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The computer numerical control (CNC) machine has recently taken a fundamental role in the manufacturing industry, which is essential for the economic development of many countries. Current high quality production standards, along with the requirement for maximum economic benefits, demand the use of tool condition monitoring (TCM) systems able to monitor and diagnose cutting tool wear. Current TCM methodologies mainly rely on vibration signals, cutting force signals, and acoustic emission (AE) signals, which have the common drawback of requiring the installation of sensors near the working area, a factor that limits their application in practical terms. Moreover, as machining processes require the optimal tuning of cutting parameters, novel methodologies must be able to perform the diagnosis under a variety of cutting parameters. This paper proposes a novel non-invasive method capable of automatically diagnosing cutting tool wear in CNC machines under the variation of cutting speed and feed rate cutting parameters. The proposal relies on the sensor information fusion of spindle-motor stray flux and current signals by means of statistical and non-statistical time-domain parameters, which are then reduced by means of a linear discriminant analysis (LDA); a feed-forward neural network is then used to automatically classify the level of wear on the cutting tool. The proposal is validated with a Fanuc Oi mate Computer Numeric Control (CNC) turning machine for three different cutting tool wear levels and different cutting speed and feed rate values.