帶隱蔽式護(hù)欄的多功能兒童床設(shè)計(jì),帶隱蔽式護(hù)欄的多功能兒童床設(shè)計(jì),隱蔽,隱秘,護(hù)欄,多功能,兒童床,設(shè)計(jì) 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 C211 Springer Science+Business Media B.V. 2008 Abstract To 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 satisfied 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 and polymer concrete core was designed and manufactured for a high-speed gantry type milling machine through static and dynamic analyses using finite 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/s 2 , respectively. Keywords Polymer concrete C1 Machine tool C1 Damping C1 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/s 2 acceleration and deceleration (Suh and Lee 2002). At these high operation speeds, machine tool structures are vulner- able to vibration, which results in poor surface finish 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/m 3 to $2,000/m 3 ), if it is compared with conventional cement concrete ($50/m 3 $80/m 3 ), 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 numbers such as #1.01.5, #1.53.2, #3.26.4, #6.412.0 and larger than #12 that is classified as sand. To determine the approximate mixing ratio of aggregates, it was assumed that the smaller aggre- gates occupy the void formed by the larger 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 filled 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.% 30.3 15.4 7.1 7.1 30.0 10.0 Vol.% 26.7 13.6 6.3 6.3 26.4 21.8 114 J. 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 0 50 100 150 200 250 300 Frequency Hz r o t c a f g n i p m a D Polyester Granite Fig. 1 Damping factors g of raw materials for polymer concrete under flexural 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 Specimen Length (mm) Height (mm) Width (mm) 1 240 97 97 2 360 97 97 3 480 97 97 Table 3 Properties of polymer concrete Density (kg/m 3 ) E (GPa) G (GPa) m 2260 25.2 10.5 0.2 0.00 0.02 0.04 0.06 0.08 0.10 100 1000 10000 Frequency Hz r o t c a f g n i p m a D Steel Polymer concrete Fig. 3 Damping factors g of polymer concrete under flexural 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 bed 115 123 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). FR 1 : Increase structural stiffness FR 2 : 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). DP 1 : Thickness of steel plates composing the steel base (Face of sandwich structure) DP 2 : Damping characteristics of polymer concrete FR 1 FR 2 C26C27 X0 x X C20C21 DP 1 DP 2 C26C27 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 specifications 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 filled its inside cavity. The machine tool bed of this type has two functions, i.e., the linear motor 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 0.40 0.60 0.80 1.00 1.20 1.40 Ra m a P M h t g n e r t s r a e h S Fig. 5 Shear strength between steel and polymer concrete w.r.t. surface roughness of steel Fig. 6 Machine tool structure (FV400, Daewoo Heavy Industries The total strain energy U in unit width of beam is calculated from strain energies in the steel faces U S and the concrete core U C . Table 6 Deformation of the machine tool bed under inertia and attraction forces (lm) Case Linear motor LM-guide Max d m Min d m D d m Max d g Min d g D d g 1 48.8 6.5 42.3 14.5 6.5 8.0 2 51.2 6.5 44.7 15.0 6.5 8.5 3 55.6 6.5 49.1 15.5 6.6 8.9 4 48.8 6.8 42.0 14.5 6.8 7.7 5 51.5 6.8 44.7 15.0 6.8 8.2 6 55.7 6.9 48.8 15.5 6.9 8.6 Table 7 Dimensions (mm) of the steel plates composing the steel base Case X 1 X 2 X 3 Y 1 Y 2 Y 3 Y 4 Y 5 Y 6 Z 1 Z 2 Z 3 1 202020101010101010105020 2 152015101010101010105020 3 102010101010101010105020 4 20202010555510105020 5 15201510555510105020 6 10201010555510105020 Fig. 9 Mode shapes of vibration of the machine tool bed : (a) 1st, (b) 2nd, (c) 3rd, and (d) 4th 118 J. D. Suh, D. G. Lee 123 U U S U C ZZ A S r z;S C0C1 2 2E S r zx;S C0C1 2 2G S ! dz dx ZZ A C r z;C C0C1 2 2E C r zx;C C0C1 2 2G C ! dz dx 2 where S and C represent steel and concrete while A S and A C designate areas occupied by steel and polymer concrete, respectively. The stress in the steel faces and polymer concrete core are calculated as follows. r z;S E S C1 M C1 x D 3 r zx;S V C1 E C C1 R T C3 C 0 XdX D V C1 E S C1 R x T C3 C XdX D 4 r z;C E C C1 M C1 x D 5 r xz;C V C1 R x 0 E C C1 XdX D 6 where x and T C3 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 flexural rigidity, respectively. Once thicknesses of steel faces and polymer concrete core are defined, 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 W D 2pU W D;S W D;C 2pU S U C g S C1 U S g C C1 U C U S U C 7 where W D represents the energy dissipation per cycle of vibration. Since the 1st vibration frequency is close for all cases in Table 8, the damping factor of concrete g C was assumed to be 8.8% by extrapolation at 100 Hz from Fig. 3, while the damping factor of steel g S was 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 were also 3.3%, 3.4% and 3.7% because the corresponding plate thicknesses in the X-direction were the same as Case 13 while the plate 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) Case 1st 2nd 3rd 4th 1 104 108 185 203 2 103 107 179 199 3 99 104 172 191 4 104 106 185 203 5 102 105 179 198 6 99 102 172 190 Polymer concrete Steel 674 424 P 1 P 2 8 2 1 3 8 2 X 1 X 2 X 3 Z X t C 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 0 0.2 0.4 0.6 0.8 1 Normalized position Z / Z max t n e m e c a l p s i d d e z i l a m r o N / X X x a m Amplitude of the 1st mode shape Static deflection Fig. 11 Comparison between the 1st vibration mode ampli- tude and static deflection of the vertical column by concentrated loads in Fig. 10 Design and manufacture of hybrid polymer concrete bed 119 123 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 filled 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) Curing of polymer concrete at room 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). Acknowledgement This work was supported by the Korea Research Foundation Grant funded by the Korean 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. References Clancy, B.E., Shin, Y.C.: A comprehensive chatter prediction model for face turning operation including tool wear effect. Int. J. Mach. Tool. 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CIRP 51(1), 285288 (2002) Suh, J.D., Lee, D.G.: Thermal characteristics of composite sandwich structures for machine tool moving body applications. Compos. Struct. 66, 429438 (2004) Sun, C.T., Lu, Y.P.: Vibration Damping of Structural Element. Prentice-Hall, New Jersey (1995) Tobias, S.A.: Machine Tool Vibration. John Wiley & Sons, New York (1965) Table 9 Dynamic characteristics of the machine tool bed obtained by impulse dynamic test Mode Natural frequency (Hz) Damping factor g (%) 1 93 4.13 2 130 3.15 3 155 5.69 4 200 2.93 Design and manufacture of hybrid polymer concrete bed 121 123