Model-supported Improvement of Stability Limit Predictions in Milling Through Artificial Neural Networks

Abstract

Stability lobe diagrams are a well-known method to differentiate stable from unstable cutting conditions and to indicate stability pockets with high productivity in milling. Unstable process conditions lead to self-excited vibrations between the tool and the workpiece, so-called chatter vibrations, which have highly negative consequences such as reduced machine and tool lifetimes and deteriorated workpiece surface qualities. The creation of stability lobe diagrams, however, is typically associated with an extensive measurement effort and the usage of expensive equipment. At the same time, model-based predictions of the required input parameters are usually associated with a high uncertainty, which leads to significant discrepancies between predicted and experimentally observed stability limits. Hence, the creation process of such stability lobe diagrams needs to be developed further to make them attractive for industrial applications. This thesis proposes strategies on how existing models and experimental data-driven machine learning approaches can be combined to enable precise stability forecasts and make the exploitation of stability pockets in industrial milling operations possible. Three approaches are presented on how neural networks and analytical models for the machine dynamics, the cutting coefficients and the stability evaluation can be linked to allow for a rapid estimation of the shape of the stability lobes. Different from any previously developed approach, any stable or unstable cut recorded during arbitrary cutting operation can be included in the optimizations, and dedicated experiments become obsolete. With the acquisition of more data, the precision of the stability predictions increases over time. These points make the developed approaches valuable tools for an application in a real production environment. In the first approach, neural networks are implemented upstream of the stability solution to identify unknown relationships between easily measurable and unknown, hard-to-measure parameters. The networks are trained with a genetic algorithm using a cost function that compares model stability predictions with the experimental stability states of the training samples. The second approach extends this idea by including a modularized model of the machine structure and of the cutting coefficients, which allows transferring the gained knowledge to new cases with different machine and process configurations. The realized modularization scheme is the result of a tradeoff between an accurate representation of the behavior of the single components and a reasonable characterization complexity. In the optimization process, the algorithm can correct the assumptions on the model behavior of the components. By introducing a penalty for cases where the algorithm deviates strongly from the expected model parameters, physically reasonable solutions are favored and the physical interpretability of the results is enabled. Furthermore, the introduction of a sensitivity analysis step helps selecting only the most relevant optimization parameters, and, hence, reduces the computation time significantly. Finally, the third approach proposes a concept that can also correct the assumed stability model. The approach is based on transfer learning for deep neural networks. The analytical models are transformed into a deep neural network, which is trained with simulated data. This network is then fine-tuned with a much smaller experimental data set. An ensemble technique is proposed to enhance the prediction accuracy. The proposed approaches are steps towards the self-enhancing milling machine, which continuously monitors process conditions and stability states of cuts, and which uses this data to yield increasingly precise stability lobe diagrams over time. In several application cases it is shown how the proposed methods can yield large gains in productivity since an efficient exploitation of stability pockets becomes finally feasible. Compared to the outcomes of state-of-the-art analytical modeling approaches, results show prediction accuracy improvements of more than 40%. Contrasted to state-of-the-art algorithms that are solely based on machine learning, approximately five times fewer experimental training samples are necessary to reach the same prediction accuracy on a test set.