1. A device for estimating machining dimensions of a workpiece by a machine tool which employs one or more tool members each being rotatably driven by a driving unit, the device comprising: a vibration sensor adapted for detecting vibrations generated from the driving unit; a characteristics extracting unit adapted for extracting amounts of characteristics having a plurality of parameters from a target signal which is an output of the vibration sensor; a competitive learning neural network adapted for classifying the amounts of characteristics extracted by the characteristics extracting unit into categories; a conversion unit adapted for converting, into a machining dimension for a workpiece, the Euclidean distance between an amount of characteristics of a target signal generated by freely rotating a tool member without load attached to the driving unit and a weight vector of an excited neuron for the competitive leaning neural network which has been trained; and an output unit adapted for outputting the machining dimension for the workpiece from the conversion unit as an estimated dimension; wherein amounts of characteristics of the target signal generated by freely rotating the tool member with out load attached to the driving unit serve as training samples of the tool member for training the competitive learning neural network; and the training samples are inputted again to the trained competitive learning neural network to excite neurons so that the relationships between Euclidean distances and machining dimensions of workpieces are registered in the conversion unit, wherein the Euclidean distances are obtained between weight vectors of the excited neurons and respective corresponding training samples, and the machining dimensions are obtained when the workpieces are machined by the tool members at the same condition as the respective corresponding training samples are obtained.