Research on the End-Milling Surface Quality of Paulownia Based on Response Surface Model in Terms of Force and Chip Morphology

: To investigate the impact of different milling parameters on milling forces, chip morphology, and machined surface quality during the Paulownia milling process, we conducted experiments using cemented carbide single-tooth shank milling cutters. Additionally, we established a response surface model (RSM) to analyze milling surface quality. The key findings are as follows: milling forces along the parallel and tangential axes decrease with an increased tool rake angle and spindle’s rotational frequency, but they exhibit a positive correlation with milling depth. The effect of spindle’s rotational frequency on the milling force along the lateral axis differs due to the complex fiber characteristics of Paulownia . As milling depth decreases, chip morphology transitions from a block structure to a sheet structure, eventually becoming fragmented with shallow milling. Higher spindle’s rotational frequency and tool rake angle lead to a more fragmented direction in Paulownia chip morphology, while machined surface quality improves. Notably, under specific conditions, a striped chip morphology significantly enhances machined surface quality compared to similar milling parameters. The established RSM for machined Paulownia surface roughness is reliable and holds reference value for inhibiting surface damage in Paulownia machining.


Introduction
The genus Paulownia is originated in China, it has ability to grow large sizes in a very short time [1,2].As a raw material widespread used to make boards and decorative materials, such as particleboard, plywood, house siding, window shutters, etc. Due to its straight texture, uniform structure, and easy processing, Paulownia has been widely consumed in the field of furniture manufacturing [3].Meanwhile, Paulownia furniture has been highly praised in China and Japan.However, some Paulownia wood density and hardness is too low to avoid plastic deformation and defects during cutting, such as tear, burr and pits in the cutting process, which will have a great impact on the quality of products and subsequent processing [4].
Milling is the most commonly used cutting process in the wood cutting and furniture industry [5,6].Some studies have shown that, in wood material processing, cutting tools and cutting parameters have a decisive effect on the surface quality [7,8].No matter whether one is milling soft or solid wood, it has been found that the cutting angle, feed speed, wood fiber orientation angle, and milling depth that are used have significant influences on the cutting force, chip formation, and surface quality [9,10].As a typical Forests 2024, 15, 325 2 of 12 soft wood, Paulownia requires fundamental investigation into its machinability due to the currently lack of information surrounding it in the literature.
The most basic movement in milling is the action of force: the tool cuts into the wood's surface; then, the chips separate to form a machined surface.In this process, there are a series of actions, such as shear force, friction force, workpiece rebound force, and so on; finally, these synthesize into the milling force [11,12].Therefore, the importance of studying the cutting force is self-evident.Marchal et al. [13] presented a case evidencing the strong relationship between the cutting force and surface roughness.Furthermore, a higher cutting force is likely to introduce the severe vibrations in the tools, leading to severe defects on the machined surface.In addition, the orientation angle of wood fibers plays a significant role in relation to the cutting force component in the machining of wood [14].
Milling movement is accompanied by chip removal; different milling parameters will produce different shapes of chip, indicating that the milling mechanism is presently variable.Study of the relationship between chip shape and surface quality is helpful in determining the chip formation mechanism and thus enabling practitioners to set appropriate machining parameters [15][16][17].
In general, although much of the literature has made great efforts in researching the wood milling process, there is little research on the machining of Paulownia.This work presents the following differences from previously published studies: (1) a fundamental investigation into the effect of milling parameters on milling performance, including milling force, chip morphology, and the surface quality of Paulownia; (2) an analysis of the mechanisms of chip formation during milling of Paulownia under different milling parameters; (3) an initial regression model of surface quality in the milling of Paulownia is established.
The objective of this work is to study the machinability of Paulownia under different milling parameters in terms of the milling force, chip morphology, and surface quality.The designed full-factor experiments were carried out to reveal the relationship between milling parameters and resulting characteristics.This work provides new knowledge of Paulownia milling, which will serve to guide high-efficiency and high-quality Paulownia machining.

Materials
As shown in Figure 1c, the milling workpiece is five-year-old Paulownia from Shandong, China.This was cut into a size of 120 × 80 × 15 mm.The red number on the surface of specimen is the workpiece number during the experiment.The length direction for the wood fiber's axial direction was consistent; this ensures that the milling process is one of nearly longitudinal milling.It is important to avoid defects, such as knots and cracks on the surface, to enable processing.This was ensured to prevent any wood defects from interfering with the test results.The mean value of the equilibrium moisture content was tested by assessing 10 random specimens under controlled conditions of constant temperature and humidity in an incubator (20 • C and 65% RH, respectively).Paulownia timber properties are shown in Table 1.The woodworking tool used in the test was a cemented, carbide, single-tooth shank milling cutter (Figure 1b), produced by Leitz Co., Ltd., Oberkochen, Germany.The measurement from the cutter tooth to the rotary shaft is 30 mm, the length of the cutter tooth is 30 mm, and the maximum milling depth is 1.5 mm.The wedge angle of the cutter is fixed at 45 • .The density is 14.8 g/cm 3 .The bending strength and hardness are 2100 N/cm 2 and 89 HRC, respectively.The varied parameters of this test are shown in Table 2, based on the literature [18,19].The woodworking tool used in the test was a cemented, carbide, single-tooth shank milling cutter (Figure 1b), produced by Leitz Co., Ltd., Germany.The measurement from the cutter tooth to the rotary shaft is 30 mm, the length of the cutter tooth is 30 mm, and the maximum milling depth is 1.5 mm.The wedge angle of the cutter is fixed at 45°.The density is 14.8 g/cm 3 .The bending strength and hardness are 2100 N/cm 2 and 89 HRC, respectively.The varied parameters of this test are shown in Table 2, based on the literature [18,19].

Experiment Design
As shown in Figure 2, the Paulownia workpiece was positioned on a five-axis CNC machining center (MGK01, Nanxing Machinery Co., Ltd., Hong Kong, China, Figure 2a).The milling test of the Paulownia workpiece was carried out by changing the spindle's rotational frequency, the milling depth, and tool rake angle; a fixed feed speed was used.The milling parameters were selected according to the pre-experiment, actual factory processing parameters, and the limitations of the machining tool.During the milling test, the milling force data were transmitted to the signal amplifier in real time through the Kistler dynamometer (Kistler 9257B, Kistler Group, Winterthur, Switzerland, Figure 2b); the milling force data were obtained in three directions (Fx, Fy and Fz).The surface roughness after the test was measured by the roughness measuring instrument (DSX510, Olympus, Co., Ltd., Osaka-fu, Japan, Figure 2c).Each set of data was measured five times and averaged.The morphology of the chips was measured by a micrometer (ZW H1600, China Micro Semiconductor (Shenzhen) Co., Ltd., Shenzhen, China, Figure 2d).Our design for the milling parameters is presented in Table 2.One milling tool was used for each test to control the rounding of the cutting edge.

Experiment Design
As shown in Figure 2, the Paulownia workpiece was positioned on a five-axis CNC machining center (MGK01, Nanxing Machinery Co., Ltd., Hong Kong, China, Figure 2a).The milling test of the Paulownia workpiece was carried out by changing the spindle's rotational frequency, the milling depth, and tool rake angle; a fixed feed speed was used.The milling parameters were selected according to the pre-experiment, actual factory processing parameters, and the limitations of the machining tool.During the milling test, the milling force data were transmitted to the signal amplifier in real time through the Kistler dynamometer (Kistler 9257B, Kistler Group, Winterthur, Switzerland, Figure 2b); the milling force data were obtained in three directions (F x , F y and F z ).The surface roughness after the test was measured by the roughness measuring instrument (DSX510, Olympus, Co., Ltd., Osaka-fu, Japan, Figure 2c).Each set of data was measured five times and averaged.The morphology of the chips was measured by a micrometer (ZW H1600, China Micro Semiconductor (Shenzhen) Co., Ltd., Shenzhen, China, Figure 2d).Our design for the milling parameters is presented in Table 2.One milling tool was used for each test to control the rounding of the cutting edge.Chip thickness is the vertical distance between the milling trajectories of two adjacent cutter teeth.As shown in Figure 3, the chip thickness varies with the position of the cutter teeth in the workpiece during milling.When the cutter teeth make contact with the workpiece, the chip thickness a = 0.At the moment when the cutter teeth leave the workpiece, Chip thickness is the vertical distance between the milling trajectories of two adjacent cutter teeth.As shown in Figure 3, the chip thickness varies with the position of the cutter teeth in the workpiece during milling.When the cutter teeth make contact with the workpiece, the chip thickness a = 0.At the moment when the cutter teeth leave the workpiece, the maximum chip thickness is a max .Taking the contact arc as the average calculation point, the average chip thickness, a av , is calculated using Equation (1) [20]: where U Z (mm/Z) is the feed per tooth, U (m/min) is the feed speed, and the feed speed is fixed at 5 m/min.n (r/min) is the spindle's rotational frequency; Z is the number of teeth participating in milling; h (mm) is the milling depth; D (mm) is the maximum milling diameter of the tool (the tool used in this paper has a diameter of 30 mm).Chip thickness is the vertical distance between the milling trajectories of two cutter teeth.As shown in Figure 3, the chip thickness varies with the position of teeth in the workpiece during milling.When the cutter teeth make contact with piece, the chip thickness a = 0.At the moment when the cutter teeth leave the w the maximum chip thickness is amax.Taking the contact arc as the average calculat the average chip thickness, aav, is calculated using Equation (1) [20]: where UZ (mm/Z) is the feed per tooth, U (m/min) is the feed speed, and the feed fixed at 5 m/min.n (r/min) is the spindle's rotational frequency; Z is the numbe participating in milling; h (mm) is the milling depth; D (mm) is the maximum diameter of the tool (the tool used in this paper has a diameter of 30 mm).The response surface method (RSM) is one of the most widely used mat models.In this study, the Box-Benhnken design method was used to design input parameters at three levels via Design-Expert (Version 13) [21].The respon regression model is shown in Equation ( 2) [22].

Milling Force
In Paulownia milling, the milling parameters will have a decisive influen milling force.The milling force can reflect the machining state of the machine The response surface method (RSM) is one of the most widely used mathematical models.In this study, the Box-Benhnken design method was used to design the three input parameters at three levels via Design-Expert (Version 13) [21].The response surface regression model is shown in Equation (2) [22].

Milling Force
In Paulownia milling, the milling parameters will have a decisive influence on the milling force.The milling force can reflect the machining state of the machine tool to a certain extent and have a profound impact on the milling quality.The experiment results are shown in Table 3.

The Influence of Milling Parameters on F x
As shown in Figure 4, by enumerating the individual data of each milling force, we were able to analyze the influence of the change of milling parameters on the milling force, F x , parallel to the X axis.F x was negatively correlated with tool rake angle and spindle's rotational frequency, and positively correlated with milling depth.With the increase in the tool rake angle, the contact area between tool rake face and workpiece (as shown in Figure 4) decreases, and the friction between them decreases.When the spindle's Forests 2024, 15, 325 5 of 12 rotational frequency increases, the amount of milling per tooth decreases (as shown in Equation ( 2)), and is reduced in the milling process; here, the cutting edge's load is small, and the vibration is reduced.Therefore, the whole machining process is more stable, which makes the F x lower [23].As the milling depth, h, increases, the amount of milling per tooth and the impact load increase, resulting in an increase in F x .

The Influence of Milling Parameters on Fy
Figure 5 shows the influence of each milling parameter on the milling force, Fy, parallel to the Y-axis.Compared with Fx, the influence regularity of the milling parameters on Fy is same.It is important to note that, in the numerical Fy, the whole is greater than Fx.This is because the milling force, Fx, parallel to the X-axis, mainly acts on milling wood fibers, and wood is relatively soft compared to cemented carbide tools.Simultaneously, because the wedge angle of woodworking tools is small and the cutting edge is sharp, the milling force value is smaller.However, the milling force, Fy, parallel to the Y-axis, separates the chips from the workpiece surface in the milling process to form the machined surface.At the same time, it overcomes the large-area friction between the chips and the rake face, and finally overcomes the elastic restoring force of the workpiece.This leads to

The Influence of Milling Parameters on F y
Figure 5 shows the influence of each milling parameter on the milling force, F y , parallel to the Y-axis.Compared with F x , the influence regularity of the milling parameters on F y is same.It is important to note that, in the numerical F y , the whole is greater than F x .This is because the milling force, F x , parallel to the X-axis, mainly acts on milling wood fibers, and wood is relatively soft compared to cemented carbide tools.Simultaneously, because the wedge angle of woodworking tools is small and the cutting edge is sharp, the milling force value is smaller.However, the milling force, F y , parallel to the Y-axis, separates the chips from the workpiece surface in the milling process to form the machined surface.At the same time, it overcomes the large-area friction between the chips and the rake face, and finally overcomes the elastic restoring force of the workpiece.This leads to the F y being larger in value [24,25].
Figure 5 shows the influence of each milling parameter on the milling force, Fy, parallel to the Y-axis.Compared with Fx, the influence regularity of the milling parameters on Fy is same.It is important to note that, in the numerical Fy, the whole is greater than Fx.This is because the milling force, Fx, parallel to the X-axis, mainly acts on milling wood fibers, and wood is relatively soft compared to cemented carbide tools.Simultaneously, because the wedge angle of woodworking tools is small and the cutting edge is sharp, the milling force value is smaller.However, the milling force, Fy, parallel to the Y-axis, separates the chips from the workpiece surface in the milling process to form the machined surface.At the same time, it overcomes the large-area friction between the chips and the rake face, and finally overcomes the elastic restoring force of the workpiece.This leads to the Fy being larger in value [24,25].

The Influence of Milling Parameters on Fz
Figure 6 shows the influence of milling parameters on the milling force, Fz, parallel to the Z-axis.Compared with Fx and Fy, the influence of the tool rake angle and the milling depth on Fz is consistent.The main difference is that, with the increase in the spindle's rotational frequency, Fz presents with an increasing trend.For longitudinal milling, the feed direction is parallel to the fiber direction; however, because of the complexity of the structure of Paulownia, in the process of the cutter's removal of the chips, it is bound to cause a tearing force that is perpendicular to the fibers' direction, resulting in an increase in Fz [26].

The Influence of Milling Parameters on F z
Figure 6 shows the influence of milling parameters on the milling force, F z , parallel to the Z-axis.Compared with F x and F y , the influence of the tool rake angle and the milling depth on F z is consistent.The main difference is that, with the increase in the spindle's rotational frequency, F z presents with an increasing trend.For longitudinal milling, the feed direction is parallel to the fiber direction; however, because of the complexity of the structure of Paulownia, in the process of the cutter's removal of the chips, it is bound to cause a tearing force that is perpendicular to the fibers' direction, resulting in an increase in F z [26].
allel to the Y-axis.Compared with Fx, the influence regularity of the milling parameters on Fy is same.It is important to note that, in the numerical Fy, the whole is greater than Fx.This is because the milling force, Fx, parallel to the X-axis, mainly acts on milling wood fibers, and wood is relatively soft compared to cemented carbide tools.Simultaneously, because the wedge angle of woodworking tools is small and the cutting edge is sharp, the milling force value is smaller.However, the milling force, Fy, parallel to the Y-axis, separates the chips from the workpiece surface in the milling process to form the machined surface.At the same time, it overcomes the large-area friction between the chips and the rake face, and finally overcomes the elastic restoring force of the workpiece.This leads to the Fy being larger in value [24,25].

The Influence of Milling Parameters on Fz
Figure 6 shows the influence of milling parameters on the milling force, Fz, parallel to the Z-axis.Compared with Fx and Fy, the influence of the tool rake angle and the milling depth on Fz is consistent.The main difference is that, with the increase in the spindle's rotational frequency, Fz presents with an increasing trend.For longitudinal milling, the feed direction is parallel to the fiber direction; however, because of the complexity of the structure of Paulownia, in the process of the cutter's removal of the chips, it is bound to cause a tearing force that is perpendicular to the fibers' direction, resulting in an increase in Fz [26].We used a mean response analysis to obtain a ranking of the influence degrees of each cutting parameter on the milling forces, F x , F y and F z , in the three directions.The rank value was sorted in descending order based on the size of delta.The results are listed in Table 4.The ranking of the influence degree of each milling parameter on the milling forces in the three different directions is different.Among them, the spindle's rotational frequency has the greatest influence on F x ; this is mainly attributable to the face that the change in the milling force of each tooth significantly affects F x .The most significant influence on F y is the tool rake angle, which shows that the friction between the chips and the rake face significantly affects F y .The milling depth has the greatest influence on F z ; it increases obviously with the increase in milling depth.As shown in Figure 7, the chip morphology changes with the spindle's rotational frequency when the tool rake angle is γ = 2 • and the milling depth h = 0.5 mm.As the spindle's rotational frequency increases, there is a transition in the chip characteristics from large, curled chips to smaller chips, accompanied by a notable decrease in chip integrity and adhesion.The relationship between the spindle's rotational frequency and the feed per tooth, as described by Equation ( 1), is inversely proportional.For a given feed speed, the corresponding feeds per tooth at the three different spindle rotational frequencies are 0.833, 0.625, and 0.500 mm/Z.Since the cutter is a single-tooth shank milling cutter, the feed per tooth is equivalent to the feed per revolution.This implies that, with higher spindle rotational frequency, the tool cuts fewer wood fibers per revolution, resulting in smaller chip morphology and reduced bonding between chips [27].
forces in the three different directions is different.Among them, the spindle's rotational frequency has the greatest influence on Fx; this is mainly attributable to the face that the change in the milling force of each tooth significantly affects Fx.The most significant influence on Fy is the tool rake angle, which shows that the friction between the chips and the rake face significantly affects Fy.The milling depth has the greatest influence on Fz; it increases obviously with the increase in milling depth.As shown in Figure 7, the chip morphology changes with the spindle's rotational frequency when the tool rake angle is γ = 2° and the milling depth h = 0.5 mm.As the spindle's rotational frequency increases, there is a transition in the chip characteristics from large, curled chips to smaller chips, accompanied by a notable decrease in chip integrity and adhesion.The relationship between the spindle's rotational frequency and the feed per tooth, as described by Equation ( 1), is inversely proportional.For a given feed speed, the corresponding feeds per tooth at the three different spindle rotational frequencies are 0.833, 0.625, and 0.500 mm/z.Since the cutter is a single-tooth shank milling cutter, the feed per tooth is equivalent to the feed per revolution.This implies that, with higher spindle rotational frequency, the tool cuts fewer wood fibers per revolution, resulting in smaller chip morphology and reduced bonding between chips [27].

The Influence of Rake Angle on Chip Morphology
Figure 8 shows the change in the chip morphology with the tool rake angle when the spindle's rotational frequency is n = 8000 r/min and the milling depth is h = 0.5 mm.With the increase in the tool rake angle, the chip morphology changes from flaky to granular.The rake angle of the tool affects the deformation of the milling layer.The larger the rake angle, the smaller the deformation of the milling layer.This is evident from the morphology of the chips.The extension along the feed direction is lower and the feed amount per tooth is the same.Under these circumstances, the chips will be scattered and broken [28].
spindle's rotational frequency is n = 8000 r/min and the milling depth is h = 0.5 mm.With the increase in the tool rake angle, the chip morphology changes from flaky to granular.The rake angle of the tool affects the deformation of the milling layer.The larger the rake angle, the smaller the deformation of the milling layer.This is evident from the morphology of the chips.The extension along the feed direction is lower and the feed amount per tooth is the same.Under these circumstances, the chips will be scattered and broken [28]. .

The Influence of Milling Width on Chip Morphology
Table 5 presents five distinct chip morphologies, along with their corresponding milling parameters and machined surface roughness.The average absolute value, aav, was calculated using Equation (1).As the milling thickness diminishes, a noticeable transformation in chip shape occurs.They transform from top block chips to middle flake chips.These progress to strip chips, characterized by excellent integrity, and ultimately to progress scattered chips.This indicates a pronounced effect of milling thickness on chip morphology.Concurrently, it is observed that, with decreasing milling thickness, there is a corresponding decrease in the roughness of the machined surface [29].
Of particular importance is the observation that, under the milling conditions of the third group, strip chips with exceptional integrity appear.Surprisingly, the machined surface of the workpiece exhibits lower surface roughness even when compared to the fourth group, with a smaller milling thickness.This highlights a significant relationship between chip morphology and milling surface quality, emphasizing the importance of studying chip morphology in understanding and optimizing the machining process [30].

The Influence of Milling Width on Chip Morphology
Table 5 presents five distinct chip morphologies, along with their corresponding milling parameters and machined surface roughness.The average absolute value, a av , was calculated using Equation (1).As the milling thickness diminishes, a noticeable transformation in chip shape occurs.They transform from top block chips to middle flake chips.These progress to strip chips, characterized by excellent integrity, and ultimately to progress scattered chips.This indicates a pronounced effect of milling thickness on chip morphology.Concurrently, it is observed that, with decreasing milling thickness, there is a corresponding decrease in the roughness of the machined surface [29].Of particular importance is the observation that, under the milling conditions of the third group, strip chips with exceptional integrity appear.Surprisingly, the machined surface of the workpiece exhibits lower surface roughness even when compared to the fourth group, with a smaller milling thickness.This highlights a significant relationship between chip morphology and milling surface quality, emphasizing the importance of studying chip morphology in understanding and optimizing the machining process [30].

Machined Surface Damage
As depicted in Figure 9, the predominant surface damage observed post Paulownia milling consists of burrs and tears.During the wood milling process, using a milling edge to generate chips, wood fibers undergo a shear force, resulting in a machined surface.Due to the inherent elastoplastic nature of wood, chip removal is not entirely smooth, leading to tearing and bonding of the wood fibers.This tearing extends upward, forming burrs, and downward, forming tears.Table 5 indicates that appropriately chosen milling parameters significantly reduce surface roughness when producing strip chips, suggesting that there is a potential to mitigate Paulownia milling surface damage and enhance machined quality by selecting suitable milling parameters.The establishment of a model correlating cutting parameters with Paulownia milling surface quality holds substantial reference significance [11].
to tearing and bonding of the wood fibers.This tearing extends upward, forming burrs, and downward, forming tears.Table 5 indicates that appropriately chosen milling parameters significantly reduce surface roughness when producing strip chips, suggesting that there is a potential to mitigate Paulownia milling surface damage and enhance machined quality by selecting suitable milling parameters.The establishment of a model correlating cutting parameters with Paulownia milling surface quality holds substantial reference significance [11].

The RSM Model of Ra
According to Equation ( 2) and the data in Table 3, a response surface model of the paulownia milling surface roughness is established, as shown in Equation ( 3).As shown in Table 6, the R-square of the model is 0.9117, which is close to 1, indicating that the model is successful.Meanwhile, Adeq precision measures the signal/noise ratio.A ratio greater than 4 is desirable.The ratio of the model is 11.258, indicating an adequate signal.This model can be used to navigate the design space.Figure 10 shows a 3D surface map and contour map of the influence of milling parameters on Ra.The surface roughness decreased with the increase in the spindle's rotational frequency and the tool rake angle and will increase with an increase in milling depth.The coefficients of the spindle's rotational frequency, the tool rake angle, and the milling depth were all more than 0.3, showing a significant influence on surface roughness.The main order of their influence on surface roughness is h > n > γ.The square terms of each factor and the interaction of the two factors are low.

The RSM Model of Ra
According to Equation ( 2) and the data in Table 3, a response surface model of the Paulownia milling surface roughness is established, as shown in Equation (3).As shown in Table 6, the R-square of the model is 0.9117, which is close to 1, indicating that the model is successful.Meanwhile, Adeq precision measures the signal/noise ratio.A ratio greater than 4 is desirable.The ratio of the model is 11.258, indicating an adequate signal.This model can be used to navigate the design space.Ra = 5.22 − 0.3575n + 0.3988h − 0.3338γ + 0.05nh −0.1475hγ − 0.1269n 2 + 0.1806h 2 + 0.0907γ 2 (3) Figure 10 shows a 3D surface map and contour map of the influence of milling parameters on Ra.The surface roughness decreased with the increase in the spindle's rotational frequency and the tool rake angle and will increase with an increase in milling depth.The coefficients of the spindle's rotational frequency, the tool rake angle, and the milling depth were all more than 0.3, showing a significant influence on surface roughness.The main order of their influence on surface roughness is h > n > γ.The square terms of each factor and the interaction of the two factors are low.

Conclusions
In this paper, the milling force, chip morphology, and surface quality in the milling process of Paulownia were studied, and the potential rules among them were explored.The main conclusions are as follows: (1) Increasing the tool rake angle and the spindle's rotational frequency leads to a de-

Figure 4 .
Figure 4.The influence of milling parameters on F x : (a) rake angle; (b) spindle rotational frequency; (c) milling depth.

Figure 5 .
Figure 5.The influence of milling parameters on F y : (a) rake angle; (b) spindle rotational frequency; (c) milling depth.

Figure 6 .
Figure 6.The influence of milling parameters on F z : (a) rake angle; (b) spindle rotational frequency; (c) milling depth.

Figure 7 .
Figure 7.The influence of n on chip morphology.Figure 7. The influence of n on chip morphology.

Figure 7 .
Figure 7.The influence of n on chip morphology.Figure 7. The influence of n on chip morphology.

Figure 8 .
Figure 8.The influence of γ on chip morphology.

Figure 8 .
Figure 8.The influence of γ on chip morphology.

Forests 2024 , 13 Figure 10 .
Figure 10.Three-dimensional surface map and contour map of the influence of milling parameters on Ra: (a) milling depth and the spindle's rotational frequency; (b) tool rake angle and the spindle's rotational frequency; (c) tool rake angle and the spindle's rotational frequency.

Figure 10 .
Figure 10.Three-dimensional surface map and contour map of the influence of milling parameters on Ra: (a) milling depth and the spindle's rotational frequency; (b) tool rake angle and the spindle's rotational frequency; (c) tool rake angle and the spindle's rotational frequency.

Table 1 .
Physical and mechanical properties of Paulownia.

Table 1 .
Physical and mechanical properties of Paulownia.

Table 2 .
The input parameters of the test.

Table 2 .
The input parameters of the test.

Table 3 .
Experimental results and standard deviations.

Table 4 .
Means response table of milling forces.

Table 4 .
Means response table of milling forces.

Table 5 .
The morphology of the chip and the corresponding milling parameters and surface roughness.

Table 5 .
The morphology of the chip and the corresponding milling parameters and surface roughness. No.

Table 5 .
The morphology of the chip and the corresponding milling parameters and surface roughness. No.

Table 6 .
Fit statistic of Ra model.

Table 6 .
Fit statistic of Ra model.