A process-reliable tailoring of subsurface properties during cryogenic turning using dynamic process control

The experiments were conducted using an 1.4301, which is a metastable austenitic steel. It was solution annealed at 1050 \(^\circ\)C for 45 min and slowly cooled in the furnace to obtain a homogeneous microstructure without any ferromagnetic phases. The alloying composition was measured using spark spectroscopy and the mass fraction amounts to 0.035 % C, 0.38 % Si, 2.0 % Mn, 18.39 % Cr, 0.238 % Mo, 8.16 % Ni, and 0.086 % N and Fe balance.

Eddy current testing was performed inside the machine tool in real-time, i.e., in situ by using an in-house built system. The test frequency was 800 Hz and the excitation current amounted to 2 A. The strength of the excitation magnetic field, directly at the sensor tip, was 3.5 kA/m. A detailed set-up can be found in Ref. [11].

The metallographic images were acquired with an optical microscope (Leica digital microscope, DM4000M). The specimens were first polished, then etched. The samples were etched with Beraha II (distilled water, hydrochloric acid, ammonium hydrogen difluoride).

Micro-hardness measurements were conducted on polished cross-sections using a Q10 A+ by Qness with a load force of 100 gf (HV0.1), for a loading time of 10 s, in the depth range from 50 \(\upmu \hbox {m}\) to 600 \(\upmu \hbox {m}\) in 50 \(\upmu \hbox {m}\) steps, in the middle of the samples.

Since the chip formation can give important information on the cutting process, and hence subsurface modification, a chip analysis of the cryogenic turning process was carried out. The chip roots were obtained using a modified Split Hopkinson test rig. Details of the modification can be found in Ref. [22]. Hereby, the temperatures were set by emerging the samples into liquid nitrogen before the mechanical test. After shooting the cutting specimens along the cutting edges, chip roots remained in the surface. The experiments were conducted at room temperature, -45 \(^\circ\)C and -110 \(^\circ\)C. Afterwards, the chip roots were mounted, polished, and then etched using Beraha II.

The workpiece temperature during machining significantly influences martensite formation. Knowledge of the temperature distribution inside the component is crucial for understanding its impact on martensite formation throughout the component depth. However, measuring this distribution requires extensive experimental efforts, necessitating the use of simulation methods. In this study, the commercial software Ansys 2019 R3 was employed to simulate the temperature distribution inside the workpiece. The simplified schematic configuration of the simulation is shown in Fig. 1.

The simulation utilized a thermally-transient model, initially assuming a Gaussian heat source with a cylindrical shape. A stainless steel shaft with a diameter of 47 mm and a machining length of L = 60 mm were considered analogous to the experimental investigations. The convective and radiative boundary conditions are included in this model, with a heat transfer coefficient of 1.44\(\cdot\)10\(^{\mathrm {-2}}\) W/(mm\(^{\textrm{2}}\cdot\)K) as well as radiation between the component surface and surrounding area. The following assumptions were made for the simulation: (1) The thermal conductivity was assumed to be constant over temperature. (2) The workpiece material is homogeneous and isotropic. (3) The change of the phase is not taken into account. The moving heat source is Gaussian distributed and is defined as follows:with q\(_{\textrm{max}}\): maximum heat flux at the center of the heat spot, \(\zeta\): radius of the beam, v\(_{\textrm{r}}\): velocity in circumferential direction, f: feed in z direction and r: radius of the Gaussian heat source.

The aim of the simulation in the first step is to show, on the one hand, basic qualitative correlations between the nozzle diameter and the temperature distribution inside the component. On the other hand, an understanding of the temperature distribution in the shear zone, with prior nitrogen cooling during cutting engagement, while turning, is to be generated. In future work, it will then be necessary to combine the two simulation approaches with a moving heat source (analogy to the heat induced by the cutting tool) and a cold source (analogy to the CO\(_{\textrm{2}}\) in-process cooling), dependending on the initial temperature of the component.

The cryogenic longitudinal turning investigations and the implementation of the process control were carried out on a turnmill center DMG Mori NTX1000 with additional turret for simultaneous machining. On this machine the hardware concept shown in Figure 2 was implemented. During the investigations, the tool spindle was used to mount the eddy current sensor for in-situ measurements of the martensite content. Additionally, a nozzle was mounted in order to provide in-process CO\(_{2}\) cooling. For the actual turning process, the turret was used, while the process forces were measured by a Kistler 9129 dynamometer. Furthermore, the turret was used to mount a thermocouple type K for temperature measurement before the process. The data measured by the thermocouple, the dynamometer, and the eddy current sensor, were transferred to a Beckhoff PLC as analog voltage signals. The PLC was also connected via a PROFIBUS interface to the Siemens Sinumerik 840D SL of the machine. This connection allows a collection of the axis data of the machine and interaction with the process running on the machine tool by synchronous variables.

The experimental investigations for the modeling and inverse modeling were conducted using uncoated indexable inserts (CNMA120408 by Kennametal). The material of the inserts consists of tungsten carbide cobalt (K68). The process parameters feed f, depth of cut a\(_{\textrm{p}}\), cutting speed v\(_{\textrm{c}}\) and initial workpiece temperature T are each varied in two factor levels: f is varied at 0.3 mm and 0.7 mm, a\(_{\textrm{p}}\) at 0.2 mm and 0.5 mm, v\(_{\textrm{c}}\) at 30 m/min and 70 m/min and T at -70 \(^\circ\)C and -110 \(^\circ\)C. The experiments were performed in a full factorial manner. They were further extended varying just f and T since those process parameters have the highest effect on the martensite formation. Further experiments with five different levels for f (from 0.1 mm to 0.5 mm) and six different levels for T (from -150 \(^\circ\)C to -50 \(^\circ\)C) were then conducted full factorially. The workpieces have a diameter of 49.7 mm and a length of 50 mm. The experiments with the varying cooling strategies were conducted with a CNMG120412-SM1 by Sandvik. The used process parameters were: f = 0.1 mm and f = 0.4 mm, v\(_{\textrm{c}}\) = 100 m/min, T = -72 \(^\circ\)C and T = 22 \(^\circ\)C

Modeling the correlation between the process parameters and the subsurface properties is necessary in the first step for setting the subsurface. Based on this, an inverse modeling approach allows the determination of necessary process parameters by combining the model with a meta-heuristic used for solving optimization problems. For the modeling approach of martensite, the Adaboost regressor was chosen. The cross validation method with five runs was used for modeling, resulting in a distribution of training to test data in the ratio of 80 % to 20 %. In this case, the data set was divided into five random blocks and one block was used as a test data set to check the trained model for overfitting based on the training data of the remaining blocks. This was done five times with different combinations, so each block was used once as a test data set. The implementation was done with the python library Scikit-learn. For the multi-criteria optimization, the genetic algorithm (GA) is used. It is suitable for multi-criteria problems and the solution tends not to remain in a local optimum because of random mutations in the iterative process for finding the optimal solution. The GA is linked with the prediction models of martensite and surface roughness. For the surface roughness, the linear regression was used.

The higher the amplitude of the 1\(^{\textrm{st}}\) and the 3\(^{\textrm{rd}}\) harmonic was, the higher is the newly generated subsurface martensite content. A correlation between the eddy current signals and the martensite content, determined by reference measurements, was created in Ref. [9]. In Fig. 3, the amplitude of the 1\(^{\textrm{st}}\) and the 3\(^{\textrm{rd}}\) harmonic of in situ eddy current testing measurements are shown. Here, only an in-process CO\(_{\textrm{2}}\) cooling was applied. Two roughing steps were conducted, using a feed of f = 0.4 mm. The amplitudes of both harmonics increased in the second turning step, meaning that more martensite was created. This is comparable to the findings by Hotz et al. [17]. The longer the process duration, the more cooling lubricant is applied, and thereby the cooler the workpiece becomes. Further, the lower the temperature was, the lower is the stacking fault energy. A low stacking fault energy promotes the deformation-induced martensitic transformation [23, 24]. Hence, more martensite is produced in the second turning step [7, 14, 17, 22].

In Fig. 4, the results of a two-step turning process are shown. Here, a roughing and a finishing process step were conducted. Comparing Fig. 4 a) and b), it can be seen that the amplitude of the 1\(^{\textrm{st}}\) harmonic of eddy current testing is higher when using a LN\(_{\textrm{2}}\) pre-cooling, see 4 a). A sufficient cooling effect is achieved [18]. The cutting parameters were kept constant for the experiments shown in Fig. 4 a) and b). First, a roughing process was conducted. Subsequently, a finishing process step was applied. The amplitude level of the 1\(^{\textrm{st}}\) harmonic of eddy current testing is lower in the second step when compared to the first one, if an LN\(_{\textrm{2}}\) pre-cooling is used. When only an in-process CO\(_{\textrm{2}}\) cooling was used, the amplitude level of the 1\(^{\textrm{st}}\) harmonic of eddy current testing is similar in the second turning step compared to the first one. This means when using solely an in-process CO\(_{\textrm{2}}\) cooling, which also results in higher workpiece temperatures in the first cutting step compared to LN\(_{\textrm{2}}\) pre-cooling, after the second turning step, a similar subsurface martensite content is gained. Here again, it is suspected that the workpiece is colder in the second turning step than in the first one. Even though the cutting feed is lower in the finishing step, the lower workpiece temperature leads to a similar martensitic transformation rate. However, unlike Hotz et al. [17] where only an in-process cooling was applied, no increase in the subsurface martensite content was detected, see Fig. 4 b).

Figure 5 again shows the amplitude of the 1\(^{\textrm{st}}\) harmonic of eddy current testing for in-process measurements. As in Fig. 4, it can be seen that the amplitude of the 1\(^{\textrm{st}}\) harmonic is higher when a pre-cooling is applied and more martensite is produced in the subsurface. However, when comparing the combination of in-process CO\(_{\textrm{2}}\) cooling and LN\(_{\textrm{2}}\) pre-cooling, a more stable progress can be seen than for the one without in-process CO\(_{\textrm{2}}\) cooling. For longer turning times, the pre-cooled workpieces heated up, and thus less martensite is produced. If an in-process cooling is applied, the sample remains cold and a homogeneous martensite subsurface content can be produced over the sample length. The validity of this assumption was proven by random temperature measurements. It was observed that a shaft, pre-cooled with LN\(_{\textrm{2}}\), reaches a final temperature of T = -48 \(^\circ\)C after turning, while a shaft with in-process CO\(_{\textrm{2}}\) cooling had a final temperature of T = -10 \(^\circ\)C, and a shaft with a combination of both cooling strategies (LN\(_{\textrm{2}}\) pre-cooling and in-process CO\(_{\textrm{2}}\) cooling) reached a final temperature of T = -59 \(^\circ\)C. In conclusion, as also described in Ref. [18], a pre-cooling leads to the highest possible martensite subsurface content. However, an in-process cooling is necessary if longer workpieces are machined, so that a homogeneous martensite subsurface content can be produced over the whole workpiece length. Otherwise, the workpiece warms up and less martensite is induced at the end of the machining process.

As it can be seen in Fig. 4 a), if the workpiece is pre-cooled using LN\(_{\textrm{2}}\), less martensite can be found in the subsurface after the subsequent finishing step, when compared to the roughing step. Without an in-process cooling, the workpiece temperature is increased in the second turning step, as well as a smaller feed being applied. This leads to a less pronounced deformation-induced martensitic transformation.

In Fig. 6, metallographic cross-sections of a two-step, a) + c), and an one-step turning process, b) + d), are shown. The black areas are deformed areas where martensite might have been created [22, 25]. More black areas, and therefore likely more martensite, are created if a roughing step is applied, compare Fig. 6 c) and d). However, a hardening compared to the base material (150 HV0.1) can also be achieved if only a cryogenic finishing process with low cutting feeds is applied.

In addition to the newly created surface using a Split Hopkinson test rig, see chapter 3.4, an analysis of chip roots, created using different cutting conditions, was possible. In Fig. 7 a–c chip roots produced at three different cutting temperatures are shown.

At room temperature, Fig. 7a, deformed black areas interspersed with colored areas can be seen. The colored areas are austenitic. That means only a little martensite was created since austenitic grains are still present within the chip. Compared to Fig. 7a, in Fig. 7b segregated, completely black areas are obvious. A segmented chip formation is visible. Between the black, deformed areas, colored stripes appear. Here, due to the shearing, and therefore heat generation, the austenite did not transform into martensite.

Compared to Fig. 7b, the colored austenitic areas in the segmented chip are smaller and less pronounced than in Fig. 7c. Due to the cutting temperature reduction, more martensite was generated within the chip. A more detailed view on the austenitic areas between the deformed areas can be seen in Fig. 8. Again, it is obvious that only a few black areas were produced at room temperature, Fig. 8a. The chip remains mostly austenitic. In Fig. 8b and c, the sheared austenitic microstructure in the segmented chip, between the deformed areas, is visible.

Moreover, in Fig. 7b and c bright white areas are obvious. In Fig. 7d, a magnification of one of the white areas is shown using less illumination. Very small, austenitic grains are visible. Hence, the appearance of the white areas is reminiscent of white etching layers. Such layers which can be found in the surface of martensitic, ferritic, or pearlitic steels after machining when high cutting speeds are used in conjunction with tool flank wear [26].In the present study, the emerging white etching layers seem to have a similar grain refinement as the white etching layers in martensitic, ferritic, or pearlitic steels. A further evaluation of the emerging white etching layers in austenitic steels was not conducted in this study but should be performed in future studies. Deep rolling can also lead to the formation of white etching layers due to the high strains in high carbon steels [27]. The white etching effect is often explained by a grain size reduction, typically between 30 and 500 nm, due to dynamic recrystallization within the turning process [26‐29]. Until now, a white etching layer in an austenitic steel has not been described in the literature. However, the grain size reduction is accompanied with a hardness increase [26]. This is also the case in the white areas within the present study. In Fig. 9, hardness indentations within the chip root of Fig. 7b are presented. Compared to the base material, the hardness in the white areas is increased tenfold. Since greater hardness often is accompanied by brittle behavior, white etching layers are unwanted in a subsurface after the turning process. However, the white etching layers have only been found within the chip and not in the newly created subsurface in the present study. Further studies should focus on the emergence mechanism of these white etching layers in the chips of metastable austenitic steels.

The microstructure of high carbon steels, where white etching layers often occur, is not austenitic. Here, due to the high temperatures within the cutting process, an austenitic phase transformation happens and retained austenite occurs. As a results of this and the dynamic recrystallisation, the grains are refined [28]. The differences in the composition of white layers are probably due to the fact that, depending on the application, different white layers are actually formed [30]. By analyzing the chip roots, it can be determined that the heat dissipation by the chip is sufficient for the LN\(_{\textrm{2}}\) pre-cooling method. Further, in the present case, the base material is already austenitic and no phase transformation has to occur in order to produce a white etching layer.

In order to investigate and evaluate the influence of different cooling strategies on the mechanical load during both the roughing and the final finishing operations, force measurements were conducted. The effect of the cooling strategies CO\(_{\textrm{2}}\) in-process cooling, pre-cooling with LN\(_{\textrm{2}}\), and the combination of both, on process forces is depicted in Fig. 10.

For reference, force measurements without cooling were also conducted. In the roughing process, the passive force emerged as the most dominant force component, while during finishing, the cutting and passive forces were observed to be at a similar level. The literature [16, 31] has previously reported significant reductions in process forces by adjusting the process parameters for the finishing step, which is confirmed in this study as well. The cooling strategy demonstrates a considerable impact on the passive and cutting forces, while the feed force is only minimally affected. In particular, the LN\(_{\textrm{2}}\) pre-cooling strategy displays a remarkable reduction in process forces when compared to other cooling strategies. This outcome may be attributed to the altered chip formation observed in Fig. 11, resulting from the pre-cooling process with LN\(_{\textrm{2}}\).

The choice of cooling strategy has a profound influence on chip morphology. Without cooling, the observed chip formation consists of lamellae with comparatively less plastic deformation than the chips produced with cooling strategy, see Fig. 11a. In contrast, employing CO\(_{\textrm{2}}\) in-process cooling (11b) preserves similar chip morphology, but with noticeably larger areas exhibiting possible martensitic transformation, as evident by the darkened regions in the microsections. A prior LN\(_{\textrm{2}}\) cooling process results in a significant transformation of the chip formation, see Figs. 11c and 11d. The formation of shearing chips with well-defined shear bands becomes apparent. The combination of LN\(_{\textrm{2}}\) pre-cooling with in-process CO\(_{\textrm{2}}\) cooling further enhances the frequency of chip formation. In both cases, there is a pronounced darkening of the microsections, indicating the occurence of martensitic phase transformations between the shear bands. In-process CO\(_{\textrm{2}}\) cooling leads to a more rapid cooling during the compression phase, resulting in an increased frequency of chip formation, i.e. leads to a reduction in the distance between the lamellae. The enhanced cooling rate promotes quicker sliding and shearing, thereby contributing to the observed changes in chip morphology and the martensitic phase transformations. The results demonstrate that a reduction in workpiece temperature significantly influences chip morphology, with LN\(_{\textrm{2}}\) pre-cooling in particular playing a key role in inducing plastic deformation. This also explains the increased deformation-induced martensitic transformation for pre-cooled workpieces. Plastic deformation is needed as a nucleation site for the strain-induced martensitic transformation [32], which occurs in the present case. Additionally, the combination of in-process CO\(_{\textrm{2}}\) cooling with nitrogen pre-cooling, enhances the frequency of chip formation.

The cooling process is a crucial aspect of turning operations, that impacts chip formation, tool wear, and process forces. These changes are used specifically to initiate the martensitic phase transformation. CO\(_{\textrm{2}}\) in-process cooling, involving liquid CO\(_{\textrm{2}}\) expansion through a nozzle, offers a promising cooling solution, see also Ref. [14, 19]. Therefore, in this study, one aim was to investigate the influence of nozzle diameter on process forces during the CO\(_{\textrm{2}}\) in-process cooling in turning processes. The nozzle diameter was varied in three stages (8 mm, 10 mm, and 12 mm) to analyze its effect on process forces. For better understanding, only the largest and smallest diameters are considered in Fig. 12. During roughing, increasing the nozzle diameter leads to an increase in process forces. A larger nozzle diameter results in higher gas flow rates and more efficient cooling. This phenomenon is attributed to the effective heat dissipation during roughing, resulting in raised cutting forces. Surprisingly, in finishing operations, increasing the nozzle diameter leads to a reduction in process forces. The finishing zone consists of both austenitic and martensitic regions (see Fig. 6), which are influenced by the prior martensite formation during roughing. A smaller nozzle diameter enhances local cooling, thereby increasing the force required for material separation during finishing.

THIS effect of nozzle diameter on process forces is particularly pronounced in turning without pre-cooling. Without pre-cooling, a smaller nozzle diameter results in significantly higher process forces during finishing. However, pre-cooling with LN\(_{\textrm{2}}\) mitigates this effect by reducing the process forces.A possible hypothesis is that a smaller nozzle diameter leads locally to a stronger cooling of the component edge zone, whereby the forces increase accordingly. However, if the component has already cooled down to -72 \(^\circ\)C, this effect decreases. Accordingly, the process forces also decrease. Another hypothesis could be that the geometry of the component changes with the temperature. The diameter of the sample shrinks with lower temperature and thus also the depth of cut in the process. This leads to different cutting depths depending on the prevailing component temperature. However, further investigations are needed in future work to explain this effect.

Finally, investigations were carried out using different workpiece batches. The batches examined differ in terms of chemical composition. Among other parameters, process forces were recorded, revealing an influence from the different workpiece batches on the process forces. In particular, the passive forces showed a scattering of approximately 60 N, while the other force components exhibited less variation, see Fig. 13. These findings are crucial to consider during dynamic pre-control for the targeted adjustment of martensite content.

For functional components that are exposed to very high mechanical loads during later use, very strict roughness requirements are placed on the component surface. Although the surface topography may appear similar across various cooling strategies at first glance (see Fig. 14), a detailed investigation reveals distinct differences contingent on the cooling approach. Turning without cooling exhibited an average surface roughness Rz of 3.1 \(\upmu \hbox {m}\) after the finishing process. In contrast, the implementation of cooling strategies led to a notable reduction in surface roughness, with values as low as 2.6 \(\upmu \hbox {m}\). Looking additionally at the associated probability distributions, differences with regard to stochastic roughness are evident.

Comparing the surface topographies between roughing and finishing processes reveals significant differences, see Fig. 15. The finishing process demonstrates remarkable efficacy in reducing the average surface roughness Rz by a factor of six when compared to roughing. This improvement in surface quality is a desirable outcome for high-load functional components. While the two-step machining process significantly enhances surface quality, there is an important consideration regarding the induced martensite content. The finishing operation results in a loss of the induced martensite content introduced during the preceding roughing process. Future research in this area could explore innovative methods to preserve the induced martensite content during finishing, while maintaining superior surface quality, when LN\(_{\textrm{2}}\) pre-cooling is used. Understanding the relationship between the machining process, surface topography, and the material’s microstructure will further enhance the design and performance of functional components in demanding applications.

The first simulation results are shown in Fig. 16. The initial temperature of the component during turning (Fig. 16 a) and 16 b)) and the CO\(_{\textrm{2}}\) nozzle diameter (Fig. 16 c)) were varied. The temperature distribution during conventional turning, without cooling, is shown in Fig. 16 a). Here, the influence of the tool cutting edge on the temperature in the separating zone is assumed with an equivalent power source in the form of a moving heat source. Here, maximum temperatures occur directly in the contact zone between the component surface and the indexable insert, with a rapidly decreasing gradient into the interior of the component. Pre-cooling with LN\(_{\textrm{2}}\) leads to a significant reduction of the maximum temperatures occurring at the component surface by approx. 100 K. In addition, the surface that has already been machined quickly heats up to \({-15}^\circ \hbox {C}\), while the starting temperature of \({-70}^\circ \hbox {C}\) is maintained inside the component. As it can be seen in Fig. 7, this cooling is sufficient to suppress the formation of white etching layers.

In the next step, the isolated influence of CO\(_{\textrm{2}}\) cooling on the workpiece temperature, without concurrent turning, was investigated (see Fig. 16 c)). The nozzle diameter was varied to analyze its effect on the formation of maximum surface temperatures and temperature distribution within the workpiece. Increasing the nozzle diameter from 8 mm to 12 mm resulted in a significant reduction of temperature at the workpiece surface, where the cooling jet impinges. Specifically, a temperature minimum of approximately \({-80}^\circ \hbox {C}\) was achieved at the workpiece surface with a nozzle diameter of 12 mm. However, this temperature minimum was localized and increased to room temperature within a few micrometers towards the inner region of the workpiece. Combining CO\(_{\textrm{2}}\) cooling with LN\(_{\textrm{2}}\) pre-cooling of the workpiece to \({-70}^\circ \hbox {C}\) did not lead to a significant increase in martensite content. This is lack of significant increase because the temperature difference between the initial surface temperature of the workpiece and the additional cooling provided by CO\(_{\textrm{2}}\) was not sufficiently high. Furthermore, due to the short cooling time during the process (feed rate f = 0.4 mm and cutting speed v\(_{\textrm{c}}\) = 100 m/min), only surface cooling is achieved, and cooling within the inner regions of the workpiece is not feasible. Consequently, the implementation of CO\(_{\textrm{2}}\) cooling during the process is only effective in keeping the martensite transformation constant for longer cutting paths, see also Fig. 5. This can be beneficial or be useful for reducing or preventing the rise in workpiece subsurface temperature due to convection and radiation with the ambient atmosphere.

Apart from the workpiece geometry, its functionality can be set by a targeted modification of the subsurface with appropriate process parameters in the machining process. In addition to the hardening through deformation-induced martensite formation in the machining process, the surface roughness also influences the workpiece properties. Thus, tailored machining, with differently required surface and subsurface properties, can be carried out if the corresponding process parameters are determined in such a way that desired target values are achieved. This can be used as the basis for an in-process control.

The Adaboost regressor for modeling the martensite content showed in pre-studies the best results compared with other regression model approaches, with a coefficient of determination R² = 0.89, an adjusted coefficient of determination R²\(_\textrm{adj}\) = 0.87, and a root mean square error RMSE = 0.5. Varying the hyperparameters showed little effect on the model performance. The default values of the hyperparameters n\(_\textrm{estimators}\) = 9 and random\(_\textrm{state}\) = 0 were found to be the most appropriate for modeling the martensite formation.

For the surface roughness, the average peak to valley height Rz (DIN EN ISO 4287 [33]) was considered. The Pearson correlation coefficients show a strong influence of the feed on the roughness with 0.99, while the other process parameters have a low correlation. Therefore, the linear regression approach was chosen for modeling the roughness Rz with the feed as the only influencing process parameter. By this, a coefficient of determination of R² = 0.92, an adjusted coefficient of determination R²\(_\textrm{adj}\) = 0.90, and a RMSE = 2.7 \(\upmu \hbox {m}\) was achieved.

Using the objective function Z, the found process parameter combination was evaluated and optimized (2). In this case, the GA solves a minimization problem. The goal is to find process parameters with which the predicted target variables M\(_\textrm{Pred}\) and Rz\(_\textrm{Pred}\) (determined from the Adaboost model) are close to the given target values M\(_\textrm{Target}\) and Rz\(_\textrm{Target}\) to be achieved. Absolute differences are considered so that the deviation remains exclusively in the positive range. Via the weights w1 and w2, the importance of the target values can be weighted during the optimization process. These must add up to one again (3).

Three different target values for the relative martensite content M were selected to test the method: M = 3, M = 4, and M = 5. The relative martensite content is a relative value, thus it does not have a unit. This has the advantage that the exact amount of martensite content does not have to be determined. For this, the measurement value of one sample was set as reference sample. The measurement values of the other samples are then linked relatively to this reference sample. A relative martensite content of e.g., M = 3 means that the measured signal of this sample is three times higher than the reference sample. The roughness was set to Rz = 10 \(\upmu \hbox {m}\) and Rz = 30 \(\upmu \hbox {m}\). The weights w1 and w2 are set to w1 = 0.99 (and w2 = 0.01) and w1 = 0.6 (and w2 = 0.4). The weights were chosen to focus on martensite transformation in the first setup. In the second setup, the weight for surface roughness w2 is increased to focus more on the roughness in the optimization process. Through its significance, only feed f and workpiece pre-cooling temperature T are the variable process parameters, while the depth of cut (a\(_\textrm{p}\) = 0.2 mm) and cutting speed (v\(_\textrm{c}\) = 70 m/min) are fixed. The range of possible solution is limited from 0.1 mm to 0.5 mm for f and from \({-150}^\circ \hbox {C}\) to \({-50}^\circ \hbox {C}\) for T. The result diagrams for the adjustment tests are shown in Fig. 17 (for martensite formation) and in Fig. 18 (for roughness). A distinction is made between target, predicted, and actual measured values after machining. The percentage deviations between those are also summarized in detail in table 1. The distinction between the percentage deviation between actual and target value allows to evaluate the performance of the whole method. The deviation between predicted and target values is good to evaluate the performance of the GA while the deviation between predicted and actual shows the deviations for the Adaboost model. The samples 1–6 include all possible target value combinations of martensite and roughness for the first setup (w1 = 0.99 and w2 = 0.01), while the samples 7–12 include the experiments for the second setup (w1 = 0.6 and w2 = 0.4).

For higher roughness target values (Rz = 30 \(\upmu \hbox {m}\)), the algorithm was able to find suitable process parameters with which the target value specifications of both target variables were met. At the lower roughness target value (Rz = 10 \(\upmu \hbox {m}\)), it is no longer possible to achieve the target values for both martensite content and roughness simultaneously. In this range, the conflict between the two target variables results from its opposite course due to the feed variation: A higher feed results in a higher martensite content, but also in a higher roughness. Hence, depending on the choice of the weights w1 and w2 in the objective function, the correspondingly higher weighted objective variable is taken into account more strongly in the selection of the process parameters. For example, it can be seen that for w1 = 0.99 (higher weighting for martensite formation than for roughness), the difference between target and modelled martensite content, resulting from the determined process parameters, is small (samples 1–3 in Fig. 17). In contrast, the other target value roughness cannot be achieved, which shows a high deviation between the target value and the predicted value (samples 1–3 in Fig. 18). In contrast, the higher weighting for the roughness with w1 = 0.6 shows the opposite (samples 7–9 in Fig. 17 and Fig. 18). This can also be seen in table 1, if the mean and median values of the percentage deviation between actual and target values for the weight w1 = 0.99 and w1 = 0.6 are compared with each other. Here, it becomes apparent that the temperature variation alone is not sufficient for higher required martensite content and an additional adjustment of the feed is necessary. However, this is limited in the lower feed range by the greater consideration of the roughness. This results in an increasing deviation between the target and the predicted value as the target martensite content increases (samples 7–9 in Fig. 17). Consequently, the conflict between the two target values becomes particularly apparent at target values for low roughness. At higher roughness target values (Rz = 30 \(\upmu \hbox {m}\)), the target conflict is not significant, even with a higher weighting in favor of roughness (samples 10–12 in Fig. 18). Thus, these results confirm the need for a two-step turning process as well, if apart from different martensite content, low roughness values are also required.

The objective of the control concept proposed in this paper is the reliable adjustment of the martensite content of the machined surface. While a process parallel measurement of the martensite content is possible, a process parallel feedback control of the martensite content is not suitable, since the local martensite content is determined during the process, and the delay time of the control would result in remaining local deviations of the martensite content. Thus, a cross process control is needed. Due to the material expenditure and process time, the required result has to be achieved process-reliably with a minimum number of cuts. That is why a simple cross process feedback control is not suitable either. Furthermore, the resulting martensite content depends non-linearly on both feed and temperature, wherefore a model of these dependencies to choose the process parameters is required.

Since deviations occur between different workpieces, e.g.,, because of different batches or slight variations of the workpiece temperature, the model-based setting of the process parameters in an open loop system is not suitable either. Therefore, the feed forward control of the martensite content, shown in Fig. 19 was developed. While in principle both workpiece temperature T and feed f could be used as manipulated variables, the feed is chosen since it can be easily and precisely lowered and increased via the NC-control of the machine. Since the workpiece temperature still acts as a disturbance, it is measured for each cut and taken into account in the feed forward control. For this control, the model described in 4.5 is adapted to consider both, the deviation between the set martensite content M\(_\textrm{set}\) and the actual martensite content M\(_\textrm{act}\), as well as the current temperature of the workpiece. This way, the actual martensite content is determined within the process using the eddy current sensor.

The communication with the machine and the data collection require a frequent actualisation in fixed intervals, while a recalculation of the manipulated variable is only necessary if the next cut has to be started. Furthermore, the computation time of the model, which is much longer than the cycle time suitable for the communication with the machine, had to be considered. Thus, the control is divided in a cycle oriented part and an event triggered part with calculation of the feed as the manipulated variable. The cycle oriented part contains the actual monitoring of the process, especially the collection of the sensor data and the communication with the machine via the PROFIBUS interface. Synchronous variables in the NC-Code are used to transmit the beginning, number and the end of each cut from the machine to the PLC, and to set the required feed as the manipulated variable. Currently the target martensite content of the control is constant over the machining length. Here, in principle, the setting of a local varied martensite content is also possible, especially if no in-process cooling method is applied. Hence, the mean value of the martensite content over the machining length is used as the controlled variable. In future applications, due to the in-process eddy current testing, even a defined set of a position dependent martensite content over the workpiece length might be possible.