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Multifunctional structure solutions for Ultra High Precision (UHP) machine tools
ARTICLE IN PRESS International Journal of Machine Tools & Manufacture 50 (2010) 366–373
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International Journal of Machine Tools & Manufacture journal homepage: www.elsevier.com/locate/ijmactool
Multifunctional structure solutions for Ultra High Precision (UHP) machine tools F. Aggogeri a,n, A. Merlo b, M. Mazzola a a b
Department of Mechanical and Industrial Engineering, University of Brescia, Via Branze, 38, 25123 Brescia, Italy Ce.S.I., Centro Studi Industriali, Via Tintoretto, 10, 20093 Cologno Monzese (MI), Italy
a r t i c l e in f o
a b s t r a c t
Article history: Received 16 March 2009 Received in revised form 14 July 2009 Accepted 1 November 2009
This paper aims to study innovative structure solutions for Ultra High Precision (UHP) Machine Tools (MT) within machining applications at micro/mesoscale level (10–10 000 mm range). There are many aspects that can affect the accuracy of UHP machining performance. The most important issues are related to the static, dynamic and thermal behaviour of the machines. This paper shows a complete study and thermal testing validation on a set of prototypes (plates and beam) based on sandwiches with core made of metal foam (open cells) material impregnated by phase change materials. The proposed multifunctional structure (which provides high stiffness to weight ratio, good damping properties together with thermal stability) consists of a machine tool part, a beam (Z-axis) of a precision milling machine. The authors have designed, realised and tested prototypes developing thermal trials and then evaluating the experimental data. The trials consisted to test the prototype thermal stability when the environmental temperature varies in a specified range (20–50 1C), in order to assess the PCM proprieties to absorb heat and maintain performances for a long duration. Furthermore, a numericalexperimental validation through finite element analysis on the beam prototype is presented. & 2009 Elsevier Ltd. All rights reserved.
Keywords: UHP-MT MT structures Phase change materials MT thermal stability Experimental trials Finite element analysis
1. Introduction The study of innovative materials in machine tool (MT) building can provide a fundamental impact on functionality and reliability of a manufacturing system. Numerous reasons for this growth include light weight, superior insulating abilities, energy absorbing performance, excellent strength/weight ratio and low cost [1]. A strong mass reduction of mobile machine parts and an increase of their stiffness and damping to obtain excellent static, dynamic and thermal stability of the structures are becoming a ‘‘must’’ to guarantee excellent results in terms of technological and cost-effective impact, especially in the submicron range [2– 4]. The introduction of composite materials in MT design can provide significant advantages in terms of static and dynamic performances, and represent a new challenge for design engineers and further opportunities for the composite manufacturers [5]. Conventional materials for MT building are cast iron, welded steel and, in some cases, aluminium-alloys. Although these materials represent a consolidated technology for MT engineers, the need to ensure high performances requires the investigation of a new class of materials with improved inherent properties in terms of
n
Corresponding author. Tel.: + 39 0303715579; fax: + 39 0303702448. E-mail address: [email protected] (F. Aggogeri).
0890-6955/$ - see front matter & 2009 Elsevier Ltd. All rights reserved. doi:10.1016/j.ijmachtools.2009.11.001
specific stiffness, structural damping, dimensional and thermal stability [6]. This study aims to show an investigation to apply metal foams impregnated by Phase Change Materials (PCM) in MT component realisation. Metal foams are a new class of materials that offer potential for lightweight structures, for energy absorption and thermal management with low costs [1]. Their particular cellular structures permit to be impregnated by PCMs that absorb heat and keep thermal stability of a machine component for a long duration when temperature changes due to different heat sources.
2. Main issues in UHP machine tool designing There are many aspects that can affect the accuracy of an UHP machining performance. According to Bryan [7], errors originating from machine tools make up the largest portion (60–65%) of the total errors in machined workpieces [8]. The most important problems are related to static, dynamic and thermal behaviour of the machines [9]. A first consideration deals with the evaluation of thermal errors. These issues are due to an increase of the MT structure and component temperature during the machining operations. Thermal distortion of MT structures is widely attributed as a significant cause of workpiece inaccuracy within modern CNC machining specially in microdomain [10–12]. It is difficult to develop a practical compensation strategy dealing with
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the different aspects of machine tool thermal behaviour. For this reason practical actions are necessary in order to guarantee thermal stability during manufacturing operations. In general, it is possible to classify thermal errors in two main categories: errors that effectively alter the linear positioning of the machine and errors that change the machine offsets [13,14]. These errors can be caused by different heat sources (i.e. bearings, drives, pumps, motors, cutting action or external sources) that should be analysed to avoid possible effects on machine accuracy. These considerations suggest to use particular structural materials (i.e. cement concrete, fibre reinforced plastics) able to reduce the deformation due to temperature changes, or to study advanced techniques that permit to compensate thermal errors analysing temperatures of machine critical points [15–18]. In this study the authors present a further solution by applying PCMs to machine tool structure building in order to absorb heat, keeping constant the temperature of a machine component in a defined time range when temperature is perturbed. Other considerations should be developed for static behaviour of an MT that can be analysed evaluating the contribution of every single structure/component of the machine on the global compliance at the tool tip [7]. Instead the dynamic behaviour and its physical causes are still not fully understood. It is noted that vibrations in MT are induced by periodic forces and can be divided into two categories: forced (and free) vibrations and self excited vibrations (chatter) [6,19,20]. The analysis of the critical frequencies of a machine is fundamental in order to know if the excitation forces can cause resonance issues and produce an unacceptable accuracy of the workpiece. In the light of this brief analysis it is important to reduce machine mass and enhance its damping and stiffness. The mass reduction involves another significant advantage: less mass to move means less inertia and so less energy ‘‘absorbed’’ by the machine. For this reason, the authors have considered lightweight materials that permit an excellent stiffness-to-weight ratio when loaded in bending and a low density with good shear and fracture strength [1]. Further-
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more, in order to reduce the temperature effect on MT structure distortion the PCMs application has been considered. This application consisted in impregnating metal foam materials with PCM wax to guarantee thermal stability when the temperature was perturbed, and dynamic stability using lightweight materials.
3. Application of multifunctional materials in MT building 3.1. Metal foams Metal foams represent a new class of materials with low density and novel physical, mechanical, thermal, electrical and acoustic properties [21,22]. They offer potential for lightweight structures, for energy absorption and thermal management with low costs [1]. These performances can be achieved thanks to their exceptionally high properties in term of stiffness-to-weight ratio and low density with good shear and fracture strength. A further advantage of these materials is the damping capacity that is larger than that of solid metals by up to a factor of 10 [23]. In this paper the authors have considered aluminium open cell foams, while evaluations and possible applications of closed cell materials are currently under testing. Open cell foams are porous structures consisting of an interconnected network [24]. Their particular structure permits to be impregnated by other materials (liquid state) as a PCM wax. The main features of these types of materials are the pore size and the relative density [22,25,26]. The pore identifies the polygonal opening through every open window while its size defines the number of pores per inch (ppi). The relative density is a fundamental property in order to understand the density of a foam divided by the density of the solid parent material of the struts [26]. In order to evaluate mechanical properties [1] and develop a comparison with other materials employable to realise structural components of an MT, a theoretical study is explained. The
Fig. 1. Selecting material chart.
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selection strategy is based on the evaluation of two parameters that can be considered merit indices: the structural index [28] and the damping coefficient. The structural index is given by the ratio between the cube root of the Young’s module E and the density of the material r. This index regards the material mass and stiffness. In particular, for a prescribed stiffness, materials with the same structural indices have the same weight. The weight is minimised (and the stiffness is increased) by selecting materials with large values of structural index. Fig. 1 shows a chart [28] that permits to select the appropriate material on the basis of its structural index. Materials with the same structural index lie on the same line whose slope is 1/3 (the chart is in logarithmic scale). Conditions on the static, dynamic and mechatronic behaviour of a structure can be translated into conditions on the structural index and damping coefficient (in particular, referring to the chart of Fig. 1, materials with the best structural index lie in the top-right zone). A comparison between commonly used materials and metal foams has been developed. The values assumed by the structural index E1/3/r and by the damping coefficient Z for these materials are listed in Table 1. The material characterised by the highest values of the structural index and damping coefficient is the aluminium metal foam. In the same way, Mg alloys have a high value of damping but it is extremely expensive, especially due to the high manufacturing costs. In the light of these considerations the authors considered metal foam materials as an excellent candidate to reduce problems of static and dynamic behaviour in MT structural building. 3.2. Phase change materials The application of PCMs can be a good solution to solve the thermal issues in MT structure designing and building. PCMs are latent energy storage materials that use their phase change to absorb heat and maintain constant the temperature for long duration (the so called ‘‘plateau’’) [29–30]. In particular a PCM temperature remains constant during the phase change. This is
Table 1 Materials structural index and damping coefficient. Material
E1/3/q [GPa1/3/Mg/m3]
g
Cast iron Steel Aluminium alloys Mg alloys Aluminium metal foam
0.63 0.77 1.5 1.9 2C5
1.2 10 3C1.7 10 3 6 10 4C10 3 2 10 4C4 10 4 10 3C10 2 4 10 3C10 2
useful for keeping the object (i.e. MT components or structure) at a uniform temperature. In this study the authors have considered a paraffin wax with a typical melting point about 31 1C, a heat capacity (latent heat) of 130 KJ/kg and a density close to 0.89 kg/l (solid state at 25 1C). This is an ecological heat storage material that uses the processes of phase change between solid and liquid (melting and congealing) to store and release large quantities of thermal energy at nearly constant temperature. Other important properties are long life product, with stable performance through the phase change cycles, ecologically harmless and non-toxic and chemically inert.
4. Prototype design and realisation In order to test the proprieties of these multifunctional materials, based on sandwiches with core made of metal foam impregnated by a PCM wax, the authors designed and realised a set of prototypes (plates and beam, Z-axis of a precision milling machine). The main goal was to test the thermal stability of prototypes when the environmental temperature was perturbed. The first part of the study consisted in designing four samples (i.e. plates), Fig. 2(a), that could permit to develop a preliminary analysis. The raw materials of samples were two steel sheets (thickness 2 mm) and four U profile beams to cover and close the core, the metal foam core (density of 20 ppi and 40 ppi), PCM materials (paraffin wax—melting temperature 31 1C) to impregnate the core and epoxy glue to assembly the plate components. The realisation process consisted of: - assembling the core with the profile beams and a steel sheet (using the epoxy glue); - inserting the wax (liquid state) into the open cells and - closing the device using the second steel sheet and obtaining a hybrid sandwich Fig. 2(b) [31–33]. In the same way the authors designed and realised a threedimensional structure; it is a Z-axis (300 300 500 mm) of a precision milling machine, Fig. 3(a and b). The metal foam used for the beam building was characterised by a density equal to 20 ppi. In the light of these tests, it was possible to verify thermal hypothesises on a realistic MT component.
5. Experimental trials and results The first experimental campaign considered the tests performed on plates previously described. Every plate had been
Fig. 2. Structural scheme (a) of the designed plates (b).
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Fig. 3. Structural scheme (a) of the designed beam prototype (b).
tested at controlled environmental conditions, reducing the noise variability as a consequence. The multifunctional material plates have been designed to perform distributed thermal stability, avoiding any undesired thermal gradient between the surfaces. Thus the experiments had to reproduce a close-to-uniform temperature, involving the plates in an appropriately controlled environment. For this reason, single plates were positioned vertically inside a box, over-dimensioned with respect to the plates and entirely coated with insulating and reflective materials. Thermal conditions have been obtained and maintained by two resistances of 600 W, symmetrically positioned at 150 mm away from the plate centre. The entire measurement system included a series of thermocouples strategically positioned on the plates. Three thermocouples have been applied to the external surfaces in order to verify the thermal stability and to approximately assess the thermal distribution; another thermocouple has been inserted inside the core to control the PCM temperature. During the design process, the surface geometry (300 300 mm) and the stiffness of the plates have been held as constant factors. Otherwise, other factors are variable. The plates differ in density, thickness and structural characteristics. The influence of variable factors can be assessed through the experimental campaign. The test campaign is resumed in Table 2, where specific characteristics are listed. Since the environment is held constant and the investigation is based on temperature trends rather than on static responses, low variability can be attributed to the repeatability of the experiments and two observations seem enough to assess thermal performances. The trends and responses of every test are compared to those of a common steel (Fe230) plate characterised by equivalent geometry of the surface. In this paper the results of Test 1 are presented in detail, exemplifying the behaviour of the designed plates. The environmental temperature at the beginning of the experiment was close to 22 1C. The experiment is monitored since the external temperature of the plate reached 45 1C (or after 35 min). Data collection has been permitted by an accurate capture system with a sampling frequency of 1 s. The diagram of Fig. 4 resumes the results of Test 1. A constant temperature phase (plateau) can be observed at 31 1C. The plateau
Table 2 First experimental campaign. Plate
Test
Thickness [mm]
Epoxy glue
PCM
Foam density
Open cells
1 2 3 4
12 30 30 12
Yes No Yes Yes
Yes Yes Yes No
40 ppi 20 ppi 20 ppi 40 ppi
Fig. 4. Experimental results of Test 1 compared with a stiffness equivalent bulk steel sheet.
ends after completion of PCM phase transition in 20 min (tp), when a linear increasing (VarT equal to 0.0245 1C/s) of the temperature is correctly observed. The external thermocouples registered a comparable temperature and the curves overlap with an average experimental error close to 1 1C (AvgT). Furthermore, an appropriate uniform distribution of the temperature on the plate surfaces has been verified, quantified by an average difference (AvgTs) between thermo-points on the same surface equal to 0.288 1C.
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Many other indices can help to quantify the achieved results. Performance indicators are calculated for every test for an easy interpretation of the results and for further comparisons. The results of Test 1 are listed in Table 3. The thermal stability of the plate can be appreciated by looking at the difference between external surface thermal curves from Test 1 and the thermal behaviour of an Fe230 bulk steel sheet (upper dashed curve in Fig. 4). The thermal gain is proportional to
Table 3 Test 1 performance indicators. Indicator
Performance
Value
tM [s] tp [s] t45 [s] VarT [1C/s]
Time to PCM melting Duration of the plateau Time to 45 1C Trend increasing velocity after completion of the plateau Average difference between opposite thermopoints Average difference between thermo-points on the same surface Temperature gain at the end of the experiment (by comparison with a bulk steel sheet)
300 s 1200 s 1900 s
AvgT [1C] AvgTs [1C]
DTFe [1C]
0.0245 1C/s 0.99 1C 0.288 1C 21.14 1C
Fig. 5. Experimental results of multifunctional material beam compared with a cast iron one.
the temperature accumulated by the wax, quantifiable by the difference between the curves (21.14 1C at the end of the experiment, DTFe). The multifunctional material controls the temperature during the plateau. In this case, at the end of the plateau the temperature does not exceed 35 1C, instead the bulk steel sheet reaches 60 1C causing potentially relevant consequences on material distortion. From MT accuracy point of view this would lead to undesired shape errors on the workpiece. A comparison between Test 2 and Test 3 demonstrated the epoxy glue effect on thermal stability is negligible. This result is much more precise as the thickness of glue layer is thinner. Finally, Test 3 and Test 1 showed comparable thermal trends, but the plateau of Test 3 was clearly characterised by a longer duration (tp close to 2 000 s), due to the greater quantity of PCM impregnated. In the light of these considerations, it is more interesting to develop three-dimensional prototypes using the solution of Test 3 that guarantee high verified performances with reasonable industrial costs. Once thermal stability is verified for simple geometries, the following objective is to evaluate the designed capabilities on three-dimensional structures. This deals with the second phase of experimental campaign whose goal is to understand the thermal behaviour of a three-dimensional structure, a Z-axis (300 300 500 mm) of a precision milling machine. In this case, the trials have been performed in an appropriate room where the temperature was perturbed in a specified range (from 20 1C to 50 1C). A thermal behaviour comparison has been developed between the beam made of PCM impregnated aluminium foam and a cast iron beam. Following this way, it was possible to understand the contribution of the PCM in evaluating the thermal stability of the MT component. For every beam, different thermocouples were located on the external lateral surface, in order to evaluate the thermal behaviour in different positions. In this paper, the analyses are performed on the data collected by the upper sensor (450 mm). Furthermore, the environmental temperature was checked continuously. Fig. 5 shows the comparison of the thermal data collected for the cast iron (light line) and innovative beam (dark line). The tests ended after 12 000 s and, in any case, after the completion of the phase change of the PCM. As for the plates, it is possible to note
Fig. 6. Experimental results of the modal analysis—Actual vs. synthesised FRF at the excitation point.
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the considerable thermal gain due to the multifunctional material. The temperature measured on the external surface of the innovative beam does not exceed 35 1C, instead that of the conventional beam rapidly reaches 45 1C, causing potentially serious consequences in terms of distortions and shape errors during machining. The authors have also studied the dynamic properties of the structure under vibration excitation. The experimental modal analysis (free–free configuration) has sown that the main vibration modes are at 482, 560, 630, 810 Hz with a modal damping value of approximately 1.6–1.7%, see Fig. 6.
6. FE modeling of the beam sample and numericalexperimental validation A Finite Element (FE) model of the beam prototype has been developed to compare experimental data with virtual one and achieve further confirmation of the assessed performances. The FE
model includes the steel skins, the top steel core, the core and the interconnecting epoxy glue (Fig. 7). The core, in Al-foam open cells impregnated with PCM-wax material has been considered as a homogeneous and isotropic material having weighted properties in accordance with micromechanics of composites. This simplification, reasonable at this preliminary validation stage, can be justified as both Al-foam (which is a stochastic cellular metal) and PCM are isotropic, and it has been assumed that all the voids within the foam has been completely filled by the wax. The mentioned assumption should allow to avoid a FE microstructural model of cells and PCM material that can lead to a huge calculation time. This simplification, reasonable at this preliminary validation stage, should allow to avoid an FE micro-structural model of cells and PCM material that can lead to a huge calculation time. In particular has been set the density of the core rcore, its thermal conductivity Kcore and its specific heat Cpcore (Eq. (1)–(3)).
rcore ¼ rAlf VAlf þ rpcm Vpcm
ð1Þ
Kcore ¼ KAlf VAlf þKpcm Vpcm
ð2Þ
Cpcore ¼
Fig. 7. FE Model of the beam sample (estimation point at 200 mm from the middle plane).
371
CpAlf rAlf VAlf þ Cppcm rpcm Vpcm
rAlf VAlf þ rpcm Vpcm
ð3Þ
VAlf represents the volume fraction of Al-foam inside the core, equal to 0.06 from experimental measures, Vpcm the volume fraction of PCM inside the core (0.83 from experimental measurements). Correctly, the summation of Valf and Vpcm does not give 100% as the core includes some air spaces not filled in by PCM. This discontinuity has been neglected in the calculation. The density of the Al-foam (rAlf) is equal to 0.15 kg/dm3, the thermal conductivity (KAlf) is 6 W/m C and the specific heat (CpAlf) is 900 J/ kg C. PCM is characterised by a density (rpcm) of 0.87 kg/dm3, thermal conductivity (Kpcm) equal to 0.2 W/m C and specific heat (Cppcm) 2 000 J/kg C. In the FE model, the total weight of the core (Al-foam+ PCM) is 11.79 kg, while that of the whole beam is 34.40 kg. Thus the correspondence with the real case verified.
Fig. 8. FEA results: temperature variation on the external skin, evaluated at the estimation point.
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Following this way it is possible to design innovative structures for MT mobile parts or components able to maintain constant their temperature for long time when subjected to heat sources. It is clearly necessary to improve the realisation process of these structures (i.e. eliminating the glue), but the proposed solutions represent a good milestone to develop further studies aiming the static, dynamic and thermal stability of the machine. References
Fig. 9. FEA results: numerical experimental comparison at the estimation point.
The latent heat (heat storage capacity) Hpcm of the selected PCM wax is 130 KJ/kg, while for the homogeneous core of the proposed FE model it has been calculated equal to 94 KJ/kg (Eq. 4), taking into account that the density of the homogeneous composite core is different from the PCM one. In this way the total heat storage capacity of the core results congruent. Hcore ¼ Hpcm
Weight of PCM inside Weight of core
ð4Þ
A quarter portion of the beam has been modelled, imposing the due symmetry conditions. The boundary condition at interface with the environment is a free convection. A FE transient thermal analysis has been run using MSC-Nastran solver. The time variation of the environment temperature (TENV) has been imposed equal to the actual one. The FE results are reported in two plots. Fig. 8 refers to FEA results, evaluating the temparture variation at the estimation point, considering a beam model with PCM-based core and without PCM. The graph shows how the thermal stabilisation effect of PCM is relevant. In Fig. 9 is finally plotted the comparison between FEA numerical results and experimental ones. A good prediction is achieved through the proposed FE model. The mis-matching of curves within the 0–5 000 s time range could be mainly attributed to the simplifying assumption considering the foam core as a homogenoeus compound material. Moreover, the model does not take into account the uncomplete PCM filling of Al-foam pores (which happens in practice).
7. Conclusions This paper aims to investigate a possible application of multifunctional materials in realisation of structure components for Ultra High Precision MTs. The choice of aluminium (open cells) metal foams, as core of structure, is justified by their high performances that permit to guarantee light and stiffness. These properties are demonstrated looking at the structural index E1/3/r and damping coefficient Z, comparing them with other conventional materials for MT building. In the same way the authors attempted to study the thermal stability of MT structures considering PCMs to impregnate the core of the sandwiches. The thermal tests performed on the beams (Z-axis of a precision milling machine) highlight a significant thermal gain due to the multifunctional materials. The effectiveness of the described solutions has been confirmed by experimental tests and supported by FEA.
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Contents lists available at ScienceDirect
International Journal of Machine Tools & Manufacture journal homepage: www.elsevier.com/locate/ijmactool
Multifunctional structure solutions for Ultra High Precision (UHP) machine tools F. Aggogeri a,n, A. Merlo b, M. Mazzola a a b
Department of Mechanical and Industrial Engineering, University of Brescia, Via Branze, 38, 25123 Brescia, Italy Ce.S.I., Centro Studi Industriali, Via Tintoretto, 10, 20093 Cologno Monzese (MI), Italy
a r t i c l e in f o
a b s t r a c t
Article history: Received 16 March 2009 Received in revised form 14 July 2009 Accepted 1 November 2009
This paper aims to study innovative structure solutions for Ultra High Precision (UHP) Machine Tools (MT) within machining applications at micro/mesoscale level (10–10 000 mm range). There are many aspects that can affect the accuracy of UHP machining performance. The most important issues are related to the static, dynamic and thermal behaviour of the machines. This paper shows a complete study and thermal testing validation on a set of prototypes (plates and beam) based on sandwiches with core made of metal foam (open cells) material impregnated by phase change materials. The proposed multifunctional structure (which provides high stiffness to weight ratio, good damping properties together with thermal stability) consists of a machine tool part, a beam (Z-axis) of a precision milling machine. The authors have designed, realised and tested prototypes developing thermal trials and then evaluating the experimental data. The trials consisted to test the prototype thermal stability when the environmental temperature varies in a specified range (20–50 1C), in order to assess the PCM proprieties to absorb heat and maintain performances for a long duration. Furthermore, a numericalexperimental validation through finite element analysis on the beam prototype is presented. & 2009 Elsevier Ltd. All rights reserved.
Keywords: UHP-MT MT structures Phase change materials MT thermal stability Experimental trials Finite element analysis
1. Introduction The study of innovative materials in machine tool (MT) building can provide a fundamental impact on functionality and reliability of a manufacturing system. Numerous reasons for this growth include light weight, superior insulating abilities, energy absorbing performance, excellent strength/weight ratio and low cost [1]. A strong mass reduction of mobile machine parts and an increase of their stiffness and damping to obtain excellent static, dynamic and thermal stability of the structures are becoming a ‘‘must’’ to guarantee excellent results in terms of technological and cost-effective impact, especially in the submicron range [2– 4]. The introduction of composite materials in MT design can provide significant advantages in terms of static and dynamic performances, and represent a new challenge for design engineers and further opportunities for the composite manufacturers [5]. Conventional materials for MT building are cast iron, welded steel and, in some cases, aluminium-alloys. Although these materials represent a consolidated technology for MT engineers, the need to ensure high performances requires the investigation of a new class of materials with improved inherent properties in terms of
n
Corresponding author. Tel.: + 39 0303715579; fax: + 39 0303702448. E-mail address: [email protected] (F. Aggogeri).
0890-6955/$ - see front matter & 2009 Elsevier Ltd. All rights reserved. doi:10.1016/j.ijmachtools.2009.11.001
specific stiffness, structural damping, dimensional and thermal stability [6]. This study aims to show an investigation to apply metal foams impregnated by Phase Change Materials (PCM) in MT component realisation. Metal foams are a new class of materials that offer potential for lightweight structures, for energy absorption and thermal management with low costs [1]. Their particular cellular structures permit to be impregnated by PCMs that absorb heat and keep thermal stability of a machine component for a long duration when temperature changes due to different heat sources.
2. Main issues in UHP machine tool designing There are many aspects that can affect the accuracy of an UHP machining performance. According to Bryan [7], errors originating from machine tools make up the largest portion (60–65%) of the total errors in machined workpieces [8]. The most important problems are related to static, dynamic and thermal behaviour of the machines [9]. A first consideration deals with the evaluation of thermal errors. These issues are due to an increase of the MT structure and component temperature during the machining operations. Thermal distortion of MT structures is widely attributed as a significant cause of workpiece inaccuracy within modern CNC machining specially in microdomain [10–12]. It is difficult to develop a practical compensation strategy dealing with
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the different aspects of machine tool thermal behaviour. For this reason practical actions are necessary in order to guarantee thermal stability during manufacturing operations. In general, it is possible to classify thermal errors in two main categories: errors that effectively alter the linear positioning of the machine and errors that change the machine offsets [13,14]. These errors can be caused by different heat sources (i.e. bearings, drives, pumps, motors, cutting action or external sources) that should be analysed to avoid possible effects on machine accuracy. These considerations suggest to use particular structural materials (i.e. cement concrete, fibre reinforced plastics) able to reduce the deformation due to temperature changes, or to study advanced techniques that permit to compensate thermal errors analysing temperatures of machine critical points [15–18]. In this study the authors present a further solution by applying PCMs to machine tool structure building in order to absorb heat, keeping constant the temperature of a machine component in a defined time range when temperature is perturbed. Other considerations should be developed for static behaviour of an MT that can be analysed evaluating the contribution of every single structure/component of the machine on the global compliance at the tool tip [7]. Instead the dynamic behaviour and its physical causes are still not fully understood. It is noted that vibrations in MT are induced by periodic forces and can be divided into two categories: forced (and free) vibrations and self excited vibrations (chatter) [6,19,20]. The analysis of the critical frequencies of a machine is fundamental in order to know if the excitation forces can cause resonance issues and produce an unacceptable accuracy of the workpiece. In the light of this brief analysis it is important to reduce machine mass and enhance its damping and stiffness. The mass reduction involves another significant advantage: less mass to move means less inertia and so less energy ‘‘absorbed’’ by the machine. For this reason, the authors have considered lightweight materials that permit an excellent stiffness-to-weight ratio when loaded in bending and a low density with good shear and fracture strength [1]. Further-
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more, in order to reduce the temperature effect on MT structure distortion the PCMs application has been considered. This application consisted in impregnating metal foam materials with PCM wax to guarantee thermal stability when the temperature was perturbed, and dynamic stability using lightweight materials.
3. Application of multifunctional materials in MT building 3.1. Metal foams Metal foams represent a new class of materials with low density and novel physical, mechanical, thermal, electrical and acoustic properties [21,22]. They offer potential for lightweight structures, for energy absorption and thermal management with low costs [1]. These performances can be achieved thanks to their exceptionally high properties in term of stiffness-to-weight ratio and low density with good shear and fracture strength. A further advantage of these materials is the damping capacity that is larger than that of solid metals by up to a factor of 10 [23]. In this paper the authors have considered aluminium open cell foams, while evaluations and possible applications of closed cell materials are currently under testing. Open cell foams are porous structures consisting of an interconnected network [24]. Their particular structure permits to be impregnated by other materials (liquid state) as a PCM wax. The main features of these types of materials are the pore size and the relative density [22,25,26]. The pore identifies the polygonal opening through every open window while its size defines the number of pores per inch (ppi). The relative density is a fundamental property in order to understand the density of a foam divided by the density of the solid parent material of the struts [26]. In order to evaluate mechanical properties [1] and develop a comparison with other materials employable to realise structural components of an MT, a theoretical study is explained. The
Fig. 1. Selecting material chart.
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selection strategy is based on the evaluation of two parameters that can be considered merit indices: the structural index [28] and the damping coefficient. The structural index is given by the ratio between the cube root of the Young’s module E and the density of the material r. This index regards the material mass and stiffness. In particular, for a prescribed stiffness, materials with the same structural indices have the same weight. The weight is minimised (and the stiffness is increased) by selecting materials with large values of structural index. Fig. 1 shows a chart [28] that permits to select the appropriate material on the basis of its structural index. Materials with the same structural index lie on the same line whose slope is 1/3 (the chart is in logarithmic scale). Conditions on the static, dynamic and mechatronic behaviour of a structure can be translated into conditions on the structural index and damping coefficient (in particular, referring to the chart of Fig. 1, materials with the best structural index lie in the top-right zone). A comparison between commonly used materials and metal foams has been developed. The values assumed by the structural index E1/3/r and by the damping coefficient Z for these materials are listed in Table 1. The material characterised by the highest values of the structural index and damping coefficient is the aluminium metal foam. In the same way, Mg alloys have a high value of damping but it is extremely expensive, especially due to the high manufacturing costs. In the light of these considerations the authors considered metal foam materials as an excellent candidate to reduce problems of static and dynamic behaviour in MT structural building. 3.2. Phase change materials The application of PCMs can be a good solution to solve the thermal issues in MT structure designing and building. PCMs are latent energy storage materials that use their phase change to absorb heat and maintain constant the temperature for long duration (the so called ‘‘plateau’’) [29–30]. In particular a PCM temperature remains constant during the phase change. This is
Table 1 Materials structural index and damping coefficient. Material
E1/3/q [GPa1/3/Mg/m3]
g
Cast iron Steel Aluminium alloys Mg alloys Aluminium metal foam
0.63 0.77 1.5 1.9 2C5
1.2 10 3C1.7 10 3 6 10 4C10 3 2 10 4C4 10 4 10 3C10 2 4 10 3C10 2
useful for keeping the object (i.e. MT components or structure) at a uniform temperature. In this study the authors have considered a paraffin wax with a typical melting point about 31 1C, a heat capacity (latent heat) of 130 KJ/kg and a density close to 0.89 kg/l (solid state at 25 1C). This is an ecological heat storage material that uses the processes of phase change between solid and liquid (melting and congealing) to store and release large quantities of thermal energy at nearly constant temperature. Other important properties are long life product, with stable performance through the phase change cycles, ecologically harmless and non-toxic and chemically inert.
4. Prototype design and realisation In order to test the proprieties of these multifunctional materials, based on sandwiches with core made of metal foam impregnated by a PCM wax, the authors designed and realised a set of prototypes (plates and beam, Z-axis of a precision milling machine). The main goal was to test the thermal stability of prototypes when the environmental temperature was perturbed. The first part of the study consisted in designing four samples (i.e. plates), Fig. 2(a), that could permit to develop a preliminary analysis. The raw materials of samples were two steel sheets (thickness 2 mm) and four U profile beams to cover and close the core, the metal foam core (density of 20 ppi and 40 ppi), PCM materials (paraffin wax—melting temperature 31 1C) to impregnate the core and epoxy glue to assembly the plate components. The realisation process consisted of: - assembling the core with the profile beams and a steel sheet (using the epoxy glue); - inserting the wax (liquid state) into the open cells and - closing the device using the second steel sheet and obtaining a hybrid sandwich Fig. 2(b) [31–33]. In the same way the authors designed and realised a threedimensional structure; it is a Z-axis (300 300 500 mm) of a precision milling machine, Fig. 3(a and b). The metal foam used for the beam building was characterised by a density equal to 20 ppi. In the light of these tests, it was possible to verify thermal hypothesises on a realistic MT component.
5. Experimental trials and results The first experimental campaign considered the tests performed on plates previously described. Every plate had been
Fig. 2. Structural scheme (a) of the designed plates (b).
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Fig. 3. Structural scheme (a) of the designed beam prototype (b).
tested at controlled environmental conditions, reducing the noise variability as a consequence. The multifunctional material plates have been designed to perform distributed thermal stability, avoiding any undesired thermal gradient between the surfaces. Thus the experiments had to reproduce a close-to-uniform temperature, involving the plates in an appropriately controlled environment. For this reason, single plates were positioned vertically inside a box, over-dimensioned with respect to the plates and entirely coated with insulating and reflective materials. Thermal conditions have been obtained and maintained by two resistances of 600 W, symmetrically positioned at 150 mm away from the plate centre. The entire measurement system included a series of thermocouples strategically positioned on the plates. Three thermocouples have been applied to the external surfaces in order to verify the thermal stability and to approximately assess the thermal distribution; another thermocouple has been inserted inside the core to control the PCM temperature. During the design process, the surface geometry (300 300 mm) and the stiffness of the plates have been held as constant factors. Otherwise, other factors are variable. The plates differ in density, thickness and structural characteristics. The influence of variable factors can be assessed through the experimental campaign. The test campaign is resumed in Table 2, where specific characteristics are listed. Since the environment is held constant and the investigation is based on temperature trends rather than on static responses, low variability can be attributed to the repeatability of the experiments and two observations seem enough to assess thermal performances. The trends and responses of every test are compared to those of a common steel (Fe230) plate characterised by equivalent geometry of the surface. In this paper the results of Test 1 are presented in detail, exemplifying the behaviour of the designed plates. The environmental temperature at the beginning of the experiment was close to 22 1C. The experiment is monitored since the external temperature of the plate reached 45 1C (or after 35 min). Data collection has been permitted by an accurate capture system with a sampling frequency of 1 s. The diagram of Fig. 4 resumes the results of Test 1. A constant temperature phase (plateau) can be observed at 31 1C. The plateau
Table 2 First experimental campaign. Plate
Test
Thickness [mm]
Epoxy glue
PCM
Foam density
Open cells
1 2 3 4
12 30 30 12
Yes No Yes Yes
Yes Yes Yes No
40 ppi 20 ppi 20 ppi 40 ppi
Fig. 4. Experimental results of Test 1 compared with a stiffness equivalent bulk steel sheet.
ends after completion of PCM phase transition in 20 min (tp), when a linear increasing (VarT equal to 0.0245 1C/s) of the temperature is correctly observed. The external thermocouples registered a comparable temperature and the curves overlap with an average experimental error close to 1 1C (AvgT). Furthermore, an appropriate uniform distribution of the temperature on the plate surfaces has been verified, quantified by an average difference (AvgTs) between thermo-points on the same surface equal to 0.288 1C.
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Many other indices can help to quantify the achieved results. Performance indicators are calculated for every test for an easy interpretation of the results and for further comparisons. The results of Test 1 are listed in Table 3. The thermal stability of the plate can be appreciated by looking at the difference between external surface thermal curves from Test 1 and the thermal behaviour of an Fe230 bulk steel sheet (upper dashed curve in Fig. 4). The thermal gain is proportional to
Table 3 Test 1 performance indicators. Indicator
Performance
Value
tM [s] tp [s] t45 [s] VarT [1C/s]
Time to PCM melting Duration of the plateau Time to 45 1C Trend increasing velocity after completion of the plateau Average difference between opposite thermopoints Average difference between thermo-points on the same surface Temperature gain at the end of the experiment (by comparison with a bulk steel sheet)
300 s 1200 s 1900 s
AvgT [1C] AvgTs [1C]
DTFe [1C]
0.0245 1C/s 0.99 1C 0.288 1C 21.14 1C
Fig. 5. Experimental results of multifunctional material beam compared with a cast iron one.
the temperature accumulated by the wax, quantifiable by the difference between the curves (21.14 1C at the end of the experiment, DTFe). The multifunctional material controls the temperature during the plateau. In this case, at the end of the plateau the temperature does not exceed 35 1C, instead the bulk steel sheet reaches 60 1C causing potentially relevant consequences on material distortion. From MT accuracy point of view this would lead to undesired shape errors on the workpiece. A comparison between Test 2 and Test 3 demonstrated the epoxy glue effect on thermal stability is negligible. This result is much more precise as the thickness of glue layer is thinner. Finally, Test 3 and Test 1 showed comparable thermal trends, but the plateau of Test 3 was clearly characterised by a longer duration (tp close to 2 000 s), due to the greater quantity of PCM impregnated. In the light of these considerations, it is more interesting to develop three-dimensional prototypes using the solution of Test 3 that guarantee high verified performances with reasonable industrial costs. Once thermal stability is verified for simple geometries, the following objective is to evaluate the designed capabilities on three-dimensional structures. This deals with the second phase of experimental campaign whose goal is to understand the thermal behaviour of a three-dimensional structure, a Z-axis (300 300 500 mm) of a precision milling machine. In this case, the trials have been performed in an appropriate room where the temperature was perturbed in a specified range (from 20 1C to 50 1C). A thermal behaviour comparison has been developed between the beam made of PCM impregnated aluminium foam and a cast iron beam. Following this way, it was possible to understand the contribution of the PCM in evaluating the thermal stability of the MT component. For every beam, different thermocouples were located on the external lateral surface, in order to evaluate the thermal behaviour in different positions. In this paper, the analyses are performed on the data collected by the upper sensor (450 mm). Furthermore, the environmental temperature was checked continuously. Fig. 5 shows the comparison of the thermal data collected for the cast iron (light line) and innovative beam (dark line). The tests ended after 12 000 s and, in any case, after the completion of the phase change of the PCM. As for the plates, it is possible to note
Fig. 6. Experimental results of the modal analysis—Actual vs. synthesised FRF at the excitation point.
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the considerable thermal gain due to the multifunctional material. The temperature measured on the external surface of the innovative beam does not exceed 35 1C, instead that of the conventional beam rapidly reaches 45 1C, causing potentially serious consequences in terms of distortions and shape errors during machining. The authors have also studied the dynamic properties of the structure under vibration excitation. The experimental modal analysis (free–free configuration) has sown that the main vibration modes are at 482, 560, 630, 810 Hz with a modal damping value of approximately 1.6–1.7%, see Fig. 6.
6. FE modeling of the beam sample and numericalexperimental validation A Finite Element (FE) model of the beam prototype has been developed to compare experimental data with virtual one and achieve further confirmation of the assessed performances. The FE
model includes the steel skins, the top steel core, the core and the interconnecting epoxy glue (Fig. 7). The core, in Al-foam open cells impregnated with PCM-wax material has been considered as a homogeneous and isotropic material having weighted properties in accordance with micromechanics of composites. This simplification, reasonable at this preliminary validation stage, can be justified as both Al-foam (which is a stochastic cellular metal) and PCM are isotropic, and it has been assumed that all the voids within the foam has been completely filled by the wax. The mentioned assumption should allow to avoid a FE microstructural model of cells and PCM material that can lead to a huge calculation time. This simplification, reasonable at this preliminary validation stage, should allow to avoid an FE micro-structural model of cells and PCM material that can lead to a huge calculation time. In particular has been set the density of the core rcore, its thermal conductivity Kcore and its specific heat Cpcore (Eq. (1)–(3)).
rcore ¼ rAlf VAlf þ rpcm Vpcm
ð1Þ
Kcore ¼ KAlf VAlf þKpcm Vpcm
ð2Þ
Cpcore ¼
Fig. 7. FE Model of the beam sample (estimation point at 200 mm from the middle plane).
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CpAlf rAlf VAlf þ Cppcm rpcm Vpcm
rAlf VAlf þ rpcm Vpcm
ð3Þ
VAlf represents the volume fraction of Al-foam inside the core, equal to 0.06 from experimental measures, Vpcm the volume fraction of PCM inside the core (0.83 from experimental measurements). Correctly, the summation of Valf and Vpcm does not give 100% as the core includes some air spaces not filled in by PCM. This discontinuity has been neglected in the calculation. The density of the Al-foam (rAlf) is equal to 0.15 kg/dm3, the thermal conductivity (KAlf) is 6 W/m C and the specific heat (CpAlf) is 900 J/ kg C. PCM is characterised by a density (rpcm) of 0.87 kg/dm3, thermal conductivity (Kpcm) equal to 0.2 W/m C and specific heat (Cppcm) 2 000 J/kg C. In the FE model, the total weight of the core (Al-foam+ PCM) is 11.79 kg, while that of the whole beam is 34.40 kg. Thus the correspondence with the real case verified.
Fig. 8. FEA results: temperature variation on the external skin, evaluated at the estimation point.
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Following this way it is possible to design innovative structures for MT mobile parts or components able to maintain constant their temperature for long time when subjected to heat sources. It is clearly necessary to improve the realisation process of these structures (i.e. eliminating the glue), but the proposed solutions represent a good milestone to develop further studies aiming the static, dynamic and thermal stability of the machine. References
Fig. 9. FEA results: numerical experimental comparison at the estimation point.
The latent heat (heat storage capacity) Hpcm of the selected PCM wax is 130 KJ/kg, while for the homogeneous core of the proposed FE model it has been calculated equal to 94 KJ/kg (Eq. 4), taking into account that the density of the homogeneous composite core is different from the PCM one. In this way the total heat storage capacity of the core results congruent. Hcore ¼ Hpcm
Weight of PCM inside Weight of core
ð4Þ
A quarter portion of the beam has been modelled, imposing the due symmetry conditions. The boundary condition at interface with the environment is a free convection. A FE transient thermal analysis has been run using MSC-Nastran solver. The time variation of the environment temperature (TENV) has been imposed equal to the actual one. The FE results are reported in two plots. Fig. 8 refers to FEA results, evaluating the temparture variation at the estimation point, considering a beam model with PCM-based core and without PCM. The graph shows how the thermal stabilisation effect of PCM is relevant. In Fig. 9 is finally plotted the comparison between FEA numerical results and experimental ones. A good prediction is achieved through the proposed FE model. The mis-matching of curves within the 0–5 000 s time range could be mainly attributed to the simplifying assumption considering the foam core as a homogenoeus compound material. Moreover, the model does not take into account the uncomplete PCM filling of Al-foam pores (which happens in practice).
7. Conclusions This paper aims to investigate a possible application of multifunctional materials in realisation of structure components for Ultra High Precision MTs. The choice of aluminium (open cells) metal foams, as core of structure, is justified by their high performances that permit to guarantee light and stiffness. These properties are demonstrated looking at the structural index E1/3/r and damping coefficient Z, comparing them with other conventional materials for MT building. In the same way the authors attempted to study the thermal stability of MT structures considering PCMs to impregnate the core of the sandwiches. The thermal tests performed on the beams (Z-axis of a precision milling machine) highlight a significant thermal gain due to the multifunctional materials. The effectiveness of the described solutions has been confirmed by experimental tests and supported by FEA.
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