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Design and manufacture of hybrid polymer concrete bed for high-speed CNC milling machine Jung Do Suh Dai Gil Lee Received: 22 September 2006/Accepted: 11 June 2007/Published online: 23 January 2008 ? Springer Science+Business Media B.V. 2008 AbstractTo maximize the productivity of precision products such as molds and dies, machine tools should be operated at high speeds without vibration. As the operation speeds of machine tools are increased, the vibration problem has become a major constraint of manufacturing of precision products. The two impor- tant functional requirements of machine tool bed for precision machine tools are high structural stiffness and high damping, which cannot be satisfi ed simul- taneously if conventional metallic materials are used for bed structure because conventional high stiffness metals have low damping and vice versa. This paper presents the application of hybrid polymer concrete for precision machine tool beds. The hybrid polymer concrete bed composed of welded steel structure faces andpolymerconcretecorewasdesignedand manufactured for a high-speed gantry type milling machine through static and dynamic analyses using fi nite element method. The developed hybrid machine tool bed showed good damping characteristics over wide range of frequency (g = 2.935.69%) and was stable during high speed machining process when the spindle angular speed and acceleration of slide were 35,000 rpm and 30 m/s2, respectively. KeywordsPolymer concrete ? Machine tool ? Damping ? Precision machining 1 Introduction Modern precision machine tools are required to produce precise products at high machining speeds. To achieve the requirement, machine tools must have high damping as well as high structural stiffness. Modern machine tools are usually equipped with high speed spindle systems rotating up to 35,000 rpm and moving frames operating up to 30 m/s2acceleration and deceleration (Suh and Lee 2002). At these high operation speeds, machine tool structures are vulner- able to vibration, which results in poor surface fi nish and inaccurate dimensions of products (Suh and Lee 2004). Besides, chatter, a kind of self-induced vibration, adversely affects tool life (Clancy and Shin 2002). The vibration of a machine tool is frequently caused by the low damping: if the J. D. Suh Fuel Cell Vehicle Team1, Advanced Technology Center, Hyundai Motor Company, 104, Mabuk-Dong, Giheung-Gu, Yongin-Si, Gyeonggi-Do 446-912, Republic of Korea D. G. Lee ( Cortes and Castillo 2007): Although the polymer concrete is more expensive (depending on resin binder systems, their prices range from $300/m3 to $2,000/m3), if it is compared with conventional cement concrete ($50/m3$80/m3), the conventional cement concrete is not suitable for the machine tool application due to its inferior strength and impact resistance (Cortes and Castillo 2007). This paper presents the design and manufacture of a hybrid polymer concrete machine tool bed that consists of sandwich structures of welded steel faces and polymer concrete core. The static and dynamic analyses of the hybrid bed were performed after the basic properties of polymer concrete were measured. The developed hybrid polymer concrete bed has been incorporated in high-speed gantry-type mill- ing machine (FV400, Daewoo Heavy Industries the higher volume fraction of aggregate may result in the higher stiffness of polymer concrete. The aggregates were grouped by their mesh numberssuchas#1.01.5,#1.53.2,#3.26.4, #6.412.0 and larger than #12 that is classifi ed as sand. To determine the approximate mixing ratio of aggregates, it was assumed that the smaller aggre- gatesoccupythevoidformedbythelarger aggregates, which is general concept of linear packing theory. For example, gravels #1.0#1.5 form void about 40 % of the apparent volume, and this void may be fi lled with gravels #1.5#3.2 and so forth. The tentative mixing ratio was determined by the linear packing theory and the optimal mixing ratio for the dense packing of polymer concrete was determined by several trial and error experiments as shown in Table 1. Figure 1 shows the measured damping factors of polyester and granite as raw materials for polymer concrete by impulse dynamic test depicted in Fig. 2. The measured damping factors range from 2% to 4% over wide range of frequencies and the values are much higher than those of conventional metallic materials. Also, properties of polymer concrete were measured by impulse dynamic test (ASTM C215-91). Table 1 Composition of polymer concrete Gravel (Mesh #)Sand Polyester 1.01.5 1.53.2 3.26.4 6.412.0 Wt.%30.315.47.17.130.010.0 Vol.% 26.713.66.36.326.421.8 114J. D. Suh, D. G. Lee 123 Tables 2 and 3 list the sizes of specimens and mechanical properties, respectively. Figure 3 depicts measured damping factors with respect to frequen- cies. In addition, shear strength between polymer concrete and steel with respect to the surface roughness of steel was measured as shown in Fig. 4a using Instron4206 (Instron Co., USA) at a crosshead speed of 0.1 mm/min. Specimens were composed of polymer concrete and steel rod embedded in polymer concrete shown in Fig. 4b. The surfaces of steel rods were treated using abrasive papers of various mesh numbers followed by co-curing with polymer con- crete. From the experimental result in Fig. 5, it was found that the shear strength increases as the surface roughness increases. 0.00 0.02 0.04 0.06 0.08 050100150200250300 Frequency Hz ro t ca f gn i pmaD Polyester Granite Fig. 1 Damping factors g of raw materials for polymer concrete under fl exural vibration w.r.t. frequencies PC FFT Analyzer Impact hammer String Amp Amp Accelerometer Specimen Fig. 2 Impulse dynamic test to measure the mechanical properties of polyester and granite Table 2 Size of concrete specimens for impulse dynamic tests SpecimenLength (mm)Height (mm)Width (mm) 12409797 23609797 34809797 Table 3 Properties of polymer concrete Density (kg/m3)E (GPa)G (GPa)m 226025.210.50.2 0.00 0.02 0.04 0.06 0.08 0.10 100100010000 Frequency Hz ro t ca f gn ipmaD Steel Polymer concrete Fig. 3 Damping factors g of polymer concrete under fl exural vibration w.r.t. frequencies Fig. 4 Measurement of the shear strength between polymer concrete and steel: (a) Photograph of test using instron, and (b) Photograph of specimen (mm) Design and manufacture of hybrid polymer concrete bed115 123 3 Design and manufacturing process 3.1 Design of hybrid bed from the perspective of axiomatic design The functional requirements (FRs) of the machine tool bed are as follows (Tobias 1965; Kim et al. 1995). FR1: Increase structural stiffness FR2: Increase structural damping Since outer dimensions of the bed were pre-deter- mined considering assembly with other parts, basic design concept was determined as a sandwich structure composed of steel faces and polymer concrete core. The damping of a sandwich structure comes largely from the damping of core material. Therefore, design can be decoupled by following design parameters (DPs) (Suh 2001). DP1: Thickness of steel plates composing the steel base (Face of sandwich structure) DP2: Damping characteristics of polymer concrete FR1 FR2 ? X0 xX ? DP1 DP2 ? 1 Additional advantage of the sandwich structure is that the steel faces not only increase structural stiffness but also work as a mold for polymer concrete during manufacturing. Figure 6 shows the high-speed gantry-type milling machine tool structure investigated in this work, whose specifi cations are shown in Table 4. The machine tool bed is a hybrid structure composed of welded steel base in Fig. 7 and polymer concrete core fi lled its inside cavity. The machine tool bed of this typehastwofunctions,i.e.,thelinearmotor mounting and the LM-guide mounting. A moving frame, Y-slide, is guided by the LM-guide and driven by the linear motors mounted on the vertical columns of the machine tool bed as shown in Fig. 6. There- fore, the vertical columns should resist inertia force of the moving frame and pulling force of 21 kN of the linear motors which bends the vertical columns inward. Consequently, the vertical columns are major sources of large deformation during operation, and were selected for the main design part. Furthermore, their displacement during vibration is relatively larger than other parts because the vertical columns are the weakest parts of the structure. 0 5 10 15 20 25 0.400.600.801.001.201.40 Ra m aPM h t gne r t s r aehS Fig. 5 Shear strength between steel and polymer concrete w.r.t. surface roughness of steel Fig. 6 Machinetoolstructure(FV400,DaewooHeavy Industries The total strain energy U in unit width of beam is calculated from strain energies in the steel faces USand the concrete core UC. Table 6 Deformation of the machine tool bed under inertia and attraction forces (lm) CaseLinear motorLM-guide Max dmMin dmD dmMax dgMin dgD dg 148.86.542.314.56.58.0 251.26.544.715.06.58.5 355.66.549.115.56.68.9 448.86.842.014.56.87.7 551.56.844.715.06.88.2 655.76.948.815.56.98.6 Table 7 Dimensions (mm) of the steel plates composing the steel base CaseX1X2X3Y1Y2Y3Y4Y5Y6Z1Z2Z3 1202020101010101010105020 2152015101010101010105020 3102010101010101010105020 420202010555510105020 515201510555510105020 610201010555510105020 Fig. 9 Mode shapes of vibration of the machine tool bed : (a) 1st, (b) 2nd, (c) 3rd, and (d) 4th 118J. D. Suh, D. G. Lee 123 U US UC ZZ AS rz;S ?2 2ES rzx;S ?2 2GS ! dzdx ZZ AC rz;C ?2 2EC rzx;C ?2 2GC ! dzdx 2 whereSandCrepresent steel and concrete while AS and ACdesignate areas occupied by steel and polymer concrete, respectively. The stress in the steel faces and polymer concrete core are calculated as follows. rz;S ES? M ? x D 3 rzx;S V ? EC? RT? C 0 X dX D V ? ES? Rx T? C X dX D 4 rz;C EC? M ? x D 5 rxz;C V ? Rx 0 EC? X dX D 6 where x and T? C represent distance from its neutral axis to the point under concern and to the steel face, respectively. M, V and D represent bending moment, shear force and fl exural rigidity, respectively. Once thicknesses of steel faces and polymer concrete core are defi ned, the ratio of strain energies in the steel faces and the core concrete is determined. In that case, damping factor g of the vertical column is calculated by the following (Rao 1978; Sun and Lu 1995). g WD 2pU WD;S WD;C 2pUS UC gS? US gC? UC US UC 7 where WDrepresents the energy dissipation per cycle of vibration. Since the 1st vibration frequency is close for all cases in Table 8, the damping factor ofconcretegCwasassumedtobe8.8%by extrapolation at 100 Hz from Fig. 3, while the damping factor of steel gSwas assumed to be 0.2%. For Case 1Case 3 in Table 7, the calculated values of g were 3.3%, 3.4% and 3.7%, respec- tively. For Case 4Case 6, the calculated value of g werealso3.3%,3.4%and3.7%becausethe corresponding plate thicknesses in the X-direction werethesameasCase13whiletheplate thicknesses in the Y-direction were neglected. From the damping estimation, the calculated damping factors increased as the thicknesses of steel faces in the X-direction decreased. Consequently, Case 4 in Table 7 was determined as the design values for manufacturing because the machine tool structure should have high stiffness and the damping factor of 3.3% is large enough for machine tool bed structure. Table 8 Natural frequencies obtained from FE-analysis (Hz) Case1st2nd3rd4th 1104108185203 2103107179199 399104172191 4104106185203 5102105179198 699102172190 Polymer concrete Steel 674424 P1 P2 821 382 X1X2 X3 Z X tC Fig. 10 Schematic drawing of the vertical column to estimate the damping factor of the 1st vibration mode 0.0 0.2 0.4 0.6 0.8 1.0 00.20.40.60.81 Normalized position Z / Zmax tnemeca lps id dez i l amroN / XXxam Amplitude of the 1st mode shape Static deflection Fig. 11 Comparison between the 1st vibration mode ampli- tudeandstatic defl ectionoftheverticalcolumnby concentrated loads in Fig. 10 Design and manufacture of hybrid polymer concrete bed119 123 3.2 Manufacture of polymer concrete machine tool bed The polymer concrete bed was manufactured by pouring polymer concrete into the steel base in Fig. 12, followed by room temperature curing. The steel base composed of welded steel plates was positioned up side down for the pouring process and thus void space in Fig. 12a was easily fi lled with the polymer concrete. Detailed manufacturing processes for polymer concrete are as follows. (a)Cleaning aggregates with water to remove salt contained in aggregates. (b)Mixing of aggregates and polyester resin with the pre-determined weight or volume ratio. (c)Packing with vibrator to induce self packing by gravity and to obtain homogeneity of concrete. (d)Curingofpolymerconcreteatroom temperature. (e)Assembling and mounting other parts such as the LM-guide and the linear motor. Figure 13 shows the photograph of the polymer concrete bed manufactured in this work. 4 Dynamic characteristics of the polymer concrete machine tool bed The dynamic characteristics of the polymer concrete bed were measured by the impulse dynamic test using FFT analyzer (B The damping factors g were 2.935.69% depending on natural frequencies. Compared with steel or case iron bed structure (0.20.3%), those are superior values. In case of the 1st mode, the calculated and measured damping factors were 3.30 and 4.13, respectively. The difference may be attributed to the neglect of damping occurring in the interface between the steel and the polymer concrete layer during the calculation. 5 Conclusion In this study, a polymer concrete bed combined with welded steel structure, i.e. a hybrid structure, was designed and manufactured for a high-speed gantry- type milling machine. The optimal mixing ratio of aggregates for polymer concrete considering packing was obtained experimentally. Then the mechanical properties of polymer concrete as well as adhesion properties to steel adherand with respect to its surface roughness were measured. The dynamic characteris- tics of the hybrid polymer concrete bed were measured by impulse dynamic test. From the impact dynamic test, it was found that the hybrid machine tool bed had large damping factors over the wide range of frequency. The damping factors were 2.93 5.69% depending on natural frequencies, which were larger than those of steel structure or case iron bed structure (0.20.3%). The hybrid polymer concrete bed has been incorporated in a gantry type high-speed milling machine (FV400, Daewoo Heavy Industries & Machinery Ltd., Korea). AcknowledgementThis work was supported by the Korea ResearchFoundationGrantfundedbytheKorean Government (MOEHRD) (M01-2004-000-10374-0) and the Ministry of Commerce, Industry and Energy of the Korean Government. The authors wish to thank Daewoo Heavy Industries & Machinery Ltd., Korea for the cooperation during manufacturing and test of the hybrid polymer concrete bed. Reference