1 Introduction

Aluminum, with an annual production of 67,2 Mt in 2021, is the most common metal and the third most common element in the earth [6, 7]. Starting from the mineral bauxite one obtains aluminum by first refining it to alumina (Al2O3) via the Bayer process and then smelting the alumina by the Hall-Héroult process [8]. Aluminum alloys are used as structural materials in numerous fields such as automotive, aerospace, installation and apparatus, electrical engineering, food technology, chemical industry, and the optical industry [9]. Particularly in aerospace engineering, a high proportion of aluminum is required, especially in the form of thin-walled monolithic structural components. For example, these components are used in aircrafts as internal fuselage structures, wing ribs and spars, as well as window and crown frames [1]. These integral structural components, which are made of rolled sheets, extruded sections or forgings, can be up to 14 m long [4]. Thin-walled structural components are typically used because they have excellent material properties for lightweight applications, such as a high strength-to-weight ratio and good corrosion resistance [2]. For example, the mass fraction of aluminum alloys used in the B747, B757, B767, B777, A300, A380, A340, and A320 aircraft models is between 60 and 80% of the total weight [10, 11]. In these weight-optimized, monolithic components, the largest proportion of the material is removed by machining [5]. The information in the literature varies from a maximum machining volume of 80% [12] to 90% [5] and up to 95% [3] of the total volume of the semifinished product. A typical manufacturing process to produce thin-walled aluminum structural components is milling. The challenge with these monolithic thin-walled structural components is that part distortion can occur because of the manufacturing-specific process chain [4]. It is known that those distortions are caused by residual stresses (RS), which are defined as the locked in stresses being in equilibrium. They exist in materials and structures independent of the presence of any external loads [13]. Those RS typically are divided into machining induced residual stress (MIRS) and initial bulk residual stress (IBRS) due to upstream processes such as rolling, casting, and especially heat-treatments [5]. The equilibrium of the RS is disturbed due to the material removal process and the application of MIRS. Once the part is released from its clamping fixture, distortion is the result of the re-equilibrium of the RS [14]. Although the semifinished products typically undergo a process to relief the high IBRS due to quenching, e.g. by controlled compression or stretching, part distortion remains as a problem [15]. The MIRS can be found in the boundary layer of the parts and are the result of plastic deformations during machining [5]. The analysis of the effects of the cutting parameters and the tool on the MIRS was subject of research [5]. Consensus is that high mechanical loads result in compressive MIRS [16]. It was found that an increase of the feed per tooth or the cutting edge radius and a decrease of the corner radius led to greater, in terms of amount, and deeper compressive MIRS [17]. Investigations on the variation of the cutting speed did not show a clear influence on the MIRS at all: For example, Perez et al. [18] and Denkena et al. [19] noticed higher MIRS with increasing cutting speed, whereas Rao et. al. [20] and Tang et. al. [21] observed lower MIRS.

Above-mentioned research has in common that no repeated RS measurements on different or even the same sample(s) were carried out. Only limited or even no statistical confidence was present. Furthermore, there is a lack of studies that measure the MIRS of milled samples with multiple RS measuring techniques.

The literature review by Aurrekoetxea et al. highlighted that both RS types lead to the distortion of thin-walled aluminum components [22]. It is known that with decreasing wall-thickness the effect of MIRS on distortion increases. However, different critical values for material thicknesses were found to determine when MIRS dominate compared to IBRS [5].

Besides analytical models, which are based on the plate bending theory, numerical simulation models, typically finite element method (FEM) models, offer the possibility to predict the distortion due to known RS for complex part geometries. Mostly two approaches have predominantly prevailed in the literature: The RS were applied to the final machined part geometry [4, 23, 24] or the material removal process was modelled via element deletion techniques [25,26,27]. First approach provides faster results but leading potentially to a reduced accuracy [22]. However, the mutual influence of both RS types on distortion is still not fully understand. The entire RS, including MIRS on all surfaces and effects like machining-induced shear stresses were mostly not considered, although e.g. second have been shown to induce a torsional moment and thus influence the part distortion [28].

There are different ways to obtain the MIRS needed as an input for the distortion models. By RS measurements a data-basis can be built for different machining conditions varying in tools and process parameters. Using empirical regression models is a possibility to extend the data-basis within the process space. Furthermore, analytical and numerical models were used to predict the MIRS. With increasing computing power, as well as the availability of commercial FEM programs, numerical models replaced analytical and empirical ones in manufacturing, since the latter are usually only valid for a limited process space (tool, workpiece, cutting parameter combination) [29]. However, a comparative study by Jawahir showed that FEM models of different research groups, which modeled the same real-world process, led to large discrepancies in the simulated MIRS [29]. Possible sources of error are inappropriate simplifications, wrong assumptions, improper modeling of the boundary conditions, numerical run-out errors or discretization errors [30].

Two main categories of distortion control due to RS were identified in the literature review by Li et al. [5]: The postcorrection is characterized by processing the finished part with thermal or mechanical loads, like peen forming, laser heat treatments or other stress relieve techniques. The precontrol techniques on the other hand improve the machining conditions in a way that mainly the magnitude of RS is reduced, or a change of their distribution is aimed for [5]. Besides adjusting the cutting parameters to induce less MIRS, controlling the cutting sequence [31] and changing the process strategy (applying different MIRS on different machined surfaces [26], subsequent cutting steps to remove the boundary layer containing high MIRS [32], changing the milling direction [33]) led to a beneficial shift of the MIRS distribution and therefore reduced the distortion. The beneficial modification of the distribution of the IBRS was realized by changing the position of the part in the raw material [24, 34,35,36,37,38].

In summary both IBRS and MIRS lead to part distortions, which can be reduced by considering their magnitude and distribution in a favorable way. However, their mutual impact on part distortion and the potential of deriving compensation techniques are still not fully understood yet.

This research article is a summary to provide a holistic overview of our research in the field, where most of the content has already been published elsewhere ([39,40,41,42,43, 46,47,48, 51]). The novelty of this research consists of the holistic consideration of the combined influence of the part geometry, including its topology, and the machining strategy and distinguishing the dominating RS type for analyzing the part distortion; including investigations on the effect of IBRS on MIRS, the comparison of different RS measurement techniques and the repeatability of the RS and distortions.

2 Methodology

Figure 1 provides an overview of the concept developed to understand the residual stress induced distortion of milled thin-walled aluminum structural parts, predict the distortion using FEM simulations, and derive methods to minimize the distortion [39]. It contains a combination of experiments and simulation models. The experiments serve as a validation for each simulation model. As Fig. 1 illustrates, each, IBRS and MIRS, was analyzed individually before investigating the superposition of both to understand their fundamental principles and effects on part distortion. The structure of the experiments was divided into two main parts with regard to the target parameter to be investigated: RS investigations and distortion investigations. In the former, both RS types were characterized (Sect. 3.1 and 3.2) and the influence of the machining parameters, clamping strategy and tool type on the MIRS in the workpiece was identified (Sect. 3.2) [40]. This includes measuring the MIRS with various techniques [41] and a repeatability study [40]. In the distortion investigations, different thin-walled geometries were manufactured, and their distortion was determined to investigate the influence of the IBRS, the MIRS (Sect. 3.3) and their superposition on the part distortion (Sect. 3.4) [42]. The developed FEM models predict the part distortion (Sect. 4.1) based on the information about MIRS (Sect. 4.2), resulting from different machining parameters, tools, and the IBRS. The part geometry, including its topology (angle of stiffeners, wall thickness, size, complexity), and the machining strategy were varied to analyze their effect on the part distortion and to highlight possibilities to minimize the distortion (Sect. 5) [43].

Fig. 1.
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Concept to minimize distortion of milled thin-walled aluminum structural parts due to residual stresses acc. to [39]

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3 Experiments

3.1 Initial Bulk Residual Stress Characterization

To understand the effect of the IBRS on part distortion, different IBRS configurations were examined. Workpieces made of a rolled plate of the high strength aerospace aluminum alloy 7050 were investigated in two conditions: First 7050-T74, which is a solution heat treated and quenched material, containing high IBRS and secondly the 7050-T7451 state, which was in addition stress relieved by stretching and therefore containing low IBRS [44]. All blocks used for machining experiments (see Sect. 3.2 and 3.3) were cut from the original rolled plate into individual samples measuring 206 mm (x-direction: longitudinal rolling L), 102 mm (y-direction: short transverse ST) and 28.5 mm (z-direction: longitudinal transverse LT) (see Fig. 2a). The low IBRS were measured via the slitting method using wire electric discharge machining and the high IBRS via a variation of the slitting method, the so-called cut mouth opening displacement method, from which a 2D IBRS map was deduced [45]. The measurements showed that the low IBRS had a maximum of about 20 MPa (see Fig. 2b), whereas the high IBRS reached from −150 MPa to 100 MPa, which is a significant fraction of the material strength (see Fig. 2c) [45]. The quenched samples had a paraboloid spatial distribution of normal RS with a significant directionality. The stress state near the center is nearly uniaxial tension with σxx much larger than σyy. Whereas near the upper and lower boundaries the stress is nearly uniaxial compression (σxx compressive and σyy near zero) [45]. The distortion caused by those IBRS is discussed in Sect. 3.3.

Fig. 2.
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Initial bulk residual stresses for low (b) and high stress configuration (c) acc. to [45]

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3.2 Machining Induced Residual Stress Characterization

Down milling with cemented carbide end mills (Kennametal1 F3AA1200AWL, d = 12 mm, z = 3, for more details see [40]), which represents a typical tool for machining of aerospace aluminum alloys, was carried out on a 5-axis DMG Mori1 DMU 70 CNC machine to evaluate the effect of the machining on the MIRS. The above mentioned AA7050-T7451 samples with the dimensions 206 × 102 × 28.5 mm3 were face milled. To neglect the IBRS, the samples in the stress-relieved condition (T7451) with low IBRS were used. The MIRS were explicitly not measured on thin-walled milled but on thick workpieces, since a strong redistribution of the RS, which is associated with the distortion of the thin components, should be avoided to be able to capture the full distortion potential of the MIRS. Three different feeds per tooth fz and two different cutting speeds vc were analyzed, resulting in four parameter modes (EM1-4, see Table 1). The width of cut ae and depth of cut ap were kept constant at 4 mm and 3 mm respectively, and dry cutting was carried out. To further investigate the influence of the tool type on the MIRS, a second tool, a cutter with indexable inserts (Sandvik1 R590-110504H-NL H10, d = 50 mm, z = 2, for more details see [42]), which is a typical tool for face milling, was used (Index, see Table 1, ae = 40 mm, ap = 1.5 mm).

Table 1. RS experiment matrix.
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Various RS measuring techniques were investigated:

  • incremental hole-drilling (HD) following the ASTM E837-13a standard measuring with strain gauges [ASTM13] (HD-strain)

  • HD measuring with an optical laser-based principle, the electronic speckle pattern interferometry (HD-ESPI)

  • slotting

  • cos(α) x-ray diffraction (XRD)

  • sin2(ψ) XRD

The MIRS measured by the different techniques HD, slotting, sin2(ψ) XRD were largely consistent [41]. For example, in Fig. 3 the measured MIRS in orthogonal feed direction for machining set EM3 are shown. Root shaped depth profile of compressive RS, which are typical for milling induced RS, were measured. The measurements of the two HD techniques agreed for the normal direction (see Fig. 3b). Similar maximum MIRS (approx. −120 MPa) were found at different depths, which could be attributed to the depth correction applied for the HD-strain measurements (for more information see [41]). However, in shear direction more significant deviations were evident. Furthermore, it was found that MIRS data from HD-strain were most consistent with machining-induced distortion [41].

Fig. 3.
figure 3

Comparison of RS measuring techniques for σyy acc. to [41] (a)

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To investigate the repeatability of MIRS for multiple samples and the influence of different machining modes, twelve machining experiments (three for each EM mode) were carried out with three HD-strain measurements each sample. All measured MIRS depth profiles showed compressive MIRS for all three stress components σxx (feed-direction), σyy (orthogonal feed-direction), τxy (shear direction) (see Fig. 4). The normal stresses were similar in their magnitude and lower shear stresses were measured. The maximum of MIRS (MaxRS) for lower feeds (EM1, 2) existed at the shallowest depth (see Fig. 4a). Higher feed per tooth (EM3) led to larger plastically deformed areas and therefore deeper RS and the shift of the MaxRS deeper into the workpiece, due to the increased load on the sample. The repeatability standard deviation (RSTD) indicated that the RS for EM 1, 2 and 3 were repeatable with small variations within one sample and from sample to sample [40]. EM4, where a different cutting speed was chosen, showed more variability compared to the other modes, because machining for EM4 was not stable, which was indicated by the RSTD (see Fig. 4a) and vibrations detected in the force signal of Fz [40].

The different tool geometry and the chosen machining parameters led to smaller and shallower MIRS compared to the ones induced by the regular end mill (see Fig. 4b) due to the decreased mechanical load. Furthermore, a opposite sign of the shear stresses was measured.

For investigating the influence of the IBRS on the MIRS, the solution heat treated and quenched material AA7050-T74 with high IBRS was machined with the machining parameter EM3. From the IBRS measurements (see Sect. 3.1) different regions with variations of IBRS could be identified. HD-strain measurements were applied at locations where IBRS were near zero (Pos. A), tensile (Pos. B) or compressive (Pos. C) (see Fig. 5) [46, 51]. At greater depths (>0.2 mm), the different IBRS are visible. Furthermore, it is evident that the IBRS effected the MaxRS (see Fig. 5).

Fig. 4.
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Measured MIRS: End mill (a) and cutter with indexable inserts (b)

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Fig. 5.
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RS depth profiles on various positions at milled surface acc. to [46, 51]

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3.3 Machining Induced Residual Stress as Driver for Distortion

To investigate the distortion potential of the MIRS experiments, where a 1 mm thick wafer was removed at the milled surface via wire electric discharge machining, were developed [40, 41]. The distortion was defined as the out-of plane displacement of the wafer. It was measured with a laser profilometer at points with a 0.2 mm spacing at the backside. The machined surface becomes convex (∩-shaped) due to the compressive MIRS at the milled surface, which induced a bending moment (see Fig. 6a). The maximum distortion was at the top left and bottom right corner because the shear stresses caused a torsional moment in addition to the bending moment induced by the normal RS. Higher or deeper compressive RS resulted in a higher distortion (see Fig. 6c). Variations of MIRS within one machining mode for different samples resulted in a consistent variation of distortion. The highest variation for the wafer distortion was found for EM4 due to its unstable machining [40].

Fig. 6.
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Qualitative shape of wafer distortion (a), contour plot (b), and diagonal distortions for different machining modes (c) acc. to [40]

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3.4 Superposition of IBRS and MIRS and Its Effect on Distortion

The analysis of the effect of the superposition of the MIRS and the IBRS on distortion was done the same way as described in Sect. 3.3: Wafers were cut out at the positions A, B and C according to the HD measurement locations (see Fig. 5). The distortion shape and level changed compared to the low IBRS wafers due to the higher IBRS (see Fig. 8). The high IBRS act as a preload [46]. When the IBRS along the milling direction are tensile, the material flows more in the direction of tension, leading to a rotation of the convex wafer distortion away from the diagonal, closer to the milling direction (see Fig. 8b) [46]. For wafers in regions of compressive IBRS along the milling direction, the opposite occurs, and the convex distortion shape rotates even further away from the milling direction (see Fig. 8c).

The distortion of more complex workpieces than the flat wafers was analyzed as following: A small thin-walled structural component of the size 200x98x20 mm3 with one rib in the center surrounded by two pockets was milled from the initial block (206 × 102 × 28.5 mm3). The influence of different IBRS (low vs. high), MIRS, machining strategy (zig vs. spiral out), and wall thickness (3 mm vs. 7 mm) on the distortion was analyzed. For the 3 mm wall thickness (7 mm), about 84% (67%) of the initial material was removed. First the outer walls were milled by side milling with the regular end mill (vc = 450 m/min; fz = 0.055 mm; ap = 22 mm; roughing ae = 2.5 mm; finishing ae = 0.5 mm). Second the back and top side were face milled with the parameter set Index (see Table 1). To enhance the clamping, which was realized by side clamps, additional holes for clamping with screws were drilled. Finally, the pockets were milled with EM1 or EM3 to induce different MIRS. To realize high feed rates, the pockets were milled in multiple layers. To further analyze the effect of the milling path on the distortion, two strategies were investigated for the 3 mm samples: First, the milling of the pockets was done in alternating order in zig strategy (pocket milling paths from left to right). Second, a spiral milling path following the contour of the workpiece (inside-out) was used. The distortion was measured on the backside of the sample before (Pre-) and after step 5 (Post-) with a coordinate measuring machine and a spacing of 2 mm.

A general comparison of the distortion of the low and high IBRS samples (independent of their wall thickness and machining mode) showed that their distortion shape and magnitude differ (see Fig. 7). The low IBRS samples, machined with the zig strategy, showed a X-shaped distortion with its maximum distortion near the top left and bottom right corner and its minimum at the other two corners. Like the distortion behavior of the wafers, the shear MIRS were responsible for this distortion shape. In contrast, the high IBRS samples become convex (∩-shaped), and the maximum distortion was found towards the left and right edge. The magnitude of the maximum distortion was approximately 0.6 mm, which was about five times higher than for the low stress samples. This indicates that for high IBRS samples the IBRS are driving the distortion, because their RS are much higher as the MIRS, and they are contained in the entire bulk of the sample. The removal of the material led to a disequilibrium of the IBRS. The distortion was the result of the stresses gaining equilibrium again. Nevertheless, there was a systematic influence of the combined effect of both RS types evident for thin wall thicknesses (3 mm), where the maximum distortion was also found at the two opposite corners. The machining EM3, inducing more MIRS deeper into the material, led to higher distortions than EM1 (see Fig. 7). [42].

Fig. 7.
figure 7

Color maps of distortion, diagonal distortion of each configuration acc. to [42]

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4 Simulation Models

Two different simulation models were developed: First, a distortion prediction model, which uses the RS as input to calculate the distortion. Second, a cutting model, that simulates the tool workpiece interaction due to the given cutting parameters to predict the resulting MIRS. It was investigated whether that model can substitute the MIRS measurements required for the distortion model.

4.1 Distortion Prediction Model

Using a static, linear elastic FEM model, realized in ABAQUS1, the distortion due to the RS was simulated [42, 43]. The measured MIRS and the measured IBRS were implemented as an initial condition (type = stress) to the final part shape (wafer and thin-walled component) and the distortion was calculated because of the RS gaining re-equilibrium. The assumption was made that the distortion only occurs as soon as the sample is removed from the clamping device, because a rigid clamping strategy was used in the experiments [42]. That means that simulating the material removal process by element deletion was not necessary. This allowed for a fast simulation time (< 30 min for parallel simulation on a desktop PC with 8 cores). The measured MIRS (plane stress: σxx, σyy, τxy) were linearly interpolated over the depth z at the element centroids in the boundary layer of the respective milled surfaces. For the thin-walled structure in addition to the MIRS at the bottom of the pockets, the backside and top of the workpiece, the MIRS in the walls were measured and considered in the model [43]. For depths greater than the last measured depth, the measured in-plane IBRS (σxx, σyy) were linearly interpolated accordingly to their position x,y (see Fig. 2). To also consider the true milling path and therefore the exact direction of the MIRS, the G-Code was exported from the CAD/CAM system [43]. In this way, the direction of milling could be identified at each location. The elements of those regions containing MIRS were detected and the MIRS were assigned to each element according to their direction, calculated via the coordinate transformation. The mesh was refined at the machined surfaces in z-direction to precisely resolve the MIRS. A coarser mesh was used in other regions to reduce the total number of elements for calculation time reasons.

Fig. 8.
figure 8

Comparison of measured and predicted wafer distortion acc. to [51]

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Figure 8 shows the comparison between the measured wafer distortion and the simulated one for machining conditions EM3/EM3-HS at different positions (see also Sect. 3.2.). The results show that the simulation can predict the shape and level of distortion qualitatively and quantitatively for each scenario [40, 46].

The simulation model is also able to predict the shape of the distortion of the thin-walled structure qualitatively for all different configurations (see Fig. 9). All the different effects discussed in Sect. 3.3, such as the X-shape for the zig strategy of low, the U-shape for spiral strategy of low and the ∩ -shape of distortion of high IBRS samples, are covered by the simulation. Furthermore, the magnitudes of distortion for simulated and measured distortions were on a similar level [42]: The relative error of the simulation for the maximum distortion found at the samples with a wall thickness of 3 mm and machined with the zig (spiral) strategy was 9% (−19%). The deviation for machining with the spiral milling strategy was higher, because in general lower distortions were measured and therefore deviations in the measured RS, used as input, have a bigger influence on the distortion prediction accuracy. In addition, the application of only MIRS or IBRS, showed that the MIRS in the pockets, especially the shear stresses, are driving the distortion for milling the investigated thin-walled structure with 3 mm wall-thickness and stress relieved (T7451) material when using the zig strategy [42]. In contrast, the low IBRS are driving the distortion when choosing the spiral strategy, because the shear MIRS in the pockets equilibrate each other almost fully. But still, for both strategies, the superposition of the IBRS and the MIRS is evident [43].

Fig. 9.
figure 9

Comparison of measured and predicted distortion acc. to [43]

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Since the model was validated, it could be used for investigating more use cases than experimentally examined: A mutual influence of the part geometry, topology respectively (angle of stiffeners, wall thickness, size, complexity), and the machining strategy (IBRS configuration, milling path) on the part distortion was evident [47]. For example, a change of the angle of stiffener from 90° towards 45° led to a significantly reduced distortion (−66%) of the part machined in zig milling strategy (see Fig. 10), because the sample was stiffened along the principal direction with maximum displacement. Whereas machining in a spiral path increased the distortion for the geometry with 45° stiffener because shear stresses did not fully equilibrate each other anymore.

A decreasing wall thickness was found to increase the distortion with accompanying more dominant MIRS in comparison to low IBRS.

Fig. 10.
figure 10

Distortions with varying stiffener angle and machining path acc. to [47]

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The simulation of the distortion of a more complex part, a small-scaled airplane wing-rib, showed similarities in distortion shape as for the investigated smaller parts (see Fig. 11): For milling with zig strategy, the X-shaped distortion was present with the MIRS dominating. But their contribution was less than for the small parts. Again, for milling with a spiral strategy the maximum distortion was reduced by −45% with a minimization of the effect of the MIRS.

Defining a universal crucial wall thickness when MIRS are the main factor for the distortion for thin-walled monolithic structural parts is deceptive, because that depends on the part geometry and the machining strategy [47].

Fig. 11.
figure 11

Predicted distortion of structural part with varying mach. path acc.to [47]

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4.2 Cutting Model to Predict the MIRS

By means of explicit, dynamic, elastic-plastic 3D FEM cutting simulations the tool workpiece interaction was modeled in ABAQUS1 to predict the MIRS [48]. Two different cutting conditions, one for each tool and milling process (pocket milling EM3, face milling Index, see Table 1), were modelled (see Fig. 12). The tools were assumed as rigid bodies, neglecting wear. This assumption was valid, because the elastic modulus of the cemented carbide tools was significantly higher, resulting therefore in a low elastic deflection compared to the large plastic deformation of the aluminum workpiece. Besides, only one revolution (EM3), two respectively (Index), of the respective tool were simulated. To furthermore save computational time, the workpieces were modelled smaller as in experiments. To account for thermal and mechanical effects, thermo-mechanical elements (C3D8RT) were chosen for the workpiece. The contact between workpiece and tool was modeled using a general contact interaction with Coulomb friction. The elastic-perfectly plastic material behavior was modeled temperature dependent with given values from the literature [49]. Material damage was implemented by the Johnson-Cook damage initiation criterion, which is a special case of the ductile criterion. The JC damage parameters were chosen according to the literature [50]. Although the simulations were run on the high-performance computer “Elwetritsch” at the TU Kaiserslautern the simulation time was 7 to 10 days. The MIRS, resulting from the plastic deformation and temperature gradients during the cutting process, were analyzed in the boundary layer and the machined surface. Therefore, the stresses at nodes in an area with the size that is equal to the measurement area were extracted and averaged for each element depth. Besides, the standard deviation was computed. The predicted MIRS depth profiles showed the typical root-shape of compressive RS (see Fig. 12). In general, for both milling conditions the magnitude of the simulated MIRS were on a similar level as the measured ones and the sign of the shear stresses was predicted correctly. However, there were still significant deviations found in comparison to reality: For EM3 lower penetration depth and lower values of the MaxRS were predicted (see Fig. 12a). For the Index case higher penetration depth and higher values of the MaxRS were simulated (see Fig. 12b). Possible reasons are that the microscopic geometry of the tools deviated from reality (cutting edge radius: CAD model ideal sharp vs. reality ~ 10 µm). Furthermore, the model is only a simplification of reality. When using the predicted MIRS from the cutting model as input for distortion model, the same shape but significant differences in magnitude of distortion were predicted (see [48]). Another disadvantage of this approach is, that modelling machining with lower feeds per tooth than the simulated 0.2 mm would require smaller elements in the cutting area, which would increase the already high simulation time drastically. In general, modelling the MIRS is difficult, because accurate material models are required. Also, the uncertainty is too high, meaning RS measurements are required anyway due to validation purposes. Besides, it was shown that measurements were transferable: Meaning it would be possible to carry out the RS measurement on test specimens that have been machined with the same machining strategy as the component itself. In summary, using measured residual stress data as input for the distortion model is favorable.

Fig. 12.
figure 12

FEM cutting models for machining EM3 acc. to [48] (a) and Index (b)

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5 Development of Compensation Techniques

It was shown both experimentally (see Sect. 3.3) and simulatively (see Sect. 4.1) that the distortion can be reduced by changing the machining strategy from zig to spiral milling: A distortion reduction of 41% was achieved for small parts with 3 mm thick walls and 45% for a more complex structural part. Especially for smaller wall thicknesses the potential of minimizing the distortion by changing the direction of the milling is higher than for parts with thicker walls. [43]. Furthermore, by applying similar MIRS at the backside of the sample than those at the bottom of the pockets, an opposite bending moment could be induced to minimize the distortion. Adjusting the part topology, for example by aligning the stiffener along the principal direction of stresses, decreased the distortion as well. Those methods fall into the category of precontrol compensation techniques [5] or also called offline methods [22], which can be divided into the following categories [43]:

  • The process parameters, such as the tool properties and cutting parameters effect the MIRS (depth and magnitude) and therefore the part distortion directly.

  • The process strategy effects both the MIRS and the IBRS. The positioning of the part in the semi-finished product determines the re-distribution of the IBRS. Subsequent cutting steps remove layers of MIRS and introduce others. The milling path effects the direction of MIRS and therefore the induced bending moments.

  • The part topology determines the location of the removed material and therefore the redistribution of the IBRS effecting the distortion. The stiffness of the structural component itself is also affected.

Due to the higher distortion of high IBRS samples other minimization techniques are required: For example, by using the developed distortion prediction model in advance to machining, the distortion could be compensated by milling the inverse distortion onto the backside of the sample. This led to a distortion reduction by 77% [43].

6 Summary

In our research the effect of the residual stresses, the machining strategy, the part topology and the geometry, including the wall-thickness, on distortion were investigated experimentally, and simulatively by validated virtual models based on the finite-element method. First, the effect of each RS type on the part distortion was analyzed individually before understanding their superposition. A repeatability analysis of the MIRS formed the basis and showed that for stable machining, repeatable MIRS led to repeatable distortions [40]. Furthermore, a set of different machining parameters were identified causing different MIRS, where higher and deeper MIRS resulted in higher distortions. Hereby a simple experiment was developed highlighting the distortion potential of RS in the boundary layer of parts: A 1 mm thick wafer was removed at the milled surface. A static, linear elastic finite element model was developed to simulate the distortion due to the measured RS in a short time [42]. The model considers all RS (IBRS and MIRS) contained in the entire part at different locations as well as the milling path. It was validated by various experiments (different geometries, RS, milling paths). It could be shown that the shear MIRS are crucial and contribute much to distortion (when not compensated for), because they induce a torsional bending moment in addition to the bending moment of the normal MIRS [42].

In general, the part topology, part size and the machining strategy have a mutual impact on the part distortion. By decreasing the wall thickness the distortion increases with a shift of the RS type dominating the distortion towards the MIRS. Defining a universal crucial wall thickness when MIRS are the main factor for the distortion for thin-walled monolithic structural parts is deceptive, because of the dependence on the part geometry and the machining strategy. For the investigated geometry (wall thickness < 3 mm) and machining parameters, it could be shown that for low IBRS samples (stress relieved), the MIRS introduced in the surface layer of the pockets are driving the distortion when a zig milling path strategy is used [42]. In comparison, when milling the pockets in spiral form, the low IBRS dominate the lower distortion [43]. For high IBRS samples the IBRS are driving the distortion. Nevertheless, there is a systematic influence of the combined effect of both RS types found for thin wall thicknesses (<3 mm) and the zig milling strategy [42]. The knowledge gained from investigating smaller and simpler parts (size and complexity) could partially be transferred to bigger parts.

The process parameters, the part topology and the process strategy were identified as precontrol distortion compensation techniques, because they effect either the MIRS, the IBRS or both and therefore the distortion. An appropriate milling strategy, applying opposite bending moments and balancing shear stresses, minimized the distortion.

Furthermore, a 3D FEM cutting simulation was developed [Webe21c]. It was able to predict the MIRS for high feed machining qualitatively. However, they could not be used as an adequate replacement for the measured MIRS for the distortion model.

In future research, the investigations will be expanded to include more cutting parameters, especially the investigation of cooling lubricants or cryogenic machining and its effect on the MIRS and part distortion.