 |

Grinding wheel particle size | 100#, 200#, 300# |

Grinding wheel concentration | 100% |

Elongation δ5 (%) | Coefficient of Thermal Conductivity | Density | Tensile Strength | Hardness |
---|---|---|---|---|

≥10 | 7.955 W/m·K | 4.5 g/cm^{3} | ≥850 MPa | HRC30 |

Exp. Number | Grinding Depth (μm) | Speed of Grinding (Wheel r/min) | Feed Speed (mm/min) | Ultrasonic Amplitude (µm) |
---|---|---|---|---|

1 | 1/3/5/7 | 4000 | 150 | 4 |

2 | 3 | 2000/3000/4000/5000 | 150 | 4 |

3 | 3 | 4000 | 100/150/200/250 | 4 |

4 | 3 | 4000 | 150 | 0/2/4/6 |

**Table 6.**Single-factor experimental results of grinding wheel wear rate in LTUAG of TC4 titanium alloy.

Grinding Depth (µm) | Wheel Speed (r·min ^{−1}) | Feed Speed (mm·min ^{−1}) | Longitudinal Amplitude (µm) | Grinding Length (mm) | Wear Rate (g/s) |
---|---|---|---|---|---|

1 | 4000 | 150 | 4 | 150 | 0.0813 |

3 | 4000 | 150 | 4 | 150 | 0.0951 |

5 | 4000 | 150 | 4 | 150 | 0.1313 |

7 | 4000 | 150 | 4 | 150 | 0.1525 |

3 | 2000 | 150 | 4 | 150 | 0.1090 |

3 | 3000 | 150 | 4 | 150 | 0.1130 |

3 | 4000 | 150 | 44 | 150 | 0.0950 |

3 | 5000 | 150 | 4 | 150 | 0.0910 |

3 | 4000 | 100 | 4 | 150 | 0.1183 |

3 | 4000 | 150 | 4 | 150 | 0.1255 |

3 | 4000 | 200 | 4 | 150 | 0.1294 |

3 | 4000 | 250 | 4 | 150 | 0.1378 |

3 | 4000 | 150 | 0 | 150 | 0.1317 |

3 | 4000 | 150 | 2 | 150 | 0.1196 |

3 | 4000 | 150 | 4 | 150 | 0.0953 |

3 | 4000 | 150 | 6 | 150 | 0.1079 |

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**MDPI and ACS Style**

Liu, J.; Liu, Z.; Yan, Y.; Wang, X.
Study on the CBN Wheel Wear Mechanism of Longitudinal-Torsional Ultrasonic-Assisted Grinding Applied to TC4 Titanium Alloy. *Micromachines* **2022**, *13*, 1480.
https://doi.org/10.3390/mi13091480

**AMA Style**

Liu J, Liu Z, Yan Y, Wang X.
Study on the CBN Wheel Wear Mechanism of Longitudinal-Torsional Ultrasonic-Assisted Grinding Applied to TC4 Titanium Alloy. *Micromachines*. 2022; 13(9):1480.
https://doi.org/10.3390/mi13091480

**Chicago/Turabian Style**

Liu, Junli, Zhongpeng Liu, Yanyan Yan, and Xiaoxu Wang.
2022. "Study on the CBN Wheel Wear Mechanism of Longitudinal-Torsional Ultrasonic-Assisted Grinding Applied to TC4 Titanium Alloy" *Micromachines* 13, no. 9: 1480.
https://doi.org/10.3390/mi13091480