Bolted connection modeling and validation through lar-aided testing
Kaoshan Dai*a, Changqing Gong b, and Benjamin Smith c
a College of Civil Engineering, Tongji University, and State Key La
b of Power Transmission
Equipment & System Security and New Technology, Chongqing University; 1239 Siping Rd,
Shanghai, China 200092;
b College of Civil Engineering, Tongji University, 1239 Siping Rd, Shanghai, China 200092;
c Department of Civil & Environmental Engineering, University of North Carolina, Charlotte, 9201
University City Blvd., Charlotte, NC, USA 28223
ABSTRACT
Bolted connections are widely employed in facility structures, such as light masts, transmission poles,
and wind turbine towers. The complex connection behavior plays a significant role in the overall dynamic characteristics of a structure. A finite element (FE) modeling study of a bolt-connected square tubular steel beam is prented in this paper. Modal testing was performed in a controlled laboratory condition to validate the FE model, developed for the bolted beam. Two lar Doppler vibrometers were ud simultaneously to measure structural vibration. A simplified joint model was propod to further save computation time for structures with bolted connections. This study is an on-going effort to marshal knowledge associated with detecting damage on facility structures with bolted connections.
Keywords: bolted connection, finite element modeling, modal testing, lar Doppler vibrometer, model validation
1. INTRODUCTION
Bolted joints are widely ud as structural connections. Tubular steel towers in wind energy industry, for instance, are usually constructed with veral truncated cone ctions connected by bolted flanges. However, behaviors of bolted connections have not been well understood and they are simplified into rigid components in the conventional design and analysis of steel structures [1]. Som
e study concludes that this simplification overestimates stiffness of a structure [2]. Structural behaviors of bolted flange joints are affected by various factors, such as physical characteristics of bolt as well as member plate, contact surface friction, bolt-hole clearance, and clamp-up force [3]. It is a difficult task to accurately model the bolt-connected joints to include all the features. Several different techniques have been developed for finite element (FE) modeling of bolted joints. Modeling the joint through 3D solid elements, as one of the methods, can simulate bolted connection behaviors more precily [4-9]. Although 3D modeling can prent bolted joint accurately, it is computationally expensive for large structures. Various approaches, therefore, have been propod to simplify joint modeling in order to save computing time and enhance analyzing efficiency. For instance, shell elements and beam elements were ud in some modeling work [10]. The couple bolt model and the contact bolt model were developed by Pu et al. (2009) [11] to simplify joint modeling for modal analysis. Luan et al. (2012) [12] propod a simplified dynamic model with bilinear springs to simulate bolted flange joints of pipe structures and this model can reveal both longitudinal vibration and transver vibration in detail. To study global vibration of structures with L-shaped beams and bolted joints, simplified models and model updating techniques were developed by He and Zhu [13]. It is, therefore, indicated from existing rearch that reasonable simplifications are mostly esntial in dynamic study of a large-scale structure with bolted connections.
To investigate the feasibility of developing a vibration-bad damage detection technique for facility structures such as wind turbine towers, modeling bolt-connected square tubular steel beam structures was performed. Both 3D solid FE
*kdai@; phone: 86-21-65985374; fax: 86-21-65982668.
Nondestructive Characterization for Composite Materials, Aerospace Engineering, Civil Infrastructure, and Homeland Security 2013, edited by Tzu Yang Yu, Andrew L. Gyekenyesi, Peter J. Shull, Aaron A. Diaz, H. Felix Wu, Proc. of SPIE Vol. 8694, 869424 · © 2013 SPIE · CCC code: 0277-786X/13/$18 · doi: 10.1117/12.2009466
models and the model constructed with beam elements were developed and compared. Modal testing was conducted in laboratory with the aid of a single point lar Doppler vibrometer and a scanning lar Doppler vibrometer. With experimental data available, model updating was implemented for both the single beam ction modeling and two-beam-asmbling connected with bolts; and therefore, the FE models were validated and updated. A simplified model that can reflect the rotational behavior of a bolted joint in dynamic analysis of beams with bolt-flange connections under small deformation condition was developed in this study. Comparison between the propod model and the validated FE analysis confirms the effectiveness of the propod method.
2. FINITE ELEMENT MODELING
A single square tubular steel beam ction was first modeled. The beam geometry information is shown in Figure 1. The 3D FE model of the single beam with flanges, shown in Figure 2, was established under the ANSYS environment by using the solid element SOLID45 provided by the software (Model A). This 3D model constructed in ANSYS was exported into ABAQUS. Then two single beam ctions were asmbled with the bolts developed directly in ABAQUS by using the C3D8I element (Figure 3) (Model B). The surface-to-surface contact was considered in the two-beam asmbled model between the bolt nut/head surface and the contacted flange as well as two contact flanges. Limited slippage was t but contact surface friction was neglected. The FE model of the single beam was also developed in ANSYS by using the high-order beam element (BEAM188) (Model C); while the two-beam asmbling was constructed with beam elements (BEAM188), spring elements (COMBIN14) and mass elements (MASS21). The bolted joint, in this type of model (Model D), was simplified into a rotational spring and the end flange of the beam was modeled with a structural mass (MASS21). Although tension, shear and rotation stiffness exists for a bolted connection, rotation contribution dominates in bending. Studies also show that bolt preloading has little influence on modal behaviors of bolt-connected structures [14, 15] becau the conventional m
odal analysis is a linear dynamic analysis. The joint clamp-up force was not modeled in modal analys performed in this study. Table 1 listed the FE models.
Table 1 FE models and application cas
FE model Development method Application ca
Model B 3D solid FE model of the two-beam asmbling developed in ABAQUS Static loading analysis of the bolted beam
Model C FE model of the single beam constructed with beam elements in
ANSYS
Single beam modal analysis Model D FE model of the two-beam asmbling developed with beam
elements and spring elements in ANSYS
Modal analysis of the bolted beam
Figure 1 A square tubular steel beam
Figure 2 FE model of the single beam with flanges in ANSYS (Model A)
Figure 3 FE model of two-beam connected with bolt-flange joint in ABAQUS (Model B)
3. TEST PROGRAM
Modal testing was conducted in laboratory on both the single beam and the asmbled beam under a suspension condition in order to validate and update the FE models developed in the previous ction. Test t-ups are shown in Figure 4. The experimental program was designed for the two-beam asmbling with the bolts being t to two states: tight and loo. During testing, the suspended structure was excited by a shaker with a frequency sweep mode (10 Hz to 2000 Hz). Two lar Doppler vibrometers, a single point lar (PDV-100) and a scanning lar (PSV-400), were ud for measurement: the PDV-100 was pointed at a fixed location on the structure as a reference while the PSV-400 scanned the entire structure to obtain vibration frequencies and mode shapes (Figure 4). A total of 93 points were scanned for the single beam and 99 points were scanned for the bolted beam. Testing results from the single beam were ud to update the steel material properties; while the modal information from the two-beam asmbling was ud to identify the rotation spring stiffness of the joint. Test results are listed in Table 3.
Figure 4 Modal testing t-ups
4. FE MODEL VALIDATION AND UPDATING
The original FE models (Model A-D) were developed with estimated steel material properties; and spring rotation stiffness was also arbitrarily t in Model D. Modal testing results were therefore ud to validate and update the original FE models. Model updating is an optimization process and it is usually performed by iteratively tuning lected parameters so that correlation between FE simulation and target values improves. The difference between the simulation result and the target value needs to be controlled to a specified level before this optimization iteration can stop. With natural frequencies from simulation (i f ) and testing (e i f ) available, model updating is to minimize the error between two natural frequencies (Equation (1)). The correlation of mode shapes between FE analysis and testing results are often evaluated through the Modal Assurance Criterion (MAC), as shown in Equation (2). It is indicative that optimization goes toward the right direction to reduce the mode shape difference between FE analysis and testing if the MAC value approaches to 1.
%e
i i i e
i f f ER f −= (1) in which,ER reprents the difference between simulation and measurement; and 1,2,3i =⋅⋅⋅.
()()()2
T e
i i i T eT e i i i i MAC φφφφφφ= (2)
where φis the mode shape vector from FE analysis; e φis the mode shape vector obtained from experiment; and 1,2,3i =⋅⋅⋅.
Natural frequency and mode shape results from modal testing of a single beam were ud as target values for updating Young's modulus and density of steel beams. Optimization was completed by following the first order optimization method with the algorithm built in ANSYS [16]. Table 2 provides natural frequencies from testing and simulation with different FE models as well as updating results. The MAC values after such an optimization are shown in Figure 5 with mode shapes of the single be
am from both Model A and Model C. It is found that the frequency difference increas and the MAC value decreas at a higher order vibration mode, which is indicative that that the updating becomes harder to converge for higher order modes. It is obvious from the final results shown in Table 2 and Figure 5 that both updated Model A and updated Model C yield modal parameters clo to the experimental results. The maximum frequency difference is 1.57% for the updated Model A and 4.18% for the updated Model C, respectively; and the minimum MAC value is 98% and 96% for the two updated models, respectively. Therefore, the model developed with beam elements was validated for vibration analysis with an acceptable accuracy but a great computation saving. The steel modulus of elasticity and density for the square tubular beam before and after the updating were listed in Table 3. In the following analys of the bolted beam, the Young's modulus and density obtained from updating this single beam were ud to reduce the uncertain parameters during two-beam asmbling modeling.
Table 2 Model updating bad on natural frequency (unit: Hz)
Mode Testing Initial Model A Updated Model A Initial Model C Updated Model C Frequency Frequency ER Frequency ER Frequency ER Frequency ER
1st 207.5 215.06 3.64% 206.65 -0.41% 213.15 2.72% 207.5 0.00% 2nd 613.75 638.12 3.97% 613.18 -0.09% 641.59 4.54% 617.4 0.59% 3rd 1205.63 1262.4 4.71% 1213 0.61% 1274.1 5.68% 1232 2.19% 4th 1908.13 2017 5.71% 1938.1 1.57% 2067.4 8.35% 1987.8 4.18%
Table 3 Steel modulus of elasticity and density of the beam
Material parameter Original estimation Updated value Difference
Young's modulus 2.06×1011 N/mm 2 1.93×1011 N/mm 2 -6.45% Density 7800 kg/m 3 7902.4 kg/m 3 1.31 %
Figure 5 Mode shapes and MAC values of the updated modes: (a) Model A, (b) Model C.
Model updating was then implemented for Model D with the spring rational stiffness as the variable since material information was validated during the single beam updating. Natural frequencies from the testing and the updated model D are listed in Table 4 with the corresponding MAC values for each mode. From the table, it is en that the updated model can yield relative accurate vibrational parameters for the two-beam asmbled with a bolt-connected joint. Through this updating process, the rotational rigidity for the bolted joint was identified as 1.5×105 N/mm2.
Table 4 Model D updating results
Mode Frequency from
testing Frequency from the
updated Model D
Frequency
difference
MAC value
2nd 174.38 Hz 169.72 Hz -2.67% 97%
3rd 274.38 Hz 277.95 Hz 1.3% 98%
4th 571.25 Hz 574.33 Hz 0.54% 98%
5. A SIMPLIFIED JOINT MODEL
To further simplify the bolted joint connection, a nonlinear static loading analysis was conducted by using Model B. With the application of 0.1 N clamp loading at each bolt, the flanges were deformed as shown in Figure 6. It is obrved that the flange deforms to create a small gap at both the center and the edge of the flange. This deformation feature indicates that the components between the bolt and flange edge contribute little to joint stiffness. Therefore, the bolted flange was simplified into a beam model with the bolt as the support (Figure 7). The rotational stiffness of simplified model is compod of bolt stiffness and flange stiffness; the tubular beam contribution was ignored in flange stiffness computation. From Figure 7, the joint stiffness can be obtained from Equations (3)-(5). With geometrical information (Figure 1) and Young's modulus 1.93×1011 N/mm2 from the model updating
study in ction 4, the joint stiffness was calculated to be 1.36 ×105 N/mm2 bad on Equation (3)-Equation (5), which is only 9.34% difference from the rotational stiffness identified from the bolted beam FE model updating (1.5×105 N/mm2). However, the simplified model improves the efficiency of bolted joint modeling by avoiding going through model updating process as that for Model D. With the rotational stiffness of 1.36 ×105 N/mm2 estimated directly bad on the propod simplified model, a FE model similar to Model D was developed and modal analysis was conducted. It is shown in Table 5 that the numerical analysis results are clo to the testing results, which confirms the validity of the simplified bolted flange joint model.
