According to Eq. (18), Fx has little influence on the residual stress in the Y direction. The maximum error between the fitting value and the actual value of surface residual stress in X direction is 15.5% and the minimum error is 0.2%. The maximum error between the fitting value and the actual value of surface residual stress in Y direction is 15.6% and the minimum error is 0.1%. The details are shown in Table 5.
It can be seen from section 4.1 that the radius of the blade arc and the parameters of feed per tooth play a major role in the generation of residual stress. Quantifying the relationship between the two can control the generation of residual compressive stress during machining. In this section, the finite element simulation is used to analyze the relationship between r and fz and the residual stress. The relationship between machining parameters is quantified to achieve the generation of controlling residual compressive stress on workpiece surface.
4.3.1 Analysis of the influence of blade edge radius on residual stress
In this part, 10 different blade edge radius were set. The 2D orthogonal cutting simulation model in Section 2.1.2 was used to analyze the influence of blade arc radius on residual stress.The milling speed ,depth of cut and feed per tooth were respectively 301.6m/min,5mm and 0.05mm.The simulation results are shown in Fig. 10.
In previous studies, the large residual tensile stress generated during machining will accelerate the deformation of the workpiece and affect its life. The lower residual tensile stress or residual compressive stress will delay the fatigue failure time of the workpiece [2]. As can be seen from Fig. 10(a), if r is 0.02mm-0.08mm, the maximum residual compressive stress in the X direction is 0mm.It is shown that the residual compressive stress produced by r is strongest at the machined surface. If r is 0.1mm-0.5mm, the residual stress curve shows a negative extreme value around 0.25mm. This indicates that the optimal position of residual compressive stress at the arc radius of these blades is near the depth of 0.25mm. The maximum residual compressive stress in the X direction of the workpiece surface is at r = 0.08mm.
The position of residual stress curve in Fig. 10(b) can be judged as follows. In Y direction, the negative extremum of all residual stress curves is located near the depth of 0.3mm. After milling, the residual stress of the surface in Y direction is compressive stress. The maximum value of residual compressive stress in Y direction on the workpiece surface is -229MPa at r = 0.1mm. Combined with the analysis results of residual stress in X direction, the residual compressive stress on the workpiece surface reaches the peak value if r is about 2 times fz.
4.3.2 Analysis of the influence of feed per tooth on residual stress
In the previous section, the influence of the blade edge radius on the generation of residual compressive stress was analyzed under the condition of constant feed per tooth.It is found that the residual compressive stress on the workpiece surface reaches the peak value when the ratio of r to fz is about 2.To further quantify this ratio, this section used two cutting tools with different blade edge radius of 0.1mm and 0.2mm.Both tools were set with multiple different fz.The influence of different fz on residual stress is analyzed.The simulation results are shown in Fig. 11-Fig. 12.
According to Fig. 11(a), when r = 0.1mm and fz=0.02mm-0.05mm, the maximum residual compressive stress in the X direction appears at 0mm.This indicates that the best place for residual stress generation is on the machined surface. When the depth from surface is greater than 0.6mm, the difference of residual stress becomes smaller. This indicates that the residual stress is less affected by fz. It can be seen from Fig. 12(a) that it behaves if r is 0.2mm. The maximum residual compressive stress in X direction is located at the machined surface when fz=0.06mm-0.15mm.
The residual stress curve in the Y direction in Fig. 11(b) can be seen as follows. When r = 0.1mm and fz=0.02mm-0.05mm, the maximum residual compressive stress corresponding to fz is located on the machining surface. According to Fig. 12(b), the specific details are as follows. When r = 0.2mm and fz=0.02mm-0.1mm, the maximum residual compressive stress is located on the machined surface. The residual stress curve is divided into two parts around fz=0.05mm when r = 0.1mm. Only when fz <0.05mm, the maximum residual compressive stress appears on the workpiece surface. Similarly, r = 0.2mm and fz <0.1mm, the maximum residual compressive stress appears on the workpiece surface.
It can be seen from the above analysis that the residual stress distribution on the workpiece surface changes regularly with the ratio of r and fz. It assumes that the ratio of fz and r is shown in Eq. (19):
$$\frac{{{f_z}}}{r}=\alpha$$
19
It is substituted into the surface residual stress prediction formula Eq. (18). The result is shown in Eq. (20). Combined with the analysis results in Fig. 10-Fig. 12, the surface residual stress values in X and Y directions can be obtained. The details are shown in Fig. 13.
$$\left\{ \begin{gathered} {\sigma _{xx}}= - 8.21 \times {10^4} \times \Delta {T^{ - 2.8113}}+5668.96 \times {\left( {\frac{{{F_x}}}{{\alpha \times r+{r^{1.44 \times {{10}^4}}}}}} \right)^{ - 0.00275}} - 5.98 \times {10^3} \times {\left( {\frac{{{F_y}}}{{{r^{ - 1.76}}+{V_c}}}} \right)^{0.01067}} \hfill \\ {\sigma _{yy}}= - 1.779 \times {10^8} \times \Delta {T^{ - 5.7954}} - 1.266 \times {10^{ - 40}} \times {\left( {\frac{{{F_x}}}{{\alpha \times r+{r^{ - 0.06116}}}}} \right)^{25.87798}} - 976.8167 \times {\left( {\frac{{{F_y}}}{{{r^{ - 82.503}}+{V_c}}}} \right)^{0.00874}} \hfill \\ \end{gathered} \right.$$
20
According to the variation trend in Fig. 13(a), when r = 0.1mm, fz=0.05mm ~ 0.06mm, that is αxx = 0.5 ~ 0.6, the residual compressive stress in the X direction is the maximum. When fz=0.06mm ~ 0.07mm, that is αyy = 0.6 ~ 0.7, the residual compressive stress in the Y direction is the maximum. Similarly, r = 0.2mm, the residual compressive stress in the X and Y directions takes the maximum value respectively when αxx = 0.55 ~ 0.65 and αyy = 0.6 ~ 0.65. According to Fig. 13(b), when fz=0.05mm and αxx = 0.42 ~ 0.63, the residual compressive stress in the X direction of the workpiece surface is the maximum. In the same way, αyy = 0.36 ~ 0.5, the residual compressive stress in the Y direction of the workpiece surface is the maximum. In conclusion, when αxx = 0.42 ~ 0.65, the surface residual compressive stress in the X direction of the workpiece reaches the maximum. When αyy = 0.36 ~ 0.7, the surface residual compressive stress in Y direction is the maximum.
4.4 Verification of the prediction model of surface residual stress and method of quantification of milling parameters
In order to verify the accuracy of the quantitative relationship between the residual stress and the prediction model of fz and r, 6 groups of aluminum alloy parts with the size of \(50mm \times 50mm \times 40mm\) were processed separately in this section. The material was the same as the workpiece used in Table 3. First, the inner cavity was roughed with three edge flat-bottomed cutter \(\phi 8\)mm, spindle speed 8000 rpm, cutting depth 3 mm, feed rate 0.1mm/tooth. Then, the workpiece was processed into a thin-walled frame part with a wall thickness of 4mm with \(\phi 3\)mm flat end milling cutter, spindle speed 12000 rpm, cutting depth 0.25 mm, feed rate 0.4mm/tooth. The machining parameters shown in Table 6 were used to process the parts along the external surface into a thin-walled part with a wall thickness of 2mm after the stress removal treatment. It was processed by filling the inner cavity with paraffin to reduce the deformation when milling the outer surface. The residual stress on the outer surface of 6 groups of parts was measured respectively. Six points were randomly selected on the outer test surface to test the residual stress value, and the average value was taken as the residual stress value. Milling experimental instruments and specific test procedures are shown in Section 2.2.
The details are as shown in Fig. 14. Under the condition that r and Vc are constant, the milling temperature and the milling force in each direction of the thin-walled part increase linearly with the increase of fz. According to the experimental results, when Vc and r were constant, the force and temperature of group A are smaller than that of group B and C. The working part of group A is fz =0.5r. The milling forces Fx and Fy are 44.6% and 21.8% smaller than those of group C with fz >0.5r. Similarly, the milling force in X and Y direction of group E is 30.1% and 9.1% smaller than that of group F.
Table 6
Experimental machining parameters
Group
|
A
|
B
|
C
|
D
|
E
|
F
|
Feed per tooth fz(mm)
|
0.01
|
0.025
|
0.03
|
0.01
|
0.015
|
0.02
|
Tool edge radius
r(mm)
|
0.02
|
0.02
|
0.02
|
0.03
|
0.03
|
0.03
|
Cutting speed
Vc (m/min)
|
201.1
|
201.1
|
201.1
|
201.1
|
201.1
|
201.1
|
Other parameters
|
z = 3; R = 4mm; ap=5mm; ae=2mm
|
In order to verify the proposed surface residual stress prediction model, the milling parameters in Table 6 and the measured milling force and temperature change parameters were substituted into Eq. (13). The predicted and actual measured values of surface residual stress were shown in Fig. 15.The error between the predicted value and the actual test value of the surface residual stress in the X direction is between 10.6% and 17.5% and that in the Y direction is 8.7%-18.8%. As can be seen from the experimental results in Fig. 15, other processing conditions were the same, the residual compressive stress in X and Y directions of the working parts in group E is the maximum. αxx and αyy of group E are both 0.5, the residual compressive stress in X and Y directions are respectively 16.2% and 18.1% higher than that in group F. αxx and αyy of group A are both 0.5. The residual compressive stress in X direction is 9.5% higher than that in group B. The residual compressive stress in the Y direction increased by 16%. It is verified the conclusion in Section 4.3 that when αxx = 0.42 ~ 0.65, the surface residual compressive stress in X direction of the workpiece reaches the maximum value. When αyy = 0.36 ~ 0.7, the surface residual compressive stress in Y direction reaches the maximum value.