the graph of fig1 c it is evident that the method of the present invention can more accurately estimate the thermal displacement of the rotatable component of the machine tool regardless of the manner in which the rotational speed is changed as can be understood from the foregoing description according to the present invention the time constant of thermal displacement is calculated by the function of the rotational speed of the main shaft of a machine tool in order to accurately estimate the thermal displacement of the main shaft therefore it is no longer necessary to store a large number of time constants of the thermal displacement corresponding to different rotational speeds as has been required by conventional methods this means that time constants of the thermal displacement can be calculated from rotational speeds that are not included in an experiment moreover since only the relational expression rather than a large data volume in matrices has to be stored to obtain time constants of thermal displacement from rotational speeds the method of the invention provides the advantages that it reduces both time required for calculations and the required size of the storage device of a numerical control unit furthermore by using the time constant ratio r calculated by dividing the time constant of thermal displacement by the time constant of temperature change more accurate compensation can be performed for the thermal displacement of a machine tool component whose temperature and thermal displacement time constants are subject to change due to various operating conditions such as the performance of the.