Compensation of Machine Tool Thermal Errors Based on Transfer Functions

Abstract

ver its application on thermo-mechanical system is relatively new phenomenon [Fraser 1998a]. 2.1 Thermal transfer function A thermal transfer function (thermal TF) contains the nature of the heat transfer principles, thus the calibration of the empirical parameters is simple and the model is in addition more reliable with untested inputs, because the data are forced to conform to the same principles as the real process. At the same time the results are obtained by two orders of magnitude faster [Fraser 1998b]. These parameters make the thermal TF very suitable for real-time modelling and diagnostics of varied thermo-mechanical systems. This topic is rarely discussed in a technical literature; therefore authors firstly created terminology used for thermal TF which is described in Tab. 1. The thermal TF can be employed for wide spectrum of application including diagnostics, determination of boundary conditions for a thermo-elastic FEA or a compensation of thermal errors at TCP, e.g. an inverse temperature transfer function (ITTF) is suitable for real-time heat source identification [Horejš 2009] etc. 2.2 Principle of the compensation techniques Thermal errors of a machine tool are result of a very complex thermo-mechanical process. In order to create high quality real-time thermal error model of a machine tool using transfer functions, these functions must contain dynamic parameters resulting from the current thermo-elastic state of a machine tool. The real-time self tuning of TF parameters will lead to a precise real-time estimation of current thermal errors. When these thermal errors are compensated, long-term thermal stability of a machine tool can be achieved. Compensation of thermal errors at TCP have been developed and experimentally verified on different real machine tools using two different compensation strategies. First method is based on control of the cooling systems which has to cause deformation right opposite to instantaneous thermal errors. This method is thoroughly described in [Bárta 2007]. This paper is focused on a second developed compensation technique using indirect software compensation. Principle of the method is shown in Fig. 1.

Effects of Cooling Systems on the Thermal Behaviour of Machine Tools and Thermal Error Models

“…TFs are commonly used in the analysis of analogue electronic circuits and mechanical systems. Application of TFs on thermo-mechanical systems has recently become an appealing phenomenon [18][19][20][21][22].…”

Thermal issues in machine tools

“…For a combination of different inputs, temperature sensors placed on the machine tool structure, and rotational spindle speed, the transfer functions are presented in [78,79,140]. The model uses different transfer functions, based on actual rotational speed.…”

Compensation of thermo-dependent machine tool deformations due to spindle load: investigation of the optimal transfer function in consideration of rough machining

“…The input of the estimated transfer function can be NC-data like spindle speed, effective power, electric current, torque or feed rate [19][20][21]. The temperatures of the machine structure can be used as an input, too [22][23][24][25][26][27][28][29][30][31]. An advantage of this method in case of compensation by using NC-data is the fact that no external sensors are required.…”