In-process approach for editing the subsurface properties during single-lip deep hole drilling using a sensor-integrated tool

The soft sensor is to be implemented as a multiple regression model, which is derived from the characteristic fields of the subsurface properties. The fields are generated by experimental investigations and FEM simulations. First, a response surface design was created in order to statistically validate the experimental results and still keep the test effort within limits compared to a full factorial test plan. The response surface design was set up with the machining parameters cutting speed v_c or rotational speed n and feed rate v_f as factors. For the test factors, an application-oriented range was defined and extended over the process boundaries, for the rotational speeds 1057.89–1683.11 min⁻¹ and the feed rates 3.77–71.62 mm/min. In addition, at least three repetitions are provided, for better statistical validation. In total 39 repetitions with different process parameters are required. The parameter range is set around the cutting data recommended by the VDI, taking into account the machine performance. The cutting parameters were also taken above the minimum and maximum limits in order to push the process stability to the limits. In the test plan in Table 1 the so-called point type indicates whether the process parameters are above the limits or not: a central point is marked with a “0” (below the limit), a corner point with a “1” (at the limit) and a grid point with a “− 1” (above the limit). All experimental parameters are processed under the same conditions, for example, same machine tool, same batch of workpiece material, same tool with new inserts, etc., which is described by a “1” in the category blocks. The quenched and tempered steel 42CrMo4 + QT is used as the workpiece material. Despite its widespread use in mechanical engineering, this material is nevertheless demanding in terms of machining because its k_c1.1 value is high with 2500 N/mm². As a result, wear on the guide pads as well as cutting edge rounding occurs relatively quick, amplifying the change in thermomechanical state. Zylindrical specimens with an outer diameter of 25 mm and a length of 100 mm are used as specimens in order to minimize the effect of workpiece geometry on the heat distribution. The accelerations and temperatures are measured with the sensory tool and additionally, on the machine side, the feed force F_f and the drilling torque M are recorded. The oil flow and pressure are also measured, but remain constant.

In this project, the hypothesis is pursued that the subsurface properties are dependent on the thermomechanical state in the cutting zone and that any disturbing factors, such as cutting edge wear, can be detected via this thermomechanical state. Thus, the subsurface condition can be adjusted or kept in a constant range via the temperature on the cutting insert and via the mechanical variables such as the force, the drilling torque and the acceleration. In the first step towards the soft sensor the correlation between the thermomechanical quantities and the control variables n and v_f was investigated. The mechanical quantities that characterize the deep hole drilling process are the feed force F_f and the drilling torque M. They were recorded with a KISTLER 9125A rotational dynamometer. Figure 6 shows a measured evolution of the feed force from the response surface design at medium rotational speed and feed rate. The diagram shows a typical increase in force at the start of drilling—here a drill bush was used—before the force reaches a steady state. To generate the characteristic field, the average force in the steady state was determined and collected for each machining parameter set from Table 1. Figure 7 shows the correlation of the averaged feed force with all the investigated cutting parameter sets. The surface was created by interpolating the result values using the second-order distance method. As a result, the feed force increase with increasing feed velocity is due to increasing chip thickness and metal removal rate as well as the asymmetrical tool geometry. According to Patra et al. and Biermann et al. [1, 18] a correlation exists between the increase in rotational speed and increase in radial force, which is mainly caused by the asymmetric tool geometry resulting in stronger deformation of the bore wall. With increasing rotational speed, the feed force increases, too, which is in contrast to the expected feed force decrease caused by a reduction of the chip thickness with increasing rotational speed and constant feed velocity. Supporting the presented results, Nickel et al. also found that in single-lip deep hole drilling of 42CrMo4 + QT, the feed force increases with both the increase in feed rate and the increase in cutting speed [19]. In addition, these observations were confirmed by the FE simulation results in Fig. 16.

The drilling torque evolution behaves similar to the feed force with the peak at the start of drilling and the subsequent steady state, but the load gradient and the fluctuations at the bore exit are more pronounced, see Fig. 8. This effect may be due to the non-uniform load distribution on the cutting edge due to partial and progressive exit of the tool tip. The correlation of the averaged drilling torque with the cutting parameters is shown in Fig. 9. At low rotational speed, the drilling torque initially increases with v_f and then decreases again slightly. This phenomenon can also be observed at high feed rate and with increasing rotational speed.

Furthermore, the acceleration at the drill head tip in the tangential, axial, and radial directions was measured with the previously described sensory single-lip deep hole drilling tool. The acceleration signal can be used not only to detect unwanted vibrations, but also to calculate the position or the rotational speed of the cutting insert. Figure 10 shows the acceleration values at intermediate cutting data of the investigated parameter range (pass sequence = 3). As expected, the dominant component is the tangential acceleration. The measurement in three axial directions offers a great advantage, such as the identification of occurring disturbance factors. For example, it was found that the strong noise development, which is often problematic in deep drilling processes, is caused by the radial vibration. The selected measuring range of ± 200 g of the ADXL 377 is sufficient, as the measurements have shown. The sampling rate is 1 kHz.

For the soft sensor and the associated closed loop control, the information of the actual rotational speed is to be used from the acceleration signal. The rotational speed specified in the machine tool control does not correspond to the actual rotational speed at the cutting edge, which is due to the forces acting in the process and the tool elasticity at a length of 644 mm. Therefore, the actual cutting speed should be included in the regression model. The cutting speed can be calculated from both radial and tangential acceleration, with the radial acceleration method being the more accurate since no integration is required [16]. Another method of obtaining velocity information from the acceleration signal is real-time FFT analysis. Figure 11 shows an example block diagram in LabVIEW that filters the acceleration data and performs an FFT to calculate the rotational speed or cutting speed using the frequency information. Figure 12 shows the deviation between the rotational speeds specified in the machine control system and the measured maximum rotational speed amplitudes, which are the arithmetic averages of each process parameter set. With higher feed rate, the deviation from the preset becomes smaller and more independent of the rotational speed. With higher spindle rotational speed, the difference to the current rotational speed at the tool tip calculated from the frequency also increases, since this increases the drilling torque (Fig. 8) and thus also the cutting force, which can lead to a higher torsional displacement of the tool and vibrations. However, the overall difference is just in a low range between 1 and 2%. The entire control is to be implemented in LabVIEW.

The temperature measurement with the sensor-integrated tool at three positions under the cutting insert (Fig. 2) with intermediate cutting parameters (pass sequence = 3) can be seen in Fig. 13. The overall temperature level is significantly lower than the expected temperatures in the process zone. This can be explained by the positions of the sensors behind the cutting insert. An approach to obtain the actual temperature in the cutting zone from these measured values has been extensively investigated and proposed in [20]. However, for controlling the process the absolute value of the temperature is less important than the changes during the measurement. For this purpose, the uncertainty and the temporal resolution of the measured values is more important, which is sufficiently low and high, respectively. The good resolution and low measurement uncertainty can be seen from the fact that the shape of the temperature evolution curve of all three sensors agrees very well but at slightly different temperature levels, which can be attributed to the positions of the sensors. The temperature at the start of drilling rises rapidly and then remains quasi constant until the exit was reached, which is comparable to the behavior of the feed forces. At the exit, the temperature rises again. This steep increase is due to the missing cooling lubricant, which shoots out of the backside of the cylindrical sample and thus remains no longer around the cutting edge to dissipate the heat. The highest mean temperature with 53 °C is measured at position T2 (red), as this sensor is located in the outer part of the circuit board and thus closest to the cutting corner of the insert, which is in contact with the bore wall. Sensor T1 (green) measures a lower mean temperature with 47 °C, as it is located further away from the cutting zone. The lowest mean temperature was measured with 45 °C at position T3 (blue). The latter sensor is closest to the axis of rotation, which leads to a lower cutting speed in this position. To create the temperature characteristic field and making the system more robust against deviations, the average of the mean temperature in the steady state in all three positions was considered. Figure 14 shows this correlation of the mean temperature with the machining parameters. The temperature tends to increase with the feed rate and the cutting speed, although it drops again slightly at high values.

Beside the experimental investigations of the SLD process to acquire data for the soft sensor a numerical framework was set up to support the measurements by delivering additional insights into the process. Recent numerical investigations employ a coupled Eulerian–Lagrangian (CEL) approach to model the extreme deformations in the cutting processes with less mesh sensitivity and higher computational performance compared to the often applied arbitrary Lagrangian Eulerian formulation (ALE) [21]. Thus, the presented numerical investigations on SLD focuses on the CEL approach. As discussed before, the investigated process parameters were obtained from design of experiment (DoE) to parametrize regression models (see Table 1). Finally, these regression models will be included in the control concept for SLD. In addition, the experimental results were employed to validate the simulations results.

Basically, the CEL modelling approach combines the advantages of the Lagrangian formulation with the advantages of the Eulerian formulation [22]. In the Lagrangian formulation, the Lagrangian body is meshed from a discrete geometric part instance, which corresponds to the shapes of the parts being modeled. Each individual mesh node with its material point is moved and deformed as one entity in space, so the material boundary coincides with the element boundary. This conventional formulation offers geometrical accuracy, robustness and computational efficiency. However, it tends to exhibit severe mesh distortion when undergoing very large deformations. In contrast, the Eulerian formulation uses compressible Navier–Stokes equations and can be utilized to obtain a reasonable solution in situations where the material undergoes extreme deformations such as gas and fluid flow or machining problems. The Eulerian mesh is fixed in space and does not deform, whereas the material within the Eulerian domain can move and deform separately from the mesh nodes. The Eulerian elements may be partially or completely void from material, which is then represented by volume fractions within each Eulerian mesh element [23]. The solver Abaqus offers this promising simulation approach with the functionality of the typical Lagrangian FE models, such as constitutive laws or contact definitions.

The setup of the assembled simulation model consisted of the tip of the drill head including the cutting insert and the two front guide pads as well as a penny-shaped workpiece (see Fig. 15). The geometry of the drill head was extracted from CAD data of Gühring KG and the geometry of the workpiece based on the cylindrical samples in the experiment. To reduce the computational costs a thickness of 5 mm of the workpiece was considered and just the radius of 12.5 mm was taken over from the experiment. As mentioned before, the drill head was shortened to represent the drill head tip with the prefrontal guide pads and the cutting insert. Due to the high stiffness of the insert and the guide pad in the drill head, which are based on cemented carbide, the whole drill head was considered as one rigid body part. The insert possesses an ideal sharp cutting edge radius. In order to move the driller in the correct way with respect to feeding and rotation, a reference node was defined, which is linked to all of the nodes in the drill head. Thus, on this reference node a lateral velocity along the driller axis and an angular velocity around this axis were applied. Furthermore, the degrees of freedom at the bottom surface as well as the lateral surface of the penny-shaped workpiece were restricted to avoid rigid body movement of the workpiece.

As contact conditions, a general contact was defined between the drill head surface and the upper surface of the workpiece with a hard pressure overclosure correlation, which describes the interaction of the cutting insert and the workpiece in direction orthogonal to the surface. Further selected interaction properties are the Coulomb friction model with a friction coefficient of 0.32 [24].

The coupled thermomechanical simulation setup even requires heat generation due to friction assigning a factor of 0.99, which determines the distribution of heat between the interacting surfaces and an initial temperature, which was set to room temperature. In contrast to the experiments, the drilling condition within the simulations were assumed as dry.

The mesh of the Eulerian domain contains hexahedral elements with an averaged edge length of 0.25 mm. To represent the material behavior properly, thermal properties as well as mechanical properties with temperature and strain rate dependency were assigned. For machining simulations, the so-called Johnson–Cook (JC) model in combination with its damage model has proven to deliver realistic mechanical response. For the summary of the material data of the drill head as well as the workpiece and for further details of the FE model it is referred to Guski et al. [25].

Due to the high computational effort, a mass scaling factor of 1.0 × 10⁵ was selected to perform the whole simulation study. In total simulations with nine different process parameter combinations, which can be found in the table of the response surface design (Table 1), were run and analyzed using this mass scaling factor. To remove the effect of the mass scaling factor on the simulation results the process parameter set with the highest feed and thus shortest calculation time was selected to perform a sensitivity analysis. The resulting quantities, such as the feed force, the drilling torque and the temperature at the cutting edge for different mass scaling factors were used to extrapolate to values without mass scaling. For this purpose, the following nonlinear regression model using the so-called Huber loss as weight function was applied [26]:where A, B and C are the regression coefficients of the non-linear model, which have to be determined for each quantity. The determined coefficients are summarized in Table 2.

By comparing the extrapolated quantities with the quantities at a mass scaling factor of 1.0 × 10⁵, values for the mass scaling effect were calculated. The evaluation of feed force, the drilling torque and the temperature leads to mass scaling correction factors of 0.30, 0.37 and 0.24, respectively. These values were then applied to the corresponding simulation results. This procedure has delivered more realistic results, which were used to parametrize the polynomial regression models for the soft sensor.

All simulation results were evaluated with respect to the feed force, the drilling torque, the temperature at the cutting edge as well as the residual stress in the bore hole wall and adjusted by the mass scaling correction factor. Each simulation delivers a value for the whole parameter space, which was defined by using the response surface design (Table 1). For evaluating the feed force and drilling torque, the reaction force and torque at the reference point in feeding direction were evaluated. For each process parameter set the simulation time was adjusted to reach the steady state regime with constant quantities. Then the arithmetic average was calculated within the steady state regime. This resulting value was plotted for each simulation with respect to the feed rate and cutting speed.

Then, a polynomial surface fit of second order with respect to the feed velocity (X) and a linear dependency according to rotational speed (Y) was applied to determine the parameters of the regression model with the form:where b_ij are the estimated regression coefficients to plot a three-dimensional surface that captures the predicted value of the dependent variable (Z) at every combination of the two independent variables (X, Y).

For comparison reasons, the fitting procedure was repeated for the experimental data.

Figure 16 shows the simulation results (circle) and the experimental values (triangle) visualized by marker of the feed forces (top) and the drilling torque (bottom). In addition, the determined regression surfaces are shown. For both quantities the surfaces show a comparable shape: increasing force with increasing feed and increasing rotational speed, but a slightly higher level for the experiments. The overall behavior is correctly approximated. However, in the experiment for a high feed a decrease of the torque with increasing rotational speed and a maximum deviation of the simulation results and the experimental values for a high feed and a low rotational speed was observed. This deviation can be attributed to the influence of the absence of a lubricant and thus significantly higher workpiece temperatures, which softens the workpiece material in the simulation. As indicated by the positions of the regression surfaces to each other the simulation results underestimate the experimental results for both, the feed force and the torque. To quantify this observation a mean value for the nine different process parameters were calculated: for the feed force a mean difference of 32% and for the torque a mean difference of 26% was obtained, respectively. These mean values cover a variance from 9% (high feed velocity) to 62% (low feed velocity) of the whole process parameter space.

The procedure to identify the regression model was repeated with the temperature at the cutting edge and the temperature values of the PT1000 located directly under the cutting insert for all process parameter sets. The observed values as well as the determined regression surfaces are shown in Fig. 17 top. The deviation of the results between simulation and experiment is larger compared to the feed force or drilling torque. Due to the lubricant and measurement positions, a temperature between 40 and 60 °C in the whole parameter space was measured. In contrast, the simulations provide much higher temperatures but the same trends, an increasing temperature with increasing feed and increasing rotational speed. Whereas, the increase in temperature with increasing rotational speed is less pronounced. Overall higher temperatures are observed, which was expected due to the difference in the location of RTD underneath the insert, which is different from the evaluation point on the outer corner of the cutting insert in the simulation. On the other hand, the temperatures from the CEL simulation are underestimated compared to the temperatures in the cutting zone from the literature and from the preliminary investigations [27]. This analysis is supported by a mean difference of 66% with a maximum difference of 300% for a high feed velocity. Much smaller deviations can be found for low feed velocities.

The residual stresses in the bore hole wall were analyzed and collected for all nine process parameter sets. The analyzed values are the arithmetic average of the tangential stress in four positions around the bore hole. These values were compared with results from residual stress determination measurements with the hole drilling method. For robustness reasons the values in a depth of 50 µm were employed. Each process parameter set leads to compressive stresses in tangential direction in the subsurface region of the drill hole wall. Then, a polynomial surface fit of second order was applied to determine the parameters of the regression models according to Eq. 2. The regression surfaces and the corresponding numerical results and experimental determination of the residual stress shows Fig. 17 bottom. Overall, a good match between the numerical and experimental results were obtained. The deviations in the shape of the regression surfaces showing a concave shape for the simulation results and a convex shape for the experimental results, respectively, can be originated from an overestimation in the simulation for a small feed and small rotational speed as well as an underestimation for a high feed and a high rotational speed. In addition, the high tensile stress of 336 MPa for a high feed velocity and low rotational speed, which is close to the yield strength of the material at room temperature (410 MPa [28]) was considered as an outlier. These observations are caused by the remarkable scatter of the experimental results of the hole drilling method within the process parameter sets, which has to be taken into account for the assessment of the results. However, except of the outlier, all the determined values are in the compressive regime from − 530 to − 30 MPa.

The resulting regression coefficients and the estimated error (R²) are summarized in Table 3. Especially, the R² is remarkable small for the feed force and the drilling torque. Since the temperature is almost constant in the entire parameter space in the experiment the agreement with the polynomial model is rather poor, as expected. The same observation holds for the residual stress but due to a large scatter in the obtained values. For this quantity, a third order polynomial model reduces the estimated error significantly.

The presented numerical investigations show, that the CEL approach is able to deliver realistic results for drilling processes. Due to simplifications of the FE models, such as a shorter workpiece, comparable large element sizes, and dry drilling condition, which are necessary due to the high computational effort, expected deviations occur in comparison to experimental results. Nevertheless, especially the mechanical quantities, such as feed force, drilling torque and residual stress, deliver a good agreement in most of the parameter space. Just in the range of high feed velocity (50–70 mm/min) and low rotational speeds (1000–1200 min⁻¹) larger deviations were observed. Within the framework of this numerical study, the parameters of the second order polynomial regression surfaces were determined and provided to the soft sensor for online monitoring the thermomechanical status during the drilling process.

Beside the development of the sensory tool and the determination of the characteristic fields for describing the thermomechanical conditions as a function of the process parameters the correlation between the subsurface properties and the thermomechanical conditions were investigated. Finally, this connects the process parameters with the subsurface properties, which are the target variables of the controller and soft sensor to be developed. The thermomechanical conditions, such as the feed force or the temperature are the measured variables of this closed loop controller, which are accessible during the process with the aid of the sensor-integrated tool. The process parameters are correspondingly the control variables of the controller. In order to describe the subsurface properly, the 39 specimens from the response surface design must be investigated in depth. For describing the subsurface quality, the residual stresses in the bore wall were determined and the microhardness, the roughness, the grain size and the grain morphology were examined. Afterwards, characteristic fields of the subsurface properties were generated and a multiple regression model was derived, which predicts the subsurface condition by taking into account the measured variables and the control variables.

The residual compressive stresses were measured using the hole drilling method in a distance of approx. 10 mm from the driller exit, due to better accessibility (see Fig. 18 right). First, a strain gauge rosette is adhesively bonded to the bore wall, then the specimen is cut along the axis of rotation and the released strains are measured. Subsequently, a hole is drilled in the strain gauge rosette and the strains dependent on the depth are also recorded. Finally, these strains were converted to the residual stresses in the subsurface. Figure 18 shows the resulting tangential and axial stress dependent on the depth of an example measurement at medium rotational speed and low feed rate (pass sequence = 7). As can be seen, high residual compressive stresses are generated in both directions in the single-lip deep hole drilling process, which decrease with the distance to the machined surface. The final residual compressive stress is a superposition of the stresses resulting from the cutting process as well as from the forming by the guide pads. Figure 19 shows the resulting residual stress in a depth of 50 µm for all the investigated samples as characteristic fields of the residual stresses in tangential and axial direction. The residual stress was evaluated in a depth of 50 µm due to the high uncertainty in smaller depths. On the top, the residual stresses are shown in the axial direction relative to the workpiece geometry, and on the bottom in the tangential direction. In the tangential direction, the residual compressive stresses are higher. This can be explained by the guide pads, which form the bore wall in this direction.

Furthermore, it can be clearly seen that lower rotational speeds and feed rates, or lower temperatures and feed forces tend to cause higher compressive residual stresses. Similar effects could also be observed in the turning process of aluminum alloys [29], lower cutting speed lead to compressive residual stresses. This could be explained by the temperature effect of the residual stress: higher temperatures tend to induce tensile residual stresses, while the lower the temperature is, the higher are the compressive stresses in the workpiece. This effect can be explained by the interaction of thermally and mechanically induced residual stress. For elevated temperatures, the thermal effect become more dominant and the generation of mechanical residual stresses is counteracted by a thermal component due to the frictional heat generated and the work of deformation. In this case, the residual compressive stresses are reduced in the subsurface region, as the high-temperature yield strength is exceeded during the process [30]. The comparison of the characteristic field of the temperature (Fig. 14) with the characteristic field of the residual stress in Fig. 19 shows this correlation, nicely.

For characterizing the subsurface of the bores further, microhardness measurements were performed. Thin slices were cut out in the center of the cylindrical specimen. Then the cut samples were embedded in resin for the surface preparation to carry out the hardness (HV 0.05) measurements radially outward from the bore wall. The total thickness of the bore wall is 3.5 mm. The first measuring point is located 20 µm from the bore surface; all other points are located at a distance of 100 µm from each other. The resulting hardness values are the mean values from three repetitions. As can be seen in Fig. 20 top, the scatter of the confidence interval is high, but a clear decreasing trend of the hardness with the distance from the bore surface is observed. This observation is valid for all investigated cutting parameters. By this method, the gradient can be determined and thus the degree of hardening in the subsurface. The red measuring point with a hardness of 395 HV 0.05 is located at a distance of 100 µm from the bore wall and is the mean value of 10 measurements on the circumference of the investigated slice. The standard deviation is approx. ± 6.7 HV 0.05. The mean value in this depth will be used for the soft sensor because the strain orthogonal to the indentation direction of the Picodentor HM500 Helmut Fischer close to the edge falsifies the measured values leading to an underestimation. The characteristic field in Fig. 20 bottom shows the mean values of all samples at a distance of 100 µm from the bore wall. A similar tendency as for residual stresses can be observed; with decreasing cutting speed and feed rate (i.e. at lower temperatures and feed forces) the highest hardness is achieved. However, the hardness measurements are also high at very high rotational speed and feed rate, which is a positive effect from an efficiency point of view.

In addition, the depth of grain refinement of the deep-drilled specimens was examined. For this purpose, the same slices from the center of the specimen as for the microhardness measurements were examined using the electron backscatter diffraction (EBSD) data from SEM analyses. Figure 21 shows the microstructure in the area below the surface in the sample produced with the process parameters n = 1057.89 min⁻¹, v_f = 29.09 mm/min, p = 20 bar, V̇ = 5 l/min (pass sequence = 1), exemplarily. The colors of the grains refer to a certain crystallographic orientation, which were just used to separate each grain during automatic evaluation of the microstructure.

A pearlitic microstructure with randomly orientated lamellar grains is observed for the whole area. However, a closer look on the subsurface, which shows Fig. 22 left, deliver an affected area adjacent to the surface.

The surface of the bore wall is in the upper part of the image. Close to the surface a clearl grain refinement was observed with very small equiaxed grains due to the machining up to a depth of 2 µm. Below this depth, it is also clearly seen that the grains increase and become aligned in the cutting direction. In order to quantify the depth of impact, the number of grain center in the horizontal section across the depth was evaluated. As a result, two regimes were observed: close to the surface with a high number of grains and apart from the surface with a continuously decreasing number of grains, see Fig. 22 right. The transition depth, which is assumed as the transition from the first to the second regime, was defined as the intersection of the regression lines based on a Gaussian model. In this example, a transition or impact depth (d_im) of 1.82 µm was determined. This value will be used for the subsurface quantification via the regression model. With the aid of the EBSD investigations, it was found, that the drilling process affects the microstructure especially within a distance from the surface up to 5 µm depending on the process parameters. This leads to the conclusion that this subsurface area possesses a major impact on the increase in microhardness in the subsurface region, finally.

Additionally, the roughness Ra in the center of the specimen was also investigated and plotted as a characteristic field in Fig. 23. It can be seen that the surface quality improves with increasing feed velocity and rotational speed.

Four quantities have been presented that are used for as subsurface properties, the residual stresses, the microhardness, the impact depth of grain refinement and the roughness. Thus, four target variables and two control variables (n, v_f) are available for the controller. This leads to a requirement of eight transfer functions, which is challenging to implement in the controller design and not robust enough because the subsurface characteristics can have opposite effects. Therefore, a promising approach is to normalize the subsurface properties and to condense them to one characteristic value, which is called SUBS for subsurface, see Eqs. 3–7. SUBS is the mean value from the normalized subsurface properties and can have a value between 0 and 100. The algebraic sign of the individual subsurface characteristic values and whether a maximum or a minimum is striven for must be taken into account. This approach enables the fitting of a multiple polynomial regression function, which describes the characteristic factor SUBS_reg as a function of the control variables (n, v_f) and measured variables (M, F_f, T and a respectively n_ist), thus condensing all the characteristic fields presented (Eq. 8). For the realization, the Minitab software is used. As a specification, terms up to second order should be used and interactions between predictors should be considered. The statistical software calculates the best fit. As can be seen, the feed velocity has a great impact on the subsurface quality. R² is a measure of how well the model fits. An R² of 1 indicates that the regression predictions perfectly fit the data.

In the preliminary investigations, it was found that a dynamic excitation in e.g. sinusoidal form or as chirp excitation, as it is done for highly dynamic systems to derive the transfer function, is not reasonable for a comparably slow system with a dead time of 150 ms [17]. Therefore, in the coming investigations, the transfer functions for the closed loop controller will be determined experimentally by first changing the feed velocity in steps at constant rotational speed and next changing the rotational speed at constant feed velocity. With the introduction of the characteristic value SUBS, only two transfer functions are required, for n and v_f. For the experimental data the transfer function will be determined by using Matlab software with the System Identification tool. The core of the multivariable controller are two proportional–integral–derivative (PID) controllers each for v_f and n and the soft sensor (SUBS_reg) that predicts the subsurface quality. The PID controllers will be parameterized in Simulink using the two transfer functions. The overall design of the multivariable controller in LabVIEW can be seen in Fig. 24. The regression model is used as a function and receives real-time measurement data from the sensory tool and the measurement equipment as well as the current set values of the control variables v_f and n, which guide the process and are specified by the external hardware respectively (Fig. 5). Therefore, the soft sensor possesses the function of an observer; the current process state and the control variables will be used to feed back the predicted target variable SUBS, which allows the calculation of the control deviation. In addition to the soft sensor and the PID controllers, the design includes a feedforward control, which prevents the intervention until the cutting edge is engaged. Besides, a control is implemented, which only switches on the rotational speed controller if the feed velocity has reached the upper or lower limit and the target value is not yet achieved or the control deviation is still too large. Furthermore, two function units are implemented, which convert the control values specification into a binary signal for the machine control. The next step in this work contains testing and optimizing the design.