# Research on the Design of a Hexagonal Shaft Straightening Machine Based on Quality Function Development and Evidence Theory

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## Abstract

**:**

## 1. Introduction

## 2. The Methods of QFD and Evidence Theory

#### 2.1. QFD Theory

#### 2.2. Evidence Theory and Its Synthesis Rules

- (1)
- Frame of discernment

- (2)
- Basic probability assignment

^{Θ}be the power set of Θ. For any subset A belonging to 2

^{Θ}, the set function $M\left(M:{2}^{\Theta}\to \left[0,1\right]\right)$ satisfies

^{Θ}. M(A) is called the basic credible number of A, which reflects the degree to which proposition An occurs, and set An of all $M\left(A\right)>0$ is called the focal element.

- (3)
- Belief function

- (4)
- Plausibility function

- (5)
- D-S evidence theory synthesis formula

## 3. Construction of House of Quality for Hexagonal Shaft Straightening Machine

#### 3.1. Demand Indicator Identification

#### 3.2. Construction of Relational Matrix

- (1)
- Define the recognition framework: four experts evaluate the degree of correlation, and all possible values are strong correlation, relatively strong correlation, medium correlation, weak correlation, and irrelevant. The value range was [0, 1] in a quantitative way, named: {irrelevant, weak correlation, medium correlation, strong correlation, strong correlation}→{0, 0.25, 0.50, 0.75, 1}.
- (2)
- Based on the original composition rules, let the conflict coefficient be:

#### 3.3. Competitive Evaluation and Weight Calculation Method

#### 3.4. Design of House of Quality

- (1)
- According to the user competitiveness evaluation of the right wall of the quality house, users pay more attention to the requirements of straightening results, speed, automation and cost, and the relative weight accounts for more than 50%. Moreover, the level improvement rate and product characteristic value of these demand indicators are relatively high, which is consistent with the survey of demand importance. Combined with the current research technology level, it is difficult to meet the goals of fast straightening efficiency, up to standard results, automation and low cost. Therefore, this product needs to strengthen its market competitiveness on relevant demand indicators, focus on the market, and pay attention to the problem of meeting multiple demand indicators.
- (2)
- Through the competitive evaluation and analysis of technical indicators, the scores of technical indicators “automation” and “cost” are higher, which is consistent with the high proportion of relative weights of demand indicators “high degree of automation” and “low cost”. Second, from the autocorrelation matrix, the cost is almost related to all the demand indicators of the straightening machine, and this technical characteristic should be considered emphatically in the design process of the straightening machine. From the weight of technical indicators, “automation” and “cost” also have a relatively high weight proportion, and the high proportion of straightening results, detection accuracy and straightening times reflects the importance of hexagonal shaft straightening effect and efficiency. For technical indicators with low scores for this product, measures should be taken to improve and enhance the market competitiveness.
- (3)
- From the correlation weight matrix, there are many correlations between the “straightening result reaches standard,” “fast straightening speed,” and “low cost” and the technical indicators, which are consistent with the above analysis results. The research results show that the fusion of expert opinion consistency evaluation results is accurate and effective, which also shows that the demand indicator has a higher share in the market competitiveness analysis, and the straightening of shaft parts tends to develop in the direction of effect, efficiency and high cost performance of straightening equipment.

## 4. Trial Results and Discussion

#### 4.1. Design Implementation

- (1)
- Detection accuracy

- (2)
- Pressing accuracy

- (3)
- Automation, man-machine interaction

#### 4.2. Discussion of the Results

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

- Wang, X.H.; Yang, J.Y.; Song, H.Y.; Xu, H. The Process Research and Analysis of House of Quality in Conceptual Design of Railway Vehicle. Comput. Integr. Manuf. Syst.
**2020**, 37, 113–117. [Google Scholar] - Gotzamani, K.; Georgiou, A.; Andronikidi, A.; Kamvysi, K.; Ton, V. Introducing multivariate Markov modeling within QFD to anticipate future customer preferences in product design. Int. J. Qual. Reliab. Manag.
**2018**, 35, 762–778. [Google Scholar] [CrossRef] - Sivasamy, K.; Arumugam, C.; Devadasan, S.R.; Murugesh, R.; Venkatachalam, S.; Thilak, V. Prevention of water leakage in the shallow well jet pump through the application of total quality function deployment technique. Int. J. Bus. Innov. Res.
**2018**, 15, 381–402. [Google Scholar] [CrossRef] - Haber, N.; Fargnoli, M.; Sakao, T. Integrating QFD for product-service systems with the Kano model and fuzzy AHP. Total Qual. Manag. Bus. Excell.
**2020**, 31, 929–954. [Google Scholar] [CrossRef] - Efe, B. Analysis of operational safety risks in shipbuilding using failure mode and effect analysis approach. Ocean Eng.
**2019**, 187, 106214.1–106214.9. [Google Scholar] [CrossRef] - Gündoğdu, F.K.; Kahraman, C. A novel spherical fuzzy QFD method and its application to the linear delta robot technology development. Eng. Appl. Artif. Intell.
**2020**, 87, 103348. [Google Scholar] [CrossRef] - Neira-Rodado, D.; Ortíz-Barrios, M.; Hoz-Escorcia, S.; Paggetti, C.; Fratea, N. Smart Product Design Process through the Implementation of a Fuzzy Kano-AHP-DEMATEL-QFD Approach. Appl. Sci.
**2020**, 10, 1792. [Google Scholar] [CrossRef] [Green Version] - Mistarihi, M.Z.; Okour, R.A.; Mumani, A.A. An integration of a QFD model with Fuzzy-ANP approach for determining the importance weights for engineering characteristics of the proposed wheelchair design. Appl. Soft Comput. J.
**2020**, 90, 106136. [Google Scholar] [CrossRef] - Liu, X.; Gong, M.; Zhou, Z.H.; Li, B.T.; Dong, J.Y. An Efficient Mechanical Structure Reliability Analysis Method based on Evidence Theory. China Mech. Eng.
**2020**, 31, 2031–2037. [Google Scholar] - Cui, Q.; Li, Y.L.; Li, Z.H. Transformer State Assessment Based on Evidence Synthesis and Cloud Model. Electrotech. Electr.
**2019**, 12–16, 51. [Google Scholar] - Zhang, L.Z.; Jing, L.Y.; Xu, W.X.; Tan, J.W. A Composite Fault Diagnosis Method of Gearbox Combining with Convolution Neural Network and D-S Evidence Theory. Mech. Sci. Technol. Aerosp. Eng.
**2019**, 38, 1582–1588. [Google Scholar] - Roy, D.K.; Datta, B. Saltwater intrusion prediction in coastal aquifers utilizing a weighted-average heterogeneous ensemble of prediction models based on Dempster-Shafer theory of evidence. Hydrol. Sci. J.
**2020**, 65, 1555–1567. [Google Scholar] [CrossRef] - Cheng, J.T.; Xiong, Y.; Ai, L. Fault Diagnosis of Wind Turbine Gearbox Based on Neighborhood QPSO and Improved D-S Evidence Theory. Recent Pat. Comput. Sci.
**2020**, 13, 248–255. [Google Scholar] [CrossRef] - Sarabi-Jamab, A.; Araabi, B.N. An information-based approach to handle various types of uncertainty in fuzzy bodies of evidence. PLoS ONE
**2020**, 15, e0227495. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Behrouz, M.; Alimohammadi, S. Uncertainty Analysis of Flood Control Measures Including Epistemic and Aleatory Uncertainties: Probability Theory and Evidence Theory. J. Hydrol. Eng.
**2018**, 23, 04018033.1–04018033.15. [Google Scholar] [CrossRef] - Violante, M.G.; Vezzetti, E. Kano qualitative vs. Quantitative approaches: An assessment framework for products attributes analysis. Comput. Ind.
**2017**, 86, 15–25. [Google Scholar] [CrossRef] - Dewi, D.; Rahaju, D. An Integrated QFD and Kano’s Model to Determine the Optimal Target Specification. In Proceedings of the International Conference on Industrial Engineering IEEE, Jeju, Korea, 23–26 May 2016; pp. 1–5. [Google Scholar]
- Xiong, W. Quality Function Deployment Theory and Method; Science Press: Beijing, China, 2016. [Google Scholar]
- Elleuch, H.; Dafaoui, E.; Mhamedi, A.E.; Chabchoub, H. A Quality Function Deployment approach for Production Resilience improvement in Supply Chain: Case of Agrifood Industry. IFAC Pap.
**2016**, 49, 125–130. [Google Scholar] [CrossRef] - Shafer, G. A Mathematical Theory of Evidence; Princeton University Press: Princeton, NJ, USA, 1976. [Google Scholar]
- Aminravan, F.; Sadiq, R.; Hoorfar, M.; Rodriguez, M.J.; Francisque, A.; Najjaran, H. Evidential Reasoning Using Extended Fuzzy Dempster-Shafer Theory for Handling Various Facets of Information Deficiency. Int. J. Intell. Syst.
**2011**, 26, 731–758. [Google Scholar] [CrossRef] - Wang, X.Y.; Fan, D.W.; Li, J. Application of KANO Model in Smart Pots Design. Mach. Des. Manuf.
**2017**, 36, 46–48. [Google Scholar] - Zhou, J.; Yu, Z.H.; Hou, Z. Fuzzy cognitive maps and evidence theory based research on quality control decision-making mode. Syst. Eng. Theory Pract.
**2016**, 36, 1288–1296. [Google Scholar]

**Figure 4.**Schematic diagram of house quality in overall planning of hexagonal shaft straightening machi.

User Demand | Reverse Problem | ||||
---|---|---|---|---|---|

Satisfaction | As It Should | It Does Not Matter | Acceptable | Dissatisfied | |

Satisfaction | Q | A | A | A | O |

As it should | R | I | I | I | M |

It does not matter | R | I | I | I | M |

Acceptable | R | I | I | I | M |

Dissatisfied | R | R | R | R | Q |

Item | Number | Demand Indicator | Demand Type | Importance |
---|---|---|---|---|

Straightening effect Ontology performance | A1 | Straightening results meet the standard | M | 9 |

A2 | Many applicable specifications | O | 7 | |

A3 | Fast straightening speed | O | 8 | |

A4 | Small processing damage | M | 6 | |

A5 | High degree of automation | O | 8 | |

A6 | Easy to use | O | 7 | |

A7 | Convenient supervision | O | 7 | |

A8 | Safe and reliable | A | 8 | |

A9 | Long lasting | A | 6 | |

A10 | Low cost | A | 6 | |

A11 | Easy to maintain | A | 5 |

Indicator Number | Technical Indicator Matrix |
---|---|

Y_{1} | Straightening results |

Y_{2} | Detection accuracy |

Y_{3} | Straightening times |

Y_{4} | Straightening range |

Y_{5} | Loading capacity |

Y_{6} | Downforce stroke |

Y_{7} | Downforce precision |

Y_{8} | Automation |

Y_{9} | Human-machine interaction |

Y_{10} | Safety |

Y_{11} | Service life |

Y_{12} | Failure rate |

Y_{13} | Cost |

Y_{1} | Y_{2} | Y_{3} | Y_{4} | Y_{5} | Y_{6} | Y_{7} | Y_{8} | Y_{9} | Y_{10} | Y_{11} | Y_{12} | Y_{13} | |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|

Y_{1} | ◯ | ▲ | ⚫ | △ | |||||||||

Y_{2} | ▲ | ||||||||||||

Y_{3} | ⚫ | ▲ | △ | ||||||||||

Y_{4} | ⚫ | ⚫ | △ | ||||||||||

Y_{5} | ◯ | ⚫ | ◯ | △ | |||||||||

Y_{6} | △ | ||||||||||||

Y_{7} | ▲ | ||||||||||||

Y_{8} | ⚫ | ◯ | ▲ | ||||||||||

Y_{9} | ◯ | △ | |||||||||||

Y_{10} | △ | △ | |||||||||||

Y_{11} | ⚫ | ▲ | |||||||||||

Y_{12} | △ | ||||||||||||

Y_{13} |

**Table 5.**Calculation results of the membership strength relationship between “straightening result reaching the standard” and “straightening effect.”

State | 0 | 0.25 | 0.50 | 0.75 | 1 |

Expert 1 | 0 | 0 | 0 | 0.13 | 0.87 |

Expert 2 | 0 | 0 | 0 | 0.36 | 0.64 |

Expert 3 | 0 | 0 | 0 | 0.29 | 0.71 |

Expert 4 | 0 | 0 | 0 | 0.15 | 0.85 |

State | 0 | 0.25 | 0.50 | 0.75 | 1 |

Expert 1 | 0 | 0 | 0 | 0.13 | 0.87 |

Expert 2 | 0 | 0 | 0 | 0.36 | 0.64 |

Synthesis result 1 | 0 | 0 | 0 | 0.078 | 0.922 |

State | 0 | 0.25 | 0.50 | 0.75 | 1 |

Synthesis result 1 | 0 | 0 | 0 | 0.078 | 0.922 |

Expert 3 | 0 | 0 | 0 | 0.29 | 0.71 |

Synthesis result 2 | 0 | 0 | 0 | 0.033 | 0.967 |

State | 0 | 0.25 | 0.50 | 0.75 | 1 |

Synthesis result 2 | 0 | 0 | 0 | 0.033 | 0.967 |

Expert 4 | 0 | 0 | 0 | 0.15 | 0.85 |

Synthesis result 3 | 0 | 0 | 0 | 0.006 | 0.994 |

Demand Indicator | Current Levels | Target Value | Improvement Rate | Product Characteristic Value | Absolute Weight | Relative Weight |
---|---|---|---|---|---|---|

Straightening result reaches standard | 3 | 4 | 1.33 | 1.2 | 14.36 | 10.18% |

Many applicable specifications | 4 | 4 | 1 | 1.0 | 7 | 4.96% |

Fast straightening speed | 2 | 4 | 2 | 1.5 | 24 | 17.02% |

Small processing damage | 4 | 4 | 1 | 1.0 | 6 | 4.26% |

High degree of automation | 2 | 4 | 2 | 1.5 | 24 | 17.02% |

Simple operation | 3 | 4 | 1.33 | 1.2 | 11.17 | 7.92% |

Convenient supervision | 4 | 5 | 1.25 | 1.2 | 10.50 | 7.45% |

Safe and reliable | 4 | 5 | 1.25 | 1.2 | 12 | 8.51% |

Long service life | 3 | 3 | 1 | 1.0 | 6 | 4.26% |

Low cost | 2 | 4 | 2 | 1.5 | 18 | 12.77% |

Convenient maintenance | 3 | 4 | 1.33 | 1.2 | 7.98 | 5.65% |

Technical Indicators | Competitive Evaluation | Absolute Weight | Relative Weight |
---|---|---|---|

Straightening results | 4 | 39.84 | 11.54% |

Detection accuracy | 4 | 36.73 | 10.64% |

Straightening times | 3 | 38.32 | 11.10% |

Straightening range | 4 | 4.95 | 1.43% |

Loading capacity | 3 | 10.20 | 2.95% |

Downforce stroke | 3 | 8.02 | 2.32% |

Downforce precision | 3 | 32.59 | 9.44% |

Automation | 5 | 46.75 | 13.54% |

Human-machine interaction | 4 | 42.48 | 12.30% |

Safety | 2 | 14.24 | 4.12% |

Service life | 4 | 10.65 | 3.08% |

Failure rate | 4 | 13.08 | 3.79% |

Cost | 5 | 47.38 | 13.72% |

Number | Measurement Results of Straightening Machine (mm) | Measuring Results of CMM (mm) | Deviation Values (mm) |
---|---|---|---|

1 | 0.1857 | 0.1954 | −0.0097 |

2 | 0.1964 | 0.1940 | +0.0024 |

3 | 0.1632 | 0.1551 | +0.0081 |

4 | 0.1843 | 0.1855 | −0.0012 |

5 | 0.1894 | 0.1819 | +0.0075 |

6 | 0.1745 | 0.1760 | −0.0015 |

7 | 0.1610 | 0.1635 | −0.0025 |

8 | 0.1762 | 0.1785 | −0.0059 |

9 | 0.1968 | 0.1878 | +0.0090 |

10 | 0.1659 | 0.1707 | −0.0048 |

The First Straightness Test (mm) | Straightness after Straightening (mm) | Theoretical Straightening Times | Actual Straightening Times |
---|---|---|---|

2.09 | 0.15 | ≤4 | 4 |

0.94 | 0.12 | ≤3 | 3 |

1.68 | 0.11 | ≤4 | 3 |

1.39 | 0.08 | ≤3 | 4 |

1.72 | 0.18 | ≤4 | 3 |

0.99 | 0.11 | ≤3 | 2 |

2.13 | 0.17 | ≤4 | 7 |

1.12 | 0.09 | ≤3 | 3 |

2.21 | 0.13 | ≤4 | 5 |

1.87 | 0.08 | ≤3 | 4 |

Technical Indicators | Master Plan Target Value | Actual Satisfaction Condition |
---|---|---|

Straightening results | Straightness error is controlled within ±0.2 mm | The average straightness error after straightening is 0.122 mm |

Detection accuracy | Detection error is controlled within ±0.01 mm | The average straightness detection error is −0.00014 mm |

Straightening times | No more than four single roots | The average number of straightening is about four |

Straightening range | The length of hexagonal shaft is 500~1200 mm | The hexagonal shafts of 500 mm and 1200 mm were tested respectively |

Loading capacity | Maximum load 12 KN | Maximum load 12 KN |

Downforce stroke | Maximum stroke 80 mm | Maximum stroke 80 mm |

Downforce precision | The position error is controlled within ±0.01 mm | The position error is controlled within ±0.01 mm |

Automation | Realizing automatic feeding, straightening and sorting | It can automatically detect straightness and straighten test |

Human-machine interaction | Rich functions and simple operation | The detection process can be monitored in real time through the state monitoring interface |

Safety | It has alarm and error-proof function | It can automatically track the abnormal operation events in the process of detection, alarm and protective protection can be carried out |

Cost | Less than 180,000 RMB | The straightening machine costs about 50,000 RMB |

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## Share and Cite

**MDPI and ACS Style**

Zhou, J.; Huang, Y.; Yu, Z.
Research on the Design of a Hexagonal Shaft Straightening Machine Based on Quality Function Development and Evidence Theory. *Symmetry* **2021**, *13*, 707.
https://doi.org/10.3390/sym13040707

**AMA Style**

Zhou J, Huang Y, Yu Z.
Research on the Design of a Hexagonal Shaft Straightening Machine Based on Quality Function Development and Evidence Theory. *Symmetry*. 2021; 13(4):707.
https://doi.org/10.3390/sym13040707

**Chicago/Turabian Style**

Zhou, Juan, Yuhang Huang, and Zhonghua Yu.
2021. "Research on the Design of a Hexagonal Shaft Straightening Machine Based on Quality Function Development and Evidence Theory" *Symmetry* 13, no. 4: 707.
https://doi.org/10.3390/sym13040707