- Email: [email protected]
epoxy composites
Composite Structures 66 (2004) 439–447 www.elsevier.com/locate/compstruct
Design of inspecting machine for next generation LCD glass panel with high modulus carbon/epoxy composites Soon Chul Jung, Jae Eung Lee, Seung Hwan Chang
*
School of Mechanical Engineering, Chung-Ang University, 221, Huksuk-Dong, Dongjak-Ku, Seoul 156-756, South Korea Available online 2 June 2004
Abstract In this paper, an imperfection detecting machine which has composite–aluminium hybrid beam structure with high-modulus carbon/epoxy composites in order to enhance dynamic stiffness and damping capacity of the structure is introduced. For the optimal design of the composite-aluminium hybrid beam structure, geometric shape of cross-section of aluminium beam, the stacking sequence and thickness of composite which is to be reinforced onto the aluminium beam are determined by considering the fundamental natural frequency and deformation of the structure under service conditions. The dynamic characteristics of the structure are analyzed by the finite element method, and the results show good agreement with the modal testing results. In addition, new designs of beam structure are also proposed for the next generation inspecting system which has much longer beam length. Parametric study for composite X -axis beam system and optimisation scheme of joint inserts are performed in the designing process. 2004 Elsevier Ltd. All rights reserved. Keywords: LCD glass panel; Aluminium–composite hybrid X -axis beam; Fundamental natural frequency; Parametric study; Air bearings
1. Introduction High precision machines such as defect inspection machines or ultra precision grinding machines need robust structures with high stiffness and damping characteristics to cope with intermittent movement during processing, which may causes vibrations and deflections due to inertia forces. As the processing time becomes faster the requirements of inspection machines and machine tools are hard to be achieved with the conventional materials like steel and aluminium because of their intrinsic high density. As LCD glass panel size becomes larger (the size of the 6th generation LCD glass panel becomes larger than about 1300 mm · 1700 mm) the speed of the imperfection detecting process of panel pixels should be faster to cope with manufacturing productivity. But the inspection process generates vibrations by intermittent movement, which makes the precious inspection process to become slow. Imperfection detecting machines for LCD glass panel, in general, have gantry-type structures,
*
Corresponding author. E-mail address: [email protected] (S.H. Chang).
0263-8223/$ - see front matter 2004 Elsevier Ltd. All rights reserved. doi:10.1016/j.compstruct.2004.04.066
which are composed of guide beams and supporting structures made of aluminium to reduce its inertial forces. But machine becomes larger, this conventional material no longer provide enough stiffness and damping to the machine structure. A high dynamic stiffness of structure is essential for the inspecting machine to improve the speed of the defect detection of LCD glass panels. On the other hand, fibre reinforced composite materials are widely used for design precision structures such as robots, ultra precision grinding machines because they have high specific stiffness and strength and also have good damping characteristics. There are several researches on structural robustness of machine tools introducing fibre reinforced composite materials. Chang et al. [1] and Lee et al. [2] designed and manufactured high precision grinding machine components such as column and headstock with fibre reinforced composite materials and cast iron (or steels) to improve damping capacity. Surface damping treatment technology [3] was introduced to design both of components and it was proved by using modal test and analysis that the metal– composite hybrid structures have good damping capacity. Haranath et al. [4] designed milling machines, radial drilling machines and lathes with viscoelastic
440
S.C. Jung et al. / Composite Structures 66 (2004) 439–447
layers using damping treatment method. Lee et al. [5] designed and manufactured steel–composite hybrid boring bar replacing conventional tungsten carbide boring bar, which has 30% higher dynamic stiffness. Jeong et al. [6] investigated, as a fundamental research on the damping capacity of fibre reinforced composite materials, dynamic characteristics of carbon fibre/epoxy composites using thin beams with respect to the stacking angles and so on. In this paper, an aluminium–composite hybrid beam for LCD glass panel defect-inspecting machine is designed using high stiffness carbon/epoxy composites to increase specific stiffness and damping characteristics. Maximum deflection due to dead weight and bending natural frequencies are analytically estimated with respect to the different composite thickness, and the modal testing is performed to validate the analytical results. Parametric study for designing a new composite X -axis beam is also carried out to determine the crosssectional dimensions. Optimisation scheme of joint inserts for a new composite beam system is performed considering joining length and thickness of the insert.
2. Structure of inspecting machine for LCD glass panel Fig. 1 shows the inspecting machine for LCD glass panel to be analyzed in this paper. It has gantry type structure as shown in Fig. 1 comprising X -axis beam with carriage which carries pick-up camera for error detection and repairing systems and Y -axis beam which guides X axis beam in Y -direction connected by Y -axis carriages at the ends of X -axis beam. The gantry structure is mounted
Z Y
on a granite bed and the glass panels are placed on it. Therefore, X -axis carriage moves x–y plane to inspect the surface of glass panels which are mounted on the bed as shown in Fig. 1. Air spring system is introduced to enhance precise movement of carriage and beam structures and to reduce vibration-causing friction as well.
3. Composite reinforcement of existing X-axis beam 3.1. Static and dynamic analysis of X -axis beam The existing X -axis beam for LCD inspecting machines are made of aluminium to reduce inertia forces cause by intermittent movement during the inspection process. The cross-section and geometric dimensions are as shown in Fig. 2 and its length is 1800 mm for the LCD glass panels of the 5th generation. In order to determine the specification of the composite reinforcement such as stacking sequence and thickness two essential finite element analyses (maximum deflection and natural frequency of the beam structure) were performed. Mitsubishi prepreg (HYEJ34M45, Japan) was used for composite reinforcement and its materials properties are listed in Table 1. In general, high stiffness materials such as carbon/ epoxy composites should be reinforced in the outer surface of the beams to get effective performance but in this case innermost surface was chosen to be reinforced because the outer surface should be polished to mirror surface for being used as air bearing surfaces. SOLID45 structural element was used for modelling of composites (orthotropic property was used for calculation) and aluminium structures including Y -axis carriage (see Fig. 1) and the air springs (spring constant is 127 MN/m2 ) for supporting Y -axis carriage was modelled by COMBIN14 element which comprises 3-D spring element. To
X
Y-axis carriage X-axis carriage 220 mm
X-axis beam Aluminium
Composite 220 mm
10 mm
Bed Y-axis beam
10 mm
Glass panel Fig. 1. The shape of inspecting machine for next generation LCD.
Fig. 2. Cross-section of aluminium–composite hybrid X -axis beam.
S.C. Jung et al. / Composite Structures 66 (2004) 439–447
Tensile modulus (GPa) Tensile strength (MPa) Poisson’s ratio Density (kg/m3 ) Thickness (mm)
30 of
carbon/epoxy Longitudinal Transverse Longitudinal Transverse
composite
(Mitsubishi 270 5.9 1580 46 0.28 1730 0.280
improve the bending stiffness of the aluminium–composite hybrid beam structure composite stacking sequence of [±5]nT is selected. One end of each spring element is attached to the bearing points on Y -axis carriage and the other end is fixed in space in three directions as shown in Fig. 3(b). In order to estimate static stiffness of the X -axis beam due to the dead weight of the beam structure including an X -axis carriage static deflection with respect to the stacking thickness was calculated. Fig. 4 shows the calculation result. The static deflection of the beam is composed not only of the bending deflection of the beam itself but also deflection and rotation of the air
25 Static deflection [µm]
Table 1 Material properties HYEJ34M45)
441
15
10
5
0
0
2
4 6 8 10 The staking thickness [mm]
12
14
Fig. 4. Static deflection of the beam structure with respect to the stacking thickness.
bearings attached to the Y -axis carriage as shown in Fig. 5. The deflections are compared with at the same point; that is, middle bottom-point of the beam (see Fig. 5). From the calculation result it was found that the static deflection decreases with the increment of composite thickness because of high specific stiffness of the composite laminate. But as the stacking thickness increases the decrement rate of deflection of the hybrid beam system decreases because the additional composite laminates do not affect much on the enhancement of bending stiffness while they add the weight of the beam structure. The static deflection (d) of the aluminium–composite hybrid beam structure has the following relation: d/
Fig. 3. FE model of the beam structure: (a) total beam structure including X -axis carriage; (b) boundary condition of the spring elements.
20
qL4 ðq AA þ qC AC ÞgL4 ¼ A ; EA IA þ EC IC EA IA þ EC IC
ð1Þ
Fig. 5. Deformation of the beam structure due to dead weight.
S.C. Jung et al. / Composite Structures 66 (2004) 439–447
where subscripts ‘A’ and ‘C’ represent aluminium and composite, respectively and q is mass density, E is Young’s modulus, I is the 2nd moment of inertia of the cross-section, g is the gravitational acceleration, L is the length of the beam and A is area of the material. Every geometry of aluminium structure is constant and the Young’s modulus of the composite laminate (EC ) is constant if the stacking sequence is fixed. Moreover the area and the 2nd moment of inertia of the cross-section of the composite tube can be expressed by using inner (di ) and outer (do ) diameters, which means the only variable is inner diameter (di ), as expressed in the following equations: 2 ! di 2 2 2 AC / ðdo di Þ ¼ do 1 ; do ð2Þ 4 ! d i IC / ðdo4 di4 Þ ¼ do4 1 : do Eq. (2) represents that the decrement of inner diameter (that is, increment of composite thickness) of the composite tube may affect much on the cross-sectional area rather than the 2nd moment of inertia of crosssection so the decreasing rate of the deflection of the hybrid beam gradually decreases as the composite thickness (do di ) increases. Therefore, the stacking thickness should be determined with consideration of this effect. The variation of the first natural frequencies of the beam structure, which is one of the most important aspects to design precise structures is also investigated with respect to the stacking thickness. Boundary conditions (see Fig. 3) and stacking sequence ([±5]nT ) are the same as those for the deflection calculation. The bending natural frequency of the aluminium X -axis beam without reinforcement is 70.3 Hz and as the stacking thickness increases the natural frequency keeps increasing but the increasing rate becomes lower as shown in Fig. 6. This is also caused by increase mass of composite laminates and inefficient stacking position (inner surface of the aluminium beam). The bending natural frequency (f ) of the aluminium– composite hybrid beam has the following relation: X2 f ¼ 2pL2
sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi EA IA þ EC IC ; qA AA þ qC AC
ð3Þ
where X 2 is proportional constant depending on boundary conditions [7] and L is beam length. From the above equation it is found that the natural frequency of the hybrid beam has similar trend (saturation after increment or decrement) as the case of deflection calculation with the increment of the thickness tð¼ do di Þ.
100 90 80 The 1st natural frequency [Hz]
442
70 60 50 40 30 20 10 0
0
2
4 6 8 10 The staking thickness [mm]
12
14
Fig. 6. The first natural frequency of the hybrid beam with respect to the stacking thickness.
From the above results it is found that the static deflection may decrease by 30% and the first bending natural frequency increase by 21% in case that the 10mm-thick composite laminate is reinforced onto the inner surface of the aluminium beam structure. By considering the above calculation results and manufacturing efficiency 10-mm-thick reinforcement of composite with [±5]18T stacking sequence was determined. 3.2. Experimental work: modal test of X -axis beam For the verification of dynamic analysis modal test was performed with 10-mm-thick composite reinforced hybrid X -axis beam. The hybrid beam is mounted on the Y -axis beam using the air bearings to get the same boundary condition as the operational one (see Fig. 7). The frequency response function (FRF) is as shown in Fig. 8. From the test results it is found that there are three apparent bending natural frequencies (82, 174, 327 Hz) which has the similar ratio between frequencies for a beam with free–free boundary condition [7], which is the similar boundary condition as air bearing supporting at the ends of beam, and these values have good agreement with those of modal analysis (87, 190, 315 Hz) using finite element method with 8.9% maximum error (at the second mode; others have only 3–4% errors). And from the above verification procedure it is also found that the hybrid X -axis beam with 10-mm-thick composite reinforcement has about 17% higher natural frequency than that of the aluminium X -axis beam.
S.C. Jung et al. / Composite Structures 66 (2004) 439–447
443
Table 2 The calculation results of static and dynamic analysis w.r.t. the beam length
Accelerometers Impact Position
Beam length (mm)
Mass of beam (kg)
Maximum deflection (lm)
First natural frequency (Hz)
1800 2500
77.4 111.2
2.38 8.36
319 203
Note: The maximum deflection and the natural frequency in this table are calculated using simply supported boundary condition for comparison.
Based on the above equations, considering the increment of the beam length from 1800 to 2500 mm, it is calculated that the mass of the existing aluminium– composite X -axis beam increases 44% and the deflection increases 250% and the first bending natural frequency decreases 36% as listed in Table 2. 4.1. Parametric study for cross-section of the new beam Fig. 7. Modal test of the hybrid beam system: sensors and impact positions.
In order to determine the optimal cross-section of the new beam structure parametric study considering materials and aspect ratios of rectangular cross-section and so on was done. Fig. 9 shows the cross-sections considered in this study. Using the suggested shapes of X -beam specific bending stiffness (EI=q) and deflection (d) due to dead weight are compared with. For the rectangular type hybrid beam (see Fig. 9(a)) the equivalent bending stiffness (EI) has the following relation: EI ¼ EA IA þ EC IC ;
ð4Þ
where bh3 1 fðb 2tA Þ ðh 2tA Þ3 g; ð5Þ 12 12 1 1 3 IC ¼ fðb 2tA Þ ðh 2tA Þ g fðb 2tA 2tC Þ 12 12 3 ðh 2tA 2tC Þ g; ð6Þ
IA ¼
Fig. 8. Frequency response function of the hybrid beam with the real boundary condition.
4. New design of composite X-axis beam for glass panel of the 6th generation inspecting machine In order to cope with the inspection machine for next generation LCD glass panels more robust X -axis beam which has higher stiffness and damping characteristics is needed because the size of glass panel is becoming larger. The conventional aluminium–composite hybrid beam structure is no longer fulfil these requirements because the deflection due to the dead weight is proportional to L4 and the natural frequency of the beam is inversely proportional to L2 as shown in Eqs. (1) and (3).
where the subscripts ‘A’ and ‘C’ represent aluminium and composite, respectively and t is thickness, h and b are height and width of the beam, respectively and I is the 2nd moment of inertia of cross-section and E is Young’s modulus. Then the maximum deflection (dmax ) due to dead weight (q: force per unit length) with simply supported boundary condition is 5qL4 ; ð7Þ 384EI ðmA þ mC Þg ; ð8Þ q¼ L where L is length of beam and m is mass. For the rectangular type hybrid beam with a vertical rib (see Fig. 9(b)) the 2nd moment of inertia of crosssection of each material part has following relation: dmax ¼
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S.C. Jung et al. / Composite Structures 66 (2004) 439–447
tA
Composite
h
tC Aluminum
Specific Bending Stiffness [MNm2/kg]
24000
b
ta=tc=10mm-with Rib ta=tc=10mm-without Rib ta=8,tc=15mm-without Rib ta=8,tc=15mm-with Rib
20000 16000 12000 8000 4000 0 0
50
100
(a)
150 200 Height h [mm]
250
300
350
0.04
(a) 0.03 Deflection [mm]
b
Composite
0.02
ta=tc=10mm-with Rib ta=tc=10mm-without Rib ta=8,tc=15mm-without Rib ta=8,tc=15mm-with Rib
0.01
tA h
0
(b)
tC
0
50
100
150 200 Height h [mm]
250
300
350
Fig. 10. Calculation results for parametric study: (a) specific bending stiffness, (b) deflection.
Aluminum
(b) Fig. 9. Cross-sections for new design of X -axis beam: (a) rectangular cross-section, (b) rectangular cross-section with a vertical rib.
bh3 1 b 3 3 IA ¼ tA ðh 2tA Þ ; ð9Þ 2 2 12 12 1 3 1 3 b tA ðh 2tA Þ3 b tA 2tC IC ¼ 2 12 2 12 2
3 ðh 2tA 2tC Þ : ð10Þ By using the above relations between parameters specific bending stiffness and the maximum deflection with respect to some selected thickness combinations of aluminium (tA ) and composite (tC ) and the height of the beam h with constant width (b ¼ 160 mm) are calculated as shown in Fig. 10. The composite is Mitsubishi prepreg (material properties are listed in Table 1) and the stacking sequence is [±5]nT . From the calculation results it is found that the deflections between various combinations of thickness
of each material have no remarkable difference but fully depend on the height of the beam as shown in Fig. 10(b). With the consideration of this tendency, the new composite X -axis beam is designed without aluminium structure modifying the aspect ratio (h=b) of the composite tube as shown in Fig. 11. The composite X -axis beam is composed of rectangular composite tube whose thickness is 10 mm and two granite thin plates (E ¼ 50 GPa, q ¼ 2600 kg/m3 ) whose thickness is 5 mm on the surfaces of the composite tube for air bearing surfaces. From the calculation results the composite beam has excellent performance especially when the aspect ratio is between 1.5 and 2.0 as shown in Fig. 12. Moreover, manufacturing cost of composite material is reasonable as compared in Fig. 13. With consideration of the results from the parametric study width and height of the composite beam are selected to be 150 and 300 mm (aspect ratio: 2), respectively and 10 mm thickness of composite tube. This new design of composite X -axis beam makes the equivalent spring constant increase by 60% and beam mass and deflection decrease by 58% and by 75%, respectively relative to the aluminium–composite hybrid beam which
S.C. Jung et al. / Composite Structures 66 (2004) 439–447
12000
Composite Tube
Specific Bending Stiffness [MNm2/kg]
Granite Thin Plates
445
10000 8000 6000 4000 ta=tc=10mm-without Rib ta=8,tc=15mm-without Rib Composite+Stone
2000 0 0
0.5
1
(a)
1.5
2
2.5
3
2.5
3
Aspect Ratio 0.014 0.012
Deflection [mm]
Fig. 11. Composite X -axis beam for the next generation LCD error detecting machine.
0.01 0.008 0.006 0.004
ta=tc=10mm ta=8,tc=15mm Composite+Stone
0.002
is introduced in the previous chapter (see Fig. 2) with 2500 mm length.
0 0
Connecting method between the X -axis beam and Y -axis carriage is also optimised to enhance bending stiffness of the beam structure. The original aluminium X -axis beam has joints at the top of both ends of the beam as shown in Fig. 14(a) which is vulnerable to z-directional bending. On the other hand, for the composite X -axis beam cap type aluminium insert is designed as shown in Fig. 14(b). For determining the optimal joining length and thickness of the insert the maximum deflection of the beam whose cross-sectional dimensions were determined in the previous section with various thickness and length of joining inserts (see Fig. 15) is analyzed using finite element method. For the thickness of joining inserts 30 and 50 mm are considered and the length of joining parts varies from 80 to 500 mm. Fig. 16 shows the calculation results. The results show that thickness change of joining insert affect little on the deflection while the variation of deflection is strongly affected by the length of joining insert to some degree; that is, the deflection decreases with the increment of the joining length and saturates beyond 400 mm joining length. Considering the calculation results the thickness and length of the joining insert are determined to be 50 and 400 mm, respectively.
1
1.5
2
Aspect Ratio
Fig. 12. Calculation results for parametric study of composite beam with granite thin plates: (a) specific bending stiffness, (b) deflection.
3000 2500 Composite Price [US $]
4.2. Joint design
0.5
(b)
2000 1500 1000
ta=tc=10mm-without Rib ta=8,tc=15mm-without Rib
500
Composite+Stone
0 0
0.5
1
1.5 Aspect Ratio
2
2.5
3
Fig. 13. Composite price for manufacturing composite beam.
With 400 mm length joining inserts and simplified Y axis carriage which are supported by air bearing system the maximum deflection of the newly designed composite X -axis beam was calculated using finite element analysis. The finite element model of the beam system
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S.C. Jung et al. / Composite Structures 66 (2004) 439–447
1.2
Static deflection [µm]
1 0.8 0.6 0.4 Thickness of insert(30mm) Thickness of insert(50mm)
0.2 0 80
200
300 400 Joining length [mm]
500
Fig. 16. The variation of beam deflection with respect to the thickness and length of joining insert.
Fig. 14. Connecting method between X -axis beam and Y -axis carriage (shading area is the joining region): (a) existing aluminium beam; (b) new design with composite beam.
Fig. 15. Connecting joint between X -axis beam and Y -axis carriage.
(including Y -axis carriage and air bearing systems) is as shown in Fig. 17. From the calculation result it is found that the maximum deflection of new composite X -axis beam is 16.9 lm which is 11% lower than that of aluminium–composite hybrid X -axis beam system with 1800 mm length of the beam (the 5th generation inspection machine). The deflection is generated not only by the beam deflection itself but also by the rotation of Y -axis carriage supported by air bearing system.
Fig. 17. Newly designed composite X -axis beam system with the optimised joining inserts.
5. Conclusion In this paper, several beam structures for LCD glass panel defect-inspecting machine are proposed, analyzed, and validated. The results can be summarized as follows:
S.C. Jung et al. / Composite Structures 66 (2004) 439–447
(1) Composite reinforcement of existing aluminium X axis beam of inspection machine for LCD glass panel was considered. Bending natural frequencies and maximum deflection were calculated with respect to the different composite thickness using finite element analysis considering appropriate boundary condition, and the calculated bending natural frequencies show good agreement with the modal testing results. The aluminium–composite hybrid X -axis beam reduces the static deflection by 30% and increases the first bending natural frequency by 21% in case that the 10-mm-thick composite laminate is reinforced onto the inner surface of the aluminium beam structure. (2) Using parametric study, composite X -axis beam for glass panel of the 6th generation inspecting machine with granite thin plates for the air bearing surfaces was proposed and designed. This new design of composite beam makes the equivalent spring constant increase by 60% and beam mass and deflection decrease by 58% and by 75%, respectively relative to the aluminium–composite hybrid beam with 2500 mm length. (3) Finally, the joint inserts for newly designed composite X -axis beam was optimised modifying its joining
447
length and the thickness of the insert. From the analysis results it was found that the new composite X -beam system has 11% lower deflection than that of aluminium–composite hybrid X -axis beam system with 1800 mm length of the beam.
References [1] Chang SH, Kim PJ, Lee DG, Choi JK. Steel–composite hybrid headstock for high-precision grinding machine. Compos Struct 2001;53:1–8. [2] Lee DG, Chang SH, Kim HS. Damping improvement of machine tool columns with polymer matrix fiber composite material. Compos Struct 1998;43:155–63. [3] Nashif AD, Jones DIG, Henderson JP. Vibration damping. New York: Wiley; 1985 [chapter 6]. [4] Haranath S, Ganesan N, Rao BVA. Dynamic analysis of machine tool structures with applied damping treatment. Int J Mach Tools Manufact 1987;27:43–55. [5] Lee DG, Hwang HY, Kim JK. Design and manufacture of a carbon fiber epoxy rotating boring bar. Compos Struct 2003;60: 115–24. [6] Jeong KS, Lee DG, Kwak YK. Experimental investigation of the dynamic characteristics of carbon fiber epoxy composite thin beams. Compos Struct 1995;33:77–86. [7] Lalanne M, Berthier P, Der Hagopian J. Mechanical vibrations for engineers. New York: Wiley; 1983 [chapter 4].
Design of inspecting machine for next generation LCD glass panel with high modulus carbon/epoxy composites Soon Chul Jung, Jae Eung Lee, Seung Hwan Chang
*
School of Mechanical Engineering, Chung-Ang University, 221, Huksuk-Dong, Dongjak-Ku, Seoul 156-756, South Korea Available online 2 June 2004
Abstract In this paper, an imperfection detecting machine which has composite–aluminium hybrid beam structure with high-modulus carbon/epoxy composites in order to enhance dynamic stiffness and damping capacity of the structure is introduced. For the optimal design of the composite-aluminium hybrid beam structure, geometric shape of cross-section of aluminium beam, the stacking sequence and thickness of composite which is to be reinforced onto the aluminium beam are determined by considering the fundamental natural frequency and deformation of the structure under service conditions. The dynamic characteristics of the structure are analyzed by the finite element method, and the results show good agreement with the modal testing results. In addition, new designs of beam structure are also proposed for the next generation inspecting system which has much longer beam length. Parametric study for composite X -axis beam system and optimisation scheme of joint inserts are performed in the designing process. 2004 Elsevier Ltd. All rights reserved. Keywords: LCD glass panel; Aluminium–composite hybrid X -axis beam; Fundamental natural frequency; Parametric study; Air bearings
1. Introduction High precision machines such as defect inspection machines or ultra precision grinding machines need robust structures with high stiffness and damping characteristics to cope with intermittent movement during processing, which may causes vibrations and deflections due to inertia forces. As the processing time becomes faster the requirements of inspection machines and machine tools are hard to be achieved with the conventional materials like steel and aluminium because of their intrinsic high density. As LCD glass panel size becomes larger (the size of the 6th generation LCD glass panel becomes larger than about 1300 mm · 1700 mm) the speed of the imperfection detecting process of panel pixels should be faster to cope with manufacturing productivity. But the inspection process generates vibrations by intermittent movement, which makes the precious inspection process to become slow. Imperfection detecting machines for LCD glass panel, in general, have gantry-type structures,
*
Corresponding author. E-mail address: [email protected] (S.H. Chang).
0263-8223/$ - see front matter 2004 Elsevier Ltd. All rights reserved. doi:10.1016/j.compstruct.2004.04.066
which are composed of guide beams and supporting structures made of aluminium to reduce its inertial forces. But machine becomes larger, this conventional material no longer provide enough stiffness and damping to the machine structure. A high dynamic stiffness of structure is essential for the inspecting machine to improve the speed of the defect detection of LCD glass panels. On the other hand, fibre reinforced composite materials are widely used for design precision structures such as robots, ultra precision grinding machines because they have high specific stiffness and strength and also have good damping characteristics. There are several researches on structural robustness of machine tools introducing fibre reinforced composite materials. Chang et al. [1] and Lee et al. [2] designed and manufactured high precision grinding machine components such as column and headstock with fibre reinforced composite materials and cast iron (or steels) to improve damping capacity. Surface damping treatment technology [3] was introduced to design both of components and it was proved by using modal test and analysis that the metal– composite hybrid structures have good damping capacity. Haranath et al. [4] designed milling machines, radial drilling machines and lathes with viscoelastic
440
S.C. Jung et al. / Composite Structures 66 (2004) 439–447
layers using damping treatment method. Lee et al. [5] designed and manufactured steel–composite hybrid boring bar replacing conventional tungsten carbide boring bar, which has 30% higher dynamic stiffness. Jeong et al. [6] investigated, as a fundamental research on the damping capacity of fibre reinforced composite materials, dynamic characteristics of carbon fibre/epoxy composites using thin beams with respect to the stacking angles and so on. In this paper, an aluminium–composite hybrid beam for LCD glass panel defect-inspecting machine is designed using high stiffness carbon/epoxy composites to increase specific stiffness and damping characteristics. Maximum deflection due to dead weight and bending natural frequencies are analytically estimated with respect to the different composite thickness, and the modal testing is performed to validate the analytical results. Parametric study for designing a new composite X -axis beam is also carried out to determine the crosssectional dimensions. Optimisation scheme of joint inserts for a new composite beam system is performed considering joining length and thickness of the insert.
2. Structure of inspecting machine for LCD glass panel Fig. 1 shows the inspecting machine for LCD glass panel to be analyzed in this paper. It has gantry type structure as shown in Fig. 1 comprising X -axis beam with carriage which carries pick-up camera for error detection and repairing systems and Y -axis beam which guides X axis beam in Y -direction connected by Y -axis carriages at the ends of X -axis beam. The gantry structure is mounted
Z Y
on a granite bed and the glass panels are placed on it. Therefore, X -axis carriage moves x–y plane to inspect the surface of glass panels which are mounted on the bed as shown in Fig. 1. Air spring system is introduced to enhance precise movement of carriage and beam structures and to reduce vibration-causing friction as well.
3. Composite reinforcement of existing X-axis beam 3.1. Static and dynamic analysis of X -axis beam The existing X -axis beam for LCD inspecting machines are made of aluminium to reduce inertia forces cause by intermittent movement during the inspection process. The cross-section and geometric dimensions are as shown in Fig. 2 and its length is 1800 mm for the LCD glass panels of the 5th generation. In order to determine the specification of the composite reinforcement such as stacking sequence and thickness two essential finite element analyses (maximum deflection and natural frequency of the beam structure) were performed. Mitsubishi prepreg (HYEJ34M45, Japan) was used for composite reinforcement and its materials properties are listed in Table 1. In general, high stiffness materials such as carbon/ epoxy composites should be reinforced in the outer surface of the beams to get effective performance but in this case innermost surface was chosen to be reinforced because the outer surface should be polished to mirror surface for being used as air bearing surfaces. SOLID45 structural element was used for modelling of composites (orthotropic property was used for calculation) and aluminium structures including Y -axis carriage (see Fig. 1) and the air springs (spring constant is 127 MN/m2 ) for supporting Y -axis carriage was modelled by COMBIN14 element which comprises 3-D spring element. To
X
Y-axis carriage X-axis carriage 220 mm
X-axis beam Aluminium
Composite 220 mm
10 mm
Bed Y-axis beam
10 mm
Glass panel Fig. 1. The shape of inspecting machine for next generation LCD.
Fig. 2. Cross-section of aluminium–composite hybrid X -axis beam.
S.C. Jung et al. / Composite Structures 66 (2004) 439–447
Tensile modulus (GPa) Tensile strength (MPa) Poisson’s ratio Density (kg/m3 ) Thickness (mm)
30 of
carbon/epoxy Longitudinal Transverse Longitudinal Transverse
composite
(Mitsubishi 270 5.9 1580 46 0.28 1730 0.280
improve the bending stiffness of the aluminium–composite hybrid beam structure composite stacking sequence of [±5]nT is selected. One end of each spring element is attached to the bearing points on Y -axis carriage and the other end is fixed in space in three directions as shown in Fig. 3(b). In order to estimate static stiffness of the X -axis beam due to the dead weight of the beam structure including an X -axis carriage static deflection with respect to the stacking thickness was calculated. Fig. 4 shows the calculation result. The static deflection of the beam is composed not only of the bending deflection of the beam itself but also deflection and rotation of the air
25 Static deflection [µm]
Table 1 Material properties HYEJ34M45)
441
15
10
5
0
0
2
4 6 8 10 The staking thickness [mm]
12
14
Fig. 4. Static deflection of the beam structure with respect to the stacking thickness.
bearings attached to the Y -axis carriage as shown in Fig. 5. The deflections are compared with at the same point; that is, middle bottom-point of the beam (see Fig. 5). From the calculation result it was found that the static deflection decreases with the increment of composite thickness because of high specific stiffness of the composite laminate. But as the stacking thickness increases the decrement rate of deflection of the hybrid beam system decreases because the additional composite laminates do not affect much on the enhancement of bending stiffness while they add the weight of the beam structure. The static deflection (d) of the aluminium–composite hybrid beam structure has the following relation: d/
Fig. 3. FE model of the beam structure: (a) total beam structure including X -axis carriage; (b) boundary condition of the spring elements.
20
qL4 ðq AA þ qC AC ÞgL4 ¼ A ; EA IA þ EC IC EA IA þ EC IC
ð1Þ
Fig. 5. Deformation of the beam structure due to dead weight.
S.C. Jung et al. / Composite Structures 66 (2004) 439–447
where subscripts ‘A’ and ‘C’ represent aluminium and composite, respectively and q is mass density, E is Young’s modulus, I is the 2nd moment of inertia of the cross-section, g is the gravitational acceleration, L is the length of the beam and A is area of the material. Every geometry of aluminium structure is constant and the Young’s modulus of the composite laminate (EC ) is constant if the stacking sequence is fixed. Moreover the area and the 2nd moment of inertia of the cross-section of the composite tube can be expressed by using inner (di ) and outer (do ) diameters, which means the only variable is inner diameter (di ), as expressed in the following equations: 2 ! di 2 2 2 AC / ðdo di Þ ¼ do 1 ; do ð2Þ 4 ! d i IC / ðdo4 di4 Þ ¼ do4 1 : do Eq. (2) represents that the decrement of inner diameter (that is, increment of composite thickness) of the composite tube may affect much on the cross-sectional area rather than the 2nd moment of inertia of crosssection so the decreasing rate of the deflection of the hybrid beam gradually decreases as the composite thickness (do di ) increases. Therefore, the stacking thickness should be determined with consideration of this effect. The variation of the first natural frequencies of the beam structure, which is one of the most important aspects to design precise structures is also investigated with respect to the stacking thickness. Boundary conditions (see Fig. 3) and stacking sequence ([±5]nT ) are the same as those for the deflection calculation. The bending natural frequency of the aluminium X -axis beam without reinforcement is 70.3 Hz and as the stacking thickness increases the natural frequency keeps increasing but the increasing rate becomes lower as shown in Fig. 6. This is also caused by increase mass of composite laminates and inefficient stacking position (inner surface of the aluminium beam). The bending natural frequency (f ) of the aluminium– composite hybrid beam has the following relation: X2 f ¼ 2pL2
sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi EA IA þ EC IC ; qA AA þ qC AC
ð3Þ
where X 2 is proportional constant depending on boundary conditions [7] and L is beam length. From the above equation it is found that the natural frequency of the hybrid beam has similar trend (saturation after increment or decrement) as the case of deflection calculation with the increment of the thickness tð¼ do di Þ.
100 90 80 The 1st natural frequency [Hz]
442
70 60 50 40 30 20 10 0
0
2
4 6 8 10 The staking thickness [mm]
12
14
Fig. 6. The first natural frequency of the hybrid beam with respect to the stacking thickness.
From the above results it is found that the static deflection may decrease by 30% and the first bending natural frequency increase by 21% in case that the 10mm-thick composite laminate is reinforced onto the inner surface of the aluminium beam structure. By considering the above calculation results and manufacturing efficiency 10-mm-thick reinforcement of composite with [±5]18T stacking sequence was determined. 3.2. Experimental work: modal test of X -axis beam For the verification of dynamic analysis modal test was performed with 10-mm-thick composite reinforced hybrid X -axis beam. The hybrid beam is mounted on the Y -axis beam using the air bearings to get the same boundary condition as the operational one (see Fig. 7). The frequency response function (FRF) is as shown in Fig. 8. From the test results it is found that there are three apparent bending natural frequencies (82, 174, 327 Hz) which has the similar ratio between frequencies for a beam with free–free boundary condition [7], which is the similar boundary condition as air bearing supporting at the ends of beam, and these values have good agreement with those of modal analysis (87, 190, 315 Hz) using finite element method with 8.9% maximum error (at the second mode; others have only 3–4% errors). And from the above verification procedure it is also found that the hybrid X -axis beam with 10-mm-thick composite reinforcement has about 17% higher natural frequency than that of the aluminium X -axis beam.
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Table 2 The calculation results of static and dynamic analysis w.r.t. the beam length
Accelerometers Impact Position
Beam length (mm)
Mass of beam (kg)
Maximum deflection (lm)
First natural frequency (Hz)
1800 2500
77.4 111.2
2.38 8.36
319 203
Note: The maximum deflection and the natural frequency in this table are calculated using simply supported boundary condition for comparison.
Based on the above equations, considering the increment of the beam length from 1800 to 2500 mm, it is calculated that the mass of the existing aluminium– composite X -axis beam increases 44% and the deflection increases 250% and the first bending natural frequency decreases 36% as listed in Table 2. 4.1. Parametric study for cross-section of the new beam Fig. 7. Modal test of the hybrid beam system: sensors and impact positions.
In order to determine the optimal cross-section of the new beam structure parametric study considering materials and aspect ratios of rectangular cross-section and so on was done. Fig. 9 shows the cross-sections considered in this study. Using the suggested shapes of X -beam specific bending stiffness (EI=q) and deflection (d) due to dead weight are compared with. For the rectangular type hybrid beam (see Fig. 9(a)) the equivalent bending stiffness (EI) has the following relation: EI ¼ EA IA þ EC IC ;
ð4Þ
where bh3 1 fðb 2tA Þ ðh 2tA Þ3 g; ð5Þ 12 12 1 1 3 IC ¼ fðb 2tA Þ ðh 2tA Þ g fðb 2tA 2tC Þ 12 12 3 ðh 2tA 2tC Þ g; ð6Þ
IA ¼
Fig. 8. Frequency response function of the hybrid beam with the real boundary condition.
4. New design of composite X-axis beam for glass panel of the 6th generation inspecting machine In order to cope with the inspection machine for next generation LCD glass panels more robust X -axis beam which has higher stiffness and damping characteristics is needed because the size of glass panel is becoming larger. The conventional aluminium–composite hybrid beam structure is no longer fulfil these requirements because the deflection due to the dead weight is proportional to L4 and the natural frequency of the beam is inversely proportional to L2 as shown in Eqs. (1) and (3).
where the subscripts ‘A’ and ‘C’ represent aluminium and composite, respectively and t is thickness, h and b are height and width of the beam, respectively and I is the 2nd moment of inertia of cross-section and E is Young’s modulus. Then the maximum deflection (dmax ) due to dead weight (q: force per unit length) with simply supported boundary condition is 5qL4 ; ð7Þ 384EI ðmA þ mC Þg ; ð8Þ q¼ L where L is length of beam and m is mass. For the rectangular type hybrid beam with a vertical rib (see Fig. 9(b)) the 2nd moment of inertia of crosssection of each material part has following relation: dmax ¼
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tA
Composite
h
tC Aluminum
Specific Bending Stiffness [MNm2/kg]
24000
b
ta=tc=10mm-with Rib ta=tc=10mm-without Rib ta=8,tc=15mm-without Rib ta=8,tc=15mm-with Rib
20000 16000 12000 8000 4000 0 0
50
100
(a)
150 200 Height h [mm]
250
300
350
0.04
(a) 0.03 Deflection [mm]
b
Composite
0.02
ta=tc=10mm-with Rib ta=tc=10mm-without Rib ta=8,tc=15mm-without Rib ta=8,tc=15mm-with Rib
0.01
tA h
0
(b)
tC
0
50
100
150 200 Height h [mm]
250
300
350
Fig. 10. Calculation results for parametric study: (a) specific bending stiffness, (b) deflection.
Aluminum
(b) Fig. 9. Cross-sections for new design of X -axis beam: (a) rectangular cross-section, (b) rectangular cross-section with a vertical rib.
bh3 1 b 3 3 IA ¼ tA ðh 2tA Þ ; ð9Þ 2 2 12 12 1 3 1 3 b tA ðh 2tA Þ3 b tA 2tC IC ¼ 2 12 2 12 2
3 ðh 2tA 2tC Þ : ð10Þ By using the above relations between parameters specific bending stiffness and the maximum deflection with respect to some selected thickness combinations of aluminium (tA ) and composite (tC ) and the height of the beam h with constant width (b ¼ 160 mm) are calculated as shown in Fig. 10. The composite is Mitsubishi prepreg (material properties are listed in Table 1) and the stacking sequence is [±5]nT . From the calculation results it is found that the deflections between various combinations of thickness
of each material have no remarkable difference but fully depend on the height of the beam as shown in Fig. 10(b). With the consideration of this tendency, the new composite X -axis beam is designed without aluminium structure modifying the aspect ratio (h=b) of the composite tube as shown in Fig. 11. The composite X -axis beam is composed of rectangular composite tube whose thickness is 10 mm and two granite thin plates (E ¼ 50 GPa, q ¼ 2600 kg/m3 ) whose thickness is 5 mm on the surfaces of the composite tube for air bearing surfaces. From the calculation results the composite beam has excellent performance especially when the aspect ratio is between 1.5 and 2.0 as shown in Fig. 12. Moreover, manufacturing cost of composite material is reasonable as compared in Fig. 13. With consideration of the results from the parametric study width and height of the composite beam are selected to be 150 and 300 mm (aspect ratio: 2), respectively and 10 mm thickness of composite tube. This new design of composite X -axis beam makes the equivalent spring constant increase by 60% and beam mass and deflection decrease by 58% and by 75%, respectively relative to the aluminium–composite hybrid beam which
S.C. Jung et al. / Composite Structures 66 (2004) 439–447
12000
Composite Tube
Specific Bending Stiffness [MNm2/kg]
Granite Thin Plates
445
10000 8000 6000 4000 ta=tc=10mm-without Rib ta=8,tc=15mm-without Rib Composite+Stone
2000 0 0
0.5
1
(a)
1.5
2
2.5
3
2.5
3
Aspect Ratio 0.014 0.012
Deflection [mm]
Fig. 11. Composite X -axis beam for the next generation LCD error detecting machine.
0.01 0.008 0.006 0.004
ta=tc=10mm ta=8,tc=15mm Composite+Stone
0.002
is introduced in the previous chapter (see Fig. 2) with 2500 mm length.
0 0
Connecting method between the X -axis beam and Y -axis carriage is also optimised to enhance bending stiffness of the beam structure. The original aluminium X -axis beam has joints at the top of both ends of the beam as shown in Fig. 14(a) which is vulnerable to z-directional bending. On the other hand, for the composite X -axis beam cap type aluminium insert is designed as shown in Fig. 14(b). For determining the optimal joining length and thickness of the insert the maximum deflection of the beam whose cross-sectional dimensions were determined in the previous section with various thickness and length of joining inserts (see Fig. 15) is analyzed using finite element method. For the thickness of joining inserts 30 and 50 mm are considered and the length of joining parts varies from 80 to 500 mm. Fig. 16 shows the calculation results. The results show that thickness change of joining insert affect little on the deflection while the variation of deflection is strongly affected by the length of joining insert to some degree; that is, the deflection decreases with the increment of the joining length and saturates beyond 400 mm joining length. Considering the calculation results the thickness and length of the joining insert are determined to be 50 and 400 mm, respectively.
1
1.5
2
Aspect Ratio
Fig. 12. Calculation results for parametric study of composite beam with granite thin plates: (a) specific bending stiffness, (b) deflection.
3000 2500 Composite Price [US $]
4.2. Joint design
0.5
(b)
2000 1500 1000
ta=tc=10mm-without Rib ta=8,tc=15mm-without Rib
500
Composite+Stone
0 0
0.5
1
1.5 Aspect Ratio
2
2.5
3
Fig. 13. Composite price for manufacturing composite beam.
With 400 mm length joining inserts and simplified Y axis carriage which are supported by air bearing system the maximum deflection of the newly designed composite X -axis beam was calculated using finite element analysis. The finite element model of the beam system
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1.2
Static deflection [µm]
1 0.8 0.6 0.4 Thickness of insert(30mm) Thickness of insert(50mm)
0.2 0 80
200
300 400 Joining length [mm]
500
Fig. 16. The variation of beam deflection with respect to the thickness and length of joining insert.
Fig. 14. Connecting method between X -axis beam and Y -axis carriage (shading area is the joining region): (a) existing aluminium beam; (b) new design with composite beam.
Fig. 15. Connecting joint between X -axis beam and Y -axis carriage.
(including Y -axis carriage and air bearing systems) is as shown in Fig. 17. From the calculation result it is found that the maximum deflection of new composite X -axis beam is 16.9 lm which is 11% lower than that of aluminium–composite hybrid X -axis beam system with 1800 mm length of the beam (the 5th generation inspection machine). The deflection is generated not only by the beam deflection itself but also by the rotation of Y -axis carriage supported by air bearing system.
Fig. 17. Newly designed composite X -axis beam system with the optimised joining inserts.
5. Conclusion In this paper, several beam structures for LCD glass panel defect-inspecting machine are proposed, analyzed, and validated. The results can be summarized as follows:
S.C. Jung et al. / Composite Structures 66 (2004) 439–447
(1) Composite reinforcement of existing aluminium X axis beam of inspection machine for LCD glass panel was considered. Bending natural frequencies and maximum deflection were calculated with respect to the different composite thickness using finite element analysis considering appropriate boundary condition, and the calculated bending natural frequencies show good agreement with the modal testing results. The aluminium–composite hybrid X -axis beam reduces the static deflection by 30% and increases the first bending natural frequency by 21% in case that the 10-mm-thick composite laminate is reinforced onto the inner surface of the aluminium beam structure. (2) Using parametric study, composite X -axis beam for glass panel of the 6th generation inspecting machine with granite thin plates for the air bearing surfaces was proposed and designed. This new design of composite beam makes the equivalent spring constant increase by 60% and beam mass and deflection decrease by 58% and by 75%, respectively relative to the aluminium–composite hybrid beam with 2500 mm length. (3) Finally, the joint inserts for newly designed composite X -axis beam was optimised modifying its joining
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length and the thickness of the insert. From the analysis results it was found that the new composite X -beam system has 11% lower deflection than that of aluminium–composite hybrid X -axis beam system with 1800 mm length of the beam.
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