Machinability Evaluation of PM Vanadis 4 Extra Steel Under Varying Milling Conditions

Abstract

Powder metallurgy tool steels, such as Vanadis 4 Extra (1.2210), are increasingly used in cold-work applications due to their superior hardness, wear resistance, and microstructural uniformity. Despite their growing popularity, there is limited data regarding their machinability, especially in milling processes. In this study, experimental milling tests were performed on Vanadis 4 Extra steel using AlCrN-coated carbide tools. A full factorial experimental design (3⁴) was applied to investigate the effects of cutting speed, depth of cut, width of cut, and feed per tooth on cutting forces (Fx, Fy, Fz, Fc), surface roughness parameters (Ra, Rz), and tool wear. Cutting forces were measured using a Kistler dynamometer, and surface roughness was evaluated using a contact profilometer. Regression models were developed and statistically validated. The results indicate that depth of cut had the most significant influence on cutting force, while cutting speed had the greatest impact on surface roughness. Moderate correlation between cutting forces and roughness was observed, particularly under low-load conditions. SEM analysis revealed abrasive wear and chipping of the coating layer. The findings provide insights into the machinability of Vanadis 4 Extra and offer guidelines for optimizing milling parameters to enhance tool life and surface integrity.

1. Introduction

In the automotive industry, the selection of cold-work tool steels used in dies, cutting and forming molds, and plastic injection molds largely depends on the mechanical properties and thickness of the processed sheet metal. This often leads to challenges in selecting an appropriate material considering the aforementioned material characteristics [1]. As a result, molds—being key tools in industrial production—are prone to premature wear or require maintenance before reaching their intended service life. One of the commonly applied methods to extend tool life lies in applying the appropriate surface treatment.

Achieving the desired service life of molds and dies is possible through the proper selection of materials and operating conditions [2,3,4]. An example of a material used for such applications is tool steel 1.2210 (115CrV3), commercially known as Vanadis 4 Extra. This is a cold-work tool steel manufactured using powder metallurgy, characterized by high hardness and excellent wear resistance. The steel is produced by UDDEHOLM (Hagfors, Sweden).

Compared to low-alloy steels, tools made from high-alloy steels present greater challenges in both heat and mechanical processing, which may lead to increased production costs. Yan et al. [5] demonstrated that the use of powder metallurgy technology, as in the case of Vanadis 4 Extra steel, enables a uniform distribution of carbides within the microstructure, which translates into improved mechanical properties of the material.

Tool steel 1.2210 is particularly suitable for applications where adhesive wear and chipping are the primary wear mechanisms. Examples of dies made from this material are presented in Figure 1.

Thanks to its properties, this steel is widely used in the production of innovative punches and dies applied in precision blanking. It is distinguished by its enhanced wear resistance, which contributes to extended tool life. The components or tools used in punching, drawing, bending, and similar processes that are manufactured from this material grade exhibit superior performance compared to those made from other materials, due to the ability to achieve complex geometric shapes with high dimensional accuracy and low surface roughness,

With the growing demand for metal components in the metalworking industry, powder metallurgy (PM) has become an increasingly attractive manufacturing technology. It enables the production of parts with complex geometries, a reduction in machining costs, and effective competition with other forming methods in high-volume production [6,7]. Moreover, PM is recognized as the most common technique for manufacturing particle-reinforced metal matrix composites [8]. One of the main advantages of this technology is improved microstructural control, allowing for a more uniform distribution of reinforcement phases in PM products [9].

Tool steel 1.2210 is a powder metallurgy-based alloy that contains high amounts of vanadium, chromium, and molybdenum. In terms of heat treatment and machinability, it is similar to the AISI D2 grade (1.2379—X153CrMoV12), but it exhibits a more homogeneous microstructure and uniform carbide distribution [5,10]. Due to its optimized chemical composition and production technology, steel 1.2210 offers better machinability compared to conventional AISI D2 steel. Particularly important is its high dimensional stability after hardening and tempering, which surpasses other high-alloy cold-work tool steels.

As a chromium–molybdenum–vanadium alloy, steel 1.2210 features excellent toughness, high wear resistance, and superior compressive strength. According to the manufacturer (Uddeholm), it also exhibits relatively good machinability [11]. It is used in the production of specialized tools and tooling systems for cold-forming applications. Due to operational requirements such as high hardness and wear resistance, the carbon content in this steel is relatively high. Owing to the PM production process, Vanadis 4 Extra also demonstrates optimized strength properties [12].

In contrast to conventionally cast steels, which often exhibit intense dendritic segregation and the presence of extensive eutectic carbide networks, PM steels do not require homogenization or hot forging to break down and disperse carbide phases. This allows for uniform properties throughout the cross-section of the material and eliminates detrimental segregation effects [13,14,15].

Vanadis 4 Extra contains high concentrations of carbon and alloying elements (mainly Cr, V, and Mo), which significantly lower the austenite-to-martensite transformation temperature during hardening. As a result, a considerable amount of austenite may remain after hardening, which adversely affects wear resistance and operational durability [12,15]. To eliminate retained austenite, cryogenic treatment (below 0 °C) is commonly applied [16,17,18,19,20].

The microstructure of this steel contains two dominant types of carbides: MC (primarily vanadium-based) and M7C3 (mainly chromium-based). VC carbides exhibit an extremely high hardness (~2800 HV) and melting point (2830 °C), making them effective grain stabilizers during heat treatment [13]. M7C3 carbides reach hardness levels around 1600 HV and a melting point of 1765 °C. Partial substitution of chromium with iron results in the formation of mixed M7C3-type carbides, also known as K2 carbides [21].

During austenite destabilization, occurring at temperatures of 1000–1100 °C, secondary chromium-rich M7C3 carbides precipitate, raising the Ms temperature and reducing the amount of retained austenite [22,23,24]. Additionally, tempering can induce secondary hardening via precipitation of M7C3 and M23C6 carbides, which also contain chromium [20,25,26]. At lower tempering temperatures, cementite carbides are present, which dissolve above 500 °C due to diffusion of Fe and C atoms.

Drilling tests were conduced on Vanadis 4 Extra powder metallurgy steel using HSS drills coated with a TiN layer. The surface roughness of the internal walls of the holes, the hardness around the drilled areas, and the tool wear were evaluated using an optical microscope. Additionally, chip formation was analyzed after each experiment [27,28].

Gutnichenko et al. [29] analyzed and monitored the initial damage of PcBN tools and the degradation of the TiAlN coating during hard milling of Vanadis 4 Extra steel.

Although the manufacturer claims the good machinability of 1.2210 tool steel, the literature lacks detailed studies on its cutting behavior. Previous research has primarily focused on the influence of alloying additions on mechanical properties, as reported by Chang et al. [30]. Investigations into corrosion resistance and tribological wear were conducted by Üstünyagiz et al. [31] and Yan et al. [32]. Structural modifications have been discussed by Arslan et al. [19] and Yan et al. [5], while the influence of heat treatment on microstructure has been presented by Yan et al. [14]. Sudhakar et al. [33] analyzed the EDM and WEDM machining of components made from 1.2210 steel.

The surface quality of machined components is a key indicator of evaluation of the machineability of engineering materials. Appropriate surface roughness enhances tribological performance, fatigue resistance, and the aesthetic aspect of components, as confirmed by Kivak [34] and Chen et al. [35].

Despite numerous studies on the machining of high-alloy tool steels, there is a noticeable lack of detailed predictive models specifically addressing the relationship between machining parameters and output responses—such as cutting forces and surface roughness—during the milling of Vanadis 4 Extra steel. Most existing works focus either on general machinability assessments or tool wear mechanisms, without providing quantitative models applicable to process optimization for this specific material. This gap hinders the ability to effectively predict machining outcomes and select optimal cutting conditions for industrial applications. Therefore, the present study aims to address this research gap by developing and validating mathematical models for cutting force and surface roughness prediction during the milling of Vanadis 4 Extra steel under varied input parameters.

Although various studies have explored the machining of tool steels, there remains a significant research gap in the development of predictive models linking cutting parameters with cutting forces and surface roughness during the milling of Vanadis 4 Extra and 1.2210 steels. Existing literature tends to focus on general machinability or tool wear, offering limited guidance for process optimization. The present study addresses this gap by experimentally evaluating the influence of milling parameters on cutting forces and surface roughness, and by developing predictive models to support machining optimization.

2. Materials and Methods

This section describes the experimental setup, machining process, and measurement equipment and methods used in this study.

2.1. Work Material

In this study, tool steel 1.2210, commercially known as Vanadis 4 Extra (Sandvik and Uddeholm, Sweden), was selected as the workpiece material due to its advanced production via powder metallurgy (PM) and its growing industrial relevance, particularly in the manufacturing of cold-work tooling. Compared to conventionally produced tool steels, powder metallurgy steels exhibit significantly improved structural homogeneity and isotropy of mechanical properties, which result in more stable cutting conditions—specifically, reduced and more predictable fluctuations in cutting forces.

Furthermore, Vanadis 4 Extra is increasingly applied in the production of dies and punches subjected to severe mechanical, thermal, and abrasive loads, such as in forging, stamping, and precision cutting operations.

Machining Vanadis 4 Extra steel presents specific challenges, such as high hardness and a tendency to cause significant tool wear, all of which negatively impact tool life and surface quality.

Despite its growing industrial use, literature data on the machining characteristics of this steel—especially in milling—remain limited. Therefore, the choice of Vanadis 4 Extra is justified both from a scientific perspective (to address a research gap) and from a practical standpoint, aligned with current demands in tool manufacturing.

The test specimens were blocks with dimensions of 100 × 50 × 50 mm³. The basic mechanical properties and chemical composition of the steel are presented in

Table 1. Chemical composition of tool steel 1.2210, weight% [12].

C	Mn	Si	Cr	Mo	V
1.4	0.4	0.4	4.7	3.5	3.7

and

Table 2. Physical properties [12].

Propery	Value
Temperature	20 °C	200 °C	400 °C
Density [kg/m3]	7700	-	-
Young’s modulus [Mpa]	206,000	200,000	185,000
Thermal expansion coefficient [°C from 20]	-	10.9 × 10−6	11.7 × 10−6
Thermal conductivity [W/m °C]	-	30	30
Specific heat [J/kg °C]	460	-	-

, respectively [12].

2.2. Milling Tools

The cutting tools used in the experiments were solid carbide end mills with a diameter of 12 mm, cutting length of 26 mm, and total length of 83 mm. Detailed tool geometry is shown in

Table 3. Geometric parameters of the carbide end mills used in the experimental milling tests.

Parameters	Value
Shank diameter D	12 mm
Tool diameter d	12 mm
Tool length L	83 mm
Number of teeth Z	4
Helix angle β	35°
Radial rake angle γ	10°
Radial relief angle α	6°
CER rꜪ	8–10 μm
Corner	0.3 × 45˚

. The end mills were manufactured using 5-axis grinding from solid WC-Co carbide rods (Guangzhou, China). Before the application of protective coatings in the PVD process, the tools underwent an additional technological procedure: edge rounding using the drag finishing method on an OTEC DF-5 machine (Schwäbisch Gmünd, Germany).

The tools were coated with a hard protective layer produced by Oerlikon Balzers Co. Ltd—Balzers, Liechtenstein. The coating was an AlCrN-based layer (BALINIT^® ALDURA, hereafter referred to as AlCrN—Balzers, Liechtenstein), deposited using cathodic arc evaporation (ARC-PVD, where PVD stands for physical vapor deposition). This type of coating was selected due to its high hardness, excellent thermal resistance, and wide applicability in cutting tools. The AlCrN coating is recommended for machining hardened steels up to 54 HRC, both with and without coolant, as well as for low-alloy and high-strength steels. The properties of the AlCrN coating are listed in

Table 4. Main properties of the AlCrN coating applied on the cutting tools.

Properties	AlCrN
Nanohardness [GPa]	36–38
Coefficient of friction [μ]	0.5
Coating thickness [μm]	1–5
Max. service temperature [°C]	1100
Coating temperature [°C]	400–500
Color	grey

.

2.3. Milling Process

The machining process involved shoulder milling of the 1.2210 tool steel block. Successive experimental steps (n) included material removal according to a predefined experimental plan. The aim of the experiment was to analyze the influence of fundamental milling parameters on selected output variables, such as cutting force components (Fx, Fy, Fz) and surface roughness parameters (Ra, Rz). A full factorial design (3⁴) was adopted for the experiment. The advantage of using a full factorial design is that it allows for a comprehensive analysis of both the individual effects of the factors and their interactions. The large amount of collected data enables statistical analysis, regression modeling, and even the application of machine learning techniques [36].

This study was designed for four independent variables (factors), each tested at three levels, as presented in

Table 5. Input parameters (factors) of the experiment.

Parameters		Level 1	Level 2	Level 3
Cutting speed	vc [m/min]	100	125	150
Cutting depth	ap [mm]	5	10	20
Cutting width	ae [mm]	2	3	4
Feed per tooth	fz [mm/tooth]	0.02	0.03	0.04

. The input parameter values listed in Table 5 were selected to ensure both practical relevance and applicability to industrial milling operations of Vanadis 4 Extra steel. The selection process was based on a combination of factors, including manufacturer recommendations for carbide cutting tools, insights gained from preliminary experimental trials, and a comprehensive review of existing literature concerning the machining of high-hardness tool steels. This multifaceted approach guarantees that the chosen cutting parameters are representative of realistic machining conditions, enabling meaningful experimental results and valid model development.

Each combination of parameters (vc, ap, ae, fz) was tested once. A portion of the full factorial design matrix (3⁴ = 81 trials) for the defined parameter levels is shown in

Table 6. A fragment of the full factorial design used in the experiment.

Sample No.	vc [m/min]	ap [mm]	ae [mm]	fz [mm/tooth]
1	100	5	2	0.02
2	100	5	2	0.03
3	100	5	2	0.04
4	100	5	3	0.02
5	100	5	3	0.03
…	…	…	…	…
81	150	20	4	0.04

.

2.4. Test Stand, Measurement Methods

The primary experimental setup was based on a multi-axis milling center DMU 100 monoBLOCK (Pfronten, Germany). The coolant-lubricant fluid used during the milling trials was Fuchs ECOCOOL GLOBAL 10 at a concentration of 7% (Mannheim, Germany).

Cutting forces were measured using a Kistler 9257B (Winterthur, Switzerland) piezoelectric dynamometer with a measurement range of ±5 kN, mounted on the machine table (Figure 2). The signal from the dynamometer was transmitted to a charge amplifier and then sent to a computer via USB using a 16-bit analog-to-digital converter with a measurement range of ±10 V. Signal visualization, processing, and recording were performed using custom-developed software in the LabVIEW environment. The sampling frequency was set at 20 kHz.

Surface roughness measurements of the machined surface were performed postprocess using a Mitutoyo Surftest SJ-210 (Saitama, Japan) device on a dedicated measuring stand.

3. Results

3.1. Models for Cutting Force Components and Total Cutting Force

All statistical analyses were conducted using JMP 12 software [37], with a significance level of 0.05 adopted for all tests.

To develop mathematical models correlating the cutting force components, total cutting force, and surface roughness parameters with the controllable milling parameters (cutting speed vc, cutting depth ap, cutting width ae, and feed per tooth fz), forward stepwise regression was employed [38].

The distributions of the cutting force components Fx, Fy, Fz and total cutting force Fc were visibly right-skewed (skewness ~1 for Fy, Fz, and Fc; skewness ~2 for Fx). To approximate normal distributions, logarithmic transformations were applied. The Anderson–Darling normality test [39] (α = 0.05) confirmed that the variables log(Fc), log(Fy), and log(Fz) followed a normal distribution. However, log(Fx) remained significantly skewed, requiring further transformation via the Box–Cox method [40]. After applying the Box–Cox transformation, the normality of the transformed Fx variable was confirmed by the Anderson–Darling test.

Initial models were additive and included only main effects. For models predicting Fc, Fy, and Fz, residual plots versus ap indicated a nonrandom distribution of residuals (Figure 3a): positive residuals at mid-values of ap and negative at extreme values. These models thus violated the assumption of homoscedasticity. For Fc and Fy, residuals versus predicted values also showed signs of non-normality (Figure 3b). These observations indicated the need to introduce a quadratic term for ap in the regression models. After including the ap² term, the residual distribution improved, validating the revised models.

(a)

Model for the Total Cutting Force Fc

The model was developed for the logarithm of the total cutting force log(Fc). The regression equation for raw data is as follows:

$$log\left(F_c\right)= 4.2918 - 0.00132 \cdot v_c+ 0.08337 \cdot a_p+ 0.24793 \cdot a_e+ 17.1351 \cdot f_z- 0.00236 \cdot {\left(a_p- 11.67\right)}^2$$

(1)

The regression coefficients for raw data (Estimate), standardized data (Std Beta), and t-test significance levels are shown in

Table 7. Coefficients of the equation for the output variable log(Fc).

Term	Estimate	Std Beta	Std Error	t Ratio	Prob > |t|
Intercept	4.291787	0	0.03158	135.90	<0.0001 *
vc	−0.00132	−0.04916	0.000186	−7.10	<0.0001 *
ap	0.0833688	0.948581	0.000723	115.30	<0.0001 *
ae	0.2479331	0.369358	0.004648	53.34	<0.0001 *
fz	17.135064	0.255269	0.464842	36.86	<0.0001 *
(ap −11.67) $\times$(ap −11.67)	−0.002363	−0.11858	0.000164	−14.41	<0.0001 *

*—result marked as highly statistically significant (p << 0.05).

. The adjusted coefficient of determination was R²_adj = 0.996. The graphical representation of the influence of milling parameters on Fc is presented in Figure 4.

(b)

Model for the Fx component of the cutting force

The Fx component was modeled using the Box–Cox transformed variable ($F_{xBC}$). The transformation function had the following form:

$$F_{xBC}={\displaystyle \frac{F_x^{-0.8}-1}{-0.0001567}}$$

(2)

The regression equation for raw data is as follows:

$$F_{xBC}= 6034.25 - 0.0208·v_c+ 4.05·a_p+ 33.49·a_e+ 1317.91·f_z+ 0.247·{\left(a_p- 11.67\right)}^2$$

(3)

The regression coefficients for the raw data (Estimate), standardized data (Std Beta), and the results of the Student’s t-test assessing their significance are presented in

Table 8. Coefficients of the equation for the output variable $F_{xBC}$.

Term	Estimate	Std Beta	Std Error	t Ratio	Prob > |t|
Intercept	6034.2498	0	19.44719	310.29	<0.0001 *
vc	−0.020794	−0.00917	0.114502	−0.18	0.8564
ap	4.0502422	0.545679	0.445286	9.10	<0.0001 *
ae	33.485163	0.590677	2.862555	11.70	<0.0001 *
fz	1317.9074	0.232479	286.2555	4.60	<0.0001 *
(ap −11.67) × (ap −11.67)	0.2469356	0.146703	0.100981	2.45	0.0168 *

*—result marked as highly statistically significant (p << 0.05).

. The adjusted coefficient of determination for the model was R²_adj = 0.796. The influence of milling parameters on the total cutting force is illustrated graphically in Figure 5.

(c)

Model for the Fy component of the cutting force

The model was developed for the logarithm of the Fy component of the cutting force, log(Fy). The regression equation for raw data is as follows:

$$\log \left(F_y\right)= 4.252 - 0.00135·v_c+ 0.0862·a_p+ 0.243·a_e+ 17.10·f_z- 0.00274·{\left(a_p- 11.67\right)}^2$$

(4)

The regression coefficients for the raw data (Estimate), standardized data (Std Beta), and the results of the Student’s t-test assessing their significance are presented in

Table 9. Coefficients of the equation for the output variable log(F_y).

Term	Estimate	Std Beta	Std Error	t Ratio	Prob > |t|
Intercept	4.2520114	0	0.034678	122.61	<0.0001 *
vc	−0.001347	−0.04927	0.000204	−6.60	<0.0001 *
ap	0.086154	0.962816	0.000794	108.50	<0.0001 *
ae	0.2426579	0.355062	0.005104	47.54	<0.0001 *
fz	17.103382	0.25026	0.510444	33.51	<0.0001 *
(ap −11.67) × (ap −11.67)	−0.002744	−0.13524	0.00018	−15.24	<0.0001 *

*—result marked as highly statistically significant (p << 0.05).

. The adjusted coefficient of determination for the model was R²_adj = 0.996. The influence of milling parameters on the total cutting force is graphically illustrated in Figure 6.

(d)

Model for the Fz Component of Cutting Force

The model was developed for the logarithm of the Fz component of the cutting force, log(Fz). The regression equation for raw data is as follows:

$$\log \left(F_z\right)= 1.9147 - 0.00087·v_c+ 0.09573·a_p+ 0.248·a_e+ 27.34·f_z- 0.00342·{\left(a_p- 11.67\right)}^2$$

(5)

The regression coefficients for the raw data (Estimate), standardized data (Std Beta), and the results of the Student’s t-test assessing their significance are presented in

Table 10. Coefficients of the equation for the output variable log(F_z).

Term	Estimate	Std Beta	Std Error	t Ratio	Prob > |t|
Intercept	1.9147088	0	0.067935	28.18	<0.0001 *
vc	−0.000866	−0.02793	0.0004	−2.17	0.0335 *
ap	0.0957299	0.942985	0.001556	61.54	<0.0001 *
ae	0.24798	0.319827	0.01	24.80	<0.0001 *
fz	27.344473	0.35267	0.999977	27.35	<0.0001 *
(ap −11.67) × (ap −11.67)	−0.003418	−0.14846	0.000353	−9.69	<0.0001 *

*—result marked as highly statistically significant (p << 0.05).

. The adjusted coefficient of determination for the model was R²_adj = 0.987. The influence of milling parameters on the cutting force component is graphically illustrated in Figure 7.

The model developed for the Fx component of the cutting force showed noticeably lower fit quality (coefficient of determination of approximately 0.80) compared to the models for the remaining force components and the total cutting force, which exhibited coefficients close to 0.99 or 1. This indicates that the Fx component is significantly affected by factors not included in the regression equation. One of these factors may be vibrations occurring during the machining process. Although vibrations were not recorded during the experiments, the literature provides several references describing this phenomenon. Examples include articles [41,42], in which the authors present experimental results related to this issue.

By analyzing the curvature of the plots illustrating the influence of milling parameters on the cutting force and its components (Figure 2, Figure 3, Figure 4 and Figure 5), it can be concluded that the relationships were approximately linear. An exception is the influence of the depth of cut (ap) on Fx. Among the investigated milling parameters, the cutting speed had the least influence on the total cutting force and its individual components. In the case of F_xBC, this factor was not statistically significant; however, it was retained in the model to maintain a consistent structure across all models.

The effect of cutting speed (vc) on Fc and its components was inversely proportional—that is, as the speed increased, the corresponding forces decreased. However, this influence was very small—the slope of the Fi(vc) plots (Figure 2, Figure 3, Figure 4 and Figure 5, where Fi represents either the total cutting force or one of its components) relative to the horizontal axis was slight.

The depth of cut (ap) had the greatest influence on the analyzed forces within the studied parameter space. It should be noted that the strength of this influence also depends on the parameter’s variation range. In the conducted experiments, ap was varied over a wider range than ae, which explains its greater impact on Fc. The influence of ap on Fc and its components was proportional—i.e., increasing ap led to increased force values. The width of cut (ae) and feed per tooth (fz) also had proportional effects on Fi. Overall, based on all developed models, it can be stated that the influence of ae and fz on Fi was similar. For all models except the one for Fz, the effect of ae on the dependent variable was greater than that of fz. In contrast, for the F_xBC component, the influence of ae was comparable to that of ap and clearly greater than that of fz.

The obtained results are consistent with general cutting theory. Increasing cutting speed reduces force, whereas increasing ap, ae, and fz increases the volume of material removed per unit time.

Two additional models were developed to verify the importance of separately including ap, ae, and fz in modeling the cutting force. The first model used the following input factors: vc, fz, and the cross-section of the machined material perpendicular to the feed direction (A = ae × ap). The second model included vc and the material removal rate (Q = ae × ap × fz × z), where z denotes the number of teeth.

Due to the skewed distributions of the variables Q, A, and Fc, logarithmic transformations were applied. The regression models included only main effects. The coefficients of the model log(Fc) = f(vc, fz, A) (6) are presented in

Table 11. Coefficients of the model equation log(F_c) = f(v_c, f_z, A).

Term	Estimate	Std Beta	Std Error	t Ratio	Prob > |t|
Intercept	3.1244238	0	0.059884	52.17	<0.0001 *
vc	−0.00132	−0.04916	0.000328	−4.03	0.0001 *
fz	17.135064	0.255269	0.819098	20.92	<0.0001 *
Log(A)	0.8304408	0.959664	0.010559	78.64	<0.0001 *

*—result marked as highly statistically significant (p << 0.05).

, while those of the model log(Fc) = f(vc, Q) (7) are shown in

Table 12. Coefficients of the model equation log(F_c) = f(v_c, Q).

Term	Estimate	Std Beta	Std Error	t Ratio	Prob > |t|
Intercept	5.4997733	0	0.076356	72.03	<0.0001 *
Log(Q)	0.7739375	0.980359	0.017073	45.33	<0.0001 *
vc	−0.00132	−0.04916	0.000581	−2.27	0.0258 *

*—result marked as highly statistically significant (p << 0.05).

. The adjusted coefficient of determination for the model incorporating the cross-sectional area of the uncut chip was R²_adj = 0.988, whereas for the model including the material removal rate, it was R²_adj = 0.963. These models are graphically illustrated in Figure 8 and Figure 9.

$$\log \left(F_c\right)=3.1244-0.00132·v_c+17.1351·f_z+0.8304·\mathit{log}\left(A\right)$$

(6)

$$\mathrm{l}\mathrm{o}\mathrm{g}\left(F_c\right)=5.4998+0.7739 \cdot \mathrm{l}\mathrm{o}\mathrm{g}\left(Q\right)-0.00132 \cdot v_c$$

(7)

The comparison of cutting force models developed with varying levels of detail regarding the parameters ap, ae, and fz is summarized in

Table 13. Goodness of fit for models describing cutting force as a function of process parameters.

Input Variables	Remarks	Radj
vc, fz, ap, ae	-	0.996
vc, fz, A	$A=a_e\times a_p$	0.988
vc, Q	$Q=a_e\times a_p\times f_z\times z$	0.963

. The influence of these parameters largely stems from their combined effect on the material removal rate (Q). Including the feed per tooth (fz) as a separate factor in the model accounts for an additional ~1.5% of the total variance. Separating ap and ae from the cross-sectional area of the uncut chip explains less than 1% of the total variance.

3.2. Models for Surface Roughness Parameters Ra and Rz

For each milled surface under a defined set of machining parameters, the surface roughness parameters Ra and Rz were measured three times. During data processing, it was observed that certain samples exhibited very low repeatability, with the coefficient of variation (CV = standard deviation/|mean|) exceeding 100%. In each of these cases, this was caused by the presence of a single outlier. The outlier values were excluded from further analysis, affecting four Ra values and one Rz value.

Due to the generally low repeatability of roughness measurements (with a mean CV of approximately 22%), the models describing the influence of milling parameters on surface roughness were constructed based on the average Ra and Rz values for each sample.

The distributions of the average Ra and Rz values were clearly right-skewed (skewness of 2.1 for Ra and 1.4 for Rz). To approximate a normal distribution, the data were subjected to logarithmic transformation. The Anderson–Darling normality test confirmed that the transformed variables log(Ra) and log(Rz) followed a normal distribution.

The resulting models were second-degree polynomial models with second-order interactions, developed using backward regression.

(a)

Models for arithmetic mean height of roughness profile Ra

The model was developed for the logarithm of the average Ra value (log(Ra)) for each sample. The regression equation for raw data is as follows:

$$\begin{gathered} log\left(R_a\right)= -2.3319 - 0.01086 \cdot v_c+ 0.06388 \cdot a_p+ 0.2324 \cdot a_e+ 18.9921 \cdot f_z \\ \hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}+ 0.000715 \cdot {\left(v_c- 125\right)}^2- 0.00075 \cdot \left(v_c- 125\right)\left(a_p- 11.67\right) \\ \hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}- 0.003999 \cdot {\left(a_p- 11.67\right)}^2- 1.2905 \cdot \left(a_p- 11.67\right)\left(f_z- 0.03\right) \end{gathered}$$

(8)

The coefficients of the equation for the raw data (Estimate) and for the standardized data (Std Beta), as well as the results of the t-test for their significance, are presented in

Table 14. Equation coefficients for the output variable log(Ra) (R_adj² = 0.81).

Term	Estimate	Std Beta	Std Error	t Ratio	Prob > |t|
Intercept	−2.331882	0	0.239655	−9.73	<0.0001 *
vc	−0.010856	−0.37537	0.001391	−7.80	<0.0001 *
ap	0.0638784	0.674803	0.00541	11.81	<0.0001 *
ae	0.2324069	0.32145	0.034778	6.68	<0.0001 *
fz	18.99212	0.262687	3.477751	5.46	<0.0001 *
(vc −125) × (vc −125)	0.0007149	0.35682	9.638× 105	7.42	<0.0001 *
(vc −125) × (ap −11.67)	−0.00075	−0.16169	0.000223	−3.36	0.0012 *
(ap −11.67) × (ap −11.67)	−0.003999	−0.18628	0.001227	−3.26	0.0017 *
(ap −11.67) × (fz −0.03)	−1.290534	−0.11131	0.557681	−2.31	0.0235 *

*—result marked as highly statistically significant (p << 0.05).

. The adjusted coefficient of determination for the model was R_adj² = 0.81. The influence of milling parameters on the surface roughness, expressed by Ra, is graphically shown in Figure 10 and Figure 11.

(b)

Model for maximum height of roughness profile Rz

The model for the logarithm of the average value of the Rz parameter for a given sample, log(Rz), was determined. The regression equation for raw data is as follows:

$$\begin{gathered} log\left(R_z\right)= -0.756529 - 0.008921 \cdot v_c+ 0.0654238 \cdot a_p+ 0.2489122 \cdot a_e \\ \hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}+ 18.894455 \cdot f_z+ 0.0007071 \cdot {\left(v_c- 125\right)}^2- 0.004497 \cdot \\ {\left(a_p- 11.67\right)}^2- 0.153264 \cdot {\left(a_e- 3\right)}^2 \end{gathered}$$

(9)

The equation coefficients for raw data (Estimate) and standardized data (Std Beta), as well as the results of the Student’s t-test evaluating their significance, are presented in

Table 15. Equation coefficients for the output variable log(Rz) (R_adj² = 0.78).

Term	Estimate	Std Beta	Std Error	t Ratio	Prob > |t|
Intercept	−0.756529	0	0.265173	−2.85	0.0056 *
vc	−0.008921	−0.31036	0.001518	−5.88	<0.0001 *
ap	0.0654238	0.695366	0.005904	11.08	<0.0001 *
ae	0.2489122	0.34639	0.037952	6.56	<0.0001 *
fz	18.894455	0.262938	3.795154	4.98	<0.0001 *
(vc −125) × (vc −125)	0.0007071	0.355082	0.000105	6.72	<0.0001 *
(ap −11.67) × (ap −11.67)	−0.004497	−0.21076	0.001339	−3.36	0.0012 *
(ae −3) × (ae −3)	−0.153264	−0.12314	0.065734	−2.33	0.0225 *

*—result marked as highly statistically significant (p << 0.05).

. The adjusted coefficient of determination for the model was R_adj² = 0.78. The influence of milling parameters on surface roughness, expressed by Rz, is graphically presented in Figure 12.

Description of the Roughness Models

In the examined range of variability, the cutting speed vc had the greatest impact on the Ra and Rz parameters. The predominant trend was a decrease in Ra and Rz values with an increase in cutting speed. The effect of vc on roughness was most significant for low values of vc. For the other milling parameters, a proportional effect on the Ra and Rz values was observed. In the case of the model for the Ra parameter, two interactions with cutting depth ap were statistically significant: the interaction with vc and feed per tooth fz. However, when comparing the standardized regression coefficients and the interaction plot, it can be seen that the influence of the interactions was relatively weak.

The similarity between the models for Ra and Rz arises from the high correlation between these parameters (Spearman’s rank correlation coefficient ρ = 0.92). The Rz parameter has a less averaging characteristic than Ra. Therefore, it may be more sensitive to types of surface irregularities that are not dominant, such as material drag or cracking. For both parameters, the regression models can be considered as having a moderate fit. The models do not explain about 20% of the total observed variance in Ra and Rz. Other significant factors in the process, such as vibrations, tool wear, and tool coating clogging, also influence roughness. These factors are discussed in the literature [43,44] as major causes of deterioration in surface quality.

On the surface of the cutting tool (flank face) after use, parallel grooves and lines were observed, caused by contact with the workpiece material, indicating abrasive tool wear. Numerous areas with microchipping of the AlCr outer coating were also observed (Figure 13)—this could be a result of machining hard materials, tool vibrations, or improper selection of cutting parameters. The areas where coating loss occurred on the tool differed in size and depth (Figure 13a,b).

SEM observations revealed that some of the layer losses were very small (several μm) and shallow, while others were significantly larger and deeper (Figure 13a and Figure 14b). Chemical composition analysis using EDS in areas where the layer loss occurred showed that the white layer visible at the bottom of the deeper microchippings was tungsten carbide with cobalt (WC-Co), which formed the substrate beneath the AlCr outer coating (Figure 14b,c). At the bottom of the wear areas, the presence of contaminants was found, mainly containing Ca, Cl, K, C, and O, indicating the formation of products associated with the tool’s operational process and the machining environment interaction (Figure 14b,c).

As mentioned earlier, the nature of the Rz parameter may be the cause of the slightly poorer fit of the regression model compared to Ra.

Considering how milling parameters affect cutting force (described in Section 3.1) and roughness parameters, it can be inferred that surface roughness, expressed by Ra and Rz, is dependent on the cutting load. This is consistent with the general theory of cutting and the results of many empirical studies, such as [45,46,47,48]. When analyzing the dependence of roughness on cutting force, it was observed on scatterplots that the correlation between surface roughness and force was stronger at lower loads. Cutting forces were divided into two ranges: below the median (Me = 510 N) and above the median. The correlation between roughness parameters depending on the load is shown in Figure 15. The correlation coefficients ρ\rhoρ between the Ra and Rz parameters and cutting force Fc for low values of force were 0.69 and 0.67, respectively. For high values of force, the calculated correlation coefficients were around 0.3 and were not statistically significant.

4. Discussion

The results of the experiments and the developed regression models provide valuable insights into the behavior of Vanadis 4 Extra tool steel during milling. Statistical analysis confirmed that among the investigated cutting parameters, the depth of cut (ap) had the most significant influence on all components of the cutting force (Fx, Fy, Fz), as well as on the total cutting force (Fc). This finding aligns with classical metal cutting theory, which indicates that an increased volume of removed material results in greater mechanical loading on the tool. Additionally, the feed per tooth (fz) and width of cut (ae) also showed a significant impact, while the cutting speed (vc) exhibited a relatively weak yet statistically significant inverse effect on cutting forces.

Regarding surface roughness, cutting speed emerged as the most influential parameter, particularly at lower speed levels, where increases in vc led to a noticeable reduction in Ra and Rz values. This trend is consistent with results reported in previous studies (e.g., Kivak, Chen et al. [34,35,36]), suggesting that higher cutting speeds reduce the formation of built-up edges and result in smoother surfaces. However, the influence of ap and ae on surface roughness was also evident, which can be attributed to increased tool engagement and thermal effects on the machined surface.

The moderate coefficient of determination for surface roughness models (~80%) indicates that other unaccounted-for factors, such as tool vibrations, microchipping of the cutting edge, or material smearing, significantly affect surface quality. SEM observations of worn cutting tools supported this conclusion. Visible abrasive wear and microchipping of the AlCrN coating suggest that local thermomechanical loads exceeded the coating adhesion strength or fatigue resistance, particularly under high cutting force conditions.

Interestingly, the correlation between cutting force and surface roughness was stronger at lower force levels, indicating that surface integrity deteriorates more sharply when the tool is subjected to increased loading. This nonlinear relationship suggests that machining stability and tool wear progression may amplify changes in roughness, a phenomenon also observed in the works of Liu et al. [43,44] and Luo et al. [42].

From a practical perspective, this study highlights the need for a balanced selection of parameters—particularly depth of cut and feed per tooth—to maintain both efficient material removal and acceptable surface quality. Moreover, the results confirm that factorial design and regression modeling are effective tools in machinability research for advanced tool steels such as Vanadis 4 Extra.

5. Conclusions

In this study, the influence of fundamental milling parameters on cutting forces, surface roughness, and tool wear was investigated during the machining of Vanadis 4 Extra tool steel produced by powder metallurgy. Based on a full-factorial experimental design and regression modeling, the following conclusions can be drawn:

• The depth of cut (ap) had the most significant effect on the components of cutting force and the total cutting force. A considerable influence was also observed for the width of cut (ae) and feed per tooth (fz). The cutting speed (vc) exhibited an inversely proportional effect, although its overall influence was relatively minor.
• Surface roughness parameters Ra and Rz were most sensitive to changes in cutting speed. An increase in vc led to improved surface quality, whereas higher values of ap, ae, and fz resulted in a deterioration of the machined surface.
• The developed regression models for cutting forces showed excellent agreement with the experimental data (R² > 0.99), indicating high predictive accuracy. In contrast, the models for surface roughness exhibited moderate fit (R² ≈ 0.80), suggesting the influence of additional factors such as vibrations or tool wear on surface integrity.
• SEM analysis of worn tools revealed abrasive wear mechanisms and microchipping of the AlCrN coating. In some cases, exposure of the WC-Co substrate and the presence of oxide contaminants were observed, indicating localized thermomechanical overload.
• A correlation was observed between cutting force and surface roughness, particularly under lower loading conditions. Beyond a certain force threshold, surface quality deteriorated significantly, emphasizing the importance of maintaining stable cutting conditions.
• The results provide practical insights for optimizing the milling process of Vanadis 4 Extra steel, enabling a balance between machining efficiency, tool life, and surface quality. This study also confirms the usefulness of advanced statistical analysis in assessing the machinability of modern tool steels.
• Summary of Recommended Machining Parameters. Taking into account the results of this study and the experimental conditions applied, the following machining parameters are recommended—

  Table 16. Recommended milling parameters for Vanadis 4 Extra tool steel.

  Parameter	Typical Value	Remarks
  Tool type	Solid carbide end mill (VHM) with AlCrN or AlTiN coating	High hardness and temperature resistance
  Cooling	Abundant emulsion cooling (e.g., Fuchs Ecocool Global 10)	Reduces tool wear and improves surface quality
  Cutting speed (vc)	100–150 m/min (for carbide tools)	Lower values for finishing, higher for roughing
  Feed per tooth (fz)	0.02–0.04 mm/tooth	Depends on tool diameter and milling type (roughing/finishing)
  Depth of cut (ap)	0.5–5 mm	Smaller for finishing, larger for roughing
  Width of cut (ae)	10–30% of tool diameter	For peripheral side milling

  . These guidelines are intended to enhance process performance while ensuring both high quality and operational efficiency in milling.

Future research should focus on integrating vibration monitoring and tool wear diagnostics to improve the understanding of the cutting process dynamics and further enhance the accuracy of predictive models.