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1 Thermo-energetic issues in 5-axis machine tools Simon Züst, Philip Blaser, Josef Mayr, Wolfgang Knapp, Konrad Wegener Institute of Machine Tools and Manufacturing (IWF), ETH Zürich, Switzerland Abstract Thermally induced errors on machine tools are one of the most important error sources in precision machining as up to 75 % of the overall geometrical errors on workpieces are caused by thermal errors of the machine tool [1]. In this paper research carried out on Mori Seiki NMV 5 DCG machine tool at IWF of ETH Zürich is presented. The paper focusess on three different aspects of thermal error research. A thermo energetic model of the machine tool is developed evaluating the energetic flows inside the machine tool structure and derives essential temperature boundary conditions. The second part of the paper deals with a thermal test-piece used for evaluating thermal machine tool errors. The evaluation is compared to R-Test measurements showing correlating results. The third aspect considered in this paper deals with an adaptive learning control for compensating thermal errors on 5.axis machine tools Keywords: Thermal error reduction, thermo-energetic behavior, thermal test piece 1 INTRODUCTION Machine tools are used in manufacturing to produce and modify workpieces by means of energy. Figure 1 shows the generic machine tool life-cycle required for machine tool production are according to [1]: Firstly, the raw materials procured, secondly the machine is produced by the raw material and set in operation, thirdly the machine is used for production and finally, the end-of-life measures are taken. Studies [1,2] have shown the significant contributionn of the use-phase to the total energy and resource demand of a machine tool during its life time. Hence, energy efficiency measures must primary focus on the use-phase of machine tools. During the use-phase, products are produced, whose properties are characterized by the manufacturing properties of the machine tool used. This is indicated in Figure 1 by the overlap of the machine tool and workpiece life cycles. Figure 1: Interacting life-cycles of a machine tool (black) and the products (grey) manufactured during the use-phase of the machine tool. The imprint of workpiecee properties can be in the form of grey energy [2] or due to performance related factors, such as surface properties of bearing seatss [3]. Since a single machine tool in general produces up to thousands of parts during its life time, a significant leverage is offered: Small improvements on the energy and resource efficiency of the manufactured goods in use, due to the performancee of the machine tool used, multiplied by the number of parts produced with the machine tool scale up to a significant environmental contribution. Hence, energy efficient machine tools have to be able to produce workpieces with requirements in precision even with measures causing an inefficient use of the energy and resources supplied. Regarding the geometric quality of the manufactured workpieces, thermal issues in machine tools are one of the 217 The Proceedings of MTTRF 217 Annual Meeting major challenges to be tackled [4]. Heat sources and sinks in the environment of the machine tool structure have a direct impact on the temperature distribution. Non-nominal and non-uniform temperature distributions cause thermally induced deformations leading to tool center point (TCP) position and orientation errors. The relevance of these effects is shown in [5] in the function related energy demand for the operation of machine tools: In the range of 2% of the energy supplied to machine tools is required for tempering measures, while another 25% are required for the supply of cutting fluid. In contrast, only 15% of the energy supplied to machine tools is used to operate the axis-drives and the main spindle. The vital coupling between a machine tool s energetic and thermal dynamics illustrates that with reduced energetic losses the thermal errors induced by internal influences are recued. Designing machine with high requirements in precision requires a profound knowledge of the underling thermo-energetic aspects of machine tools. The paper presents some work performed at IWF of ETH Zürich on NMV 5 DCG regarding thermo-energetic aspects of machine tools. In section 2 an energetic model of the 5-axis machine tool is presented followed by a thermal test-piece used for evaluating thermally induced machine tool errors. In section 4 an adaptive learning control (ALC) approach for compensation of thermal machine tool errors is presented. In section 5 an outlook of the research work planned on NTX 2 is given. 2 ENERGETIC MODELS FOR THE IDENTIFICATION AND PREDICTION OF HEAT SOURCES Thermally induced TCP-displacementss of machine tools are caused by heat sources, as shown in Figure 2. Modelling of the resulting temperaturee field and resulting deformation of the machine tool structure can be achieved by FDM [6], FEM [7] or a combinationn of both [6]. These approaches are well elaborated, but rely on the models of boundary conditions representing the heat source characteristics for the simulated scenario. Energetic machine tool models, as presented in [8-1, are motivated by environmental considerations. Hence, these models predict the energy and resource demand on component level given for a use scenario. The machine component models presented by Gontarz et al. [ 1] are extended to be used for the prediction of internal heat

2 sources of machine tools. The macro models describe the thermo-energetic effects of machine tools on component level by efficient, reduced models with low computational effort. Additional macro models are characterizing the heat transfer between structural elements and coolants inside the machine tool s structure. Figure 2: Root causality between energetic and thermal effects on machine tools inducing TCP displacements [11]. 2.1 Macro models for components In total, three types of lossy electrical consumers have to be modeled for describing machine tools: Drives, amplifiers and pumps. Drives are modeled using the approach presented in [12] for motor spindles with asynchronouss drives. For synchronous axis drives, the ohmic losses are modeled using the equivalent circuit of a DC drive with parameters provided by the manufacturer. Amplifiers are described by a linear approach of their base consumptionn, and the load dependent efficiency :, (1) is the upstream demand for electric power providedd by the amplifier. Using the characteristic relationship provided by pumpp maps, describing the relationship between flow rate, power demand,, pressure raise Δ and hydraulic efficiency the energy transformations in pumps by frictional losses, and ohmic losses, can be described by:, Δ and,, Δ (2) 2.2 Macro models for convective heat transfer Heat transfer between structural parts of machine tools and coolants by forced convection depend on the geometry, flow regime and the fluid properties. The flow regime, i.e.. the flow rate, depends on the topology of the cooling system and the used elements, such as pumps, the distribution system and the cooling channels. Computing the heat transfer in cooling systems requires two steps: Fist, the quantification of the coolant flow rate in each element and second, the computation of the flow rate dependent heat transfer coefficient in each cooling channel. The identified flow rates must fulfill the Kirchhoff laws for hydraulic circuits: The pressure drop in parallel streams in the circuit, must be equal, and the pressuree drops of all elements in a loop must add up to zero. Cooling channel design in machine tools are a result of geometrical limitations and highh energy density. In order to reduce the complexity for pressure loss and forced heat transfer computations macro models based on generic geometry features, as presented in [13] and [14], are used. The shape of the cooling channels is characterized as a series of macro elements, such as straight pipes, edges, helical coils and others. For each macro element in series, the resulting pressure loss coefficient and heat transfer coefficient are computed using empirical correlations, described in [15], and are aggregated over the whole geometry using the macro element s surface, length, hydraulic diameter and cross section : 2.3 Modeling of NMV 5 DCG Based on the implemented model presented, the different energy flows depending on the operational schedule can be computed. Figure 3 shows the Sankey diagram of the average energy fluxes during machining exemplarily the thermal test-piecee of section 3. Three different kind of energy fluxes are distinguished: Electric ( ), hydraulic ( and enthalpy ( ). Given the energy fluxes as shown in Figure 3, the component internal heat sourcess can be computed by assuming that all residual energy is transformed into thermal energy. For a given node the electric, hydraulic and thermal arrows, connected to the residual energy and thus, can be computed by:, and,, Figure 3: Visualization of the average energy flows on the NMV 5 DCG during machining the thermal test piece presented in section 3. Arrows to the investigated node are of positive sign. Vice versa arrows from the node are of negative sign. The analyzed heat sources are the required boundary 217 The Proceedings of MTTRF 217 Annual Meeting (3) (4)

3 conditions for the subsequent FEM analysis of the machine tool s thermal behavior. The extensions of energetic machine tool models together with the macro model based prediction of convective heat transfers in coolants, the gap between energetic and thermal modeling is closed. 3 SIMULATION BASED OPTIMIZATION OF THERMAL TEST-PIECES FOR THE VISUALIZATION OF THERMAL ERRORS In [17] a thermal test-piece for the visulatization of thermal errors of machine tool rotary axes is presented. As some machined features of the thermal test-piece tool error, the thermal test- are not unique related to a thermal machine piece design is optimized with the help of thermo- the mechanical FEM computations. E.g. when rotating turning table of NMV 5 DCG, with high rotational speed, the thermal growth of the aluminum test-piece caused by the table temperature rise is the major contributor to the total thermal test-piece displacements. One focus of the new design cares therefore about the optimization of the fixturing. In Figure 4 the result of the FEM computation shows displacements in Z-direction of the original thermal test-piece design. This shows that the deviations at the center of the thermal test-piece in Z-direction are smaller than at the corner. It becomes obvious that after cooling down a convex shaped surface occurs, as the amount of removed material is larger at the corners of the thermal test-piece than in its center. test-piece deformation in Z-direction is significantly reduced. Additionally due to the homogeneous deformation in Z-direction it becomes possible to also evaluate angular thermal errors. Figure 5: : Computation results of thermo-mechanical deformation in Z-direction of the thermal test-piecee with optimized design, caused by heat up of the machine table by 1 K. The thermal test-piece is virtually supported with precision ground parallel washers. 3.2 Experimental resultss To evaluatee the thermal behavior of the NMV 5 DCG, a test cycle of four hours heating up and four hours cooling down is selected to be comparable with measurements regarding ISO 23-3 [18]. During heating up the C-axis is running with 12 rpm. During the cooling down period, all machine tool axes are in NC-hold. The load cycles are interrupted when the evaluation surfaces of the thermal test-piece are machined. One set of measurement surfaces are machined after each hour operation time. Figure 4: Computation results of thermo-mechanical displacement of the thermal test-piece in Z-direction, caused by heat up of the machine table by 1 K. 3.1 Optimized thermal test-piece geometry The FEM computations show that the major influences on the thermal test-piece deformation is caused by the thermal elongation differences between thermal test-piece (alumina) and the machine tool table (cast iron). The four fixture points then cause an overdetermined mechanical constrained mounting, which induces uncontrolled fixture deformations from the table. The overdetermined fixture is overstressed and deforming, what is directly transferred to deformations of the thermal test-piece. To decouplee the fixture and machine tool influence and to avoid an overdetermined fixturing a 3-point support is designed. In addition precision ground parallel washers are used to support the thermal test-piece on the fixture thermally decoupled from the support. In Figure 5 the results of the FEM computations of the modified thermal test-piece supported with washers is shown. It can be seen that the deformation in Z-direction is homogenous over the whole measurement areaa in the top center of the test-piece. This leads to unambiguous results when evaluating the thermal test-piece in Z-direction. Due to the use of the precision ground parallel washers the thermal test-piece temperaturee is rising less. The influence of the thermal 217 The Proceedings of MTTRF 217 Annual Meeting Figure 6: Milling cycle for the evaluation surfaces The machining cycle is illustrated in Figure 6. The milling cycle startss with cutting the evaluation surface for the deviations in Z-direction, Afterwards the evaluation surfaces for the deviations in X- and Y-direction are machined. The evaluation surfaces in X- and Y-direction are milled on both sides of the thermal test-piece to double the thermal deviations measured on the thermal test-piece. Figure 7 shows the thermal position errors E YC and E ZT evaluated with the thermal test-piece, measured on a coordinate measuring machine (CMM), compared to R-Test measurements on the machine for the same motion sequence. As with the modified thermal test-piece both

4 sidess in Y-direction are milled and measured using CMM, the deviation E Y C is evaluated independently from the radial growth of the thermal test-piece. The results show, that the thermal behavior of the machine tool is captured with the optimized thermal test-piece. The differences between the measurements are mostly influenced by the workspace temperature change during the test on the machine tool. In Figure 8 the workspace temperature and the environmental temperature during the tests with the different machining setups are shown. It is illustrated, thatt during machining of the thermal test-piece the temperaturee in the workspace rise approximately by 5 K. On the other hand, during the R-Test measurement there is only an increase of approximately 3 K measured. 1 Test-Piece R-Test Test-Piece R-Test time [h] Figure 7: Thermal deviations of the machine tool rotary table, for a four hour heat up followed by a four hour cool down cycle. The heat is generated with a rotary speed of 12 rpm of the C-axis during the heating up Thermal Test-Piece 23 Date: 217 Feb 23 Time: 1:3-18: R-Test measurments Workspace 27 Date: 217 Feb 2 Environment Time: 16:4 - : Workspace Environment time [h] Figure 8: Temperatures of the machine workspace and environmental temperature during the machining time of the thermal test-piece and the R-Test measurement. 4 ADAPTIVE LEARNING CONTROL FOR THERMAL ERROR COMPENSATION Based on the phenomenological model for compensating the machine tool s B- and C- axis thermal errors induced by cutting fluid, environmental and internal influence,,, introduced in 215 to MTTRF. [19] and in 216. [2], an adaptive learning control (ALC) for thermal error compensation is and implemented on NMV 5 DCG. A system of differential equations is used to compute the model based compensation values [2]: (5) with the actual thermal error,,, the input parameter for environmental influences, the axis thermal load and the cutting fluid temperature,,,, and are constant parameters. The model predicts thermal TCP- displacements induced by environmental and load dependent temperature changes, coolant and cutting fluid influences, especially changes between dry and wet cutting. The compensation model for the thermal rotary axis errors of a 5 axis machine tool is derived from on-machine measurements. The information gained by the process- intermittent probing is used to adaptively update the model parameters. The model learns how to predict thermal position and orientation errors. The approach maintains residual thermally induced errors of the investigated rotary axes small for a theoretically infinite period of time. This approach not only reduces the thermal machine tool errors to a predefined tolerance band, but it further reduces the time required for a first model parameterr identificationn during setup. Additionally an algorithm has been developedd to dynamically adjust the interval lengths between two on- machine measurements to maintain high productivity with the desired precision from the intended measures of a part below a specified threshold. Figure 9: Illustration of the adaptive learning control (ALC) for thermal error compensation [21]. Figure 9 illustrates the ALC approach for thermal error compensation. During the calibration phase of 12 hours at the beginning of the measurement the thermally inducedd TCP-displacements and the related thermal information, such as environmental temperature, axis speeds, cutting fluid temperature etc., are captured. The data are used to obtain a first set of model parameters for the thermal error model of the machine tool using least squares. This step is required once after the machine is set up. Afterwards the already existing compensation model is used, even when re-starting the production run after breaks, and updated by the approach. After the calibration phase the model is parametrized and ready for use in computing thermally induced TCP-displacements of the machine tool in real- time. During the production run, on-machine measurements, using a touch probe system fixed in the spindle and a precision sphere on the table, are performed to capture the thermal TCP-displacements at predefinedd times. As long as the thermal machine tool errors are below the threshold the measurements are repeated all 3 minutes to check whether the machine tool is already in the tolerance band. When the measured errors exceed a predefined threshold or the timespan since the last model 217 The Proceedings of MTTRF 217 Annual Meeting

5 parameter update surpasses a predefined value, set to 12 hours, the parameters of the thermal compensation model are updated. To update the model, the measurement data captured during the last six hours are used. 4.1 Implementation of Adaptive Thermal Error Compensation on NMV 5 DCG The idea for the adaptive thermal error compensation is to ensure long term stability in reducing thermally induced TCP-displacements of the machine tool. The procedure is capable of adapting the model parameters to changes in the external and internal thermal error sources, considered by the compensation model used. The approach is further used to adjust the on-machine measurement time intervals according to the predefined tolerance band to avoid unnecessary production interruptions by measurements. Figure 1 shows the control block diagram of the proposed ALC approach using a phenomenological model for thermal error compensation. At first a measurement procedure is developed for the investigated machine tool that is capable of identifying the thermal position and orientation errors of the machine tool s rotary axis with a touch probe system and a precision sphere mounted on the machine table. The axis error model used is based on the kinematic model of the machine tool and the use of homogeneous transformation matrices (HTM) to obtain the thermal TCPare the displacement. The input to the HTM model computed thermal machine tool errors and the current axes positions. The HTM model outputs are the axes offsets. These offsets are used to shifts the machine tool coordinate systems in the opposite directions of the computed thermal errors. The thermal errorr model computational results, the predicted thermal machine tool errors, are compared to the on-machine measurements obtained by the touch probe at predefined times. This comparison is used to trigger the periodical update of the parameters of the thermal error model. To adapt to changing working conditions the approach is capable of modifying the parametric programmed NC-Code, using the distributed numerical control (DNC) interface, adjusting the time intervals between on-machine measurements on-line. The developed on-machine measurement cycle for capturing the relevant thermal machine tool errors only needs a few measurement points and allows measuring the thermal TCP-displacements with a production interruption of less than one minute. Figure 1: Control loop of thermal compensation procedure using adaptive thermal error compensation (ALC) for numerically controlled machine tools. The dashed line representss the trigger for on-machine measurements [21]. 4.2 Resultss An experiment of 96 hours is performed with the NMV 5 DCG. The primary calibration time is chosen to be 12 hours, while performing a measurement cycle every 5 minutes. During this period no compensation is active. After this initial calibration time the first set of parameters of the phenomenological model is obtained and the thermal TCP-displacements are compensated using the machine tool s axes and the HTM model. a) compensated -2 Threshold uncompensated -3 b) compensated 2 Threshold uncompensated c) 3 5 Environment Workspace Coolant e) d) C-axis rotational speed measurement interval time time [h] Figure 11: Compensation results using the ALC approach performed on NMV 5 DCG for a 96 hours measurement. Compensation starts after 12 hours calibration time. a) and b) shows exemplarily for the thermal machine tool error E YC and E ZT a comparison for uncompensated and compensated machine tool. The vertical dashed magentaa colored lines represent the times at which an error measured exceeds its threshold, the dashed black lines represent parameter updates. e) shows the time intervals between on-machine measurements [22]. Afterwards on-machine measurementss are performed every 3 minutes. The predefined thresholdss are set to 1 µm for the linear errors and 3 µm/m for the angular errors. The thresholds represent the objective on the machine tool for the accuracy achieved with compensation. If a thresholds is exceeded by a measured error, the measurement interval time is automatically decreased to 15 minutes for two hours to ensure that sufficient data of the actual machine state is available, and a new set of parameters is obtained The Proceedings of MTTRF 217 Annual Meeting

6 If the error stays in the defined tolerance band and does not exceeded the thresholds, the model parameters are updated every six hours. Figure 11 shows measurements of the thermal position and orientation errors of the machine tool gathered while running the ALC. In a) and b) the brighter lines show the thermal errors for uncompensated machine tool while the darker lines show the errors measured using the ALC compensation approach. It is obvious, that after 12 hours, when the compensation starts with a first set of parameters, the linear error E YC and E ZT are significantly decreased. After 17 hours E ZT exceeds the threshold for a first time. The measurement interval time is reduced to 15 minutes, as illustrated in e), and the parameters are updated two hours later accordingly. Afterwards the measurement interval time is set back to 3 minutes until a threshold is exceeded by an error. Over the whole experiment the threshold of 3 µm/m for the angular thermal errors axes are never surpassed. The compensation accuracy of E YC and E ZT is noticeably increased by the dynamic parameter updates. Due to the limited axis resolution the thresholds are fairly large for Mori Seiki NMV 5 DCG and the compensation accuracy could be increased by smaller controllable axis resolutions. 5 FURTHER STEPS In the presented work thermo energetic issues in machine tool errors will be continued in the next period. With the new MTTRF machine tool Mori Seiki NTX 2 a focus on the research will be given to linear axis thermal error compensation. In the first step the machine tools thermal behavior will be investigated and measurement set-ups, also for on machine measurements, will be developed. The ALC compensation approach will be extended using NTX 2. ACKNOWLEDGEMENT The authors would like to thank the Machine Tool Technologies Research Foundation (MTTRF), the Swiss Federal Office for Professional Education and Technology (CTI) and the Swiss National Science Foundation (SNSF) for their support. REFERENCES [1] Züst S, Züst R, Schudeleit T, Wegener K (216) Development and Application of an Eco-design Tool for Machine Tools, Procedia CIRP 48: [2] Züst R, Züst S (21) Ecodesign-Potentialanalyse in der Schweizer MEM-Industrie - eine explorative Studie, hlussbericht_ecodesign-mem_kurzfassung.pdf. [3] Akbari J, Oyamada K, Saito Y (21) LCA of Machine Tools with Regard to Their Secondary Effects on Quality of Machined Parts. IEEE ( ): [4] Weber M, Züst R (213) Neue MAG-Prozesskette für die Kurbelwellenherstellung - Schneller, günstiger und umweltgerechter. in Sonderausgabe Umwelt Perspektiven: Energieeffzienz, Produktionseffzienz, Materialeffzienz - Best Practice Guide, ed. Galledia Verlag AG: 8-1. 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