# Energy Prediction Models and Distributed Analysis of the Grinding Process of Sustainable Manufacturing

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^{2}

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## Abstract

**:**

## 1. Introduction

_{2}emission models for grinding. The energy was considered when evaluating CO

_{2}emissions. Deng et al. [37] built a model for energy and carbon efficiency of the wheel spindle using the genetic algorithm. The specific grinding energy and material removal energy of the spindle has been well-modelled [38,39]. In our previous studies, both total and active energies of the spindle were analysed and optimized using machine learning and genetic algorithms [40,41,42]. However, repeated and intermittent infeed movements and high-speed approaching stages consume a large portion of energy and their influence on grinding energy cannot be ignored. Additionally, power laws and time histories for x-, y-, and z-infeed are complex and different. Therefore, an integrated energy model for grinding was built, including all infeed motions and wheel rotation up, down, approaching, and material removal states. Distributed analysis and discussions of grinding energy characteristics were obtained to help managers formulate reasonable optimization schemes for energy-efficient manufacturing.

## 2. Integrated Energy Prediction Model

#### 2.1. Energy Flow Analysis during Grinding

_{e}, E

_{c}, E

_{s}, E

_{x}, E

_{y}, and E

_{z}represent the energy consumed on the electric controller, cooling system, wheel rotation, x-infeed, y-infeed, and z-infeed, respectively.

#### 2.2. Energy Modelling of Wheel Air Cutting Rotation and Material Removal

_{s}is wheel speed and A

_{sa}and B

_{sa}are undetermined coefficients that are associated with wheel motor performance.

_{w}is workpiece infeed speed.

_{z}is infeed times along the z-axis during a grinding stroke and n

_{z}is the number of grinding strokes.

_{p}is the depth of cut, and W is the workpiece width.

_{ci}and B

_{ci}are the linear shape coefficient and slope and intercept, respectively.

_{ci}is the time history in the cutting-in stage.

_{co}and B

_{co}are the linear shape coefficient and slope and intercept, respectively.

_{co}is time history during the cutting-out stage.

#### 2.3. Energy Modelling of x-Infeed

_{x}, B

_{x}, and C

_{x}are coefficients determined by properties of motor drivers and workbench friction.

_{gx}is the gravity acceleration and deceleration time.

#### 2.4. Energy Modelling of y- and z-Infeed

_{y}, is regarded as a constant for a certain grinder. The energy model of the y-infeed is expressed using Equation (26).

_{y}is y-infeed power and t

_{y}is y-infeed time. m

_{z}is calculated using Equation (7).

_{z}and t

_{z}are z-infeed power and time, respectively. n

_{z}is calculated using Equation (8).

#### 2.5. Energy Modelling of the Electric Controller and Cooling System

_{e}is electric controlling power and t

_{total}is the total time from start-up to shut down.

_{e}is the waiting time for the electric control system.

_{c}is the cooling power and t

_{c}is the cooling process time.

## 3. Parameters for Grinding Energy Models

#### 3.1. Grinding Experiment Setup

_{2f}/SiO

_{2}) is 50 mm × 50 mm × 25 mm. A diamond grinding wheel with a radius of 100 mm and a width of 10 mm is employed. For the installed wheel, spindle rotating speeds were 10.46 m/s–73.26 m/s (spindle rotating speeds for the grinder were 1000 r/min–7000 r/min). The workpiece infeed speed is best kept within 25 m/min. A water-based hybrid liquid is used for cooling purposes. Grinding parameter settings for this kind of material and wheel, workpiece infeed speed, depth of cut, and wheel speed were investigated in our previous study [43]. The grinding parameters for the three-factor and four-level experimental design are set out in Table 1.

#### 3.2. Experimental Results

_{e}, P

_{c}, P

_{y}, and P

_{z}, which are summarized in Table 2. The infeed time along the y-axis, t

_{y}, and the z-axis, t

_{z}, are 0.6 s and 0.3 s, respectively. The gravity acceleration and deceleration time along the x-axis, t

_{gx}, is 0.05 s.

_{s}, v

_{w}, and a

_{p}. Table 3 shows the grinding parameters and experimental values of wheel rotation power during approaching and material removal stages, as well as x-infeed and x-acceleration power along the x-axis.

#### 3.3. Parameter Studies and Model Verification

_{sa}, is associated with the unique grinding parameter, v

_{s}. The experimental results in No.1–No.4 are used to obtain the model coefficients, A

_{sa}and B

_{sa}. A Gauss-Newton gradient method is employed to calculate A

_{sa}and B

_{sa}using the reverse gradient. A total of 200 iterations are set. Similarly, the x-infeed power and x-acceleration power are associated with workpiece infeed speed. v

_{w}. η, ξ, Ψ, ω in Equation (22) and A

_{x}, B

_{x}, C

_{x}in Equation (23) are obtained from the fourth to the eighth experimental groups. All 10 experimental groups are required to solve four model parameters for the stable cutting power, P

_{sm}. The coefficients P

_{sa}, P

_{sm}, P

_{xm}, and P

_{x}in power models are summarized in Table 4.

## 4. Energy Distribution Analysis and Discussion

#### 4.1. Energy Distribution Analysis and Discussion of Different Components

#### 4.2. Energy Distribution Analysis and Discussion of Wheel Spindle in Different Machining Stages

#### 4.3. Energy Efficiency Analysis and Improvement Strategies

## 5. Conclusions

- (1)
- Predicted power and energy errors compared with measured values were kept within 5%. The integrated energy model is regarded as acceptable for further energy distribution and efficiency analysis.
- (2)
- More than 90% of electrical energy is wasted on two auxiliary systems: electrical controlling and cooling. Energy-saving chips, lightweight worktable utilization, and minimal lubricant quantity techniques are recommended in the next-generation design of grinders.
- (3)
- Grinding parameters have a larger effect on the energy distribution of both the spindle and the x-axis system. A larger workpiece infeed speed is desired to improve both energy-saving and process efficiency.
- (4)
- Energy efficiency reaches 36–45% (over a general level in machining) due to more grinding strokes; it may increase grinding time. A novel balance between energy efficiency, process time, and surface quality should be studied in depth.

## 6. Patents

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 1.**Energy flow during grinding: (

**a**) Structural composition of the grinder; (

**b**) Energy flow across different machining stages and parts.

**Figure 2.**Wheel rotation power during a grinding run: (

**a**) Power variation over time; (

**b**) Relative position between wheel and workpiece.

**Figure 3.**x-infeed power during a grinding run: (

**a**) Power variation over time; (

**b**) Relative position of the wheel and workpiece.

**Figure 5.**Measured power variation along the spindle and x-axis: (

**a**) Power waveform of wheel rotation; (

**b**) Rotation power during material removal; (

**c**) Rotation power during a grinding stroke; (

**d**) Power waveform of x-infeed; (

**e**) x-infeed power during material removal; (

**f**) x-infeed power during a grinding stroke.

**Figure 6.**Comparisons between measured and predicted power values of material removal and idle motion along the spindle, acceleration, and infeed along the x-axis.

**Figure 7.**Energy distribution comparisons for different components in four testing groups: (

**a**) Energy distribution in the electrical controller, coolant, spindle rotation, x-infeed, y-infeed, and z-infeed parts; (

**b**) Energy distribution in four motion parts: spindle rotation, x-infeed, y-infeed, and z-infeed.

**Figure 8.**Comparisons of energy distributions in wheel spindle in front–back approaching, left–right approaching, cutting-in, cutting-out, and stable cutting stages.

**Figure 9.**Comparisons of the proportions of energy used in the material removal and non-material removal stages.

Factors | Parameters |
---|---|

Machining mode | Plane grinding |

Workpiece material | SiO_{2f}/SiO_{2} ceramics |

Coolant | Water-based |

Workpiece size (mm) | 50 (L) × 50 (W) × 25 (H) |

Grinding wheel geometry (mm) | 100 (R) × 10 (Wd) |

Grinding width, w (mm) | 5 |

Material removal, d (μm) | 12, 24, 36, 48 |

Distance, a (mm) | 5 |

Distance, b (mm) | 10 |

Workpiece infeed speed, v_{w} (m/min) | 1, 2, 3, 4 |

Depth of cut, a_{p} (μm) | 3, 6, 9, 12 |

Wheel speed, v_{s} (m/s) | 15, 20, 25, 30 |

No. | P_{e} (W) | P_{c} (W) | P_{y} (W) | P_{z} (W) |
---|---|---|---|---|

1 | 443.623 | 65.781 | 0.923 | 16.017 |

2 | 438.888 | 67.520 | 0.947 | 16.889 |

3 | 438.900 | 66.580 | 0.947 | 14.581 |

4 | 436.142 | 67.143 | 0.997 | 16.330 |

5 | 431.938 | 68.081 | 0.889 | 16.255 |

Average | 437.898 | 67.021 | 0.941 | 16.014 |

**Table 3.**Measured results of approaching and material removal power along the spindle and x-infeed and x-acceleration power along the x-axis in 10 experimental groups.

No. | v_{s} (m/s) | v_{w} (m/min) | a_{p} (μm) | P_{sm} (W) | P_{sa} (W) | P_{xm} (W) | P_{x} (W) |
---|---|---|---|---|---|---|---|

1 | 30 | 4 | 12 | 19.77 | 21.61 | 31.92 | 38.63 |

2 | 25 | 4 | 12 | 15.58 | 16.17 | 31.63 | 38.28 |

3 | 20 | 4 | 12 | 14.97 | 7.73 | 31.63 | 38.53 |

4 | 15 | 4 | 12 | 10.65 | 4.77 | 31.58 | 38.52 |

5 | 30 | 1 | 12 | 10.16 | 21.96 | 8.32 | 10.27 |

6 | 30 | 2 | 12 | 10.70 | 24.41 | 11.90 | 13.81 |

7 | 30 | 3 | 12 | 15.09 | 22.91 | 21.51 | 24.43 |

8 | 30 | 4 | 9 | 17.90 | 21.30 | 31.33 | 39.86 |

9 | 30 | 4 | 6 | 12.60 | 22.81 | 31.82 | 38.30 |

10 | 30 | 4 | 3 | 7.72 | 22.34 | 31.75 | 38.94 |

Power | Coefficients | |||
---|---|---|---|---|

P_{sa} | A_{sa} | B_{sa} | ||

−13.9620 | 1.1792 | |||

P_{sm} | λ | α | Β | χ |

0.1216 | −0.1986 | 0.6083 | 0.6014 | |

P_{xm} | A_{x} | B_{x} | C_{x} | |

6.3500 | 0.1100 | 1.5500 | ||

P_{x} | η | ξ | Ψ | ω |

17.22 | −13.33 | 6.947 | −0.5679 |

**Table 5.**Comparisons between measured and predicted values of material removal and idle motion along the spindle, acceleration, and infeed along the x-axis.

No. | Grinding Parameters | Measured Values | Predicted Values | ||||||||
---|---|---|---|---|---|---|---|---|---|---|---|

v_{s}(m/s) | v_{w}(m/min) | a_{p}(μm) | P_{sm}(W) | P_{sa}(W) | P_{xm}(W) | P_{x}(W) | P_{sm}^{′}(W) | P_{sa}^{′}(W) | P_{xm}^{′}(W) | P_{x}^{′}(W) | |

11 | 16.7 | 2 | 12 | 7.73 | 4.36 | 12.19 | 14.43 | 7.88 | 5.73 | 12.77 | 13.80 |

12 | 25 | 2 | 9 | 9.20 | 17.25 | 12.54 | 13.81 | 9.16 | 15.52 | 12.77 | 13.80 |

13 | 23.4 | 1 | 6 | 4.50 | 13.43 | 8.23 | 10.27 | 4.47 | 13.63 | 8.01 | 10.27 |

14 | 26.7 | 3 | 8 | 11.10 | 18.67 | 20.96 | 24.19 | 11.52 | 17.52 | 20.63 | 24.41 |

**Table 6.**Individual and total energy prediction results for wheel rotation, x-infeed, y-infeed, z-infeed, electrical controller, and coolant.

No. | E_{s} (J) | E_{x} (J) | E_{y} (J) | E_{z} (J) | E_{e} (J) | E_{c} (J) | E_{total} (J) |
---|---|---|---|---|---|---|---|

11 | 1104.487 | 1273.128 | 2.256 | 230.544 | 63,206.49 | 8685.792 | 74,502.69 |

12 | 2283.218 | 1273.128 | 2.256 | 230.544 | 63,206.49 | 8685.792 | 75,681.42 |

13 | 3594.717 | 1607.916 | 2.256 | 230.544 | 112,601.6 | 16,245.65 | 134,282.7 |

14 | 1764.019 | 1366.116 | 2.256 | 230.544 | 46,741.446 | 6165.84 | 56,270.221 |

**Table 7.**Individual and total energy prediction results for the wheel spindle in front–back approaching, left–right approaching, cutting-in, cutting-out, stable cutting, and material removal stages.

No. | E_{a1} (J) | E_{a2} (J) | E_{ci} (J) | E_{co} (J) | E_{cu} (J) | E_{sm} (J) | E_{s} (J) |
---|---|---|---|---|---|---|---|

11 | 137.52 | 165.024 | 17.9862 | 17.9862 | 765.9708 | 801.9432 | 1104.4872 |

12 | 372.48 | 446.976 | 37.386 | 37.386 | 1388.9904 | 1463.7624 | 2283.2184 |

13 | 654.24 | 785.088 | 58.95434 | 58.95434 | 2037.4808 | 2155.38948 | 3594.71748 |

14 | 280.32 | 336.384 | 28.8672 | 28.8672 | 1089.5808 | 1147.3152 | 1764.0192 |

No. | E_{mrr} (J) | E_{n-mrr} (J) | E_{total} (J) |
---|---|---|---|

11 | 29,901.564 | 44,601.1292 | 74,502.6932 |

12 | 30,524.5836 | 45,156.8408 | 75,681.4244 |

13 | 59,776.98504 | 74,505.70244 | 134,282.6875 |

14 | 20,808.2168 | 35,462.0044 | 56,270.2212 |

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## Share and Cite

**MDPI and ACS Style**

Tian, Y.; Wang, J.; Hu, X.; Song, X.; Han, J.; Wang, J.
Energy Prediction Models and Distributed Analysis of the Grinding Process of Sustainable Manufacturing. *Micromachines* **2023**, *14*, 1603.
https://doi.org/10.3390/mi14081603

**AMA Style**

Tian Y, Wang J, Hu X, Song X, Han J, Wang J.
Energy Prediction Models and Distributed Analysis of the Grinding Process of Sustainable Manufacturing. *Micromachines*. 2023; 14(8):1603.
https://doi.org/10.3390/mi14081603

**Chicago/Turabian Style**

Tian, Yebing, Jinling Wang, Xintao Hu, Xiaomei Song, Jinguo Han, and Jinhui Wang.
2023. "Energy Prediction Models and Distributed Analysis of the Grinding Process of Sustainable Manufacturing" *Micromachines* 14, no. 8: 1603.
https://doi.org/10.3390/mi14081603