一篇外国的经典论文

Keynote Papeis

Reduction and Compensation of Thermal Errors in Machine ToolsM. Weck (I), RWTH Aachen, Laboratory for Machine Tools and Production Engineering (WZL), Germany, Active Member P. McKeown (11, Cranfield University, Cranfield Precision Engineering Ltd, UK (retired), Honorary Member R. Bonse and U. Herbst, RWTH Aachen, Laboratory for Machine Tools and Production Engineering (WZL), Germany, Non-Members with Contributions from ClRP Members Noted in the Reference

AbstractThe main reasons for dimensional and geometric errors in workpieces produced on machine tools include low static stiffness of the machine structure, low dynamic performance of feed drives, tool wear and thermal deformations of the tool, machine and workpiece. This paper describes the latest research in analysing and reduction of thermally induced deformations in machine tools which lead to thermal drift displacements between tool and workpiece. A brief introduction to the problem is followed by an analysis of different heat sources and how they deformations. Attention is drawn to measures for reducing thermal drift as a mayor cause of errors in machine tools.

Keywords: Accuracy, Thermal Stress, Optimisation, Compensation

NomenclatureCi Ti t x, y, constant time constant time coordinates

Heat Sourc esHeat sources can be classified as internal and external. Internal ones are primarily the heat produced by running the machine and the process itself. External heat sources are mainly the changes in environment e.g. solar radiation, space heaters, lighting etc. E X T E R N A L H E A T SOURCES Variation of the ambient temperature causes temperature gradients both vertical and horizontal and these causes thermo-elastic deformations of the machine tool.

IntroductionInternal and external heat sources cause thermo-elastic deformations of machine tools and in the end result in geometric inaccuracies of the work-piece. Thermal effects can contribute more than 50% to the overall error. The necessity of reducing this error source has been recognised in the early Sixties, and research in this field was pioneered by Bryan et al.[l, 2. It is the responsibil1 ity of both the machine tool manufacturer and the user for diminishing thermally induced errors. Fiaure 1 gives an overview on the subject of thermal effects. Different heat sources combined with different mechanisms of heat transfer lead to a uniform temperature other than 20"C or to a non-uniform temperature distribution over the machine structure causing size and geometric errors in the measuring system, the machine structure and thus the workdece.

F J THERMAL ERR0

Figure 2: Influences on the temperature distribution in a machine hall[3] The amplitude of the temperature will vary with the geographical location, the season and the thermal character-

Figure 1: Diagram of thermal effects 11 2

Annals of the ClRP Vol. 44/2/1995

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istic of the machine shop. The upper part of shows the solar energy radiation over a 12

month period for Frankfurt and the temperature range over the same time. The lower part shows the typical variation of the temperature in a machine shop. A dynamical temperature range of 5"C during winter time and 15"C during summer time is not unusual.

m,then in a positive direction. After 12 hours the drift at thecutting edge is nearly zero again. Other work has demonstrated that changes of environmental temperature cause thermal drift even if the spindle is running. This and other internal heat sources cause machine temperatures significantly higher than the changes in the ambient temperature[6]. Equalising the time constants for components involved is effective in reducing thermal drift caused by external heat sources.Rob*m

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Figure 3: Horizontal and vertical temperature distribution in a machine shop[3] The temperature distribution within a machine shop depends on its location and height. Differences of temperature of more than 5"C at the same time can be seen, Eaure 3. The influence of the ambient temperature can be measured in an excellent way in climatic chambers[4, 51. This procedure is very time consuming and the costs of climatic chambers are very high. Fiaure 4 shows how a rapid ambient temperature change of 10"C causes distortion of a lathe[3].

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Figure 5: Reducing the sensivity of machine structural components to environment temperature affects (71 Fiaure 5 shows this effect for a large portal milling machine that was exposed to a poor environment[7]. Due to different wall thicknesses of the front and back of the column, the back wall warms up faster in the morning when the hall temperature rises and cools down more quickly in the afternoon than the front wall. This results in bending of the machine and thus in misalignments of two bore holes by 100 pm. Investigations revealed a larger thermal inertia of the front made of 150 mm steel plates than the 25 mm thick rear wall. By insulating the thin wall with 25 mm polystyrene the time constants can be made more equal. By this means the misalignments due to such workshop temperature changes were substantially reduced.INTERNAL

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Figure 4: Radial drift displacements of a lathe caused by rapid jumps of the ambient temperature in a climatic chamber[3] After the rapid cooling and heating of the chamber the ambient temperature is kept constant for approx. 12 hours. During the first three hours after the temperature rise the distance between tool and spindle reduces quickly by 40 pm followed by a slow increase during the following 8 hours. This result shows that the thermal driftbehaviour of a machine has large time-constants in reacting to ambient temperature changes. Reaching a steady state is more a matter of days than hours. The different time constants for different machine components cause the thermal drift displacements at the point where these are measured, firstly in a negative direction and

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nternal sources directly conduct the heat into the machine structure and cause deformations and thermal drift. Understanding the effect of each of these sources has been focus of extensive production research. One of the main sources in terms of its contribution to the total heat generation and resulting deformations is the spindle system and its bearings. Based on the thermal load, design and cooling conditions, the spindle and box growth in the axial direction can amount to 100 pm or more. Depending on the bearing type and on the diameter of the spindle the power loss can be up to 100 Watt for a 100 mm ball bearing running at 10000 rpm and up to 1 kW for a hydrostatic bearing of the same size and rotational speed. The feed drives of a machine are also major heat sources which can result in considerable thermal drift at the tool depending on the encoder system of the machine. Schulz and Schmitt have determined the energy loss of the feed drives of high speed machines theoretically and experimentally[8]. The roller bearings, the ball screw and its nut as well as the rolling element guideways are taken into consideration. They found that the main heat source is the ball screw and its nut generating

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up to 190 W for feed rates of 25 m h i n due to the preloaded nut. This results in steady-state temperature increase of 75"C for 15 d m i n feed rate and up to 82"C for 30 d m i n feed rate. This is therefore a major cause of thermal drift. Another important internal heat source is the cutting process itself, which warms up the tool, toolholder, workpiece and clamping device. The table, machine and other components can also be heated up indirectly by hot chips. This problem can easily be overcome by using enough cooling lubricant. techniaues For chine Accuracv lncreasina Ma-

more than 20.000 l/min (n.dm=2.5.106) with small thermal deformations were achieved by under race jet lubrication and by internal oil cooling of the spindle. Also smaller power loss was achieved than with usual oil-jet lubrication.I

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The first step for reducing thermal drift errors in machine tools is to reduce the power loss of internal heat sources. If the heat generation is inevitable the heat source should either be insulated from the rest of the structure, shifted to locations of the machine where it has no influence on the structure deformation or it should be cooled e.g. by forced draught cooling or temperature controlled lubricant. Finally, algorithms describing the deformation depending on on-line temperature measurements of representative machine points can be used for compensating the deformations and drift by means of the CNC. Examples for all of these measures are given below.REDUCTION AND INSULATION

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Figure 6: Temperature rise of hybrid and steel angular contact ball bearings Naturally, the preload of the spindle system has significant influence on the friction torque and therefore o

n the power loss. Spindle bearings must be preloaded for achieving the necessary stiffness for machine tool applications. Dependent on the preload mechanism the preload of the spindle system changes with the spindle speed. Nakamura et al. have developed a preload switching spindle[17]. Up to a defined speed the spindle is preloaded in a fixed position, i.e. the preload increases with the spindle speed. At a certain speed upwards an hydraulic device adjusts for constant pressure preload allowing higher spindle speeds with lower friction, Fiaure 7.

Reduction of the heat source can take place only with the knowledge of the influence of different sources on the drift between tool and workpiece. This knowledge can be gathered either by thermal drift tests[9, lo], i.e. empirically, or by Finite Element Analysis. Thermal drift testing of machine tools and CMM's is a very important and powerful technique for understanding and optimising both the environmental and operating effects on the accuracy capability of these machines. Finite Element Analysis is very helpful especially during the design phase of a new machine. Although the thermal boundary conditions are seldom exactly known, progress has been made by many researchers in the recent years. McKeown reports that all machine tools designed and built by Cranfield Precision are based on FEA for static and dynamic stiffness and thermal drift optimisation. Moriwaki et al. have introduced a dynamic thermal analysis system that is capable of taking the motion between parts of the machine into consideration[ l 1, 121. Nottebaum developed algorithms for optimising structures of fibre reinforced materials by adjusting the winding angles with respect to thermal and mechanical stress automatically with the help of Finite Element Analysis and Optimisation techniques[13]. The power loss of spindle bearings as one of the major heat sources can be reduced by optimising the lubrication by using new materials for the balls and by optimising the preload. Koch has shown that hybrid bearings with ceramic balls have less friction than conventional bearings under the same conditions, Fiaure 8[14]. Lubricating the bearings through small drillings in the outer ring of the bearing also increases the quality of the lubrication and leads to higher permissible speed with smaller temperature rise. The optimisation of the lubrication was examined by Bryan[l5] and also by Nakamura[16]. Rotating speeds of

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Figure 7: Characteristic of spindle bearing preload switching diagram[17] Insulating the spindle from the bearings and its influence on the spindle preload has also been examined by Jedrezejewski[18], Fiaure 8. He discovered that a layer of insulating material placed between the inner bearing ring and the spindle journal leads to smaller temperature increases especially for high speed spindles. The speed at which this has a positive influence begins at approx. 2.500 l/min.

In their papers Spur, Hoffman, Paluncic, Bottger and Weck report on the results of years of spindle box research[19, 201. Spur et al. determined the heat transfer of a lathe's head stock analytically. The use of

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ceramic and carbon reinforced plastic spindles instead of the conventional steel spindle resulted in a reduction of the axial thermal drift by a factor 7 for the ceramic and factor 15 for the latter spindle, Fiaure 9 Realising that the . temperature distribution of the complete component is important for its elongation, they implemented a resistance wire in the spindle to measure the integrated component temperature rise. They found a very good correlation between the elongation of the spindle and the change of resistance. I

Sugishita, Nishiyama, Renker, Sahm, Weck and McKeown have all reported on the use of concrete as a bed and column material for a machine tools[22, 231. Concrete was chosen due to its high damping ratio in comparison to cast iron, promising longer tool life. Another advantage of concrete is low thermal diffusivity. The concrete structure of a machine tool has about the same thermal drift at the tool tip as a cast iron machine but a much higher time constant. Thus, rapid changes of the internal and external heat sources cause lower distortions and drift amplitudes than those of steel or cast iron structures, i.e. they are less thermally responsive. T E M P E R A T U R ECONTROLTOOLS OF MACHINE

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Impressive results have been gained by controlling internal and external temperature rises of machine tools[15, f 241. These results often justify the additional costs o the temperature control system especially for high precision applications. The positive influence of oil showers over the machine was shown by Bryan[15, 241 as well as Zhang and Zhuang[25]. Deflections of a grinding machine were reduced by more than 50%. McKeown proved the positive effect of oil cooling for the field of Ultra Precision Machining[26]. In addition to the conventional process coolant supply he installed five temperature loops, each operating with a resolution of better than f 0,Ol C. Two temperature loops were installed in the workhead: one for the hydrostatic spindle and one for the spindle motor. Axial thermal drift of the workhead spindle could be controlled to better than 20 nm within 7 minutes of start up. He also controlled the temperature of the hydrostatic linear and rotary bearings of the x, z and b axes as well as the motor and bearings of the grinding wheel. The polymer granite base was kept constant by"showering" it with oil. He was able thus to achieve profile accuracy of better than 90 nm in diamond turning of components up to 250 mm diameter, Fiaure 10.al, C,.t

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Figure 10: Schematic of a multi loop temperature control system[26] Temperature controlled"air shower" techniques have also been successfully used for ultra precision machine tools such as diamond turning machines. However the thermal capacity of liquids such as water or oil is much higher than gases and they are faster in action and thus effective in thermal control of subsystems and complete machine tools. BBttger has developed a spindle speed dependent temperature control for cooling the oil of a hydrostatic spindle

Figure 9: Overhang section displacement Az for three different materials[19] . . Moriwaki, Weck et al. minimised the influence of the tool holder expansion by making it out of low expansion lnvar material instead of the usual tool steel. Machining a 400 mm long workpiece on a standard lathe resulted in 30% smaller -straightness errors for roughing and 50% for finishing due to thermal effects[21].

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bearing on an ultra precision lathe[20], Fiaure 11. The thermo-elastic deformation of the spindle nose could be reduced to less than 100 nm.

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during machining. The sensors can be exposed to hot chips and lubricant. Schafer has developed an exemplary direct intermittent compensation for a grinding machine 1301. From time to time, the machine positions the grinding wheel in the measuring position and an eddy current sensor determines the distance between the tailstock and the grinding wheel. This distance is used as a compensation value that is automatically transferred to the numerical control of the machine. The displacements of initially more than 20 pm were reduced to less than 4 IJmMachine tool mounted robust probe units have been developed and are commercially available for use on CNC machining centres and lathes. The tool can periodically touch these centres to establish tool wear and thermal drift of the tool to the work table. Another efficient measure is finding the position of the tool relative to the workpiece table by means of a laser beam,[3]. Periodically the machine moves the rotating tool through the laser beam. The position of the tool tip in y- and zdirection is registered by the interrupted laser beam. This method compensates not only thermo-elastic deformations, but also tool wear and radial run out of the tool.

Figure 11: Schematic design of the speed dependent temperature control[20] In his system the outer circuit water is cooled to a defined temperature (13 C) with a chilled water circuit. This water is then used to cool the oil for the hydrostatic bearing. In order to give a fast response and precise control a spindle speed controlled pump is installed. The cooling power is adjusted to the estimated power loss of the bearing system. Using only temperature controlled cooling the machine reached a constant offset of about 4 pm after 30 minutes. By the introduction of the speed dependent cooling this axial thermal drift could be reduced to less than 0.1 pm. In recent years, so-c

alled heat pipes have been introduced into research on thermal effects. Heat pipes conduct the heat from one end of the pipe by a working liquid to the other end of the pipe, where it is cooled by air circulation. The effect of this conductivity increase has been exploited by Inasaki, Pyra, Zhang, Weck et al. By applying heat pipe panels on the headstock lnasaki increased the thermal conductivity of the headstock, from 260 kJ/mK to 2,000-7,000 kJ/mK[27]. Consequently, the warming up time was reduced from 4 hours to 2 hours. More important than that is the fact that temperature gradients in the structure result in distortions. Equalising the temperature all over the structure with highly conductive heat pipes reduced the amount of thermal drift to 113 or 114 of the initial situation without heat pipes. For cooling the hydraulics and equalising the temperature differences of a grinding machine, Zhang also used heat pipes[28]. The deformations were reduced from initially 104 pm to 22 pm i.e. a factor of almost 5. He achieved even better results for a lathe by applying heat pipes at the spindle bearing system. The dislocations were reduced from 155 pm to 12 pm in the vertical direction and from 63 pm to 8 pm in the horizontal direction[ 9 . 2]COMPENSATION

Figure 12: Direct compensation of thermal drift with the help of a laser[3] The other possibility of compensation is an indirect technique. Thermo-elastic deformations are calculated at representative temperature measurement points in the machine structure. The calculated deflections are either compensated by means of the CNC or perhaps by additional special built in actuators. Hocken, Donmez et a/. recognising that the complete temperature distribution in. a component must be known for a precise indirect compensation[31]. Spur, Paluncic, Weck et al. also discussed the limits of an indirect compensation if the temperature is only measured at a few points of a component[19, 321. They showed that although it is impossible to compensate exactly with only a few measuring points a tolerable error is made if the significant temperature locations are found. Finding temperature points that have reasonable correlation with the displacements has been the focus of recent research. The main interest of research activities world wide is directed to the question of how to find an acceptable mathematical model with a minimum of temperature sensors within an acceptable time scale. For a long time, linear equation systems were the most common approach. However in the case of several heat

A lot of research has been carried out in the field of compensating the thermally induced deformation of machine tools. Generally, compensation techniques are subdivided into direct and indirect compensation. For the direct compensation the drift displacements between the tool and the workpiece are directly measured. The indirect compensation uses a model. Signals correlating with the drift values are used to calculate the

displacement via this mathematical model. Compensating directly is often difficult because the measurement of the deflections is not always possible

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sources this method does not work well. Recently Neural Networks have been used for modelling thermo elastic behaviour and have been successfully tested.

Networks. The capability of Neural Networks to classify and to fit curves is well known from different applications not only in production engineering. Mitsuishi, Nagao, Hatamura et al. use Neural Nets for controlling the cooling and heating jackets which are mounted on the column of a machining centre[35]. By cooling and heating different parts of the machine column the tilt due to internal and external heat sources can be compensated,& ure 16.

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Figure 13: Set-up for measuring thermo-elastic behaviour of machine tools[3] Fiaure 19 shows the set-up for thermal drift testing, i.e. measuring linear and tilt motions relatively between the spindle and the workpiece table at the same time as temperature is measured at different points in the machine structure and the environment. External and internal heat sources generated over a wide range of duty cycles guarantee a wide range of temperature changes over the structure of the machine tool in order to get sufficient input data. With this quantity of data it is possible to build a linear equation system, Fiaure 14.

Figure 15: Measured and calculated drift in y-direction using 9 of 39 temperature sensors[34]

Figure 14: Indirect compensation of thermo-elastic displacements of machine tool[33]. Using regression analysis and minimisation of the quadratic errors the best-fit mathematical description with respect to the measured data of the teaching phase can be found. Schellekens et al. calculated all possible temperature combinations for using a given number of sensors. By observing the remaining sum squared error they found that combination which fits the teaching data best. Jlgue demonstrates the good results of an example. The error could be reduced to less than 8% of the uncompensated machine[34]. Most recently, many researchers have tried to model the thermal behaviour of machine tools using Artificial Neural

Figure: 16 Locations of thermal actuators and deformation sensors[35] The deformations are measured by special developed sensors incorporating strain gauges. Eight such sensors provide the input to the Artificial Neural Networks. It was shown that a three layer network can predict the.deformations better than a 4 layer network, Fiaure 17, This is also the experience of other scientists. The drift were reduced to less than 10 pm whereas the initial displacement values amounted to 50 pm. Dehaes, Klewais, Moriwaki, Weck et al. have also shown that thermal deformations can be estimated by Neural Networks[36, 371. Moriwaki used 6 temperature points as input. The 6 un

its in the hidden layer possess sigmoid monotonic inputloutput relation. The net had three output units referring to the dislocation in y- and z-direction and the inclination in y-z-plane. He found out that Neural

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Networks are capable of estimating the deformations very precisely when they are trained with data of the same operational conditions. In addition to that they can also estimate the deformations under different conditions but the accuracy depends on the range of variations in the training data[36].

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Figure 17: Fundamental structure of thermal distortion control by a Neural Network method[35]0.12

Weck et al. found out that 3 layer networks (1 hidden layer) fulfil the requirements as a model for the thermo elastic behaviour best. Higher numbers of hidden layers will neither lead to higher accuracy nor to shorter training time but the net will lose its ability of generalisation. He developed algorithms which determine the number of hidden units as well as the numbers of entrance units, i.e. the significant temperature sensors. First the net is trained with all temperature sensors (approx. 30) and an initial number of sigmoid units in the hidden layer. During training the net error is watched. If the training success rate is too small additional hidden units are implemented in the net. If the success rate is high and the net error is low some units are deleted. After finding a minimum number of units for a given accuracy the algorithm starts deleting one temperature sensor after an other. By monitoring the correlation between calculated and measured displacement the algorithm determines which temperature sensor makes a significant contribution to the correct estimation. Finally it deletes the one with the smallest contribution and repeats the algorithm until the net error increases too much. Fiaure 19 shows the result of this algorithms. The net was trained with a spindle duty cycle according to the German standard DIN V8602 and tested with constant spindle speeds. With only 5 temperature sensors out of 30 the errorof the training data could be reduced to 12% and of the testing data to 25%.

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Figure 18: Results of compensation with a Neural Net[371 Eiaure 18 shows the results of a Neural Network for a training data set. Dehais, Klewais et al. used one hidden layer of 4 neurons with tangent hyperbolic activation function and one linear output unit. The prediction accuracy in y-direction of the training set was 4 pm and for an independent second data set 15 pm[37]. Veldhuis, Elbestawi et al. showed that a Neural Network can also be used to identify significant temperature points[38]. The topology of the net consists initially of 30 input units corresponding to the numbers of temperature sensors, three hidden layers with sigmoid units and a linear output unit. Sen

sors with small influence are deleted automatically in this algorithm. Afterwards the net will be trained again and the correlation between the deleted input temperature and the residual error of the drift value is determined. If there is correlation this input can contribute to reducing the error and is implemented in the net again. In this way the number of input sensors were reduced considerably.

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Figure 19: Measured and calculated displacement with the help of a neural net[39] Srinivasa makes use of the classifying power of Neural nets[40]. He creates classes of displacements in intervals of one micron, which is the positioning resolution of the machine. Any temperature pattern corresponds to one of the classes. Faster training is the advantage of such a net. In order to determine the share of each component to the thermal drift of the machine at the cutting edge, Bueno et al. have developed a"Thermal Modal analysis"[41]. The machine tool is exposed to a step-like heat load (either by internal heat sources or by changes of ambient temperature). The resulting drift displacement values can be analysed as a sum of exponential functions with different time constants

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Conclusiom

Bueno likens the time constants Ti that are derived from the measured curve of the thermal modes of the machine to the modes of its dynamic behaviour. He also describes the temperatures as a combination of exponential functions with the same time constants that the displacement have but different proportional factors Ci. After determining as many linearly independent temperature points as there are thermal modes, the variable 'time' can be substituted for the variable 'temperature' of different structure points. In the end Bueno gets a temperature dependent equation for the displacement. He recognises the problem that the solution is unambiguous. Depending on which temperature point is chosen very different results are achieved. Weck and Bonse have developed a very similar procedure and proved its validity for a lathe that has been exposed to rapid step change of the ambient temperature in a climatic chamber mentioned previously, Fiaure 2 1[3].

The thermo-elastic behaviour of a machine tool can be the most important factor in determining its accuracy capability. The relationship between thermal load of the machine and the thermal drift displacement at the cutting edge is very complex. Due to inaccurate knowledge of heat source, thermal boundary conditions, mechanism of heat transfer etc. precise prediction of the behaviour in particular of a standard type of machine tool at the design stage is very difficult.sham of Qlocslion and tempamlure pmbe

Figure 21: Procedure for determining relevant temperature probes for compensating for thermal drift displacement[3] In the design of ultra precision machines however[24, 261 where low expansion materials are used together with well designed temperature control systems thermal drift have been achieved in the orde

r of only 20 nm. For standard types of machine tools that can learn from these achievements the most important design rules are reduction of heat sources, location them in the least"damaging" positions, the use of low expansion materials, insulation techniques, forced draught cooling and temperature control of coolants and lubricants. Concerning improvements in design the main attention is drawn to the reduction of heat sources the hindrance of the heat flow and the use of adequate materials. The inevitable remaining deformations and thermal drifts can be further reduced by means of direct and indirect compensation. Thermal drift reduction by up to 90% is possible. Figure 20: Comparison between thermal and dynamic modal analysis[41] The displacement can be understood as the sum of two exponential functions. Any of the exponential functions is characteristic of one component contributing to the resulting error. The time constant is characteristic of the thermal inertia of this component. By searching for temperature points with the same time constant as each of the two deformation functions, the characterising temperature points are determined. Regarding indirect compensation Neural Nets are proving to be a successful method for modelling and improving thermo-elastic behaviour. Similar to dynamic modal analysis, thermal modal analysis is a powerful tool for determining the thermal weak points of machine structure.

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366McKeown, P.: 1995, Design of the Nanocentre, personal contribution Inasaki: 1995, Suppression of Thermal Deformations with Heat Pipes, personal contribution Zhang, B., Li, Y., Zhuang, Y.: 1991, Reducing the Thermal Deformations of Machine Tools by Heat Pipes, Proceedings of the ClRP Conference on PE& MS, Sept. 1991,pp. 651-662 Zhang, B., Li, Y.P., Xiao, S.H., Sung, W.F: 1995, Improving the Thermal Properties of Turning Center by Seperating Heat Pipe System, will be presented on the"9th International Heat Pipe Conference May 1-5, 1995,U.S.A. Schafer, W.: 1994,3 s t i o n thermoelastischer Verformunaen an Werkzeuamaschinen, dissertation RWTH Aachen Donmez, Hocken et al.;"A general methodology for machine tool accurcy enhancement by error compensation", Precision Engineering, 1986a Weck, M., Schulze, O., Michels

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1489Nakamura, S.,Kakino, Y.: 1994, A Performance Evaluation of Preload Switching Spindle, Joumal of Japan Society of Precision Engineering, Vol. 60. NO. 5,1994,pp.688-692 Jedrezejewski, J.: 1988, Effect of Thermal Contact Resistance on Thermal Behaviour of the Spindle Radial Bearing, Int. J. Mach. Tools Manufact. Vol. 28 NO. 4,pp. 409-416

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一篇外国的经典论文

[36] Moriwaki, T., Zhao C.: 1992, Neural Network Approach to Identify Thermal Deformations of Machining Center, G.J. Olling and F. Kimura (Editors), Elsevier Science Publishers B.V. (North Holland), 1992 IFIP, pp. 685-697[37] Dehaes, J., Kleiwas, P., Nuttin, M., Vanherck, P.: 1995, Compensation of Thermal Deformations in Machine Tools with Neural Nets, Preprints Second International Workshop on Learning in Intelligent, Manufacturing Systems, Budapest, 1995,746-756[38] Veldhuis, S.C., Elbestawi, M.A.: 1995, A Strategy for the Compensation of Errors in Five-Axis Machining, to appear in the ClRP Annals 1995[39] Weck, M.: 1995, recent research results[40] Srinivasa, N.: 1994: Modeling and Prediction of Thermally Induced Errors in Machine Tools Using a Laser Ball Bar and a Neural Network, dissertation presented at the Graduate School of the University of Florda, 1994[41] Bueno, R., Almandoz, S.: 1995, Thermal Modal Analysis of Machine Tools, personal contribution

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