Progress in improving the accuracy of metal-cutting machines is inextricably linked and driven by deeper knowledge gained through the study of thermal processes and effects occurring in machines, which can be used to manage them. This led to the dominance of temperature errors in the balance of machine accuracy, the share of which changed from 20-30% to 70% during the period from 1950 to 2020, which is determined by the absolute value of the achievable machine accuracy. Types and forms of compensation methods were formed (1990-2020), which were based on the use of linear and nonlinear regression or correlation methods. Performing experiments can establish the functional relationship between the measured temperature in the machine nodes and the amount of displacement. With good repeatability and stable reproducibility of the result, an equation expresses this functional relationship. Applying this equation to a program, a control device compensates the thermal deformations. However, in all cases, it is necessary to determine the number and location of temperature measurements on the machine, determining the compensation accuracy. The proposed sensorless model is based on a thermal behavior model and does not require temperature measurements. A method is presented and justified for estimating the number of temperature measurement locations based on thermophysical analysis by applying the finite element method in comparison with the analytical method in order to achieve the required compensation accuracy. For several machine tool types, a comparison is given regarding the control method of the TCP spindle displacement without sensors and with temperature sensors. The limits of their rational use are presented.
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