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- 1. INTERNATIONALMechanical Engineering and Technology (IJMET), ISSN 0976 – International Journal of JOURNAL OF MECHANICAL ENGINEERING 6340(Print), ISSN 0976 – 6359(Online) Volume 4, Issue 2, March - April (2013) © IAEME AND TECHNOLOGY (IJMET)ISSN 0976 – 6340 (Print)ISSN 0976 – 6359 (Online)Volume 4, Issue 2, March - April (2013), pp. 53-78 IJMET© IAEME: www.iaeme.com/ijmet.aspJournal Impact Factor (2013): 5.7731 (Calculated by GISI)www.jifactor.com ©IAEME ANALYSIS AND SIMULATION OF CHIP FORMATION & THERMAL EFFECTS ON TOOL LIFE USING FEM Prabhat Kumar Sinha, Chandan Prasad, MohdKaleem, Raisul Islam Mechanical Engineering Department Shepherd School of Engineering and Technology Sam Higginbottom Institute of Agriculture, Technology and Sciences (Formerly Allahabad Agriculture Institute) Allahabad 211007 ABSTRACT The main objective of this paper on metal cutting machine tools particular on turning and milling machines. The investigation of thermal issues in machine tools including measurement of temperature and displacement at the tool centre point, computation of thermal error of machine tools due to temperature distribution and displacement. It is also focused to avoid thermal error with temperature control. The increased tool temperature has great effect on tool life, machining efficiency and the quality of the product. Another objectives of this study to forecast the transient average tool temperatures under different cutting conditions and chip formation with fixed cutting velocities and metal removal rate. Chip formation allows for incorporation of various factors in the chip formation process. It can therefore be used to simulate the occurrence of vibration in practical conditions and to predict the conditions that lead to stable cutting. Finite element simulations of orthogonal metal cutting as to predetermine the evolution process of heat source on tool rake face. It is also provide information for the optimum cutting condition for longest tool life can be obtained. Keyword: Vibration, Finite element method, Thermal effects, Machine Tool INTRODUCTION The main objective of this paper on metal cutting machine tools particular on turning and milling machines. The investigation of thermal issues in machine tools including measurement of temperature and displacement at the tool centre point, calculation of thermal 53
- 2. International Journal of Mechanical Engineering and Technology (IJMET), ISSN 0976 –6340(Print), ISSN 0976 – 6359(Online) Volume 4, Issue 2, March - April (2013) © IAEMEerror of machine tools and its errors. Computation of thermal error of machine tool due to machinetemperature distribution and displacement. It is also focused to avoid thermal error with displacement.temperature control. The increased tool temperature has great effect on tool life, machiningefficiency and the quality of the product. The another objectives of this study to forecast thetransient average tool temperatures under different cutting conditions with fixed cuttingvelocities and metal removal rate. Finite element simulations of orthogonal metal cutting asto pre-determined the evolution process of heat source on tool rake face. determined1. FEM MODELLING OF CUTTING PROCESS To simulate the effect of tool flexibility on development of chatter vibration, anorthogonal cutting configuration is considered. The regeneration of waves on the surface ismade possible by considering a round work-piece which rotates around an axis, similar to work sturning operation. The analysis type is two-dimensional plane strain analysis. In this work, two dimensionalMSC-MARC software is utilized because of its robustness in adaptation techniques and the MARCability of simulating dynamic and transient phenomena and active remeshing under all phenomenasimulation procedures. The material and cutting parameters are selected to represent realisticcutting conditions. An updated Lagrangian formulation is used for solution.1.1. Machine tool, tool and workpiece models Fig.1 shows the model that is used for simulation of the regeneration phenomenon.The model of the vibratory system includes a one degree of freedom spring and dampersystem which supports the tool. The tool and a work-piece are also part of the dynamic work piecesystem. Fig 1. One degree of freedom model 54
- 3. International Journal of Mechanical Engineering and Technology (IJMET), ISSN 0976 –6340(Print), ISSN 0976 – 6359(Online) Volume 4, Issue 2, March - April (2013) © IAEME1.2. Work-piece material model Due to the large strain rate and large deformations and temperature rise, Johnson-Cook material model is used to represent material behaviour. The workpiece material isconsidered to be 42CrMo4 steel, with the material parameters given in table 1. ത ఌሶ ்ି் ߪ ൌ ሾ ܣ ܤሺߝҧሻ ሿ ቂ1 ln ቀఌሶ ቁቃ ሾ1 െ ቀ்ത ത ି் ቁ ሿ (1) The variablesσ, εҧ , εሶ ҧ and T represent shear stress, shear strain, shear strain rate and the absolute തtemperature, respectively. Also n, m and C represent the strain hardening exponent, the strainrate sensitivity, and the thermal softening coefficient, respectively. A, B,εሶ ҧ ୭ are the constants,Tr is the reference temperature and Tm is the melting temperature. Chip formation process isunder the effect of following parameters:The Shear stress field in primary deformation zone.• Mean friction coefficient in the contact surface of tool and workpiece.• Orientation of the shear plane.• Cutting conditions such as cutting speed, cutting depth, cutting angles, etc. Table 1. Johnson-Cook parameters of 42CrMo4 steel A B ҧ ߝሶ n C M Tr Tm 0 0 1/s C C 612 436 0.001 0.15 0.008 1.46 23 15201.3. Friction model To simulate cutting process under practical conditions, a speed dependent frictionmodel is introduced. An arctangent model is used to simulate a smooth transient statebetween sliding and sticking states. ଶ ሾሿ ሾሿ݂௧ ൌ ߤ. ݂ గ arc tanሺ ோேௌ் ሻ. ݐ (2)In this equation, ft is the friction force, µ is the friction coefficient, Vr is the relative speedbetween tooland work -piece, RVCNST is a measure of tool work piece relative velocity atwhich sticking starts, and t is the unit tangential vector. In this work, RVCNST is consideredas 10% of the relative speed.2. PROCESS SIMULATION After creating the model in the software, parameters such as cutting speed, penetrationrate of the cutting tool, boundary conditions on the tool and work-piece and suitablecoefficients are specified and the simulation is run to study stability in chatter in a onedimensional model. The tool flexibility should be included in terms of mass, stiffness anddamping parameters. 55
- 4. International Journal of Mechanical Engineering and Technology (IJMET), ISSN 0976 –6340(Print), ISSN 0976 – 6359(Online) Volume 4, Issue 2, March - April (2013) © IAEME Fig. 2. Updated model in softwareThe mass of the tool is entered by specifying proper density for the tool, and the stiffness anddamping parameters are implemented through defining a link element which connects the definingtool to the ground. Other parameters used in the model are given in table 2. Table 2. List of parameters used in FE simulation Parameters Value Stiffness 107 N/m damping 500 N.s/m Tool Mass 2.5 Kg Elasticity modules GPa 200 Poisson’s ratio 0.3 Thermal conductivity coefficient 50.9 w/(m*k) Thermal specially capacity 486 J/kg*k Density 7800 Kg/m3 Minimum length of elements 0.5 Tool Clearance Angle 50 Tool Rake angle 00 Edge reduce mm 0.1 work-piece Inner reduce mm 30 work-piece outer reduce mm piece 35 Depth of cut mm 0.4-1.5 Feed mm/rev 0.2 Spindle speed rpm 450-2300 DOF 1 in feed direction Friction coefficient 0.64 Fraction of friction energy transformed to heat 0.9 Fraction of plastic energy transformed to heat ergy 0.9 56
- 5. International Journal of Mechanical Engineering and Technology (IJMET), ISSN 0976 –6340(Print), ISSN 0976 – 6359(Online) Volume 4, Issue 2, March - April (2013) © IAEME2.1. Simulation results Several simulations were carried out using the above model at various cuttingconditions. Cutting depth was introduced through specifying the plane strain element depthperpendicular to the simulation plane. In these simulations, cutting depths was varied from n0.4mm to 1.5mm in different cutting speeds while the penetration rate (radial feed) was keptconstant at 0.2 mm/rev. The regeneration of surface waves started in a particular width of cutat each speed, which represented the transition between stable cut and chatter occurrence. hThe instability could be recognized by observing the wavy shape of the chip and bymonitoring the trend of cutting forces and the displacement of the tool tip. Since the g goal ofthis research is to study the effect of heat on chatter, simulations were carried out with andwithout thermal effects, and comparison between these two approaches was made. Fig.3shows a sample result of the simulation of chip formation process. In cutting speeds below 100m/min, no chatter was observed, which could beattributed to process damping effects at lower range of speeds. At the speed of 100m/min,simulations showed that when thermal effects are considered, instability is observed at thecutting depth of 0.6mm. However, the cutting became unstable at a depth less than 0.4 mm ttingwhen thermal effects were neglected. This showed that temperature rise in the cutting zonecan affect the border of stability in machining. Fig. 3. Chip formation in thermal simulation Fig. 4. Comparison between stability with and without thermal effects included. The solid line is the analytical e stability lobe diagram. The borders of stability of a machine-tool system are often described using the machine toolstability lobe diagram. In these diagrams, the lobes separate the stable and unstableconditions at various values of cutting speed [1], [2]. The stability lobes are determined based rious bilityon various conditions of both widths of cut and spindle speeds. In a specific spindle speed (orconsequently cutting speed), at a certain critical depth of cut, the dynamic system switchesfrom stable to unstable condition. Fig.4 depicts the stability lobe diagram for the simulated condition 57
- 6. International Journal of Mechanical Engineering and Technology (IJMET), ISSN 0976 –6340(Print), ISSN 0976 – 6359(Online) Volume 4, Issue 2, March - April (2013) © IAEMEprocess from analytical (solid lines) and numerical results (points). The stability diagram isbased on an analytical nonlinear model that takes into account friction and tool wear. It isnotable that the critical stability value is not constant and varies with cutting speed. Thesimulation results show a trend similar to that of Moufki [58], but it is also obvious that theborder of stability is displaced when thermal effects are included in the simulation. It may beconcluded that ignoring thermal effects in chatter simulation may lead to inaccurateprediction of stability border. Simulation results, shows that heat generation due to plasticdeformation and frictional work creates a larger stability region, and allows stable cutting atlarger cutting depth. This may be attributed to the effects of heat on softening the work-pieceand decreasing material stiffness which result in the decrease in machining forces. Figures 5 and 6 show the graphs of the displacement of the tool tip versus time inmarginally stable and unstable regimes, respectively, with thermal effects included. Thedisplacements are given for a time period corresponding to more than two revolution of thework piece. In Fig. 5, borderline stability is observed under cutting speed of 100m/min andcutting depth of 0.4mm, because the displacement amplitudes remain constant. Fig.6 showsthe case in which the cutting depth increases to 0.8mm at the same speed. The increasingtrend of displacements shows that the process has become unstable. Fig. 5. Borderline stability in cutting speed of 100m/min Fig. 6. .Instability in cutting speed of 200m/min and depth of and depth of 0.4mm 0.6mm without thermal effects To observe the change from stable to unstable cutting when thermal effects areneglected, Figures 7 shows the displacement diagram for the same cutting conditions, withand without thermal effects. The figures show that stability increases in thermal approach asheat effects softens the materials and damps the vibrations. In these figures, the cutting speedis 200m/min and the depth of cut is 0.6mm. 58
- 7. International Journal of Mechanical Engineering and Technology (IJMET), ISSN 0976 –6340(Print), ISSN 0976 – 6359(Online) Volume 4, Issue 2, March - April (2013) © IAEMEFig.7. Stability in cutting speed of 200m/min and depth of 0.6mm when thermal effects are andincluded When machining process goes to unstable state, a marked increase in surface waveson the chip could be seen. In some cases the phenomenon of tool jumping out of the cut caneven be observed. Figures 8 and 9 show samples of the chip forms in stable and unstablecutting regimes, respectively. Finally, it is noted that since temperature in the cutting zone ishighly dependent on cutting speed, its effect is expected to be large at higher speeds.Referring to figure 4, it can be seen that the difference between borders of stability with and igurewithout thermal effects is larger at higher speeds, e.g. at 400 m/min, where the border ofstability is increased by around 0.5mm when thermal effects are included in the modmodel. Fig. 8. Stable cutting state in cutting speed e Fig. 9. Unstable cutting state in cutting of 100m/min and depth of 0.4mm speed of 100m/min and depth of 0.8mm 59
- 8. International Journal of Mechanical Engineering and Technology (IJMET), ISSN 0976 –6340(Print), ISSN 0976 – 6359(Online) Volume 4, Issue 2, March - April (2013) © IAEME3. COMPUTING THERMAL ERRORS OF MACHINE TOOLS Temperature influences the geometry of work pieces, measuring equipment, andmachine tools. Deviations from the reference temperature of 20 8C [45,39,35], temporal andspatial temperature variations [50], as well as the material coefficient of thermal expansion(CTE) have to be known for thermal error compensation. A deviation of the temperature fromthe reference temperature causes, in case of an isotropic CTE, a linear length change in space.In case of an anisotropic CTE, the length change varies in space. Temporal temperaturevariations cause varying length changes in time. Spatial temperature variations causedeformations depending on position. In high-precision length measurements it is commonpractice to numerically correct linear length changes due to constant temperature deviationsfor both work pieces and machine scales. The challenge nowadays lies in the determinationand correction of non-linear length changes. In Fig. 10, for instance, the influence of aconstant temperature gradient of a machine tool is illustrated. It bends the machine bed whichfinally contributes to straightness, rotational, and squareness errors of the guide ways. Thetemperature gradient can be measured by means of temperature sensors. This kind of errorcan be described in a thermal kinematic model and finally corrected. Fig. 11 shows geometricmachine deviations caused by a local heat source.3.1. Criteria and ways of determining thermal errors Tracing back the history of research on the identification and reduction of machinetool thermal errors, one can notice that the research became much more effective when theFEM started to be applied and developed.Fig. 10. Influence of a constant temperature Fig. 11. Roll due to inhomogeneous temperaturegradient on a coordinate measuring[9]. distribution in the guides of a machine tool [9].machine The FEM has enabled in-depth analysis of the thermal behaviour of machine toolsunder the influence of heat sources present inside the machine tool structure and in itssurroundings. Moreover, thanks to FEM one can examine the effect of the individualstructural components, both the ones incorporating heat sources and the ones subjected to theinfluence of external heat sources, e.g., varying ambient temperature. The FEM is also usedto determine the influence of heat transfer coefficient (film coefficient) due to free and forcedconvection [47,90,49,84]. The accuracy of the geometrical modelling of the machine toolstructure has increased significantly, if thermal displacements are caused directly by differenttemperatures, by strains, or even by power losses. A machine tool error in a numerical 60
- 9. International Journal of Mechanical Engineering and Technology (IJMET), ISSN 0976 –6340(Print), ISSN 0976 – 6359(Online) Volume 4, Issue 2, March - April (2013) © IAEMEcontrolled (NC) axis results from the mutual displacements of the individual componentsdepending on the operating conditions. The error changes with the heat generation and heattransmission conditions. Therefore the computing of thermal errors must be based on the veryprecise modelling of all the major thermal phenomena taking place in the machine tool as itoperates [3,7,8,18]. In order to accurately represent the behaviour of the individual machinetool components, a model should be fine-tuned on the basis of precise measurements of thetemperature and displacements at specified points of the machine tool. The preciseidentification of temperatures and displacements in a machine tool prototype is vital for thecreation of an accurate model and for its evaluation, especially when thermal errors are to becompensated on the basis of the model and numerically simulated displacements[5,11,53].Today, the ambition of every designer of highly efficient machine tools, particularlythe ones to be used for precision machining, is to be able to accurately predict thermal errorsthrough numerical simulations. Accurately predicted errors are the basis for their effectiveand easy compensation. The most rational, although difficult and laborious, way of modellingis the integrated modelling of entire machine tool structures, which takes into account thethermal interactions between the individual assemblies and the machining processes. Anintegrated computing model enables one to effectively improve the thermal performance ofthe whole machine tool, i.e., to minimise thermal errors, and to precisely predict thermalerrors for error compensation purposes [73,74]. In many cases, however, machine tooldesigners need a quick assessment of the possibility of improving the main (e.g., spindle andfeed) assemblies. The modelling of assemblies isolated from the whole machine tool is muchless time-consuming. Such modelling of thermal errors is often justified and in many casesprecedes integrated modelling. FDEM – a serial simulation-tool FDM- MODEL Temperature T(t) FEA- Model Temperature T(t) & Nodal displacement u(t) Fig. 12. Schematic of the FDEM 61
- 10. International Journal of Mechanical Engineering and Technology (IJMET), ISSN 0976 –6340(Print), ISSN 0976 – 6359(Online) Volume 4, Issue 2, March - April (2013) © IAEME3.2. Numerical modelling of thermal errors In the last 20 years great advances in the modelling of machine tool thermal errorshave been made. The need to minimise and compensate the errors is dictated by the demandfor higher efficiency of machining processes [88]. The development of error modellingbecame possible thanks to the increased computing power of modern computers, thedevelopment of advanced FEM algorithms, and the increasing knowledge about heatgeneration, power losses, and heat transmission in the assemblies and in the whole machinetool structure, especially at high rotational and feed speeds [25,26,46,61,75,32,34,63,64]. Anideal model is one which accurately represents the thermal processes taking place in theoperational conditions in which the particular assemblies work as machining operations areperformed by the machine tool. Moreover, in order to ensure that the cycle and cost ofmachine tool improvement are acceptable, the modelling of the machine tool shall not belabour-intensive or time-consuming. In the early 1990s a breakthrough in the modelling ofthe thermal behaviour of machine tools was achieved. It consisted in the integratedcomputing of power losses, temperatures, strains, and thermal displacements whereby theirinteractions were taken into account (i.e., computing transitions instead of steady state) [10].As a result, it became possible to predict thermal displacements. The FEM and the finitedifference method (FDM) are used to model the heating and the thermal deformation ofmachine tool structures. In a combination of both numerical simulation approaches, thestaggered algorithm Finite differences element method (FDEM) [91,81,82,71,72] (Fig. 12),the advantages of both methods are combined in an efficient way. The FDEM uses in a firststep Finite Differences to compute the multidimensional temperature distribution of machinetools efficiently. In a second step Finite Elements are used to compute the thermally induceddeformation of machine tools with a linear system of equations. A linear system of equationsenables solving multiple time steps together and to reduce the system of equations. If forexample the TCP displacements are evaluated, the FEM model can be reduced to a fewdegrees of freedom. This can reduce the computation time significantly, which is important ifa number of simulations, for example several load cases, are to be evaluated. Furthermore,FDM is highly suitable for the modelling the thermal behaviour of cylindrical parts [66]. Theassemblies which affect thermal errors most strongly must be modelled with highest precisionfor geometry, heat generation and transmission [15]. • Determine the amount of heat generated in the rolling bearings, depending on the type of bearing, the rotational speed, the load, the lubrication, the material properties, the assembly tolerances, the ambient conditions and running clearances. • Model the flow of heat in the spindle assembly, taking into account the interactions between the above factors. • Model the forced cooling of the spindle bearings and the other elements, depending on the type and velocity of the flow of the cooling medium. • Determine the amount of heat generated in the spindle motor, depending on the rotational speed and the load. • Model the distribution of the heat generated in the stator and in the rotor and • Model the motor cooling system. 62
- 11. International Journal of Mechanical Engineering and Technology (IJMET), ISSN 0976 –6340(Print), ISSN 0976 – 6359(Online) Volume 4, Issue 2, March - April (2013) © IAEMEThe drawback of the programs is that there are several constraints concerning, e.g., thepossibility of automatic fast discretisation, the number of finite elements, and variety ofelements. Universal commercial software for FEM computations has no such limitations.Thanks to their fast solvers the programs are very attractive to the user. Furthermore, the pre-and postprocessors are relatively easy to operate. They are suitable for parallel computing,extended finite element bases, and sophisticated algorithms for the analysis of linear and non-linear phenomena, including contact. They offer the possibility of extending the range of theirapplication by writing specialised procedures (subroutines). A major advantage of thecommercial FEM systems is the frequently offered possibility of integration with programsfor computational fluid dynamics, which in the case of machine tool computationssignificantly extends their application range. A serious limitation of the commercial programsis the lack of access to the source code and possibility of analysing or changing the way inwhich the solver operates. There is one more limitation to the use of commercial programsfor modelling the thermal behaviour of machine tools: the programs do not ensure therequired accuracy of modelling the thermal phenomena taking place in machine tool spindleassemblies, toothed gears, ball screws, guides, and so on. When computing machine toolerrors, the best solution is to use one of the commercial programs for modelling machine toolgeometry and combine it with dedicated computing programs which represent the thermalphenomena taking place in the individual machine tool assemblies, e.g., in the motorspindle,the ball screw, the guide assemblies, and so on.3.3. Modelling and computing thermal errors in spindles and rotating axes The assemblies in which thermal errors are generated in NC rotating axes are spindleheadstocks and rotary tables of various designs [27,78,80]. Generally speaking, the higher therotational speeds and torque at which they operate and the greater the machining loads, thelarger the complexities of the phenomena taking place and the larger the errors.According to decreasing complexity, the thermal models of errors in the rotating axes foundin the literature can be ordered as follows: • The complex hybrid spindle unit model (group 1). • The motorspindle model (group 2) • The spindle unit model (group 3); and • Other compensation oriented models (group 4).A model representative of the group 3 is the Hokup model of a high-speed spindle unit withball bearings [75] (Fig. 13). In this FEM-based model the main emphasis was placed on theaccurate modelling of rolling element loads as a function of spindle rotational speed andtemperature distribution. The effects that the latter have on bearing power losses and spindleunit thermal deformations determine the thermal error in the rotation axis of the spindle.Other error models aimed at compensating the thermal axial displacement of machine toolspindles are models based on data from measuring temperatures alone, displacements aloneor both temperatures and thermal displacements. This group 4 also includes error modelsexploiting: artificial neural networks, linear and non-linear regression, dynamic models,transfer function, adaptation models, and other [52,17,19,65,16,41,23,54–56]. 63
- 12. International Journal of Mechanical Engineering and Technology (IJMET), ISSN 0976 –6340(Print), ISSN 0976 – 6359(Online) Volume 4, Issue 2, March - April (2013) © IAEME heat transfer through air gap: outer spacers-housing heat transfer through air cavity Static parts- cavity – rotating parts heat transfer through air gap: inner spacers - shaft Fig.13. Thermal FEM model of a bearing and its surroundings [87].Among the models in group 4, the model developed by Kim et al. [51] deserves to be presented. Forthe compensation of Z-axis errors in a machining centre with a maximum spindle speed of 25,000rpm, it distinguishes two errors: an axial offset error, which is assumed to stem from the behaviour ofthe test bar/spindle joint, and a thermal error which is defined as the sum of the temperature-dependent deformations and deflections of the headstock and column components. Each thermalmode is correlated with the temperature of the corresponding component through a thermal modegain. Mathematical models for Y- and Z-axis thermal distortions are expressed asδ = G .T (1)For six-temperature measuring points, whereGy = Gh , Gh , GC, GC (2) T3 + T4 T5+ T6Ty = , T3 – T4 , , T5 - T6 (3) 2 2 Tests were carried out to investigate the two errors. Plane milling was used to identify thethermal error. The latter was reduced from 70 mm to below 10 mm for the Z-axis (Fig. 14), but a goodmachining effect was obtained only after compensatory control smoothing (Fig. 15).It becomes apparent that it is not enough to compensate the distortion in Z because the compensationeffects visible on the surface still need to be smoothed. Thermal error (µm) X-direction of work piece (mm) Fig.14. Comparisons of spindle axial shift with and without compensation [48]. 64
- 13. International Journal of Mechanical Engineering and Technology (IJMET), ISSN 0976 –6340(Print), ISSN 0976 – 6359(Online) Volume 4, Issue 2, March - April (2013) © IAEME Fig.15. Machined surface with thermal error compensation (thermal distortion in Z), left: without smoothing, right: with smoothing [51]3.4. Modelling and computing thermal errors generated in linear axes Thermal errors in linear axes are generated in the ball screw transmission and in directdrives with linear motors [28]. The source of thermal errors in the ball screw transmission isthe thermal changes in the active length of the screw. The changes depend on: the type anddimensions of the screw, the tension of the turning parts, the nut and the bearings, theexternal load, the rotational speed, the work cycle, the load resulting from the torque ofelastohydrodynamic friction in the lubricating film of the turning parts, and the heat transferconditions. In order to reduce power losses, air–oil lubrication is used on high-speed screwswith a large pitch. Relations for losses due to load and friction in the lubricating medium can be found inball screw manufacturer catalogues. But the modelling of heat transmission, both natural andforced (the cooling of the nut and the internal cooling of the screw), is difficult. Similarly asin the case of the fast change of the headstock position relative to the machine tool’s bed orstand, an effective method of modelling heat transmission and temperature and straindistributions in thermally non-stationary states is sought for the fast travel of the screwrelative to the nut. A simplified approach to the modelling of the thermal behaviour of the ball screwtransmission was presented in [69]. An attempt to experimentally and computationallydetermine temperatures in the nut area and the temperature at one point of the screw for anintermittently working, pre-tensioned screw was made in [20]. When determining thermalerrors arising in ball screws, it is very important to accurately identify the distribution oftemperature along the screw and on this basis determine its axial thermal elongation. In theresearch undertaken by Heisel et al. [62], an infrared camera was used to identifytemperatures. An example of an experimentally determined temperature distribution for 4000cycles, modelled and measured positioning errors are shown in Fig. 16. 65
- 14. International Journal of Mechanical Engineering and Technology (IJMET), ISSN 0976 –6340(Print), ISSN 0976 – 6359(Online) Volume 4, Issue 2, March - April (2013) © IAEME Temperature (0C) Positioning error (µm) Fig.16. Ball screw thermal behaviour for a travel distance of 100 mm: top: temperature distribution measured on the screw (at the beginning: blue, after 4000 cycles: red), bottom: modelled positioning errors compared with experimental data [20] Fig.17. Schematic of a thermo-mechanical model of a ball screw [68] Similar investigations were carried out by Horejs et al. [68]. A simple thermal–mechanical model of a ball screw with bearings at both ends (Fig. 17) was used to performFEM. The numerical model covers the friction torque of the bearings, all heat transferconditions, the nut friction torque, and the external load. The model was verified bycomparing the measured (by resistance thermometers) temperatures at points located alongthe screw with the ones calculated using the numerical model. The discrepancy was found toamount to 7%. The positioning error along the screw with one fixed bearing, calculated from 66
- 15. International Journal of Mechanical Engineering and Technology (IJMET), ISSN 0976 –6340(Print), ISSN 0976 – 6359(Online) Volume 4, Issue 2, March - April (2013) © IAEMEa temperature profile obtained by means of infrared thermography, differed from themeasured one by 10% in the loaded part of the screw and by 8% in the free part. The thermo-mechanical model is a substantial step towards the development of an accurate integratedmodel for calculating power losses, temperatures, and thermal displacements of a ball screwwith pretensioned bearings on both sides in its natural operating conditions. The positioningerrors under thermal load will be smaller with fixed bearings at both ends, as schematicallyshown in Fig. 18. In [42] thermal error modelling by FEM is limited to the heating andthermal elongation of the ball screw alone, neglecting the effects originating from themachine tool structural bodies. Only the influence of the bearings and the trapezoidaldistribution of thermal load in the screw–nut joint were taken into account. Good agreementwith measurements was obtained, but the analysis was limited to the table system isolatedfrom the machine tool. Fig.18. Impact of bearings configuration on positioning errors [68] In [36] attention was drawn to the fact that it is necessary to take into account changesin the tension of the ball screw that accompany the changes in its temperature. A relationshipforscrew stiffness was presented. It was also shown that the thermal errors of the screw canbe reduced by modifying its mounting stiffness and reducing the significant influence of themachine tool body in which the screw is mounted. In [33,40] an attempt was made to developa model for predicting the thermal errors of a three-axis machining centre due to heatgeneration in its linear NC axes as a function of varying operating conditions. The model wasbased on experimental tests which indicated that the rise in the temperature of the ball screwnut during operation has the strongest effect on the thermal errors in the NC axes. The mainfactors that determine the magnitude of thermal errors in the NC axes were: the machine tooloperating conditions, the power losses in the ball screw nut, and the rate of travel. Mutualinteraction between NC axes and the table was observed. It was found that in the cold statethe table load and the load generated by the machining forces have a significant effect on thethermal errors. It was shown that the thermal error rapidly increases at the moment when wetcutting with a coolant becomes dry cutting (Fig. 19). The hybrid Bayesian network for theclassification of tests and the powerful regression tool support vector machine model (SVM)for the efficient mapping of temperature data with a positioning error were used to predict thethermal error of positioning. A comparison of the predicted positioning errors in axis X withthe measured ones showed that the difference amounted to 10 mm. This is unsatisfactory inthe case of machine tools for precision machining. But one should bear in mind that themachining process introduces many disturbances which until now have not been taken intoaccount in thermal error compensation. 67
- 16. International Journal of Mechanical Engineering and Technology (IJMET), ISSN 0976 –6340(Print), ISSN 0976 – 6359(Online) Volume 4, Issue 2, March - April (2013) © IAEME X-axis Positioning error (µm) Time(min) Fig.19. Thermal error variation under dry and wet machining conditions [40]. Artificial neural networks (ANN) have been used to model thermal errors inpositioning for axes with preloaded ball screws [43,44]. A new generation artificial neuralnetwork based on the wavelet theory deserves attention [89]. Wavelet neural networkssupported by the evolutionary particle swarm optimisation (PSO) technique, dramaticallyincrease convergence and assure much smaller screw nut temperature and positioningprediction errors than conventional ANNs. In the case of high power losses in the nut andhigh rates of feed, a substantial reduction in thermal errors can be achieved by cooling the nutand the whole screw from the inside. In [76] one can find an analysis of the effect of internalcooling of the screw in axes X and Z of a lathe slide on the thermal errors in these axes.Fig. 20 shows calculated losses in the ball screw–nut unit for X- and Z-axes when movingwith and without a load, as a function of travel rate. Also the effect of cooling in the two axeson the thermal error of the Z-axis is presented. It was demonstrated that using even smallamounts of cooling oil reduces the thermal error twofold and that cooling in the two axesmutually affects the thermal error in each of the axes. This provides an argument for theintegrated computing and analysis of thermal errors for similar designs, particularlyconsidering applications of high loading generated through high machining forces. In [85,92] a thermal equivalent circuit model of a ball screw is presented. It has beenshown that cooling the nut can reduce the thermal errors. Furthermore, the influence of thecoolant temperature variation is considered in the simulation. Nut cooling was chosen in thisstudy since the nut was the non-rotating element making it more practical to feed throughwith cooling fluid. In drives with linear motors, thermal errors of NC axes appear significantly inencoders. They are mainly due to changes in the length of the linear scale and the thermaldisplacements of the encoders relative to the machine tool body. It is important whether theencoder is made of steel or special glass, i.e., what the thermal expansion of its material is.The displacements of the encoder reference points depend on the thermal strains in thecasings, the heat generated in the motor winding and in the permanent magnets, and the heattransmitted by other significant sources. In the existing literature there is no adequateassessment of encoder displacements, but research reports indicate that the thermaldisplacements of an encoder may significantly affect the thermal errors of the machine tool[66]. 68
- 17. International Journal of Mechanical Engineering and Technology (IJMET), ISSN 0976 –6340(Print), ISSN 0976 – 6359(Online) Volume 4, Issue 2, March - April (2013) © IAEME Power losses in ball screws/ nut of Z axis preload of screws: Z1820N, X-1019N X-axis Positioning error (µm) Feed velocity (m/min) Displacement Z of tool tip internal cooling of ball screws X,Z X-axis Positioning error (µm) Oil flow rate (l/min) Fig. 20. Top: computed power losses in ball screw-nut unit for X- and Z-axes of a lathe, bottom: cooling effect (cooling of nut and ball screw) for thermal error in Z-axis [76]. When investigating, by means of a computational model and experimentally, thermalerrors in the NC axes of a horizontal high speed machining centre with linear drives, Kim etal. [48], made the following observations: • the main heat sources are the linear motors, the spindle motor, and the coolers; • high temperature rises (in the region of 25 8C) occur in the stationary parts of the linear motors in the course of changing duty cycles and the differences between the left and right motor of the Y-axis reach 10 8C (Fig. 21a); 69
- 18. International Journal of Mechanical Engineering and Technology (IJMET), ISSN 0976 –6340(Print), ISSN 0976 – 6359(Online) Volume 4, Issue 2, March - April (2013) © IAEME • temperature rises in the live part of the motor, the linear scale, and the guide block were similar and did not exceed 3 8C (Fig. 21b); • the thermal error changed in a similar way as the temperature, reaching 30 mm and 25 mm in the Y-axis and the Z-axis respectively; and • the thermal error comprised the elongations/shortenings of the linear motor body, the guide and the linear scales, and depends on the performance of the cooling system and changes in ambient temperature. Temperature Change (0C) Time (h) Thermal error (µm) Temperature (0C) Time (h) Fig.21. Measurement results: (a) temperature variations of Y-axis linear motor, (b) temperature variations and thermal error (LM: linear motor) [48].In [48] heat sources in linear drives are modelled. The temperatures measured for a givenlinear motor operation are used to calculate the heat fluxes and the thermal errors in the NC-axes. From the research presented here, one can conclude that efforts should be concentratedon the creation of an accurate integrated thermal model. 70
- 19. International Journal of Mechanical Engineering and Technology (IJMET), ISSN 0976 –6340(Print), ISSN 0976 – 6359(Online) Volume 4, Issue 2, March - April (2013) © IAEME3.5. Integrated models of thermal errors for complete machine tools Due to the interactions between the internal and external heat sources, the machine tool’sthermal error is highly complex [60]. The interactions may result in changes in the output of the heatsources and in the deformation of the machine tool bearing elements. Therefore the error affecting thework piece cannot be modelled as a simple sum of the thermal errors generated by the isolatedindividual assemblies (e.g., spindle, moving axes). This indicates a need for the creation and use ofintegrated models.An example of such a model for a five-axis machining centre is shown in Fig. 22[93].The above-integrated model shows the possibility to: • model very large and complex machine tool structures and complex process interactions; • highly automate geometrical modelling with CAD support, ensuring high computing speed; • take into account the effect of the mutual interactions between heat sources on the thermal errors in the NC axes; • estimate the intensity of heat sources by means of a dedicated computing system; and • Fully integrate commercial and dedicated computing systems through proper interfaces.Within the FEM environment an interaction model considering the thermo mechanics of the cuttingprocess and the machine tool structure is developed [86]. The model computes the cutting forces, chipshape, chip size, temperature distribution, and thermal deformation of machine tool and work piece. Fig.22. Integrated model of thermal behaviour of a high-speed 5-axis machine tool[93] 71
- 20. International Journal of Mechanical Engineering and Technology (IJMET), ISSN 0976 –6340(Print), ISSN 0976 – 6359(Online) Volume 4, Issue 2, March - April (2013) © IAEME3.6. Temperature analysis and thermal deformation simulation of machine tool structures The accuracy of machine tools depends on positioning errors. The total positioning errorcan consist of up to 70% thermal derived errors, which combines influences of the machine tool’sinternal heat sources and environment. Continuous usage of a machine tool generates heat, whichleads to thermal errors due to thermal expansions of structural linkages. The heat generated bydrive systems (linear motors, ball screws, etc.) enters into the machines structure, passes throughmechanical joints, and causes the thermal deformation of the machine tool structure [33]. Againstthis background, the thermal behaviour of a 5-axis machining centre equipped with linear motorswas analysed using an FEM system. It calculates the temperature distributions in a structure using non-linear heat transfermethods [67]. Internal and external heat sources have to be modelled for the simulation of thetemperature distribution and the thermal deformations of a machine tool. The most importantexternal heat source is represented by the ambient temperature which was not considered, withthe assumption of a machine tool in a constant temperature workshop. The spindle and theprimary and secondary sections of the linear motors were regarded as the most important internalheat sources. Thus, the spindle with integral drive motor and linear motors were simplified andrepresented as heat sources of the machine tool. Heat generated by the linear motors wasmodelled via positive heat fluxes. Most of the heat is dissipated by the cooling system. This effectwas implemented by a negative heat flux. In the FEM, the elements close to the heat source weremeshed in more detail than in other regions in order to get an optimum between computationprecision and speed. The calculated heat fluxes were applied as heat sources with the simulationset for 90 min. The resulting maximum displacement appeared at the top of the Z-carriage,whereas the maximum temperature was at the XZ-plate. The thermal displacements at the TCPwere also generated to investigate the effect of the thermal error on the TCP. Maximumdisplacements of the TCP of Dx = 5 mm,Dy = 10 mm, and Dz = 6 mm arise when taking thelinear motor´s cooling system into account. With a knowledge-based description of the boundaryconditions, simple types of load were simulated using FEM [83]. A procedure for computing theheat transfer coefficient at a machine tool surface depending on air temperature, temperaturedistribution of the machine tool, and orientation of the surface was developed [84]. Theadaptation of the heat transfer coefficient allows a more accurate modelling of convective heattransfer. To model the influence of surface roughness and pressure [12] in the heat transfer injoints, special FEM elements are developed in [37]. In [34] a formula to compute the thermalconductivity of joints is given.4. REDUCTION OF THERMAL ERRORS The knowledge achieved through improved measurements and simulations is used withnew methods for compensation of thermal errors of machine tools. A lot of models to compensatethe thermal errors via readjustment of the axes positioning by the machine tool’s control aredeveloped [4,6,14,22,59,79,24,29,30,31,70,38,11,13,57,77,21]. The movements are often realisedwith the machine tool feed drive systems. Sometimes special compensation axes are used. Severalindirect compensation procedures based on linear expansion models, rigid body models, neuralnetworks, or other models have been developed. These approaches are based on auxiliary valueslike temperature measurements. Other types are direct compensation approaches where thethermal displacements, e.g., of the tool relative to a fixed measuring probe in the workingenvelope, are measured periodically. 72
- 21. International Journal of Mechanical Engineering and Technology (IJMET), ISSN 0976 –6340(Print), ISSN 0976 – 6359(Online) Volume 4, Issue 2, March - April (2013) © IAEME5. CONCLUSIONS The effects of heat generation and temperature rise on the occurrence of chatter inorthogonal cutting process were studied. The main aim of this research was to study howtemperature rise due to plastic deformation and friction can affect the border of stability. ADynamic finite element model of the chip formation process was developed in which the toolwas modelled as a one degree of freedom system capable of vibration in the direction of chipthickness. The simulations were computationally very intensive for every run. The studyshows that increasing the temperature in the cutting zone can have a marked effect on thestability of the cutting system. When temperature is risen, the heat softens the material andreduces its stiffness and as a result, the threshold of instability is raised as well. Several casesof cutting at various speeds and depth of cut were simulated with and without thermal effects.Comparison between the results revealed that the system is more stable when thermal effectsare included. Also, the forces and displacements decrease. It may be concluded that chatterstudies ignoring thermal effects yield conservative predictions of the stability lobes. In the future, precise work pieces of different materials with different coefﬁcients ofthermal expansion have to be manufactured on machine tools. One of the main errorsources in production is a changing ambient temperature as well as ambient temperaturesother than 200C. In order to compensate the errors caused by the ambient temperature, thethermal behaviour of the machine tool itself, the coefﬁcients of thermal expansion of themachine tool components and the work pieces, and the thermal conductivity of the materialshave to be known well. More precise measurement devices and measurement strategiesshould be developed to reduce the uncertainties of temperature and displacementmeasurement of machine tools and work pieces. Compared to the research effort on measurement, simulation, and compensationstrategies related to thermal errors, the inﬂuence of the machining process and theinﬂuence of the coolant have not been studied with the same intensity. These are certainlyﬁelds where future work should focus to reduce thermal errors of machined parts.REFERENCES[1] H. E. Merritt, “Theory of self-excited machine tool chatter,” Journal of Engineering forIndustry, vol. 87, no. 4, pp. 447–454, 1965.[2] S. A. Tobias, Machine-tool vibration. J. Wiley, 1965.[3] Jedrzejewski J, et al, (1977) Warmeubergangsverhaltnisse an Spindelkasten vonDrehmaschinen. Industrieanzeiger 99(74):1436–1439.[4] Jedrzejewski J (1985) KompensationthermischerVerlagerungeneinerDreh- maschine.Werkstatt und Betrieb 118:85–87.[5] Jedrzejewski J, et al, (1998) An Approach to Integrating Intelligent Diagnos- tics andSupervision of Machine Tools. Journal of Intelligent Manufacturing 9:295–302.[6] Donmez MA, et al, (1986) A General Methodology for Machine Tool AccuracyEnhancement by Error Compensation. Precision Engineering 8(4):187–196.[7] Jedrzejewski J, et al, (1988) Description of the Forced Convection along the Walls ofMachine-tool Structures. Annals of the CIRP 37(1):397–400.[8] Jedrzejewski J (1988) Effect of the Thermal Contact Resistance on Thermal Behaviourof the Spindle Radial Bearings. International Journal of Machine Tools and Manufacture28(4):409–416. 73
- 22. International Journal of Mechanical Engineering and Technology (IJMET), ISSN 0976 –6340(Print), ISSN 0976 – 6359(Online) Volume 4, Issue 2, March - April (2013) © IAEME[9] Teeuwsen JWMC, et al, (1989) A General Method for Error Description of CMMs UsingPolynomial Fitting Procedures. Annals of the CIRP 38(1):505–510.[10] Jedrzejewski J, et al, (1992) A new Approach to Modelling Thermal Beha- viour of aMachine Tool under Service Conditions. Annals of the CIRP 41(1):455–458.[11] Jedrzejewski J, et al, (1992) Thermal Displacements Compensation of Man- ufacturingCells Using a Universal Correcting Temperature Function. Pro- ceedings of CSME Forum675–680.[12] Itho S, et al, (1992) Behavior of Interface Pressure Distribution in a Single Bolt-FlangeAssembly Subjekt to Heat Flux. Journal of Engineering for Industry 114:231–236.[13] MaischM (1993) Software korrigiertgeometrische und thermischeFehlerWerkstatt undBetrieb 126(11):691–694.[14]Bonse R, Weck M (1994) IndirekteKompensation Thermo-elastischerVerlager-ungenbeiEinwirkungmehrererWa¨rmequellen, VDW 8493.[15] Jedrzejewski J, et al, (1994) Directions in Improving Thermal Behaviour of SpindleBearing Assemblies in FMS Moduls. Manufacturing Systems 23(4):317–322.[16] Veldhuis SC, Elbestawi MA (1995) A Strategy of Compensation of Errors in Five-Axis Machining. Annals of the CIRP 44(1):373–377.[17] Chen JS, et al, (1995) Quick Testing and Modelling of Thermally-induced Errors onCNC Machine Tools. International Journal of Machine Tools and Manufacture35(7):1063–1074.[18] Jedrzejewski J, et al, (1996) ThermischesVerhalten von Werkzeugmaschi- nen-Gestellen. IndustrieAnzeiger 99(65):1243–1245.[19] Chen JS (1996) Neural Network-based Modelling and Error Compensation ofThermally-induced Spindle Errors. International Journal of Advanced Manu- facturingTechnology 12:303–308.[20] Kim SK, et al, (1997) Real-time Estimation of Temperature Distribution in a Ball-screw System. International Journal of Machine Tools and Manufacture 37:451–464.[21] Bonse, R., 1998, Thermisches Last-Verformungsverhalten von Werkzeug- maschinen,Diss. RWTH Aachen. ISBN 3-8265-6102-3.[22] Fraser S, et al, (1998) Modelling, Identiﬁcation and Control of Thermal Deformationof Machine Tool Structures, Part 1: Concept of Generalized Modelling. Journal ofManufacturing Science and Engineering 120:623–631.[23] Weck M, et al, (1998) Compensation of Thermal Errors in Machine Tools with aMinimum Number of Temperature Probes Based on Neural Networks. Proceedings of theASME DSC 64:423–430.[24] Fraser S, et al, (1998) Modelling, Identiﬁcation and Control of Thermal Deformationof Machine Tool Structures, Part 2: Generalized Transfer Func- tions. Journal ofManufacturing Science and Engineering 120:632–639.[25] Grossmann G, et al, (1998) ThermischesVerhaltenvera¨ nderlicherStrukturen.Konstruktion 50(6):27–31.[26] Grossmann K, Jungnickel G (1999) Genauigkeitssteigerung an Werkzeug- maschinen.Zeitschriftfu¨rwirtschaftlichenFabrikbetrieb 94(6):320–323.[27] Chen TY, et al, (1999) Optimum Design of Headstocks of Precision Lathes.International Journal of Machine Tools and Manufacture 39:1961–1977.[28]Yun WS, et al, (1999) Thermal Error Analysis for a CNC Lathe Feed Drive System.International Journal of Machine Tools and Manufacture 39:1088–1101 74
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