A motor spindle includes a spindle shaft for receiving a tool. The spindle shaft is accommodated in the housing of the motor spindle in a fixed bearing and a loose bearing. The received tool enters into contact with the machined workpiece in a tool interface when the spindle shaft is driven and the tool interface is displaced in an axial direction of the spindle shaft when a workpiece is machined. A displacement sensor is provided on the spindle bearing in order to determine the axial displacement of the tool interface. There is also a motor spindle including a spindle shaft for receiving a tool. The spindle shaft is accommodated in the housing of the motor spindle in a fixed bearing and in a loose bearing with an axially displaceable bearing bushing. The tool enters into contact with the machined workpiece at the tool interface when the spindle shaft is driven, and an adjusting element which is used to adjust the axial displacement of the bearing bushing of the motor spindle is also provided.