Arrangement for a tool spindle with a moveable pulling rod (3) axially displaceable in the spindle axle (1) for firmly attaching the tool. The pulling rod is surrounded by at least one spool (9) that is stationary in relation to the axial displacement of the pulling rod (3) which gives a specific current flow that differs depending on the axial position of the pulling rod (3) in the spool (9), whereby the rotating part (1, 3) of the tool spindle in the form of the spindle axle (1) or the end part (10) of the pulling rod (3) that projects out from this, is accommodated in a stationary unit (4) that is at the end of the tool spindle opposite to the tool and which has an axial bore (6), that the stationary unit (4) is provided with an inlet for introducing coolant fluid under pressure to the bore (6) and that a gap sealing is arranged between the rotating part (1, 3) and the stationary unit (4) adjacent to the inlet to allow leakage of fluid through the gap sealing.