# Optimal Parameter Selection in Robotic Belt Polishing for Aeroengine Blade Based on GRA-RSM Method

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## Abstract

**:**

## 1. Introduction

## 2. Experiment Procedure

#### 2.1. Experimental Design

_{f}determines the contact time between the belt and the workpiece. The amount of compression a

_{p}causes the contact wheel to be crushed and deformed, and the belt has a change in the normal force of the workpiece. Therefore, the cutting state of the abrasive grains is greatly affected by the amount of compression, a

_{p}. The belt line speed v

_{s}determines the number of abrasive cuts involved in the polishing process. Therefore, the main influencing parameters in aeroengine blade polishing include feed rate v

_{f}, compression amount, and belt line speed v

_{s}. In order to investigate the relationship between the polishing process parameters and MRR and SR, the main influencing factors and parameter levels were selected, as shown in Table 1.

#### 2.2. Experimental Materials and Experimental Preparation

#### 2.3. Measurement Methods

^{2}/min), v

_{f}is the feed rate, ∆h is the blade thickness variation (mm), P is the programmed track pitch (mm), n is the number of polishing times, and B is the belt width (mm).

## 3. Multiobjective Optimization Method

_{i}and Zw

_{i}are the values of SR and MRR for the i-th test, respectively.

_{0i}(k) is the corresponding deviation sequence for the reference sequence ${x}_{0}^{*}$(k) and the compared sequence ${x}_{i}^{*}$(k), namely Δ

_{0i}(k) =|${x}_{0}^{*}$(k) − ${x}_{i}^{*}$(k)|, Δ

_{max}= $\stackrel{max}{i}$ $\stackrel{max}{j}$ Δ

_{0i}(k), Δ

_{min}= $\stackrel{min}{i}$ $\stackrel{min}{j}$ Δ

_{0i}(k), and λ is the resolution coefficient, λ ∈ [0,1].

_{k}is the weight factor of the k-th response variable, and is derived from the results of the principal component analysis in Step 4.

## 4. Results and Discussion

#### 4.1. Effect of Polishing Parameters on a Single Response Variable

_{s}was the main process parameter affecting SR, followed by the amount of compression a

_{p}; the feed rate v

_{f}had little effect on SR. The amount of compression a

_{p}was the main process parameter affecting the MRR, followed by the belt line speed v

_{s}. The feed rate v

_{f}had the same effect on the MRR. The main reason for the small influence of the feed rate v

_{f}on SR and MRR was that the feed rate v

_{f}was sufficiently small relative to the belt line speed v

_{s}, so the change in feed rate v

_{f}had little effect on the speed of the synthesis of the abrasive particles involved in polishing.

#### 4.2. Gray Correlation Analysis

_{0i}(k), the deviation sequence, was calculated according to Step 3. Then the gray relation coefficient was determined by Equation (5), wherein the resolution coefficient λ was set to 0.5. The results are presented in Table 5.

_{k}of each response variable. Principal component analysis was used in this study to determine the weight of SR and MRR [16]. As listed in Table 6, SR is the priority principal component, followed by MRR. The corresponding contribution rates were 54.6% and 45.4%, respectively. Therefore, the weight values β

_{1}and β

_{2}were 0.546 and 0.454. The gray correlation degree was calculated by Equation (6). Table 5 converts multiple responses to a single goal. The larger the GRG, the closer the value to the desired quality characteristic value. Figure 5 shows the value of GRG, and the maximum value (0.7014) was found in the 11th experiment. The results show that in 15 tests, the combination of a feed rate of 200 mm/min, a compression of 0.08 mm, and a belt line speed of 16 m/s achieved the best multiresponse characteristics. A minimum was found in the fifth experiment. This indicates that the worst parametric combination condition was a feed rate of 100 mm/min, a compression of 0.05 mm, and a spindle speed of 8 m/s.

#### 4.3. Model Establishment

^{−3}v

_{f}− 1.12643 a

_{p}− 2.93385 × 10

^{−3}v

_{s}+ 4.6518 × 10

^{−3}v

_{f}× a

_{p}

− 3.05046 × 10

^{−5}v

_{f}× v

_{s}+ 5.42413 × 10

^{−5}a

_{p}× v

_{s}− 3.62566×10

^{−6}v

_{f}

^{2}+ 15.99582 a

_{p}

^{2}

+ 1.85397 × 10

^{−3}v

_{s}

^{2}

#### 4.4. Optimal Gray Correlation Prediction

_{f}was 232.09 mm/min, the compression amount a

_{p}was 0.08 mm, and the belt line speed v

_{s}was 16 m/s. Meanwhile, the corresponding optimal solution of the gray correlation degree was GRG = 0.784105.

#### 4.5. Verification

## 5. Conclusions

- In the robotic belt polishing for aeroengine blades, the main parameters influencing the aeroengine blade polishing include feed rate v
_{f}, compression amount a_{p}, and belt line speed v_{s}. The belt line speed v_{s}is the main process parameter affecting material removal rates and surface roughness. - The results of principal component analysis show that surface roughness is the priority principal component, then followed by material removal rate. The corresponding contribution rates were 54.6% and 45.4%, respectively. The proposed GRA-RSM method can effectively predict the optimal setting of process parameters in the robotic belt polishing for aeroengine blades, then achieving the important aim of reducing the surface roughness, and improving the material removal rate simultaneously.
- For the maximum grey correlation grade, which increased by 10.96%, the optimum polishing parameter combination was selected as follows: the feed rate v
_{f}is 232.09 mm/min, the compression amount a_{p}is 0.08 mm, and the belt line speed v_{s}is 16m/s. Finally, the surface roughness was reduced by 6.29%, and the material removal rate was increased by 16.11%.

## Author Contributions

## Funding

## Conflicts of Interest

## References

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Experimental Parameters | Symbol | Units | Levels of Experimental Parameters | ||
---|---|---|---|---|---|

Level 1 | Level 2 | Level 3 | |||

Feed rate | v_{f} | mm/min | 100 | 200 | 300 |

Compression | a_{p} | mm | 0.02 | 0.05 | 0.08 |

Belt line speed | v_{s} | m/s | 8 | 12 | 16 |

Number | Experiment Parameters | SR | MRR | ||||
---|---|---|---|---|---|---|---|

v_{f} | a_{p} | v_{s} | Ra (μm) | S/N | Zw (mm²/min) | S/N | |

1 | 200 | 0.02 | 8 | 0.415 | 7.6390 | 0.0123 | −38.2019 |

2 | 100 | 0.08 | 12 | 0.448 | 6.9744 | 0.0374 | −28.5426 |

3 | 200 | 0.08 | 8 | 0.527 | 5.5638 | 0.0428 | −27.3711 |

4 | 200 | 0.05 | 12 | 0.383 | 8.3360 | 0.0337 | −29.4474 |

5 | 100 | 0.05 | 8 | 0.558 | 5.0673 | 0.0181 | −34.8464 |

6 | 300 | 0.05 | 8 | 0.543 | 5.3040 | 0.0262 | −31.6340 |

7 | 200 | 0.05 | 12 | 0.407 | 7.8081 | 0.0351 | −29.0939 |

8 | 100 | 0.02 | 12 | 0.413 | 7.6810 | 0.0234 | −32.6157 |

9 | 300 | 0.05 | 16 | 0.394 | 8.0901 | 0.0574 | −24.8218 |

10 | 200 | 0.02 | 16 | 0.311 | 10.1448 | 0.0193 | −34.2889 |

11 | 200 | 0.08 | 16 | 0.413 | 7.6810 | 0.0701 | −23.0856 |

12 | 100 | 0.05 | 16 | 0.347 | 9.1934 | 0.0457 | −26.8017 |

13 | 300 | 0.08 | 12 | 0.476 | 6.4479 | 0.0547 | −25.2403 |

14 | 300 | 0.02 | 12 | 0.403 | 7.8939 | 0.0281 | −31.0259 |

15 | 200 | 0.05 | 12 | 0.421 | 7.5144 | 0.0381 | −28.3815 |

Chemical Composition | Al | V | Fe | Si | C | N | H | O | Other |
---|---|---|---|---|---|---|---|---|---|

% | 5.5–6.8 | 3.5–4.5 | ≤0.30 | ≤0.15 | ≤0.10 | ≤0.05 | ≤0.01 | ≤0.20 | 0.11 |

Source | Process Parameters | ||
---|---|---|---|

v_{f} | a_{p} | v_{s} | |

SR | |||

Level 1 | 7.2290 | 8.3397 | 5.8935 |

Level 2 | 7.8124 | 7.3305 | 7.5222 |

Level 3 | 6.9340 | 6.6668 | 8.7773 |

Max-min | 0.8785 | 1.6729 | 2.8838 |

Rank | 3 | 2 | 1 |

Optimal level | A2 | B1 | C3 |

MRR | |||

Level 1 | −30.7016 | −34.0331 | −33.0134 |

Level 2 | −29.9815 | −29.2895 | −29.1924 |

Level 3 | −28.1805 | −26.0599 | −27.2495 |

Max-min | 2.5211 | 7.9732 | 5.7639 |

Rank | 3 | 1 | 2 |

Optimal level | A3 | B3 | C3 |

Number | Deviation Sequence Δ0i | Gray Relational Coefficients | Gray Relational Grades | ||
---|---|---|---|---|---|

SR | MRR | SR | MRR | ||

1 | 0.4935 | 1.0000 | 0.5033 | 0.3333 | 0.4105 |

2 | 0.6244 | 0.3610 | 0.4447 | 0.5807 | 0.5190 |

3 | 0.9022 | 0.2835 | 0.3566 | 0.6382 | 0.5103 |

4 | 0.3562 | 0.4209 | 0.5840 | 0.5430 | 0.5616 |

5 | 1.0000 | 0.7780 | 0.3333 | 0.3912 | 0.3649 |

6 | 0.9534 | 0.5655 | 0.3440 | 0.4693 | 0.4124 |

7 | 0.4602 | 0.3975 | 0.5207 | 0.5571 | 0.5406 |

8 | 0.4852 | 0.6304 | 0.5075 | 0.4423 | 0.4719 |

9 | 0.4047 | 0.1149 | 0.5527 | 0.8132 | 0.6949 |

10 | 0.0000 | 0.7411 | 1.0000 | 0.4029 | 0.6740 |

11 | 0.4852 | 0.0000 | 0.5075 | 1.0000 | 0.7014 |

12 | 0.1874 | 0.2458 | 0.7274 | 0.6704 | 0.6963 |

13 | 0.7281 | 0.1425 | 0.4071 | 0.7782 | 0.6097 |

14 | 0.4433 | 0.5253 | 0.5300 | 0.4877 | 0.5069 |

15 | 0.5181 | 0.3503 | 0.4911 | 0.5880 | 0.5440 |

Principal Component | Eigenvalue | Contribution |
---|---|---|

SR | 1.0924 | 54.6% |

MRR | 0.90476 | 45.4% |

Total | 100% |

Initial Factor Setting | Optimal Process Condition | Improvement | ||
---|---|---|---|---|

Prediction | Validation | |||

v_{f} | 200 mm/min | 232.09 mm/min | 232.09 mm/min | |

a_{p} | 0.08 mm | 0.08 mm | 0.08 mm | |

v_{s} | 16 m/s | 16 m/s | 16 m/s | |

SR | 0.413 μm | 0.387 μm | 6.29% | |

MRR | 0.0701 mm²/min | 0.0814 mm²/min | 16.11% | |

GRG | 0.7014 | 0.7841 | 0.7783 | 10.96% |

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**MDPI and ACS Style**

Guo, J.; Shi, Y.; Chen, Z.; Yu, T.; Zhao, P.; Shirinzadeh, B.
Optimal Parameter Selection in Robotic Belt Polishing for Aeroengine Blade Based on GRA-RSM Method. *Symmetry* **2019**, *11*, 1526.
https://doi.org/10.3390/sym11121526

**AMA Style**

Guo J, Shi Y, Chen Z, Yu T, Zhao P, Shirinzadeh B.
Optimal Parameter Selection in Robotic Belt Polishing for Aeroengine Blade Based on GRA-RSM Method. *Symmetry*. 2019; 11(12):1526.
https://doi.org/10.3390/sym11121526

**Chicago/Turabian Style**

Guo, Jian, Yaoyao Shi, Zhen Chen, Tao Yu, Pan Zhao, and Bijan Shirinzadeh.
2019. "Optimal Parameter Selection in Robotic Belt Polishing for Aeroengine Blade Based on GRA-RSM Method" *Symmetry* 11, no. 12: 1526.
https://doi.org/10.3390/sym11121526