Statistical study of the spindle dilatation phenomena—Application to a NC lathe

Spindle dilatation in one of the most important causes of defects on parts machined on CNC lathes. Experiments and models have been established to determine the average value of the spindle's dilatation. The problem of determination of confidence interval associated to those predictions remains open. If the average value of dilatation can be estimated, any existing model can predict how near or far from the average value will be the spindle's dilatation. This work deals with the problem of type of dilatation measures repartition. A Khi-2 test done on dilatation measures reveals that dilatation measures spread under a normal repartition law. So, a model to determine the confidence interval associated to the dilatation prediction is presented. The repartition law of the samples of dilatation allows to set up this model. Then, a method to calculate an upper bound of the standard deviation of the dilatation repartition law is proposed. The model proposed can be used to determine the confidence interval of spindle dilatation phenomenon. This determination allows a useful prediction of the dilatation because of the confidence interval that can now be associated to the prediction.