Study of distortion on milled thin-wall aluminum parts influenced by initial residual stress and toolpath strategy

Monolithic aluminum alloy parts are highly required in the aeronautical industry, but they show significant geometrical distortion after the machining process. This work investigated the distortion attributed by the initial residual stress of the raw material and the machining-induced residual stress during the milling process, as well as exploring the effects of the machining toolpath strategy. Single-/multi-pocket parts were milled from 7050-T7451 aluminum blocks with different initial residual stresses, and an element deletion method was developed for the numerical study to simulate different sequences of material removal. It was revealed that the toolpath parallel to the long side of the block caused more distortion on the side surfaces of the final part. The value of distortion was positively correlated to the magnitude of the initial residual stress of raw material. The simulation results indicated that the distortion attributed by machining-induced residual stress accounted for about 15% of the final distortion. The finding promotes the design optimization of machining monolithic parts by minimizing distortion, thereby benefitting the application of large monolithic parts in industry.


Introduction
The demand for aluminum alloys (AAs) has increased enormously over the last decade in the fields of automobile, aerospace, aviation, marine, and other industries. Aircraft manufacturing especially promotes the application of AAs due to its great machinability, outstanding corrosion resistance, and favorable strength-to-weight ratio with the requirements of fuel efficiency and lightweight [1,2]. For example, car wheels, panels, and structures use AA6061; aircraft structures are made of AA7050-T7451; fittings, gears, and shaft use AA7075-T6; the skin of the aircraft is made of AA2024-T3; and engine chambers use AA2014, respectively [3]. 7xxx series AAs are the most important structural materials in aviation and aircraft production with high strength, stiffness, and toughness in addition to excellent processing performance [4]. Generally, mechanical machining processes play a dominant role in the manufacturing of monolithic and thin-wall metallic components with good flexibility, high surface finish, excellent dimensional accuracy, and capability of material types [1,4]. However, distortion easily occurs after unclamping, resulting from the low stiffness of large parts, high inherent residual stress, and high material removal rates of up to 90% [5]. Subsequent correction processes and part rejections after distortion critically increase the cost and waste of material in the production environment, which makes the distortion issue become a serious challenge to the aviation industry.
The machining distortion is defined in the form of deviation between the final part shape and the original intent after being released from the fixture [6]. The machining distortion source is the release of residual stress (RS). RS can be divided into initial residual stress (IRS) and machining-induced residual stress (MIRS) [7]. RS is the inherent internal stress remaining in the body after eliminating any external effect of the environment. The distribution is largely dependent on the metallurgical and mechanical history in the fabrication process [7][8][9]. There are plenty of methods to detect the RS state of material. Guo et al. [10] classified the experimental RS measurement methods according to whether they test internal or surface RS and 1 3 whether they are destructive or non-destructive. Among the destructive methods, the hole-drilling method and ringcore method are used to test surface RS, and the stripping method, crack compliance method, and contour method are used to measure internal RS. Besides, the non-destructive methods including diffraction method, ultrasonic method, and Raman spectroscopy method are used to avoid the physical trace after tests. Prime [11] developed the cross-sectional mapping method to measure the surface contour (contour method) to destructively determine the internal RS of beams. This method applies a simulation to calculate the distribution of IRS from the input of surface displacement based on Bueckner's superposition principle [12]. Chighizola et al. [13] assessed the surface RS testing methods including the hole-drilling method, slotting method, and X-ray diffraction methods and revealed that the hole-drilling method and slotting method have good repeatability at larger depths. Tabatabaeian et al. [14] supplemented the analytical methods to predict RS states and summarized the source of RS for various material types induced by thermal and mechanical loads. The thermal effect increases tensile components of RS near the surface from phase change, while the mechanical load induces compressive components of RS generation from the plastic deformation on the contact surface. Both work together to produce the complex residual stress states near the surface.
Finite element simulation (FEM) has been widely used to investigate the material processing. The element deletion method (EDM) used in subtractive manufacturing simulation is a convenient method to simulate the material removal process within the framework of conventional FEM. It directly deactivates the pending elements in the removal zones and applies additional boundary conditions on the new element surfaces rather than simulates the collision process between tooling and workpiece. In this method, there is unnecessary to integrate complicated fracture and damage evolution criteria, define complex geometrical contact interaction, or consider other interfacial conditions. Therefore, EDM is efficient for a long-term manufacturing simulation. However, the chip formation cannot be simulated as similar as the realistic machining process, so EDM is not a good choice when research focuses on the chip morphologies. Generally, EDM in machining simulation starts with predefining IRS, then deletes the excess elements as cutting sequences, and ends with applying MIRS [5]. Some research created numerous sub steps along the cutter trace and incrementally removed elements and applied loads instead of applying MIRS [15].
Previous research focuses on the causes and consequences of distortion as well as to develop analytical methodologies and deliver solutions to structural design and manufacturing improvement. Chighizola et al. [16] investigated the interactions of bulk RS and milling-induced RS on the distortion of aluminum parts and verified them through elastic stress models. Huang et at [17]. investigated the effects of IRS and MIRS on the deformation of 0.75 ~ 1.75 mm thick plates with tensile and compressive IRS states and revealed that tensile RS promotes the distortion and MIRS has greater effects when the thickness is less than 1.25 mm. Wan et al. [18] developed a theoretical model considering the cutting mechanism and the instantaneous contact status of the tool and the part to predict the MIRS of the milling process. Madariaga et al. [19] studied the effects of IRS and MIRS on the distortion of monolithic aluminum parts and revealed that machining strategy optimization can minimize the part distortion. Mathews et al. [20] investigated the coupling effects of RS on the final-state RS and distortion of highspeed-machined and high-aspect-ratio aluminum components via 3D end-milling simulation and declared that the effects are nonlinear but the toolpath is more significant. Yang et al. [21] studied the interactive effect of IRS and cutting force on machining distortion and found that the IRS is the main factor of distortion for aluminum alloys, but the cutting force is the main one for titanium alloy. Weber et al. [22] studied the repeatability of the machining-induced RS for different machining parameters and clamping strategies on distortion and revealed that more and deeper MIRS causes more distortion. Wan et al. [23] summarized the modeling to predict the MIRS, including empirical, analytical, and FEM models, and stated that MIRS is influenced by cutting parameters. They indicated that a hybrid model of FEM and an analytical model can reduce time consumption and complexity. Zhao et al. [24] introduced a data-driven and physics-based model to predict the distortion and inner RS states of machined parts from deformation force and obtained good results. Cerutti and Mocellin [25] used a numerical tool to predict the distortion and machining quality considering the machining sequence and IRS to optimize the accuracy of the process and ensure the conformity of the part. Chabeauti et al. [26] used a numerical method coupling 2D-FEM and beam model to reveal that the die positioning is highly sensitive to the distortion of a forged part. Hao et al. [27] proposed a new locating principle of fixtures to increase workpiece stability during machining. Chen et al. [28] established an analytical prediction model for H-section multi-frame beam structures considering IRS to investigate the stress redistribution and distortion of different processing methods. Xue et al. [29] proposed a qualitatively theoretical model of IRS and machining distortion and revealed that the effect of non-uniform radial IRS and tangential IRS induces the variable ellipticity of thin-wall rings. Aurrekoetxea et al. [30] developed a quantifying uncertainty procedure for the no-machine layer removal method in ribbed structures to rapidly assess the RS measurement accuracy related to machining distortion. Zhu et al. [31] proposed annealing treatment planning of multiple-sequence production of thin-wall superalloy components to reduce the machining distortion. Wang et al. [32] developed an energy-based analytical model to predict machining distortion considering IRS, MIRS, and the structural characteristics and reduced distortion by adjusting processing parameters. Sun et al. [33]. proposed an uncertainty calibration hybrid model involving cutting contact, tool wearing, mechanism, and unquantified uncertainty to estimate machining distortion. Li et al. [34] investigated the effects of material removal strategies and IRS on the deformation of frame parts and reduced the deformation by removing the layer material.
The above literature review concludes the inducement of distortion related to residual stress states and the theoretical models for distortion estimation. However, the influence of milling toolpath strategies on the distortion of thin-wall part is still unclear with the interactive effects of residual stress. In this study, a contour method was applied on the original billets to determine the IRS of material, and a hole-drilling method was applied on the milled parts for the MIRS. Their interactive effects on the distortion of the thin-wall pocket parts were investigated through the FEM simulation. Meanwhile, EDM was introduced to efficiently simulate the material removal process with various toolpath strategies and investigate their effects on part distortion, and the results were verified by experiments. This work promotes the optimization of process parameters during the machining of aerospace thin-wall parts and improves the selection of toolpath by considering the shape of the final part and the distribution of IRS, thereby reducing the distortion of milled parts.

Experimental material
AA7050-T7451 is widely used in aeronautics and aviation since it has high fracture toughness, high fatigue resistance, and high resistance to exfoliation corrosion and stresscorrosion cracking. Rolled AA7050-T7451 blocks of 1020 × 245 × 100 mm 3 in size from five suppliers were used in this study, and their mechanical and chemical properties are listed in Table 1.

Contour method
The cold rolling process during fabrication results in residual stress in the original blocks, which finally makes an influence on the milled parts. To determine the internal RS states of the original blocks, the contour method [11] was introduced in this study as a destructive measurement method to obtain the IRS results. Due to the size limitation of the wire cutting machine, the long AA block was cut into three smaller pieces by milling, and then 20-50 mm depth below the cut surface was removed by wire cutting to avoid the milling effect on tested billets. Finally, three billets of 290 × 245 × 100 mm 3 in size were obtained from one original block, as shown in Fig. 1. Their cut surfaces were tested by a coordinate-measuring machine (CMM), namely, a Reinshaw Technical Centre -CMM 2JHH98, to obtain the section contour. There were approximately 100,000 measuring points established on each cut surface so that the repeatability error could be ignored.
The IRS of the billets was evaluated from the section contour by FEM simulation [11,19]. Figure 2 shows the procedure of how to obtain the IRS distribution through the CMM test and FEM simulation. In the original block, the rolling-induced residual stress was balanced statically until split by wire cut. Due to the characteristic of rolling, the distortion Ux was strongly correlated to the position of height (y) but weakly correlated to the position of width (z) on the cut section, which means the longitudinal direction had the major part of residual stress along the rolling direction, thus the block needed to be cut perpendicular to the longitudinal direction. After the splitting of the block, the stress was released and redistributed so that the cut section was distorted. The distortion along the longitudinal direction was measured by CMM as Ux. The polynomial function Ux = f(y) was fitted as a mathematical expression, and the opposite displacement -f(y) normal to the cross section was applied on the nodes of one side, as well as the opposite side being fixed as the boundary conditions of the FEM model by using script in Abaqus/Standard. The model was meshed with a total of 56,840 C3D8R elements with 5 mm in size and 20 nodes on the thickness direction. Considering that the stress relaxation is an elastic linear problem [11], it is unnecessary to use a very fine mesh size. As the result, the distribution of s11 to s13 was determined as the restored initial state of billet, while the results of s23 and s13 were very small so be ignored. The values on the midline were recorded due to the laminal distribution as the IRS of blocks.

High-speed milling of thin-wall parts
The split billets were then used for milling. The milling process was conducted on a STAR RAG ECOSPEED F HT2 1010 high-speed machining center with a maximum spindle speed of 30,000 rpm and a maximum velocity of 50 m/min. The milling process of thin-wall parts is shown in Fig. 3a, and the dimension of the parts is shown in Fig. 3b. The billet was held on the platform through pre-drilled holes to avoid vibration during milling. Component rigidity and reduction in vibration particularly with high unsupported thin section walls are very difficult to control without correct fixture tooling. Finally, multi-pocket parts and single-pocket parts were machined as case studies.

Machining-induced residual stress
The MIRS of the milled thin-wall parts was tested by the hole-drilling method following the ASTM/E837-13A standard, as shown in Fig. 4a. The measured result is illustrated in Fig. 4c, where the MIRS is mainly concentrated on the surface layer and reduced significantly with depth. Additionally, four geometric models representing different situations were established in Abaqus/Standard for static analysis, as illustrated in Fig. 4b. The thin-wall part was predefined a stress field on the bottom following the test results. The bottom had a thickness of 4 mm with 0.2 mm mesh, and a 0.6 mm layer of mesh was refined in 0.03 mm. A fixed value of xx was applied through the bottom as the IRS, and a stress field

Element deletion method for simulation
In this research, the element deletion method (EDM) was developed in Abaqus/Standard to efficiently simulate the long-term material subtractive process. Figure 5 illustrates a schematic of a simulation case using EDM. As shown in Fig. 5a, the final part is a half of U-shaped thin-wall part of size 183 mm × 63 mm × 100 mm with a 3 mm wall and 4 mm bottom. The geometric model consists of the final part, which is meshed by 10 mm × 1.5 mm × 4.8 mm C3D8R elements. The to-be-deleted parts, including a profile cut one and a pocket cut one, are both meshed by 10 mm × 10 mm × 4.8 mm C3D8R elements. To increase the efficiency of EDM, the to-be-deleted part is coarsely meshed, while the mesh size of the final part is refined along the wall thickness direction. Meanwhile, the billet in simulation is half of the realistic billet, so a surface is set as a symmetric plane. A narrow band near the top edge of the billet is fixed by an encased boundary condition as clamping and released in the last step. The bottom surface is fixed in the y-direction and released in the last step. Five different predefined stress fields are applied on the billets based on the experimental results obtained by the contour method. Moreover, the elements deletion process contains hundreds of sub steps. Each sub step is an implicit step with 0.001 s step time. Figure 5b shows a schematic of one element deletion sub step, where a block of elements is selected and deleted; after that, the cutting force is applied on the exposed surface; then the sub step ends, and a new sub step starts. The size of the block is dependent on the cutting parameters including feed, depth, and width of cut. The subtractive blocks are selected in a way that follows an imaginary cutter motion path. Figure 5c illustrates the simulation process collecting the sub steps, where the profile is milled in one round and the pocket is milled progressively. Figure 6 illustrates the clamping situation and its corresponding boundary conditions in the simulation. In the actual processing, the final part is cut out of the inside of the billet. Initially, fixing holes are drilled to fix the billet on the machining platform. A deep groove is milled first surrounding the outer profile of the final part, and 2 mm thick of material is remained to connect the part and billet. Afterwards, the billet is reverse-fixed for pocket milling. After the shape of the final part is milled, the connecting material is thinned and cut to form "break off" lugs for part removal. Similar to the actual processing, the boundary condition in the simulation is that a band of nodes on the upper side of the billet are fixed throughout the element deletion and the extra edge is deleted at the last step to release distortion.
To evaluate the effect of material removal strategy on machining distortion, three milling toolpaths were proposed based on the element deletion sequences in simulation. Considering the structural stiffness decreases gradually with the material removal, the change of localized stiffness during the processing could affect the distortion of the final part. The toolpath design in this study was concerned with being parallel to the longer or shorter side of the block. Hence, three element deletion routes including the zig-zag route (ZZ), rotated zig-zag route (NN), and helical route (LL) were applied on the pocket cut in simulation. In detail, the ZZ route is that the cutter moves and feeds along the rolling direction forward and backward alternately, the NN route is to rotate the ZZ route by 90° to make the cutter move perpendicular to the rolling direction, and the LL route is that the cutter moves like homocentric squares from the center to outer. In addition, the route strategies and cutting parameters were empirically determined as summarized in Table 2. An instantaneous milling process was first conducted in simulation to detect the force response at the milling tool for the cutting force in the subsequent EDM simulation. The cutting force was a vector along the feed direction, the radial direction, and the axial direction. After a block of elements were deleted, shear forces (resultant force parallel to the interface) were applied on the exposed interfaces as the milling force. Taking the NN route as an example, the strategy of element deletion is illustrated in Fig. 7. First in the profile cut, one layer of material was removed in one pass and three rounds in depth, while the block of elements deleted in a sub step was in size of 2 × 1 × 6. In the pocket cut, a large bulk of elements was removed following the designed tooling route in several to tens of passes and four rounds in depth. In each sub step, a 1 × 1 × 5 block of elements was deleted.

Results and discussion
In this section, the results of the IRS distribution of original billets as well as the machined distortion on the single and multi-pocket parts from simulations and experiments are presented and discussed.

Initial residual stress of billets
As shown in Fig. 8a, the original contour data were the absolute positioning coordinates (x, y, z) of points on the tested surface. About 100,000 points were measured on each surface, so the repeatability error could be ignored. To mathematically illustrate, the original data was nominalized by the following method. Since the longitudinal direction (perpendicular to the cut section) of aluminum plates is along the rolling direction, the thickness direction (perpendicular to the rolling plane) should present a much higher influence on the distortion than the width direction. Therefore, the data was grouped by the width position (z) into 23 groups in which the z-coordinates of points were set as their mean value, thus the relationship between y-coordinates and x-coordinates of points in each group was the major consideration. On the other hand, the wire cut plane was not horizontal/vertical, thus linear fitting was first conducted to obtain a middle plane of points, and the x-coordinates were nominalized as the distance to the middle plane, which traces a wavy shape as shown in figure. It is noticed that the maximum deviation of data points to the fitted curve is 0.007 mm. A fifth-order polynomial function was used to mathematically describe the relationship between distortion and y-coordinates on the surface, and the results of the material from five different suppliers are illustrated in Fig. 8b. It can be seen that the curves of different groups are close to each other except S3, generally representing the shape of one peak and two valleys. It can be seen that the profile variation along the thickness direction is much larger than that along the width direction. The undesirable deviation of the curves in S3 is probably due to the rolling method in the fabrication of aluminum alloy billets. By taking the average result of each supplier, the surface distortion can be simplified as a single variable function of thickness position (y-coordinates)   Table 3.
Through the contour method, the IRS results of the AA blocks from five suppliers are illustrated in Fig. 9. It is revealed that the distributions of hydraulic stress (s11, s22, and s33) are generally two-peak and symmetric to the midline, while the shear stress (s12) are antisymmetric with one peak. The results of the left and right surfaces after wire cut of the same material are close to each other, which verifies Axial direction 2 2 Fig. 8 The nominalized distortion of cut surface varified with y-position, obtained by CMM tests from 5 suppliers (S1-S5) the accuracy of the results. Meanwhile, the variation of IRS is simultaneous, and S5 has the lowest values as well as S3 has the largest values.

Surface distortion of machined parts
The multi-pocket thin-wall parts machined in the high-speed milling process are divided into two groups, which have U-shaped or L-shaped sections, and four types of feature can be recognized as P1 to P4, as illustrated in Fig. 10. P1 is fully closed in the middle of U-shaped parts, P2 has a longside opened wall located at the middle of L-shaped parts, P3's short-side wall is opened as the two end of U-shaped parts, and P4 has adjacent opened walls as the two end of L-shaped parts, respectively. The results of MIRS-induced distortion in the simulation of the four features are shown in Fig. 11. It is found that the large z-displacement occurs near the open side for P2, P3, and P4 and in the center of P1. To numerically analyze the results, the distortions of 4 types of feature with various IRS are summarized in Fig. 12.
The distortion is calculated as the difference between the maximum and minimum z-displacement values on the tested surface. As shown in Fig. 12a, the distortion is positively correlated with the absolute value of IRS. Meanwhile, the both-side-opened part has more distortion than the one-sideopened part and full-closed part. It is noticed that when the IRS equals zero, the distortion is only attributed by MIRS, which represents about 15% considering a common IRS  . 9 The results of initial residual stress (s11, s22, s33, and s12) of the billet from 5 suppliers. Solid and dashed lines are the results from the right and left surfaces after wire cut 1 3 value at 30 MPa. As discussed in the previous studies, IRS has a more dominant effect on distortion than MIRS for aluminum alloy components, and the latter represents about 10% of the total distortion [21,36]. The experimental verification results are illustrated in Fig. 12b. The distortion was measured by taking the maximum height deviation among ten points on the test surface where measuring error could occur. Besides, the IRS and MIRS fields in simulation were estimated by the previous experiments, which was different from the distributions in the actually used billets. Therefore, the experimental results of distortion have a rising trend with the values of IRS but are not as clear as the simulation results; however, it is still noticed that the length of opened side promotes distortion.

Distortion of machined pockets in simulation
The results of the EDM simulation are discussed in this section. For a better comparison, the reference case (RF) in simulation is to delete the to-be-deleted elements directly in  Fig. 13. The LL and NN cases show much lower displacement magnitude than the ZZ case, even a little lower than the reference case. In the back-and-forth milling toolpath, the MIRS of two opposite adjacent passes is neutralized. Due to a longer single-pass distance in the ZZ case than that in the LL and NN cases, the distortion is accumulated more within one cutting pass; therefore, it could result in more permanent deformation and more distortion in the final parts.
The simulation results are illustrated in Fig. 14 for the displacement along X, Y, and Z directions normal to the three surfaces of the pocket, viz., X-displacement on the short side, Y-displacement on the bottom side, and Z-displacement on the long side. As shown in Fig. 14a, the X-direction displacement for the ZZ case is obviously different from the other two, where all the bottom side trends to be distorted outside but the top side of the ZZ case is distorted inside greatly. Meanwhile, the Y-direction displacement in Fig. 14b indicates that the ZZ case has the larger-area opposite distortion on the bottom side compared to the other cases, but their extreme values are near. Additionally, for the Z-direction displacement in Fig. 14c, all three cases have medium-area inside distortion and outside distortion on the open edge, and their trends are similar. Comprehensively, the NN case has the most balanced distortion distribution with appreciable displacement values on the surfaces of pocket compared with the other two cases. The distortion accumulates in the wall-opening sides of the part.
As for the influences of IRS from 5 suppliers (S1 to S5), the distributions and values of displacement are obviously different. In general, S5 with the lowest IRS has the smallest difference of displacement, but it is found that the variation is not linearly correlated to the IRS by comparing the scale bar of displacement. This is partly contributed to the MIRS-induced distortion. To numerically investigate the influences of IRS, the relationship of the initial equivalent residual stress and the distortion on X-, Y-, and Z-surfaces is illustrated in Fig. 15,  where the initial equivalent residual stress is calculated as Von Mises stress in the middle of original blocks and the distortion is defined as the difference between maximum and minimum displacements on the current surface. It is revealed that the X-and Z-distortion have an increasing trend with the rising initial equivalence residual stress, and in the ZZ case, they are obviously greater than them in LL and NN cases. However, this tendency disappears in Y-distortion, which could be induced by the y-direction layer-patterned distribution of IRS, and thus, the stress release is uneven. Generally, the value of IRS has a positive correlation to the distortion, and different cutting strategies induce the obviously different values and distributions of distortion.

Comparison with experiments
The coordinates on the bottom surface of final parts machined from the billets of S3 and S4 were tested by CMM and compared with the U2 displacement in simulation results. The surface plots of relative positions are illustrated in Fig. 16. The parts were machined in the LL toolpath. It can be found in S3 experimental results that the surface shows a little asymmetrical distribution, since the machining asymmetry is not fully reflected by the simulation. In the actual machining condition, the material is removed in a helical route side by side along the central line, but in the simulation, both sides are removed simultaneously as the symmetrical boundary condition is applied. Besides, the CMM test results are also influenced by the dimensional deviation, as the part is put bottom upside on the test platform. The dimensional deviation of the thin-wall structure could cause the surface sloping in one direction. On the other hand, the shape of the S3 surface is convex, but the shape of the S4 surface is concave. It is because of the difference of the IRS. Noticing the IRS in the thickness range of 0.95 to 1 in Fig. 9, which is the bottom domain of the final part, the S3 is negative, and the S4 is positive. That results in the converse shapes of the bottom, reflected by both experiment and simulation. However, the results of experiment and simulation have a similar distribution but a quantitative difference. It is shown that the deviation from maximum to minimum values of S3 is 0.024 mm for simulation and 0.04 mm for experiment. The deviation of S4 is 0.006 for simulation and 0.06 for experiment. The difference can be regarded as the conditional deviation between the simulation and production in milling loads, residual stress, clamping conditions, thermal effects, or structural deviation. The similar surface trend of simulations and experiments supports the simulation study to some extent.

Conclusions
In this study, the distortion after milling induced by machining-induced residual stress (MIRS) and initial residual stress (IRS) with the effect of cutting strategy was investigated by numerical and experimental methods. The element deletion method was introduced to simulate different cutting routes and material removal strategies. The main conclusions drawn are as follows: 3) The simulation results have multiple differences from the experimental results, but the trend is similarly correlated, which still proves that the laws obtained from this research are applicable to actual production. To reduce the distortion of thin-wall parts, the single long pass in the toolpath should be avoided, and the billets with lower initial residual stress are recommended.

Competing interests
The authors declare no competing interests.