Optimization method for rough-finish milling allowance based on depth control of milling affected layer

The optimization of machining allowance has an important influence on the machining quality of workpieces. This paper determined an optimization method for rough-finish milling allowance based on depth control of milling affected layer. Firstly, the coupling influence of rough-finish milling cutting depth on milling affected layer depth was studied by experiment. Secondly, the influence rule of rough milling and finish milling on the affected layer depth was studied by experiment, and the prediction model of the milling affected layer depth based on the cutting depth of rough milling and finish milling was established, as well as the surface roughness prediction model of the finish milling cutting depth. Finally, the effectiveness of the optimization results was verified by experiments. The experimental results show the optimized machining parameters can increase the machining efficiency by 31.2%, and the milling affected layer is 91 μm, which indicates that the depth of milling affected layer is effectively controlled.


Introduction
The workpiece often needs to go through rough milling, finish milling and other processes to reach the final service state in the milling process. The formation of the workpiece service surface usually undergoes multiple thermal loads during this process, and the final surface quality often depends on the whole machining process. The variation of allowance in rough milling and finish milling has a significant influence on the final surface quality of the workpiece, so optimizing the allowance of rough milling and finish milling is of great significance for achieving efficient and high-quality milling process.
At present, scholars at home and abroad have done a series of research work on the allowance optimization and put forward many theories and methods. Many scholars have carried out research on optimizing algorithm strategy to distribute machining allowance. Averchenkov et al. [1] proposed a new method for optimizing milling operations on Computer Numerical Control (CNC) machines when programming in CAM-systems, and this method can improve the efficiency of processing three-dimensional workpieces by 2.5-coordinate milling on CNC machines. Li et al. [2,3] presented a novel model for finishing allowance optimization based on the simplex algorithm. The feasibility of this method was proved by the actual machining experiments. He et al. [4,5] presented an improved method to optimize machining allowance distribution and parameters comprehensively considering energy-saving strategy and other multi-objectives of different phases. This proposed method can be easily extended to other machining scenarios and can be used as guidance of process planning for meeting various engineering demands. Tian et al. [6] carried out the process allowance distribution optimization in the semi-finishing stage based on the eigenvalue sensitivity method. This method can effectively improve the stability of thin-walled workpiece processing. In order to solve the problem of optimal flow distribution in NC machining with small allowance for complex precision castings, Zou et al. [7] presented a fast constraint registration algorithm based on geometric features. This method has technical advantages and effectiveness in terms of working efficiency and machining accuracy. Zhang et al. [8] proposed a workpiece localization method for machining allowance optimization of complex parts based on CMM inspection. This method ensures sufficient stock allowance for the single parts as well as the whole integrated parts. Sun et al. [9] proposed a unified localization technique for sculptured surface machining to ensure sufficient stock allowance during the machining process. This method is appropriate and feasible to distribute the stock allowance for proper sculptured surface machining.
The optimization of machining model in the milling process is also a research hotspot of scholars. Wan et al. [10] proposed an optimization method to improve the blade machining qualified rate and reduce carbon emissions by finding the optimal free-form surface machining model in condition of the near-net-shape allowance. Deng et al. [11] proposed a method to establish a multi-objective optimization model of a multi-pass milling considering positiondependent machine tool dynamics. This method can improve the machining efficiency and part quality.
The optimization of machining parameters is of great significance to the control of processing quality, so many scholars pay attention to it. Daniyan et al. [12,13] proposed a milling process optimization method for processing parameters, and this method can improve material removal rate effectively. Wu et al. [14,15] proposed a feed speed optimization method based on machining allowance optimization and constant power constraint of spindle. This method effectively combines allowance optimization and feed speed optimization to optimize process parameters. Zhang et al. [16] proposed a feed rate optimization method by combining the monitored cutting force in the whole milling process with off-line optimization. This method improves machining efficiency for roughing process. Zhang et al. [17] proposed a milling parameter optimization method for efficient rough machining by combining the off-line optimization and real-time monitoring. This parameter optimization method can greatly improve the machining efficiency.
From the above analysis, it can be seen that the research on allowance optimization has accumulated some achievements, and a large number of research contents are focused on optimization of algorithm strategy, optimization of machining model, optimization of machining parameters, etc. However, it is rare to pay attention to multi process collaborative allowance optimization. In this paper, a rough-finish milling allowance optimization method based on depth control of milling affected layer is proposed. The rough milling, finish milling and rough-finish milling experiments with variable cutting depth are carried out to study the coupling influence of the rough-finish milling cutting depth on the milling affected layer depth, and the influence rule of rough milling and finish milling on the affected layer depth is studied by experiment. The prediction model of the milling affected layer depth based on the cutting depth of rough milling and finish milling is established, and the prediction model of surface roughness based on the finish milling cutting depth is established.

Milling affected layer
The strong interaction of forces (high strain and strain rate) and heat (high temperature and rate of temperature change) during the milling process results in significant machined texture (residual height) and microscopic unevenness on the machined surface, as well as significant changes in the surface material properties distinct from the substrate to produce the metamorphic layer, which is evaluated by quantitative indicators mainly in the microstructure, microhardness field and residual stress field. Numerous studies have shown that the fatigue failure behavior of workpieces under service loading conditions occurs with cracks sprouting at the surface or within the metamorphic layer. For cracks sprouting on the surface, the stress concentration induced by the surface micro-unevenness is the main source of initiation. For cracks sprouting in the metamorphic layer, amorphous phase transformation, dislocations, residual stresses and microhardness gradients are the main triggers [18][19][20]. As shown in Fig. 1, the milling affected layer mainly considers two influencing factors: the first is the geometric factor of residual height generated by the milling process of the tool, which further forms surface micro-unevenness under the action of thermo-mechanical coupling, characterized numerically by the surface roughness S a ; the second is the surface affected layer depth D i formed on the workpiece material surface layer under the action of thermo-mechanical coupling. In the milling process, the microstructure affected layer is the shallowest, the microhardness affected layer is the second and the residual stress affected layer is the deepest, that is, the surface affected layer depth can be expressed by the residual stress affected layer depth D i = h ry .
In the actual machining, due to the different formation mechanisms of the surface roughness S a and the surface affected layer depth D i , their trends with the cutting depth a p may be different. There will be different sensitivities to the surface and surface layer states during the actual service state of the workpiece. In order to evaluate comprehensively the state of machined surface affected layer, it is necessary to establish the evaluation function of surface state characterized by the surface roughness S a and the surface affected layer depth D i ; the specific expression is shown in Eq. (1). Equation (1) describes the influence degree of surface roughness S a and surface influence depth D i on surface state D. The values of coefficients a and b are determined by the subsequent processing technology, design requirements of parts, service load type and other factors. For the rough milling process, the surface roughness S a after milling will be completely removed by the finish milling process in the future. Then it can be considered that b = 0, and the effect of the depth of the metamorphic layer is mainly considered. For the finish milling process, if there are subsequent surface treatment processes such as polishing, a should be taken a larger value, focusing on the influence of influence depth D i on surface state D. When there is a surface strengthening process in the future, b should be taken a larger value, focusing on the influence of surface roughness S a on surface state D. In this paper, it is considered a = b = 0.5.

Optimization method
Rough milling and finish milling have different ideas for parameter optimization due to their different process objectives. The rough milling process seeks to maximize the material removal rate, with machining efficiency as the primary goal of parameter optimization. The material removal rate (MRR) is calculated as shown in Eq. (2), and it can be seen that the material removal rate (MRR) is positively correlated with the feed per tooth f z , the cutting depth a p and the cutting width a e for a fixed milling tool (number of teeth N), the cutting speed v c (speed n) and other cutting conditions.
For rough milling, the usual optimization idea is to increase the feed per tooth f z , the cutting depth a p and the cutting width a e as much as possible to improve the material removal rate, while controlling the cutting speed v c considering the performance of tools, fixture, machine tools and other premises.
Radical process parameters will increase the milling influence layer. When finish milling removes the excessive milling influence layer left by rough milling, under the influence of the residual stress superposition effect, it is bound to cause the milling influence layer of the final machined surface to be inconsistent with the value by the finishing parameters. Therefore, on the basis of improving the processing efficiency by increasing the feed per tooth f z , cutting depth a p and cutting width a e in rough milling, the residual stress superposition effect is studied by the roughfinish milling test, obtaining the constraint condition of milling affected layer depth to ensure that the affected layer left by rough milling will not affect the final machined surface.
The finish milling process pursues high surface quality, with the control of the workpiece surface integrity as the primary goal, and ensures that the machined surface roughness S a and the surface affected layer depth D i are minimized. According to the previous experimental study, the cutting speed v c , the feed per tooth f z and the cutting width a e are selected as the fixed parameters for finish milling, and the finish milling cutting depth a p2 is selected as the optimized parameter, and the single-factor milling experiment with variable cutting depth is designed to obtain the function relationship between the finish milling cutting depth a p2 and the surface roughness S a , the surface affected layer depth D i . The optimal solution of the finish milling cutting depth a p2 is sought under the constrained conditions to obtain the high-quality machined surface. To sum up, the optimization process of rough-finish milling allowance based on the depth control of milling affected layer is shown in Fig. 2. Through the collaborative optimization of rough and finish milling processing parameters a p , an efficient and high-quality milling process is achieved. The specific optimization steps are as follows: Step 1: The total milling allowance H, the range of values for the rough milling cutting depth a p1 and finish milling cutting depth a p2 are determined by the milling workpiece.
Step 2: The constrained conditions for depth control of milling affected layer are obtained by rough-finish milling experiment.
Step 3: The functional relationship between the rough milling cutting depth a p1 and the surface affected layer depth h r1 = f (a p1 ) is obtained by rough milling experiment with variable cutting depth a p1 .
Step 4: The functional relationship between the finish milling cutting depth a p2 and the surface affected layer depth h r2 = f (a p2 ) is obtained by finish milling experiment with variable cutting depth a p2 .
Step 5: The functional relationship between the finish milling cutting depth a p2 and the surface roughness S a = f (a p2 ) is obtained by finish milling experiment with variable cutting depth a p2 .
Step 6: The range of the finish milling cutting depth a p2 is obtained by the constrained conditions, and functional relationships are solved simultaneously in steps 2 to 4.
Step 7: Within the range of the finish milling cutting depth a p2 , the optimal finish milling cutting depth a p2 is obtained by minimizing the milling affected layer depth.
Step 8: The corresponding rough milling cutting depth a p1 is calculated by a p1 + a p2 = H, and the optimization is completed.

Experiment
The experiment material was GH4169 superalloy, and the milling experiment was carried out on a pendulum-head five-axis machining center with a 60° forward tilt of the tool axis and a 0° side tilt. The machining method was unidirectional reciprocating plane milling with the milling toolpath parallel to the cutting surface. The machine coolant is Blasor emulsion coolant with a pressure of about 30 bar. The milling tool is a Rui Feng carbide ball-tipped milling cutter, specification D6 × 20 × 80-Q4-K44, with a front angle of 6°, a rear angle of 10°, a helix angle of 40°, a number of cutting edges of 4 and a material of K44. The machining process is shown in Fig. 3. In its upper surface to 10 mm spacing to divide the cutting processing area, first is rough milling cutting experiment, then the next area is for finish milling cutting experiment and finally the third processing area is for rough-finish milling cutting experiment. In order to ensure that the experiment process is not affected by the transient factor of tool wear, observe and measure the tool wear value after each group of experiments. If the tool wear amount exceeds 200 VB, then replace it with a new tool [21,22]. The residual stress on the surface of the machined area was measured by X-ray diffraction, as shown in Fig. 4.
The phenomenon of multivariate coupling exists in the rough-finish milling process, and it is difficult to directly study the influences of rough milling and finish milling parameters on the final surface condition of the workpiece. Therefore, they were decoupled by designing single-factor experiments for the rough milling (Group A) and the finish milling (Group B) to study respectively the distribution rules of residual stresses in rough milling and finish milling, and after that the coupling influence rules were studied by designing experiments for the rough-finish milling (Group AB), and the experimental scheme is shown in Table 1 below.
The residual stresses in the surface affected layer after milling machining mainly come from the interaction of mechanical stresses and thermal stresses. The rough milling often uses more radical machining parameters in order to pursue machining efficiency, the cutting force and cutting temperature are larger during the machining process and the residual stresses affected layer is also deep. And the finish milling usually uses more conservative machining parameters in order to achieve the required surface quality and form accuracy, the cutting force and cutting temperature are small during the machining process and the residual stress affected layer is also shallow. In the rough-finish milling, the first rough milling results in a large depth of residual stress affected layer. After the finish milling, if the cutting depth is small, the rough milling left over in the affected layer is not completely removed. Meanwhile, the finish milling further applies force and thermal load to the residual stress field; the residual stress field of the final machined surface is formed by the superposition of the stress field left by rough machining and the stress field generated by finish machining.
The test and fitting results of residual stress in rough-finish milling experiment are shown in Fig. 5. It is easy to see that the residual stress affected layer depth, the peak value of residual stress and the surface residual stress in the step direction are greater than those in the feed direction. And the distribution curve of residual stress in the step direction is similar to that in the step direction, so the residual stress in the step direction is used to represent the distribution rule of residual stress in the subsequent analysis. As shown in Fig. 5a, b, the deepest residual stress affected layer depth of rough milling Group A 1 is 167 μm, the shallowest affected layer depth of finish milling Group B 1 is 49 μm and the affected layer depth of rough-finish milling Group A 1 B 1 is Obtaining the corresponding rough milling cutting depth a p1 by a p1 +a p2 =H Obtaining the optimal finish milling cutting depth a p2 by minimizing the milling affected layer depth

End
Establisging the functional relationship h r1 =f (a p1 ) between the rough milling cutting depth a p1 and the surface affected layer depth h r1 89 μm. The variation trend for the peak value of residual stress and the surface residual stress are the same as the residual stress affected layer depth. Obviously, due to the larger affected layer generated in rough milling, the cutting depth a p = 0.1 mm is less than the affected layer depth 0.167 mm in finish milling, resulting in a superimposed influence, which causes the affected layer depth of Group A 1 B 1 to exceed that of Group B 1 . As shown in Fig. 5c, d, the residual stress affected layer depth of rough milling Group A 2 is 127 μm, the affected layer of finish milling Group B 2 is 96 μm, the affected layer depth of rough-finish milling Group A 2 B 2 is slightly greater than that of Group B 2 at 106 μm, and it can also be seen from the figure that Group A 2 B 2 is close to that of Group B 2 , which is due to its finish milling cutting depth a p = 0.14 mm, which is greater than the affected layer depth caused by rough milling. That is, the affected layer brought by rough milling is removed by the finish milling process, which leads the superimposed influence of depth to be not significant. As shown in Fig. 5e, f, the residual stress affected layer depth of Group A 3 B 3 reaches 178 μm, which exceeds 140 μm of Group B 3 for rough milling and 80 μm of Group A 3 for finish milling. There are two reasons for this abnormal phenomenon: the first is that the finish milling cutting depth a p = 0.06 mm is too small, and due to the serious tool wear in rough milling before finish milling, the cutting edge radius is originally 0.02 mm, which is further worn and increases to close or even exceeds the cutting depth a p . The cutting process becomes sliding and squeezing, producing an effect similar to rolling, which introduces most of the mechanical energy into the material to form an abnormally high residual stress distribution; the second is that the rough milling cutting depth is too large, and the finish milling cutting depth is too small, the residual stress affected layer from rough milling is mostly retained, which is superimposed on the affected layer from finish milling, and the superimposed layer eventually produces an abnormally high residual stress distribution. For the peak value of residual stress and the surface residual stress, they also produce certain changes during the rough-finish milling process. In Fig. 6, the peak value of residual stress in both Group A 1 , B 1 , A 1 B 1 and Group A 2 , B 2 , A 2 B 2 experiments shows that the peak values after rough-finish milling are larger than after finish milling, while the peak values after rough milling are much larger than the finish milling and rough-finish milling, which is the same phenomenon produced by the superposition effect of the affected layer in the previous section. In the Group A 3 , B 3 , A 3 B 3 experiment, the maximum peak value of residual stress occurs after rough finish milling and even exceeds the peak value of residual stress after rough milling, which is caused by the double influences of too small cutting depth for finish milling and superposition effect. In Fig. 7, the rough milling surface residual stress changes very little, and the rough-finish milling also has the same change rule, while in the finish milling, it can be clearly seen that the surface residual stress of the Group A 3 , B 3 , A 3 B 3 experiment is much smaller than that of the Group A 1 , B 1 , A 1 B 1 and Group A 2 , B 2 , A 2 B 2 . Overall, the surface residual stresses all show the rule that the maximum value appears after rough milling, and the surface residual stresses after rough-finish milling are greater than after finish milling. Combining the above studies, when the affected layer depth D i1 generated by rough milling is larger than the finish milling cutting depth a p2 , the milling affected layer depth of the final machined surface is formed by the superposition of the affected layer depth D i1 generated by rough milling and the affected layer depth D i2 generated by finish milling. When the affected layer depth D i1 generated by rough milling is smaller than the finish milling cutting depth a p2 , the milling affected layer depth of the final machined surface is equal to the affected layer depth D i2 generated by finish milling, which is only determined by the finish milling cutting depth a p2 . Therefore, the constrained condition based on depth control of milling affected layer is the affected layer depth D i1 generated by rough milling is smaller than the finish milling cutting depth a p2 .

Model
According to the established optimization method above, the optimization of rough-finish milling parameters is carried out. The following machining parameters are selected for rough milling: the cutting speed v c = 80 m/min, the feed per tooth f z = 0.025 mm/z, the cutting width a e = 0.4 mm as fixed machining parameters for rough milling to improve the machining efficiency and the rough milling cutting depth a p1 as the machining parameter to be optimized. The following machining parameters are selected for finish milling: the cutting speed v c = 180 m/min, the feed per tooth f z = 0.03 mm/z, the cutting width a e = 0.3 mm as fixed machining parameters for finish milling to ensure the surface quality and the finish milling cutting depth a p2 as machining parameters to be optimized. The single-factor milling experiment with variable cutting depth is designed as shown in Table 2. The influence rule of rough milling and finish milling on the affected layer depth is studied, and the relationship models between the affected layer depth D i of rough milling and finish milling and the cutting depth a p are established, and the relationship model between the surface roughness S a and the finish milling cutting depth a p2 is established. Fig. 6 The peak value of residual stress experimental results for step direction Fig. 7 The surface residual stress experimental results for step direction The distribution of residual stress in the step direction under different cutting depth can be seen in Fig. 8. It can be seen that with the increase of cutting depth, the surface residual stress, the peak value of residual stress and the residual stress affected layer depth increase. However, when the cutting depth increases to a certain value (greater than 0.6 mm), it is not difficult to find that the change in the values of the characteristic parameters for the residual stress distribution is very small comparing the data and fitting curves of the Group A 3 , A 4 and A 5 , and in the Group A 5 , there is even a small decrease. This shows that the residual stress generated by milling does not increase infinitely with increasing cutting depth, and there is a certain process limit under the experiment conditions. Figures 9 and 10 show the variation rule for the surface residual stress σ 0 and the peak value of residual stress σ Cmax with the cutting depth a p . The residual stress first increases and then decreases with the cutting depth, with a minimum value of 529.9 MPa at the cutting depth a p = 0.4 mm and a maximum value of 683.3 MPa at the cutting depth a p = 0.8 mm. The variation rule of peak value of residual stress is similar to that of the surface residual stress, the peak value of residual stress achieves a minimum value of 667 Mpa at the cutting depth a p = 0.4 mm and the peak value of residual stress achieves a maximum value of 892 Mpa at the cutting depth a p = 0.6 mm. Overall, the variation range of surface residual stress is 529.9-683.3 Mpa, which is small, while the variation range of peak value of residual stress is 667-892 Mpa, which is large.
The influence rule of rough milling cutting depth on residual stress affected layer depth is shown in Fig. 11, the residual stress affected layer depth increases with the increase of cutting depth and the variation range is large, ranging from 62 to 142 μm. A polynomial fitting is performed on the Fig. 11, the functional relationship between the affected layer depth and the rough milling cutting depth is obtained as shown in Eq. (3). The influence rule of finish milling cutting depth on residual stress affected layer depth is shown in Fig. 12, and a polynomial fitting is performed in Fig. 12; the functional relationship between the affected layer depth and the finish milling cutting depth is obtained as shown in Eq. (4). Fig. 8 Residual stress with different cutting depth for step direction   Table 3. Figure 13 shows the relationship between the surface roughness S a and the finish milling cutting depth a p2 . A polynomial fitting is performed, and the relationship function between the surface roughness S a and the finish milling cutting depth a p2 is obtained as shown in Eq. (5).
In summary, the initial conditions for the optimization of rough-finish milling allowance are obtained by milling experiments with variable cutting depth a p and fitting the  4) and (5). The rough-finish milling experiment proves that when the affected layer depth D i1 generated by rough milling exceeds the finish milling cutting depth a p2 , the affected layer generated by finish milling will increase sharply, that is, the constrained condition based on depth control of milling affected layer is the affected layer depth D i1 generated by rough milling is smaller than the finish milling cutting depth a p2 . In the actual milling process, considering that the tool stiffness has a certain threshold value during milling, the excessive cutting depth usually leads to very serious let-off, tool chipping and even tool broken, resulting in poor accuracy. According to the machining experience of superalloy, the rough milling cutting depth should not exceed 1/6 of the tool diameter, so the supplementary constraint a p2 < = 1 mm. Due to the influence of grooving process [23,24], the cutting depths of a p1 and a p2 usually have the following basic relationship during rough-finish milling: where H is the total milling allowance.

Experimental verification
Based on the obtained optimization parameters above, a certain type of aeroengine high-pressure compressor blade is machined. Figure 14 shows the blade after milling with the optimized machining parameters. The test area of surface roughness and milling influence layer is shown in the figure, which is experimented to verify the accuracy of the optimization parameters and methods. The experiment results are shown in Figs. 15 and 16. As shown in Tables 4  and 5, in the original machining parameters, the rough milling adopts large cutting depth, low speed and slow feed, and the machining time is unit 1; the finish milling adopts small cutting depth to ensure the machining surface quality, which makes the surface roughness smaller than 0.173 μm, but the affected layer generated by rough milling is not completely removed, which makes the final surface affected layer depth reach to 115 μm. The optimized rough milling parameters with high speed and large feed improve significantly the machining efficiency. Compared with the original machining parameters, the machining time is 0.688 s, and the   16 Blade surface roughness before and after parameter optimization machining efficiency is increased by 31.2%. At the same time, in order to control the milling affected layer, the rough milling cutting depth is slightly smaller, while the finish milling cutting depth is slightly larger, which enhances the thermo-mechanical coupling effect; the surface roughness has increased to a certain extent to 0.185 μm, but the surface affected layer depth is effectively controlled, only 91 μm. In summary, the rough-finish milling allowance optimization method based on depth control of milling affected layer can effectively improve the machining efficiency and control the milling affected layer depth, but it will increase the surface roughness, which can be improved by the subsequent polishing process.

Conclusions and discussions
This paper determines an optimization method for roughfinish milling allowance based on depth control of milling affected layer. The influence rule for the affected layer depth and coupling influence of rough milling and finish milling is studied. The research shows that the affected layer generated by rough milling is too deep, which will lead to a significant increase in the finish milling affected layer depth. Consequently, the constrained condition based on depth control of milling affected layer is the affected layer depth D i1 generated by rough milling should be smaller than the finish milling cutting depth a p2 . The single-factor experiment with variable cutting depth for rough milling and finish milling are designed, and the polynomial models for the affected layer depth with cutting depth for rough milling and finish milling are established respectively. The milling parameters of cutting depth for rough milling and finish milling are optimized collaboratively with the objective of controlling the affected layer depth, and the effectiveness of the optimization results and method are verified by the blade milling experiment. The optimized machining parameters can increase the machining efficiency by 31.2%, and the milling affected layer is 91 μm, which indicates that the milling affected layer depth is effectively controlled. In this paper, through the collaborative optimization of rough and finish milling processing parameters a p , an efficient and high-quality milling process is achieved. Nevertheless, this paper only considers the influence of the cutting depth a p on the milling affected layer, and the influence of cutting speed v c , the feed per tooth f z , the cutting width a e , tool wear amount and cutting fluid on the milling affected layer are not taken into account. In the future, it is necessary to consider the influence of each process parameter on the influence layer, so as to establish a multiprocess parameter and multi-objective optimization method to achieve the control of processing quality.

Data availability
The data sets supporting the results of this article are included within the article and its additional files.

Declarations
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Consent for publication
The publication has been approved by all authors.

Competing interests
The authors declare no competing interests.