Integrating Taguchi Method and Finite Element Modelling for Precision Ball Joint Manufacturing with AISI 1045 Medium Carbon Steel

This study optimized the hot forging conditions for AISI 1045 medium carbon steel ball joints by integrating the Taguchi method with Finite Element Method (FEM) simulations. The research focused on three key process parameters: billet temperature (1000-1200°C), billet length (153-160 mm), and friction factor (0.15-0.64). The analysis of Variance (ANOVA) identified billet temperature and friction factor as the most influential parameters, accounting for over 96% of the variation in forging loads. Optimal forging conditions were determined as a billet temperature of 1200°C, billet length of 153 mm, and friction factor of 0.15. The linear regression models exhibited high predictive accuracy, with R² values of 0.978 and 0.988 for maximum preforming and finishing loads, respectively. FEM simulations incorporating the Johnson-Mehl-Avrami-Kolmogorov (JMAK) model effectively predicted the microstructural evolution with grain sizes ranging from 5.10 to 41.22 , showing a mean deviation of 15.51% from experimental measurements. The simulations also accurately predicted the pearlite phase transformation, achieving a 37-42% pearlite volume fraction with only a 5.33% error and tensile strength distributions ranging from 642.04 to 642.12 MPa. Experimental validation confirmed defect-free die cavity filling, with FEM simulations and predictive models showing satisfactory agreement with experimental forming loads for both preforming and finishing stages. This integrated approach offers a robust framework for optimizing complex forging processes, ensuring consistent product quality, and minimizing material waste.

ANOVA; FEM; hot forging; JMAK microstructure evolution model; Taguchi method

    In the automotive industry, producing high-quality components ensures vehicle safety, durability, and optimal performance. Hot forging, a fundamental process that shapes metals by heating and deformation, plays a vital role in achieving these objectives. Forging, one of the oldest metalworking techniques, continues to be widely used in modern manufacturing because of its unmatched reliability, efficiency, and capacity to deliver superior mechanical properties. Additionally, it reduces material waste, making it indispensable in sectors such as aerospace, automotive, and agriculture (Harris, 2014; Altan, 2005). The hot forging process involves shaping a malleable metal billet through hammering and pressing, which induce plastic deformation at approximately 75% of the material’s melting point. The process involves heating the billet to its plastic deformation temperature and forging it between dies to achieve the desired shape, which refines the coarse-grain structure of the billet into finer grains. After the forging process, the product typically undergoes an additional heat treatment (Zhan, Sun, and Yang, 2014; Debin and Lin, 2014). 

2.1. Chemical composition

The material used in this study was AISI 1045 steel, a medium-carbon steel widely utilized in various industries, particularly in the automotive and machinery sectors. Table 1 details the chemical composition of AISI 1045 steel in accordance with standard specifications. Table 2 compares its international grades, highlighting equivalents in the AISI, DIN, JIS, GB, and BS standards. To validate these specifications, chemical composition analysis was performed on two specimens using an optical emission spectrometer. The results, summarized in Table 3, confirm the presence of key elements such as carbon (C), nickel (Ni), chromium (Cr), and molybdenum (Mo) in AISI 1045 steel.  The combination and proportion of these elements enhance its high strength, hardenability, and corrosion resistance. The analyzed chemical composition demonstrated compliance with the standard AISI specifications, affirming its conformity to the AISI 1045 steel standards.

Table 1 Chemical composition of the AISI 1045 steel (AISI standard)

Table 2 International grades of AISI 1045 steel

Table 3 Chemical composition testing results for AISI 1045 steel

2.2. Mechanical properties

Mechanical properties of AISI 1045 steel were investigated through thermal compression experiments using a Baehr DIL-805 deformation dilatometer to investigate the mechanical properties of AISI 1045 steel. For the experimental setup, twelve cylindrical samples, each with a diameter of 5 mm and a height of 10 mm, were prepared using a laser cutting tool. The deformation temperature was directly monitored by attaching a thermocouple to the surface of each sample. The experiments were conducted at four deformation temperatures (900°C, 1000°C, 1100°C, and 1200°C) and three strain rates (0.1 s^-1, 1 s^-1, and 10 s^-1). Each sample was placed in a vacuum chamber filled with argon gas to prevent oxidation. Heating was performed using an induction coil at a controlled rate of 1.625°C per second until the target temperature was reached. To achieve thermal equilibrium the samples were held at the target temperature for 1 minute to ensure uniform temperature distribution. The deformation process consisted of compressing to a height reduction of 60% using an Alumina punch, immediately quenched in argon gas, and cooled at 40°C per second to room temperature. The deformation route of the hot compression experiment is depicted in Figure 1(a). Flow stress  data, derived from the hot compression tests and represented as functions of strain and temperature (T), were integrated into the FEM simulation software. Representative flow curves for various deformation conditions are shown in Figures 1(b) and 1(c). Table 4 summarizes the mechanical properties of AISI 1045 medium carbon steel, including its density, modulus of elasticity, ultimate tensile strength, yield strength, Poisson's ratio, and Brinell hardness. These properties provide critical insights into the material’s characteristics under different forging conditions and are essential inputs for simulations and analyses.

Table 4 Mechanical properties of the AISI 1045 medium carbon steel.

Figure 1 (a) Schematic diagram of hot compression tests and examples of flow stress curves for AISI 1045 medium carbon steel varying conditions at a strain rate of (b) 1 s^-1, and temperature of (c) 1100°C.

2.3. Microstructure characterization

The validation of FEM simulation results was accomplished through grain size and phase analysis. The cut sample was mounted using a hot mounting press, and the cutting surfaces were polished in stages. Initial polishing was performed using 400-grit SiC abrasive paper, followed by sequential polishing with 600, 800, 1000, and 1200-grit SiC papers. Final polishing used 0.3 µm alumina particles to achieve a smooth surface. After polishing, the surfaces were etched for 4 s using 4% picral solution and 3% Nital solution to reveal the microstructure. Microstructural observations were conducted using Light Optical Microscopy (LOM). The initial microstructure of the AISI 1045 medium carbon steel was composed of proeutectoid ferrite and pearlite, as shown in Figure 2. To determine the average grain size, the Metallographic method was applied following the ASTM E1382 standard.

Figure 2 Initial Microstructure of AISI 1045 medium carbon steel, as observed through OM at a magnification of 200x, depicting proeutectoid ferrite and pearlite structures.

2.4. Microstructure Evolution Model

In hot forging, dynamic recrystallization (DRX) initiates due to the accumulation of dislocations resulting from plastic deformation. DRX begins when the dislocation density surpasses a critical threshold, referred to as the critical strain for DRX  (Wu et al., 2018). Various studies have attempted to predict the critical strain. Wang et al. (2021) observed that the stress peak in the flow curve at a constant strain rate corresponds to an inflection point in the strain hardening rate versus stress plots. Building upon this observation, Poliak and Jonas (2003) demonstrated that this inflection point indicates the onset of an additional thermodynamic degree of freedom in the system, which marks the initiation of DRX. To enhance analytical efficiency, Mirzadeh and Najafizadeh (2010), and  Najafizadeh and Jonas (2006) refined Poliak and Jonas’s approach by fitting a third-order polynomial equation to the curves. Using this method, the normalized critical strain can be expressed as the following ratio: is derived by incorporating parameters such as the initial grain size temperature (T), strain rate and the activation energy for deformation (Q) (Chen et al., 2022; Wang et al., 2011). These relationships are further elaborated in Equation 1.

(1)

This study utilizes a computational approach to predict the microstructure evolution of forged components, with DRX kinetics serving as a key aspect of the analysis. The widely adopted JMAK equation underpins the modeling of DRX kinetics. The validity and reliability of this equation have been extensively demonstrated in numerous studies (Zhang et al., 2022a; 2022b; Joun et al., 2022; Ji et al., 2021; Zhang et al., 2020a; Ji et al., 2020; Zhang et al., 2019; Marques Ivaniski et al., 2019).

(2)

Equation 2 defines the evolution of the DRX volume fraction as a function of strain. The strain required to achieve a 50% DRX volume fraction, as determined by Equation 3, is derived from the correlations established in the existing literature.

(3)

The average DRX grain size is defined as

(4)

The microstructural evolution during DRX is mathematically represented by Equations 1-4, which incorporate coefficients derived from experimental data. In this study, the coefficients specific to AISI 1045 medium carbon steel are presented in Table 5, as reported by Siripath et al. (2024). Their research on the DRX characteristics and microstructure evolution of AISI 1045 medium carbon steel under high temperatures and varying strain rates established a strong correlation between the simulation results and experimental observations, validating the accuracy of the developed models. Using these equations, a FEM model was integrated into the finite element software to predict the microstructure evolution in the forged components, with a particular focus on ball joints.

Table 5 Coefficients of the microstructure equations for the investigated steel.

2.5. Experiment design

The Taguchi method, developed by Dr. Genichi Taguchi at Japan's Electronic Control Laboratory in the late 1940s, is a standardized Design of Experiments (DOE) technique that enables the simultaneous analysis of multiple variables to identify optimal outcomes. This approach offers a robust and efficient means of examining the intricate relationships between process parameters while streamlining production processes to improve operational efficiency. As a cost-effective method, the Taguchi method reduces the required specimens and the time needed for investigations without compromising accuracy (Budiyantoro et al., 2024). The Taguchi method uses two essential tools: an orthogonal array (OA) for structuring experimental runs and the signal-to-noise (S/N) ratio for assessing performance quality. The OA is constructed based on the control factors (design parameters) and their respective levels. The S/N ratio is calculated using performance characteristics to quantify variations, with a higher S/N ratio indicating better quality performance, where noise represents variance. The S/N ratios are categorized into three types based on optimization goals: “lower is better” (LB), “nominal is best” (NB), and “higher is better” (HB) (Khentout, 2019; Sudeesh, 2018; Kumar, 2012; Wu and Chang, 2004)

The most critical stage of the Taguchi method is selecting the appropriate control factors. In this study on forging, three key control factors were identified: initial billet temperature, billet length, and friction factor (as outlined in Table 6). To structure the experiment, an L9 orthogonal array, outlined in Table 7, was used, allowing for a set of nine simulations incorporating three levels for each of the three factors. The simulations were designed and analyzed using MINITAB 19.2 software. For this study, the "LB" S/N ratio was chosen because minimizing the forging loads and maximum stresses is a key objective. The S/N ratio was calculated using Equation 5, where n represents the number of trials and yi denotes the value of the i-th observation.

(5)

Table 6 Control factors and their levels.

In industrial practice, billets are typically heated to around 1100 °C, consistent with the findings of Murugesan and Jung (2019), which highlight that optimal forgeability of AISI 1045 medium carbon steel occurs within the temperature range of 850 °C to 1250 °C. Regarding billet length, the standard industrial practice employs a length of 160 cm. However, to enhance practicality and reduce initial billet volume, shorter lengths of 160 mm, 157 mm, and 153 mm were evaluated in this study. Research by Soranansri et al. (2021) demonstrates that optimizing billet size significantly improves metal flow into the die cavity, reduces material waste, and enhances cost efficiency. Similarly, Siripath et al. (2023b) identified 153 mm as the optimal billet length for hot closed-die forging of ball joints using FEM analysis across five tested sizes. This length achieved effective die filling without defects, improving manufacturing efficiency and minimizing material waste, although temperature and lubrication effects were not assessed in their study. The friction factor, a critical variable in the forging process, was also investigated. Poungprasert et al. (2024) determined friction factors under varying lubrication conditions: 0.64 for dry conditions, 0.50 for water with black graphite, and 0.15 for oil with black graphite. These values were derived from hot-ring compression tests on AISI 1045 medium carbon steel and validated through FEM-based predictive calibration curves that monitored changes in the sample height and internal diameter during compression. These findings are directly relevant to ball joint production. By carefully selecting these control factors of initial billet temperature, billet length, and friction factor, this study ensures a comprehensive understanding of their impact on the forging process, thereby justifying their inclusion in this study.

2.6. FE Simulation of Ball Joints

In this study, a ball joint was manufactured using a hot-forging process. The procedure began by heating the billet in an induction furnace, followed by transferring the heated billet to a mechanical press in a forging station. The hot forging process consisted of three primary stages: preforming, finishing, and flash-trimming. During the performing stage, the billet was shaped to distribute the mass and form an approximation of the desired shape. The finishing stage refined the part to achieve precise geometrical and dimensional accuracy. Finally, the flash-trimming operation removed the excess material from the forged part. After the finishing stage, the flash was trimmed, and the workpiece was cooled to ambient temperature. The upper and lower dies used in the forging process were made of SKD61 steel. The preforming die surface was designed to be approximately 1 mm deeper than the finishing die surface, and the die gap between the upper and lower dies was maintained at 3 mm for both preforming and finishing operations. A Crank press JFP-1350 M/C, a 1350-ton mechanical press with a total stroke of 240 mm and an operating speed of 85 strokes per minute, was used to forge the ball joint. To simulate the ball joint manufacturing process, a 3D-CAD model was developed to represent the entire hot forging process, including the upper die, lower die, and billet. The 3D-CAD model was imported into the FEM simulation software for analysis. The FEM model employed tetrahedral elements, with remeshing applied during the numerical solution phase to accommodate significant plastic deformation within the elements. The flow stress-strain and microstructure evolution models were integrated into the FEM simulation software. The simulation conditions were designed to closely replicate the actual hot forging process. The cylindrical billet was designated as a deformable body, while the upper and lower dies were designated as rigid bodies. Ambient heat transfer coefficients were applied based on the recommended values in the software library.

3.1. Taguchi’s experimental design

To optimize the forging conditions, three key parameters—friction factors, billet length, and billet temperature—were analyzed in finite element (FEM) simulations. The maximum forging loads (comprising preforming and finishing loads) and the maximum stress were recorded for each FEM simulation trial. These values served as inputs for calculating the signal-to-noise (S/N) ratios for both the forging loads and the maximum stress using Taguchi response analysis. The results are summarized in Table 7. 

According to the Taguchi method, a higher S/N ratio indicates better quality, indicating optimal conditions can be achieved by selecting the parameter combination with the highest S/N ratio. In this study, the S/N ratio analysis focused on three quality characteristics: maximum forging loads (including preforming and finishing loads) and maximum stress. A "smaller-the-better" criterion was applied because very high stresses and forging pressures can have adverse effects. Excessive stresses may lead to undesirable deformations or defects in the forged product, while elevated forging pressures can damage the dies. Based on the S/N ratio analysis presented in Table 8, the optimal control factor levels were identified for both maximum forging loads and maximum stress parameters. Figure 3 illustrates the relationships between the control factors and their S/N ratio. The optimal forging conditions were determined to be a billet temperature of 1200°C, a billet length of 153 mm, and a friction factor of 0.15. These levels exhibited the highest S/N ratio among all other levels.  

Table 7 Simulation results for maximum forging loads (ton-force, tf) and maximum stresses (MPa).

Table 8 S/N response table for maximum loads and maximum stresses.

Figure 3 Main effect plot of control parameters on the S/N ratio: (a) Maximum preforming loads, (b) Maximum finishing loads, and (c) Maximum Stresses

However, closer examination of the friction factor data for maximum stress revealed a potential anomaly. The S/N ratio for the friction factor remained identical across all three levels at maximum stress. This issue could be attributed to either a data error or the possibility that, within the range studied, the friction factor had a negligible effect on the maximum stress. To validate these findings and assess the significance of each control factor, further analysis using Analysis of Variance (ANOVA) was conducted for both maximum forging loads and maximum stress.

3.2.  ANOVA

The ANOVA results presented in Table 9 evaluate the influence of three factors (billet temperature (°C), billet length (mm), and friction factor) on three distinct responses: maximum preforming load, maximum finishing load, and maximum stress. Each factor’s impact was analyzed based on its percentage contribution to variability, F-value, and corresponding P-value, offering a comprehensive understanding of its statistical significance. The percentage contribution to variability reflects the proportion of the total variation in each response attributable to a specific factor, facilitating the identification of the most influential variables. The F-value, calculated as the ratio of between-group variance to within-group variance, indicates the relative significance of each factor, with higher F-values indicating more substantial differences between group variances. The observed P-values were all less than 0.05, indicating a statistically significant relationship between the factors and the responses (Muhammad Sayuti, 2022; Zhang et al., 2020b; Montgomery, 2010).

Table 9 Results of ANOVA for maximum forging loads and maximum stresses.

The ANOVA results indicate that billet temperature and friction factor significantly affect the maximum preforming load response. Billet temperature contributes 46.03% to variability with a low P-value of 0.014, demonstrating its statistically significant impact. Similarly, the friction factor accounts for 50.78% of the variability, with a low P-value of 0.013, reinforcing its considerable influence. In contrast, billet length had a minor effect, contributing only 2.53% of the variability, with a higher P-value of 0.206, suggesting its impact may not be statistically significant. For the maximum finishing load response, the billet temperature and friction factor again emerged as important contributors. Billet temperature accounts for 69.07% of the variability, with a P-value of 0.01, indicating a strong influence. The friction factor contributes 29.12% to the variability, with a P-value of 0.023, confirming its significant impact. In contrast, billet length has a negligible effect, contributing only 1.12% to the variability, with a higher P-value of 0.381. For maximum stress, billet temperature emerges as a highly significant factor, accounting for 89.13% of the variability. However, its P-value of 0.074, which was moderately high, suggests that additional investigation may be necessary to confirm its significance. Both billet length and friction factor exhibited minimal effects on maximum stress, with relatively high P-values indicating non-significance. In summary, the ANOVA results underscore the critical importance of billet temperature and friction factor in determining maximum preforming and finishing loads. Additionally, they suggest a possible, although less certain, effect of billet temperature on the maximum stress.

3.3. Linear Regression Analysis

This study examined the relationship between dependent and independent variables through regression analysis. The dependent variables included the maximum preforming load, maximum finishing load, and maximum stress, while the independent variables comprised billet temperature (Tb), billet length (lb), and friction factor at the die and workpiece interface (m). The predictive equations derived from the linear regression analysis for the maximum forging loads and maximum stress are provided in Equations (6)–(8) below:

Maximum preforming load (tf) = 1058 - 1.544 Tb + 6.53 lb + 612.9m (6)

Maximum finishing load (tf) = 1376 - 1.5273 Tb + 4.57 lb + 374.4m (7)

Maximum Stress (MPa) = 233.2 - 0.1274 Tb + 0.651 lb - 1.56m (8)

Figure 4 Comparison of (a) the maximum preforming load, (b) the maximum finishing load, and (c) the maximum effective stresses from the simulation against predictions made by the linear regression model

The plots illustrating the maximum preforming load and maximum finishing load, simulated and predicted by regression Equations 6 and 7, are shown in Figures 4(a) and 4(b), respectively. The regression analysis produced average absolute relative errors (AARE) of 4.6118% and 2.78723%, with Coefficient of Determination (R²) of 0.978 and 0.988 for maximum preforming and finishing loads, respectively. The root mean square error (RMSE) values were 31.0974 tf and 18.6350 tf.  Similarly, Figure 4(c) shows the maximum stress, which was both simulated and predicted by using regression Equation 8. This analysis yielded an AARE of 1.57423%, an R² value of 0.909, and an RMSE of 3.79452 tf. The AARE, expressed as a percentage, was a key metric for assessing the model’s overall prediction accuracy, offering a comprehensive assessment of its performance. The R² values, approaching 1, indicate a strong correlation between the predicted and simulated values, affirming the reliability of the regression model. Additionally, the RMSE values highlight the accuracy of the predictions, with lower values reflecting a closer match between predicted and simulated data points (Siripath et al., 2023a; Chen et al., 2021; Gabb et al., 2005). In Figure 4, the blue dashed lines represent the 95% confidence interval (CI), and the purple dashed line denotes the 95% prediction interval (PI).

3.4. Verification results of the FEM

The Taguchi method was used to determine the optimal forging conditions, which were found to be an initial temperature of 1200°C, a billet length of 153 mm, and a friction factor of 0.15. These conditions were subsequently implemented in the simulation software and verified through shop floor experiments for ball joint manufacturing. The FEM simulation mesh details for the ball joint, including the discretization level and element numbers used to represent the geometry and behavior of the initial billet, were as follows: the initial model contained 2093 nodes, 2640 surface elements, and 8532 volumetric elements. Remeshing was required during the numerical solution due to significant plastic deformation.  After the preforming process, the workpiece included 72,474 nodes, 75,358 surface elements, and 331,745 volumetric elements. After the finishing process, these numbers changed to 80,728 nodes, 80,654 surface elements, and 374,564 volumetric elements.

During the experimental trials, the material filled the die cavity without any observable defects in the workpiece, confirming that the forming conditions were successful. Figure 5(a) presents a direct comparison of the ball joint geometry, showcasing the smooth, gray-colored simulation model alongside the actual manufactured component, which exhibits the typical metallic surface finish and texture found in forged parts. The simulated and manufactured parts displayed identical geometric features, including the spherical socket and extended arm with circular indentations. The close alignment between the predicted and actual results validates the reliability of the simulation in accurately predicting the final shape of the manufactured ball joint. 

Figure 5 The final shape of ball joint: (a) simulation and (b) actual object; (c) Bar graph comparing forging loads between experimental data, predictive equation, and FEM simulation.