Machine tools are increasingly being equipped with edge computing solutions to record internal drive signals with high frequency. A large amount of available data may be used to develop new data-driven approaches to process optimization and quality monitoring. This paper presents a new approach to predict the quality of finished workpieces for three-axis milling processes with end mills. For this purpose, internal machine tool data provided by an edge computing solution was recorded and used to develop a Machine Learning based method for quality prediction. For the preparation of the data, an introduced domain knowledge-based slicing algorithm is applied, which allows the recorded data to be automatically and precisely assigned to the corresponding geometric elements on the workpiece. During data-driven modeling, 9 Machine Learning algorithms are compared to 4 Deep Learning architectures for multivariate time series classification. The results show that ensemble methods like Random Forest and Extra Trees as well as the Deep Learning algorithms InceptionTime and ResNet reach the best performances for the use case of data-based quality prediction.