Multi-Factor Analysis of Cutting Parameters for Bamboo Milling

Abstract

In industrial bamboo machining, the suboptimal selection of cutting parameters leads to elevated cutting power and increased surface roughness. To enhance the machinability of bamboo, a multi-objective optimization of cutting parameters was conducted using orthogonal experimental methods, with special focus on the influences of fiber direction, feed per tooth, and cutting speed on cutting power and surface roughness. The main findings of this study are summarized as follows: feed per tooth exhibited the greatest effect on cutting power, followed by cutting speed and fiber direction. In contrast, fiber direction exerted the most substantial influence on surface roughness, with feed per tooth and cutting speed ranking second and third, respectively. Furthermore, the optimal milling parameters for minimizing both cutting power and surface roughness were identified as a fiber direction of 0°, a feed per tooth of 0.2 mm/z, and a cutting speed of 400 m/min. Therefore, the obtained optimal parameters are recommended for industrial bamboo machining to achieve reduced cutting power and improved surface quality.

1. Introduction

Bamboo is an eco-friendly material that is gradually replacing wood in various fields because of its structural performance, good processability, and its natural color and grain [1,2,3], which consumers typically find aesthetically pleasing [4,5,6]. Cutting power is a measure of the energy used when a tool cuts material from a workpiece during machining [7,8], and it is a crucial factor in production machining, influencing both efficiency and cost. Excessively high power potentially reduces tool life despite faster processing, whereas appropriate power balances productivity and economy. Surface roughness is a measure of the unevenness of a part’s surface after machining [9,10], a key indicator of the quality and performance of machined parts. Surfaces that are too rough can hinder component mating, compromise surface sealing, and negatively affect appearance. Such surfaces may also be less resistant to wear and corrosion [11], which can be direct indications of the effectiveness of a machining process.

In bamboo machining, cutting power and surface roughness are both important factors in cutting performance and surface quality [12,13]. In production planning, machine tool power is a frequent target of optimization [14,15,16], because improving machine tool efficiency and reducing energy consumption can enhance corporate benefits such as cost savings and consistent product quality [17]. Surface roughness is an important indicator of bamboo surface quality and affects product aesthetics, adhesive bonding, and material usage [18]. Thus, optimizing the process to boost machine tool energy efficiency and improve processing quality is vital for cost savings and quality enhancement. Based on related studies [19,20,21,22], the feed per tooth and cutting speed are key factors that influence cutting power. Additionally, the fiber direction directly affects cutting forces, surface quality, and machining efficiency. These parameters are therefore crucial in bamboo processing. In the machining of bamboo materials, the fiber direction of the workpiece is considered an important factor affecting cutting force and the integrity of the machined material surface. However, only a few researchers have focused on the effect of bamboo fiber direction on cutting power and surface roughness. Researchers worldwide have extensively studied cutting power and surface roughness with different cutting parameters. Zhu et al. [23] built a response surface model to evaluate the impact of different factors and their interactions on energy efficiency and surface quality, and found that power efficiency correlates positively with milling depth and changes non-monotonously under different feed-per-tooth rates and helix angles. Yu et al. [24] examined the variations in processing power, temperature, and surface roughness under different conditions via factor analysis, which highlighted the large influence of cutting depth. Additionally, Piernik et al. [25] tested how the chosen settings changed power use and surface quality when machining beech wood on machine. The results help industry improve surface quality and save energy. Liu et al. [26] used response surface methods to improve diamond-tool milling of bamboo. A math model was built to predict results within the tested cutting range. The optimized parameters improved the bamboo surface roughness.

Orthogonal experimental design can reduce the mutual influence between multiple factors and systematically optimize multiple factor conditions by reducing the number of experiments, thereby maximizing efficiency. Therefore, it is widely used in process optimization [27,28,29]. In multi-factor experiments, this design helps identify factors that significantly impact results, enabling researchers to focus on the most consequential factors. Cao et al. [30] designed an orthogonal cutting experiment in which polycrystalline diamond tools were used to plane stone–plastic composites to study cutting force, heat, chip formation, and quality. Wu et al. [31] analyzed the impact of cutting parameters on cutting force and temperature trends and their fluctuations, and clarified machining mechanisms in wood–plastic composite through research on chip formation. In the orthogonal experimental analysis, contribution quantified the relative weight of each factor in explaining total response variability, thereby distinguishing dominant from secondary parameters and providing a data-driven basis for prioritizing optimization and validating experimental reliability.

As an eco-friendly material, bamboo has been widely adopted in furniture manufacturing. In the industrial machining of bamboo, cutting power and surface roughness serve as critical indicators of cutting performance [26]. However, research remains limited regarding these aspects, particularly on the influence of bamboo fiber direction on cutting power and surface roughness. Moreover, in current machining practices, especially when processing bamboo with diverse fiber directions, the inappropriate selection of cutting parameters has led to issues such as high cutting power and poor surface quality. To address these challenges, this study aims to enhance the cutting performance of bamboo by systematically investigating the effects of fiber direction and cutting parameters on cutting power and surface roughness, and to determine the optimal combination of cutting parameters, thereby providing valuable guidance for industrial bamboo machining.

2. Materials and Methods

2.1. Experimental Materials

The bamboo used in this study was naturally grown Moso bamboo (Phyllostachys edulis) harvested in Fujian, China, at age of five years. Specimens were prepared as 130 mm × 80 mm × 18 mm laminated bamboo panels.

In this work, up peripheral milling was used, employing fluoride nanocoated cemented carbide cutting tools with a 14 mm diameter, six teeth, a clearance angle of 10°, and a rake angle of 15°. The coating was applied by immersing the cutter in a heated fluorine nanocomposite solution for approximately 15 min, and then performing thermal curing at 100 °C for 120 min. The fluorine coating consisted of 0.1% to 10% fluorinated organic polymeric surfactant, 0% to 10% functional additives, and 80% to 99.9% environmentally friendly fluorinated solvents. The physical parameters of the tools are shown in

Table 1. Material properties of cemented carbide tool.

Density (g/cm3)	Elastic Modulus (GPa)	Poisson Ratio	Thermal Conductivity (W/(m K))	Heat Capacity (J/(kg K)	Melting Point (°C)
14	6000	0.22	4.5	220	2870

.

All machining tests were performed on a high-speed wood-based composite machining center (MGK01, Guangdong Nanxing Equipment Technology Co., Ltd., Dongguan, China). The working envelope measured 1200 mm × 3300 mm, with axis travels of 3500 mm (X), 1500 mm (Y) and 2500 mm (Z); the maximum spindle speed reached 2400 rpm. The experimental procedure was as shown in Figure 1.

2.2. Test Equipment

Changes in cutting power were obtained by a high-precision power meter. The three-phase power analyzer was connected to the machine tool power supply, with a sampling frequency of 50 kHz (AN87300, Aino Technology Co., Ltd., Jinan, China). Ra as an important parameter for evaluating the quality of machined surfaces, is widely specified as a technical requirement in most manufacturing processes, and it was acquired based on the arithmetic mean deviation. The arithmetic mean deviation of the assessed profile (Ra) was used to quantify the surface roughness. Ra value of machined surface was measured by using the contact-type surface roughness tester with a 2 µm radius natural diamond stylus (JB-4C, Shanghai Optical Co. Ltd., Shanghai, China) based on EN-ISO 21920 [32], and the moving direction of the stylus is parallel to the cutting feed direction. The length of the machined surface was 20 mm. Ra values were calculated according to Equation (1) [18,31].

$$Ra={\displaystyle \frac{1}{n}}{\displaystyle \sum _{i=1}^n\left|yi\right|}$$

(1)

where yi is the height deviation of the i measurement point relative to the reference line, and n is the total number of measurement points.

In the experimental design, the feed per tooth (f_z) was determined in accordance with Equation (2), and the cutting speed (V) had been ascertained through Equation (3).

$$f_z={\displaystyle \frac{v_f}{z\cdot n}}$$

(2)

where v_f denotes the feed speed, z is the number of cutter teeth, and n is the spindle speed.

$$V={\displaystyle \frac{\pi Dn}{1000}}$$

(3)

where D represents the diameter of cutter.

2.3. Experimental Methods

An orthogonal experimental design was employed, with fiber direction (θ), cutting speed (V), and feed per tooth (f_z) selected as the influencing factors. The experimental parameters and the L9 (3³) orthogonal array were determined based on actual processing conditions. Range analysis and analysis of variance (ANOVA) were performed using SPSS software (Version 25.0), with a significance level set at α = 0.05. Each experiment was repeated three times to ensure data accuracy, and the experimental sequence was randomized to prevent systematic errors. The orthogonal experimental layout is presented in

Table 2. Orthogonal experimental scheme.

Number	Cutting Speed V (m/min)	Feed per Tooth fz (mm/z)	Fiber Direction θ (°)
1	400	0.2	0
2	400	0.4	45
3	400	0.6	90
4	500	0.2	90
5	500	0.4	0
6	500	0.6	45
7	600	0.2	45
8	600	0.4	90
9	600	0.6	0

.

The degrees of freedom were fully explained in Equation (4). The sum of squares was detailed in Equation (5), Equation (6) gave the mean square.

$$d{f}_T=N-1\hspace{1em}d{f}_B=k-1\hspace{1em}d{f}_W=N-k$$

(4)

where df_T is the total degrees of freedom, df_B is the between-group degrees of freedom, and df_W is the within-group degrees of freedom. n denotes the total sample size, and k is the number of treatment levels.

$$S{S}_T={\displaystyle \sum _{i=1}^k{\displaystyle \sum _{j=1}^{n_i}(X_{ij}}}-\overline{X}{)}^2\hspace{1em}S{S}_B={\displaystyle \sum _{i=1}^k{n}_i({\overline{X}}_i}-\overline{X}{)}^2\hspace{1em}S{S}_W={\displaystyle \sum _{i=1}^k{\displaystyle \sum _{j=1}^{n_i}(X_{ij}}}-{\overline{X}}_i{)}^2$$

(5)

where SS_T stands for the total of squares, SS_B is the sum of squares between groups, and SS_W is the sum of squares within groups. X_ij is the j observation in the i group, $\overline{X}$ is the overall mean, n_j is the sample size of the i group, and $\overline{X}$_i is the mean of the i group.

$$M{S}_B={\displaystyle \frac{S{S}_B}{d{f}_B}}\hspace{1em}\hspace{1em}M{S}_W={\displaystyle \frac{S{S}_W}{d{f}_W}}$$

(6)

where MS_B denotes the between-group mean square and MS_W denotes the within-group mean square.

Within the ANOVA framework, the F-value was used as a core indicator to quantitatively evaluated whether a certain factor has a statistical impact on the experimental results. The calculation method for the F-value is detailed in Equation (7).

$$F={\displaystyle \frac{M{S}_B}{M{S}_W}}$$

(7)

In the statistical analysis, the contribution rate (%Cont.) of each factor was calculated using the formula in Equation (8).

$$\%Cont.={\displaystyle \frac{S{S}_B}{S{S}_T}}$$

(8)

where SS_T represents the total sum of squares.

3. Results and Analysis

3.1. Cutting Power Analysis

The experimental results at different combination of cutting parameters were listed in

Table 3. Orthogonal experimental results.

No.	Cutting Power P (W)	Tolerance of P	Surface Roughness Ra (μm)	Tolerance of Ra
1	264.10	±10.26	1.35	±0.03
2	815.76	±24.10	4.61	±0.12
3	945.36	±36.44	8.06	±0.18
4	691.92	±32.73	5.55	±0.09
5	824.80	±35.22	3.65	±0.07
6	1352.04	±44.81	4.66	±0.15
7	503.60	±17.35	5.30	±0.13
8	1064.70	±40.35	6.97	±0.19
9	1388.20	±46.59	3.44	±0.06

. The values in parentheses were the standard deviations of the results from three repeated experiments.

Figure 2a illustrated that cutting power increased with the rise in cutting speed from 400 to 600 m/min. Specifically, when the cutting speed increased from 400 to 500 m/min, the cutting power showed a substantial rise of 41.67%. A further increase to 600 m/min resulted in a more moderate increase of 3.04%. This was mainly because the cutting speed is primarily influenced by the spindle speed. When the cutting speed increases, the spindle requires more energy consumption to drive it. Therefore, the cutting power increases as the cutting speed rises. Similarly, as the feed per tooth and fiber direction increased (Figure 2b,c), cutting power also rose, by 152.55% and 9.08%, respectively. The increase in feed per tooth enlarges the contact area between the tool and the workpiece, leading to higher load and cutting force, and consequently requiring greater cutting power. These findings are consistent with existing studies in wood machining, particularly the work of Li et al. [17], which highlighted the pronounced influence of feed per tooth on cutting power, with larger values resulting in elevated power consumption. Moreover, cutting power increased as the fiber direction shifted from 0° (parallel to grain) to 90° (perpendicular to grain). When cutting along the grain, the tool primarily separates the bamboo fibers, resulting in lower cutting resistance. In contrast, cross-grain cutting requires severing individual fibers, demanding higher force and increasing resistance. Nevertheless, the change in cutting power across fiber direction was relatively minor compared to the effect of feed per tooth. The growth in cutting power was more significant during the initial increases in both cutting speed and fiber direction, with the rate of increase tapering off thereafter. This moderation can be explained by the stabilization of the cutting process at higher speeds, which dampens further increases in power. Additionally, the percentage contribution of each factor reflects its influence on cutting power: feed per tooth (f_z) was the most influential factor at 76.7%, followed by cutting speed (V) at 16.3%, and fiber direction (θ) at only 9.0%. Thus, feed per tooth had the greatest effect on cutting power, followed by cutting speed and fiber direction.

ANOVA (α = 0.05) was summarized in

Table 4. Variance analysis of cutting power.

Factors	Degree of Freedom	Sum of Square	Mean Square	Contribution Percentage	F Value	Prominence
V (m/min)	2	176,282.275	88,141.138	16.300	0.521	Insignificant
fz (mm/z)	2	829,741.387	414,870.694	76.700	2.450	Insignificant
θ (°)	2	9917.627	4958.813	9.000	0.029	Insignificant
Error	2	66,554.402	33,277.201	—	—	—
Corrected total	8	1,082,495.692	—	—	—	—

. A factor is considered statistically insignificant if its F-value is below the critical F_0.05 value of 5.14. According to the ANOVA (Table 4) and range analysis (

Table 5. Range analysis results of cutting power at different cutting conditions.

Factors	Cutting Speed V (m/min)	Feed per Tooth fz (mm/z)	Fiber Direction θ (°)
K1	675.073	486.540	825.700
K2	956.373	901.753	890.467
K3	985.500	1228.653	900.660
RP	310.427	742.113	74.960

Note: K_i represented the average value of level i (1–3) of a factor, and R_P meant the difference between the maximum and minimum p values of K_i of each factor.

) results, the contribution percentage of feed per tooth had the higher value of 76.7% than those of cutting speed and fiber direction. Thus, the order of influence on cutting power was: feed per tooth > cutting speed > fiber direction. However, all three factors had F-values below the threshold, indicating that their effects on cutting power were not statistically significant.

3.2. Surface Roughness Analysis

As shown in Figure 3a and

Table 6. Range analysis results of surface roughness at different cutting conditions.

Factors	Cutting Speed V (m/min)	Feed per Tooth fz (mm/z)	Fiber Direction θ (°)
K1	4.673	4.067	2.813
K2	4.620	5.077	4.857
K3	5.237	5.387	6.860
RRa	0.617	1.320	4.047

Note: K_i represented the average value of level i (1–3) of a factor, and R_Ra meant the difference between the maximum and minimum Ra values of K_i of each factor.

, the surface roughness initially decreased and then increased with rising cutting speed. When the cutting speed increased from 400 to 500 m/min, the surface roughness decreased by 1.13%. However, as cutting speed increased to 600 m/min, the surface roughness increased by 13.35%. In the range of low cutting speeds of 400–500 m/min, as the cutting speed increased, the cutting volume per unit time decreased, and the cutting resistance was reduced. This cutting process became more stable. Consequently, the surface roughness decreased and the machining quality improved. However, with the continuous increase in cutting speed, the speed at which the cutting edge engages and disengages the workpiece accelerated. Owing to the structural characteristics of bamboo, the milling cutter induces pre-splitting of bamboo fibers ahead of the blade, which results in irregular cracks that deviate from the intended cutting path. This pre-splitting effect gave rise to surface defects, thereby increasing the apparent surface roughness. Therefore, the surface roughness of bamboo first decreased and then increased with the increase in cutting speed. With increases in feed per tooth and fiber direction (Figure 3b,c), the surface roughness increased by 32.46% and 143.85%, respectively. A higher feed per tooth increased the depth of cut, leading to greater cutting resistance and higher cutting forces. This intensified contact deformation between the tool and workpiece, increasing the likelihood of tool displacement and vibration. The resulting process instability produced uneven surfaces and higher roughness. Furthermore, as the fiber direction increased, the angle between the cutting direction and the bamboo fibers widened, requiring more fibers to be fully severed. This raised cutting resistance and altered the magnitude and direction of cutting forces, reducing process stability and increasing surface roughness. During tool entry and exit, fibers became more prone to tearing and cracking; the interwoven fiber structure hindered clean cutting, resulting in fiber pull-out, burr formation, and pitting, all of which contributed to increased surface roughness [33,34]. Furthermore, increased fiber direction intensified friction and energy consumption, generating more heat in the cutting zone. The non-uniform thermal distribution caused localized softening and deformation of the workpiece, further increasing surface roughness. These observations aligned closely with the work of Guan et al. [34] on bamboo machining behavior, which demonstrated that fiber direction governed crack propagation and surface damage patterns, thereby exerting a decisive influence on surface roughness.

Figure 4 shown surface roughness example profiles from the nine experimental tests. The labels in the figure corresponded to the experimental test numbers. According to the percentage contribution results in

Table 7. Analysis variance of surface roughness.

Factors	Degree of Freedom	Sum of Square	Mean Square	Contribution Percentage	F Value	Prominence
V (m/min)	2	0.700	0.35	2.2	0.075	Insignificant
fz (mm/z)	2	2.859	1.429	9.1	0.305	Insignificant
θ (°)	2	24.564	12.282	78.6	2.620	Insignificant
Error	2	3.139	1.570	—	—	—
Corrected total	8	31.262	—	—	—	—

, fiber direction (θ, % Cont. = 78.6%) had the greatest influence on surface roughness, followed by feed per tooth (f_z, % Cont. = 9.1%) and cutting speed (V, % Cont. = 2.2%). Thus, the factors affecting surface roughness ranked in the following order: fiber direction > feed per tooth > cutting speed. In the ANOVA for surface roughness, the F-values for all three factors were below the critical F_0.05 value, indicating that their effects were not statistically significant.

3.3. Optimization and Verification of Cutting Parameters

In bamboo processing, cutting power is a crucial indicator affecting the energy consumption of machine tools, and it directly influences the production costs of enterprises. Surface roughness Ra directly impacts the quality of subsequent surface treatments of bamboo, such as painting and veneering, and thus stands as a key factor affecting the surface roughness of products [18]. Thus, an optimization aimed at achieving the lowest surface roughness and cutting power was conducted on the selection of parameters, including fiber direction, cutting speed, and feed per tooth.

According to the results of the range analysis in the Section 3.1 and Section 3.2, multi-objective optimization was performed to obtained the minimize cutting power and surface roughness. The optimal cutting parameter combination was determined as the A1B1C1 setting (0° fiber direction, 0.2 mm/z feed per tooth, 400 m/min cutting speed), with the lowest cutting power of 264.1 W and surface roughness of 1.35 µm.

4. Conclusions

This study investigated the effects of fiber direction, cutting speed, and feed per tooth on cutting power and workpiece surface roughness in the up-milling of Moso bamboo with fluoride nanocoated cemented carbide cutting tools. The main conclusions were given as follows:

(1)

As the fiber direction increased from 0° to 90°, the cutting power increased by 9.08% and the surface roughness rose by 143.85%. When the feed per tooth increased from 0.2 mm/z to 0.6 mm/z, the cutting power increased by 152.55% while the surface roughness went up by 32.46%. As the cutting speed increased from 400 m/min to 600 m/min, the cutting power increased by 41.67% and the surface roughness increased by only 13.35%.

(2)

According to the result of ANOVA, feed per tooth (76.7%) had the greatest contribution to the cutting power, followed by cutting speed (16.3%) and fiber direction (9.0%). While, fiber direction (78.6%) had the greatest impact on the surface roughness, followed by feed per tooth (9.1%) and cutting speed (2.2%).

(3)

The optimal combination of cutting parameters was determined to achieve lowest cutting power and surface roughness, where fiber direction was 0°, feed per tooth was 0.2 mm/z, and cutting speed was 400 m/min, this combination of parameters is hoped to offer guidance for the machining of bamboo.