| Citation: | Sheng He, Lanying Lin, Zaixing Wu, Zhangmin Chen. Application of Finite Element Analysis in Properties Test of Finger-jointed Lumber[J]. Journal of Bioresources and Bioproducts, 2020, 5(2): 124-133. doi: 10.1016/j.jobab.2020.04.006
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Finger-jointed lumber production has now become the most extensively used method for spliced lumbers jointing together endwise. The properties of finger-jointed lumber are affected by many different factors such as the end- pressure. The main mechanical properties to be tested for structural use finger-jointed lumber include the modulus of elasticity in static bending and the bending strength. The most commonly used method for testing these properties at present is the experimental test. In this study, we used finite element method to investigate the end-pressure range, the modulus of elasticity in static bending and the bending strength for Pinus sylvistriv var. finger-jointed lumber under three different fitness ratios (0 mm, 0.1 mm, 0.3 mm). With finite element analysis (FEA) modelling results compared with the experimental test results, it is possible to find the relationship between these two kinds of results and use the FEA to predict the properties of finger-jointed lumber. The FEA applied in the end pressure tests showed a narrower range compared with the modelling results. It indicated that the FEA could be used in the prediction of the end pressure for finger-jointed lumber. The modelling results for modulus of elasticity (MOE) test and bending strength (MOR) test showed about 20% discrepancies compared with the experimental results. Moreover, the MOE modelling results showed the same trend as experimental results under three different fitness levels while the MOR modelling results showed the different trend. It can be concluded that the FEA is a feasible way in analyzing the properties of finger-jointed lumber if the errors could be eliminated properly. Some modifications should be made in order to realize the prediction of the properties of finger-jointed lumber more accurately.
Finger joint is a type of end joint developed from scarf joint; it has been used for many years (Roland, 1981). Such joints can not only joint the short pieces of lumber to long ones, but also effectively enhance the utilization of low-grade materials. Finger- joined lumbers present remarkable properties such as straightness, dimensional stability and unlimited length (Lara-Bocanegra et al., 2017). They are commonly used to produce engineered wood products for their excellent mechanical performance (Cecilia et al., 2003). Finger-jointed lumber production has now become the most extensively applied method for splicing lumbers together endwise.
The properties of finger-jointed lumber are affected by many different factors such as the wood species, adhesive, length of finger joints, processing parameters (Khelifa et al., 2016). End-pressure refers to the pressure applied on the end of the lumbers to be jointed lengthwise, which brings the mating surfaces so close together that the glue forms a thin and continuous film between them (Cecilia et al., 2003). Several researches on end pressure indicated that the pressure must be applied to force fingers together to form an interlocking connection (Raknes, 1982). However, the excessive pressure which caused the cell damage or spitting of the finger root could induce the decrease of the strength of finger joints (Marra, 1984; Kutscha and Caster, 1987). Therefore, the end pressure should be identified before the finger joints were jointed.
Finger-jointed lumber is classified as two different groups according to its use, structural and nonstructural use finger-jointed lumber. Nonstructural use finger-jointed lumber is more emphasized on the appearance quality while the structural use finger-jointed lumber is focused on the mechanical properties. The main mechanical properties to be tested for structural use finger-jointed lumber include the modulus of elasticity in static bending and the bending strength. The main method for testing these properties at present is experimental method. With the rapid development of the nondestructive test technology, more and more researchers applied these methods such as the acoustic emission method (Kiyoko et al., 2007; Rescalvo et al., 2018), stress wave method (Liang et al., 2008; Du et al., 2018), ultrasonic method (Lin and Fu, 2007; Philippe et al., 2018), vibration method (Zhang et al., 2005), the near infrared spectrum technology (Zhao et al., 2009; Gillespie et al., 2019) in the testing of mechanical properties tests, gaseous emissions for wood based products.
As an efficient method of numerical analysis, finite element analysis (FEA) is now extensively used in the modelling analysis of material properties. Several researchers have successfully applied this method in the analysis of properties for wood based materials (Davalos et al., 1995; Tabiei and Wu, 2000; Moses and Prion, 2004; Serrano, 2004; He et al., 2012; Khelifa et al., 2016).
In order to save materials which should be used in experimental tests, the present study investigated the end-pressure range, the modulus of elasticity in static bending and the bending strength for Pinus sylvistriv var. finger-jointed lumber under three different fitness ratios (0 mm, 0.1 mm, 0.3 mm) using finite element analysis method. With the FEA modelling results compared with the experimental test results, it is possible to find the relationship between these two kinds of results and use the FEA to predict the properties of finger-jointed lumber.
The dimensions of the lumbers used in the experiment were 600 mm × 88 mm × 24 mm (Length × Width × Thickness). The moisture content (MC) of the lumbers ranged from 8% to 11% while the density ranged from 0.4 g/cm3 to 0.7 g/cm3. The resin used in the production of finger-jointed lumber was a mixture of water-borne carbamate emulsion (the main agent) and macromolecular isocyanate (the firming agent) with a mixture ratio of 100꞉15 (Dynea, Shanghai). The solid content of the resin is 53%, and the pH is 7.3. The amount of resin sprayed on the finger joints is 250–300 g/m2.
Finger joints with three different fitness ratios were cut in the cutting machine (FS-520R, Japan) according to the parameters shown in Table 1.
| Fitness (mm) | Length of finger (mm) | Tip thickness (mm) | Pitch (mm) | Slope |
| 0 | 25.0 | 1.2 | 8.2 | 1/8.6 |
| 0.1 | 23.7 | 1.3 | 8.2 | 1/8.6 |
| 0.3 | 21.0 | 1.5 | 8.2 | 1/8.6 |
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A series of 15 finger-jointed lumbers were produced in the end- pressure test experiment. Each fitness lever was represented by five finger jointed lumbers. The two finger joints of the same fitness were jointed together by hand after sprayed with resin. They were subsequently loaded lengthwise on the cross section of the lumber in a mechanical experimental machine (INSTRON 5582, America) until they were compressed with crush. At the same time, the curve of Load-Displacement was recorded when the finger joints were loaded.
Fifty-four finger-jointed lumbers were manufactured in the finger jointing machine (FJ-500OA-2, Japan). Each fitness lever was represented by 18 finger-jointed lumbers. The end pressure applied on the finger joints was determined by the end pressure test experiment. The pressure was kept for 5–10 s and then the finger-jointed lumbers were kept in room temperature for at least 48 h to let the glue cure completely. All finger-jointed lumbers were tested for modulus of elasticity in static bending (modulus of elasticity, MOE; n = 18) and bending strength (n = 18). Analysis of variance (ANOVA) was performed to compare the means of each test (P < 0.05).
The lumber was assumed to be an orthotropic, linear elastic and nonlinear elastoplastic material having the following engineering constants. The constants and yield stress were shown in Table 2 and Table 3. The data input for the glue and gaskets (Zheng et al., 2004; Li 2009; He et al., 2012) were listed in Table 4.
| Elastic constant | Value | Elastic constant | Value |
| ELμ(MPa) | 9171 | ERμ(MPa) | 831.6 |
| μLR | 0.472 | μRT | 0.765 |
| μLT | 0.558 | μRL | 0.053 |
| ET (MPa) | 460.4 | GRT(MPa) | 44.48 |
| μTR | 0.337 | GLT(MPa) | 521.7 |
| μTL | 0.033 | GLR(MPa) | 666.7 |
| Notes: EL, ET, ER represent modulus of elastic in longitudinal, tangen-tial and radial direction, respectively; μLR, μLT, μTR, μTL, μRT, μRL rep-resent the poisson ratio in section of longitudinal-radial, longitudinal-tangential, tangential- radial, tangential-longitudinal, radial-tangential and radial-longitudinal, respectively; GRT, GLT, GLR represent shear modulus of elasticity in section of radial- tangential, longitudinal-tangential and longitudinal-tangential, respectively. | |||
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| Longitude | Radial | Tangential | |
| Tensile | 32.290 | 4.00 | 4.00 |
| Compression | 11.031 | 4.74 | 4.36 |
| Shear | 4.130 | 4.41 | 4.13 |
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| Constant for material | ||
| E (MPa) | μ | |
| Adhesive | 3000 | 0.37 |
| Gaskets | 1000 | 0.20 |
| Notes: E and represent modulus of elastic and poisson ratio of adhesive and gaskets. | ||
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The finite element method was adopted to set up the 3D models for end-pressure test, modulus of elasticity and bending strength tests. Solid 45 was chosen as the finite element type and free meshing method was used to mesh the model.
(1) FEA of end-pressure test Fig. 1 and Fig. 2 show the model created and its mesh results for the end-pressure test of finger-jointed lumber respectively. The three-dimensional displacement constraints were added to one end of the model and the pressure was applied on the other end following the load step (Fig. 3). Then the calculation was carried out in the software and the relation between the displacement and load step (the same as load) was output in the post-process part of the software.
According to the principles for finger-jointed lumber manufacturing, the end pressure applied on the finger joints should not be too large to result in the fracture of the lumber which may decrease the strength of the finger-jointed lumber. Thus the stress of the elements under pressure should not be larger than the yield stress of the lumber, and the end pressure which caused the damage of the elements was the upper limit whereas the lower limit pressure should be high enough to cause the plastic deformation ensuring the good adhesion of the finger joints.
(2) FEA of MOE Fig. 4 and Fig. 5 show the model and its mesh results for the MOE test of finger-jointed lumber respectively. After adding the appropriate displacement constraints to the model and applying the pressure on the loading gaskets following the load step (Fig. 6), the calculation was carried out in the software.
When the calculation was done, the modelling results was checked and the node which exhibited the largest deformation along the loading direction was found out. Then the displacement-load curve for the node was output and a record of the displacement was kept when the load increases from the lower limit to upper limit. The MOE of the finger-jointed lumber can be calculated according to Eq. (1).
| $$ E = \frac{{23P{l^3}}}{{108b{h^3}f}} $$ | (1) |
where E is the MOE of finger jointed lumber (MPa); P is the load difference between the upper limit and lower limit (N); l is the span length (mm); b is the width of the specimen (mm); h is the height of the specimen (mm); and f is the deformation of specimen when the load increases from the lower limit to upper limit (mm).
(3) FEA of bending strength Fig. 7 and Fig. 8 show the model and its mesh results for the bending strength (MOR) test of finger-jointed lumber respectively. The appropriate constraints were added to the model and the pressure was applied on the loading gasket follow the load step which was shown in Fig. 9. Then the calculation was carried out in the software and the relationship between the displacement and load step (the same as load) was output in the post-process part of the software.
After the calculation was done, the modelling result was checked and the node which exhibited the stress exceed the yield stress of the lumber was found out. Then the displacement-load curve was output for the node and a record of the pressure was kept when the deformation reached the highest value. The MOR of the finger-jointed lumber can be calculated according to Eq. (2).
| $$ \sigma = \frac{{3{P_{{\text{max}}}}l}}{{2b{h^2}}} $$ | (2) |
where σ is the MOR of finger jointed lumber (MPa); Pmax is the ultimate bending load (N); l is the span length (mm); b is the width of the specimen (mm); and h is the height of the specimen (mm).
When load was applied on the end of finger joints, the stress was mainly concentrated on the top of the finger joints according to the modelling results. With the increase of pressure, elastic deformation first developed. When the stress exceeded the elastic limited stress, the plastic deformation then developed. After the stress exceeded the yield stress of the lumber, it indicated that the collapse happened in the finger joints which would affect the ultimate strength of the finger-jointed lumber.
The appropriate end-pressure for finger-jointed lumber manufacturing is between the value which causes the plastic deformation and failure of the finger joints. Fig. 10 shows the modelling results and experimental results of end pressure test for finger joints at three different fitness levers (0 mm; 0.1 mm; 0.3 mm). From the modelling results, it could be concluded that the end pressure range were 1.5–3.0 MPa, 2.0–3.5 MPa and 2.5–4.5 MPa for fitness 0 mm, 0.1 mm and 0.3 mm, respectively.
The modelling results showed some discrepancies when compared with the experimental results. Firstly, the node developed elastic deformation when end pressure was low in the modelling process. While the displacement increased fast with the increase of pressure in the experimental process because two finger joints could not fit seamlessly which caused a process that two finger joints fit together (the gap between them eliminated gradually under low end pressure). The difference was shown in the initial part of the pressure-displacement curves of modelling and experimental results. Secondly, as Table 5 shown, both the lower limit (Pmin) and upper limit (Pmax) of end pressure in modelling tests were lower than those in the experimental test results, extremely for Pmax. It was mainly caused by the different ways of judging the failure of finger joints under pressure. In the experimental tests, Pmax of end pressure was set as the macroscopic crack developed in the finger joints, whereas the failure was accounted as the stress on one node of exceeded the yield stress in the modelling process; when one node of the model reached the failure, the others were still in good state. Thus, it is reasonable that the end pressure was smaller in the FEA than that in experimental test results.
| Fitness (mm) | Experimental result (MPa) | Modelling result (MPa) | |||
| Pmin | Pmax | Pmin | Pmax | ||
| 0 | 2.6 | 5.8 | 1.5 | 3.0 | |
| 0.1 | – | 5.9 | 2.0 | 3.5 | |
| 0.3 | 2.6 | 5.3 | 2.5 | 4.5 | |
| Average | 2.6 | 5.7 | 2.0 | 3.7 | |
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As the appropriate end pressure range was determined through experimental and modelling tests, three levels of the end pressure (2.6 MPa; 3.5 MPa; 4.4 MPa) were selected in an experiment conducted to find the optimum end pressure for P. Sylvistriv var. finger-jointed lumber. The experiment test results showed that finger-jointed lumber was manufactured when end pressure was 3.5 MPa, exhibiting the highest mechanical strength compared with other two levels of end pressure (He,2011; He et al., 2012). It was close to Pmax of the modelling test results. So, it can be concluded that the optimum end pressure for finger- jointed lumber manufacturing could be found through the FEA process.
Under low pressure, the stresses spread on the finger-jointed lumber were quite uniform. In the direction along the load, elements exhibited the largest deformation. Fig. 11 shows the relationship between the displacement and time (the same as load) of the node which developed the largest deformation. According to the Chinese National Standard for testing the MOE of wood, the deformation taken in the calculation of MOE should be the increment when the load increases from 300 N to 700 N. It can be drawn from the Fig. 11 that when fitness is 0 mm, the corresponding deformation is 0.45 mm, whereas the deformation are 0.40 mm and 0.44 mm when fitness is 0.1 mm and 0.3 mm, respectively. Thus, the MOE for finger-jointed lumber of three different fitness are 16.36 GPa, 18.40 GPa and 16.73 GPa, respectively.
As shown in Table 6, the modelling test results for the MOE were over 20% higher than the experimental test results under three different fitness levels. The error might comprise of two parts. First, knots, rot, oblique grain and other flaws weaken the strength of the timber which resulted in strength decrease of finger-jointed lumber (Xu, 2000). However, in the modelling process, lumbers were regarded as a cylinder symmetry and orthotropic material without taking the defects of lumber into account. The parameters input in the modelling process were measured using flawless specimens. Therefore, it is possible to cause the difference between these two testing methods. In addition, the other cause of the error could be the manufacturing deficiencies such as the broken of the finger joints, the impurity of the glue mixed with sawdust, which affected the strength of the finger-jointed lumber greatly (Liu, 1995). However, these factors were neglected in the modelling process.
| Fitness (mm) | Experimental result (GPa) | Modelling result (GPa) | Error (%) |
| 0 | 13.42 | 16.36 | 21.9 |
| 0.1 | 14.40 | 18.40 | 27.8 |
| 0.3 | 13.19 | 16.73 | 26.8 |
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As both the experimental and modelling results shown, when fitness was 0.1 mm the MOE of finger-jointed lumber exhibited the highest value whereas for fitness 0 mm and 0.3 mm, the MOE did not show significant difference. The filling of adhesive in the tip top would definitely increase the strength of finger-jointed lumber, thus it was natural that the MOE for fitness 0.1 mm was higher than the lumber of fitness 0 mm. However, with the increase of fitness, the length of finger joints decreased which resulted in the decrease of bond area. As the results for scarf joint shown, the increase of bond area would make the joints withstand higher load, namely increased the strength of the joints, including the MOE. So, it was reasonable that the MOE for lumbers of fitness 0.3 mm were lower than that of fitness 0.1 mm. The combined effects of filling of adhesive and the length of finger joints resulted in the insignificant difference for lumbers of fitness 0 mm and 0.3 mm.
With the increase of pressure, the deformation of the finger-jointed lumber along the direction of the load increased until the stress in the finger joints reached the yield stress. When the node reached failure, the load (corresponding to load step) was the ultimate load of bending for finger joints. Fig. 12 showed the relationship between displacement and time (load step) for node which reached the yield stress. The ultimate load of bending under three different fitness levels for finger-jointed lumbers were 2600 N, 2400 N and 1500 N, respectively shown in the figure. Thus, the corresponding bending strength were 78.0 MPa, 72.0 MPa and 45.0 MPa.
Compared with the experimental results, the modelling results showed some discrepancies in Table 7, especially for lumbers manufactured when fitness was 0.3 mm (35.3%). The lumbers of fitness 0.1 mm exhibited the highest value for the MOR while the corresponding value for fitness 0 mm and 0.3 mm almost at the same level in the experimental results. However, the MOR for fitness 0 mm showed the highest value in modelling result, fitness 0.1 mm followed, and the lowest was the lumbers of fitness 0.3 mm.
| Fitness (mm) | Experimental result (MPa) | Modelling result (MPa) | Error (%) |
| 0 | 68.4 | 78.0 | 14.0 |
| 0.1 | 75.9 | 72.0 | –5.1 |
| 0.3 | 69.6 | 45.0 | –35.3 |
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Same as the explanation for results of the MOE, the filling of adhesive in tip top would increase the strength which made the MOR for lumbers of fitness 0.1 mm higher than that of fitness 0 mm; but when the fitness was too high (0.3 mm), the length of finger joints decreased. It would affect the strength of finger joints to a large extend. Also, the filling of adhesive in large tip top gap would decrease the strength as bond area between adhesive and the lumber would develop the concentration of stress because adhesive had different prosperities compared with wood, thus the MOR for lumber of fitness 0.3 mm was lower than that of fitness 0.1 mm.
The modelling process is different from the actual condition in experimental process to a certain extent. The finger joints would have some plastic deformation when load with end pressure in finger-jointed lumber manufacturing process. This phenomenon would cause the decrease of the fitness and lengthen the finger joints which was helpful for guaranteeing the strength of the finger-jointed lumber. But in the modelling process, the effect of the factor was neglected. Therefore, it could be seen that the modelling results for fitness 0.1 mm and 0.3 mm were lower than the experimental results. For lumbers of fitness 0 mm, the compression under end pressure would cause some damage to the finger joints as there were no tip top gaps between two finger joints, and then it would decrease the strength of the finger-jointed lumber. This was not taken into account in the modelling process, so the modelling results were higher than experimental results in such condition.
The experimental end pressure tests showed a narrower range compared with the finite element modelling results. This was mainly caused by the different ways of failure judging of finger joints. In the experimental tests, the upper limit of end pressure was set as the macroscopic cracking developed in the finger joints; whereas the failure was accounted as the stress on one node which exceeded the yield stress in the modelling process. Moreover, the upper limit from modelling results was close to the optimum end pressure for finger-jointed lumber manufacturing which was obtained from experimental test. It was indicated that the FEA could be used in the prediction of the end pressure for finger-jointed lumber.
The modelling results for the MOE test of finger-jointed lumber were about 20% higher than experimental results. The error may result from the neglection of the natural flaws existed in lumbers and the manufacturing deficiencies when conducting the modelling process. Besides, the modelling results showed the same variation tendency for the MOE of finger-jointed lumber under three different fitness levels. Thus, the conclusion could be made that the FEA was a feasible way for predicting the MOE of finger-jointed lumber if the errors could be avoided properly.
The modelling results for the MOR test of finger-jointed lumber also showed some discrepancies compared with the experimental test results. The plastic deformation developed from the load of end pressure in finger-jointed lumber manufacturing process caused the decrease of the fitness and lengthened the finger joints which was helpful for guaranteeing the strength of the finger-jointed lumber. But in the modelling process, the effect of the factor was neglected. Also, the damage of the finger joints under end pressure when fitness was 0 mm which was not taken into account in the modelling process resulted in the different trend between experimental and modelling results of the MOR for finger-jointed lumber under three fitness levels.
In order to realize the predicting of the properties of finger-jointed lumbers, some modifications such as proper element type and element mesh method chosen should be made for the models. Further studies should be done to investigate the ways to improve the simulate accuracy in the modelling processes.
The work is supported by National Key Research & Development Program of China (No. 2016YFD0600904); Integration and Demonstration of the Value-added & Efficiency-increased Technology across the Industry Chain for Bamboo.
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| 3. | Rodríguez-Grau, G., Cordonnier, P.-L., Navarrete, B. et al. The Adhesion Performance in Green-Glued Finger Joints Using Different Wood Ring Orientations. Sustainability (Switzerland), 2024, 16(16): 7158. doi:10.3390/su16167158 | |
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Figures(12) / Tables(7)
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Supported by: Beijing Renhe Information Technology Co. Ltd support: info@rhhz.net
Sheng He, Lanying Lin, Zaixing Wu, Zhangmin Chen. Application of Finite Element Analysis in Properties Test of Finger-jointed Lumber[J]. Journal of Bioresources and Bioproducts, 2020, 5(2): 124-133. doi: 10.1016/j.jobab.2020.04.006
| Fitness (mm) | Length of finger (mm) | Tip thickness (mm) | Pitch (mm) | Slope |
| 0 | 25.0 | 1.2 | 8.2 | 1/8.6 |
| 0.1 | 23.7 | 1.3 | 8.2 | 1/8.6 |
| 0.3 | 21.0 | 1.5 | 8.2 | 1/8.6 |
DownLoad:
CSV
| Elastic constant | Value | Elastic constant | Value |
| ELμ(MPa) | 9171 | ERμ(MPa) | 831.6 |
| μLR | 0.472 | μRT | 0.765 |
| μLT | 0.558 | μRL | 0.053 |
| ET (MPa) | 460.4 | GRT(MPa) | 44.48 |
| μTR | 0.337 | GLT(MPa) | 521.7 |
| μTL | 0.033 | GLR(MPa) | 666.7 |
| Notes: EL, ET, ER represent modulus of elastic in longitudinal, tangen-tial and radial direction, respectively; μLR, μLT, μTR, μTL, μRT, μRL rep-resent the poisson ratio in section of longitudinal-radial, longitudinal-tangential, tangential- radial, tangential-longitudinal, radial-tangential and radial-longitudinal, respectively; GRT, GLT, GLR represent shear modulus of elasticity in section of radial- tangential, longitudinal-tangential and longitudinal-tangential, respectively. | |||
DownLoad:
CSV
| Longitude | Radial | Tangential | |
| Tensile | 32.290 | 4.00 | 4.00 |
| Compression | 11.031 | 4.74 | 4.36 |
| Shear | 4.130 | 4.41 | 4.13 |
DownLoad:
CSV
| Constant for material | ||
| E (MPa) | μ | |
| Adhesive | 3000 | 0.37 |
| Gaskets | 1000 | 0.20 |
| Notes: E and represent modulus of elastic and poisson ratio of adhesive and gaskets. | ||
DownLoad:
CSV
| Fitness (mm) | Experimental result (MPa) | Modelling result (MPa) | |||
| Pmin | Pmax | Pmin | Pmax | ||
| 0 | 2.6 | 5.8 | 1.5 | 3.0 | |
| 0.1 | – | 5.9 | 2.0 | 3.5 | |
| 0.3 | 2.6 | 5.3 | 2.5 | 4.5 | |
| Average | 2.6 | 5.7 | 2.0 | 3.7 | |
DownLoad:
CSV
| Fitness (mm) | Experimental result (GPa) | Modelling result (GPa) | Error (%) |
| 0 | 13.42 | 16.36 | 21.9 |
| 0.1 | 14.40 | 18.40 | 27.8 |
| 0.3 | 13.19 | 16.73 | 26.8 |
DownLoad:
CSV
| Fitness (mm) | Experimental result (MPa) | Modelling result (MPa) | Error (%) |
| 0 | 68.4 | 78.0 | 14.0 |
| 0.1 | 75.9 | 72.0 | –5.1 |
| 0.3 | 69.6 | 45.0 | –35.3 |
DownLoad:
CSV
| Fitness (mm) | Length of finger (mm) | Tip thickness (mm) | Pitch (mm) | Slope |
| 0 | 25.0 | 1.2 | 8.2 | 1/8.6 |
| 0.1 | 23.7 | 1.3 | 8.2 | 1/8.6 |
| 0.3 | 21.0 | 1.5 | 8.2 | 1/8.6 |
| Elastic constant | Value | Elastic constant | Value |
| ELμ(MPa) | 9171 | ERμ(MPa) | 831.6 |
| μLR | 0.472 | μRT | 0.765 |
| μLT | 0.558 | μRL | 0.053 |
| ET (MPa) | 460.4 | GRT(MPa) | 44.48 |
| μTR | 0.337 | GLT(MPa) | 521.7 |
| μTL | 0.033 | GLR(MPa) | 666.7 |
| Notes: EL, ET, ER represent modulus of elastic in longitudinal, tangen-tial and radial direction, respectively; μLR, μLT, μTR, μTL, μRT, μRL rep-resent the poisson ratio in section of longitudinal-radial, longitudinal-tangential, tangential- radial, tangential-longitudinal, radial-tangential and radial-longitudinal, respectively; GRT, GLT, GLR represent shear modulus of elasticity in section of radial- tangential, longitudinal-tangential and longitudinal-tangential, respectively. | |||
| Longitude | Radial | Tangential | |
| Tensile | 32.290 | 4.00 | 4.00 |
| Compression | 11.031 | 4.74 | 4.36 |
| Shear | 4.130 | 4.41 | 4.13 |
| Constant for material | ||
| E (MPa) | μ | |
| Adhesive | 3000 | 0.37 |
| Gaskets | 1000 | 0.20 |
| Notes: E and represent modulus of elastic and poisson ratio of adhesive and gaskets. | ||
| Fitness (mm) | Experimental result (MPa) | Modelling result (MPa) | |||
| Pmin | Pmax | Pmin | Pmax | ||
| 0 | 2.6 | 5.8 | 1.5 | 3.0 | |
| 0.1 | – | 5.9 | 2.0 | 3.5 | |
| 0.3 | 2.6 | 5.3 | 2.5 | 4.5 | |
| Average | 2.6 | 5.7 | 2.0 | 3.7 | |
| Fitness (mm) | Experimental result (GPa) | Modelling result (GPa) | Error (%) |
| 0 | 13.42 | 16.36 | 21.9 |
| 0.1 | 14.40 | 18.40 | 27.8 |
| 0.3 | 13.19 | 16.73 | 26.8 |
| Fitness (mm) | Experimental result (MPa) | Modelling result (MPa) | Error (%) |
| 0 | 68.4 | 78.0 | 14.0 |
| 0.1 | 75.9 | 72.0 | –5.1 |
| 0.3 | 69.6 | 45.0 | –35.3 |
DownLoad:
