Keywords

1 Introduction

High-value products such as aircraft engines require effective maintenance, repair, and overhaul services to increase economic efficiency and sustainability (Uhlmann et al. 2013). In the case of jet engines, components like blades need specialized repair technologies to maintain or even improve their functional properties throughout the life cycle (Eberlein 2007). Designing these repair processes is a challenging task and differs from new part production (Denkena et al. 2015a, b). Typically, a material deposit is needed to replace missing areas of the damaged part or to attach repair patches or fill cracks. Afterwards, the excess material has to be removed to restore the desired geometrical shape. This removal is referred to as recontouring, where milling processes are commonly used (see Fig. 1). The uniqueness of repair cases, different materials (e.g., base and weld material) and parts prone to vibration complicate the repair. Additionally, 5-axis machining processes are required to restore the complex part geometries and to overcome the limited accessibility. Compared to new part production, it is hardly possible for recontouring processes to test the process with a spare part beforehand. This leads to the necessity of a tailored and precise process planning procedure to ensure high geometric accuracy and surface quality for minimizing scrap and flow loss (Eberlein 2007).

Fig. 1
A flow diagram starts with scanning of unknown blade shape with a crack, goes to material deposit, re contouring unknown process conditions, to inspection of repaired blade, process induced part distortion.

Repair process chain in terms of manufacturing aspects

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In most cases, the target shape of the blade is not immediately known due to operational deformation processes in the engine, such as thermal creep, so a CAD-technical restoration of the contour is necessary (Gao et al. 2008, Wu et al. 2012). In addition to the measurement of the actual geometry, the planning of the recontouring process requires knowledge about the target geometry. The goal of current research projects is a higher degree of automation since a manual derivation of the target geometry is associated with a high expenditure of time. This is based on measurements of the damaged blade (Rong et al. 2014; Schlobohm et al. 2014). The limits of automation in the repair of engines are largely determined by the complicated component shape combined with a high degree of individualization. For this reason, current research and development projects are concerned with pushing this limit in the direction of optimized and highly efficient recontouring systems. Bremer et al. have developed an automated repair system for turbine components. Here, the CAD surface reconstruction of the unknown target shape (reverse engineering) is taken into account and integrated into an overall process for recontouring the components (Bremer 2006). In particular, the integration of the obtained data into the overall process plays an increasingly important role. Yilmaz developed an automated and integrated process chain for turbine component repair that includes optical 3D measurement, surface reconstruction, and customized milling processes. The aim was to restore the shape of the damaged components within their geometric tolerances with reduced process time (Yilmaz et al. 2010).

For ball end milling, there are numerous studies dealing with process design for new part production. Methods exist to predict process stability, surface topography, and productivity (Markworth 2005; Knobel 2000). They can be categorized into empirical, analytical, and numerical methods. One example of an empirical model was presented by Vakondios et al. (2012), where mathematical regression between the process parameters and the resulting surface parameter Rz is used. Empirical models are very accurate and easy to use but are limited to the experimental scope. Analytical models mathematically describe the shape (Markworth 2005; Knobel 2000) and/or the trajectory of the cutting edges (Arizmendi et al. 2008). For instance, the analytical model of Arizmendi et al. (2008) show the importance of tool runout and its impact on surface topography. However, the analytical equations can get too complex to handle by adding more simulation features, such as vibrations or special tool shapes etc. Therefore, numerical simulations in the time domain are required. They are called material removal simulations (MRS) and use, e.g., Voxel, Dexel or constructive solid geometry (CSG) to discretize the workpiece. In contrast to common analytical approaches, numerical simulation offers advantages regarding the flexibility of their application possibilities and adaptability. The milling kinematics of the machine and a digital model of the workpiece geometry can be used. Thus, it is possible to calculate the cutting conditions engagement parameters even for complex geometries and tools. It has been shown by Liu et al. (2005) that the movement of the cutting edge is a superior approach in terms of accuracy compared to a Boolean subtraction between the workpiece and the rotation body of the milling tool, e.g., a sphere for ball end mills. The resulting surfaces after MRS are perfectly smooth without stochastic influences. This often leads to underestimated surface parameters (Bouzakis et al. 2003; Chen et al. 2005; Liu et al. 2005). Several investigations concerning the interaction of the wall and the near-wall flow have shown that the topography of the wall surface significantly influences the aerodynamic losses that occur on blades or vanes (Abuaf et al. 1998; Bons 2010). Particularly the height and the shape of the surface structure, as well as their alignment with respect to the direction of the flow can increase the overall friction loss (Hohenstein and Seume 2013). Even relatively small structures may have an effect on the friction between the wall and the fluid, as is exemplified by riblets (Boese 2002). Due to their shape and direction on the surface, they reduce the aerodynamic losses. This suggests that every change in the surface topology can have an influence on the aerodynamic loss behavior of an airfoil.

Ball end milling is mainly used for finishing operations and manufacturing of complex parts (Layegh and Lazoglu 2017). Besides high geometric accuracy and low surface roughness, a compressive residual stress state is often required, e.g., in aerospace parts like compressor blades. Compressive residual stresses can be achieved using rounded cutting edges (Denkena et al. 2014b). The disadvantages of using rounded cutting edges are increased process forces because of additional ploughing as well as a possible burr formation (Denkena et al. 2014a, b; Wyen 2011). To reduce process forces causing tool displacements and shape deviations, process parameters can be optimized using process force models. Controlling burr formation, however, is still challenging because the burr formation not only depends on process parameters but also on the workpiece material, tool geometry, and tool path (Link 1992). Burrs deteriorate the surface roughness which is often not acceptable (Aurich et al. 2009). To avoid burrs during the process planning stage, various models for predicting burr are investigated. Sokolowski et al. (1994) apply neural networks and fuzzy logic based on an experimentally determined database. Chu and Dornfeld (2002) uses computed engagement conditions depending on the workpiece geometry, tool path, and cutting parameters as input parameters of a database containing different burr types. Chen et al. (2012) used Finite Element (FE) simulations to predict burr formation in micro ball end milling of Ti-6Al-4 V.

2 Objective

The objective of the subproject C1 of the Collaborative Research Center (CRC) 871 was to establish a cross-process simulation and planning of the machining recontouring process for the functional improvement of the application behavior of the regenerated workpiece. The generated knowledge can be used for common planning, taking into account the interactions between the regeneration processes. The following sub-goals were achieved:

  1. 1.

    Availability of a simulation model for the prediction of the material deposition

  2. 2.

    Digital machine, tool, and workpiece models for efficient process simulations

  3. 3.

    Availability of methods for an optimized surface prediction

  4. 4.

    Knowledge about influences of the material deposition on the recontouring process

  5. 5.

    Method for individual CAM-planning for recontouring processes

The results were combined in a holistic concept for adaptive process planning which was established within the sub project C1. The concept of the adaptive process planning method for blade repair is shown in Fig. 2.

Fig. 2
A flow diagram starts with individual geometry data, goes to generation of target geometry, target geometry goes to process planning, geometric process simulation, adaptation to process analysis, process knowledge to process adaptation, to G code.

Concept of adaptive process planning method for blade repair

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In the initial step, based on 3D scan data of the damaged blade, a target geometry model is created (Sect. 3.1). This forms the basis for the subsequent simulation-based process planning of the material deposition process (Sect. 3.2) and the recontouring process (Sect. 3.3). By means of a digital process twin, relevant process variables for the material deposition and recontouring process are predicted during process planning. This includes both technological process data and information about the resulting workpiece geometry. By simulating the material deposition, knowledge is generated about the geometric characteristics of the material deposition, such as the minimum height of the allowance. This knowledge is taken into account in the process design of the recontouring. By simulating the recontouring process, the cutting conditions in the contact zone are calculated. Subsequently, technological process variables and quality data are estimated as part of the process analysis. The data are used to adapt both processes with the aim of increasing process quality and reducing process time. The adaptation of the process parameters as well as the tool path is implemented in the NC code and then transferred to the processing machine.

3 Results

3.1 Individual Process Planning for Recontouring Processes

The concept of the individual planning method can be divided into the two sub-methods geometry processing and process planning. The geometry processing method is used to calculate a suitable target model. First, the individual actual geometry is reconstructed on the basis of the 3D scan data. Based on this, a target model is generated. Within the process planning, a 5-axis toolpath is calculated and in combination with the most suitable process parameters used for the generation of the NC code for the tool machine. The method for the individual process planning is shown in Fig. 3.

Fig. 3
A flow diagram starts with damaged blade, goes to geometry acquisition, data processing, point cloud of 3 D scan model, reconstruction of geometry, identification of target geometry, process planning, tooth path planning, generation of N C code, to N C code for recontouring.

Adaptable process planning method

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As discussed in the state of the art, highly stressed components such as turbine blades are subject to continuous operational wear. Macroscopically visible damage such as chipping or cracking is completely removed before the weld preparation and is therefore not relevant for the subsequent repair process chain. In addition, there is typically a slight degeneration in terms of thermal creep effects and abrasive wear of the entire blade. This results in a loss of material, which leads to a significant change in the geometry of the blade. The change in geometry has a particularly strong influence on the repair result and should therefore be taken into account in the entire repair process chain. The resulting deviations from the nominal component geometry (CAD file) necessitate a method for creating a new target geometry for each individual component.

Based on the given geometric information about the current component geometry, the following necessary requirements for the method can be derived:

  1. 1.

    The current component geometrical shape (actual geometry) must be taken into account when creating the nominal geometry.

  2. 2.

    When calculating the nominal geometry, the aim should be to achieve a transition between the actual geometry and the newly calculated geometrical shape (damaged geometry area) that is as smooth as possible in terms of curvature.

The method for the individual computation of a suitable target geometry is carried out in two steps. The calculation of the target geometry requires a continuous surface model without gaps. The approach in praxis for surface reconstruction is done manually in the current state-of-the-art (Bremer 2006, Gao et al. 2008, Rong et al. 2014, Yilmaz et al. 2014). In order to avoid this time-consuming process, first, a new algorithm for the automated reconstruction of the actual geometry for the case of a tip repair was developed. Moreover, by using sliced profile curves the aerodynamical parameters in terms of the position of the leading and trailing edge, the profile thickness as well as the camber line are calculated for each profile. At this stage, the damaged part of the blade is unknown due to the degeneration and thus, requires a restoration of the target model. Therefore, in the second step, the unknown area of the component is calculated by a knowledge-based extrapolation of the reconstructed actual geometry using profile curves and the aerodynamical parameters. Three-dimensional regression functions are built up for the profile thicknesses and the camberlines of all profiles. In order to calculate the geometry of the blade in the unknown area, both functions are extrapolated up to the required target height of the blade. Since the regression functions have a wider space within the planes of the profiles, a trimming at the leading and trailing edge is conducted. This is done by a two-dimensional extrapolation function of the leading and trailing edge points up to the target height of the blade. Then, the information on the profile thicknesses is added to the camber lines in the unknown area. This is done by circles whose diameter corresponds to the thickness and which are positioned along the camber line. The resulting contour in the damaged area is generated by calculating the envelope curve of all the cycles. Finally, the reconstructed actual geometry and the geometry in the damaged area are stitched together. In this way, a suitable target geometry for the blade could be generated.

To validate this approach, a reference model in analogy of a turbine blade of the second stage of the high-pressure turbine (HPT) was designed where the repaired area is known. A damaged model was created by using this reference model and removing the tip area as it is the case for the tip repair. Afterward, a target model was generated on the basis of the damaged model using the developed process planning method. The target model was then digitally machined in a geometric simulation of the recontouring process using the individually and automated generated NC-Code. In this way, the resulting quality of the generated target model could be evaluated by comparing the deviations between the target model and the reference model in the tip area. The results of the comparison are shown in Fig. 4 for the pressure side and the suction side.

Fig. 4
Two diagrams display the, a, suction side and, b, pressure side of the model. In the suction side, the maximum values are at the base and some areas in the middle. In the pressure side, the maximum values are at the base.

Surface comparison between generated target model and reference model

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The criteria for a successful recontouring are a transition from the undamaged to the recontoured area that is as free of offsets and as continuous as possible, while at the same time complying with the shape, dimensional and positional tolerances with regard to the nominal geometry, which includes none damage of the actual geometry. These criteria were proven by the surface comparison. The surface comparison of the repaired blade model shows a good correspondence to the reference model with a maximum deviation of about 0.02 mm. A small step in the transition area can be observed which has a height of 0.02 mm. The deviations decrease with higher z-levels and are nearly negligiblely small at the top of the tip. In addition, it could be ensured that no damage to the actual geometry exists, thus fulfilling the requirements of the repair manual. Thus, the automated planning method for generating the target model can be stated as valid for the considered blade type and repair type.

3.2 Geometric Process Simulation of Additive Process for Blade Repair

To improve the process planning of the recontouring process, knowledge about the geometry of the material deposition is needed. This section introduces a method for the prediction of the geometry of the material deposition after the additive process based on a Dexel-based simulation model. The method was used afterwards to determine the influence of the material deposition on the recontouring process.

An empirical model for the prediction of the geometrical shape of the deposited material according to the process parameters was built. The method is explained in detail in (Böß et al. 2021). The model was parametrized based on experiments by micro-plasma welding as the DED process for titanium alloy Ti6Al4V. The model predicted the width b and the height h of the shape of the deposited material depending on the given process parameters travel velocity v and current I. In the experiments, the material was deposited as a straight line with a length of 70 mm on a titanium substrate with a constant wire feed rate f of 0.3 m/min using argon inert gas. Each experiment was repeated three times.

The cross section of the welding seams in perpendicular direction were measured at five distinct points to calculate the mean weld seam width using a tactile profile measuring device (MarSurf LD 130, Mahr GmbH Göttingen, Germany). In addition, the welding seam were measured in longitudinal direction in the middle of the welding seam to calculate the mean value of the height of the deposited material. By increasing the applied current intensity the height of the deposited material decreased and the width in- creased. This is due to the higher energy input at a higher current. The higher energy input leads to a lower viscosity of the molten material, and thus to a lower ratio between the height and the width of the deposited material. Besides, an increase of the travel velocity led to a decrease of the height and width of the deposited material, which can be explained by the decreasing volume of deposited material per unit length. This resulted in a smaller cross-section profile of the deposited material. Figure 4 shows this effect on the height of the deposited material (Fig. 5).

Fig. 5
Above, a box and whiskers plot of height versus current. At 20 Amperes, v equals 2 millimeters per second. At 25 Amperes, v equals 0.5 millimeter per second. At 30 Amperes, v equals 1 millimeter per second. Below is a table of wire feed rate, inert gas, substrate, and filler metal.

Measured height for different travel velocity and currents

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Based on the experimental results, an empirical regression model was established to predict the height and width of the deposited material based on the process parameters. The quadratic regression functions for the prediction of the width and height as a function of the specified travel velocity and current are shown in Fig. 6. To simulate the shape of deposited material, the developed regression models were implemented in the simulation software IFW CutS (Denkena and BöB 2009). According to the process parameters, the width and height were calculated by means of the regression model, and the digital tool was scaled accordingly. In this way, the geometrical shape of the deposited material could be simulated.

Fig. 6
Above, 2 3 dimensional graphs of weld seam height and feed rate versus current, and weld seam width and feed rate versus current. Below is a table of microplasma welding values of regression type, det coefficient, regression equation, det coefficient R squared, and regression equation.

Regression functions for prediction of welding seam height and width

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By means of the digital tool, the geometry of the solidified and chilled material deposition was modeled whereby a half-ellipsoid was used. With this simulation method, the geometrical shape of the deposited material can be adjusted by scaling the height and width of the digital tool, which in combination with multi-axis machine kinematics allows the simulation of different weld seam shapes and multi-layer depositions. Furthermore, it enhances the efficient process planning of additive manufacturing processes. The simulation method was used for modeling the material deposition process of blade repair using the scalable digital tool model in combination with a digital workpiece model of the individual damaged blade, which is shown in Fig. 7.

Fig. 7
Left, Two diagrams display the top and side views of the scalable tool model with length b and height h. Right, an illustration of an individual workpiece model, where dexel based material deposition, machine prepared blade tip, and digital tool are enlarged in the inset.

Geometric simulation of the material deposition process

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It has become apparent that the resolution of the multi-Dexel model has a high influence on the simulation accuracy. In order to find an appropriate resolution, an experimental setup was conducted in order to show the simulation results of the material deposition simulation for five different Dexel-densities, which are shown in Fig. 8.

Fig. 8
Above, 5 diagrams display the layers at rho x y z equals 10, 20, 30, 40, and 50 per millimeter. Below is a bale of simulation parameters. The values are Octree level equals 12, resolution of digital tool model equals 0.001 millimeter, and simulation cycle time equals 0.01 second.

Simulation accuracy in dependence on the Dexel-resolution

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On one hand, the results show the influence of the Dexel density on the accuracy of the workpiece model. While at a Dexel density ρXYZ of 10 mm−1, the individual layers of the material buildup are weakly pronounced, a continuous increase in the model accuracy can be seen when the Dexel density is increased. The highest simulation accuracy was achieved with a Dexel density ρXYZ of 50 mm−1. On the other hand, the computational effort increased from 15 MB (ρXYZ = 10 mm−1) to 280 MB (ρXYZ = 50 mm−1) of storage space for the Dexel-model.

An important parameter for the process planning of the recontouring process is the material allowance, which is a function of the weld geometry, the shape of the blade profile, and the tool path during the additive process. To plan the weld seam geometry knowledge-based, the influence of the weld seam width on the material allowance has to be investigated. For this purpose, geometric simulations of the material deposition process were carried out on a reference blade geometry with four different weld seam widths br of 1.4, 1.8, 2.2, and 2.6 mm. The material allowance was then determined, which is defined as the deviation between the nominal geometry and the actual geometry after the material deposition along the profile curve. The calculated material allowance over the profile length xprofile of a blade section is shown in Fig. 9.

Fig. 9
A line graph of material allowance versus profile position. b r equals 1.4, 1.8, 2.2, and 2.6 start at different material allowances, raggedly decrease and increase at the end of pressure side, abruptly decrease and increase on the suction side. Below are simulation parameter values.

Influence of weld seam width on the material allowance

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The diagram shows a linear relationship between the weld seam width and the material allowance. In addition, the results show a high dependence of the local material allowance on the position along the blade profile. The variation along the length of the curve can be attributed to deviations due to abrupt changes in blade geometry that cannot be taken into account by the material application process, such as the cooling air holes in the area of the pressure side of the blade or high curvatures at leading or trailing edge. In order to achieve the planned target geometry after recontouring, the material allowance along the entire profile curve must not only be at least positive (>0 mm) but also higher as the maximum error of the process chain due to process-induced deviations, which is empirically ± 200 µm. This way, it can be ensured that the planned target geometry can be manufactured in the recontouring process. At the same time, the material allowance should be as small as possible to reduce cutting volume and consequently, tool wear and process time. Therefore, in this case, a weld seam width of 1.8 mm is mostly suitable with regard to an efficient recontouring process without any gaps due to missing material.

To improve the performance of the simulation, a new approach was developed which allows the determination of different material properties of the workpiece. This can be used to distinguish between the undamaged part of the blade and the material deposition (Denkena et al. 2011). Furthermore, a method for a local adaption of the Dexel-density was investigated in the second funding period. This allows the increase of the Dexel resolution within the machined area as well as a decrease within the machined area which leads to lower simulation times (Denkena et al. 2014b). In order to analyze the surface topography of the workpiece at a microscopic level, an abstracted cylinder model for the tool model comes to the limits. Thus, a higher resolution of the tool model is needed which is in conflict with an appropriate simulation time. To solve this problem, a novel simulation method was developed and researched. This method includes a simplified cylinder model in combination with a detailed tool model with distinct cutting edges. Thereby, the modeling of the cutting edges is only active when the tool comes in contact with the interfering geometry (patch or weld seam). This increases the accuracy with only a slight increase in calculation time (Denkena et al. 2015b) (Fig. 10).

Fig. 10
Three illustrations display, 1, the tool and workpiece with weld seam, 2, cutting edge and varying cutting depth, and, 3, cutting edge and inhomogeneous cross section.

Simulation with different materials and tool model with distinct cutting edges

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An important advantage of the multi-Dexel-based additive process simulation is the ability to combine this method directly with the subsequent cutting process simulation. Using a coherent discretization model (multi-Dexel-model) for additive and subtractive process simulations allows an integrated digital process chain for hybrid or combined manufacturing (Fig. 11). This makes the approach ideal for the repair process of blades, whereby the influence of material deposition on the recontouring process can be investigated.

Fig. 11
Three labeled illustrations with the labels, a, material deposition at the top of triangulated blade model, b, tool model, and, c, recontoured area.

Simulation results: a triangulated blade model with material deposition, b geometric simulation of recontouring, c recontoured blade model after simulation

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In respect to the following recontouring process, taking technological aspects into account, a higher material removal rate generally leads to higher process forces, and thus, to both higher mold defects as a result of displacement and increased tool wear. For the planning of the material deposition process, two goals can be stated which are building a trade-off. On one hand, a minimum material allowance should be planned in order to keep the material removal rate during recontouring as low as possible to reduce process forces (Fig. 11). On the other hand, the material allowance should be kept high enough to ensure a defect free manufacturing of the target geometry (Fig. 9). For the generation of knowledge about the influence of the material deposition on the machining process, simulation experiments were carried out. The influence of the material deposition geometry on the material removal rate was analyzed for the recontouring of four different weald seam widths (Fig. 12). Thereby, the 5-axis tool paths were generated individually for the considered blade model with the adaptable process planning method with a line width br of 0.3 mm.

Fig. 12
A line graph of material removal rate versus time. b s equals 1.4, 1.8, 2.2, and 2.6 start at (0, 0) and follow a pattern of curving upward and going back to 0 rate, with b s equals 2.6 the highest peak around (10, 15). Below are parameter values.

Material removal rate during the recontouring process for different weld seam widths

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The twelve distinct peaks of the material removal rate along the process time are corresponding to the twelve planes of the tool path. The first path curve is at a height z = 56.1 mm, and thus slightly higher than the maximum of the material deposition. As a result, the tool is not engaged at the beginning of the first path and only begins to remove material in the area of the leading edge. This leads to a sudden increase in the material removal rate at the beginning. This is also the reason for the high maximum material removal rate of the first and second tool path curves.

In all paths, part of the material of the next paths is removed. This can be traced back to the diameter of the tool d = 3 mm. The larger the tool diameter and the larger the depth of cut ap, the larger the area that is machined. As a result, the remaining material in the following paths decreases which leads to a steady decrease of the material removal rate. It can be observed, that the material removal rate is quite low in the last two paths. The slight irregularities in the material removal rate are due to minor deviations in the creation of the tool path which are resulting from the cooling holes.

Moreover, a clear difference in the material removal rate between the four weld seam widths can be recognized in the first eight paths. The generated knowledge can be used for the determination of the ideal material allowance and enhances the efficient planning of the deposition process.

3.3 Influence of the Process Parameters on the Main Residual Stresses

It is known from the literature that the welding process causes tensile residual stresses on the surface and inside the component due to the cooling or phase transformations (Dattoma et al. 2006; Zain-ul Abdeina et al. 2009). However, the interactions with the introduced residual stresses due to recontouring are unknown or neglected (Dattoma et al. 2006). For this reason, the influence of the process parameters of the recontouring process on the superficial residual stresses was investigated on Ti6Al4V in the first founding period, cf. Figure 13 (Nespor 2015).

Fig. 13
A histogram of the effects on superficial residual stress versus process parameters. The highest and lowest residual stress in feed direction and in step over direction are at feed per tooth and tilt angle, and edge radius, respectively.

Influence of the process parameters on the superficial residual stresses (Nespor 2015)

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The factor with the highest significance on the superficial residual stresses is the cutting edge rounding rβ of the tool, whose effect is about five times higher than for all factors. This means that a cutting edge rounding of rβ = 30 μm always shifts the residual stresses towards compression by about Δσ ≈ 200 MPa, compared to a work-sharp tool. The factors cutting speed vc, depth of cut ap, down and up cut, clearance angle α, and rake angle γ show no significant influence on the residual stresses. Furthermore, the tooth per feed fz, the step over br, and the lead angle λ have an influence on the residual stresses, which is, however, significantly lower than the cutting edge rounding.

For this reason, the effect of the cutting edge rounding is considered in particular below. In Fig. 14a), the cutting edge rounding rβ is plotted against the step over br and in Fig. 14b) against the tooth per feed fz. The curves of the residual stresses σ1 under variation of fz, br, and rβ are similar. With an increase of the tooth per feed fz or the step over br, the residual stresses close to the surface shift slightly in the direction of tension. Further, when the cutting edge rounding rβ is increased, the compressive residual stresses increase and reach a minimum at about rβ ≈ 30 μm. By further increasing the cutting edge rounding rβ, the residual compressive stresses at the surface decrease again. The residual stress minimum is for the work-sharp cutting edges and rounded tools up to rβ ≈ 30 μm directly on the workpiece surface. The recommended cutting edge rounding for industrial use is therefore between 30 and 40 μm. The tooth per feed fz and the step over br should be selected as small as possible depending on the required productivity to achieve residual compressive stresses.

Fig. 14
Two area graphs of, a, step over versus and, b, feed per teeth versus cutting edge rounding at lambda equals 40 degrees, f x equals 0.20 millimeters and b r equals 0.2 millimeters, respectively. The maximum residual stresses are in between 30 and 30. Below are ball end milling parameter values.

Influence of the cutting edge rounding on the superficial residual stresses (Nespor 2015)

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The results showed that the process parameters have a significant influence on the residual compressive stresses. With this knowledge, the process can be controlled regarding higher residual compressive stresses which lead to positive material properties (Nespor 2015). In contrast, residual tensile stresses have a negative impact since they can lead to part distortion, especially for thin-walled titanium workpieces such as compressor blades. For this purpose, in the second funding period, a novel method for the compensation of part distortions within process planning for recontouring of thin walled workpieces was developed. The technique includes an optimization of tool angles in 5-axis recontouring. It is based on the recontouring areas as well as the simulated surface-generating cut volume (SGCV). The second part of the method relates to the safe implementation of the tool angles in an automatic tool path modification. The recontouring of two blades shows that the method allows a compensation of part distortion of 21% compared to a conventional process. Currently, the method is based on the equilibrium of internal loads (Böß et al. 2019).

3.4 Prediction of the Workpiece Surface

In addition to the residual stresses, the resulting workpiece surface is also of great significance in recontouring. When machining with ball-end cutters, burr formation also plays a decisive role. For this purpose, a new approach for the prediction of burr formation in 5-axis ball end milling was investigated in the second and third funding periods by applying an MRS considering the micro geometry dependent minimum chip thickness. Therefore, an existing MRS environment, which is able to include dynamic tool deflection based on the tool engagement, was extended by the theory of the plastically deformed volume Qe, which is penetrated by the cutting edge with an active chip thickness below the minimum chip thickness. Using this theory, multiple cutting processes with different tool orientations and process parameters were investigated and the occurring surface defects are correlated with the previously determined volume Qe.

To consider the workpiece surface generation effects in process planning, a time-discrete MRS, which uses a multi-Dexel model to discretize the workpiece, was applied. The MRS is described in (Denkena et al. 2019). The Dexel resolution used is approximately 1 µm/Dexel in each direction. The geometries of the rake and flank faces of the tool were derived from a measurement of the tool geometry using the Alicona Infinite Focus G5. The rake and flank faces of the two fluted cemented carbide tools were extracted from the measured geometry and modelled discretely using quadrilaterals with edge lengths of the elements of dS = 0.1 mm (Fig. 15, left). By using the force model of Engin and Altintas (2011) and the consideration of the structural dynamic of the machine tool and workpiece, the simulation is capable of considering the dynamic behaviour for stable and unstable processes as shown in (Denkena et al. 2020). Moreover, the simulation can include the influence of the cutting edge roughness on the surface generation for a more accurate prediction of the milled surface. An example of the surface prediction using the MRS is shown in Fig. 15. Figure 15a) shows the surface of the milling experiment. With the simulation the surface topography can be accurately predicted by taking into account runout error and dynamic displacement of the tool, Fig. 15b). By additionally including the cutting edge roughness in the tool model of the simulation, the characteristic grooves of the workpiece surface can be displayed, Fig. 15c). Overall, it can be stated that the simulation is a suitable tool for the prediction of the milled surface topography of 5-axis ball end milling with arbitrary geometric engagement situations.

Fig. 15
6 parts. Left, a diagram of tool and workpiece modeling displays discretized tool, discretization using quadrilaterals, and discretized workpiece of multidexel model. Right, a diagram displays the comparison of experiment, dynamic simulation without and with cutting edge roughness.

Dynamic simulation of the workpiece surface

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Furthermore, burrs can also form on the surface of the workpiece during machining. For the prediction of burr formation, it is important to know which factors have an influence on the development of burr formation and under which conditions burrs may appear. Experimental studies were carried out to investigate burr formation. The tool orientation, the tooth per feed fz, and the strategy of up and down milling were varied, thus changing the engagement conditions. The resulting generated surfaces were then evaluated by means of video microscopy. The topographies show that the tooth per feed has a significant influence on the formation of the burr on the milling grooves. Thus, at fz = 0.06 mm, strong burr formation is evident, while at fz = 0.12 mm, burr formation is significantly reduced. If a tooth per feed of fz = 0.18 mm is used, burr formation is no longer noticeable (Fig. 16).

Fig. 16
2 parts. Above, 3 diagrams display the burr visibility at f z equals, a, 0.06, b, 0.12, and, c, 0.18 millimeters. Below are ball end milling parameters.

Burr as a function of the tooth feed (Muecke 2020)

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Figure 17 shows video microscope images of surface topographies for three different lead angles λ = 15°, λ = 30° and λ = 45°. For the cutting edge rounding SS = 15 µm, a slight burr is visible on the surface at a lead angle of λ = 15°, despite the use of a larger tooth feed of fz = 0.21 mm compared to the result shown above in Fig. 16 with fz = 0.18 mm. With increasing lead angle, λ = 30°, no burr can be observed in this example. For SS = 30 µm, strong burr formation can be seen at the edges of the milling grooves at both λ = 15° and λ = 30°. If the lead angle is increased to λ = 45°, the burr can be significantly reduced. After considering all angle combinations and this example, it becomes clear that no universal recommendation can be derived for the choice of tool orientation to reduce burr. With regard to the selected strategy, down or up milling, no general statement can be made either, because there are interactions of the strategy with the tool orientation with regard to the down or up milling parts of the process. At this point, it can only be said that burr formation increases with increased cutting edge rounding and is influenced by the tool orientation and the strategy. Therefore, for the process design to avoid burrs, an individual investigation of the respective process parameter combination is necessary when rounded tools are used. Accordingly, knowledge about the causes of burr formation is required, for which the material removal simulation to be developed is used.

Fig. 17
Six diagrams display the burr visibility at S equals 15 and 30 micrometers, and lambda equals 15, 30, and 45 degrees. Below are ball end milling parameters.

Burr as a function of the cutting edge rounding and the tool orientation (Muecke 2020)

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Plastic surface deformations such as burr formation emerge before the chip formation begins and material is ploughed underneath the cutting edge rounding (Wyen 2011). Therefore, knowledge about the minimum chip thickness depending on the cutting edge rounding is needed. Further, for ball end milling, it has to be taken into account that the final surface is generated only at a small portion of the tooth engagement. Consequently, only those periods of the tooth engagement are of interest for burr formation where the final surface is generated. To determine this specific time interval, a method was developed that allows the calculation of the surface-generating periods using the MRS. The method is explained in detail in (Denkena et al. 2021). With the help of this method it was possible to find out that the time of the final surface generation is depicted within one tooth engagement and correlated with the timely progression of the maximum undeformed chip thickness hmax. The surface generation period only depends on br and vc and is independent of fz. Significant burr formation is expected to happen from the beginning of the tooth engagement up to the point where the minimum chip thickness is exceeded and the chip formation begins. The point tsp (Fig. 18) marks the intersection between the maximum undeformed chip thickness in the process and the minimum chip thickness. It has to be mentioned that the maximum undeformed chip thickness during the time of the surface generation is not necessarily reached by a cutting edge element that generates the final surface. However, for the considered application this simplification is valid due to the low depth of cut and the orientation of the helix angle.

Fig. 18
A diagram displays material removal simulation setup. Machines volume during one tool revolution, workpiece, tool, burr, cutting tooth at time t s p, h min, A t s p, and engaged cutting elements are labeled. Q e equals integral of A t s p with respect to d phi on an interval 0 to phi.

Determination of the burr with the help of the material removal simulation (Denkena et al. 2021)

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Therefore, during the time of the surface generation, most of the engaged cutting elements contribute to the surface generation. For small cutting edge roundings SS, tsp is reached soon after the tooth entry. With increasing SS and decreasing feed per tooth fz the intersection point is reached later in the process. With large cutting edge roundings, the minimum chip thickness is exceeded after the surface generation. Therefore, no chip formation occurs during the surface generation and this often results in burr formation. To evaluate the occurrence of burrs based on a characteristic value, the plastically deformed volume Qe is introduced. This value represents the engagement volume of the tooth up to the beginning of chip formation. As visualized in Fig. 18, Qe can be calculated by integrating the uncut chip area A from the beginning of surface generation (t = 0) to the point, where the minimum chip thickness is reached (t = tsp). For this calculation, a MRS can be utilized. A larger value of Qe correlates with a higher volume portion deformed underneath the flank face.

To verify the use of Qe for the prediction of plastic surface defects, Qe was calculated with the MRS for experimental cases. The calculated Qe and the corresponding experimental surfaces are shown in Fig. 19.

Fig. 19
Eight diagrams display the machined surfaces at S equals 30 micrometers, Q e equals 179, 127, 63, and 39, and S equals 5 micrometers, 9.1, 3.9, 2.5, and 0.8. The values of Q e are times 10 to the fourth power micrometer cube.

Machined surfaces and the resulting Qe (Denkena et al. 2021)

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An increase in the feed per tooth results in decreasing values of Qe because the minimum chip thickness is exceeded earlier during the cut. Furthermore, the applied variation in tool orientation (λ, t) influences Qe based on the kinematics and the resulting temporal progression of the chip cross-section. The most significant influencing factor is the applied cutting edge rounding size, as it influences the value of the minimum chip thickness itself. The depicted surface plots show a trend of increasing surface defects with increasing Qe. However, the resulting surface debris, which deviates from the deterministic structure induced by the milling kinematics, is not homogenously distributed over the surface or within one feed track. A reason for the inhomogeneous nature of the remaining burrs on the surface is on one hand the interaction between subsequent milling tracks. Thereby, the milling tool will remove potential burrs from the previous milling track. On the other hand, all specimens were subject to an ultrasonic cleaning bath before the surface investigations. Taking into account this considerations, burrs are also influenced by stochastic effects such as local differences in workpiece microstructure.

4 Conclusions

With regard to the requirements for the resulting workpiece surface, it was possible to determine that residual compressive stresses can be achieved with the use of ball end mills. Here it could also be shown that a medium cutting edge rounding, low feed per tooth, and low step-over are advantageous. In order to achieve a low surface roughness, a large cutting edge rounding, low feed per tooth and low step-over should be used. Furthermore, burr formation should also be avoided. Small cutting edge roundings, high feed per tooth, and larger lead and tilt angle are suitable for this purpose. Here it becomes clear that a compromise must be made for the choice of the process parameters. With the help of the knowledge generated, however, a process with reduced burr formation and good surface quality can be designed, in which high residual compressive stresses are generated.

Furthermore, during the entire funding period, a Dexel-based material simulation method was developed and parametrized by means of welding experiments. With the method, it is possible to predict the geometry of the material deposition process. With the help of the investigation carried out the Dexel-based material deposition simulation allowed the investigation of the influence of the material allowance on the recontouring process in order to identify suitable process parameters. In addition, by means of the adaptive planning method, it is possible to generate the NC-code for the machining individually for each blade and in an automated way.