Stiffness and vibration damping capability are important criteria in design of machine tool structure. In other sides, the weight of machine tool structure must be reduced to increase  the handling capability. This paper presents  an analysis of the effect of geometric structure on stiffness and vibration damping of wood structure.  The stiffness was analysed  using numerical method, so called finite element method (FEM), while the vibration damping capability was experimentally tested. Vibration testing was also performed to wood structures with sand powder filled  into  its rectangular hole to observe the its effect on damping factor. Simulation results show  that the cross ribs structure yielded minimum mass reduction ratio compared to the three square holes as well as the single rectangular hole structures. While the vibration test results explained that the damping factor of Shorea laevis wood was higher than that Hevea braziiensis wood. The use of sand powder as vibrating  mass in closed-box structure effectively increased the damping capability, for single rectangular hole structure the damping factor was increased from 0.048 to 0.07

Achmad, Widodo

David, Siahaan

Sri, Nugroho

Susilo, Adi Widyanto

English

Diponegoro University Institutional Repository

Internat. J. of Sci. and Eng., Vol. 4(2)2013 : 57-60,  April 2013, Susilo A.W.  et al.      ISSN: 2086-5023  57  © IJSE – ISSN: 2086-5023, April 15, 2013, All rights reserved   International Journal of Science and Engineering (IJSE)  Homepage: http://ejournal.undip.ac.id/index.php/ijse  The effect of geometric structure on stiffness and damping factor of wood applicable to machine tool structure  Susilo Adi Widyanto, Achmad Widodo, Sri Nugroho, David Siahaan Mechanical Engineering, University of Diponegoro, Jl. Prof Sudarto, SH, Semarang, Indonesia 1susilo70@yahoo.com  Abstract — Stiffness and vibration damping capability are important criteria in design of machine tool structure. In other sides, the weight of machine tool structure must be reduced to increase  the handling capability. This paper presents  an analysis of the effect of geometric structure on stiffness and vibration damping of wood structure.  The stiffness was analysed  using numerical method, so called finite element method (FEM), while the vibration damping capability was experimentally tested. Vibration testing was also performed to wood structures with sand powder filled  into  its rectangular hole to observe the its effect on damping factor. Simulation results show  that the cross ribs structure yielded minimum mass reduction ratio compared to the three square holes as well as the single rectangular hole structures. While the vibration test results explained that the damping factor of Shorea laevis wood was higher than that Hevea braziiensis wood. The use of sand powder as vibrating  mass in closed-box structure effectively increased the damping capability, for single rectangular hole structure the damping factor was increased from 0.048 to 0.079.   Keywords — Shorea laevis, Hevea braziiensis, stiffness, damping factor, machine tool structure Submission: December 10,  2012              Accepted: 21 February 2013  I. INTRODUCTION Wood is a natural material commonly used as building construction. Various woods have been sold commercially with low cost compared to metal materials.  In engineering application, production process of wood material is easier than metal, so that it also reduces the cost production. This paper presents  the results of stiffness analysis using FEM and experimental testing of vibration damping of wood structure aimed to develop main structure of machine tool. When a structure is vibrated, its damping capability reduces the amplitude of oscillation and changes the vibration energy into heat. Damping factor  is defined as a loss factor or energy loss ratio that was referred to energy transformed into other energy along one cycle vibration (Ouis, 2002). Many research works have been conducted in developing measurement method and observation damping capability of wood materials, mechanical characteristic and other aspects which affects it. Measurement of damping factor by means of measuring decrement of vibration response has been studied by Ciornei et al (2009). In this work, vibration response was measured using piezoelectric transducer and transferred to a storage data oscilloscope. Then the vibration database was processed into a computer system to determine vibration damping through logarithmic decrement method and displayed as data interpretation. Logarithmic decrement is an internal damping indicator of the material and its oscillated frequency determines elastic constant of probe and longitudinal elastic modulus of the wood.  There are three factors which affect on vibration damping characteristic of wood material, namely: geometric sample, material properties toward scatter and scatter absorption. Scatter and scatter absorption characteristic depend on frequency of vibration, anisotropic direction and wood species (Buccur, 2006). Effect of notch on elastic modulus and vibration damping factor was studied by Hossein et al (2011). This research work used a wood rectangular bar of Cupressus arizonica. He used five sample wood plants with diameter around of 36 cm, and cut them on temperature of 21oC and the moisture content of 65%. The experiments was based on free vibration mode with bending test model. The results show that the elactic modulus as well as vibration damping factor decreased significantly if notch achieved higher than  60%. Spectrum modes of Fast Fourier Transform (FFT) of un-notch specimens shown the Internat. J. of Sci. and Eng., Vol. 4(2)2013 : 57-60,  April 2013,    symmetrical condition, while for notch specimens, FFT spectrum was un-symmetric.  In development of machine tool structure, Nakaminami et al (2007) investigated the design method of multi axis machine tool structure. They analysedstatic and dynamic stiffness and also the movement accuracy using FEM. The results showed that the box structure gives maximum accuracy and productivity applicable to multi axis machine tool (Nakaminami2007). In experimental analysis, internal damping concept of machine tool structure was proposed by Slocum(2003). They used an internal beam in liquid media was localized in machine tool structure (Slocum2003). In addition, material modification of  machine tool structure was also developed by Lee  et al (2004). They used reinforced composite for high speed milling machine which substitutes cast iron material. This investigation showed that the weight of structure was reduced 30%, and the damping capability was increased from 15.7 without reducing stiffness. Positioning accuracy also increased to 0.5 µm for displacement of 300 mmat al, 2003). Wakasawa et al (2004) proposed the method of increasing damping capacity in machine tool structure by using balls packing. In structures closely packed with balls, various damping characteristics appear in correspondence with the ball size and other conditions.The results showed that the dimension of ball was an important factor in this method. Excitation of structure is required to achieve an optimum packing ratio where the maximum damping capacity is obtained. For a 50% packing ratio, this excitation process is not necessary to obtain a stable damping capacity (Wakasawa et alTo increase the dynamic stiffness of machine tool, testing method of dynamic characteristic of mawas proposed by Koci (2003). While, the nodal analysis concept to yield frequency modus for operated mtool was developed by Harms (2006).  This paper proposes the use of wood material machine tool structure. This work is aimed to the effect of mass reduction on static stiffness and damping capability through variation of geometric structure. The wood materials used in this were Hevea braziiensis and Shorea leavis.  II. MATERIALS AND METHODS Stiffness is a major criterion of machine tool structure to produce high dimension accuracy of cutting product. The other side, the weight of machine tool structurbe minimized to reduce the cost production and increase handling capability. Due to the minimumand maximum stiffness requirements, a various geometric model of machine tool structures of wood (Figure 1) was analysed and simulated using FEM. Static load simulation of modelled structures were 15 kg located at position.  Every specimens was tested by vibration test to calculated the damping factor. Set-up of vibration testing is depicted in Figure 3. The tests were run for four locations of specimens with the similar relative position from the accelerometer. Vibration response data were Susilo A.W.  et al.  © IJSE – ISSN: 2086-5023, April 15, 2013, All rights reserved  the use of  et al,  et al which  et al, around .5 – was  (Lee  , 2004).  chine tool achine for investigate experiment e must to  weight the middle acquired and stored in computer through data device of Spectra Quest. The presentation of vibration transient response is shown in Figure 4. Determination of the damping factor was conducted by calculating logarithmic decrement of sequenced amplitudes as presented in Eqs. (1)-(3).   (a)  (c)  Figure 1. Structure model for stiffness simulation and vibration testing: a. Three square-holes structure, b. Cross ribs structure, c. Single rectangular-hole structure, d. Closed- Figure 2. Free body diagram of stiffness simulation.  Figure 3. Set-up of the vibration test of the wood structure. The effect of vibrating mass in closedon damping factor was also observed. The sand powder of 0.3 mm particle size was filled into single rectangularand cross ribs structure as presented in Figure 5a. Holes, then was covered using wood plate (Figure 5b) and vibration test was conducted using hammer and accelerometer sensor to obtain vibration transient     ISSN: 2086-5023 58 acquisition  (b)  (d) box structure.     -box structure -hole Internat. J. of Sci. and Eng., Vol. 4(2)2013 : 57-60,  April 2013, Susilo A.W.  et al.      ISSN: 2086-5023  59  © IJSE – ISSN: 2086-5023, April 15, 2013, All rights reserved  response. The similar procedures of logarithmic decrement were used to calculate the damping factor of structures under test.   X1XX2ΔX2  Figure 4. Transient vibration response data used to determining decrement logarithmic.   = ln足撇1撇挠卒= ln纵 nd)邹= 毁归蛔 ...........................(1) 蛔= 23d税1−n2 = ʬ IJSE  龟 棍逛I逛柜 ........................(2)  = 挠3n税1−n2.............................................................(3)    (a)   (b) Figure 5 a. Structure with sand powder, b. The cover of wood plate.  III. RESULTS AND DISCCUSION In the structure, stiffness can be represented by deflection when the structure was loaded by static load. The simulation of deflection contour of each structures are shown in Figures 6a-6d. Table 1 summarizes the maximum deflection of each specimens when the load was applied. Observing the results, the cross ribs structure yielded the minimum reduction of deflection per unit mass. Therefore, the cross ribs structure models is better than the single rectangular hole as well as three holes structure.     (a)  (b)  (c)   (d)  Figure 6. The simulation results of structure deflection: a. Three square-holes structure, b. Cross ribs structure, c. Single rectangular-structure, d. Closed box strcuture. Table 1. The maximum deformation of structure variation caused by static load of 15 kg (Shorea leavis)          No Structural Model Max deformation (δmaks) x e-9 Massa (kg) Δ δ/Δm  x e-9 1 Three holes structure 9,4711 2,9 3,3179 2 Cross ribs structure 5,572 3 0,5738 3 Single hole structure 14,6 2,6 5,7494 4 Closed-box structure 4,826 4,3 -  Vibration measurement of each specimens was executed for four locations with the same relative position between stimulated point and accelerometers. The vibration transient response reconstruction of measurement data is depicted in Figure 7. The cross ribs structure gave the higher damping factor than the single as well as three holes structures, that was around of 0.063. The damping factor of all structure are presented in Table 2. These data shows that the damping factor does not clearly correlate with the percentage of wood volume. The geometric structure is the dominant factor which affects on the damping capability.  The damping factor of Shorea laevis wood is higher than Hevea braziiensis wood. The calculation gave results Internat. J. of Sci. and Eng., Vol. 4(2)2013 : 57-60,  April 2013, Susilo A.W.  et al.      ISSN: 2086-5023  60  © IJSE – ISSN: 2086-5023, April 15, 2013, All rights reserved  of closed-box structure of Shorea laevis and Hevea braziiensis woods are 0.065 and 0.045, respectively.    Gambar 7. Plotting vibration transient response data.   TABLE 2. The Damping Factor of Four structures of Shorea leavis and Hevea braziiensis No Ribbing Structure % wood volume  Damping factor 1 Three holes- Shorea leavis 70,62937 0,044309 2 Cross ribs- Shorea leavis 83,36429 0,063796 3 Single hole- Shorea leavis 65,58129 0,048145 4 Closed-box-Shorea laevis 100 0,065197 5 Closed-box -Hevea braziiensis 100 0,045203  The use of vibrating mass actually increased damping capability of the structures. The addition of vibrating mass in single rectangular hole structure (with mass of 2,9 kg) enhanced the damping factor from 0.048 to 0.079 (around of 1,64 times). While for cross ribs structure, correlation between vibrating mass addition and damping factor is depicted in Figure 8. This figure shows that the increasing of vibrating mass is proportional with the enhancement of the damping factor.     Figure 8. Correlation between vibrating mass and damping factor of cross ribs structure.  The enhancement of damping capability is caused by vibrating mass follows this phenomenon: when force was stimulated to the structure, all the particles mass vibrates with random vibration mode. The damping capability were produced by the different phase of this vibration.  IV. CONCLUSIONS Cross ribs structure is the best model of wood machine tool structure which gives minimum weight and maximum stiffness compared to single and three holes structures. Damping factor cannot be correlated to the mass as well as the volume of wood but it closely correlates to the geometric structure. The addition of vibrating mass is effective method to increase damping capability of wood structure. ACKNOWLEDGMENT This paper was supported by Hibah Kompetensi under Contract  no 120/SP2H/PL/Dit.Litabnas/III/2012. The outhors thanks  Vighormes and Subroto for their help in preparing the experiments, as well as Agus Suprihanto for the discussions and assistance in conducting the experiment.  REFERENCES Buccur, V. (2006). Acoustics of wood 2nd ed, SPRIN-GER VERLAG Ciornei, M., Diaconescu, E., and Glovnea, M. (2009). Experimental Invertigations of Wood Damping and Elastic Modulus. DOCT-US, 1(1): 56-61 Harms, A. (2006). Increasing the dynamic stiffness of Machine tools by means of Modal Analysis. in PROCEEDING MACHINE TOOL CONSTRUCTION CONFERENCE 23th March 2006, Munich, Germany    Hossein, M.A., Shahverdi, M., and Roohnia. (2011). The Effect of Wood Knot as a Defect on Modulus of Elasticity (MOE) and Damping Correlation. NOTE SCI BIOL, 3(3): 145-149    Koci, P. (2003). Assessment of machine tool dynamic properties. ACTA MONTANISTICA SLOVACA, 8(4): 179-181 Lee, D. G., Suh, J. G., Kim, H. S., and Kim, J. M. (2003). Design and manufacture of composite high speed machine tool structures. COMPOSITES SCIENCE AND TECHNOLOGY, 64: 1523–1530. http://dx.doi.org/10.1016/j.compscitech.2003.10.021 Nakaminami, M., Tokuma, T., Matsumoto, K., Sakashita, S., Moriwaki, T., and Nakamoto, K. (2007). Optimal Structure Design Methodology for Compound Multiaxis Machine Tools. INTERNATIONAL JOURNAL OF AUTOMATION TECHNOLOGY, 1(2): 87 Ouis, Q. (2002). On the frequency dependence of the modulus of elasticity of wood. WOOD SCIENCE AND TECHNOLOGY, 36(4): 335–346. http://dx.doi.org/10.1007/s00226-002-0145-5 Slocum, A. H., Marsh, E. R., and Smith, D. H. (1994). A new damper design for machine tool structures: the replicated internal viscous damper, PRECISION ENGINEERING, 16(3): 174-183. http://dx.doi.org/10.1016/0141-6359(94)90122-8 Wakasawa, Y., Hashimoto, M., and Marui, E. (2004). The damping capacity improvement of machine tool structures by balls packing. INTERNATIONAL JOURNAL OF MACHINE TOOLS AND M ANUFACTURE, 44: 1527-1536.  http://dx.doi.org/10.1016/j.ijmachtools.2004.05.001           0,060,0650,070,0750,080,0850,090 0,5 1 1,5Damping FactorVibrating Mass (kg)

The effect of geometric structure on stiffness and damping factor of wood applicable to machine tool structure

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The effect of geometric structure on stiffness and damping factor of wood applicable to machine tool structure

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