Force Prediction and Cutting-Parameter Optimization in Micro-Milling Al7075-T6 Based on Response Surface Method

Optimization of cutting parameters in micro-milling is an important measure to improve surface quality and machining efficiency of the workpiece. Investigation of micro-milling forces prediction plays a positive role in improving machining capacity. To predict micro-milling forces and optimize micro-milling cutting parameters (per-feed tooth (fz), axial cutting depth (ap), spindle speed (n) and tool extended length (l)), a rotatable center composite experiment of micro-milling straight micro-groove in the workpiece of Al7075-T6 were designed, based on second-order response surface methods. According to the experiment results, the least square method was used to estimate the regression coefficient corresponding to the cutting parameters. Simultaneously, the response prediction model of micro-milling was established and successfully coincide the predicted values with the experiment values. The significance of the regression equation was tested by analysis of variance, and the influence of micro-milling cutting parameters on force and top burrs morphology was studied. The experiment results show that in a specific range of cutting parameters, ap and fz have a significant linear relation with the micro-milling force and the top burrs width. According to the optimal response value, the optimized cutting parameters for micro-milling obtained as: n is 11,393 r/min, fz is 6 µm/z, ap is 11 μm and l is 20.8 mm. The research results provide a useful reference for the selection of cutting parameters for micro-milling.


Introduction
Because micro-milling has a wide range of applications in the aerospace, biomedical, electronics, automotive and other related fields, the cutting mechanism and performance have been extensively studied to improve the quality of the machined surface [1]. Compared with traditional milling methods, micro-milling technologies are effective means to manufacture micro-and mesoscale parts with high efficiency and high precision [2,3]. Micro-milling is a micromanufacturing process that has the ability to produce microproducts with the three-dimensional curved surface, and it is suitable for machining various metal and nonmetal materials. Therefore, it has received extensive attention from experts and scholars.
Surface quality and tool wear are important for the machined product function and factors greatly influencing the manufacturing cost [4]. In micro-milling, the surface quality and the milling force have drawn much attention from researchers because the quality of the workpiece surface (such as burrs [5] and roughness) is directly related to whether the workpiece can be used. The micro-milling force is an important factor that causes tool vibration [6] or workpiece deformation which can indirectly affect tool life [7,8] and the quality of the workpiece surface [9]. Therefore, micro-milling forces and optimizing cutting parameters have been investigated with emphasis on micro-milling. In the past, there have been many studies focusing on this content. Wu et al. [10] studied burr formation mechanisms in micro-milling to reduce burrs on the workpiece surface. Zhang et al. [11] proposed a new universal instantaneous force model, which considered size effects in force coefficients and included the tool runout effect in the instantaneous uncut thickness. Bao et al. [12] proposed a new micro-end milling cutting force analysis model. This model calculates the chip thickness in consideration of the tool tip trajectory when the tool is continuously rotating and advancing. Jing et al. [13] proposed a model for exactly prediction cutting force, comprehensively established by considering the variety of entry and exit angles for each engaged cutting edge and an accurate instantaneous uncut chip thickness. Wang et al. [14] analyzed the milling force, specific cutting force, surface roughness and burrs width at different feed rates to optimize the micro-milling process. To improve the machined surface, Rahman et al. [15] establishes a mechanics model from a new perspective, taking into account the influence of material microstructure and tool geometry.
With its excellent inherent qualities such as light weight, good strength, corrosion resistance and excellent machining performance [16,17], aluminum and its alloys have a wide range of applications in the micro-milling fields. Regarding the machining of aluminum and its alloys, certain theories and principles have been proposed by the researchers who have used traditional macro-machine tools. In recent years, micro-machining of aluminum alloy is increasingly important due to the development of miniaturized industries [18]. A large number of studies have shown that the difference between traditional milling and micro-milling includes the existence of minimum cutting thickness, scale effects and strengthening of non-free cutting. Research on the cutting mechanisms of micro-milling is aimed at improving the machining capacity and efficiency, ultimately to reduce the cost [19,20]. Therefore, many studies focused on the optimization of cutting parameters in the past to further study the influence of the cutting parameters selection. Campatelli et al. [21] analyzed the machining technology using a response surface method to obtain a model fit for the fine tuning of the cutting parameters and minimizing power consumption in the milling of carbon steel. Due to the large amount of data involved, optimization of cutting parameters need to use the corresponding algorithm for processing. Among methods of cutting-parameter optimization, the genetic algorithm [22,23], Taguchi method [24,25], response surface method [26], etc. are widely used. The Genetic algorithm is often used to deal with nonlinear problems that are difficult to solve with traditional search methods. The Taguchi method is difficult to determine the optimal value and define the interaction between various factors and response [27]. The response surface method can find the interaction between multiple factors and response, obtain the optimal combination of cutting parameters to optimize product or machining capacity. The experimental design means of response surface method mainly includes center composite design, BOX design, uniform design, etc.
Al7075-T6 aluminum alloy has high strength-far better than any mild steel-and is widely used in aerospace and automotive equipment. In a previous micro-milling Al7075-T6 study, the relationship between burrs and some cutting parameters has been be followed with interest [28,29]. However, the method about improve the surface quality of the workpiece was missing and the force prediction was insufficient. The cutting parameters selection was currently the main reason for affecting the surface quality of the workpiece and the tool wear [30,31]. Therefore, the rotatable center composite experiment was selected, and the quadratic response surface model was analyzed by variance and combined to obtain the response surface graph, which intuitively analyses the relationship between the cutting parameters and the response (micro-milling force and top burrs width). The cutting parameters were optimized with the minimum response value as the goal and the effect of improving the workpiece surface quality was obvious, while a force prediction model was established.

Micro-Milling Experiment Setup
The experiment of micro-milling Al7075-T6 workpieces were conducted on a DMU 40 mono-Block CNC machine center (Bielefeld, Germany). As shown in Figure 1a, the equipment consists of three slide-guided on the XYZ axes, two rotary index tables on the BC axes and a five-axis control system. The maximum spindle speed was 18,000 r/min, the maximum stroke in the X, Y and Z directions was 450 mm, 400 mm and 480 mm, respectively and the positioning accuracy of the machine tool was 3 µm. In this experiment, a two-edged flat-bottomed micro-milling tool with a diameter of 1 mm (MX230, NS, Osaka, Japan) was used, as shown in Figure 1b,c. The tool material was the super-hard alloy and its tip area was covered with TiAlN coating. The rake angle was 12 • , the clearance angle was 5 • and the helix angle was 30 • . To realize the milling force prediction of the micro-milling Al7075-T6 and optimize the surface quality, the experiment of micro-milling straight micro-groove was carried out on the workpiece material (Al7075-T6) under the dry cutting conditions. As shown in Figure 1a,c, the dynamometer was installed between the workpiece and the machine tool. The Kistler-9119AA1 (Winterthur, Switzerland) cutting force measurement system was used to collect micro-milling forces in all directions during the micro-milling experiment and its sampling frequency was set to 36 kHz. To eliminate the error, ensure cutting depth, determine the workpiece datum plane and avoid interference with the subsequent measurement of the burrs size due to the oxide layer or defects on the surface of the workpiece, the workpiece surface was finely milled before the micro-milling experiment officially started. Then, the micro-groove structures with a length of 5 mm and a width of 1 mm were milled on the workpiece datum plane.

Micro-Milling Experiment Setup
The experiment of micro-milling Al7075-T6 workpieces were conducted on a DMU 40 mono-Block CNC machine center (Bielefeld, Germany). As shown in Figure 1a, the equipment consists of three slide-guided on the XYZ axes, two rotary index tables on the BC axes and a five-axis control system. The maximum spindle speed was 18,000 r/min, the maximum stroke in the X, Y and Z directions was 450 mm, 400 mm and 480 mm, respectively and the positioning accuracy of the machine tool was 3 µm. In this experiment, a two-edged flat-bottomed micro-milling tool with a diameter of 1 mm (MX230, NS, Osaka, Japan) was used, as shown in Figure 1b,c. The tool material was the super-hard alloy and its tip area was covered with TiAlN coating. The rake angle was 12°, the clearance angle was 5° and the helix angle was 30°. To realize the milling force prediction of the micro-milling Al7075-T6 and optimize the surface quality, the experiment of micro-milling straight micro-groove was carried out on the workpiece material (Al7075-T6) under the dry cutting conditions. As shown in Figure 1a,c, the dynamometer was installed between the workpiece and the machine tool. The Kistler-9119AA1 (Winterthur, Switzerland) cutting force measurement system was used to collect micro-milling forces in all directions during the micro-milling experiment and its sampling frequency was set to 36 kHz. To eliminate the error, ensure cutting depth, determine the workpiece datum plane and avoid interference with the subsequent measurement of the burrs size due to the oxide layer or defects on the surface of the workpiece, the workpiece surface was finely milled before the micro-milling experiment officially started. Then, the micro-groove structures with a length of 5 mm and a width of 1 mm were milled on the workpiece datum plane.

Experimental Design
In micro-milling, the primary factors affecting micro-milling force and top burr width are the cutting parameters, tool geometry and workpiece material characteristics, etc. Compared with other factors, the cutting parameters have obviously multivariable, nonlinear characteristics and interactive effects. Therefore, the response surface method was adopted to select reasonable cutting parameters. The response surface method combines experimental design and statistical principles, focuses on solving nonlinear regression problems and explores the mathematical relationship between input impact factors and output responses. Moreover, the quadratic response surface model could fully consider the interaction effect and the quadratic effect. Therefore, in this study, the quadratic response surface method was used to focus on the independent variables (different cutting parameters: , , … ) and the relationship between the response (experimental result y), so as to optimize the input of multiple variables and predict the response.
Response surface method is adopted to study the mathematical relationship between the response (micro-milling force and the top burrs) and the independent variables (per-feed tooth, axial

Experimental Design
In micro-milling, the primary factors affecting micro-milling force and top burr width are the cutting parameters, tool geometry and workpiece material characteristics, etc. Compared with other factors, the cutting parameters have obviously multivariable, nonlinear characteristics and interactive effects. Therefore, the response surface method was adopted to select reasonable cutting parameters. The response surface method combines experimental design and statistical principles, focuses on solving nonlinear regression problems and explores the mathematical relationship between input impact factors and output responses. Moreover, the quadratic response surface model could fully consider the interaction effect and the quadratic effect. Therefore, in this study, the quadratic response surface method was used to focus on the independent variables (different cutting parameters: x 1 , x 2 , x 3 . . . x n ) and the relationship between the response (experimental result y), so as to optimize the input of multiple variables and predict the response.
Response surface method is adopted to study the mathematical relationship between the response (micro-milling force and the top burrs) and the independent variables (per-feed tooth, axial cutting depth, spindle speed and tool extended length). For a specific response surface model, the relationship between the response variable and the independent variables is: where, y is the response variable and x 1 , x 2 , x 3 . . . x n are the independent variables. Considering the linear effects, interaction effects and quadratic effects between four factors, a second-order Taylor expansion is used to approximate the real function, which is described as follows: where, β 0 is the constant term, β i is the linear effect regression coefficient of x i , β ij is the interactive effect regression coefficient between x i and x j , β ii is the secondary effect regression coefficient of x i , ε is the error term assumed to have normal distribution N(0, σ 2 ). The experimental design method uses an orthogonal rotatable center compound experimental design, which is the most practical experimental design method for multifactor saliency analysis in the response surface. The factor point, axial point and center point make up 31 sets of experiments. The specific experiment parameter settings for each group are shown in Table 1; the experiment plan contains three parts: Micromachines 2020, 11, x FOR PEER REVIEW 4 of 16 cutting depth, spindle speed and tool extended length). For a specific response surface model, the relationship between the response variable and the independent variables is: where, y is the response variable and , , … are the independent variables. Considering the linear effects, interaction effects and quadratic effects between four factors, a second-order Taylor expansion is used to approximate the real function, which is described as follows: where, is the constant term, is the linear effect regression coefficient of , is the interactive effect regression coefficient between and , is the secondary effect regression coefficient of , ε is the error term assumed to have normal distribution N(0,σ 2 ).
The experimental design method uses an orthogonal rotatable center compound experimental design, which is the most practical experimental design method for multifactor saliency analysis in the response surface. The factor point, axial point and center point make up 31 sets of experiments. The specific experiment parameter settings for each group are shown in Table 1; the experiment plan contains three parts:    No.

Variables
Response Value Per-feed tooth (x 1 ), axial cutting depth (x 2 ), spindle speed (x 3 ) and tool extended length (x 4 ) will affect top burrs width and micro-milling force. The range of these factor levels is selected according to previous micro-milling experience [2,28]. The range of f z is 2−18 µm/z, the range of a p is 10-50 µm, the range of n is 8000-16,000 r/min and the range of l is 17-33 mm. To facilitate later experimental design analysis, the main factor coding and level settings are shown in Table 2.

Experimental Results
A laser confocal optical microscope (VK-X, Keyence, Osaka, Japan) was used to observe the micro-groove morphology and measure the top burrs width on both sides of the micro-groove. As shown in Figure 3a, after the micro-milling, there were few burrs at the bottom of the groove, and  Using 800-Hz low-pass filtering remove the high-frequency interference signal of the measured micro-milling force. As shown in Figure 3b, the micro-milling force mainly includes vertical-feed-direction force (F x ), feed-direction force (F y ) and normal direction force (F z ). In micro-milling, the amplitude of the normal direction force is smaller than the other two directions, which is because the force in the normal direction is mainly affected by the elastic recovery of the material and it is less affected by the cutting parameters. Therefore, only studying F x and F y , using the 10-point average method simplifies the calculation of the corresponding response value of F x and F y . The response values (b 1 and b 2 , F x and F y ) can be used as the evaluation indicators of the micro-milling workpiece quality. The experimental results of the actual measurement are summarized in the response value section of Table 1.

Micro-Milling Force Analysis
According to the experimental results of 31 groups in Table 1, taking cutting parameters as input-and considering the main effects or interaction effects that may affect the response value-the least squares algorithm is used in the commonly used statistical analysis software Minitab to fit the coefficients of the secondary response model of the micro-milling force. The equations for the F x and F y quadratic response surface prediction model are as follows: Equations (3) and (4) include the cutting parameter input items that have a significant influence on the micro-milling force. The absolute value of the regression coefficient of the first term also represents the influence of the cutting parameters on the micro-milling force to a certain extent. By comparing the absolute values of the corresponding regression coefficients, the primary term is much larger than the square term and the interaction term, as known from Equation (3) decreasing f z or increasing l is likely to decrease F x . Equation (3) can be used to preliminarily determine the factors that have significant effects on F x as f z , a p and l, and Equation (4) can preliminarily determine the factors that have significant effects on F y as f z , a p . Figure 4 shows the comparison between the predicted values and the measured values of the F x and F y . It can be seen from Figure 4a,b that the predicted force value and measured force value are basically in the same waveform, which further verifies the accuracy of the prediction model about micro-milling quadratic response surface obtained from Equations (3) and (4). The accuracy of the predictions is excellent, but it is found that F x has a higher fitting degree than F y between the predicted value and the measured value. In addition, the pros and cons of the prediction model can be evaluated by the goodness of fit (R-sp). R-sp refers to the ratio of the sum of squared regressions to the sum of squared deviations. The fitting degree of the model is better when the R-sp value is closer to one. The quadratic response surface prediction model of the micro-milling force in this experiment obtained R-sq about F x and F y are 89.48% and 86.41% in turn, which shows that it fits well with the measurement results after the experiment and has high reliability. Further significant analysis of the regression model is carried out to validate the ability of the prediction model on reflecting the relationship between cutting parameters and the micro-force. P-value of the micro-milling force regression model is zero, which indicates the significance of independent variables. F-value is a statistic used to judge the significance of the regression model. It shows that the regression model is significant, indicating that there is a linear significant relationship between some cutting parameters and the micro-force.
Micromachines 2020, 11, x FOR PEER REVIEW 7 of 16 comparing the absolute values of the corresponding regression coefficients, the primary term is much larger than the square term and the interaction term, as known from Equation (3) decreasing fz or increasing l is likely to decrease Fx. Equation (3) can be used to preliminarily determine the factors that have significant effects on Fx as fz, ap and l, and Equation (4) can preliminarily determine the factors that have significant effects on Fy as fz, ap. Figure 4 shows the comparison between the predicted values and the measured values of the Fx and Fy. It can be seen from Figure 4a,b that the predicted force value and measured force value are basically in the same waveform, which further verifies the accuracy of the prediction model about micro-milling quadratic response surface obtained from Equations (3) and (4). The accuracy of the predictions is excellent, but it is found that Fx has a higher fitting degree than Fy between the predicted value and the measured value. In addition, the pros and cons of the prediction model can be evaluated by the goodness of fit (R-sp). R-sp refers to the ratio of the sum of squared regressions to the sum of squared deviations. The fitting degree of the model is better when the R-sp value is closer to one. The quadratic response surface prediction model of the micro-milling force in this experiment obtained R-sq about Fx and Fy are 89.48% and 86.41% in turn, which shows that it fits well with the measurement results after the experiment and has high reliability. Further significant analysis of the regression model is carried out to validate the ability of the prediction model on reflecting the relationship between cutting parameters and the micro-force. P-value of the micro-milling force regression model is zero, which indicates the significance of independent variables. F-value is a statistic used to judge the significance of the regression model. It shows that the regression model is significant, indicating that there is a linear significant relationship between some cutting parameters and the micro-force. To obtain the influence degree of each cutting parameter on the micro force, this study conducted a significant analysis on the regression coefficients of micro-force models. Tables 3 and 4 are the variance analysis table of Fx and Fy, which is usually used to analyze the primary and secondary influence of cutting parameters on the output response, and the F-value is used as a key indicator to measure the influence level of cutting parameters on the response surface. Further, the significance of the significant results can be 95% when the p-value is less than 0.05, which indicates that the main effect, secondary effect or interaction effect of the cutting parameters have a significant effect on the response. It is known from Tables 3 and 4 that the p-values of fz and ap are both 0, which shows that fz and ap have a significant linear effect on Fx and Fy. In addition, the response values (Fx and Fy) contain the same significant interaction terms fz*ap and fz*l and multiple significant quadratic terms fz 2 , ap 2 , n 2 appear in Fx, which indicates that the effect of changes in cutting parameters in Fx, compared with Fy, is more significant. This may be due to the micro-milling tool's radial runout in the vertical feed direction during micro-milling. As shown in Figure 3a, the measured width of the micro-groove is 1005 µm, which is slightly larger than the theoretical diameter of the micro-milling tool, 1000 µm. To obtain the influence degree of each cutting parameter on the micro force, this study conducted a significant analysis on the regression coefficients of micro-force models. Tables 3 and 4 are the variance analysis table of F x and F y , which is usually used to analyze the primary and secondary influence of cutting parameters on the output response, and the F-value is used as a key indicator to measure the influence level of cutting parameters on the response surface. Further, the significance of the significant results can be 95% when the p-value is less than 0.05, which indicates that the main effect, secondary effect or interaction effect of the cutting parameters have a significant effect on the response. It is known from Tables 3 and 4 that the p-values of f z and a p are both 0, which shows that f z and a p have a significant linear effect on F x and F y . In addition, the response values (F x and F y ) contain the same significant interaction terms f z *a p and f z *l and multiple significant quadratic terms f z 2 , a p 2 , n 2 appear in F x , which indicates that the effect of changes in cutting parameters in F x , compared with F y , is more significant. This may be due to the micro-milling tool's radial runout in the vertical feed direction during micro-milling. As shown in Figure 3a, the measured width of the micro-groove is 1005 µm, which is slightly larger than the theoretical diameter of the micro-milling tool, 1000 µm. Significance analysis of regression coefficient about vertical-feed-direction force F x : (1) Individual effect: a p > f z > l > n; (2) Interaction effect: f z *l > f z *a p > f z *n > a p *l > n*l > a p *n; (3) Quadratic effect: n 2 > f z 2 > a p 2 > l 2 .
Significance analysis of regression coefficient about feed-direction force F y : (1) Individual effect: f z > a p > l > n; (2) Interaction effect: f z *l > f z *a p > n*l > a p *l > f z *n > a p *n; (3) Quadratic effect: a p 2 > n 2 > f z 2 > l 2 .  Figures 5 and 6 indicate the pairwise interactive influence between per-feed tooth, axial cutting depth, spindle speed and tool extended length on vertical-feed-direction force and feed-direction force. The contour lines are more intensive at a higher per-feed tooth than at a lower per-feed tooth with the increase of axial cutting depth, which indicates that the interactive influence between axial cutting depth and per-feed tooth on the vertical-feed-direction force and feed-direction force is significant. Similarly, it can be seen from the contour map between per-feed tooth and tool extended length on the micro-milling force is significant. In the other small graphs in Figures 5 and 6, the density of the contour line remains basically unchanged, which indicates that other pairwise factor interactive influence with the cutting force is not significant.    The fz*ap and fz*l with significant interaction effects can be quantitatively analyzed by the response surface graph of Fx and Fy. Figures 7 and 8 show that reducing both fz and ap can effectively reduce the micro-milling force Fx. Under the experimental conditions of spindle speed n = 12,000 r/min and l = 25 mm, the response value Fx is more sensitive to the change of ap than fz. Figures 7 and  8 show that reducing both fz and l can effectively reduce the value of the response result Fx. Under the experimental conditions of n = 12,000 r/min and ap = 30 µm, the response value Fy is more significant to the change of fz compared to l. It is particularly noteworthy that the tool extended length and micro-milling force have a profound influence on the tool wear and the workpiece surface quality, which is also proposed in previous studies [32]. In summary, the goal of reducing the micromilling force can be achieved by reducing fz, ap and l. The relationship between the micro-milling force and the cutting parameters is mainly a linear effect and there are certain interaction effects and secondary effects. Among them, Fx, Fy and fz, ap have a linear positive correlation and fz, ap affects the micro-milling force the effect increases in turn. The f z *a p and f z *l with significant interaction effects can be quantitatively analyzed by the response surface graph of F x and F y . Figures 7 and 8 show that reducing both f z and a p can effectively reduce the micro-milling force F x . Under the experimental conditions of spindle speed n = 12,000 r/min and l = 25 mm, the response value F x is more sensitive to the change of a p than f z . Figures 7 and 8 show that reducing both f z and l can effectively reduce the value of the response result F x . Under the experimental conditions of n = 12,000 r/min and a p = 30 µm, the response value F y is more significant to the change of f z compared to l. It is particularly noteworthy that the tool extended length and micro-milling force have a profound influence on the tool wear and the workpiece surface quality, which is also proposed in previous studies [32]. In summary, the goal of reducing the micro-milling force can be achieved by reducing f z , a p and l. The relationship between the micro-milling force and the cutting parameters is mainly a linear effect and there are certain interaction effects and secondary effects. Among them, F x , F y and f z , a p have a linear positive correlation and f z , a p affects the micro-milling force the effect increases in turn.

The Top Burrs Morphology Analysis
In the same way as the above method for calculating the micro-milling force quadratic response model, the equations for the prediction models about b1 and b2 quadratic response surfaces are as follows: According to the absolute value of the linear regression coefficients in Equations (5) and (6), it can be preliminarily determined that the cutting parameters that have a significant effect on the top burrs (b1 and b2) are fz, ap and l. Figure 9 is a comparison of the predicted and measured values of the top burrs width after each group of experiments. Figure 9a shows that the change waveform of the predicted value and the measured value about b1 are basically the same, but the fitting degree is poor, which indicates that the quadratic response surface model of b1 is in a statistically insignificant state and the accuracy of the prediction model is average. The comparison between the measured value and the predicted value about b2 in Figure 9b shows that the established response regression model has a high fitting degree, which indicates that quadratic response surface model of b2 has high credibility and can be preferentially used for the top burr analysis.

The Top Burrs Morphology Analysis
In the same way as the above method for calculating the micro-milling force quadratic response model, the equations for the prediction models about b 1 and b 2 quadratic response surfaces are as follows: According to the absolute value of the linear regression coefficients in Equations (5) and (6), it can be preliminarily determined that the cutting parameters that have a significant effect on the top burrs (b 1 and b 2 ) are f z , a p and l. Figure 9 is a comparison of the predicted and measured values of the top burrs width after each group of experiments. Figure 9a shows that the change waveform of the predicted value and the measured value about b 1 are basically the same, but the fitting degree is poor, which indicates that the quadratic response surface model of b 1 is in a statistically insignificant state and the accuracy of the prediction model is average. The comparison between the measured value and the predicted value about b 2 in Figure 9b shows that the established response regression model has a high fitting degree, which indicates that quadratic response surface model of b 2 has high credibility and can be preferentially used for the top burr analysis. The R-sq of b1 and b2 are 62.67% and 85.50%, respectively based on the quadric response surface prediction model of the top burr width on the up-milling side in this study, which indicates that the quadric response prediction model of b2 response is in a significant state. The model of b2 fits well with the experimental results and is highly reliable. The R-sq of b1 is 62.67% smaller than 70%. Therefore, the quadric surface prediction model of the top burrs width on the down-milling side The R-sq of b 1 and b 2 are 62.67% and 85.50%, respectively based on the quadric response surface prediction model of the top burr width on the up-milling side in this study, which indicates that the quadric response prediction model of b 2 response is in a significant state. The model of b 2 fits well with the experimental results and is highly reliable. The R-sq of b 1 is 62.67% smaller than 70%. Therefore, the quadric surface prediction model of the top burrs width on the down-milling side needs to be used carefully, and the correlation between the cutting parameters and the top burrs width on the down-milling side is weak, which may be because the response value (b 1 ) is mainly affected by the main linear effect, while the secondary effect and the interaction effect are not significant. Tables 5 and 6 are the analysis of variance of b 1 and b 2 , where the p-values of f z and a p are both less than 0.05, indicating that f z and a p have a significant first-order linear effect on b 1 and b 2 . Reducing f z or a p means reducing the burrs width at the top micro-groove. Both b 1 and b 2 contain the same quadratic term n 2 , but multiple quadratic terms f z *a p , f z *n and a p *n appear in b 2 , which indicates that b 2 is more sensitive to changes in cutting parameters than b 1 . This may be because the chip outflow direction is opposite to the tool rotation direction on the micro-groove up-milling side compared to the micro-groove down-milling side, and some chips do not escape when flowing out along the micro-groove edge, which is more likely to form long burrs at the top, resulting in a large change in top burrs width.  As shown in Figure 10a, when axial cutting depth was fixed at 30 µm, spindle speed was fixed at 12,000 r/min and tool extended length was fixed at 25 mm, width of up-milling side micro-groove top burrs (b 2 ) decreased with the increase of per-feed tooth. As shown in Figure 10b, when per-feed tooth was fixed at 10 µm/z, spindle speed was fixed at 12,000 r/min and tool extended length was fixed at 25 mm, b 2 increased with the increase of axial cutting depth. The per-feed tooth is the most significant factor contributing to the width of top burrs. Figure 11a,b are photomicrograph of the top burrs under Figure 10a conditions when f z is 2 µm/z and 18 µm/z, respectively.
Micromachines 2020, 11, x FOR PEER REVIEW 12 of 16 As shown in Figure 10a, when axial cutting depth was fixed at 30 µm, spindle speed was fixed at 12,000 r/min and tool extended length was fixed at 25 mm, width of up-milling side micro-groove top burrs (b2) decreased with the increase of per-feed tooth. As shown in Figure 10b, when per-feed tooth was fixed at 10 µm/z, spindle speed was fixed at 12,000 r/min and tool extended length was fixed at 25 mm, b2 increased with the increase of axial cutting depth. The per-feed tooth is the most significant factor contributing to the width of top burrs. Figure 11a,b are photomicrograph of the top burrs under Figure 10a conditions when fz is 2 µm/z and 18 µm/z, respectively.   According to the density of the contour lines, it can be known that the cutting parameters (fz, ap, n, l) have no obvious effect on b1, but have a significant effect on b2. As can be seen in Figure 13, the pairwise interactions (fz*ap, fz*n and ap*n) have the most significant impact on b2. In addition, the pairwise interactions (fz*ap, fz*n and ap*n) with the most significant interaction effects can be quantitatively analyzed by the response surface graph of b2. Figure 14a shows that decreasing ap and increasing n can effectively reduce b2. Under the experimental conditions of fz = 10 µm/z and l = 25 mm, b2 is more sensitive to the change of ap than n. Figure 14b shows that increasing fz and ap can effectively reduce the value of response b2. Under the experimental conditions of n = 12,000 r/min and l = 25 mm, the change of ap has a more significant effect on b2 than fz. Figure 14c shows that choosing moderate fz and n can effectively reduce the value of response b2. Under the experimental conditions of ap = 30 µm and l = 25 mm, the change of n has a more significant effect on b2 than fz.  Figures 12 and 13 indicate the pairwise interactive influence between per-feed tooth, axial cutting depth, spindle speed and tool extended length on width of top burrs. According to the density of the contour lines, it can be known that the cutting parameters (f z , a p , n, l) have no obvious effect on b 1 , but have a significant effect on b 2 . As can be seen in Figure 13, the pairwise interactions (f z *a p , f z *n and a p *n) have the most significant impact on b 2 . In addition, the pairwise interactions (f z *a p , f z *n and a p *n) with the most significant interaction effects can be quantitatively analyzed by the response surface graph of b 2 . Figure 14a shows that decreasing a p and increasing n can effectively reduce b 2 . Under the experimental conditions of f z = 10 µm/z and l = 25 mm, b 2 is more sensitive to the change of a p than n. Figure 14b shows that increasing f z and a p can effectively reduce the value of response b 2 . Under the experimental conditions of n = 12,000 r/min and l = 25 mm, the change of a p has a more significant effect on b 2 than f z . Figure 14c shows that choosing moderate f z and n can effectively reduce the value of response b 2 . Under the experimental conditions of a p = 30 µm and l = 25 mm, the change of n has a more significant effect on b 2 than f z .

Cutting-parameter optimization.
The Fx quadratic response surface prediction model with the highest credibility was selected and the combined minimum response micro-milling force (Fx and Fy) and width of top burrs (b1 and b2) were the constraints. According to the prediction model of Equation (3) can be output minimum response value combination: Fx = 2.31 N, Fy = 2.13 N, b1 = 59 µm, b2 = 75 µm. In addition, a set of corresponding optimized combinations of cutting parameters can be obtained: n = 11,394 r/min, fz =

Cutting-parameter optimization.
The Fx quadratic response surface prediction model with the highest credibility was selected and the combined minimum response micro-milling force (Fx and Fy) and width of top burrs (b1 and b2) were the constraints. According to the prediction model of Equation (3) can be output minimum response value combination: Fx = 2.31 N, Fy = 2.13 N, b1 = 59 µm, b2 = 75 µm. In addition, a set of corresponding optimized combinations of cutting parameters can be obtained: n = 11,394 r/min, fz =

Cutting-Parameter Optimization
The F x quadratic response surface prediction model with the highest credibility was selected and the combined minimum response micro-milling force (F x and F y ) and width of top burrs (b 1 and b 2 ) were the constraints. According to the prediction model of Equation (3) can be output minimum response value combination: F x = 2.31 N, F y = 2.13 N, b 1 = 59 µm, b 2 = 75 µm. In addition, a set of corresponding optimized combinations of cutting parameters can be obtained: n = 11,394 r/min, f z = 5.8 µm/z, a p = 11.6 µm, l = 20.9 mm. The machined micro-groove morphology using a set of optimized cutting parameters is shown in Figure 15. Simultaneously, the roughness value of the micro-groove bottom was 0.38 µm, which was acceptable. The top burrs were analyzed in conjunction with Figure 3 and it was found that the number of micro-groove top burrs were significantly reduced. This shows that the optimized combination of cutting parameters, solved by the quadratic response surface model, used in actual micro-milling, could achieve the purpose of improving the workpiece surface quality.
cutting parameters is shown in Figure 15. Simultaneously, the roughness value of the micro-groove bottom was 0.38 µm, which was acceptable. The top burrs were analyzed in conjunction with Figure  3 and it was found that the number of micro-groove top burrs were significantly reduced. This shows that the optimized combination of cutting parameters, solved by the quadratic response surface model, used in actual micro-milling, could achieve the purpose of improving the workpiece surface quality. Figure 15. Micro-groove morphology after optimization of cutting parameters.

Conclusions
The response surface method was used to study the influence of micro-milling four cutting parameters on micro-milling force and surface quality (mainly the top burrs width). A quadratic response surface model was established, and the cutting parameters were optimized. Finally, a combination of cutting parameters that could improve the quality of the machined surface was obtained. The specific conclusions are as follows: (1) The change of cutting parameters had a significant effect on the micro-milling force and the width of up-milling side top burrs. The prediction model of the quadratic response surface around micro-milling force (Fx and Fy) and the width of burrs on the up-milling side (b2) was in a significant state. The experimental measured value and the predicted value had a high fitting degree; (2) During micro-milling workpiece material Al7075-T6, ap and fz show a significant linear effect on force and width of top burrs. The response values (Fx, Fy, b1 and b2) were mainly affected by ap, followed by was fz, but n and l had few significant effects; (3) In addition, mainly considering the linear effects of ap and fz, the optimization of cutting parameters also needs to consider the interaction effects and secondary effects between each cutting parameter. Simultaneously reducing fz and ap or simultaneously reducing fz and l could actively reduce the micro-milling force, while reducing ap and increasing n or simultaneously increasing fz and ap could effectively reduce the top burrs; (4) The reasonable setting of cutting parameters could improve the quality of machined surface.
According to the quadratic response surface model, the optimal response value could be obtained by optimizing combination of cutting parameters: n = 11,394 r/min, fz = 5.8 µm/z, ap = 11.6 µm and l = 20.9 mm.
The above research conclusions will provide theoretical reference and technical support for the improvement of micro-milling surface quality and optimization of micro-milling cutting parameters.

Conclusions
The response surface method was used to study the influence of micro-milling four cutting parameters on micro-milling force and surface quality (mainly the top burrs width). A quadratic response surface model was established, and the cutting parameters were optimized. Finally, a combination of cutting parameters that could improve the quality of the machined surface was obtained. The specific conclusions are as follows: (1) The change of cutting parameters had a significant effect on the micro-milling force and the width of up-milling side top burrs. The prediction model of the quadratic response surface around micro-milling force (F x and F y ) and the width of burrs on the up-milling side (b 2 ) was in a significant state. The experimental measured value and the predicted value had a high fitting degree; (2) During micro-milling workpiece material Al7075-T6, a p and f z show a significant linear effect on force and width of top burrs. The response values (F x , F y , b 1 and b 2 ) were mainly affected by a p , followed by was f z , but n and l had few significant effects; (3) In addition, mainly considering the linear effects of a p and f z , the optimization of cutting parameters also needs to consider the interaction effects and secondary effects between each cutting parameter. Simultaneously reducing f z and a p or simultaneously reducing f z and l could actively reduce the micro-milling force, while reducing a p and increasing n or simultaneously increasing f z and a p could effectively reduce the top burrs; (4) The reasonable setting of cutting parameters could improve the quality of machined surface.
According to the quadratic response surface model, the optimal response value could be obtained by optimizing combination of cutting parameters: n = 11,394 r/min, f z = 5.8 µm/z, a p = 11.6 µm and l = 20.9 mm.