Abdelaziz Bazoune

A finite beam element for vibration analysis of rotating tapered timoshenko beams

A finite beam element for vibration analysis of a rotating tapered beam including shear deformations and rotary inertia is derived in this paper. The finite element has four degrees of freedom, and accounts for linear tapering in two planes. This formulation permits any combination of taper ratios as well as unequal element lengths. Explicit expressions for the finite element mass and stiffness matrices are derived using the consistent mass approach, while accounting for the centrifugal stiffness effects. The generalized eigenvalue problem is defined and numerical solutions are generated for a wide range of rotational speed and taper ratios. Results obtained include the first ten free vibrational modes for both fixed and hinged end conditions. Comparisons are made whenever possible with exact solutions and with numerical results available in the literature. The results display high accuracy when compared with other numerical results.

Dynamic response of spinning tapered Timoshenko beams using modal reduction

A method for dynamic response analysis of spinning tapered Timoshenko beams utilizing the finite element method is developed. The equations of motion are derived to include the effects of Coriolis forces, shear deformation, rotary inertia, hub radius, taper ratios and angular setting of the beam. Modal transformations from the space of nodal coordinates to the space of modal coordinates are invoked to alleviate the problem of large dimensionality resulting from the finite element discretization. Both planar and complex modal transformations are presented and applied. The reduced order modal form of equations of motion is computer generated, integrated forward in time, and the system dynamic response is evaluated. Numerical results and comparisons with the full order model (FOM) are presented to demonstrate the accuracy of the reduced order model (ROM).

Effect of Tapering on Natural Frequencies of Rotating Beams

The problem of free vibration of a rotating tapered beam is investigated by developing explicit expressions for the mass, elastic and centrifugal stiffness matrices in terms of the taper ratios. This investigation takes into account the effect of tapering in two planes, the effect of hub radius as well as the stiffening effect of rotation. The equations of motion are derived; the associated generalized eigenvalue problem is defined in conjunction with a suitable Lagrangian form and solved for a wide range of parameter changes. The effect of tapering on the natural frequencies of the beam is examined with all parameter changes present. Results are compared with those available in literature and are found to be in excellent agreement.

Survey on modal frequencies of centrifugally stiffened beams

This survey is concerned with the problem of determining the dynamic modal characteristics (natural frequencies and associated mode shapes) of rotating beams. Modal characteristics are of paramount importance to the design and performance evaluation of rotating beams, and have been the subject of interest to many investigators. Accurate prediction of the dynamic characteristics of such structures is necessary in the early stages of the design process in order to avoid any possible conditions susceptible to resonance within the range of operating speed, and to prevent any failure that may occur because of sustained vibration at or near the resonant frequency range. While developing beam models, various parameters pertinent to the functional requirements were added in order to cope with aerodynamic issues as well as technical and economical issues. With all parameters present in the model, solving the problem becomes extremely complicated. An exact solution is almost impossible. Many simplified mathematical models with a variety of geometries and properties have been developed in the literature to investigate the dynamic characteristics of such rotating beams using a variety of methods.

Experimental and Finite Element Modeling of Friction Stir Seal Welding of Tube-Tubesheet Joint

Tube-tubesheet joints are critical in some applications, where contact between shell and tube side fluids is not tolerable. To ensure joint tightness, standards (ASME and TEMA) recommend performing a combination of rolling-or expansion of tube-tubesheet and seal welding. Available techniques for seal welding are based on fusion welding that sometimes results in a number of defects such as cracking and porosity formation, and such defects may take a newly fabricated heat exchanger out of service. In this work, friction stir welding (FSW) was used for tube-tubesheet seal joint and simulated using a 3D thermo-mechanical finite element model (FEM). The model was analyzed using a commercial finite element (FE) package. The model included the thermal effect of the tool workpiece interaction along with axial load, ignoring the metal flow around the tool. The material model took into account temperature dependency of thermal and mechanical properties. The model objectives were to evaluate the temperature distribution and residual stress in the workpiece resulting from the thermal cycle and axial load during welding for various process parameters, and to study how residual stresses in adjacent roller expanded tubes are affected during welding. The FE results show that the maximum temperature at the welding zone does not exceed the solidus temperature (except at high tool rotational speeds); the process can thus be classified as cold working. Moreover, adjacent tubes temperature does not exceed the annealing temperature. An experimental setup was designed and manufactured to show the feasibility of the process in this constrained size joints and to validate the numerical results. A test cell and a special FSW tool were designed and manufactured for this purpose. Many tests were performed with welding quality depending on process parameters.

Effect of pin tool profile on mechanical and metallurgical properties in friction stir spot welding of pure copper

In this paper, the influence of thread feature on mechanical and metallurgical properties of friction stir spot weldments is studied. Two pin tools, plain cylindrical and threaded cylindrical, having the same size are used to produce lap joints by friction stir spot welding (FSSW) of commercially pure copper. All experiments have been performed under the same welding parameters. The results revealed that joints produced with threaded pin tool have more than double the tensile shear strength of those produced by plain cylindrical pin. Moreover, the samples that were FSS welded with threaded pin tool failed in a plug failure mode, which is a desirable ductile failure mode. On the other hand, the weldments that were produced using plain cylindrical pin tool failed in interfacial failure mode or shear fracture mode. Effective upper sheet thickness analysis showed upward hook formation and less effective upper sheet thickness, which indicate better material mixing in the case of threaded pin tool. Furthermore, the transition bonding region was found to be very narrow in the case of plain tool while that of the threaded pin tool showed a transition region that is almost equal to complete bonding region, indicating gradual change from unbonded to complete bond; resulting in the above observed higher strength. Scanning electron microscopy analysis of the hook formation region revealed that, contrary to the weldments performed by plain pin tool, which showed the presence of large voids around the hook region, weldments performed with threaded pins were free of defects.

Microstructure and Hardness of Friction Stir Weld Bead on Steel Plate Using W-25%Re Pin Tool

One of the challenges that impede the use of the relatively new friction stir welding (FSW) process in joining steels and high temperature alloys, as well as dissimilar materials, is the development of the right pin tool material that can stand the severe welding conditions of these alloys. Recent developments in FSW tool materials include tungsten rhenium (W-Re) alloys. The ductile to brittle transition temperature of pure tungsten is reduced by the addition of rhenium (Re).. The addition of Re also improve fracture toughness of the alloy. The major focus of this paper is studying the process of making a friction stir welding bead on mild steel using a proprietary W-25%Re alloy pin tool and investigating the effects of process parameters (i.e. tool rotational and welding speeds) on microstructure, microhardness as well as tool reaction loads. Grain refining of the steel microstructure was observed in all beads. Certain process conditions produced a bead with needle like microstructure with the highest values of hardness. Reaction forces were found to increase with the increase in the tool welding speed and to decrease with the increase of the tool rotational speed. Although the spectroscopic analysis of the beads confirmed the diffusion wear of the tool, the overall tool has shown excellent resistance to mechanical wear.Copyright

Experimental Investigation of Friction Stir Seal Welding of Tube-Tubesheet Joints

To ensure heat exchanger tube-tubesheet joints tightness, industrial standards may recommend performing a combination of roller expansion and seal welding, using conventional fusion welding processes. Solid state friction stir welding (FSW) has several advantages over the conventional fusion welding but has not yet proven its usefulness in seal and strength welding of heat exchanger tube-tubesheet joints where the available space is very limited and weld pass is of a relatively complex contour.In this work, a newly designed tool and procedure are applied to friction stir seal weld (FSSW) tube-tubesheet joints. The effects of process conditions such as welding speed and tool offset on dependent process parameters including welding loads and joint quality are investigated on a 600-series aluminum three-tube test cell.The results revealed that the quality of the seal weld of tube-tubesheet joints is affected by the preceding parameters at different levels.Copyright

Experimental and Numerical Investigations of Friction Stir Welding of Aluminum to Copper

In this paper, results of performing successful butt-welding of aluminum grade Al6061-T6 to commercial pure copper using the relatively new friction stir welding (FSW) process are presented and discussed in conjunction with finite element results. A sound weld joint between these dissimilar materials has been achieved only when the pin tool was offset a certain distance from the center of the weld line and the harder material (copper) was placed at the advancing side of the FSW tool. On the other hand, the tool offset was not required when joining the similar materials of aluminum to aluminum and of copper to copper. A combined use of temperature distribution of the aluminum to copper weld nugget determined by a finite element model, the elemental concentration of copper and aluminum in the weld nugget from EDS analysis, and aluminum-copper phase diagram have been used to identify the phases present in the different weldment zones. The aluminum-copper joint was found to consist of several single and two phase intermetallic compounds such as Al2Cu, Al4Cu9, and (Al + Al2Cu). The results revealed higher hardness values for the weld nugget compared with the two base metals.

Residual Stresses in Friction Stir Welded Tube-Tubesheet Joint

In this paper, a 3-D thermo-mechanical finite element model (FEM) is developed to simulate the process of friction stir seal welding (FSSealW) of tube-tubesheet joint, using a commercial finite element (FE) package considering temperature dependent material properties. The model is used for the prediction of temperature and stress distributions, as well as the prediction of the residual stresses in the seal welded joint, including the expanded tube and surrounding ligaments. Validation of the model is achieved using experimental temperature measurements. The FEM results are found to be in good agreement with experimental ones. Temperatures of the joint material away from the processed zone are below the annealing temperature. The calculated residual stresses are found to be compressive and help to enhance the contact stress in the tube-tubesheet joint.Copyright