Dexterous Regeneration Cell

Abstract

Complex capital goods such as components from aircraft engines or gas and steam turbines usually have free-form geometry features, individual material deposits, and poor machining accessibility. The recontouring of these components requires increased machine and process flexibility. In sub-project B2, “Dexterous Regeneration Cell”, a dexterous milling repair cell was researched, representing a central component of the real regeneration path in the Collaborative Research Centre (CRC) 871. “Dexterousness” is understood as the ability to carry out a self-optimizing, best possible repair machining. The combination of advanced methods for process design, novel machine tool technologies and adaptive machining functionalities allows the reliable 5-axis recontouring of individual damage cases despite repair-specific variances, influences from upstream processes, and flexibility of the workpiece or tool. In this paper, a force model is created using artificial intelligence to determine variances. Further process knowledge is obtained to minimize shape deviations. Furthermore, the displacement in the recontouring process of turbine blades is carried out with the help of a magnetically guided spindle.

1 Introduction

The repair and maintenance of aircraft engines are safety-related but also of economic interest to the airlines and engine manufacturers. High-value products like aircraft engines require effective maintenance, repair, and overhaul services to increase economic sustainability and efficiency (Uhlmann et al. 2013). Compressor and turbine blades made from Ti–6Al–4V or Inconel 718 are an example of products for which a repair is highly motivated. Because of the complex geometry and their integral design, these repair processes are a challenging task and differ from new part production (Denkena et al. 2015). A typical repair process chain for blades consists of four phases, namely pretreatment, material deposit, recontouring and post-treatment (Eberlein 2007; Kelbassa et al. 2002).

By recontouring, excess material that was deposited on the part by welding or soldering is removed. This process is challenging due to freely formed geometric features and individual material deposits. Therefore, it is often executed by skilled workers with handheld tools. In addition to the need for component-specific process planning (SP C1), form deviations due to cutting force are the key challenge for automated recontouring on milling machines (Denkena et al. 2021). Therefore, the aim of this sub-project is the process-safe 5-axis recontouring of individual damage cases despite repair-specific variances, influences from preceding processes, and compliances of the workpiece and tool.

Every milling process is associated with forces due to the material separation at the cutting edges. These process forces act in the contact zone between the milling cutter and the workpiece and deform all components in the flow of forces. The tool and the workpiece are deformed, including the machine tool structure, which closes the force flow between the tool and the workpiece (Fig. 1). The deflection of the tool and the workpiece leads to a shift in the Tool Center Point (TCP) and results in a deviation of the finished workpiece shape from the nominal shape.

Fig. 1

Tool, workpiece, and machine tool deflection in milling processes

The shape deviations caused by displacement are minimized by adequately adapting the process parameters. In addition, adaptive machining approaches can be used to reduce errors. The state of the art for these two areas is briefly outlined in the sections below.

1.1 Modelling of Milling Processes, Process Force Models and Process Design

For predictive error avoidance and, therefore, for process planning, a high level of knowledge about the milling process is required. Following the material deposit, the excess material must be removed. The removal is done via milling or grinding. For the repair of compressor or turbine blades, 5-axis ball end milling is often used to restore the complex shape (Eberlein 2007; Gao et al. 2008). Furthermore, in addition to high geometric accuracy and low surface roughness, compressive residual stresses in the component surface can be achieved with ball end milling tools (Denkena et al. 2014b). Subsequently, post treatment processes such as shot peening can be used to improve surface integrity. As already mentioned, the machining of blades poses some challenges, in particular, shape deviations, which are primarily caused by the deflection of the workpiece and tool during machining. The low Young’s modulus of titanium as well as Inconel and wall thicknesses less than 2 mm may result in vibrations. Adjusted process parameters and special clamping systems are therefore often necessary for a successful recontouring. In principle, it is very important to avoid vibrations in the recontouring process of compressor and turbine blades due to the long projection length of the blades. In addition, the recontouring of these components also involves different material properties between the base material and the deposited material, which can lead to local variances in the milling process. This also poses a special challenge to the recontouring process. Using 5-axis processes, selecting an appropriate tool orientation during process planning can help avoid vibrations and increase surface quality (Ozturk et al. 2009). There are a few studies on the influence of tool orientation on process dynamics in 5-axis milling. For example, Ozturk and Budak (2007) developed a model to predict cutting forces and investigated the effect of tool inclination on chatter stability during 5-axis ball end milling. Tuysuz et al. (2013) extended the model by considering the tool indentation effect. Layegh et al. (2015) analyzed the effect of tool orientation during the 5-axis ball end milling of flexible parts. They proposed mechanics-based tool posture maps, which reveal part deflection and cutting torque values depending on the inclination angle. All these studies have their focus on machining new parts and do not specifically address the recontouring process.

Thus, boundary conditions like different material properties between the deposited material and the base material are not considered. In this respect, it has already been shown along with the CRC 871 that the angle of attack during the recontouring of turbine blades has a significant influence on the process stability (Denkena et al. 2016).

In conjunction with 5-axis ball end milling in the recontouring process, there are many influencing factors on the resulting component quality. In addition to the process parameters, the tool geometry, the machine rigidity, and the previous material deposit process also influence the surface quality and the existing process forces (Denkena et al. 2020; Engin and Altintas 2011). Variances in the recontouring process can be determined by deviations in the process forces. Therefore, the expected process forces must be continuously compared with the real process forces. The difference between the predicted and the measured process forces can then be used to determine local variances in the workpiece properties. For process force prediction, Machine Learning (ML) can be applied.

The use of ML in machining is already widespread. Many researchers have successfully applied ML techniques in studying various manufacturing problems. In Cho et al. (2005), the authors used Support Vector Machines (SVMs) to provide a detection system which is able to define process anomalies during a milling process based on power consumption and process forces. In their investigations they show that, compared to a multilinear regression model, the Support Vector Regression (SVR) model performs with higher accuracy. They concluded that SVR models can lead to a reduction in machine downtime and thus to a reduction in production costs. Hashemitaheri et al. (2020) compared the SVR and the Gaussian Process Regression (GPR) for the prediction of cutting forces and maximum tool temperature. They observed that both SVR and GPR models predict these parameters accurately although the former is marginally better than the latter. Further, Jurkovic et al. (2018) compared three different ML models to predict cutting parameters in a high-speed turning process. They used SVR, polynomial (quadratic) regression and Artificial Neural Networks (ANNs) based on input parameters of cutting forces, surface roughness, and tool life. In their study, the SVR and polynomial regression models show a higher accuracy in the prediction than the ANN model. In addition, Charalampous (2020) used four ML models to predict the cutting forces in milling AISI 4140 QT. He studied the accuracy of SVR, ANN, Polynomial Regressor and Random Forest. His results show the best performance was recorded from the SVR, followed by the ANN, the Polynomial Regressor, and lastly the Random Forest model. He reached an accuracy of about 96% with the SVR model. Krizek et al. (2007) applied the ML models response surface methodology, evolutionary algorithms, SVR and ANN to their data sets. They aimed to find the best approach to determine the cutting force based on the input variables spindle speed, feed rate, and depth of cut. The best percent deviation was reached by the SVR model. In summary, ML with different models is already being used to predict the process forces in cutting processes. However, it is not yet possible to identify the most suitable model for all processes. In addition, there is still no knowledge about the use of ML for process force prediction in the ball end milling of Inconel and titanium.

1.2 Adaptive Machining for Reduced Shape Deviations

Since repair cases are individual and underlie variances, a priori information from offline process simulations also shows a certain degree of uncertainty. This does not question their suitability for general process design but makes them insufficient for the adaptation of, e.g., a specific toolpath. On the one hand adaptive machining approaches react to the process forces in realtime (online), on the other hand they obtain the latest data from the running process. Therefore, they can make short-term adaptions and deal with unpredictable effects like tool wear or variations in the material properties.

Adaptive machining approaches for reduced shape deviations can be classified according to their working principle into process force restriction and deflection compensation. The process forces are usually restricted by reducing the feed rate in an automatic control loop. This way, productivity is sacrificed for accuracy (Dittrich et al. 2019; Denkena and Boujnah 2018). Furthermore, the displacement cannot be fully avoided since chip formation is always accompanied by forces and the structural stiffness of the machining setup is always limited. The compensation of deflection is a different approach. It accepts the deformation of the machine tool components and continuously counteracts the deflection by corrective movements. Thus, the shape error can be reduced without any loss of productivity (Boujnah 2019). Reactive deflection compensation has already been investigated for various areas of application. Usually, the displacement between the tool and the workpiece is determined indirectly. The process forces are measured and the deflections of tool or workpiece are calculated based on a compliance model. The necessary compensation movement is then carried out either by the NC axes of the machine tool or by additional actuators.

However, Brecher et al. (2019) and Boujnah (2019) have shown that control delays limit the effect of reactive deflection compensation when abrupt changes in the process forces occur. Since signal delays cannot be completely avoided, attempts were made to overcome this issue with an online force prediction. Hähn and Weigold (2020) combined a reactive compensation with an offline process simulation to reduce errors due to predictable force changes in Robot machining. Altintas (2011) has described an adaptive generalized predictive control of the process forces in milling. To avoid high peak forces, Stemmler et al. (2016) proposed a model predictive control (MPC) approach for the feed rate. For deflection compensation, a comparable approach is not yet known. Although a short-term force prediction for online compensation was considered (Hähn and Weigold 2020), it has not been implemented and researched yet. Predictive and anticipatory approaches for deflection compensation were also investigated within the sub-project B2 of CRC 871. These approaches have already been successfully implemented in flank milling processes (Mücke 2020; Denkena et al. 2021).

1.3 Approach

In the sub-project B2, “Dexterous Regeneration Cell” a dexterous repair cell is being researched, representing a central component of the physical regeneration path. In this project, new types of machines and cutting technologies were developed. The aim is the process-reliable 5-axis recontouring of individual damage cases despite repair-specific variances, influences from preceding processes and deflection of the workpiece and tool. The approach to reach this aim is a 2-step solution with a predictive error avoidance and reactive error compensation as shown in Fig. 2. Predictive error avoidance is carried out as part of the process planning. The results of process simulations are used to design processes that result in the lowest possible shape deviations. This includes planning the individual tool path, the process parameters, the process kinematics (tool orientation) and the force-stiffness alignment.

Fig. 2

Two-step solution for the reduction of shape deviations

Since the process forces and thus the deflection cannot be completely avoided, the remaining deflection is compensated during machining in a second step. For this reactive error compensation, the process forces are recorded, converted into compensation values and superimposed on the position of the tool by an electromagnetic guide, which serves as an additional actuator. This technology was developed and investigated throughout the CRC 871 regarding its characteristics, its behavior in milling processes and its additional functionalities (Denkena et al. 2014a, b, 2016; Flöter 2017). The predictive error avoidance is explained in Sects. 2 (Modelling of process forces using Machine Learning) and 3 (Process design to minimize shape deviation). Further, Sect. 4 (Electromagnetic guide system for adaptive machining) introduces the regeneration cell with the electromagnetic guide, and the following Sects. 5 (Deflection compensation in flank milling) and 6 (Deflection compensation in 5-axis recontouring processes) discuss the reactive error compensation.

2 Modelling of Process Forces Using Machine Learning

The tool deflection can be determined with the help of the process forces. For this reason, knowledge about the existing process forces at different process parameters during the recontouring process is necessary. Therefore, four ML models were used for predicting process forces during 5-axis ball end milling under stable cutting conditions. The main objective is to identify a suitable ML model that accurately predicts the process forces, thereby enabling variance detection. For this purpose, the methods SVR, ANN, and the Automatic Machine Learning models Auto_ML and Tpot were used. The required training data was generated by varying the process parameters during the 5-axis ball end milling of Inconel. All milling investigations were carried out on a DMG Mori Milltap 700 5-axis CNC milling center. The ball end mills used are provided by SECO and have a diameter of 6 mm and six teeth. The cutting tools have a helix angle of 38°, a cutting edge rounding $\bar {\varvec{S}}$ = 15 μm and a TiAlN coating. The DMG Mori Lasertec 65 3D DED was used to manufacture the workpieces. Rectangles were welded onto a base plate made of Inconel 718. Powder PWA 1480 with a powder diameter of 60–105 µm was used for the laser build-up welding process. A power of P = 400 W and a feed of f_l = 800 mm/min as well as a delivery rate of f_p = 2 g/min were selected. The manufactured rectangles have a length of 40 mm, a width of 30 mm, and a height of 3 mm. After the welding process, the rectangles were face-milled to ensure equal infeed. The corresponding test setup for the investigations is shown in Fig. 3.

Fig. 3

Experimental setup for data collection of the ML models

A Kistler-type 9257A three-axis piezoelectric dynamometer was used to measure the process forces during the milling process. The measurement device cooperates with one Kistler-type 5011 signal amplifier per axis. Additionally, the dynamometer was connected with a LabVIEW data acquisition system in which the force signals were acquired and transformed into a numerical format. The cutting procedures were performed in dry milling without any applied cooling liquid. The reason for choosing one of the dry machining processes is a trend towards environmentally friendly manufacturing technology, as this avoids pollution from cutting fluids and reduces the overall cost.

During the cutting tests, the process parameters step over b_r, depth of cut a_p, feed per tooth f_z, lead angle λ and tilt angle τ were varied. The cutting speed v_c was held constant at 30 m/min during all investigations. A total of 258 process parameter combinations were carried out with two repetition tests each. One test consisted of machining a complete path with a length of 40 mm on the welded material. To keep the influence of tool wear low, the number of paths a tool can machine at constant process parameters without significant changes in the process forces was determined in advance. After eleven paths, a significant increase in the process forces was observed. For this reason, each tool was used for nine paths. For the process parameters investigated, one cutting edge of the tool was always engaged in the workpiece. This keeps the measured forces at a constant level. Therefore, the mean value of the process forces F_x, F_y and F_z is used to evaluate the process forces over the engagement range along the path. For the analysis of the prediction accuracy of the respective ML models, 10 milling tests of the 258 performed tests were extracted. These tests were excluded from the training step and utilized for the validation phase of the developed ML models. Further two criteria, Mean Absolute Error (MAE) and Mean Relative Error (MRE) were used to evaluate the forecasting efficiency. These criteria are calculated using the following Eqs. (1) and (2):

$$MAE=\frac{1}{N}\sum _{k=1}^{N}\left|{y}_{k}-{\widehat{y}}_{k}\right|$$

(1)

$$MRE=\frac{1}{N}\sum _{k=1}^{N}\frac{\left|{y}_{k}-{\widehat{y}}_{k}\right|}{{y}_{k}}$$

(2)

where N is the total number of data points, y_k and ${\widehat{y}}_{k}$ represent the ith observation and models prediction, respectively.

A total of four methods were applied: Support Vector Regression, Artificial Neural Networks and the Automatic Machine Learning models Auto_ML and Tpot. It is observed that all four models generally provide predictions accurately. Further, Fig. 4 demonstrates that the Automatic Machine Learning models Auto_ML and Tpot achieve higher accuracy in predicting the forces with a small data size available in this investigation. With an average MRE of 2.2%, Tpot has an MRE that is at least 70% lower than that of the ML methods SVR and ANN. The developed methods allow the expected process forces to be continuously compared with the real process forces. This means that the difference between the predicted and measured process forces can be used to identify local variances in the workpiece properties during machining.

Fig. 4

Comparison of the investigated ML methods

With the help of the ML model the generated variances in the milling process are detected. Variances can occur during the welding process. To investigate the effects, the process parameters power (P = 400/800/1,200 W) and feed (f_l = 400/800/1,200 mm/min) were each varied in three steps. The hardnesses of these samples were then measured with the Struers Duramin measuring device according to DIN EN ISO 6507-1. Table 1 shows the resulting hardness values for the respective process parameter combinations of the welding process. The hardness values are averaged from six randomly distributed indentations per surface. It is noticeable that the hardness of the workpieces decreases with an increase in power P of the welding process. Furthermore, it can be concluded that the feed rate also has a significant influence on the workpiece hardness. Increasing the feed rate in the build-up welding process also reduces the hardness of the workpiece.

Table 1 Differences in hardness after the welding process

In the next step, the influence of the hardness on the process forces was analyzed. For this purpose, milling tests were carried out with six different hardnesses for one process parameter combination. The hardness 667 HV1 was generated with welding process parameters used previously in this section (P = 400, f_l = 800 mm/min, f_p = 2 g/min).

In Fig. 5, it is apparent that the forces generally increase with an increase in hardness. However, it can also be seen that not all force components increase equally. The force F_x does not change significantly with values between 583 and 635 HV1, as can be seen in Fig. 5. Only for hardnesses 667 HV1 and higher is there an increase in this force component as well. On average, the force in the milling process increases by 42.5% from hardness of 583 HV1 to a hardness of 713 HV1. The smallest increase in force is 4.4% for the force component F_x. An increase in hardness of 20% leads to an average increase in force of 42.5% for the process parameters used here. A deviation in hardness in the build-up welding process consequently leads to deviations in the process forces. These can be determined with the ML model. If a deviation of 10% of the predicted process forces compared to the real process forces occurs, the machining process is stopped. Since the greatest deviation of these process parameters is seen in the process force F_y at the different hardnesses, a tolerance of 10% is set along with this force component. In this way, slight process force fluctuations are not detected, but larger deviations due to the hardness differences are recognized (Fig. 5). At lower hardnesses, the process forces are outside the tolerance and can thus be recorded. This allows local variances in the process to be detected and possible errors in the recontouring process to be avoided.

Fig. 5

Influence of the hardness on the process force

Another possible cause for deviations in the process forces during milling is tool wear. The cutting tools can reach an advanced state of wear during their use. To determine the influence of wear on the resulting process forces, a flank wear width of 100 µm was provoked on the tools. These were also used for three different process parameters of the cutting process (Fig. 6). For all process parameters investigated, the process force increases significantly when the worn tools are used. Parameter sets 1 and 3 exhibit a similarly large increase in the force of 29.1% and 28.6%, respectively. Parameter set 2 exhibits a smaller average increase in the force of 16.7%. The force components also increase to different extents here. For example, the force component F_x only shows an increase of 4.8% for the second parameter set. To determine and recognize the deviation, all three force components of the cutting process must be considered. This means that a deviation from the predicted process forces in the real process can be attributed to a worn tool or deviations in the welding process. Thus, local variances in the recontouring process can be detected early and major errors in the recontouring chain can be avoided.

Fig. 6

Forces when using worn tools

3 Process Design to Minimize Shape Deviations

A significant factor for shape deviations during ball end milling is, in addition to the chipping and the occurring vibration of the tool-workpiece system, especially the process kinematics. In recontouring, changing the process kinematics offers the potential for reducing shape deviation. The causes of the shape deviations were investigated during the entire duration of CRC 871 (Denkena and Flöter 2012; Nespor 2015). With the knowledge gained about the causes of shape deviations, the process design can be carried out to minimize the shape deviations, as shown in Fig. 7. The aim was to determine a combination of process parameters that result in low shape deviations and increased productivity at the same time. For a small shape deviation in the transition area between the weld and the base material, a small step over, a small tool radius, a small cutting edge rounding and small contact angles should therefore be selected. To avoid a high step height due to displacement, all process parameters except for the cutting speed should be minimized as far as possible.

Fig. 7

Causes of the shape deviations and recommendations for minimization (Mücke 2020)

The measured topography of the reference process considered is shown in Fig. 8. A sharp tool was used to reduce the process force-induced displacements due to the long toolholder. For these investigations, a weld seam with a width of 10 mm and height of 1 mm was applied to a base plate, which was subsequently machined into individual paths. The target roughness in this example was set to f_z = b_r = 0.5 mm. This results in an average step height of ∆H = 32.2 µm and a maximum step height of ∆H_max = 63.2 µm with a roughness of Sz = 25.5 µm. In addition, concentricity errors, process kinematics and the elastic chip thickness springback were not compensated for, resulting in an error at the transition area of ≈10 µm. The material removal rate is used to evaluate productivity. The material removal rate at maximum cutting depth a_p = 0.5 mm for the reference process is Q_w = 318.3 mm³/min. To maintain the kinematic roughness of the process, i.e. f_z = b_r = 0.5 mm = const., the recontouring process was optimized with the help of process simulation. To consider the workpiece surface generation effects in process planning, a time discrete material removal simulation MRS, which uses a multi-dexel model to discretize the workpiece, was applied (Denkena et al. 2019). For this purpose, the lead and tilt angles were first reduced in accordance with the recommendations shown in Fig. 8. In addition, a variation of the cutting speed was carried out to identify a range with the highest possible productivity with given process stability and minimal shape deviations. Furthermore, the strategy for up milling was adapted. In addition, the runout error, the process kinematics, and the elastic chip thickness springback were considered for a minimum error at the transition area. The result of the simulation to improve the process is shown in the middle of Fig. 8. The corresponding experimental result is shown below.

Fig. 8

Comparison of the topographies of the reference and the improved process (Mücke 2020)

By comparing the topographies of the improved process with the topography of the reference process and the corresponding profile lines (Fig. 9), the benefit of the virtual improvement of the process becomes clear. As can be seen from the profile lines, the error at the transition area is prevented by considering the runout error, the process kinematics and the elastic chip thickness recovery. This allows a smooth transition between the base material and the recontoured area. The maximum step height of the reference process was reduced by 86% from ∆H_max = 60.7 µm to ∆H_max = 8.5 µm. Likewise, the average step height was reduced from originally ∆H = 31.0 µm to ∆H = 0.3 µm, and thus, by 99%. The predicted parameters from the simulation are in close accordance with the parameters of the actual process. In addition, the shape deviations described by the roughness parameters Sz and Sa were also significantly reduced. Thus, the maximum height of the roughness Sz was reduced by 31%, while the mean arithmetic height Sa of ≈2 µm remained unchanged. These parameters also match the measurement results of the experimental investigation. Because minimal shape deviations were achieved in this example at a higher cutting speed v_c = 120 m/min, productivity was also increased by 300%. The material removal rate is Q_w = 954.75 mm³/min.

Fig. 9

Evaluation of the minimization of the shape deviations (Mücke 2020)

The results show that a significant reduction in shape deviations can be achieved by applying a novel simulation-based process design. The simulation allows for the first time to take into account the knowledge about chip formation and the dynamics of the process. This allows a process-safe recontouring of individual damage cases despite repair-specific variances. However, the process design for complex components is restricted by further constraints like accessibility. Therefore, the deflection of the workpiece and tool should be additionally compensated during machining, as shown in the next sections.

4 Electromagnetic Guide System for Adaptive Machining

The “dexterous regeneration cell” is based on the 5-axis milling machine prototype shown in Fig. 10. The workpiece is clamped on a rotary swivel table with A and C axes, which are mounted onto the Y-axis. The X and Z axes are arranged on the tool side. The special feature of this machine tool is the electromagnetic guide of the Z-axis. Eight electromagnets with a maximum force capacity of 15 kN each are arranged on the Z-axis slide. By appropriate control of the magnetic forces F₁, …, F₈, the slide hovers completely contactless in its housing. In addition to the translatory movement of the Z-Axis, it can also be precisely positioned in 5 degrees of freedom (x, y, φ, ψ, θ) by the electromagnetic guide. While the five NC axes (X, Y, Z, A, C) of the machine tool are controlled by a standard NC control, the electromagnetic guidance is controlled by a separate industrial PC (IPC). The correction values for the deflection compensation are also calculated on the IPC.

Fig. 10

Dexterous regeneration cell with electromagnetic guide (Denkena et al. 2021)

The advantage of the magnetic guide compared to the NC axes for deflection compensation is the high positioning dynamics and the short reaction time. The process forces are measured using a Kistler 9257B dynamometer on the machine table and are then fed to the compensation algorithm via a charge amplifier (Kistler 5015a) and an AD-converter (BECKHOFF EL3702) at a sample rate of 20 kHz. The calculation of the compensation set point takes place on the IPC within the PLC-cycle of 50 µs. For compensation using the NC axis, the actual set-point is transferred to the NC control via PROFIBUS, as depicted in Fig. 10. There, it is superimposed to the axis position within the interpolator. Alternatively, the compensation set point is directly used as a reference input for the state-space controller of the electromagnetic guide.

Figure 11 shows how fast a calculated compensation value can be executed. The reference signal for the position set-point is a step of 50 µm. The step response of the Y-axis stays within the 10% error band around the end value (25 µm) after 74.2 ms. The long delay is due to the signal transmission via the fieldbus and the signal processing within the NC control at an interpolation cycle of 8 ms. In contrast, the electromagnetic guide finishes the 50 µm step in about 11.9 ms, which corresponds to a positioning time reduction of 84%. This allows a faster compensation of variances. As a result, better surface quality can be achieved on the workpieces in the entire recontouring chain.

Fig. 11

Reaction time for position set-point step of 50 µm (Denkena et al. 2021)

5 Deflection Compensation in Flank Milling

The effect of the dynamic advantage of the magnetic guide over the NC axes was investigated for deflection compensation on the experimental setup presented in Fig. 12. A steel plate was clamped onto the dynamometer. The front flank was prepared with a step of 0.4 mm height and then face-milled with a 10 mm diameter end mill. The resulting flank profile was then measured with a skidless surface finish gauge (Mahr LD130 perthometer). The direction of movement of the milling cutter was the negative x-direction. The contour data depicted in the diagram was therefore generated from right to left. The geometric reference (y = 0 µm) for the measurement was derived from a reference surface of the prepared workpiece. In the experiment, the surface in front of the step was passed by the milling cutter without radial infeed. Under ideal conditions, no material would be removed from this surface since there would be no radial immersion. In reality, however, a slight material removal takes place, and the contour shows an undersize of about 5 µm.

Fig. 12

Flank milling experiment with abrupt change in the width of cut a_e

At the prepared step in the workpiece surface, the width of the cut a_e and the process forces increase abruptly, and the milling cutter is deflected. Without any compensation, a step of 38 µm remains in the measured contour after machining (blue contour plot). The other measurements show the contours that were created with deflection compensation activated. For the green contour plot, the compensation movement was carried out by the NC axes of the machine tool, and for the red one by the electromagnetic guide. In both cases, the compensation reacted with a delay to the increase in force, so that a significant contour deviation remained directly at the step transition. While the compensation by the NC axes reduced the error at the transition only insignificantly, the magnetic guide reacted much faster, so that the error could be reduced by 71%. These results show that reactive deflection compensation can reduce contour errors caused by static force components without any loss of productivity. This allows a reduction of the shape deviation in the entire recontouring process chain. However, since it is a causal process with a finite reaction time, corrective movement can only take place after a change in force has been detected. This time delay leads to significant errors in case of abrupt changes in the cutter engagement. The electromagnetic guide offers higher performance in comparison to the NC axis due to its shorter reaction times. This simple experiment was discussed in (Denkena et al. 2021) in more detail. Furthermore, an anticipatory approach for deflection compensation was proposed and investigated. This method reduces the error in the transition even further (Denkena et al. 2021).

6 Deflection Compensation in 5-Axis Recontouring Processes

In contrast to the previous, simple experiment, determining the compensation values for recontouring processes on real turbine blades is much more challenging. With rotary and tilting movements of the machine table during 5-axis simultaneous machining, the orientation of the workpiece coordinate system (WCS) is constantly changing concerning the machine coordinate system (MCS) (Fig. 13). While the forces are measured in the WCS, the positioning movements of the magnetic guide are specified in the MCS. Furthermore, the static weight force of the components on the dynamometer becomes a variable disturbance concerning the moving WCS. The current orientation must therefore be considered for the compensation. The following subparagraphs therefore discuss the information flow within the controller, the position-dependent compliance model of the workpiece and the results of the compensation in a recontouring process on a real turbine blade from a Rolls-Royce V2500 turbo fan engine.

Fig. 13

Setup for turbine blade recontouring

6.1 Information Flow

The entire information flow for deflection compensation is shown in Fig. 14. The NC control provides the set-points for the 5 NC axes following the planned toolpath. The raw signal $\overrightarrow{F}$_raw,WCS from the dynamometer was cleaned from the weight force component $m{\overrightarrow{g}_{WCS}}$ on the IPC and then used to calculate the deflections. The displacement of the workpiece ${\overrightarrow{\Delta}_{WP,WCS}}$ was calculated in the WCS and then transformed into the MCS. The displacement of the tool ${\overrightarrow{\Delta}_{T,MCS}}$ was calculated after transformation into the MCS. The tool and workpiece deflections were then superimposed and filtered in the MCS. Finally, they were applied to the magnetic guide as a correction value.

Fig. 14

Information flow

The transformation between the coordinate systems was done by rotation matrices that depend on the current axis angles of the A and C axes. The tool-side compliance at the ball end mill can be determined experimentally and was assumed to be approximately constant. The compliance of the workpiece depends strongly on the point of force application onto the blade. Therefore, a position-dependent compliance matrix is required to determine the deflection of the workpiece. This matrix is discussed in the next section.

6.2 Workpiece Compliance Model

The position-dependent compliances of the workpiece were determined in a finite element simulation. The reference coordinate system was located at the corner of the blade holder (Fig. 15). Using APDL scripting language, each node in the tip surface was successively defined as a load node and three load cases were simulated. A static load of F = 1 N was applied first in the x-, then in the y-, and finally in the z-direction. In the end, a result table contains the displacements (u, v, w) of the load nodes in all three spatial directions for each load direction (x, y, z). A node displacement in the x-direction due to a load in the y-direction is denoted as u_y, for example.

Fig. 15

Determination of the position-dependent workpiece compliance

A 3-by-3-compliance matrix with six independent entries can then be constructed for every node.

$$\left[\begin{array}{c}\Delta \bf{x}\\ \Delta \bf{y}\\ \Delta \bf{z}\end{array} \right]=\frac{1}{1N}\left[\begin{array}{ccc}{\bf{u}}_{\bf{x}}& {\bf{u}}_{\bf{y}}& {\bf{u}}_{\bf{z}}\\ {\bf{v}}_{\bf{x}}& {\bf{v}}_{\bf{y}}& {\bf{v}}_{\bf{z}}\\ {\bf{w}}_{\bf{x}}& {\bf{w}}_{\bf{y}}& {\bf{w}}_{\bf{z}}\end{array}\right]\cdot \left[\begin{array}{c}{\bf{F}}_{\bf{x}}\\ {\bf{F}}_{\bf{y}}\\ {\bf{F}}_{\bf{z}}\end{array}\right]=\underbrace{{ \left[\begin{array}{ccc}{\bf{g}}_{\bf{xx}}& {\bf{g}}_{\bf{xy}}& {\bf{g}}_{\bf{xz}}\\ {\bf{g}}_{\bf{yx}}& {\bf{g}}_{\bf{yy}}& {\bf{g}}_{\bf{yz}}\\ {\bf{g}}_{\bf{zx}}& {\bf{g}}_{\bf{zy}}& {\bf{g}}_{zz}\end{array}\right]}}_{\bf{G}} \cdot \left[\begin{array}{c}{\bf{F}}_{\bf{x}}\\ {\bf{F}}_{\bf{y}}\\ {\bf{F}}_{\bf{z}}\end{array}\right]$$

(3)

$${\bf{g}}_{\bf{xy}}= {\bf{g}}_{\bf{yx}},{\bf{g}}_{\bf{yz}}= {\bf{g}}_{\bf{zy}},{\bf{g}}_{\bf{zx}}$$

(4)

To use the compliance matrices G of the ideal blade for real-time compensation, interpolation must be performed between the nodes. Furthermore, the toolpath may also run through the deposited material. In this case, the compliance must also be extrapolated to force application points that do not lie exactly in the ideal tip surface.

To achieve a distinct mapping between tool position and compliance, the three-dimensional relation was reduced to a two-dimensional surrogate model. Therefore, the tip points of the blade were projected into a plane. This projection plane was constructed as a parallel to a compensation plane through all tip points (Fig. 16). All points of force application can then be referenced by their coordinate along the z and L-axis, which span the projection plane, as shown in Fig. 16.

Fig. 16

Inter- and extrapolation of the workpiece compliance

The top view on the right of Fig. 16 shows that opposite points on the suction and pressure side with the same L and z coordinates are very close to each other (red mark). Therefore, the same compliance can be assumed for them approximately.

It was also shown that the entries of the compliance matrices over L and Z can be approximated very well with fourth degree polynomial functions. This reduces the compliance model of the blade to 6 polynomials, which must be evaluated in real-time for the current cutter position.

$$\bf{G}\left(\bf{x},\bf{y},\bf{z}\right)= {\left[\begin{array}{ccc}{\bf{g}}_{\bf{xx}}& {\bf{g}}_{\bf{xy}}& {\bf{g}}_{\bf{xz}}\\ {\bf{g}}_{\bf{yx}}& {\bf{g}}_{\bf{yy}}& {\bf{g}}_{\bf{yz}}\\ {\bf{g}}_{\bf{zx}}& {\bf{g}}_{\bf{zy}}& {\bf{g}}_{\bf{zz}}\end{array}\right]}_{\bf{x},\bf{y},\bf{z}}\approx \left[\begin{array}{ccc}{\bf{P}}_{11}\left(\bf{L},\bf{z}\right)& {\bf{P}}_{12}\left(\bf{L},\bf{z}\right)& {\bf{P}}_{13}\left(\bf{L},\bf{z}\right)\\ {\bf{P}}_{12}\left(\bf{L},\bf{z}\right)& {\bf{P}}_{22}\left(\bf{L},\bf{z}\right)& {\bf{P}}_{23}\left(\bf{L},\bf{z}\right)\\ {\bf{P}}_{13}\left(\bf{L},\bf{z}\right)& {\bf{P}}_{23}\left(\bf{L},\bf{z}\right)& {\bf{P}}_{33}\left(\bf{L},\bf{z}\right)\end{array}\right]$$

(5)

6.3 Results

The results of the compensation on the turbine blade are shown in Fig. 17. Three areas were welded for material deposition on the suction side of the blade. The entire tip-surface was then milled with an infeed of 200 µm. Compensation was switched on in the upper area of the machined surface. It was deactivated in the area below. Finally, the entire blade tip was scanned with a coordinate measuring machine (Leitz Reference Xi 1076). To evaluate the result, the diagram shows a comparison of the measurement data with the nominal shape or the nominal toolpath of the machine tool.

Fig. 17

Result of the compensation

Due to the relatively large infeed, especially at the weld seams, there were also large shape deviations of up to 200 µm. Although displacement compensation reduces those deviations, a large shape error remains. One reason for this is that the compliance model only considers a highly simplified blade geometry without the inner cooling channels and cavities. Further compliance, such as that of the workpiece carrier or the contact between the components, was neglected. Thus, the workpiece-side compliance was underestimated by the model. The second cause is that the determined displacements cannot be fully compensated for by the magnetic guide, as this only allows movement in the x–y plane. Thus, only the projection of the total displacement on the x–y plane can be compensated. Nevertheless, the error could be reduced significantly by up to 50% through the deflection compensation, although the blade is more flexible in the upper area. This increases the accuracy of the entire recontouring process chain.

7 Conclusions

The deflection of the tool and workpiece is the main source of error in recontouring. This paper discusses two complementary approaches for improved process reliability of 5-axis recontouring of individual damage cases with repair-specific variances, influences from preceding processes and deflection of the workpiece and tool. At first it was shown that the choice of process parameters has a significant influence on shape accuracy during recontouring. With the help of a process simulation, the selection of individual process parameters can be supported to minimize shape deviations. In the recontouring of a welding seam, for example, the maximum shape deviation could be reduced by 86%. However, displacement effects in recontouring are unavoidable and unforeseeable to a great extent. Reacting to unpredictable influences is essential because of the variances from upstream repair processes. Based on those challenges, reactive compensation has many advantages compared to other adaptive machining approaches. The unavoidable and unpredictable deflections can be compensated reactively to further reduce shape deviations. Due to its high actuating dynamics, the electromagnetic guide offers a great advantage especially in case of abrupt changes in the process forces.

The investigations on a turbine blade showed that the developed methods led to a robust reduction of the shape deviations despite model uncertainties and unknown model parameters. The error due to deflection could be reduced by up to 50% through the deflection compensation.