Finite Element Modeling and Optimization Analysis of Cutting Force in Powder Metallurgy Green Compacts

Highlights

What are the main findings?

• Effect magnitude on cutting force, in descending order: cutting thickness, rounded edge radius, cutting speed, tool rake angle.
• Optimal process parameters identified for minimizing cutting force: cutting thickness of 0.20 mm, cutting speed of 120 m/min, tool rake angle of 0°, rounded edge radius of 40 μm—resulting in a cutting force of 887.95 N.

What is the implication of the main finding?

• Addresses the understudied area of cutting forces in powder metallurgy green compacts.

Abstract

Powder metallurgy (PM) is a manufacturing technique that employs metal powder as the raw material, which is then molded and sintered to produce various products. PM green compacts are inherently weak, rendering them prone to damage during machining due to cutting forces, which also affect the quality of the machined surface. To study the impact of different machining variables on cutting force, a finite element simulation (FEM) was employed, focusing on cutting thickness, cutting speed, tool rake angle, and rounded edge radius. The results indicated that cutting thickness had a highly significant impact on cutting force, while the rounded-edge radius and cutting speed were also significant factors. The tool rake angle was found to have minimal effects. The optimal parameters for minimizing cutting force were identified: a cutting thickness of 0.20 mm, a cutting speed of 120 m/min, a tool rake angle of 0°, and a rounded-edge radius of 40 μm, which reduced the cutting force to 887.95 N.

1. Introduction

Additive manufacturing (AM) plays a crucial role in contemporary industries, significantly contributing to societal advancements. Recent studies on AM have yielded noteworthy findings. For instance, Fang et al. [1] discovered enhanced yield and tensile strengths in alloys fabricated via laser powder deposition (LPD) compared to conventional electric arc melting and hot forging (EAM-HF) methods. Youness et al. [2,3] reported that the sintered nanocomposites of alumina (Al₂O₃) with hydroxyapatite (HA) and zirconium oxide (ZrO₂) with biphasic calcium phosphate (BCP) exhibited favorable properties for biomedical applications.

Powder metallurgy (PM), a subset of AM, utilizes metal powder as the raw material for producing metallic and composite items via molding and sintering processes [4,5,6,7]. Emerging technologies like laser cutting [8], hot stamping [9], and binder-jet 3D printing (BJT) [10] are also being integrated into PM applications. However, the porous nature of sintered PM materials presents unique challenges during machining, including severe micro-vibrations that accelerate tool wear [11,12,13]. This complexity necessitates innovative machining solutions for PM products [14]. The unique challenges in machining powder metallurgy (PM) materials largely stem from the inherent porous structure created post-sintering. This characteristic not only imparts distinctiveness to the cutting process [11] but also induces significant micro-vibrations during machining [12]. These continual micro-vibrations result in accelerated tool wear due to the repetitive impacts, further complicating the machining process [13]. Consequently, developing strategies to overcome these machining hurdles is crucial for the broader adoption and application of PM-based components.

PM and ceramics production share sintering processes, allowing for technology transfer between the two [15]. Post-sintering, ceramic materials become exceedingly hard to machine [16], so current practices involve shaping the green compacts before sintering [17] PM materials can also be improved in this way to improve their machining properties [18]. Green machining represents a transformative approach in the fabrication of PM materials, wherein the PM green compacts are machined to their desired geometries prior to the sintering process, effectively addressing the traditionally challenging machining of PM materials [19,20,21]. Drawing parallels with the low-temperature densification observed in ceramics, Paradis and colleagues discovered an innovative method through the cold sintering of surface-altered iron powders [22]. This technique facilitated the emergence of a mutually continuous phosphate phase amidst the iron powder particles, enhancing both the robustness and density of the green compacts. The resultant green compacts boasted an impressive relative density reaching 95% and a transverse rupture strength of approximately 75 MPa, a figure nearly sixfold that of standard iron green compacts derived from powdered metal.

Regarding PM material properties, considerable scholarly attention exists. Moustafa et al. [23] used PM techniques to reinforce Mg₁₀Li₅ aluminum alloy with yttrium (Y) and silica powder, noting marked improvements in material properties. Issa et al. [24] enhanced Fe-Cu alloys by adding niobium carbide (NbC) and granite. Alazwari et al. [25] found that incorporating waste ceramics improved the properties of Ti-Cu alloys. Rama-dan et al. [26] identified sintering temperature and graphene content as key factors influencing the mechanical properties of sintered composites.

Currently, powder metallurgy (PM) green compacts have been the subject of extensive machining studies. Robert-Perron et al. [27] investigated the sintering properties of cylindrical PM green compacts, demonstrating that pre-sintering machining had no impact on their tensile properties. Yang et al. [28] created a geometric model for PM green machining, outlining a distinct material removal mechanism involving particle shearing, peeling, and plowing/extruding. This highlighted the unique nature of PM material removal compared to conventional materials.

Beyond the study of PM green machining mechanisms, various investigations have explored the machining process of PM green compacts. For example, Kulkarni Harshal et al. [29] empirically demonstrated that a reduced feed rate enhances surface quality. Goncalves et al. [30] confirmed that an increased rounded-edge radius decreased surface roughness. Kumar et al. [31] employed the Gray–Taguchi method to optimize aerospace-grade titanium alloys and performed a statistical analysis. Existing research underscores the significant influence of cutting speed on surface quality.

The impact of cutting forces, notably underexplored in current literature, warrants attention, particularly in the context of PM green machining. Despite the prevailing assumption that the minimal cutting force associated with PM green machining renders such effects negligible [18], the relatively fragile nature of PM green compacts raises concerns about potential damage during machining due to these forces. An in-depth analysis of cutting forces, tailored to diverse machining scenarios, can significantly elevate both the quality and efficiency of part production in PM green compact machining. This necessitates a comprehensive study of how various machining parameters influence cutting forces, an integral aspect of material machining properties analysis. By systematically deciphering the trends within these force alterations, researchers can profoundly enrich their comprehension of material cutting dynamics, thereby potentially unlocking new avenues to optimize machining processes.

To address this research gap, this study examines the influence of cutting forces under varying machining variables. Initially, a finite element model is developed using Abaqus 2022 software and subsequently validated via experiments. This study then employs univariate analysis to assess the impact of cutting thickness, speed, tool rake angle, and rounded-edge radius on cutting force. Multivariate analysis is utilized to explore the collective influence of these parameters. Finally, this study identifies the optimal parameter combinations for minimizing cutting force.

2. Simulation Model Building and Experimental Verification

2.1. Pore Characterization and Modeling

Material porosity serves as a direct indicator of compactness, with lower porosity corresponding to higher density. The porosity P of PM green compacts is given via Equation (1):

$$\mathrm{P}=\frac{V_0 - V}{V_0}\times 100\%=\left(1 - \frac{{\rho }_0}{\rho }\right)\times 100\%$$

(1)

where P is the material porosity (100%), V₀ represents the material volume at room temperature (cm³), V is the absolute dense volume of the material (cm³), ${\rho }_0$ is the material apparent density (g/cm³), and $\rho$ is the material density (g/cm³).

Various pressing methods for PM green materials yield different levels of material porosity [32]. Figure 1a illustrates the microstructure morphology of the PM green material, indicating an internal porosity of approximately 12%. To streamline computational efforts, the pore structure in the PM green compacts was simplified using a single microprocessor. A dual-pore structure was integrated into the workpiece model matrix. Simulation of only the upper-right section of the model was performed to generate a dual-pore model, as depicted in Figure 1b.

2.2. Workpiece Model Parameters

In the simulation, the tool material is modeled as a rigid body, while the workpiece material is assumed to be plastic. To ensure robust validation in subsequent experimental stages, it is imperative that the material parameters used in the modeling closely align with those in the experimental setup. These parameters were either derived from existing literature or calculated from experiments specific to PM green materials.

In this study, test samples of green materials underwent tensile, strength, and compressive tests. Due to the material’s fragility, each experiment was conducted six times to enhance the result’s reliability. The average values were computed to ensure accuracy.

Table 1. Mechanical properties of PM green materials.

Performance	Density (g/cm3)	Vickers Hardness (HV)	Tensile Strength (MPa)	Compressive Strength (MPa)	Elastic Modulus (GPa)	Poisson’s Ratio
Parameter	7.1	87	3.9	98	210	0.018

summarizes the key performance parameters for the PM green materials based on the collected data.

The existing research in cutting and machining has led to the development of various ontological models. These models are frequently cited in the literature concerning materials like rocks, cements, ceramics, and diverse metals. The Johnson–Cook model is widely employed to delineate the strength limitations of metallic materials, particularly in contexts involving high strains, elevated strain rates, and failure processes [33]. Given that the current simulation operates under high strains, among other variables, the Johnson–Cook model was selected for this investigation. The formulation of the Johnson–Cook eigenmodel is presented as follows:

$$\begin{array}{c}{\sigma }_e=\left[A+B{\left({\epsilon }_e^P\right)}^n\right]\left[1+Cln\frac{\dot{\epsilon }}{{\dot{\epsilon }}_0}\right]\left[1-{\left(T^{\ast }\right)}^m\right]\\ { T}^{\ast }=\frac{T-T_r}{T_m-T_r}\end{array}$$

(2)

where $\dot{\epsilon }$ and ${\dot{\epsilon }}_0$ represent the equivalent plastic strain rate and the reference strain rate; B and n represent the strain hardening modulus and hardening exponent of the material; T_r and T_m represent the melting point and room temperature of the material; ${\sigma }_e$ represents the equivalent stress; ${\epsilon }_e^P$ represents the equivalent plastic deformation; A represents the initial yield stress at room temperature; C represents the material strain rate hardening parameters; m represents the material thermal softening index.

A, B, n, C, and m are five material physical characteristic parameters. These parameters are intrinsic to the material and must be determined empirically.

Table 2. Johnson–Cook constitutive model parameters for powder metallurgy green billets.

Parameter	A (MPa)	B (MPa)	C	m	n	Tm (°C)	Tr (°C)
Value	730	487	0.016	1.08	0.29	1861	25

enumerates the Johnson–Cook constitutive model parameters specific to powder metallurgy green billets.

2.3. Tool-Related Parameters

To facilitate the analysis of material removal during the simulated cutting of PM green compacts, initial tool model parameters were established as follows: rounded edge radius r_ε = 10 μm, tool rake angle γ_o = 10°, and back angle a_o = 5°.

A carbide-coated tool was selected, with specific parameters sourced from the manufacturer. These parameters are detailed in

Table 3. Relevant parameters of tool materials.

Material	Density (g/cm3)	Elastic Modulus (MPa)	Poisson’s Ratio	Coefficient of Expansion α/(×10−6/°C)	Specific Heat Capacity (J/kg·°C)	Thermal Conductivity (N/sec/°C)
WC	14.7	630	0.24	4.4	1.5	59

.

2.4. Workpiece Meshing and Overall Model Assembly

The workpiece models predominantly employ rectangular meshing. However, due to the complex deformation behavior of PM materials during removal—comprising particle shear deformation, exfoliation, and plowing/extrusion [28]—a triangular mesh was adopted for this study. The workpiece was segmented into 46,646 triangular meshes. To minimize computational burden, denser meshing was applied to the upper-right region where cutting deformation occurs, while the remaining areas employed sparser meshing. Figure 2a provides details of the mesh division, and Figure 2b depicts the assembled workpiece and tool.

2.5. Experimental Validation

To validate the fidelity of the finite element model, orthogonal cutting experiments were executed on PM green compacts. Chip morphology, ascertained from the experiments, served as the benchmark for validation.

The experiments involved turning operations. In alignment with the computational simulation, every effort was made to ensure that the cutting parameters mirrored those in the finite element model. Figure 3a depicts the cylindrical PM green compacts employed in the study. Post-experiment, the resultant chips were examined using an Axioscope 5 orthogonal microscope, as illustrated in Figure 3b. The machining schematic is presented in Figure 3c.

Comparative analyses between the simulation and experimental results at a cutting thickness of 0.15 mm are showcased in Figure 4. Notably, both sets of results depict fine, numerous chip particles. At a cutting thickness of 0.25 mm, Figure 4 reveals larger but fewer fine particles, aligning well with the experimental findings. This concurs with Yang et al.’s [28] conclusions regarding the mechanics of PM material removal, encompassing particle shear deformation, exfoliation, and plowing/extrusion. The congruence between the observed cutting morphologies further substantiates the model’s accuracy and reliability.

3. Finite Element Simulation Results and Discussion

3.1. Univariate Analysis

Initial analyses were univariate, focusing sequentially on cutting thickness, cutting speed, tool rake angle, and rounded-edge radius to individually assess their impact on cutting force.

For a nuanced understanding of cutting thickness effects, five distinct simulations were conducted. These simulations were harmonized for cutting speed at 150 m/min, tool rake angle at 10°, and rounded-edge radius at 10 μm. Varied cutting thicknesses—0.15, 0.20, 0.25, 0.30, and 0.35 mm—were applied. Figure 5 portrays the forces observed at thicknesses of 0.15, 0.25, and 0.35 mm, while Figure 5d elucidates the trend. Upon closer examination, a 1.55% change in cutting force was observed when thickness varied from 0.15 mm to 0.20 mm. In contrast, a 13.19% change materialized when the thickness ranged from 0.25 mm to 0.30 mm. This non-linear escalation indicates an exponential growth effect of cutting thickness on cutting force. Cumulatively, the cutting force surged by 31.65% across the span, from 0.15 mm to 0.35 mm. These data underscore the crucial role of cutting thickness in both process optimization and energy consumption reduction.

This paper subsequently examines the correlation between cutting speed and cutting force. Five simulations were conducted to discern the cutting force trend as influenced by variations in cutting speed. The simulations were standardized for a cutting thickness of 0.25 mm, a tool rake angle of 10°, and a rounded-edge radius of 10 m. The investigated cutting speeds were 120, 130, 140, 150, and 160 m/min, respectively. Figure 6 illustrates the forces at cutting speeds of 120, 140, and 160 m/min, while Figure 6d depicts the overall trend. Upon data analysis, a 5.46% variation in cutting force was observed when the cutting speed ranged from 120 m/min to 130 m/min. Conversely, a 3.07% variation appeared in the 140 m/min to 150 m/min range. Although these changes are modest, they indicate that increased cutting speed correlates with augmented cutting force. Overall, the cutting force saw an increment of 17.62% across the speed range of 120 m/min to 160 m/min. These findings emphasize the critical role of cutting speed in process optimization and energy conservation.

This study extends its focus to another pivotal variable: the tool rake angle’s effect on cutting force. Employing the same methodology, five simulations were conducted to examine the impact of varying tool rake angles on cutting force. These simulations standardized the cutting thickness at 0.25 mm, cutting speed at 150 m/min, and rounded-edge radius at 10 m. The tool rake angles investigated were 0°, 5°, 10°, 15°, and 20°, respectively. Forces corresponding to 0°, 10°, and 20° rake angles are illustrated in Figure 7, with Figure 7d highlighting the trends. Data analysis revealed a −0.73% change in cutting force when the tool rake angle ranged from 0° to 5°. Between 10° and 15°, the cutting force variation was −0.93%. Though these two intervals exhibit similar trends, the overall pattern indicates a decrease in cutting force with an increase in tool rake angle. Throughout the 0° to 20° range, cutting force dropped by 3.38%. This suggests that tool rake angle exerts a minor influence on cutting force, rendering it a secondary consideration for process optimization and energy reduction. Nonetheless, this study identified that even minor variations in tool rake angle can significantly impact cutting force, underscoring its relevance in tool design and selection.

Having explored the impacts of cutting thickness, cutting speed, and tool rake angle on cutting force, this study next examines the influence of rounded edge radius. Utilizing the previously established methodology, five simulations were conducted to investigate the trends in cutting force as a function of varying rounded-edge radii. These simulations standardized the cutting thickness at 0.25 mm, the cutting speed at 150 m/min, and the tool rake angle at 10°. The rounded-edge radii evaluated were 10, 20, 30, 40, and 50 μm, respectively. The forces corresponding to 10, 30, and 50 μm are depicted in Figure 8, with Figure 8d elucidating the variation trends. Upon analysis, this study found a −0.31% variation in cutting force within the 10 μm to 20 μm radius interval. In contrast, the 30 μm to 40 μm interval displayed a −0.86% change. Despite the similarity in trends across these intervals, the overarching pattern signifies a reduction in cutting force as the rounded edge radius increases. Over the 10 μm to 50 μm range, the force diminished by 2.29%. Although the impact of a rounded-edge radius on cutting force appears minor, this study concludes that even marginal adjustments to the rounded-edge radius can yield a considerable influence on cutting force. As a result, the rational modification of the rounded-edge radius remains a worthwhile consideration in the design and selection of cutting tools.

3.2. Multivariate Analysis

Understanding the variations in cutting force and machined surface quality requires a multivariate approach, as single-factor analysis is insufficient for capturing the complex relationships involved. To this end, this study extended its inquiry to a cutting thickness of 0.15 mm while maintaining other simulation parameters consistent with prior experiments. The impact of cutting speeds ranging from 120 m/min to 160 m/min on cutting force was examined through five simulation trials, the results of which are presented in Figure 9.

The simulations revealed an increasing trend in cutting force with higher cutting speeds, noting an 18.42% change over the 120 m/min to 160 m/min speed range. This growth, albeit moderate, deviates from linearity, underscoring the complex, nonlinear interdependencies among the contributing factors. Hence, a comprehensive multivariate analysis is warranted for a more nuanced understanding of these interactions.

In this simulation study, four key cutting parameters—cutting thickness (a_p), cutting speed (v_c), tool rake angle (γ_o), and rounded edge radius (r_ε)—are scrutinized. The respective values are detailed in

Table 4. Orthogonal test factors and values.

Serial Number	Cutting Thickness ap (mm)	Cutting Speed vc (m/min)	Tool Rake Angle γo	Rounded Edge Radius rε (μm)
1	0.15	120	0°	10
2	0.20	130	5°	20
3	0.25	140	10°	30
4	0.30	150	15°	40

.

The factor combinations and their corresponding cutting forces are tabulated in

Table 5. Orthogonal experimental design and corresponding results.

Test Number (i)	Column Number (g)				Cutting Force Simulation Results (N)
	A	B	C	D
1	1	1	1	1	932.99
2	1	2	2	2	1071.53
3	1	3	3	3	1047.71
4	1	4	4	4	1027.78
5	2	1	2	3	891.57
6	2	2	1	4	917.65
7	2	3	4	1	1075.34
8	2	4	3	2	1148.25
9	3	1	3	4	958.27
10	3	2	4	3	1074.77
11	3	3	1	2	1216.67
12	3	4	2	1	1230.24
13	4	1	4	2	1334.90
14	4	2	3	1	1418.63
15	4	3	2	4	1133.26
16	4	4	1	3	1377.53

, where A represents a_p, B signifies v_c, C stands for γ_o, and D denotes r_ε.

To optimize the parameters, the signal-to-noise (S/N) ratio method, frequently employed in similar studies, is adopted here [34,35,36,37,38,39]. The S/N ratio for each data set was calculated based on Equation (3), as shown below [36]:

$$\eta =-10{\log }_{10}[\frac{1}{n}\sum _{i=1}^n{y_i}^2]$$

(3)

Employing Equation (4), the S/N ratios were computed when the cutting thickness was 0.15 mm.

$$\eta =\frac{1}{4}\left[-10{\log }_{10}\left({932.99}^2\right)-10{\log }_{10}\left({1071.53}^2\right)-10{\log }_{10}\left({1047.71}^2\right)-10{\log }_{10}\left({1027.78}^2\right)\right]$$

(4)

The remaining data are also extrapolated via the application of Equation (4). For enhanced accuracy in the findings, this study adopts an approach where the mean of multiple simulations is considered the signal-to-noise ratio for the respective machining parameters. A consolidated presentation of these computational outcomes is provided in

Table 6. Signal-to-Noise Ratio results.

Machining Parameters	Parameter Value	Signal-to-Noise Ratio
ap (mm)	0.15	−60.1601
	0.20	−60.0221
	0.25	−60.9398
	0.30	−62.3537
vc (m/min)	120	−60.1348
	130	−60.8793
	140	−60.9564
	150	−61.5051
γo (°)	0	−60.7841
	5	−60.6224
	10	−61.0682
	15	−61.0011
rε (μm)	10	−61.2164
	20	−61.5033
	30	−60.7041
	40	−60.0520

, facilitating a more direct and analytical interpretation of the signal-to-noise ratio fluctuations.

The parameter yielding the highest signal-to-noise (S/N) ratio is deemed optimal, as defined via the S/N method. Consequently, the optimal machining parameters for orthogonal cutting in PM green compacts are 0.20 mm for cutting thickness, 120 m/min for cutting speed, 5° for tool rake angle, and 40 mm for rounded edge radius. Finite element simulations using these parameters resulted in a cutting force of 887.95 N.

While the preceding analysis utilized the S/N ratio method to identify minimum cutting force parameters, the primary objective of this study is to mitigate the risk of damage from excessive cutting forces in PM green compacts. As such, machining often does not employ these “optimal” parameters. Hence, a secondary analytical method is required to elucidate the role of each machining parameter in affecting cutting force. Analysis of variance (ANOVA) serves as a robust statistical tool for discerning the significance of various effects. Combining the S/N ratio method with ANOVA has emerged as an innovative approach in materials machining optimization research [37,40,41,42]. Subsequent sections of this paper will extend the ANOVA analysis to gauge the impact of different machining variables on cutting force. This will enable precise identification of parameters exerting a substantial influence on cutting force, offering valuable insights for optimization and quality enhancement in PM green compact machining processes.

Based on the data from Table 5, an ANOVA analysis was carried out, the results of which are presented in

Table 7. Results of ANOVA data processing.

Test Number (i)		Column Number (g)				FH (yi)
		A	B	C	D
1		1	1	1	1	932.99
2		1	2	2	2	1071.53
3		1	3	3	3	1047.71
4		1	4	4	4	1027.78
5		2	1	2	3	891.57
6		2	2	1	4	917.65
7		2	3	4	1	1075.34
8		2	4	3	2	1148.25
9		3	1	3	4	958.27
10		3	2	4	3	1074.77
11		3	3	1	2	1216.67
12		3	4	2	1	1230.24
13		4	1	4	2	1334.90
14		4	2	3	1	1418.63
15		4	3	2	4	1133.26
16		4	4	1	3	1377.53
$k_{\mathit{gp}}$	$k_{g1}$	4080.01	4117.73	4444.84	4657.20	17,857.09 (y·) 19,929,728.95 (CT)
	$k_{g2}$	4032.81	4482.58	4326.60	4771.35
	$k_{g3}$	4479.95	4472.98	4572.86	4391.58
	$k_{g4}$	5264.32	4783.80	4512.79	4036.96
$k_{\mathit{gp}}^2$	$k_{g1}^2$	16,646,481.60	16,955,700.35	19,756,602.63	21,689,511.84
	$k_{g2}^2$	16,263,556.50	20,093,523.46	18,719,467.56	22,765,780.82
	$k_{g3}^2$	20,069,952.00	20,007,550.08	20,911,048.58	19,285,974.90
	$k_{g4}^2$	27,713,065.06	22,884,742.44	20,365,273.58	16,297,046.04
${\mathit{SS}}_g$		243,534.836	55,650.12817	8369.133069	79,849.44587

.

In Table 7, y_i and y· represent the cutting forces for each simulation group and the total sum of simulated cutting forces, respectively. Subsequent calculations and results are outlined in Table 7. Equations for k_g1 follow the procedure described in references [42,43]:

$$k_{g1}=932.99+1071.53+1047.71+1027.78=4080.01$$

(5)

Likewise, k_g2, k_g3, and k_g4 are calculated similarly. CT denotes the correction number, computed as detailed in references [42,43].

$$\mathit{CT}=\frac{{y\cdot }^2}{16}=19929728.95$$

(6)

The sum of squared deviations is given via [42,43]

$${\mathit{SS}}_g=\left(k_{g1}^2+k_{g2}^2+k_{g3}^2+k_{g4}^2\right)÷4-\mathit{CT}$$

(7)

The total sum of squares for deviation is calculated via [42,43]

$${\mathit{SS}}_T=\sum _{i=1}^n\sum _{j=1}^k{y}_{\mathit{ij}}^2-\mathit{CT}=20328012.13-19929728.95=398283.1724$$

(8)

The outcomes of these calculations are incorporated into the ANOVA table, wherein the degrees of freedom, mean squared deviation, and F-values are determined. Statistical significance is denoted as “ns” for non-significant, “*” for significant, and “**” for highly significant. The findings are illustrated in

Table 8. Results of the analysis of variance.

Variation Source	Square of Deviance	Degree of Freedom	Sum of Mean Squares	F	Significance	F0.05	F0.01
ap (mm)	243,534.836	3	81,178.27867	29.8459722	**	6.59	16.69
vc (m/min)	55,650.12817	3	18,550.04272	6.820100999	*
γo (°)	8369.133069	3	2789.711023	1.025663995	ns
rε (μm)	79,849.44587	3	26,616.48196	9.785804695	*
Error	10,879.62933	4	2719.907334	/	/
Summation	398,283.1724	16	/	/	/

, highlighting the critical impact of cutting thickness on the cutting force during the orthogonal slicing of PM green materials. It also shows that both the rounded edge radius and the cutting speed substantially influence the cutting force, whereas the tool rake angle’s effect is negligible. Among the machining parameters, cutting thickness is the most pivotal, followed in descending order of influence by the rounded-edge radius, cutting speed, and tool rake angle.

Optimal machining parameters for PM green compacts are as follows: a cutting thickness of 0.20 mm, a cutting speed of 120 m/min, a tool rake angle of 5°, and a rounded edge radius of 40 μm. Employing parameters resulted in a cutting force of 887.95 N.

4. Conclusions

This study delves into the correlation between various machining parameters and cutting force in the context of machining PM green compact materials. Employing both univariate and multivariate analyses, this research aimed to minimize cutting forces throughout the machining process. The comprehensive research outcomes are enumerated as follows:

(1)

Cutting force exhibited a 31.65% increase when the cutting thickness ranged from 0.15 mm to 0.35 mm. Similarly, cutting speed variations between 120 m/min and 160 m/min led to a significant 17.62% rise in cutting force. The influence of tool rake angle and rounded-edge radius was comparatively minimal, with respective reductions in cutting force of 3.38% and 2.29%, respectively.

(2)

Optimal parameters for minimizing cutting force were identified as a cutting thickness of 0.20 mm, a cutting speed of 120 m/min, a tool rake angle of 0°, and a rounded-edge radius of 40 mm. Utilizing these parameters reduced the cutting force to 887.95 N, achieving significant optimization.

(3)

ANOVA results further clarified the varying degrees of influence of each parameter on cutting force. Cutting thickness exhibited the most significant impact, followed by rounded-edge radius and cutting speed, while the tool rake angle had a negligible effect. These insights are pivotal for optimizing the machining process of PM green compacts.