Modeling and Predicting the Machined Surface Roughness and Milling Power in Scot’s Pine Helical Milling Process

Abstract

Helical milling with the advantages of stable machining process, a well-machined surface quality, etc., is an interest of researchers and producers. Machined surface roughness (arithmetic mean deviation (Ra) and maximum height of the assessed profile (Rz)) and milling power consumption as two main machining characteristic parameters were studied and chosen as response factors to evaluate the machinability of Scots pine helical milling. Input variables included helical angle of milling cutter, rotation speed of main shaft, and depth of milling. Response surface methodology was applied for the design of experiments, data processing and analysis, and optimization of the processing parameters. The results showed that Ra and Rz decreased with an increase in helical angle and rotation speed of main shaft, though increased with an increase in depth of milling. Milling power increased when the helical angle and depth of milling increased and showed a slight downward trend as the rotational speed increased. The quadratic models were applied to predict the values of Ra, Rz, and milling power due to the high values of R² of 0.9895, 0.9905, and 0.9885, respectively. The plot of predicted and actual values also indicated that the created models had good predictability. The optimized combination of helical angle, rotation speed, and depth of milling are 64°, 7500 r/min, and 0.5 mm, respectively. The effects of input variables and the quantitative relation between input variables and response variables were revealed clearly. These achievements will be useful for guiding the selection of helical milling parameters to achieve the purposes of improving processed surface quality and saving the processing power consumption.

1. Introduction

In the context of green manufacturing and “Industry 4.0”, intelligent, efficient, and low-carbon manufacturing have become the main goals of modern manufacturing industry [1]. Cutting is an important process for wooden products’ manufacturing and also one of the significant energy consuming links [2,3,4]. At the same time, the machined surface roughness is a significant criterion to evaluate the quality of processed wooden materials [5,6], because the aesthetic value of the wooden products is closely related to their characteristic of surface morphology [7,8], and the surface roughness has a direct effect on the performance of gluing and coating [9,10,11,12]. Helical milling, which has the advantages of high machined surface quality and cutting stability, has been concerned and studied [13,14,15,16]. The effects of helical milling parameters on machined Scots pine wood surface roughness and milling power consumption have not yet been revealed. Hence, the milling power consumption and surface quality during the helical milling process must be modeled and predicted. Additionally, it is essential to apply optimized machining parameters to reduce milling power and improve machined surface quality so as to realize the purpose of high efficiency and low consumption processing.

In recent years, researchers have focused on the cutting parameters’ optimization and modeling methodologies to reveal the variation trend of cutting forces, power consumption, processed surface roughness, etc., and the quantitative relation between input and output parameters in materials’ helical cutting processes [17,18,19]. The results of previous studies have showed that the helical cutting parameters had a significant influence on cutting forces, cutting power, and surface roughness [15,20]. For example, the specific cutting energy and cutting power consumption of medium density fiberboard increased with the helical angle increased, but decreased with the increase in milling depth [21]. In the wood planning, the planer tool’s helical edge with the values from 45° to 65° generated almost the same amount of cutting power as the conventional straight tools. However, the cutting power consumption increased gradually when the helical angle increased to 75° and 85° [22]. Therefore, the trend of cutting power consumption varies with the changes of processing parameters.

During the evaluation of materials machining properties, the indexes of Ra and Rz are widely applied [23]. In helical cutting processes, the input parameters have a direct influence on the machined surface quality [5]. The results of published works have indicated that the helical angle had most significant influence on Ra, followed by the spindle speed and depth of milling in wood plastic composites (WPCs)’s milling process. The increased helical angle resulted in a significant increase in Ra. However, the values of Ra decreased when the spindle speed increased [15]. During the stone–plastic composite (SPC) milling process, Ra tended to decrease with the increase in helical angle and spindle speed, but decrease with the decrease in feed rate and cutting depth [13]. A similar result of the effects of helical angle and depth of cutting on Ra were also achieved in luxury vinyl tiles (LVTs)’s milling process [14]. Due to the significant effects of input parameters on machined surface quality, it is essential to create a mathematical model to predict the surface roughness in the helical cutting process and to provide guidance for selecting reasonable processing parameters.

However, a suitable and accurate model and optimization method is hard to establish for predicting the surface quality and cutting power consumption [24]. In recent years, the artificial neural network (ANN) [25], neuro-fuzzy inference system (NFIS), improved particle swarm optimization (IPSO) algorithm [19,26], and response surface methodology (RSM) [27] have been normally adopted to describe the relationship between input and output parameters (such as cutting force, surface quality, cutting power, etc.). Those different methods all show ideal prediction accuracy in their own fields. Among them, RSM can establish a continuous variable surface model to evaluate the factors and their interactions that affect the machining process and to determine the optimal level range. Moreover, the number of experimental groups is relatively small, which has the advantage of significantly saving manpower and material resources. However, up until now, there has been no complete mathematical model for predicting the milling power and surface roughness of solid wood in helical milling, especially for Scots pine (Pinus sylvestris L.).

In this study, the helical angle of milling cutter (λ), rotation speed of main shaft (n), and depth of milling (h) were selected as input processing parameters, and the RSM was chosen to arrange the experiments. The effects of input parameters on milling power consumption and surface roughness will be analyzed, then the mathematical model will be created to evaluate the relationship between the input parameters and response parameters. It will provide a solution to reveal the variation trend of surface quality and milling power, and determine the reasonable processing parameters for solid wood helical milling.

2. Materials and Methods

2.1. Materials

All the samples were prepared from the sapwood of Scots pine (Pinus sylvestris L.) logs and then dried to a moisture content of about 11%. The size of samples for milling experiments was 120 mm × 80 mm × 18 mm (Longitudinal × Tangential × radial). In total, 85 samples were prepared for the milling experiments to meet the requirement of 5 repetitions for each group. Meanwhile, the density, modulus of rupture, modulus of elasticity, and moisture content of Scots pine wood were tested by Chinese standards of GB/T1933-2009, GB/T1936.1-2009, GB/T1936.2-2009, and GB/T1931-2009, respectively. Moreover, the detailed results for these properties were shown in

Table 1. The results of some physical and mechanical properties of Scots pine samples.

Work Piece	Density	Modulus of Rupture	Modulus of Elasticity	Moisture Content
Scots pine	0.52 g/cm3	71 MPa	12,234 MPa	11.2%

.

2.2. Experimental Setup

Up-milling was chosen in this study, which was performed on a computerized numerical control milling center (MGK01, Nanxing Machinery Co. Ltd., Dongguan, China). The maximum values of the main parameters of feed rate and spindle rotation speed are 50 m/min and 24,000 r/min, respectively. The surface roughness of Ra and Rz, which is applied to describe the quality of milled wood surface, was measured by a surface topography profilometer (DSX510, Olympus, Co. Lt., Tokyo, Japan). The test area is located in the middle of milled surface, with a sampling length of 10 mm. The test direction is parallel to the wood fiber direction and also parallel to the milling feed direction. Each surface roughness test was repeated five times; the meaning value of these five results was chosen to estimate the surface roughness. The dynamic power change at different cutting stages was recorded by a three-phase power analyzer with a maximum sampling frequency of 50 KHz (AN87300, Ainuo Co., Ltd., Qingdao, China). Referring to existing literatures, the milling power is equal to the power in the cutting phase minus the power in the unloading operation phase [21,28].

2.3. Design of Experiments

In the present study, Box–Behnken Design (BBD) of RSM was selected for the experimental design as well as data analysis and processing parameters’ optimization. To obtain as high surface quality and as lower milling power consumption as possible simultaneously, helical angle of milling cutter, main shaft rotation speed, and depth of milling were chosen as the input variables, while Ra, Rz, and milling power consumption were the response variables. These three input parameters and their ranges were selected by a preliminary test, previous studies, and actual processing requirements [28,29]. The detailed levels of those input variables are presented in

Table 2. Input variables and their levels.

Variables	Codes	Levels
		−1	0	1
Helical angle of milling cutter (λ)/°	A	54	62	70
Rotation speed of main shaft (n)/r/min	B	5500	6500	7500
Depth of milling (h)/mm	C	0.5	1.0	1.5

. Both the analysis of experimental data and the illustrative figures were accomplished by using Design-Expert (Version 12.0.1.0, Stat-Ease, Inc., Minneapolis, MN, USA) software. Equation (1) [28,30] was employed to obtain the interactive effects between the input and response variables.

$$Y=b_0+{{\displaystyle \sum }}_{i=1}^k{b}_i{X}_i+{{\displaystyle \sum }}_{i,j}^k{b}_{ij}{X}_i{X}_j+{{\displaystyle \sum }}_{i=1}^k{b}_{ii}{X}_i^2$$

(1)

where Y represents the predicted response parameters, while X_i and X_j represent the input variables. The term of b₀ is the constant coefficient and the terms of b_ii, b_ij are the interaction coefficients. The quality of the fitted models was assessed by the correlation coefficient (R²). F-value (Fisher variation ratio) and probability value (Prob > F) are the two main indexes indicating the significance and adequacy of the created models.

3. Results and Discussion

3.1. Influences of Input Variables on Ra and Rz

The experimental design and results based on BBD for Scots pine up-milling are shown in

Table 3. The results of Ra, Rz, and milling power consumption in Scots pine helical up-milling.

Standard	Run	Factors			Ra/μm	Rz/μm	Milling Power/W
		λ/°	n/r/min	h/mm
1	14	54	5500	1.0	3.80	20.35	69.3
2	9	70	5500	1.0	3.30	16.34	108.7
3	13	54	7500	1.0	2.67	14.91	48.3
4	12	70	7500	1.0	1.79	9.24	103.0
5	15	54	6500	0.5	3.17	16.75	26.7
6	8	70	6500	0.5	2.36	12.10	66.0
7	7	54	6500	1.5	4.28	22.31	80.6
8	11	70	6500	1.5	3.97	20.62	121.7
9	17	62	5500	0.5	3.49	16.52	23.3
10	3	62	7500	0.5	2.25	11.58	39.3
11	2	62	5500	1.5	5.19	25.32	86.7
12	5	62	7500	1.5	4.12	19.19	69.0
13	16	62	6500	1.0	3.24	16.27	56.3
14	4	62	6500	1.0	3.25	16.29	56.3
15	6	62	6500	1.0	3.25	16.31	56.3
16	1	62	6500	1.0	3.24	16.29	56.3
17	10	62	6500	1.0	3.25	16.29	56.3

. To reveal the change rule of the response factors with the input factors, the results were analyzed by Design-Expert software, and the detailed influence trend of input factors on Ra, Rz, and milling power is shown in Figure 1.

It is obvious that the input parameters had significant effects on Ra and Rz; moreover, with the increase in the helical angle and rotation speed of the main shaft, the formation of a higher quality surface took place; that is, the values of Ra and Rz decreased. However, the parameters of Ra and Rz increased with the increase in milling depth. The probable reason for this is that the milling width increases more gently with the increase in the helical angle of the milling cutter, which induces the milling process smoother. This result has a good agreement with the LVTs’ materials helical milling process [14]. When the rotation speed of main shaft increases and milling depth decreases, the quantity removed per tooth during Scots pine wood milling process decreases, and less resistance acts on the knife edge, thus reducing the milling vibration and resulting in a smoother machined surface [13].

Apart from the main parameters, the interactions between input parameters also have influences on the response factors. The interacting effects of the helical angle and main shaft rotation speed (λ × n) and helical angle and depth of milling (λ × h) were also analyzed. Figure 2 presents how the λ × n and λ × h are related to Ra and Rz. It indicates that the values of Ra and Rz decreased with an increase in helical angle and main shaft rotation speed. Moreover, the combination of increased helical angle and decreased milling depth induced a decrease in the surface roughness. Hence, it is concluded that the Ra and Rz can be minimized with a higher helical angle, higher rotation speed, and lower depth of milling combinations. Moreover, Figure 3 and Figure 4 indicate that the minimum Ra and Rz could be achieved by the highest helical angle, the highest rotation speed, and the lowest depth of milling combination.

3.2. Influences of Input Variables on Milling Power

During the milling process, the input variables affect the materials’ removal rate, stability of machining process, and milling force, etc., which have significant influences on milling power consumption [21]. It is observed that the milling power increased with the increase in helical angle and depth of milling but decreased with the increase in the rotation speed of the main shaft (shown in Figure 1). When the helical angle increased, the resultant cutting force increased, and more energy is required to overcome these milling resistances. This result was confirmed in wood–plastic composites’ and stone–plastic composites’ cutting process [15,30]. The increase in depth of milling directly leads to the increase in material removal rate, which required more energy to take away the wood material. For the rotation speed of the main shaft, the cutting force decreased under the high rotation speed of the main shaft [2,31]. The decreasing of the cutting force has a positive effect on decreasing the milling power consumption. However, the increase in rotation speed induced the power consumption in the unloading operation phase, which will induce an increase in the total milling power and a decrease in power efficiency. This was revealed in previous research studies [32,33].

In Figure 2, the interacting influences of λ × h and n × h on milling power are also presented. Higher milling power consumption resulted from increasing helical angle and depth of milling. When the depth of milling was at a low level of the selected ranges, the increase in rotation speed did not have a significant effect on the variation of milling power (as shown in Figure 5). However, the increased rotation speed decreased the milling power when the depth of milling was at a high level. This is because the material removal rate is extremely increased when the depth of milling was at a higher level, meanwhile the milling resistance also increased. However, the rotation speed had a positive effect, decreasing the cutting force.

3.3. Analysis of Variance (ANOVA)

ANOVA is used to determine the influence of controllable factors on research results by analyzing the contribution of variation from different sources to total variation [27,34]. The detailed ANOVA results of Ra, Rz, and milling power were presented in

Table 4. ANOVA results of Ra.

Source	Sum of Squares	Degrees of Freedom	Mean Squares	F-Value	p-Value
Model	10.52	9	1.17	73.08	<0.0001
λ	0.7769	1	0.7769	48.57	0.0002
n	3.08	1	3.08	192.69	<0.0001
h	4.95	1	4.95	309.2	<0.0001
λ × n	0.0367	1	0.0367	2.29	0.1737
λ × h	0.0625	1	0.0625	3.91	0.0887
n × h	0.0079	1	0.0079	0.4954	0.5043
λ2	0.4767	1	0.4767	29.8	0.0009
n2	0.0015	1	0.0015	0.0941	0.7679
h2	1.21	1	1.21	75.47	<0.0001
Residual	0.1120	7	0.0160
Lack of fit	0.1118	3	0.0373
Pure Error	0.0001	4	0.0000
Cor Total	10.63	16

,

Table 5. ANOVA results of Rz.

Source	Sum of Squares	Degrees of Freedom	Mean Squares	F-Value	p-Value
Model	245.12	9	27.24	81.25	<0.0001
λ	32.05	1	32.05	95.63	<0.0001
n	69.68	1	69.68	207.87	<0.0001
h	116.26	1	116.26	346.82	<0.0001
λ × n	0.6867	1	0.6867	2.05	0.1954
λ × h	2.18	1	2.18	6.52	0.0379
n × h	0.3557	1	0.3557	1.06	0.3372
λ2	1.74	1	1.74	5.2	0.0566
n2	0.7998	1	0.7998	2.39	0.1663
h2	22.25	1	22.25	66.38	<0.0001
Residual	2.35	7	0.3352
Lack of fit	2.35	3	0.7819
Pure Error	0.0008	4	0.0002
Cor Total	247.47	16

and

Table 6. ANOVA results of milling power.

Source	Sum of Squares	Degrees of Freedom	Mean Squares	F-Value	p-Value
Model	11671.54	9	1296.84	67.03	<0.0001
λ	3802.65	1	3802.65	196.54	<0.0001
n	100.37	1	100.37	5.19	0.0568
h	5130.17	1	5130.17	265.15	<0.0001
λ × n	58.7	1	58.7	3.03	0.1251
λ × h	0.7744	1	0.7744	0.04	0.8471
n × h	283.36	1	283.36	14.65	0.0065
λ2	2146.5	1	2146.5	110.94	<0.0001
n2	49.59	1	49.59	2.56	0.1534
h2	112.71	1	112.71	5.83	0.0465
Residual	135.44	7	19.35
Lack of fit	135.44	3	45.15
Pure Error	0.0004	4	0.0001
Cor Total	11806.98	16

. p-values less than 0.05 indicate that model terms are significant. In this case, λ, n, h are significant model terms for Ra and Rz, and the λ, h are significant terms for milling power. The interaction of λ × h is also significant for Rz. The F-value analysis reveals the depth of milling as the most important factor for Ra and Rz, followed by the rotation speed of the main shaft and then the helical angle. For the milling power, the depth of milling is the most important factor, followed by the helical angle and then the main shaft rotation speed.

3.4. Regression Models for Ra, Rz, and Milling Power

For a quantitative description of the relationship between input variables and response variables, the quadratic models were selected due to their highest correlation coefficient (

Table 7. Results of ANOVA for the different models.

Responses Parameters	Models	SD	R2	Adjusted R2	Predicted R2
Ra	Linear	0.38	0.8281	0.7884	0.6434
	2FI	0.41	0.8382	0.7411	0.1821
	Quadratic	0.13	0.9895	0.9759	0.8317
Rz	Linear	1.51	0.8809	0.8534	0.7571
	2FI	1.62	0.8939	0.8303	0.4817
	Quadratic	0.58	0.9905	0.9783	0.8483
Milling power	Linear	14.61	0.7651	0.7109	0.5475
	2FI	15.59	0.7941	0.6706	0.1054
	Quadratic	4.40	0.9885	0.9738	0.8165

). The higher the correlation coefficient, the better the fitting effect of the model is. The graph of predicted vs. actual values for Ra, Rz, and milling power also indicates that the model prediction values are very close to the actual test-measured values (Figure 6). The coded models for the above three response parameters are shown by Equations (2)–(4).

$$\begin{gathered} Ra=3.25-0.3116\times A-0.6207\times B+0.7863\times C-0.0958\times A\times B+0.1250\times A\times C+0.0445\times B\times C \\ -0.3365\times A^2-0.0189\times B^2+0.5354\times C^2 \end{gathered}$$

(2)

$$\begin{gathered} Rz=16.29-2.00\times A-2.95\times B+3.81\times C-0.4144\times A\times B+0.7391\times A\times C-0.2982\times B\times C-0.6436\times A^2 \\ -0.4358\times B^2+2.30\times C^2 \end{gathered}$$

(3)

$$\begin{gathered} Milling power=56.33+21.80\times A-3.54\times B+25.32\times C+3.83\times A\times B+0.44\times A\times C-8.42\times B\times C \\ +22.58\times A^2+3.43\times B^2-5.17\times C^2 \end{gathered}$$

(4)

3.5. Optimization of Processing Parameters

In wood materials’ processing, smoother machined surface and lower milling power consumption are more anticipated and welcomed. In this study, the optimization conditions for input parameters are “in range” and the goals of selected two response parameters are “minimize”. The optimized combination of helical angle, rotation speed, and depth of milling are 64°, 7500 r/min and 0.5 mm, respectively. The minimized Ra, Rz, and milling power are 2.14 μm, 10.77 μm, and 42.7 W, respectively, with the desirability of 0.867 (Figure 7).

4. Conclusions

The surface roughness of Ra, Rz, and milling power consumption in the Scots pine helical up-milling process were measured and researched. The input parameters had significant effects on the response parameters, and the quadratic models were created to describe the relationships between input variables and response variables. The effects of helical angle, main shaft rotation speed, and depth of milling have good agreement with the present studies. The optimized combination of helical milling parameters was achieved by RSM, and it was meaningful to choose milling parameters reasonably in the real manufacturing process. The detailed conclusions are shown as follows:

(1)

Ra, Rz, and milling power are influenced significantly by the helical angle, rotation speed of main shaft, and depth of milling. The increased rotation speed of main shaft and helical angle decrease the values of Ra and Rz. Nevertheless, Ra and Rz increase with an increase in milling depth. Milling power also increases with an increase in helical angle and depth of milling, however decreases if the main shaft rotates at a faster speed;

(2)

The quadratic models are competent for modeling the relationship between input parameters and response parameters due to the high values of R². The relative errors between predicting results and test results are very small.

(3)

The optimized combination of helical angle, rotation speed, and depth of milling are 64°, 7500 r/min, and 0.5 mm, respectively. The minimized Ra, Rz, and milling power are 2.14 μm, 10.77 μm, and 42.7 W, respectively, with the desirability of 0.867.