Transactions of the Canadian Society for Mechanical Engineering

Volume 30 (2006), Issue 1

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This paper presents a new technique, which can apply the stress-based finite element method to Euler-Bernoulli beams. An approximated bending stress distribution is selected, and then the approximated transverse displacement is determined by twice integration. Due to the satisfaction of compatibility, the integration constants are determined by the boundary conditions related to transverse displacement and rotation. To compare with the displacement-based finite element method, this technique provides the continuities of not only transverse displacement and rotation but also stress at nodes. Besides, the boundary conditions related to stress are satisfied. Two numerical examples demonstrate the validity of this technique. The results show that the errors are smaller than those generated by the displacement-based finite element method for the same number of degrees of freedom.

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This study investigates the steady-state flow field in a circular tube filled with a viscous fluid expelled by a long gas bubble. We use a finite difference method with successive over-relaxation in the computation of the viscous flow field. An empirical bubble profile is employed to simplify the computation of the interface shape between the gas and the viscous fluid. By varying the ratio of the bubble width to the diameter of the circular tube (λ), the numerical simulation shows three fluid flow patterns: the complete bypass flow, the recirculation flow and the transient flow. The transient flow is only observed in a limited λ range of root 1/2 less than or equal λ less than or equal .7143 and isn't clearly discussed in the previous studies. The variation of vorticity also is observed by the various sizes of λ.

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A mechanism that encounters a certain changes in its topological structure during operation is called a mechanism with variable topologies (MVT). This paper is developed for the structural and motion state representations and identifications of MVTs. For representing the topological structures of MVTs, a set of methods including graph and matrix representations is proposed. For representing the motion state characteristics of MVTs, the idea of finite-state machines is employed via the state tables and state graphs. And, two new concepts, the topological homomorphism and motion homomorphism, are proposed for the identifications of structural and motion state characteristics of MVTs. The results of this work provide a logical foundation for the topological analysis and synthesis of mechanisms with variable topologies.

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An electromagnetic damper is developed to construct a tunable damped dynamic vibration absorber. The developed vibration absorber can suppress vibration of a structure subjected to a harmonic force with variable frequency. The damping of the vibration absorber can be adjusted on-line to cope with variation in the exciting frequency. The electromagnetic damper is composed of an electromagnet and a copper plate attached to the absorber mass. The relationship between the damping ratio and the damper current is discussed analytically. An experiment is conducted to determine the damping coefficients. A clamped-clamped beam is used as a primary system. The damper is connected between the absorber mass and the ground. This setup is referred to as skyhook dynamic vibration absorber in this study. The performance of a skyhook dynamic vibration absorber is compared with that of a groundhook dynamic vibration absorber where a damper is connected between the primary mass and the absorber mass. Two algorithms are proposed to tune the damper on-line. The first algorithm is FFT-based while the second one is rms-based. The control algorithms are tested against three frequency varying scenarios: multi-step change, linear change, and single-step change plus impact disturbance. Merits of each of the control algorithms are demonstrated.

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A Unified Reconfigurable Open Control Architecture (UROCA) aims at unifying the reconfiguration aspects and managing the interaction amongst the different operating levels of individual machining control systems that are likely to perform in reconfigurable manufacturing systems. The hierarchical control structure of UROCA demands the usage of a supervisory control scheme in order to manage operations of supervisory and servo controllers altogether into a reconfigurable control process. The main function of the supervisory unit is to serve as a switching/reconfiguring logic amongst different available controllers, according to need, in order to maintain motion output within the permitted limits. Due to backlash, efficiency of machine tools will be undesirably turned down causing higher vibrations, lower contouring accuracy, and may draw the whole system into instability region. A Switching control scheme designated to manage the control process where two different controllers with two different control functionalities, acting differently in two vital zones - one of them where the backlash lies, and the other when moving past the backlash - is the main topic of this paper. The proposed switching schemes emphasize a reconfiguration aspect on the control process level for machine tools as perceived, investigated and resolved by the physical and control layers located at the deliberative part of the UROCA architecture.

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The paper investigates the stability theory of a thin power law liquid film flowing down along the outside surface of a vertical cylinder. The long-wave perturbation method is employed to solve for generalized linear kinematic equations with free film interface. The normal mode approach is used to compute the stability solution for the film flow. The degree of instability in the film flow is further intensified by the lateral curvature of cylinder. This is somewhat different from that of the planar flow. The analysis results also indicate that by increasing the flow index and increasing the radius of the cylinder the film flow can become relatively more stable as traveling down along the vertical cylinder.

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A method for the determination of load and stress distributions of the instantaneously engaged teeth of cylindrical worm gears is represented in this paper. The method is based on the assumption that both the worm and gear can be modeled as a series of spur gear slices. The exact geometry and point of load application of each slice depends on its location within the mesh. By calculating the applied load and stress for each slice, the same can be determined for the entire worm gear set. The method takes into consideration tooth stiffness variation from root to tip, tooth bending deflection, local contact deformation, tooth foundation deformation and, the influence of gear parameters on load and stress. Calculated results were found to be in agreement with experimental and analytical ones obtained from literature under given operating conditions.

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Model studies of laser heating process minimize the experimental time and cost and give insight into the laser workpiece interaction mechanism. In the present study laser pulse heating is modelled and the governing equation of heat transfer, including phase change process, and thermal stresses are solved numerically using a control volume approach. In order to account for the time variation of the laser heating pulse, time exponentially varying pulse intensity is employed in the analysis. Since the heating conditions are considered to be axisymmetric, two dimensional case is introduced in the analysis. The temperature and stress fields are simulated for steel. It is found that temperature level attains considerably high values in the melt zone and pulse parameter (β/γ) with small values (1/2) results in large evaporated zones. Equivalent stress level increases rapidly in the region close to the melt surface and two stress peaks are developed in the radial direction. The location of stress peaks remains same with progressing heating period; however, the magnitude of second peak reduces with advancing heating periods.

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This paper deals with the refracted shadows generated by the n = 2 compressible vortex. A more pragmatic picture of the optical phenomenon emerges when the flow instead of being isentropic is permitted to transfer heat and dissipate mechanical energy. The visual side of the formulation adheres to the long-established shadowgraph technique. It is shown that although the constant entropy hypothesis retains the qualitative nature of the phenomenon, the present approach improves on the quantitative side of the problem. It reveals that the central dark disk boundary does not mark the vortex core radius, renders the center of the vortex slightly darker, and the halo considerably brighter than the earlier isentropic flow estimates. Furthermore, it offers an alternative explanation for the peculiar set of alternating dark and bright circular bands that appeared in the shadow imprints of an earlier blade tip vortex experiment. The improved methodology can now be used to advance the experimental description of compressible vortices through shadowgraphy.

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The coupled finite element method is used to design a novel miniaturized piezoelectric force transducer for the pulp refiners. The analysis focuses on a proposed transducer design using commercially available piezoelectric sensing element and a steel assembled housing. The software ANSYS was used to create a finite element model in order to improve transducer electromechanical behaviour. The primary goal of modeling is to design a transducer with a frequency response higher than a lab-scale refiner. Thus, modal and harmonic responses of the transducer model are studied. A coupled electromechanical model is used for prediction the output of the transducer. In order to enhance the performance of the transducer, the design is studied with respect to output magnitude and a flat frequency response. The modeling results are used for fabrication a prototype force transducer. The experimental results showed good agreement with the modeling.