The housing of a grinding spindle unit is pivotably mounted by way of a pivot axle on the receiving part of a grinding machine, e.g., on a grinding headstock. The grinding spindle unit bears a grinding wheel which is driven in rotation. The actuation of an adjusting unit extends a pressure pin, which pivots the housing of the grinding spindle unit about the pivot axle and thus slants the grinding wheel. The pivot axle is in this case formed as a film hinge through a zone of targeted elastic material deformation. A tensile spring device brings about constant contact between the pressure pin and the receiving part.
