Optimization of CNC Milling Parameters of SKD11 Material for Core Component with Different Tool Path Strategies Based on Integration Approach of Taguchi Method, Response Surface Method and Lichtenberg Optimization Algorithm

Abstract

This study proposes a useful multi-criteria optimization approach for defining the proper fabrication factors for the CNC milling process on the inclined surfaces of SKD 11 material. The method is to be used in mold fabrication technology within the field of mechanical engineering. A combination technique of the Taguchi technique (TM), response surface method (RSM), and Lichtenberg optimization algorithm (LA) was proposed to optimize the fabrication factors for enriching the superiority attributes. In the first stage, several initial experiments of the fabricating parameters were generated by the TM. Secondly, the mathematical equations among the main fabricating parameters, the surface roughness, the flatness, and the CNC milling time were then established by the RSM. Significant influences of fabrication elements on surface roughness, flatness, and CNC milling time were evaluated by variance analysis and sensitivity analysis based on three distinct CNC milling toolpath strategies. Finally, the Lichtenberg optimization algorithm was carried out based on regression equations to define the optimized factors for three cutting strategies. The optimized results showed that the reverse CNC milling toolpath strategy was the best for achieving the three quality responses. Furthermore, the results demonstrated that the inaccuracies among optimized as well as experiment confirmations for the surface roughness, flatness and CNC milling time were 6.54%, 18.182% and 11.972%, respectively. The verifications of experiment results were relatively suitable with the anticipated consequences. The outcomes reveal that an integration optimization methodology is a successful approach to tackling the multi-objective optimal problem of determining the best CNC milling parameters for the cartwheel specimen made of SKD11 material in injection mold technology. It can also be expanded to apply to complicated multi-criteria optimization problems.

1. Introduction

SKD11 material is an alloy steel with high carbon and chromium content, with many remarkable advantages applied in industrial applications, especially in mold making and cutting tool manufacturing. One of the outstanding properties of SKD11 is its high wear resistance, which helps increase the life and performance of the product. At the same time, the hardness and durability of this material ensure the ability to resist impact and maintain the sharpness of the cutting tool for a long time. In addition, SKD11 is capable of withstanding high temperatures while maintaining hardness and ensuring the dimensional stability of the product in harsh working environments. This stability makes SKD11 an ideal choice for applications requiring high precision and durability, such as mold-making in industrial production. SKD11 material not only brings high performance but also helps reduce maintenance costs and improve productivity in the production process. In addition, SKD11 has very good quenching permeability and low quenching stress, making it very suitable for post-heat treatment processing of parts that require high precision in geometric dimensions while still achieving high hardness to perform specific applications. After heat treatment, SKD11 material can reach a hardness of 58-62HRC. Nevertheless, the aforementioned attributes make SKD11 difficult to manufacture through machining processes [1,2]. If the CNC milling parameters are not appropriately utilized, the material’s toughness can lead to quick tool wear, bad surface finishes, and increased machining times. Thus, selecting appropriate settings enhances machining performance and efficiency. Several researchers have examined the fabricating procedure for SKD11 material. Specifically, Inkhamnoi et al. [3] investigated the influences of fabricating factors and coolants on the SKD11 surface hardness of the manufactured straight plan. Gong et al. [4] examined the wear and breakage of the coated carbide tool in the SKD11 milling procedure. Dong et al. [5] investigated the performance evaluation of minimum quantity for SKD 11 using MoS2 nanoparticles to improve the fabricated surfaces. Mac et al. [6] examined the effect of thermal-assisted machining ability for SKD11 material. In CNC machining of complex structures, Zhang et al. [7] proposed an adaptive nonlinear-error control approach for five-axis fabrication. In addition, Wu et al. [8]. developed an error-controlled G3-continuous oriented toolpath optimization method and adjusted speed planning for five-axis machining.

Furthermore, optimizing machining conditions [9] for SKD11 material is crucial for improving the component’s quality and minimizing manufacturing costs. Scientists have employed different techniques to enhance the CNC fabricating settings for SKD 11, each possessing distinct advantages. Specifically, the Taguchi method (TM) [10] is a widely recognized approach because it is cost-effective and can determine the most significant elements. For instance, Samtas [11] optimized machining factors for face milling with AA5083-H111 material. Nipu et al. [12] applied the TM to find suitable cutting parameters affecting the quality responses in the SKD11 turning process. In addition, the response surface method [13] effectively predicted the quality characteristic in the finishing of the fabricating process of SKD11 material. Furthermore, in prior research, several population-based algorithms were progressed. Soori et al. [14] employed the genetic algorithm to find optimal fabricating factors to reduce the error. Basu et al. [15] employed a cuckoo search algorithm to resolve the dispatch problem. Additionally, effective incorporation approaches to handle a single optimized trouble, for example, an integration technique of response surface method (RSM) as well as radian foundation function network, were employed via Kadirgama et al. [16] to determine appropriate fabricating factors to minimize surface roughness in the Al6061 milling procedure. A hybrid technique comprising the TM, RSM, and genetic algorithm (GA) was employed by Hou et al. [17] to optimize the parameters of a nano-particle wet milling process. Moreover, there has been an integration of various optimization approaches such as neural network (NN) and multi-criteria genetic algorithm (MOGA) [18], NN–particle swarm optimization (PSO) [19], GA-ANN [20], Taguchi–Fuzzy–Moth-Flame Optimization Algorithm [21], PSO-GA [22], RSM-PSO [23], ANFIS-TLBO [24], TM–RSM–water cycle algorithm [25], and RSM-MOGA [26]. More specifically, Nguyen [27] applied TM and an archive-based micro-genetic algorithm (AMGA) to optimize cutting parameters for simultaneously achieving three quality responses, including production rate, surface roughness, and machining energy in the SKD61 milling process. Zhou et al. [28] employed grey analysis-integrated NN and PSO for optimizing cutting parameters of the Inconel 718 milling process. Muaz et al. [29] utilized a hybrid approach of TM and grey relational analysis for optimizing the finishing milling process for AISI 4340 steel. More specifically, the Lichtenberg optimization algorithm (LOA) [30,31,32] was an effective approach for conducting a multi-objective optimization process for many research fields. However, the integration technique of TM, RSM, and Lichtenberg optimization algorithm (LOA) has been less investigated for optimizing fabricating factors to enhance three quality responses, including surface roughness, CNC milling time, and flatness of the CNC milling process of SKD11 material based on three cutting strategies. In addition, an artificial neural network (ANN) was used to predict the three quality responses for the three milling strategies.

This study proposes identifying appropriate machining parameters to improve the three quality responses based on an effective approach in the CNC milling process of SKD11 material for core components using various toolpath strategies for the cartwheel plastic mold. To address the multi-criteria objective, the hybrid technique of TM, RSM, and LOA is cultivated.

2. Optimization Method

2.1. Optimization Problem Form

In CNC milling fine fabrication of a plastic mold, the milling time is the significant response for ensuring high productivity. In addition, surface roughness and flatness are important quality responses to warranty the technical requirements of manufactured mold core components. Therefore, in this study, the milled specimen of SKD 11 with the inclined surface profile for the core part in a cartwheel mold should satisfy the succeeding criteria: (i) the surface roughness (f₁) ought to be as minor for ensuring the fabricated tilting face attribute, (ii) the minor flatness (f₂) should be as small as possible to increase the manufacturing efficiency as well as ensure the technical requirement, and (iii) the CNC milling time (f₃) should be as small as possible to ensure the high productivity. A combination approach of the TM, response surface method, and Lichtenberg algorithm (LA) was developed to balance them and improve output quality characteristics for three cutting strategies. As a result, the optimization problem for the CNC milling specimen of the core component is shown as follows:

Seek for the main parameters: X = [K, S, t, F]

Minimize the f₁(K, S, t, F):

$$f_1\left(K, S, t, F\right),$$

(1)

Minimize the f₂(K, S, t, F):

$$f_2\left(K, S, t, F\right),$$

(2)

Minimize the f₃(K, S, t, F):

$$f_3\left(K, S, t, F\right),$$

(3)

Subject to constraints:

$$\left\{\begin{array}{l}1500 \mathrm{rpm}\le S\le 4000 \mathrm{rpm}\\ 0.02 \mathrm{mm}\le t\le 0.4 \mathrm{mm}\\ 400 (\mathrm{mm}/\min )\le F\le 1000 (\mathrm{mm}/\min )\end{array}\right.,$$

(4)

$$f_1\left(K, S, t, F\right)\le 0.5 (\mathsf{\mu }\mathrm{m}),$$

(5)

$$f_2\left(K, S, t, F\right)\le 0.0013(\mathrm{mm}),$$

(6)

$$f_3\left(K, S, t, F\right)\le 2000(s),$$

(7)

$$f=w_1·f_1+w_2·f_2+w_3·f_3$$

(8)

$$w_1+w_2+w_3=1$$

(9)

where f₁, f₂ and f₃ are the quality responses. In addition, w₁, w₂ and w₃ are the weight factors for the quality responses, respectively. Moreover, f is the integrated function of three quality responses. In general, the total weight factors for three quality responses are set to 1 to provide a neutral baseline and to reflect a compromise solution across competing responses, rather than focusing on a single characteristic. In this research, the weight factor for each response is equally allocated because there are no predefined industrial priority coefficients for the three quality response metrics. This approach ensures a balanced consideration of surface roughness, dimensional precision, and productivity without bias toward a single performance metric.

More specifically, K are different cutting strategies including forward milling toolpath strategy (F), reverse milling toolpath strategy (R) and forward–reverse milling toolpath strategy (FR). In addition, S, t, and F are spindle speed, cutting depth and feed rate, correspondingly.

To ensure the surface fabricating attribute, the technical requirements of the surface roughness, the flatness, and the CNC milling time should be chosen as tiny as feasible. In addition, based on the technical requirements and CNC fabrication experiences, surface roughness, flatness and CNC milling time were suggested to achieve smaller 0.5 (µm), 0.0013 (mm), and 2000 (s).

The constraint range conditions of the main parameters were demonstrated in Equations (4) and (5). Based on the manufacturing ability as well as the expertise of mechanical engineers, the range limits for fabricating parameters were proposed for the experimental CNC milling process for the specimen material with SKD11 obtaining mechanical hardness after heating more than 58 HRC. In addition, the chemical composition of SKD11 material is shown in

Table 1. Chemical composition of the SKD11 material.

C	Si	Mn	V	P	S	Mo	Cr
1.5	0.25	0.45	0.36	≤0.025	≤0.01	1	12

. In addition, the flute radius end mill tools with code, namely GMSR-4, Fineness Int’l Ltd., Taiwan, from Carbide Micro Grain material with a super coating layer of ALTiN, with main parameters such as D = Ø8 mm, R = 1 mm, l = 20 mm, d = Ø8 mm, $\gamma ={30}^{°},$ and L = 100 mm, were applied in high speed machining, wet and dry cutting conditions, as illustrated in Figure 1. In addition, different end mill tools for the experimental process are shown in Figure 2.

2.2. Integration Method

The influences of the fabricating parameters on quality responses were examined by developing an integration method of the TM, RSM, as well as Lichtenberg optimization algorithm to define the optimized factors for the proposed milling specimen based on mold fabricating technology applied to precise mechanical manufacturing. The hybrid optimization approach included the main steps:

-

The TM was conducted to build an experimental orthogonal array.

-

The experimental process for milling SKD11 material under three different strategies was conducted.

-

The output responses, including surface roughness, flatness and milling time, were measured by the surface roughness tester, CMM machine and recorded by the CNC machine, respectively.

-

The ANOVA analysis was used to determine the impact of key inputs on the quality attributes for three CNC milling strategies.

-

Based on the experimental results, an ANN was applied to predict the three quality responses associated with the three milling strategies.

-

The regression equations were formed for mapping the main parameters and quality features by the response surface method. A whole model for forming a regression equation was conveyed as the following equation:

$$F_k={\gamma }_0+{\displaystyle \sum _{i=1}^n{\gamma }_i{x}_i}+{\displaystyle \sum _{i=1}^n{\gamma }_{ii}{x}_i^2}+{\displaystyle \sum _{i=1}^{n-1}}{\displaystyle \sum _{j=i+1}^n{\gamma }_{ij}{x}_i{x}_j}+{\epsilon }_k$$

(10)

where n is the number of design variables, ${\gamma }_0$ is the intercept coefficient, ${\gamma }_i$ (i = 1, 2, …, n) are linear regression coefficients, ${\gamma }_{ii}$ are the quadratic coefficients, ${\gamma }_{ij}$ (i < j) are association coefficients between x_i and x_j; x₁, x₂,…, x_n are coded independent variables, and $\epsilon$ is an arbitrary error.

Eventually, the optimization procedure was carried out using the Lichtenberg algorithm, which was based on a regression equation chain for three different toolpath strategy circumstances in order to define optimized machining parameters. Based on the optimized parameters for three strategies, a suitable strategy was proposed to conduct the machining process for SKD11 material. The algorithm utilizes a hybrid system in its optimization process, integrating population and trajectory-based approaches. Through the use of a Lichtenberg figure, which is generated with different sizes and rotations at each iteration, it showcases robust exploration and exploitation capabilities by dispersing evaluation points in the objective function. More specifically, this algorithm achieved high convergence speed for multi-objective optimization problems. Therefore, according to the regression equations, the Lichtenberg algorithm was applied to find the optimization parameters because of the convergence speed. Matlab R2021b was used to program the Lichtenberg algorithm. Figure 3 depicts a hybrid strategy flowchart for the manufacturing factor optimization process. More details about the Lichtenberg algorithm can be found in ref. [33].

3. Discussion of Experimental Results

3.1. Experiment with an Orthogonal Array

As shown in

Table 2. Input fabricating factors and their rankings.

Parameters	Range	Small Level	Medium Level	High Level	Unit
K	(F, FR, R)	F	FR	R	-
S	1500–4000	1500	2750	4000	(rpm)
t	0.02–0.4	0.02	0.21	0.4	(mm)
F	400–1000	400	700	1000	mm/min

, each element can be classified into three rankings according to expertise and manufacturing experience. The L₂₇ orthogonal array was used to establish the initial experiment plan, based on the TM.

3.2. Experimental Process and Mathematical Model

To begin, Creo software v.11 was exploited for building a 3D design of the cartwheel mold, as shown in Figure 4. Furthermore, to improve the quality products from the cartwheel mold, the mold core components were investigated to find suitable parameters for enhancing the technical requirements as well as machining productivity of the CNC milling fabricating process of core parts. Therefore, several initial core component specimens were generated according to the Taguchi method for fabricating, measuring as well as recording for producing primary data between input design variables and output responses for three CNC milling strategies. Figure 5 exhibits the mold core specimen’s green milled surfaces with a fabricated square of 909.114 mm².

Later, twenty-seven experimental specimens, as illustrated in Figure 6, were manufactured by the CNC milling machine (VMC-650,Huey Long company, Taichung city, Taiwan). Subsequently, the surface roughness was assessed using an Accretech surface roughness tester (Tokyo Seimitsu company, Tokyo, Japan), as visualized in Figure 7. Furthermore, a measuring fixture was built for mounting the milled specimen and measuring surface roughness with the medium of three various measuring times. Furthermore, as depicted in Figure 8, the CNC milling machine recorded the machining time, and the flatness was measured by a coordinate measuring machine with the machine code, namely, BELTA-564 (Measuring company, Taichung city, Taiwan). As a result, the experiment outcomes are presented in

Table 3. Experimental results.

No.	K	S (rpm)	t (mm)	F (mm/min)	f1 (µm)	f2 (mm)	f3 (s)
1	F	1500	0.02	400	0.312	0.00077	2290
2	F	1500	0.21	700	0.527	0.001	1331
3	F	1500	0.4	1000	0.455	0.00063	949
4	F	2750	0.02	700	0.534	0.00103	1336
5	F	2750	0.21	1000	0.492	0.00173	950
6	F	2750	0.4	400	0.185	0.00067	2291
7	F	4000	0.02	1000	0.254	0.0008	952
8	F	4000	0.21	400	0.244	0.00077	2292
9	F	4000	0.4	700	0.267	0.00077	1215
10	FR	1500	0.02	400	0.321	0.00083	2291
11	FR	1500	0.21	700	0.529	0.00113	1331
12	FR	1500	0.4	1000	0.378	0.00093	945
13	FR	2750	0.02	700	0.506	0.0009	1332
14	FR	2750	0.21	1000	0.741	0.00093	950
15	FR	2750	0.4	400	0.273	0.0008	2270
16	FR	4000	0.02	1000	0.304	0.00107	951
17	FR	4000	0.21	400	0.223	0.00077	2292
18	FR	4000	0.4	700	0.247	0.00093	1285
19	R	1500	0.02	400	0.258	0.00097	2291
20	R	1500	0.21	700	0.327	0.0011	1337
21	R	1500	0.4	1000	0.438	0.00093	949
22	R	2750	0.02	700	0.405	0.00113	1332
23	R	2750	0.21	1000	0.557	0.00083	950
24	R	2750	0.4	400	0.244	0.00067	1956
25	R	4000	0.02	1000	0.451	0.00083	950
26	R	4000	0.21	400	0.257	0.00067	2292
27	R	4000	0.4	700	0.284	0.00053	1331

.

Finally, based on the data in Table 3, regression equations of three output characteristics for three different milling strategies were formed as follows.

Case 1: Forward CNC milling strategy (F).

$$\begin{array}{l}{f}_1\left(F\right)=-0.7102+0.000278\times S-0.3201\times t+0.002545\times F-1.163\times t\times t-0.000001\times F\times F \\ +0.000147\times S\times t\end{array}$$

(11)

$$f_2\left(F\right)=-0.000184+0.000001\times S+0.001078\times t-0.000001\times F-0.01094\times t\times t+0.000001\times S\times t$$

(12)

$$\begin{array}{l}{f}_3 \left(F\right)=4453+0.09547\times S+562.1\times t-7.066\times F-0.000013\times S\times S-507.8\times t\times t \\ +0.003409\times F\times F-0.1670\times S\times t-0.000003\times S\times F\end{array}$$

(13)

Case 2: Forward–reverse CNC milling strategy (FR).

$$f_1\left(FR\right) =-0.4576+0.000489\times S+0.8650\times t+0.000766\times F-4.414\times t\times t+0.000285\times S\times t$$

(14)

$$f_2 \left(FR\right)=0.000771+0.002588\times t+0.000001\times F-0.002770\times t\times t$$

(15)

$$\begin{array}{l}{f}_3 \left(FR\right)=4469+0.01832\times S+127.2\times t-6.806\times F-0.000001\times S\times S-253.9\times t\times t \\ +0.003291\times F\times F-0.03649\times S\times t-0.000015\times S\times F\end{array}$$

(16)

Case 3: Reverse CNC milling strategy (R).

$$f_1\left(R\right)=-0.04581+0.000255\times S-0.2550\times t-0.000033\times F-0.5725\times t\times t+0.000108\times S\times t$$

(17)

$$f_2 \left(R\right)=0.000063+0.000246\times t+0.000003\times F-0.000046\times t\times t$$

(18)

$$\begin{array}{l}{f}_3 \left(R\right)=4455-0.2876\times S-18188\times t-5.512\times F+0.000072\times S\times S-87.72\times t\times t \\ +0.003180\times F\times F+0.4618\times S\times t-0.000293\times S\times F\end{array}$$

(19)

3.3. ANOVA Analysis for Three CNC Milling Strategies

The ANOVA consequences of surface roughness, flatness as well as CNC milling time for the forward CNC milling strategy are demonstrated in

Table 4. Surface roughness ANOVA analysis for the forward CNC milling strategy.

Resource	DF	Seq SS	Impact	Adj SS	Adj MS
Pattern	8	0.150784	100.00%	0.150784	0.018848
Linear	3	0.088115	58.44%	0.082273	0.027424
S	1	0.046640	30.93%	0.046640	0.046640
t	1	0.006208	4.12%	0.017633	0.017633
F	1	0.035267	23.39%	0.026602	0.026602
Square	3	0.050607	33.56%	0.024083	0.008028
S × S	1	0.007321	4.85%	0.007320	0.007320
t × t	1	0.014964	9.92%	0.002646	0.002646
F × F	1	0.028322	18.78%	0.015453	0.015453
2-Way Collaboration	2	0.012062	8.00%	0.012062	0.006031
S × t	1	0.000181	0.12%	0.001837	0.001837
S × F	1	0.011882	7.88%	0.011882	0.011882
Fault	0	-	-	-	-
Whole	8	0.150784	100.00%

,

Table 5. Flatness ANOVA analysis for forward CNC milling strategy.

Resource	DF	Seq SS	Impact	Adj SS	Adj MS
Pattern	8	0.000001	100.00%	0.000001	0.000000
Linear	3	0.000000	21.94%	0.000000	0.000000
S	1	0.000000	0.07%	0.000000	0.000000
t	1	0.000000	5.19%	0.000000	0.000000
F	1	0.000000	16.68%	0.000000	0.000000
Square	3	0.000001	61.46%	0.000001	0.000000
S × S	1	0.000000	27.69%	0.000000	0.000000
t × t	1	0.000000	33.45%	0.000000	0.000000
F × F	1	0.000000	0.33%	0.000000	0.000000
2-Way Collaboration	2	0.000000	16.60%	0.000000	0.000000
S × t	1	0.000000	16.57%	0.000000	0.000000
S × F	1	0.000000	0.03%	0.000000	0.000000
Fault	0	-	-	-	-
Whole	8	0.000001	100.00%

and

Table 6. Milling time ANOVA analysis for forward CNC milling strategy.

Resource	DF	Seq SS	Impact	Adj SS	Adj MS
Pattern	8	2,918,884	100.00%	2,918,884	364,860
Linear	3	2,700,656	92.52%	1,550,910	516,970
S	1	2053	0.07%	2054	2054
t	1	2522	0.09%	1323	1323
F	1	2,696,081	92.37%	1,428,990	1,428,990
Square	3	215,000	7.37%	146985	48,995
S × S	1	868	0.03%	868	868
t × t	1	709	0.02%	504	504
F × F	1	213,422	7.31%	141,220	141,220
2-Way Collaboration	2	3228	0.11%	3228	1614
S × t	1	3227	0.11%	2360	2360
S × F	1	1	0.00%	1	1
Fault	0	-	-	-	-
Whole	8	2,918,884	100.00%

, correspondingly. As portrayed in Table 4, the spindle speed and feed rate significantly affected the surface roughness with 30.93% and 23.39%; meanwhile, the figure for cutting thickness was relatively small with 4.12%. More details about interaction proportions among the main factors affecting the surface roughness were illustrated in Table 4. Consequently, the spindle speed and feed rate need to be considered for reducing the surface roughness to enhance the product attribute. Additionally, as illustrated in Table 5, the feed rate and the cutting thickness influenced flatness with 16.68% and 5.19%, respectively. However, the spindle speed insignificantly affected the flatness with 0.07%. Meanwhile, the interaction proportions among t and t, S and S, and F and F were 33.45%, 27.69%, and 0.33%, respectively. Therefore, the feed rate needs to be considered for reducing the flatness to enhance the product attribute. Furthermore, the interaction proportions among t and t and S and S should be considered for achieving the minimal flatness. As illustrated in Table 6, the feed rate greatly affected the CNC milling time with 92.37%. Conversely, the spindle speed and cutting thickness showed slight influences with 0.07% and 0.09%, respectively. Consequently, the feed rate should be regarded to decline the CNC milling time so as to enhance the productivity.

The ANOVA consequences of surface roughness, flatness as well as CNC milling time for the forward–reverse CNC milling strategy are displayed in

Table 7. Surface roughness ANOVA analysis for forward–reverse CNC milling strategy.

Resource	DF	Seq SS	Impact	Adj SS	Adj MS
Pattern	8	0.230290	100.00%	0.230290	0.028786
Linear	3	0.104607	45.42%	0.088982	0.029661
S	1	0.034353	14.92%	0.034353	0.034353
t	1	0.009048	3.93%	0.004563	0.004563
F	1	0.061206	26.58%	0.054540	0.054540
Square	3	0.116570	50.62%	0.097939	0.032646
S × S	1	0.059858	25.99%	0.059858	0.059858
t × t	1	0.050880	22.09%	0.038081	0.038081
F × F	1	0.005832	2.53%	0.000610	0.000610
2-Way Collaboration	2	0.009113	3.96%	0.009113	0.004556
S × t	1	0.009112	3.96%	0.006868	0.006868
S × F	1	0.000000	0.00%	0.000000	0.000000
Fault	0	-	-	-	-
Whole	8	0.230290	100.00%

,

Table 8. Flatness ANOVA analysis for forward–reverse CNC milling strategy.

Resource	DF	Seq SS	Impact	Adj SS	Adj MS
Pattern	8	0.000000	100.00%	0.000000	0.000000
Linear	3	0.000000	46.74%	0.000000	0.000000
S	1	0.000000	2.14%	0.000000	0.000000
t	1	0.000000	2.91%	0.000000	0.000000
F	1	0.000000	41.69%	0.000000	0.000000
Square	3	0.000000	27.12%	0.000000	0.000000
S × S	1	0.000000	7.92%	0.000000	0.000000
t × t	1	0.000000	1.98%	0.000000	0.000000
F × F	1	0.000000	17.22%	0.000000	0.000000
2-Way Collaboration	2	0.000000	26.14%	0.000000	0.000000
S × t	1	0.000000	2.39%	0.000000	0.000000
S × F	1	0.000000	23.75%	0.000000	0.000000
Fault	0	-	-	-	-
Whole	8	0.000000	100.00%

and

Table 9. Milling time ANOVA analysis for forward–reverse CNC milling strategy.

Resource	DF	Seq SS	Impact	Adj SS	Adj MS
Pattern	8	2,858,380	100.00%	2,858,380	357,298
Linear	3	2,677,174	93.66%	1,463,087	487,696
S	1	253	0.01%	253	253
t	1	913	0.03%	690	690
F	1	267,6008	93.62%	1,355,424	13,55,424
Square	3	180,893	6.33%	134,827	44,942
S × S	1	5	0.00%	5	5
t × t	1	288	0.01%	126	126
F × F	1	180,601	6.32%	131,572	131,572
2-Way Collaboration	2	313	0.01%	313	156
S × t	1	264	0.01%	113	113
S × F	1	48	0.00%	48	48
Fault	0	-	-	-	-
Whole	8	2,858,380	100.00%

, congruently. Specifically, as shown in Table 7, the spindle speed and feed rate considerably affected the surface roughness with 14.92% and 26.58%; meanwhile, the figure for cutting thickness was relatively small with 3.93%. More details about interaction proportions among the main factors influential to the surface roughness are illustrated in Table 7. Consequently, the spindle speed and feed rate need to be considered for reducing the surface roughness to enhance the product attribute. Additionally, as illustrated in Table 8, the feed rate affected the flatness with 41.69%. However, the effect proportions of the spindle speed and the cutting thickness were relatively small, with 2.14% and 2.91%, respectively. Further details about interaction proportions among the main factors influential to the flatness are illustrated in Table 8. Therefore, the feed rate should be regarded to reduce the flatness of the product so as to ensure the technical requirement. As depicted in Table 9, the feed rate affected extremely the CNC milling time with 93.62%. Meanwhile, the spindle speed and cutting thickness showed slight influences with 0.01% and 0.03%, respectively. Consequently, the feed rate should be regarded to decline the CNC milling time so as to enhance the productivity.

The ANOVA outcomes of surface roughness, flatness as well as CNC milling time for the reverse CNC milling strategy are exhibited in

Table 10. Surface roughness ANOVA analysis for reverse CNC milling strategy.

Resource	DF	Seq SS	Impact	Adj SS	Adj MS
Pattern	8	0.096493	100.00%	0.096493	0.012062
Linear	3	0.082472	85.47%	0.048910	0.016303
S	1	0.000160	0.17%	0.000160	0.000160
t	1	0.003651	3.78%	0.004256	0.004256
F	1	0.078662	81.52%	0.048641	0.048641
Square	3	0.012686	13.15%	0.012380	0.004127
S × S	1	0.008756	9.07%	0.008756	0.008756
t × t	1	0.002267	2.35%	0.000641	0.000641
F × F	1	0.001663	1.72%	0.002604	0.002604
2-Way Collaboration	2	0.001335	1.38%	0.001335	0.000667
S × t	1	0.000321	0.33%	0.000988	0.000988
S × F	1	0.001014	1.05%	0.001014	0.001014
Fault	0	-	-	-	-
Whole	8	0.096493	100.00%

,

Table 11. Flatness ANOVA analysis for reverse CNC milling strategy.

Resource	DF	Seq SS	Impact	Adj SS	Adj MS
Pattern	8	0.000000	100.00%	0.000000	0.000000
Linear	3	0.000000	83.88%	0.000000	0.000000
S	1	0.000000	47.57%	0.000000	0.000000
t	1	0.000000	32.35%	0.000000	0.000000
F	1	0.000000	3.96%	0.000000	0.000000
Square	3	0.000000	7.70%	0.000000	0.000000
S × S	1	0.000000	0.89%	0.000000	0.000000
t × t	1	0.000000	0.33%	0.000000	0.000000
F × F	1	0.000000	6.48%	0.000000	0.000000
2-Way Collaboration	2	0.000000	8.42%	0.000000	0.000000
S × t	1	0.000000	7.56%	0.000000	0.000000
S × F	1	0.000000	0.85%	0.000000	0.000000
Fault	0	-	-	-	-
Whole	8	0.000000	100.00%

and

Table 12. Milling time ANOVA analysis for reverse CNC milling strategy.

Resource	DF	Seq SS	Impact	Adj SS	Adj MS
Pattern	8	2,451,442	100.00%	2,451,442	306,430
Linear	3	2,288,281	93.34%	1,143,301	381,100
S	1	3	0.00%	3	3
t	1	18,928	0.77%	37,074	37,074
F	1	2,269,350	92.57%	941,360	941,360
Square	3	139,034	5.67%	150,385	50,128
S × S	1	25,238	1.03%	25,238	25,238
t × t	1	6767	0.28%	15	15
F × F	1	107,030	4.37%	122,837	122,837
2-Way Collaboration	2	24,127	0.98%	24,127	12,063
S × t	1	5977	0.24%	18,040	18,040
S × F	1	18,150	0.74%	18,150	18,150
Fault	0	-	-	-	-
Whole	8	2,451,442	100.00%

, correspondingly. As portrayed in Table 10, the feed rate had an enormous effect on the surface roughness with 81.52%; meanwhile, the figures for cutting thickness and spindle speed were relatively small with 3.78% and 0.17%, respectively. Consequently, the feed rate should be considered for reducing the surface roughness to enhance the product attribute. Additionally, as illustrated in Table 11, the spindle speed and cutting thickness significantly influenced the flatness with 47.57% and 32.35%, respectively. However, the effect ratio of feed rate to the flatness was relatively small, with 3.9%. Therefore, the spindle speed and cutting thickness should be considered to decline the flatness in order to ensure the technical requirement. Additionally, Table 12 revealed that the feed rate affected tremendously the CNC milling time with 92.57%. Conversely, the effect ratios of spindle speed and cutting thickness on the CNC milling time were very small 0% and 0.77%. Consequently, the feed rate should be regarded to decline the CNC milling time so as to enhance the productivity.

In brief, for the three above-mentioned CNC milling strategies, the feed rate was the main parameter affecting the CNC milling time extremely. Conversely, the spindle speed and the cutting thickness differently affected the surface roughness and the flatness for the three CNC milling strategies.

3.4. Analysis of Sensitivity for Three CNC Milling Strategies

To evaluate the degree of effect of fabrication factors on the output features, a statistical approach was utilized. More specifically, for the forward CNC milling strategy, the spindle speed slightly increased f₁ in [2000 rpm, 3000 rpm], as shown in Figure 9a and Figure 12. In addition, as illustrated in Figure 9a and Figure 10, the spindle speed in the range 3000 rpm to 4000 rpm significantly affected the decrease in surface roughness. In addition, in the range [0.02 mm, 0.21 mm], the cutting thickness steadily affected in increasing the surface roughness and in the range [0.21 mm, 0.4 mm], the cutting thickness gradually affected in decreasing the surface roughness. As depicted in Figure 9b and Figure 12, the feed rate affected dramatically in increasing the surface roughness in the range [400 mm/min, 700 mm/min]; conversely, in the range [700 mm/min, 1000 mm/min], the feed rate affected gradually in declincing the surface roughness. Furthermore, as shown in Figure 10a,b and Figure 12, there was a gradual fluctuation of spindle speed and feed rate effects on the flatness in the range [2000 rpm, 4000 rpm] and [400 mm/min, 1000 mm/min], respectively. In addition, as depicted in Figure 10b and Figure 12, the cutting thickness moderately contributed to the increase in flatness in the range [0.02 mm, 0.21 mm]; conversely, the cutting thickness slightly contributed to the reduction in flatness in the range [0.21 mm, 0.4 mm]. As illustrated in Figure 11a and Figure 12, the spindle speed and cutting thickness did not affect the CNC milling time. Conversely, as illustrated in Figure 11b and Figure 12, the feed rate extremely affected the milling time in declining in the range [400 mm/min, 700 mm/min] as well as gradually affected the milling time in declining in the range [700 mm/min, 1000 mm/min].

For the forward–reverse CNC milling strategy, as illustrated in Figure 13a and Figure 16, the spindle speed gradually affected in increasing the surface roughness in the range [2000 rpm, 3000 rpm]; conversely, the spindle speed had a dramatic impact on reducing the surface roughness in the range [3000 rpm, 4000 rpm]. In addition, Figure 13a and Figure 16, there was a sharp impact of cutting thickness on surface roughness in the range [0.02 mm, 0.21 mm]; meanwhile, the cutting thickness significantly affected the reduction in the surface roughness in the range [0.21 mm, 0.4 mm]. Furthermore, as illustrated in Figure 13b and Figure 16, the feed rate gradually impacted the surface roughness in the range [400 mm/min, 700 mm/min]; meanwhile, there was a slight impact of the feed rate on surface roughness in the range [700 mm/min, 1000 mm/min]. As illustrated in Figure 14a and Figure 16, the spindle speed had a gradual effect on the flatness in the range [2000 rpm, 3000 rpm]; meanwhile, there was a progressive increase in the spindle speed on the flatness in the range [3000 rpm, 4000 rpm]. Moreover, there was a slight fluctuation of the cutting thickness to the flatness in the range [0.02 mm, 0.4 mm]. As shown in Figure 14b and Figure 16, the feed rate had a sharp effect on the flatness in the range [400 mm/min, 700 mm/min]; meanwhile, there was a slight increase in the flatness in the range [700 mm/min, 1000 mm/min]. As demonstrated in Figure 15a,b and Figure 16, the spindle speed and the cutting thickness did not affect the CNC milling time in ranges [2000 rpm, 4000 rpm] and [0.02 mm, 0.4 mm], respectively. However, the feed rate dramatically affected the CNC milling time in the range [400 mm/min, 700 mm/min]. In addition, within the range [700 mm/min, 1000 mm/min], there was a progressive decrease in the feed rate during CNC milling time.

For the reverse CNC milling strategy, as illustrated in Figure 17a and Figure 20, the spindle speed gradually affected in increasing the surface roughness in the range [2000 rpm, 3000 rpm]. In addition, there was a progressive decrease in spindle speed on surface roughness in the range [3000 rpm, 4000 rpm]. Moreover, there was a slight decrease in the cutting thickness to the surface roughness in the range [0.02 mm, 0.4 mm]. As illustrated in Figure 17b and Figure 20, there was a sharp increase in feed rate on surface roughness in the range [400 mm/min, 1000 mm/min]. As illustrated in Figure 18a and Figure 20, there were dramatic decreases in the spindle speed and the cutting thickness on the flatness in the ranges [2000 rpm, 4000 rpm] and [0.02 mm, 0.4 mm], respectively. However, as illustrated in Figure 18b and Figure 20, the feed rate sharply affected the increase in flatness in the range [400 mm/min, 700 mm/min] and significantly influenced the reduction in the flatness in the range [700 mm/min, 1000 mm/min]. In addition, as depicted in Figure 19a and Figure 20, the spindle speed slightly affected the decrease in the CNC milling time in the range [2000 rpm, 3000 rpm]; meanwhile, there was a minor increase in spindle speed on the CNC milling time in the range [3000 rpm, 4000 rpm]. In addition, the cutting thickness remained unchanged with respect to the CNC milling time in the range [0.02 mm, 0.21 mm] and a minor decrease in the cutting thickness with respect to the CNC milling time in the range. Conversely, the feed rate had a pronounced influence on reducing milling time in the range [400 mm/min, 700 mm/min] and significantly affected this reduction in the range [700 mm/min, 1000 mm/min].

Case 1: Forward CNC milling strategy (F)

In brief, the effects of fabricating parameters on quality characteristics were exhibited in Figure 10. The figure describes the influence of the trends of each main factor on the output response. Based on the recorded results, the significant influencing parameters should be considered to attain the quality of output responses.

Case 2: Forward–reverse CNC milling strategy (FR)

Case 3: Reverse CNC milling strategy (R)

3.5. Predicted Results

Based on the experimental results, an artificial neural network was applied to predict the three quality responses associated with the three milling strategies. Different artificial neural network architectures based on minimized root mean squared error (RMSE) were used to predict three quality responses, as illustrated in Figure 21, Figure 22 and Figure 23. Specifically, the RMSEs for f₁, f₂, and f₃ based on the forward strategy were 0.082, 0.053, and 137.526, respectively. In addition, the RMSEs for f₁, f₂, and f₃ based on the forward–reverse strategy were 0.081, 0.084, and 45.26, respectively. Based on the forward strategy, the RMSEs for f₁, f₂, and f₃ were 0.005, 0.02, and 227.641, respectively. The artificial neural network architecture for predicting surface roughness (f₁) comprised two hidden layers with two nodes for the first layer and six nodes for the second layer, as depicted in Figure 21. The artificial neural network architecture predicting the flatness (f₂) comprised one hidden layer with two nodes, as described in Figure 22. The artificial neural network architecture for predicting the milling time (f₃) comprised two hidden layers with two nodes for the first layer and two nodes for the second layer, as depicted in Figure 23.

Based on the experimental results in Table 3, the predicted results were achieved according to the neural network for the three quality responses of the three milling strategies, as illustrated in

Table 13. Comparison of experimental results and predicted results.

No.	K	S	t	F	f1	f2	f3	pre-f1	pre-f2	pre-f3
		(rpm)	(mm)	(mm/min)	(µm)	(µm)	(s)	(µm)	(µm)	(s)
1	F	1500	0.02	400	0.312	0.77	2290	0.421037	8.37 × 10−1	2314.779
2	F	1500	0.21	700	0.527	1	1331	0.496574	8.62 × 10−1	1325.323
3	F	1500	0.4	1000	0.455	0.63	949	0.502888	8.85 × 10−1	945.8986
4	F	2750	0.02	700	0.534	1.03	1336	0.422881	1.10044981	1322.778
5	F	2750	0.21	1000	0.492	1.73	950	0.479002	1.12454189	945.7056
6	F	2750	0.4	400	0.185	0.67	2291	0.230618	6.09 × 10−1	2271.695
7	F	4000	0.02	1000	0.254	0.8	952	0.28266	1.18210261	945.5151
8	F	4000	0.21	400	0.244	0.77	2292	0.21063	7.85 × 10−1	2270.437
9	F	4000	0.4	700	0.267	0.77	1215	0.249938	8.09 × 10−1	1227.581
10	FR	1500	0.02	400	0.321	0.83	2291	0.255824	0.84519125	2300.015
11	FR	1500	0.21	700	0.529	1.13	1331	0.332577	0.9870176	1322.241
12	FR	1500	0.4	1000	0.378	0.93	945	0.449323	0.9935997	947.169
13	FR	2750	0.02	700	0.506	0.9	1332	0.406042	0.94923391	1330.652
14	FR	2750	0.21	1000	0.741	0.93	950	0.50077	1.01325872	948.1216
15	FR	2750	0.4	400	0.273	0.8	2270	0.249066	0.81446241	2270.44
16	FR	4000	0.02	1000	0.304	1.07	951	0.499189	1.01673375	949.1106
17	FR	4000	0.21	400	0.223	0.77	2292	0.251974	0.76326327	2276.759
18	FR	4000	0.4	700	0.247	0.93	1285	0.282817	0.91537545	1289.715
19	R	1500	0.02	400	0.258	0.97	2291	0.257798	1.06652932	2285.189
20	R	1500	0.21	700	0.327	1.1	1337	0.333203	1.05268721	1323.203
21	R	1500	0.4	1000	0.438	0.93	949	0.448477	0.9087515	976.2025
22	R	2750	0.02	700	0.405	1.13	1332	0.411953	1.04450203	1362.96
23	R	2750	0.21	1000	0.557	0.83	950	0.514557	0.87263611	939.0452
24	R	2750	0.4	400	0.244	0.67	1956	0.253236	0.68537425	1984.174
25	R	4000	0.02	1000	0.451	0.83	950	0.488466	0.83496765	952.6519
26	R	4000	0.21	400	0.257	0.67	2292	0.256139	0.65146909	2280.403
27	R	4000	0.4	700	0.284	0.53	1331	0.290507	0.53069031	1331.632

. In addition, the relationships between the experiment results and the predicted results of the three quality responses were illustrated in Figure 24, Figure 25 and Figure 26.

3.6. Optimized Results

Firstly, a numerical experiment array was generated using the TM. Twenty-seven specimens were produced, measured, and recorded to determine the worth of quality characteristics involving surface roughness, flatness, and CNC turning time, based on the original data of the TM. In addition, the RSM was utilized to construct regression equations for surface roughness, flatness, and CNC turning time using recorded data from principal manufacturing parameters and three quality criteria. The LA was adopted to tackle the optimization problem that encompasses multiple objectives. In this study, the LA was implemented using Matlab R2021b software. As illustrated in

Table 14. Optimal results for three different CNC milling strategies.

Input Parameters				Output Responses
CNC milling strategy	S (rpm)	t (mm)	F (mm/min)	f1 (µm)	f2 (mm)	f3 (s)
Forward (F)	1500	0.4	497.8147	0.4999	0.0106	1935.3648
Reverse (R)	1981.7423	0.2588	400	0.3974	0.0013	1999.999
Forward–reverse (FR)	1500	0.3753	470.872	0.4999	0.00182	1999.993

, the optimized results for the forward CNC milling strategy were found at S = 1500 (rpm), t = 0.4 (mm), F = 497.8147 (mm/min), f₁ = 0.4999 µm, f₂ = 0.0106 (mm) and f₃ = 1935.3648 (s). The optimized results for the reverse CNC milling strategy were found at S = 1981.7423 (rpm), t = 0.2588 (mm), F = 400 (mm/min), f₁ = 0.3974 (µm), f₂ = 0.0013 (mm) and f₃ = 1999.999 (s). In addition, the optimized results for the forward–reverse CNC milling strategy were found at S = 1500 (rpm), t = 0.3753 (mm), F = 470.872 (mm/min), f₁ = 0.4999 (µm), f₂ = 0.00182 (mm) and f₃ = 1999.993 (s). Comparing the optimized results, the reverse CNC milling strategy achieved better optimization output responses based on the balance of initial technical requirements.

3.7. Verification

The optimal results for the reverse CNC milling strategy were utilized to fabricate the core mold specimen so as to verify the optimization results, as illustrated in Figure 27. As illustrated in

Table 15. Errors between optimal results and verified results.

Responses	Optimization Result	Verification Result	Error (%)
f1 (µm)	0.3974	0.373	6.54
f2 (mm)	0.0013	0.0011	18.182
f3 (s)	1999.999	2272	11.972

, the verified results of the optimal specimen were at f₁ = 0.373 (µm), f₂ = 0.0011 (mm), and f₃ = 2272 (s). The inaccuracies among optimal outcomes and experiment outcomes for surface roughness, flatness, and CNC milling time were 6.54%, 18.182%, and 11.972%, respectively.

The achieved results demonstrated that the optimized surface roughness, the flatness, and the CNC milling time satisfied the technical requirements for the CNC milling procedure for inclined surfaces of SKD 11 material applied for the cartwheel mold manufacturing process. According to the optimum values, the cartwheel mold was manufactured and injected with cartwheel components, as illustrated in Figure 28.

In addition, this study was compared with the previous studies, as illustrated in

Table 16. Differences in current consequences with preceding studies.

Material	Optimal Approach	Input Factors	Shape of Fabricated Surfaces	Optimized Characteristics by Experiment Process	Authors [Ref.]
SKD11	Hybrid approach of TM, RSM, and Lichtenberg optimization algorithm	S = 1883.8678 (1500 rpm–4000 rpm); t = 0.2595 (0.02 mm–0.4 mm); F = 400 (400 mm/min–1000 mm/min) Three CNC milling strategies: reverse (forward, reverse, forward–reverse)	Inclined 3D surfaces of cartwheel components	The surface roughness is 0.373 µm, the flatness is 0.0011 (mm), and the CNC milling time is 2272 (s)	This study
45# Steel	NSGA-II	Cutting velocity vc 2174.16 rpm (60 m/min–120 m/min) F = 0.1 (0.03 mm/tooth–0.12 mm/tooth) Milling depth ap 2 (0.5 mm–2 mm) Milling depth ae 8.64 (6 mm–12 mm)	Straight surfaces	The surface roughness was 1.73 µm, total energy consumption was 497,430.29 J, and the CNC milling time was 2,272,541.94 (s)	Jia et al. [34]
4032 Al-alloy	TM–Gray Relational Analysis	S = 1883.8678 (2000 rpm–4000 rpm); t = 0.2595 (0.5 mm–1.5 mm); F = 400 (0.03 mm/tooth–1 mm/tooth)	Straight surfaces	The surface roughness was 1.742 µm, the material removal rate was 4200 mm3/min, and the micro-hardness was 138.34 HV0.2	Hammood [35]

.

4. Conclusions

The present study presents a successful hybrid optimization method for determining the ideal manufacturing parameters of core specimens using SKD11 applied to plastic mold technology. Critical parameters to explore were input design variables such as spindle speed, cutting depth, feed rate, and CNC milling toolpath strategies. To enhance surface roughness, flatness, and CNC milling time, the fabricating elements were optimized by integrating the TM, experimental data, RSM, and Lichtenberg optimization algorithm.

The contributions of fabrication factors to surface roughness, flatness, and CNC milling time were evaluated using sensitivity analysis and ANOVA. ANOVA research for three CNC milling toolpath strategies (forward, forward–reverse, and reverse) demonstrated that feed rate was the most influential parameter to CNC milling time, with 92.37%, 93.62%, and 92.57%, respectively. The contributions of spindle speed to surface roughness for three CNC milling toolpath strategies were 30.93%, 14.92%, and 0.17%, respectively. In addition, the influences of the cutting depth on the flatness for three CNC milling toolpath strategies were 5.19%, 2.91%, and 32.35%, respectively.

A hybrid technique of the TM, RSM and Lichtenberg optimization algorithm was applied to seek the optimal fabricating parameters for cartwheel inclined surfaces with SKD material utilized in the cartwheel injecting mold. The optimal results of the reverse strategy were better than the optimal results of the forward–reverse strategy. More specifically, the consequences exhibited that the optimized results for the reverse CNC milling toolpath strategy were detected at S = 1981.7423 (rpm), t = 0.2588 (mm), F = 400 (mm/min), f₁ = 0.3974 µm, f₂ = 0.0013 (mm) and f₃ = 1999.999 (s). Furthermore, the consequences showed that the errors between predicted and experiment confirmations for the roughness surface, flatness, and CNC turning time were 6.54%, 18.182%, and 11.972%, respectively. The validations of the experiment results were relatively suitable compared to the forecasted results. According to these findings, the hybrid optimization method is an efficient strategy for addressing the problem of optimizing multiple objectives applied to fabricating parameters across different CNC milling toolpath strategies. In addition, the artificial neural network was used to predict the three quality responses based on the experimental results.

This study faces various challenges in reducing flatness and CNC milling time errors. In addition, other parameters should be considered in future studies to reduce surface roughness, flatness, CNC milling time, and other quality responses, based on different CNC milling strategies. Furthermore, in future work, various suitable hard materials in plastic mold technology need to be investigated to find suitable parameters in the plastic mold fabricating process. A hybrid approach of artificial intelligence, machine learning and advanced algorithms should be considered to predict and optimize the fabricating factors to obtain proficient simultaneous quality responses.