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In this article, an effective multiobjective optimization approach is exploited to search for the best milling parameters for CNC for complex 3d surfaces of SIMOLD 2083 alloy mold core. To improve the quality responses, the cutting factors are optimized by a combination of Taguchi method (TM), response surface method (RSM), and multiobjective water cycle algorithm (MWCA). Firstly, the design for initial series experiments of the cutting factors was generated via the TM. Thereafter, the regression models between the cutting factors and the surface roughness of the machined workpiece surface as well as milling time are formed via applying the RSM. Moreover, analysis of variance and sensitivity analysis are also executed to define the influences and crucial contributions of cutting parameters on the surface roughness and milling time. The results of analysis of variance showed that the factors which have main effects on surface roughness were spindle speed (42.42%), feed rate (29.40%), and cutting depth (6.59%), respectively. Meanwhile, the feed rate with the influence of 92.6% was the most significant factor in controlling the milling time. Ultimately, based on mathematical models, the MWCA is performed to define the optimal factors. The optimal results indicated that the optimized surface roughness was about 0.260

Currently, SIMOLD 2083 alloy is well known as material with excellent mechanical characteristics such as extreme erosion resistance and self-hardening in high temperature and friction, so it is extensively utilized in the molding industries for food field. For more specifics, this material can be hardened by itself in the operating process when the working environment has friction and high temperature, so it is very appropriate for injection molding. Another benefit of SIMOLD 2083 alloy is of the stainless steel group; it is also suitable for making the molding cavities and cores for plastic products used in the food area. Meanwhile, the fabrication process of SIMOLD 2083 alloy with complex 3D surfaces meets several struggles for achieving small surface roughness and high productivity because of detrimental machining conditions. Therefore, in order to obtain the beneficial surface quality as well as ensure machining productivity, the cutting parameters should be chosen in a suitable range and be optimized to gain the optimal milling conditions. There are various parameters such as the cutting parameters and chemical composition of workpiece and tool affecting the quality characteristics of the milled components. In addition, surface roughness is one of the most characteristics of the milling parts. In this research, so as to guarantee the quality and productivity of machining part with the complex milling surfaces, the surface roughness and milling time were considered. Consequently, so as to achieve better surface finish of a milled product and ensure the productivity, the cutting parameters were regarded for multiobjective optimization problem.

In general, the surface roughness and milling time are the significant characteristics. However, two characteristics are wriggled together. Therefore, in order to equalize and obtain the requirements of a small roughness surface and low milling time, concurrently, the hybrid approach is proposed for performing the multiobjective optimization problem. In addition, the key cutting factors were optimized for gaining the above-mentioned requirements.

Generally, the Taguchi method (TM) is extensively utilized in optimal analysis engineering for creating the minimized initial data [

This paper proposes an effectual optimization approach for the cutting factors of mold core with complex 3D surfaces applied for the small ice cube mold. So as to resolve the optimization, a combination method of the TM, RSM, and MWCA is developed.

In this research, the milled component with complex milling surfaces should fulfill the following requirements: (i) the surface roughness (_{1}) should be as small as possible to assure the quality of the milling inclined surface and (ii) the small milling time (_{2}) to enhance the machining productivity. A combination method of the TM, the RSM, and the MWCA is grown for balance among them as well as advance of the superiority responses. The optimal issue for the milled component is expressed in the following form.

Find the design variables:

Minimize the _{1}(

Minimize the _{2}(

Subject to constraints:_{1} and _{2} are the quality responses.

To ensure the complex 3D surface machining quality and milling productivity, the surface roughness and the machining time should be selected as small as possible.

Based on the technical requirements and milling productivity, the value of surface roughness was proposed for being lower 0.4 (

Equation (_{1} = 12,

The composition of workpiece material.

C | Si | Mn | Cr | S | |
---|---|---|---|---|---|

0.36 – 0.42 | Max. 1.0 | Max. 1.0 | 12.50 – 14.50 | Max. 0.025 | Max. 0.005 |

Basic geometric dimensions of ball mill.

An integration approach is developed for investigating the impacts of the cutting factors for the milled component on multicriteria output characteristics and detecting the optimized factors for the proposed milled component.

Initially, the TM was exploited for identifying an orthogonal array to form an initial experiment plan. Furthermore, analysis of variance (ANOVA) was exploited to identify the important ratio impact of each cutting factor on the quality characteristics.

Subsequently, the relationships between the cutting factors and the quality characteristics are established by the RSM. A full quadratic formulation is a fitting type for the milled component as the following equation:_{i} (_{ij} (_{1}, _{2},…,_{n} is a set of _{j}, and

According to the established regression equations, the optimal procedure was performed by MWCA algorithm. The MWCA has been extensively exploited [

Ultimately, according to the regression equations, the MWCA was utilized to seek the optimization parameters. The MWCA was utilized for solving multicriteria optimization issue due to its great power for finding optimal resolutions close to the universal finest proficiently. The programing of MWCA algorithm was conducted via MATLAB 2017. Flowchart and plan of fabricating factors optimization via hybrid approach are suggested, as in Figure

Flowchart and plan of fabricating factors optimization via hybrid approach.

Every factor could be segregated for three grades based on professional knowledge and machining experiences, as indicated in Table _{9} orthogonal array was adopted for forming the initial experiment strategy.

Input cutting factors and their grades.

Factors | Range | Lower grade | Average grade | Upper grade | Unit |
---|---|---|---|---|---|

3179–6309 | 3179 | 4609 | 6309 | rpm | |

636–1206 | 636 | 831 | 1206 | (mm/min) | |

0.03–0.3 | 0.03 | 0.165 | 0.3 | (mm) |

First of all, the 3D model of the small ice cube mold was designed by Creo software, as illustrated in Figure ^{2}.

A 3D design drawing of the small ice cube mold of (a) assembly drawing and (b) exploded drawing.

The yellow milled surfaces of the mold core with square of 420.101 mm^{2}.

Secondly, the nine fabricated experimental models were fabricated according to proposed the number of experiments, as depicted in Figure _{1}) was assessed by a Mitutoyo SJ-210 surface roughness tester (Japan), as illustrated in Figure _{2}) and that recorded by CNC machine, respectively. Therefore, the experimental results are shown in Table

The nine milled experimental models.

Fixture for measuring surface roughness of milled components by surface roughness tester, namely, Mitutoyo SJ-210.

Experimental results.

No. | _{1} ( | _{2} (s) | |||
---|---|---|---|---|---|

1 | 3179 | 636 | 0.3 | 0.506 | 1081 |

2 | 3179 | 831 | 0.165 | 0.416 | 1043 |

3 | 3179 | 1206 | 0.03 | 0.96 | 1016 |

4 | 4609 | 636 | 0.165 | 0.273 | 1080 |

5 | 4609 | 831 | 0.03 | 0.423 | 1043 |

6 | 4609 | 1206 | 0.3 | 0.549 | 1016 |

7 | 6309 | 636 | 0.03 | 0.308 | 1081 |

8 | 6309 | 831 | 0.3 | 0.248 | 1043 |

9 | 6309 | 1206 | 0.165 | 0.332 | 1016 |

Thirdly, according to the experiment outcomes in Table

The mathematical models could be gained in form of

Tables

ANOVA analysis for roughness surface.

Source | DF | Seq SS | Influence (%) | Adj SS | Adj MS | |
---|---|---|---|---|---|---|

Model | 8 | 0.381007 | 100.00 | 0.381007 | 0.047626 | Considerable |

Linear | 3 | 0.298732 | 78.41 | 0.215692 | 0.071897 | Considerable |

S | 1 | 0.161615 | 42.42 | 0.158897 | 0.158897 | Considerable |

F | 1 | 0.112027 | 29.40 | 0.026421 | 0.026421 | Considerable |

t | 1 | 0.025091 | 6.59 | 0.012160 | 0.012160 | Considerable |

Square | 3 | 0.072074 | 18.92 | 0.046166 | 0.015389 | Considerable |

S | 1 | 0.007413 | 1.95 | 0.007413 | 0.007413 | Considerable |

F | 1 | 0.014310 | 3.76 | 0.019953 | 0.019953 | Considerable |

t | 1 | 0.050350 | 13.22 | 0.027617 | 0.027617 | Considerable |

2-Way interaction | 2 | 0.010201 | 2.68 | 0.010201 | 0.005100 | Considerable |

S | 1 | 0.004261 | 1.12 | 0.000098 | 0.000098 | Considerable |

S | 1 | 0.005940 | 1.56 | 0.005940 | 0.005940 | Considerable |

Error | 0 | — | — | — | — | |

Total | 8 | 0.381007 | 100.00 |

ANOVA analysis for milling time.

Source | DF | Seq SS | Influence (%) | Adj SS | Adj MS | |
---|---|---|---|---|---|---|

Model | 8 | 6330.22 | 100.00 | 6330.22 | 791.28 | Remarkable |

Linear | 3 | 5861.88 | 92.60 | 3305.79 | 1101.93 | Remarkable |

1 | 0.00 | 0.00 | 0.00 | 0.00 | Remarkable | |

1 | 5861.88 | 92.60 | 3142.36 | 3142.36 | Remarkable | |

1 | 0.00 | 0.00 | 0.00 | 0.00 | Remarkable | |

Square | 3 | 468.12 | 7.40 | 281.22 | 93.74 | Remarkable |

1 | 0.22 | 0.00 | 0.22 | 0.22 | Remarkable | |

1 | 467.68 | 7.39 | 268.56 | 268.56 | Remarkable | |

1 | 0.22 | 0.00 | 0.14 | 0.14 | Remarkable | |

2-Way interaction | 2 | 0.22 | 0.00 | 0.22 | 0.11 | Remarkable |

1 | 0.08 | 0.00 | 0.00 | 0.00 | Remarkable | |

1 | 0.14 | 0.00 | 0.14 | 0.14 | Remarkable | |

Error | 0 | — | — | — | — | |

Total | 8 | 6330.22 | 100.00 |

As described in Table _{1} of _{1} of interaction _{1}, factors

As demonstrated in Table _{2} was the highest, at 92.60%, while the influence number for interaction _{2}. Thus, so as to decline the worth of _{2}, the only factor _{1} as well as _{2} was 0%.

Statistic method was executed for identifying the influence level of input cutting factors on the output characteristics. In the range (3179, 6309), parameter _{1} in reducing gradually, as represented in Figure _{1}, but, in the range (831, 1206), it affected a gradual increase to _{1}. Furthermore, there was a fluctuation influence of parameter _{1}. Moving to a more detailed analysis, in the range (0.03,0.165), parameter _{1} to degrade slightly, but, in the range (0.03,0.165), it influenced a gradual rise to _{1}.

Influence diagram on surface roughness of (a)

On the other hand, as shown in Figure _{2}. For specifics, parameter _{2}.

Influence diagram on milling time of (a)

In summary, whole effects of input variables on quality characteristics were exhibited, as in Figure

Sensitivity diagram of the cutting factors on surface roughness and milling time.

Firstly, the number of numerical experiments was generated applying the TM. Based on initial data which were established by the TM, nine models were fabricated, measured as well as recorded so as to gain the values of output responses including surface roughness and milling time. In addition, according to these data between input variables and two output responses, the RSM was employed for establishing the regression equations for the surface roughness and the milling time. Later on, the multiobjective optimization problem was conducted via the MWCA. The MWCA algorithm was accomplished via MATLAB 2017b. The initial factors of MWCA are given in Table

Utilized initial factors for MWCA.

Factors | Value |
---|---|

Population size | 50 |

Maximum number of iterations | 100 |

The optimized results were discovered at _{1} = 0.260586713 _{2} = 1012.767751 (

Thirty-two models of the fabricated mold core.

Installation of the small ice cube mold on the plastic injection molding machine.

Small plastic ice tray products: (a) red plastic product, (b) white plastic product.

The optimal parameters (

Installation for measuring surface roughness based on optimal parameters.

Errors among predicted results and validated results.

Responses | Prediction | Validation | Error (%) |
---|---|---|---|

_{1} (micrometer) | 0.260586713 | 0.266 | 2.04 |

_{2} (s) | 1012.767751 | 961 | 5.39 |

This paper offered an effectual combination optimization approach for the mold core component with the complex milling surfaces. The spindle velocity, feed rate, and cutting depth were considered as input design variables. To enhance the surface roughness and milling time, the cutting parameters were optimized by a combination approach of the TM, experimental measurements, RSM, and MWCA.

The sensitivity analysis and ANOVA were implemented for determining the effects and crucial contributions of cutting factors on the surface roughness and milling time. The results of ANOVA analysis showed that the parameters that have significant influences on surface roughness were spindle velocity (42.42%), feed rate (29.40%), and cutting depth (6.59%), respectively. Meanwhile, the only parameter that has the most influence degree on milling time was feed rate (92.6%).

The results revealed that the optimized parameters were found at

Moreover, the results illustrated that the errors among forecasted results and experimental validations for the roughness surface and milling time are 2.04% and 5.39%, congruently. The experimental affirmations were proximate to the forecasted results. Therefore, the predicted results are appropriate with the certifications. According to the aforementioned results, the hybrid method is a powerful method for solving the multiobjective optimization issue for the cutting factors.

Additionally, this study encounters several challenges such as taking lots of time for finding suitable material in fields of injection molding and food as well as designing and manufacturing measuring fixture. Therefore, different suitable materials in the areas of injection molding and food should be regarded for machining the complex 3D surfaces.

In the future work, the milled components with complex 3D surfaces will be investigated and manufactured and its characteristics will be verifying the experimental outcomes.

The authors state that data used to support the findings of this study are included within the article.

The authors declare that there are no conflicts of interest regarding the publication of this article.

This work was supported by the project grant no T2020-12 funded by Ho Chi Minh City University of Technology and Education, Vietnam.