The article analyzes the accuracy of installation of tool conical profile mandrels with taper 7:24, 1:10, 1:20 into the hole of the machine spindle at six coordinates. After assembly of the connection the spindle received rotary motion with a speed rate typical for high-speed processing. Thereafter, the tool mandrel was loaded with a conditional external load (from cutting forces). We calculated mathematical expectations of elastic displacements (change in the position of the mandrel in the spindle hole) for six coordinates in the conditions of reusable assembly. In each calculation case, we compare the accuracy of the relative position of the RC-3 profile connection parts for different speed numbers during its operation under the influence of a conditional external load. Cross travel values of connection parts with a technological error in the geometric shape of the landing surface of a profile conical mandrel of the P-3 type at a speed rate of 10000 to 48000 rpm are no more than 3.5 microns at a taper of 1:10 and no more than 5 microns at a taper of 7:24. Accordingly, with a speed rate 50000 to 95500 rpm the values are no more than 4.5 microns with a taper of 1:10 and no more than 8 microns with a taper of 7:24 at the end of the connection.