# A Robust Scheduling Framework for Re-Manufacturing Activities of Turbine Blades

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## Abstract

**:**

## 1. Introduction and Industrial Motivation

## 2. Literature Review

## 3. Re-Manufacturing of Turbine Blades

#### 3.1. Re-Manufacturing Processes

- 1.
- Blades are disassembled at the production site and shipped to the OEM to be refurbished/renewed.
- 2.
- Upon arrival at the OEM, blades are inspected to assess the severity of wear and damages. Blades that cannot be repaired are discarded and the supply/production of new blades is issued. On the contrary, for reparable blades, the re-manufacturing process starts, whose process parameters depends on the assessed damage level.
- 3.
- The re-manufacturing process consists of removing the damaged (e.g., cracked) parts of the blades, restore the removed material through welding/additive technologies, machining/grinding the blade to reconstruct the desired shape. During the material removal phase, as well as at the end of the processing, non-destructive tests are operated to verify the complete removal of the defects.
- 4.
- The blades undergo the definition of small-size features (e.g., internal cooling ducts, specific shapes in the terminal side or in the coupling with the rotor) and are successively coated with high-resistance materials.
- 5.
- Finally, the blades belonging to the same stage are assembled together and balanced. Hence they are shipped back to the operating site of the turbine where they will be re-assembled and be ready to go into production again.

#### 3.2. Uncertainty in Re-Manufacturing Processes

- 1.
- A major source of uncertainty is embedded in the characteristics and volumes of the parts to be processed. Used parts arrives from different use-phase conditions and, thus, could be worn differently. Moreover, grounding on their characteristics, the number of parts whose re-manufacturing is feasible or attractive could be different, thus impacting on the actual volumes of parts to be re-manufactured.
- 2.
- The re-manufacturing process plan could vary for different specimens of the same products. Thus, according to the characteristic of the item (wear, presence of damages, etc), different process steps arranged in different sequences could be needed. This impact on the management of the re-manufacturing system due to the need of implementing different routines among the available resources.
- 3.
- Grounding on the characteristics of each specific part, re-manufacturing process can differ in terms of the characteristics and parameters of re-manufacturing operations. This a clear impact on the execution of the processes (forces, velocity, processing times, etc.)

## 4. Robust Scheduling Framework

#### 4.1. Shop Scheduling Model

#### 4.2. Modeling Uncertainty

#### 4.2.1. Uncertainty Affecting Processing Times

- 1.
- The number of blades in a batch depends on their level of damage. Extremely worn blades cannot be refurbished and must be discarded. A rejection rate table based on the damage level of each type of blade is defined. Thus, each batch of blades to be processed is assigned a level of damage (high, medium, low) sampled from a discrete distribution. Hence, the rejection rate is modeled as an uniform distribution defined by a lowest and highest rejection rates for that class of blades.
- 2.
- The processing time of an operation on a single blade is modeled as an interval whose boundaries can be determined grounding on historical data. Thus, the distribution of the processing time of a batch of blades can be obtained through a convolution operation between the distribution of the number of blades in the batch to be re-manufactured and the distribution of the processing time of a single blade.

#### 4.2.2. Uncertainty Affecting the Process Steps

- 1.
- A RCPSP model is defined considering both work and rework activities.
- 2.
- The processing time of rework activities is obtained through the convolution of the occurrence and processing time distributions described above.

#### 4.3. Robustness Measures

#### 4.3.1. Minimizing the Maximum Regret of the Objective Function

#### 4.3.2. Minimizing the Value-at-Risk/Conditional Value-at-Risk of the Objective Function

## 5. Case Study

## 6. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

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**Figure 1.**GE H-series power generation gas turbine [16].

**Figure 2.**New turbine blade [17].

**Figure 3.**Damaged blades resulting from exposure to high temperature and stress [17].

Damage Level | Rejection Rate LB (%) | Rejection Rate UB (%) |
---|---|---|

Heavy | 60 | 90 |

Medium | 30 | 60 |

Light | 0 | 30 |

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Liu, L.; Urgo, M.
A Robust Scheduling Framework for Re-Manufacturing Activities of Turbine Blades. *Appl. Sci.* **2022**, *12*, 3034.
https://doi.org/10.3390/app12063034

**AMA Style**

Liu L, Urgo M.
A Robust Scheduling Framework for Re-Manufacturing Activities of Turbine Blades. *Applied Sciences*. 2022; 12(6):3034.
https://doi.org/10.3390/app12063034

**Chicago/Turabian Style**

Liu, Lei, and Marcello Urgo.
2022. "A Robust Scheduling Framework for Re-Manufacturing Activities of Turbine Blades" *Applied Sciences* 12, no. 6: 3034.
https://doi.org/10.3390/app12063034