High precision grey-box model for compensation of thermal errors on five- axis machines Michael Gebhardt, Josef Mayr *, Nils Furrer, Tobias Widmer, Sascha Weikert, Wolfgang Knapp (1) Institute for Machine Tools and Manufacturing (IWF), ETH Zurich, Tannenstrasse 3, 8092 Zurich, Switzerland 1. Introduction With increasing geometric accuracy, five-axis machine tools became more important in the recent years for applications in precision manufacturing. This opened a completely new market for synchronous five-axis machining. Advantages are, beneath others: work-pieces can be manufactured without extra clamping, when using five numerical controlled (NC) axes, a more time efficient production process becomes possible due to an optimised tool inclination. Nevertheless, there is a great interest in industry for further improvements regarding the accuracy of five-axis machine tools with the aim to use them in even more precise applications. Thermal influences, which cause up to 75% of the geometric errors of a finished workpiece [1], are a big obstacle for a continuing increase of the machine tool accuracy. As the main contributors to the overall thermally induced error, Bryan [2] summarised in the ‘‘thermal effects diagram’’:  room environment;  thermal memory from previous environment;  people;  cutting process;  machine; and  coolants. When neglecting the influence of people and of the cutting process using coolant, for a long time, the focus of research regarding thermally caused deviations was on the influence of the environ- mental temperature change, the main spindle and the linear axes [3– 5]. A lot of prediction models and approaches for the compensation and correction of these thermally caused displacements were introduced [6]. Since a short time, thermally induced location errors of rotary and swivelling axes of five-axis machine tools have been investigated [7–9] in more detail. The main focus of these efforts was on the measurement procedure and on simplified prediction models in order to compensate occurring errors. In this paper, a high precision grey-box model to predict errors induced by internal heat sources such as drives or bearings is introduced. The model allows the correction of occurring tool centre point (TCP) errors based on internal signals up to 85%, which is proofed by measurements. 2. Thermally induced displacements of rotary axes In this paper, the rotary axes A and C of a machine tool with the kinematic chain V [w C2 0 A’ X’ b Y Z (C1) t], according to ISO/DIS 10791-1.2:2013-07-12 [10], i.e. a vertical five-axis machining centre with swivelling rotary table, are analysed. All thermal displacement measurements are carried out with the R-test measurement system [9,12]. The location errors of the analysed axes are listed in Table 1. Significant location errors, i.e. errors that show a systematic, temperature-dependent behaviour, are found by measurements and are indicated in bold. These errors are corrected afterwards with the compensation software. Other location errors are less important due to a thermo-symmetric design of the machine tool in these directions. In Fig. 1, the effects of the main internal heat sources of the analysed machine tool are shown: Fig. 1A and B shows the swivelling rotary table structure before and after a 5 h pendular movement of the A-axis between 908 with rotation speed F rot = 10 8008/min. Fig. 1C and D shows the same structure before and after a rotational movement of the C-axis table for 5 h with F rot = 21 6008/min. Both cases show that the movement leads to an explicit heating-up of the structure around the drives. However, this effect is quite local which can be explained by the cooling system: it prevents the heat from flowing in the adjacent machine tool structure. CIRP Annals - Manufacturing Technology xxx (2014) xxx–xxx A R T I C L E I N F O Keywords: Machine tools Thermal error Modelling A B S T R A C T Thermally induced errors of machine tools cause up to 75% of the geometric errors on workpieces. Research carried out in the last decades focused on influences by the environment, spindles and linear axes. With the increasing demand for five-axis machining, the rotary/swivelling axis units have to be checked and compensated for thermal errors. The R-test set-up is a proper measuring device to characterise these errors. This paper introduces a compensation approach to reduce up to 85% of the thermally induced location errors of rotary/swivelling axis units based on internal NC signals, like power supplied to drives. ß 2014 CIRP. * Corresponding author. Tel.: +41 446332714; fax: +41 446321159. E-mail addresses: mayr@iwf.mavt.ethz.ch, mayr@inspire.ethz.ch (J. Mayr). G Model CIRP-1140; No. of Pages 4 Please cite this article in press as: Gebhardt M, et al. High precision grey-box model for compensation of thermal errors on five-axis machines. CIRP Annals - Manufacturing Technology (2014), http://dx.doi.org/10.1016/j.cirp.2014.03.029 Contents lists available at ScienceDirect CIRP Annals - Manufacturing Technology journal homepage: http://ees.elsevier.com/cirp/default.asp http://dx.doi.org/10.1016/j.cirp.2014.03.029 0007-8506/ß 2014 CIRP.