# Digital Twin-Driven Tool Wear Monitoring and Predicting Method for the Turning Process

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## Abstract

**:**

## 1. Introduction

## 2. Related Studies

#### 2.1. Studies Regarding Tool Wear Prediction

#### 2.2. Digital Twin-Driven Machining Process

## 3. DT Model

#### 3.1. Framework

- (1)
- Physical tool system

- (2)
- Virtual tool system

- (3)
- Cutting tool service system

- (4)
- DT data

- (5)
- Connections

#### 3.2. Organization and Operational Process

- (1)
- In the working environment layer, the relevant physical environmental parameters, such as the external temperature and humidity, were first confirmed to build the environment in the virtual space. Considering the tool vibration and possible lubricant in the physical tool system, the virtual vibration and lubricant must be modeled to obtain the virtual working environment. At the same time, the virtual environment model is modified to maintain its high fidelity through interactions with the physical environment.
- (2)
- In the tool system layer, the material and geometry parameters of the cutting tool and workpiece are confirmed. The material data determine the constitutive model and damage mechanisms of the tool and workpiece. The virtual tool geometry model is mapped using detailed tool geometry data (including the tool rank angle, clearance angle, and tool edge size, etc.). Using the relevant parameters, the virtual tool system closely resembles the physical system. The geometrical model is updated during the cutting process, and the model modifies the material parameters as the temperature changes.
- (3)
- In the cutting process layer, all sensors extract data, including the cutting force, temperature, and vibration from the physical cutting process. Meanwhile, real-time simulation in the virtual space continues incessantly. The virtual cutting process is modified iteratively by comparing the data error between the physical and virtual tool systems. Following this, the tool wear status is monitored and predicted using machine learning method based on DT data, thereby realizing the maintenance of the worn cutting tool in real time.

## 4. Key Enabling Technologies

#### 4.1. Rapid Construction of the Tool System Virtual Model

- Geometry model

- 2.
- Material model

- 3.
- Environment model

- 4.
- Behavior model

#### 4.2. Modification and Data Fusion of the Tool System Virtual Model

_{pi}and d

_{vi}are the ith index of the physical and virtual models, respectively. After tool wear occurred, the original tool surface deformed, and the nodes on the original face also have a displacement. If the relative errors of geometry size reach the predefined threshold, the node of the tool surface will be updated to modify the virtual geometry model until the errors are sufficiently small. The updating scheme for the node is shown in Figure 5. If the environmental relative error reaches the set threshold, then the responding parameters in the virtual environment model will be adjusted to reduce the error.

_{ip}and r

_{iv}are the ith data of the physical and virtual systems, respectively. If the errors exceed the threshold, then the physical and virtual systems are inconsistent. After the cause is identified, the model structure is adjusted, or the step, mesh, and interaction parameters of the simulation process are modified to repeat the simulation.

_{k}, ERR_T

_{k}, and ERR_V

_{k}represent the relative error of the cutting force, temperature, and vibration between physical and virtual spaces in time k. To clean the outlier, the whisker chart is utilized. In the whisker chart, the standard of outlier can be calculated by $Q3-1.5\left(Q3-Q1\right)$, where the Q3 and Q1 are the upper quartile and lower quartile of a column in the matrix. If the element in a column exceeds the standard, the relative ERR element will be cleaned. The average error of the rest ERR elements can be calculated as follows:

_{effe}:

#### 4.3. Hybrid-Driven Model Based on Cutting Process and Simulation

## 5. Case Study

#### 5.1. Data Acquisition

#### 5.2. Realization of the Cutting Tool System DT Method

#### 5.2.1. Realization of the Symmetrical Virtual Model

_{r}is the room temperature (generally is set as 20 °C), T

_{m}is the melting temperature of the material, and m represents the thermal softening exponent. The Johnson–Cook material parameters of Inconel 718, as listed in Table 7, can be consulted from manuals [37].

_{p}, σ

_{Mises}, and ${\overline{\epsilon}}^{D}{}_{pl}$ are the hydrostatic pressure, von Mises equivalent stress, and equivalent plastic strain at the onset of damage, respectively; d

_{1}–d

_{5}are the Johnson–Cook damage constants, as listed in Table 8.

- i.
- Working condition: Machining parameters, such as the cutting speed, feed rate, and cutting depth, are affected by vibration during cutting, which can be generated from the controller of the machine tool and directly affect the simulation results.
- ii.
- Geometry size: The geometric dimension change caused by tool wear during turning.

#### 5.2.2. Hybrid-Driven Model Realization

_{xx}is separated into four segments, for ease of the balance between high distinguishability and low complexity of the calculation. The feature parameters are extracted from every divided segment, including four parameters, each based on fourth-order moment estimates of the power spectrum and fourth-order moment estimates of the frequency weighted by power. The load variation of the machine tool can result in fluctuations in the magnitude of the vibration spectra. Calculating the features of the power spectra without normalization affects the calculated features. Hence, the original PSD ${p}_{\mathit{xx}}^{0}$ must be normalized prior to calculating the eight frequency-domain features. The following normalization equation is conducted:

_{mj}is the wavelet packet coefficient of the m

_{th}segment in the lth layer.

#### 5.2.3. Multi-View Synchronization Interface in Real Time

## 6. Conclusions and Future Works

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

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Author | Year | Purpose | Measurement Technology | Calculating Method |
---|---|---|---|---|

Ong et al. | 2019 | Tool wear monitoring | Direct measurement Computer vision | Wavelet neural network (WNN) |

Garcia-Ordas et al. | 2016 | Tool wear classification | Direct measurement Computer vision | Support vector machine (SVM) |

Moldovan et al. | 2017 | Tool flank wear monitoring | Direct measurement Computer vision | Two-hidden-layer auto-encoder ANN |

Sun and Yeh | 2018 | Tool condition monitoring | Direct measurement Computer vision | Grayscale value histogram |

Duo et al. | 2019 | Tool condition monitoring | Indirect measurement | Machine learning algorithms |

Klocke et al. | 2017 | Tool condition monitoring of hobbing | Indirect measurement | Least square method |

Tangjitsitcharoen and Lohasiriwat | 2018 | Tool condition monitoring of turning | Indirect measurement | Wavelet transform |

Shi et al. | 2020 | Tool wear prediction | Indirect measurement | multiple stacked sparse auto-encoders, nonlinear regression |

Kothuru et al. | 2018 | Tool wear and failure monitoring of milling | Indirect measurement | Support vector machine (SVM) |

Li et al. | 2019 | Tool wear monitoring and prediction | Indirect measurement | Deep convolutional neural network |

Chen et al. | 2019 | Tool wear monitoring of milling | Indirect measurement | CNN and BiLSTM |

Kong et al. | 2020 | Tool wear estimation | Indirect measurement | Neighborhood preserving embedding, WOA-SVM |

Shen et al. | 2020 | Tool wear monitoring and predicting | Indirect measurement | Random Forest (RF), Gradient Boosting Regression (GBR), Support Vector Regression (SVR) |

Cai et al. | 2020 | Tool condition monitoring | Indirect measurement | Long short-term memory network (LSTM) |

Author | Year | Focused Area | Technology |
---|---|---|---|

Perez et al. | 2020 | Robotic machining | Virtual reality interface |

Bilberg and Malik | 2019 | Human–robot collaborative assembly | Object-oriented event-driven simulation |

Zhao et al. | 2020 | Process planning | Data perception, simulation optimization |

Biesinger et al. | 2019 | Process planning | Cyber-physical production system |

Liu et al. | 2019 | Process evaluation | Simulation and sensing |

Leng et al. | 2020 | Process planning | Rapid reconfiguration of automated manufacturing systems |

Tong et al. | 2019 | Intelligent manufacturing tool | Multi-sensor fusion technology and MPConnect |

Luo et al. | 2018 | CNCMT | Simulation and sensing |

Wang et al. | 2019 | Energy-efficient manufacturing system | Sensing discrete event simulation |

Qiao et al. | 2019 | Predictive maintenance of manufacturing machines | Deep Stacked GRU |

Wei et al. | 2020 | Consistency retention for CNCMT | Performance attenuation update workflow and simulation |

Luo et al. | 2020 | Predictive maintenance of CNCMT | Hybrid model based on the DT method |

Tao et al. | 2017 | Product lifecycle management | Big data, cyber and physical convergence |

Cheng et al. | 2021 | Smart manufacturing | Digital twin enhanced Industrial Internet (DT-II) |

Liu et al. | 2021 | Monitoring and controlling of product qualities | Digital twin quality knowledge model |

Category | Data | Notes | |
---|---|---|---|

Property data | Geometry data | Rank angle, clearance angle, inclination angle, tool edge geometry of cutting tool, workpiece diameter, and length. | Affecting factors of cutting process performance |

Material data | Density, specific heat, thermal conductivity, Poisson’s ratio, Young’s modulus, expansion, constitutive constants, and damage constants. | ||

Machine data | Natural frequency, damping characteristics, and stiffness. | ||

Command data | Processing data | Cutting velocity, feed rate, and cutting depth. | |

Environment data | Air humidity, room temperature, and power voltage. | ||

Real-time condition data | Cutting force, temperature distribution, and vibration. | Reflections of cutting process performance | |

Wear data | Tool wear kinds, morphology, and values. |

Signal Features | Expression |
---|---|

Mean | ${T}_{1}=\frac{1}{M}{\displaystyle \sum _{n=1}^{M}x\left(n\right)}$ |

Standard deviation | ${T}_{2}=\sqrt{\frac{1}{M-1}{\displaystyle \sum _{n=1}^{M}{\left(x\left(n\right)-{T}_{1}\right)}^{2}}}$ |

Root means square | ${T}_{3}=\sqrt{\frac{1}{M}{\displaystyle \sum _{n=1}^{M}{\left(x\left(n\right)\right)}^{2}}}$ |

Skewness index | ${T}_{4}=\frac{{\displaystyle \sum _{n=1}^{M}{\left(x\left(n\right)-{T}_{1}\right)}^{3}}}{\left(M-1\right){T}_{2}^{3}}$ |

Wavelet packet power value | ${E}_{m}^{j}={\displaystyle \sum _{k}{\left({C}_{m}^{j}\right)}^{2}}/{\left({\displaystyle \sum _{m}{\left|{\displaystyle \sum _{k}{\left({C}_{m}^{j}\right)}^{2}}\right|}^{2}}\right)}^{1/2}$ |

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

Cutting velocity (m/min) | 120 |

Feed rate (mm/r) | 0.1 |

Cutting depth (mm) | 0.5 |

Cooling condition | Dry machining |

Properties | Inconel 718 | Carbide |
---|---|---|

Density (kg/m^{3}) | 8190 | 12,000 |

Young’s modulus (MPa) | 185,000 | 800,000 |

Poisson’s Ratio | 0.33 | 0.22 |

Expansion (10−6/°C) | 11.8 | 4.7 |

Conductivity (W/(m·°C)) | 11.4 | 4.6 |

Specific Heat (mJ/ton·°C) | 481.4 | 40 |

Material | A (MPa) | B (MPa) | C | n | m | T (K) | Tm (K) |
---|---|---|---|---|---|---|---|

Inconel 718 | 1241 | 622 | 0.0134 | 0.65 | 1.03 | 300 | 1570 |

Material | d1 | d2 | d3 | d4 | d5 |
---|---|---|---|---|---|

Inconel 718 | 0.11 | 0.75 | −1.45 | 0.04 | 0.89 |

Signal Features | Expression |
---|---|

Mean | ${T}_{1}=\frac{1}{M}{\displaystyle \sum _{n=1}^{M}x\left(n\right)}$ |

Standard deviation | ${T}_{2}=\sqrt{\frac{1}{M-1}{\displaystyle \sum _{n=1}^{M}{\left(x\left(n\right)-{T}_{1}\right)}^{2}}}$ |

Root means square | ${T}_{3}=\sqrt{\frac{1}{M}{\displaystyle \sum _{n=1}^{M}{\left(x\left(n\right)\right)}^{2}}}$ |

Skewness index | ${T}_{4}=\frac{{\displaystyle \sum _{n=1}^{M}{\left(x\left(n\right)-{T}_{1}\right)}^{3}}}{\left(M-1\right){T}_{2}^{3}}$ |

Features | Expression |
---|---|

One-order moment estimate of power | ${F}_{1}=\frac{1}{{N}^{\prime}}{\displaystyle \sum _{{N}^{\prime}}{p}_{xx}\left(n\right)}$ |

Two-order moment estimate of power | ${F}_{2}=\frac{1}{{N}^{\prime}-1}{{\displaystyle \sum _{{N}^{\prime}}\left({p}_{xx}\left(n\right)-{F}_{1}\right)}}^{2}$ |

Three-order moment estimate of power | ${F}_{3}=\frac{1}{{N}^{\prime}{F}_{2}^{3/2}}{{\displaystyle \sum _{{N}^{\prime}}\left({p}_{xx}\left(n\right)-{F}_{1}\right)}}^{3}$ |

Four-order moment estimate of power | ${F}_{4}=\frac{1}{{N}^{\prime}{F}_{2}^{2}}{{\displaystyle \sum _{{N}^{\prime}}\left({p}_{xx}\left(n\right)-{F}_{1}\right)}}^{4}$ |

One-order moment estimate of frequency weighted by power | ${F}_{5}=\frac{1}{{K}_{l}}{\displaystyle \sum _{{N}^{\prime}}f\left(n\right){p}_{xx}\left(n\right)}$ |

Two-order moment estimate of frequency weighted by power | ${F}_{6}=\sqrt{\frac{{\displaystyle {\sum}_{{N}^{\prime}}[{\left(f\left(n\right)-{F}_{5}\right)}^{2}{p}_{xx}\left(n\right)]}}{{K}_{l}}}$ |

Three-order moment estimate of frequency weighted by power | ${F}_{7}=\frac{1}{{K}_{l}{F}_{6}^{3}}{\displaystyle \sum _{{N}^{\prime}}[{\left(f\left(n\right)-{F}_{5}\right)}^{3}{p}_{xx}\left(n\right)]}$ |

Four-order moment estimate of frequency weighted by power | ${F}_{8}=\frac{1}{{K}_{l}{F}_{6}^{4}}{\displaystyle \sum _{{N}^{\prime}}[{\left(f\left(n\right)-{F}_{5}\right)}^{4}{p}_{xx}\left(n\right)]}$ |

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## Share and Cite

**MDPI and ACS Style**

Zhuang, K.; Shi, Z.; Sun, Y.; Gao, Z.; Wang, L.
Digital Twin-Driven Tool Wear Monitoring and Predicting Method for the Turning Process. *Symmetry* **2021**, *13*, 1438.
https://doi.org/10.3390/sym13081438

**AMA Style**

Zhuang K, Shi Z, Sun Y, Gao Z, Wang L.
Digital Twin-Driven Tool Wear Monitoring and Predicting Method for the Turning Process. *Symmetry*. 2021; 13(8):1438.
https://doi.org/10.3390/sym13081438

**Chicago/Turabian Style**

Zhuang, Kejia, Zhenchuan Shi, Yaobing Sun, Zhongmei Gao, and Lei Wang.
2021. "Digital Twin-Driven Tool Wear Monitoring and Predicting Method for the Turning Process" *Symmetry* 13, no. 8: 1438.
https://doi.org/10.3390/sym13081438