Self-optimizing process planning of multi-step polishing processes

The implementation of the self-optimizing process planning is carried out by using algorithms for tool path generation and for deriving the locally suitable feed rate. This is based on an initially measured topography as well as the actual contact surface of the flexible polishing tool. The entire planning algorithm is implemented in the material removal simulation software IFW CutS which provides an open simulation platform for the technology-oriented simulation of manufacturing processes. IFW CutS offers basic functions of a dexel-based geometric process simulation on the basis of NC-based tool paths [32].

The initial tool path is adapted in such a way that more intensive machining is carried out in areas of poor surface quality or where a specified target roughness has not yet been reached. This is achieved by local reduction of the feed rate. Further roughness reduction is achieved by polishing multiple times at the same spot. The procedure for the adaptation of the NC-code is shown in Fig. 4. The tool moves according to the initial tool path in the material removal simulation. In each time step, the local situation is determined by reading and evaluating the extenders of the dexels penetrated by the tool and located within the contact zone determined by the contact width model. Based on the average initial roughness value of all penetrated dexels of the contact zone, the appropriate polishing case and the corresponding feed rate at this point are derived, allowing a maximum roughness reduction without falling below the selected target roughness. The roughness model used for this purpose is based on data from polishing experiments. Three different polishing cases are distinguished: no change in the feed rate necessary, change in the feed rate necessary, and no polishing.

The predicted roughness resulting from the selected feed rate is updated in the extenders of the affected dexels. The feed rate is updated in the initial NC-code at the respective position. As a result, by detecting the change of the polishing case, the NC-code segment is only added when the feed rate is changed. In places where the target roughness is already present, polishing is no longer performed and the polishing tool is moved upwards away from the workpiece.

In addition, a choice can be made between two different polishing strategies: with the undercutting strategy, polishing is performed in each case as soon as the measured roughness fails to meet the target roughness. The algorithm then selects the feed rate with which the maximal possible roughness reduction can be achieved without falling below the target roughness. If this is not possible, polishing is still performed at the feed rate which results in the smallest roughness reduction for this situation. Alternatively, with the approximate strategy, polishing will only be performed, if the roughness predicted from the selected feed rate is equal to or above the target roughness after polishing.

Areas are polished repeatedly, if the roughness has not yet reached the desired target value. This is done in the subsequent polishing iteration. The maximum number of polishing iterations is initially specified for repeated polishing. The planning of the process variables for a polishing iteration is based on the predicted roughness values of the previous iteration. For this purpose, the extenders contain so-called roughness lists, which store the roughness values for each polishing iteration. During interaction between tool and workpiece, the roughness values of the first polishing iteration are updated with the predicted roughness value. For the prediction of the following iteration, the values of the first iteration are used as initial roughness values. These are then stored in the second iteration of the roughness list. This is continued until the given number of maximum iterations is reached. The result is an adapted NC-code for the individual machining case. The generated NC-code, based on CLDATA, is converted via the postprocessor and can thus be used on the machine.

In the experiments, the isolated influence of the feed rate on the roughness is examined in more detail because this has the greatest influence according to the screening experiments in [8]. The other parameters are kept constant. In the experiments, the feed rate is varied in ten steps from v_f = 50 mm/min to v_f = 500 mm/min. The inclination angle is kept constant at α = 30° and the depth of cut at f_t = 2 mm. The cutting speed is also kept constant at v_c = 15 m/s. The data from the experiments is used to train the machine learning model. The results in Fig. 5 show that a higher roughness reduction can be achieved with a slow feed rate, which was to be expected. Thus, this parameter can be used for process planning to set desired target roughness values. In order to model the development of the surface after multiple machining steps, the samples are polished with varied repetition and feed rates. After each pass, the roughness is measured. During the experiments, polishing is repeated up to five times. The roughness reduction decreases with increasing repetition. In some cases, however, a roughness increase can also occur. The influence of different initial roughness values before polishing, generated by the different polishing repetitions, is taken into account for further modelling. The increased standard deviations may be due to uncertainty of roughness measurement or wear of the polishing tool. A systematic error can be excluded because the roughness difference is normally distributed. This is shown by the Shapiro–Wilk test, where the p-value is 0.25 and thus above the significance level of 0.05. Furthermore, five repeated measurements at the same surface location show a standard deviation of 0.003 μm regarding Ra. In this context, a reproducible measurement can be achieved by the stylus profilometer.

In order to be able to examine the influence of the curvatures of the components, two different radii of curvature (R = 60 mm and R = 120 mm) are selected for the convex and concave components respectively. For each unique geometry of the convex and concave parts, polishing tests are carried out by varying the feed rate, depth of cut, and number of repeated polishing operations. The feed rate is varied in five different step values (v_f = 133.2; 200; 300; 400; 466.8 mm/min). The depth of cut is also varied in five steps (f_t = 0.67; 1; 1.5; 2; 2.33 mm) and the number of polishing operations is varied in three steps (N = 2; 3; 4). All factor stage combinations are determined by using an orthogonal, rotatable, and centrally-composed experimental design. The polishing direction is transverse to the milling direction.

The planning algorithm is extended with a learning roughness model. In order to improve predictions of the roughness difference, the obtained polishing results are fed back to the roughness model. For this purpose, it is necessary to provide continuously updated data of the measurement after the process. For the planning and analysis of the iterative polishing process, measured values from a tactile roughness measuring instrument are used. As roughness cannot be measured over the entire surface, an interim solution is implemented by assigning the measured values over circular zones. The actual mean roughness value is measured around the center of each circular zone. Each circular zone represents one measured value so that all dexels within this circular zone have the same values. By selecting the radius and position of the circular zones, the entire surface of the workpiece is initialized with the measured values. For the plane workpiece, for example, eight circular zones are evenly distributed over the entire workpiece, as shown in the top right-hand corner of Fig. 3. The roughness measurements took place at the center of each circular zone.

The locally measured values before and after polishing, the locally selected process variables, as well as each predicted roughness are stored in the respective extenders. The resulting process information is exported from the extenders and stored in a knowledge database. The knowledge database then proceeds to grow with each polishing iteration and the generated roughness function is trained with larger data sets. Thus, a feedback of the polishing result into the roughness model is realized in order to allow a continuous, iterative update and adjustment of the prediction.

An SVM is used for modeling the acquired process data. In this study, MATLAB’s “Regression Learner” is applied. The settings are listed in Table 2. Other available model types such as Linear Regression, Decision Tree, Ensemble Learning or Gaussian Process Regression were tested, but showed low prediction accuracy for this case. The model was trained with data sets from the initial experiments and, later, from the knowledge database. The cross-validation is applied because of its suitability for smaller data sets. Due to the fixed division of the measurement data set into 50 equally sized segments, one segment is used as validation data set and the remaining 49 as training data. After 50 runs, in which the segment assignment remains unchanged and the segment changes each time as validation data set, each segment is used once for validation [34]. This allows the data to be split randomly, which leads to a more equal distribution of the data and avoids overfitting.

Figure 6 shows the derived roughness model. The roughness model achieves a coefficient of determination of 83%.

In order to transfer the ML-model from MATLAB to the simulation, an Excel file is generated as output from MATLAB, which contains the roughness function in discretized form. Different parameter combinations and the resulting changes in roughness are saved as a list for a range and step size to be set. For predicting the roughness change in process planning, the list is searched for the cases where the initial roughness of the list is closest to that of the simulation. The corresponding predicted value is used for the simulation and the appropriate feed rates are derived from this list. By means of an additional category in which the type of curvature is considered, the aspect of workpiece geometry is included in the database.

The algorithm's ability to learn over the iterations and the self-optimizing planning of polishing processes were examined using three workpieces. The workpieces included planes (P1, P2 and P3), a single convex curved surface (R = 60 mm, R60) and a double concave curved surface (R = 90 mm in both directions, R90). On the surface, different initial roughness values are produced in various areas by milling or grinding. This represents an individual machining case. The planning algorithm is tested to see how well a given target roughness can be achieved using the self-optimizing polishing process with increasing data sets. The applied initial roughness model was based on the experiments presented in Sect. 4.1. The surface is measured after each iteration, so that the next iteration is planned based on current roughness values. The actual roughness values are added to the knowledge base after each iteration and the roughness model is updated by re-training.

Table 3 gives an overview of the evaluation of all component geometries (P1, P2, P3, R60 and R90) with regard to the prediction quality of the roughness change ΔRa. The results are evaluated by means of the Root Mean Square Error (RMSE). The information from the extenders is used for the analysis by comparing the measured roughness values with the predicted roughness values. For P2 and P3, the waviness of the milling process is not taken into account in the roughness measurement and is filtered out accordingly. In addition, polishing is performed with the approximate polishing strategy. For P1, on the other hand, the waviness is taken into account, which resulted in more polishing iterations being necessary. This distinction is not necessary for the remaining components, as they do not show any waviness due to the grinding process. For P1 and the curved components, the undercutting polishing strategy is chosen. It can be generally seen that the deviation in the first iteration has increased for all parts compared to the starting data set in iteration 0. A possible explanation is the different range of the initial roughness between the experiments in Sect. 4.1 and the one generated here. Some of the workpieces exhibit initial roughness values that are also higher in some areas than those of the previous experiments. With increasing iterations, however, the RMSE value tends to decrease, which indicates a smaller deviation between the measured and predicted value. This shows the learning ability of the method with continuous adaption of the roughness model. The planning time is only significantly longer if the model is re-trained after each iteration. However, this can be done in larger intervals if the quality of prediction is sufficient.

Figure 7 depicts exemplary the development of the roughness over the course of three polishing iterations for the surfaces P2 and P3. It can be seen that four areas with different initial roughness values can be distinguished. The aim of the polishing process is in all cases to reduce the roughness to Ra = 0.2 µm. The results show that the surface quality improves with repeated machining. In this case, the target roughness is largely achieved after three iterations. In areas where the target is already achieved, repeated polishing no longer takes place (grey areas).

The validation shows that the approach works for different workpieces. In Fig. 7 it is demonstrated that P2 and P3 produce similar results after three iterations. Existing challenges are firstly the measurement method. Non-polished areas show a deviation of up to 0.06 μm after measuring again in the following iteration (Fig. 7). This is due to the fact that the previous measuring position cannot be hit exactly in the following measuring process. Moreover, the milling process produces a modified initial surface condition which differs from the training data set. Especially at higher initial roughness values around 0.7 μm, the polished roughness of P2 and P3 shows higher deviations in comparison with lower initial roughness values in further iterations. Nevertheless, the model is capable of dealing with different initial situations and is able to derive appropriate process parameters to obtain the target roughness.