The invention relates to a procedure, in abrasive engineering practice, for smoothing and fine grinding during the production of workpieces with complicated working requirements, such as extremely long holes with, for example, an interrupted cut or material which is difficult to machine. For this purpose, the smoothing or fine-finishing phase of a grinding cycle is interrupted in the 3bLm-range before reaching the zero point and a further dressing of the abrasive element is initiated to restore the cutting ability of the abrasive element.
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