Optimization of Parameter for Cutting Condition of Uhmwpe Acetabular Cup Based On Taguchi and Desirability Functions

Abstract

The use of CNC milling machines in the manufacturing industry contributes significantly to producing according to the shape desired by the consumer. It is, however, possible to determine the product quality from the amount of surface roughness and optimal processing time. UHMWPE acetabular cup is a product component that requires excellent machinability and manufacturing quality. Taguchi and desirability function methods were used in this study to determine the optimal cutting parameter conditions and data response to produce acetabular cup products. The four parameters were applied to determine the significant effect on surface roughness response and processing time, while the experimental layout used was L₉3⁴. The results showed the optimal machining parameters in the inner and outer acetabular cup product manufacturing process were able to produce an optimum Ra inner value of 0.881 µm and Tm. Inner of 1746.37 sec, Ra outer value of 0.928 µm, and Tm Outer of 942.21 sec.

Keywords:

• surface roughness
• time machining
• Taguchi method
• desirability functions
• acetabular cup

PUBLIC INTEREST STATEMENT

The use of CNC milling machines in the manufacturing industry makes a significant contribution to efforts to guarantee the quality of machining surfaces that are precise, accurate, and according to manufacturer standards for medical device products. UHMWPE acetabular cup is a product component that requires excellent machinability and manufacturing quality. The selection of optimal machining parameters based on the Taguchi experimental design and desirability function is proven to be able to help engineers and researchers in their efforts to obtain optimal UHMWPE surface quality.

1. Introduction

The material removal process has been investigated in theory and through an experiment to a particular extent. The demand for environmentally friendly processes junction rectifier to the imposition of recent parameters cherishes the utilization of borderline quantity. However, these connected processes must be studied to be optimized for specific cutting conditions (Anggoro et al., 2016, 2019, 2020; Fratila & Caizar, 2011). This is often necessary due to industries perpetually trying for lower-cost solutions with reduced intervals and higher surface quality to keep up the fight (Fratila & Caizar, 2011). Moreover, the production processes within the medical device business victimization of modern machine tools are terribly time-consuming, expensive, and environmentally hazardous. A sturdy style is an engineering methodology to get product and method conditions considered minimally sensitive to many variations. The aim is to obtain high-quality merchandise with low development and production prices (Baldwin et al., 2005; Bras et al., 2006; Brent & Visser, 2005; Fratila & Caizar, 2011). Therefore, one of the vital tools of sturdy design is Taguchi’s parameter design which offers an easy and systematic approach to optimize the look for performance, quality, and costs (Khosrow Dehnad & Dehnad, 1989; Park, 1996; Phadke, 1989); Fratila and Caizar (2011).

Several works have been previously conducted to design experiments in several areas, such as metal cutting, plastic, polymer, and rubber on the milling process with a CNC machine through the use of the Taguchi method (Anggoro et al., 2018, 2019, 2020, 2021, 2022; Asiltürk & Nesseli, 2012; Ghani et al., 2004; Hanafi et al., 2012; Sarıkaya & Güllü, 2014; Shimazaki et al., 2016; Xavior & Adithan, 2009; Yadav, 2017). It was, however, discovered that studies on the selection of cutting parameters in manufacturing acetabular cup products using the Taguchi method are limited, as observed by (Lestari et al., 2018). Moreover, the application of other methods to determine the best response has also not been comprehensively tried.

It is important to note that CNC milling operations also can process other materials apart from metals, such as Ethylene Vinyl Acetate (EVA) foam, usually used for orthotic shoe insoles (Anggoro et al., 2019, 2020, 2022) and Ultra High Molecular Weight Polyethylene (UHMWPE) for producing acetabular cups which are the supporting components of the hip joint (Kam & Demirtaş, 2021; Kam & Şeremet, 2021; Lestari et al., 2018, 2019). Previous studies showed that making the acetabular cup is not optimal due to the inability to form the product as a whole. Still, only the surface is exposed to contact and a more extended period of operation.

Milling operations are usually used to produce acetabular cups with satisfactory quality and precise size using low production costs and short machining times. Meanwhile, the best parameters to obtain the surface roughness value (Ra) and fast-milling operation time for the acetabular cup parts have not been discovered. This means an optimization technique is needed in setting the machining parameters to obtain the desired value, which is expected to be less than 2.00 µm according to the ASTM standard. The existing research was observed to have used only the toolpath strategy parameter in the 2.00 µm software.

Some of the literature observed showed systematic research is essential to obtain optimal cutting conditions toward achieving a better outcome in machining acetabular cup products using the UHMWPE material. Therefore, this research is focused on optimizing cutting parameters such as toolpath strategy, spindle speed, feed rate, step over, and depth of cut on a CNC milling machine used in producing acetabular cups. This is necessary to obtain optimal processing time and surface roughness quality in line with the ASTM standards.

2. Theoretical framework and methodology

2.1. Taguchi method

The Taguchi technique may be a sturdy and simple optimization technique for producing parameters by reducing their variations. Its final goal is to get and perceive how many process parameters influence the mean and variance of determining the characteristics and find how variables contribute considerably to the measured response.

The Taguchi method modifies and later simplifies the full factorial matrix by reducing the variation in factor combinations, collecting the most influencing treatments, and providing as much information as possible on all factors affecting the response (Fratila & Caizar, 2011). However, this matrix modification is also called an “orthogonal array.” It is important to note that this method uses means calculation and analysis of variance (ANOVA) combined with S/N or noise signal ratio calculation. It is further divided into three categories: the nominal, which is defined as the best characteristic; the smaller is, the better, and the larger is, the better characteristic, according to Fratila and Caizar (2011). This combination analysis is useful in measuring each factor’s characteristics and percentage contribution to the response. The method also examines the extent to which different process factors can influence the variance and mean value of the process characteristics and determine those with the most significant effects by Ranjit (2001). Furthermore, it defines product quality as the difference between the process result characteristics and the target value to be achieved.

Therefore, this study aims to optimize the cutting parameters required by the UHMWPE to manufacture acetabular cups to achieve the best processing time and surface roughness according to the ASTM standards. The two variables were, however, set to a minimum value, which means a smaller S/N ratio calculated using equation (1) is expected to provide a better result.

(1) $\mathit{SN}\mathit{ratio}=-10\times log\frac{1}{n}\left(\sum y^2\right)$(1)

where value y is response data from several n experimental values obtained.

2.2. Friction drag coefficient

This experiment used four cutting parameters based on the concept of Taguchi design quality. They were all set at three levels, as indicated in Table 1, to determine the nine experimental treatments. Moreover, a fractional factorial design based on an orthogonal array (O.A.) matrix was selected to be the L₉3⁴ design layout for the four factors, with each having three levels. It is also important to note that each row in the matrix represents one experimental treatment, and the sequence of these experiments was randomized. The three levels of each cut parameter selected in the matrix were represented by “1”, “2”, and “3”, as shown in Table 1. At the same time, the value of the S/N ratio was obtained by processing the measured data response, including the surface roughness (Ra) and processing time (Tm).

Table 1. L₉3⁴ orthogonal matrix

No Experiment	A	B	C	D	Inner/Outer of the acetabular cup
					R1	R2	R3	Tm	R1
1	1	1	1	1	T1.1	T1.2	T1.3	Y1	T1.1
2	1	2	2	2	T2.1	T2.2	T2.3	Y2	T2.1
3	1	3	3	3	T3.1	T3.2	T3.3	Y3	T3.1
4	2	1	2	3	T4.1	T14.2	T4.3	Y4	T4.1
5	2	2	3	1	T5.1	T5.2	T5.3	Y5	T5.1
6	2	3	1	2	T6.1	T6.2	T6.3	Y6	T6.1
7	3	1	3	2	T7.1	T7.2	T7.3	Y7	T7.1
8	3	2	1	3	T8.1	T8.2	T8.3	Y8	T8.1
9	3	3	2	1	T9.1	T9.2	T9.3	Y9	T9.1

Where: A, B, C, and D are parameter values: R₁, R₂, R₃ – responses, and T_i,j – the result of trial i, measurement j, i = 1, … 9, j = 1, 2, 3

2.3. Experiment procedure

Experimental tests were conducted on a Harford LG 800 CNC Milling machine at an accuracy of 1.00 µm, as shown in Figure 1. The factors, along with the level of factors, determined in this experiment are presented in Table 2 according to the machining conditions of the acetabular cup product shown in Figure 2a and designed using PShape 2016 software as reported by Lestari et al. (2019).

Figure 1. Machining setup for the experiment: (a) CNC Milling Harford LG 800; (b) UHMWPE on machine.

Figure 2. 1gfds 3D CAD model acetabular cup [19].

Table 2. Factors, unit, code, and levels in the experiment

Factor	Unit	Code	Levels
			1	2	3
Spindle speed	rpm	A	7000	7500	8000
Step over	mm	B	0.01	0.0125	0.015
Depth of cut	mm	C	0.55	0.6	0.65
Feed rate	mm/min	D	1300	1350	1400

The machining operation was conducted under lubrication conditions through dry cutting. The other information about the process is presented in Table 3.

Table 3. Milling machine information

Machine equipment	Hartford LG 800
Equipment	center fit, tool setter, EndMill dia 8 mm, z = 4 teeth, Ballnose diameter 6 mm, with z = 2 teeth
Cutting Fluid	Dry cutting
Workpiece	UHMWPE (density 0.93 g/cm^3; Hardness= 60–65 Shore D; Tensile Strength = 40 N/mm^2; Elongation at break = 50%

This experiment aimed to optimize the cutting parameters, including the spindle speed, step over, depth of cut, and feed rate, and obtain the best surface roughness and cutting time. It is important to note that the surface roughness was measured using Mark Surf P.S. 1 while the processing time was through a stopwatch gauge. Moreover, the Ra value was in three points based on the capacity of the sensor probe on the measuring instrument, and the results are presented in Table 4. Meanwhile, the calculation of S/N ratios for each level of Ra and Tm is indicated in Tables 5 and 6 and Figure 3.

Figure 3. Main effect plot curve of acetabular cup for S/N ratio and means: (a) Ra inner, (b) Ra outer, (c) Tm inner, (d) Tm outer.

Table 4. The L₉3⁴ observed values of surface roughness and time machining acetabular cup

Exp	A	B	C	D	Inner of the acetabular cup				Outer of the acetabular cup
					R1 µm	R2 µm	R3 µm	Tm sec	R1 µm	R2 µm	R3 µm	Tm sec
1	1	1	1	1	0.69	0.78	0.93	2696	0.71	0.89	0.92	1602
2	1	2	2	2	0.98	0.99	0.87	2094	0.98	1.12	1.11	1720
3	1	3	3	3	0.89	1.11	1.26	1799	1.13	1.23	1.44	1007
4	2	1	2	3	0.61	0.68	0.76	2498	0.73	0.93	0.59	1400
5	2	2	3	1	0.93	0.89	0.97	2260	1.24	1.19	1.27	1779
6	2	3	1	2	0.91	1.10	1.24	1853	1.57	1.73	1.03	1062
7	3	1	3	2	0.59	0.42	0.78	2452	0.89	0.37	0.63	1524
8	3	2	1	3	0.99	0.87	0.91	2085	0.97	1.30	1.26	1668
9	3	3	2	1	1.23	1.28	1.08	1947	1.45	1.44	1.10	1089

Table 5. Response for inner and outer Ra for S/N ratios and means

Factor	Ra inner					Ra outer
	Level 1	Level 2	Level 3	Delta	Rank	Level 1	Level 2	Level 3	Delta	Rank
S/N ratio (dB)
A	−0.825	−0.193	0.461	1.286	1	−0.586	−0.356	0.249	0.834	1
B	0.0489	−0.435	−0.172	0.484	2	−0.141	−1.893	−0.362	0.221	4
C	0.0025	−0361	−0.199	0.364	3	−0.394	−0.174	−0.126	0.268	3
D	−0.399	−0.049	−0.110	0.350	4	−0.051	−0.168	−0.474	0.423	2
Means (µm)
A	1.000	1.023	0,949	0.151	1	1.08	1.04	0.97	0.10	1
B	0.997	1.054	1.021	0.058	2	1.02	1.02	1.04	0.03	4
C	1.001	1.044	1.027	0.043	3	1.05	1.02	1.02	0.03	3
D	1.048	1.010	1.014	0.038	4	1.01	1.02	1.06	0.05	2

Table 6. Response for inner and outer Tm for S/N ratios and means

Factor	Ra inner					Ra outer
	Level 1	Level 2	Level 3	Delta	Rank	Level 1	Level 2	Level 3	Delta	Rank
S/N ratio (dB)
A	−66.71	−66.800	−66.65	0.14	3	−62.95	−62.82	−62.95	0.14	4
B	−68.12	−66.630	−65.42	2.7	1	−63.56	−64.72	−60.44	4.28	1
C	−66.78	−66.720	−66.66	0.13	4	−63.02	−62.79	−62.91	0.23	3
D	−67.16	−66.520	−66.48	0.68	2	−63.28	−62.96	−62.48	0.8	2
Means (µm)
A	2196	2204	2161	42	3	1443	1414	1427	29	4
B	2549	2146	1866	682	1	1509	1722	1053	670	1
C	2211	2180	2170	41	4	1444	1403	1437	41	3
D	2301	2133	2127	174	2	1490	1435	1358	132	2

The observed value optimization was, therefore, determined by comparing the standard analysis and analysis of variance using the Taguchi method and the Desirability function (D.F.).

3. Data, analysis data and discussions

The experiment was conducted using four factors: A, B, C, and D, with each set at three levels, as indicated in Table 2, to determine their respective contribution toward the machining process of the acetabular cup in the CNC milling machine. There would have been a need for 81 treatment combinations in machining the product if the experiment had been conducted in full factorial, but only nine were used due to the selection of the Taguchi method, as shown in Table 4. This method is, however, effective and efficient because it does not require a long time and cost to run the entire experiment but has a significant effect on the observed response in the form of Ra and Tm. Moreover, the treatment combination also shows the magnitude of the contribution made by each factor and the level considered to be a significant factor at the experimental point (Montgomery, 2013; Roy, 1990). The Taguchi method was selected for this research because it is considered the most effective and practical method to determine the optimal machining parameters by selecting the right orthogonal array (O.A.) matrix (Bellavendram, 1995; Unal & Dean, 1991). This study used L₉ 3⁴ as the O.A., as indicated in Table 4.

The machining performance with a significant ANOVA factor for each experiment at OA L₉3⁴ was calculated using the observed Ra and Tm values presented in Table 4. Moreover, the S/N ratio and means output for the data response are presented in Tables 5 and 6 as well as Figure 3. The quality characteristics preferred was the “smaller the better” because the two data responses required for optimal acetabular cup working characteristics were the smallest Ra and fastest Tm values. Furthermore, the data processed using Minitab v17 software showed the optimal cutting parameter conditions for Ra using the initial Taguchi method were A₃B₁C₁D₂ which is inner with an average Ra of 0.597 µm, and A₃B₁C₃D₁ which is the mean outer with Ra of 0.63 µm as presented in Table 4. This combination was found to be the optimal condition to obtain the predicted Ra value. Meanwhile, the Ra inner and Ra outer prediction values were obtained using equation (2) conveyed by (Bellavendram, 1995; Unal & Dean, 1991).

(2) $\mathit{R}{a}_{\mathit{pred}}=T_{\mathit{Raexp}}+\left(\mathit{A}3-T_{\mathit{Raexp}}\right)+\left(\mathit{B}1-T_{\mathit{Raexp}}\right)+\left(\mathit{C}1-T_{\mathit{Raexp}}\right)+\left(\mathit{D}1-T_{\mathit{Raexp}}\right)$(2)

where: T_Ra_exp is the average experimental Ra which is 1.024 µm while A₃ is 0.9489 µm, B₁ is 0.9967 μm, C₁ is 1.0011 μm, and D₂ is 1.0100 μm from Table 5. When these values are substituted in equation (2), the Ra_pred_inner value of 0.8847 μm was obtained and the same method was used for Ra_pred_outer to obtain 0.9294 μm. There was also the need to calculate the confidence interval (CI) to verify whether the experimental results presented in Table 4 are under the predicted values. According to Roy (1990), this CI value can be calculated using equations 3 and 4.

(3) $n_{\mathit{eff}}=\frac{\mathit{total}\mathit{number}\mathit{experiment}}{1+\mathit{number}\mathit{degree}\mathit{of}\mathit{freedom}\mathit{that}\mathit{used}}$(3)

$n_{\mathit{eff}}=\frac{9}{1+4}\mathit{\hspace{0.17em}}=1.8$

(4) $\mathit{CI}=\sqrt{F_{\alpha ;1;dof{v}_e}\times V_{\mathit{exp}}\times \left(\frac{1}{{\mathit{n}}_{\mathit{eff}}}+\frac{1}{r}\right)}$(4)

$\mathit{C}{I}_{\mathit{Ra}\mathit{Inner}}=\sqrt{F_{0.05;1;4}\times 0.036\times \left(\frac{1}{1.8}+\frac{1}{3}\right)}$

$\mathit{C}{I}_{\mathit{RaInner}}=04967\mathit{\mu }\mathit{m}$

The same method was applied to the CI outer to obtain 0.4827 μm. The two values were later used to predict the optimal limit of Ra inner and Ra outer values for the acetabular cup products. The same also applies to the machining time response with equations 2(2) $\mathit{R}{a}_{\mathit{pred}}=T_{\mathit{Raexp}}+\left(\mathit{A}3-T_{\mathit{Raexp}}\right)+\left(\mathit{B}1-T_{\mathit{Raexp}}\right)+\left(\mathit{C}1-T_{\mathit{Raexp}}\right)+\left(\mathit{D}1-T_{\mathit{Raexp}}\right)$(2) , 3(3) $n_{\mathit{eff}}=\frac{\mathit{total}\mathit{number}\mathit{experiment}}{1+\mathit{number}\mathit{degree}\mathit{of}\mathit{freedom}\mathit{that}\mathit{used}}$(3) , and 4(4) $\mathit{CI}=\sqrt{F_{\alpha ;1;dof{v}_e}\times V_{\mathit{exp}}\times \left(\frac{1}{{\mathit{n}}_{\mathit{eff}}}+\frac{1}{r}\right)}$(4) used to obtain the values for Tm_pred inner to be 1762.67 sec and CI_(TM_inner) was 26,913 sec while Tm_pred Outer was 944.33 sec and CI_(TM_outer) was 27.9012 sec. This was followed by the prediction of the optimal limits of Ra and Tm (inner and outer) for the acetabular cup with the following results:

R_a inner = |Ra_pred inner – CI |< Ra_pred inner < Ra_pred inner | Ra_pred inner – CI|; 0.3880 μm <0.8847 μm <1.3814 μm

R_a outer = | Ra_pred outer—CI |< Ra_pred inner < Ra_pred outer | Ra_pred outer – CI|; 0.4467 μm <0.9294 μm <1.4121 μm

Tm inner = | Tm_pred inner – CI |< Tm_pred inner < Tm_pred inner | Tm_pred inner – CI|; 1735.7567 sec <1762.67 sec <1789.5833 sec

Tm Outer = |Tm_pred outer—CI| < Tm _pred inner < Tm_pred outer |Tm_pred outer – CI|; 916.4288 sec <944.33 sec <972.2312 sec.

The CI value was also used to compare the confirmatory experiments with the calculated predicted values, as presented in Table 7.

Table 7. Comparison of calculated predicted value with the experimental results using different methods

Respond	Confirmatory Experiment Result	Calculated Value	CI	Diff	Optimization
Ra inner	0.916	0.8847	0.4967	0.0313	Success
Ra outer	1.082	0.9294	0.4827	0.1526	Success

The optimal Tm value in these conditions was in the A₃B₃C₃D₃ with the Tm inner recorded to be 2085 sec and A₂B₃C₂D₃ with the Tm outer at 1853 sec. These are, therefore, observed to be in line with the findings of previous studies (Anggoro et al., 2019, 2020; Fratila & Caizar, 2011; Sarıkaya & Güllü, 2014).

The 3D curve plot was also used to present the significant effect of all the factors determined on the two responses visually. The curve illustrates the relationship between the observed factors and the response measured in the form of a 3D plot processed using V statistic 5 software, as indicated in Figures 4 and 5. The optimal response value of Ra and Tm was, therefore, observed to be optimal at levels 1–2 for factors C and D, level 2 for factor B, and levels 2–3 for factor D. This indicates similarities in the process and results as well as the findings of previous studies (Anggoro et al., 2020).

Figure 4. The 3D plot Curve of surface roughness of acetabular cup: (a) Ra vs Dept of cut— Spindle Speed, (b) Ra vs Feed rate – Step over, (c) Ra vs Step over – Spindle speed, (d) Ra vs Feed rate vs Depth of cut, (e) Ra vs Depth of cut – Step over, (f) Ra vs Feed rate – Spindle speed.

Figure 5. The 3D plot curve of machining time for the acetabular cup: (a) Tm vs Depth of Cut – Spindle Speed, (b) Tm vs Feed rate – Step over, (c) Tm vs Step over – Spindle speed, (d) Tm vs Feed rate vs Depth of cut, (e) Tm vs Depth of cut – Step over, (f) Tm vs Feed rate – Spindle speed.

The experimental data analysis was based on ANOVA and the F or P test value which is the standard analysis. This made it possible to determine the main effect of the process parameters and define the optimal cutting conditions using the Sq-sum of square due to factor i (i = A, B, C, D), Mq—Mean square to factor i, the ratio of factor i, Sq—a pure sum of squares, and Rho% - percentage contribution of factor i according to the mathematical procedure of the Taguchi method [1]. This analysis was applied to study the trend of the effect of each factor, as shown in Figure 3, and the results were discovered to be consistent with those reported by (Anggoro et al., 2019, 2020; Asiltürk & Nesseli, 2012; Fratila & Caizar, 2011; Hanafi et al., 2012; Sarıkaya & Güllü, 2014; Yadav, 2017). Meanwhile, the ANOVA to show the machining performance for each experiment with OA L₉3⁴ was calculated by considering the Ra and Tm values in Table 4, and therefore, the results are conferred in Tables 8 and 9. It was, however, discovered that the combined two-factor interaction with the models once one-step calculation did not considerably influence a single parameter (p > 0.02). Therefore, the successive step was targeted at governing the interaction to get p < 0.02. The interactions obtained between the six factors are presented in Tables 8 and 9 to incorporate linear (single), quadratic, and cubic. Moreover, the degree of influence made up our minds from the proportion contribution of the factors to the minimum Ra mathematical model. The larger contribution value, however, indicates a higher magnitude of the factor’s influence.

Table 8. ANOVA for Ra of the acetabular cup

Factor	SS	DF	MS	F	p	% Rho
A	0.022326	1	0.022326	0.98393	0.002233	1.92
A^2	0.097795	1	0.097795	430.995	0.00978	8.41
B	0.014599	1	0.014599	0.64340	0.00146	1.26
B^2	0.202008	1	0.202008	890.270	0.020201	17.37
C	0.057817	1	0.057817	254.804	0.005782	4.97
C^2	0.178848	1	0.178848	788.203	0.017885	15.38
D	0.019718	1	0.019718	0.86902	0.001972	1.70
D^2	0.002695	1	0.002695	0.11876	0.000269	0.23
A*B	0.316437	1	0.316437	1.394.572	0.031644	27.21
A*C	0.097855	1	0.097855	431.259	0.009786	8.42
A*D	0.01921	1	0.019210	0.84660	0.001921	1.65
B*C	0.000643	1	0.000643	0.02835	6.43E–05	0.06
B*D	0.005757	1	0.005757	0.25370	0.000576	0.50
C*D	0.01578	1	0.015780	0.69544	0.001578	1.36
Error	0.249597	11	0.022691			21.47
Total SS	1.162733	25				1

Table 9. ANOVA for Tm of the acetabular cup

Factor	SS	DF	MS	F	p	% Rho
A	380713	1	380714	7.366.250	0.002014	21,04
A^2	79601	1	79601,3	1.540.168	0.024041	4,40
B	84805	1	84805,5	1.640.863	0.022655	4,69
B^2	19545	1	19545	0.378167	0.055110	1,08
C	2005	1	2004,9	0.038792	0.084745	0,11
C^2	138332	1	138332	2.676.518	0.013010	7,65
D	30442	1	30441.8	0.589004	0.045896	1.68
D^2	9525	1	9525.5	0.184304	0.067599	0.53
A*B	4913	1	4913.4	0.095067	0.076359	0.27
A*C	4742	1	4741.5	0.091741	0.076763	0.26
A*D	26359	1	26358.7	0.510003	0.049001	1.46
B*C	1992	1	1992.2	0.038547	0.084793	0.11
B*D	39744	1	39744.4	0.768996	0.039927	2.20
C*D	492206	1	492206	9.523.468	0.001036	27.21
Error	568518	11	51683.5			31.43
Total SS	1809092	25				1

Table 7 shows the interaction between factors and levels provided a significant response based on the percentage contribution value of rho, which is more than 5%. This is observed in factors A*B with 27.21%, A*C with 8.42%, C with 4.97%, B2 with 17.37%, C2 with 15.38%, and A2 with 8.41%. This, therefore, means factors A, B, and C significantly affect the observed changes in Ra values, which is consistent with the results obtained by previous researchers [1, 3, 4, 16, 17]. Similar to the results obtained from Table 8, the three factors A with 21%, B with 4.69%, C2 with 15.38%, and C*D with 27.21% also provided the largest %rho value and p-value ≤0.02 which is significant to the observed Tm response.

The ANOVA for the optimum variable of the response Ra and Tm for the second-order regression model shown in Tables 10 and 11 indicates that the F-value of the two responses is greater compared to the F-table. Meanwhile, the input parameters’ contribution or factors are thought of important once the calculated Fz values exceed the F_0.02 quoted from applied mathematics tables (Unal & Dean, 1991). The results showed all the F calculated values are much larger than F0.02 and the significant factors were categorized into two levels: those considered significant, with the main contribution and the insignificant ones. Moreover, Tables 10 and 11 show the coefficient multiple determination (R²) value, according to Montgomery (2013) is R² ≥ 90% and this means the factors selected in this experiment and the model have a significant effect on both observed responses as indicated by 96.3% and 97.5% values obtained.

Table 10. ANOVA for the optimal variable of Ra

Source	Sum of squares	DoF	Mean of square	F-value	F-table	R^2
S.S. Regression	1.051488	14	1.051488	46.340218	2.84	0.975
S.S. Error	0.249597	11	0.022691
S.S. Total	1.301085	25

Table 11. ANOVA for the optimal variable of Tm

Source	Sum of squares	DoF	Mean of square	F-value	F-table	R^2
S.S. Regression	1314925.51	14	1314925.51	2.671494	2.84	0.963
S.S. Error	568518.35	11	492206.05
S.S. Total	1883443.87	25

The experimental data analysis was based on ANOVA, and the F or P test value which is a standard analysis. This allowed the determination of the main effect of the process parameters and also defined the optimal cutting conditions. It was also possible to optimize Ra and T.M. values using a desirability function by applying the Minitab 2018 software. This method involves using the range scale between 0 and 1 (Anggoro et al., 2019, 2020, 2023; Asiltürk & Nesseli, 2012), such that when df = 1 or close to 1 the optimal response is acceptable and observed to be approaching the target value, and when it is 0 or close to 0 the response is rejected. This study used the “smaller-the-better” desirability method because the response value to be achieved is the minimum, and the results obtained for the Ra and TM. are presented in Figures 6 and 7.

Figure 6. Optimization of Ra value using desirability function analysis.

Figure 7. Optimization of TM Value using desirability function analysis.

The methods used in this study were compared to determine the one closer to the actual result based on their output, and the combined Taguchi-DF approach was found to be better than only the Taguchi. This is due to the lower Ra value, and smaller absolute error recorded with this method, as indicated in the following Table 12, and the use of the D.F. method in this paper was able to provide an improvement of 17.29%, as previously described by (Anggoro et al., 2021, 2022, 2023). This study shows the effectiveness and potential of cutting tools during the turning of samples as an effective and cost-effective option to replace machining processes. As a result of the study, with the tempering process, the machinability has improved due to toughness values by decreasing the hardness (Anggoro et al., 2022, 2023; Kam & Demirtaş, 2021, 2021).

Table 12. Comparison of the Taguchi approach with the combination of the Taguchi desirability function method

Optimization technique approach	Ra inner		Absolute error (%)
	Experiment	Calculate
	(µm)	(µm)
Taguchi approach	0.916	0.8847	3.54
Desirability Functions (DF)	0.881	0.771	1.43
Percentage improvement (%)	17.29

4. Conclusions

Optimizing the acetabular cup manufacturing process to obtain the optimum processing time and surface roughness (Ra) <2.00 µm was considered successful through the Taguchi-RSM combination method. This study emphasizes the value of surface roughness (Ra) to achieve the ASTM standard (≤2.00 µm), and this led to the selection of the parameters with optimal response conditions for the Ra value of the inner acetabular cup. The optimal result shows that Ra inner optimal = 0.881 µm and Tm inner optimal = 1746.37 sec, with optimal machining setting parameter, were A₃B₁C₁D₂ (A₃=spindle speed at 8000 rpm, B₁=step over 0.01 mm. C₁=depth of cut 0.55 mm, and D₂ = feed rate of 1350 mm/rev) Ra outer optimal = 0.928 µm, Tm outer optimal = 942.21 sec, with optimal setting parameter were A₃B₁C₃D₁ (A₃=spindle speed at 8000 rpm, B₁=step over 0.01 mm. C₃=depth of cut 0.65 mm, and D₁ = feed rate of 1300 mm/rev)

This research contributes to getting the optimal machining parameter for the optimal quality acetabular cup manufacturing process. This means combining the two methods for the optimization process is preferable due to its ability to produce surface roughness values with lower absolute error than those recorded using only one method.

These results, however, require further relation to obtain more optimal response values compared to this current research, for example, through the use of the response surface method or other optimization techniques.

Table

Nomenclatures
S N Ai Bi Ci Di	Sum of squares Number of experiment Factor A with level i = 1, 2, 3 Factor B with level i = 1, 2, 3 Factor C with level i = 1, 2, 3 Factor D with level i = 1, 2, 3
Greek Symbols
$n_{\mathit{eff}}$ $\mathit{R}{a}_{\mathit{pred}}$ $\left({\sum }^{y^2}\right)$ $T_{\mathit{Raexp}}$ $\mathit{C}{I}_{\mathit{RaInner}}$	Sum of degree experiment Value of surface roughness prediction in this experiment Sum of response data Value of Time machining based on surface roughness Value of confident interval of surface roughness of the inner surface of the acetabular cup
Abbreviations
CNC EVA UHMWPE ASTM ANOVA OA DF CI	Computer Numerical Control Ethylene Vinyl Acetate Ultra-High Molecular Weight Polyethylene American Society for Testing and Material Analysis of Variance Orthogonal Array Desirability function. confidence interval.

Acknowledgments

The authors are grateful to the tribology laboratory in the Department of Mechanical Engineering, Faculty of Engineering, Universitas Diponegoro, Semarang, Central Java, Indonesia, and the Department of Industrial Engineering, Faculty of Industrial Technology, Universitas Atma Jaya Yogyakarta for providing full support with all infrastructure during the collection and analysis of the data.

Disclosure statement

No potential conflict of interest was reported by the authors.

Data availability statement

The data presented in this study are available on request from the corresponding author.

Additional information

Funding

The authors received no funding for the research.

Notes on contributors

Y.A.W. Ninggar

Y.A.W. Ninggar, received a BS degree in engineering from the Universitas Atma Jaya Yog-yakarta.

P.W. Anggoro is a professor in industrial engineering and obtained a doctoral degree from Universitas Diponegoro, Indonesia and Lecture at Department of Industrial Engineering, Uni-versitas Atma Jaya Yogyakarta, Indonesia. His research interest focus on Reverse Innovative Design with additive and subtractive manufacturing technology.

P.W. Anggoro

P.W. Anggoro is a professor in industrial engineering and obtained a doctoral degree from Universitas Diponegoro, Indonesia and Lecture at Department of Industrial Engineering, Uni-versitas Atma Jaya Yogyakarta, Indonesia. His research interest focus on Reverse Innovative Design with additive and subtractive manufacturing technology.

B. Bawono obtained doctoral degree from Universitas Diponegoro, Indonesia.

B. Bawono

D.B. Setyohad is a professor in the system information of the Department of Universitas Atma Jaya Yogyakarta.

D.B. Setyohad

D.B. Setyohad is a professor in the system information of the Department of Universitas Atma Jaya Yogyakarta.

M. Tauviqirrahman

M. Tauviqirrahman obtained a doctoral degree from the Laboratory for Surface Technology and Tribology, University of Twente, the Netherlands.

J. Jamari

J. Jamari is a professor in tribology and received a doctoral degree from the Laboratory for Surface Technology and Tribology, University of Twente, the Netherlands.