Transactions of the Canadian Society for Mechanical Engineering

Volume 33 (2009), Issue 2

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The paper deals with the Lie group algebraic structure of the set of Euclidean displacements, which represent rigid-body motions. We begin by looking for a representation of a displacement, which is independent of the choice of a frame of reference. Then, it is a simple matter to prove that displacement subgroups may be invariant by conjugation. This mathematical tool is suitable for solving special problems of mobility in mechanisms.

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The purpose of this work is to determine the spur gear mesh stiffness and the stress state at the level of the tooth foot. This mesh stiffness is derived from the calculation of the normal tooth displacements: local displacement where the load is applied, tooth bending displacement and body displacement [15]. The contribution of this work consists in, basing on previous works, developing optimal finite elements model in time calculation and results precision. This model permits the calculation of time varying mesh stiffness and the evaluation of stress state at the tooth foot. For these reasons a specific Fortran program was developed. It permit firstly, to obtain the gear geometric parameters (base radii, outside diameter,…) and to generate the data base of the finite element meshing of a tooth or a gear. This program is interfaced with the COSMOS/M finite element software to predict the stress and strain state and calculate the mesh stiffness of a gear system. It is noted that the mesh stiffness is periodic and its period is equal to the mesh period.

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The numerical modeling of two-dimensional turbulent flow around a horizontal wallmounted circular cylinder at Reynolds numbers in the range of 1000≤Re_D≤7000 is investigated. Ansys 10.0-FLOTRAN program package is used to solve the governing equations by finite element method, and the performance of the standard k-ε, standard k-ω and SST turbulence models are examined. A sensitivity study for the three turbulence models is carried out on eight computational meshes with different densities and structures. The computational velocity fields from the present simulations are compared with the experimental results obtained from particle image velocimetry (PIV) measurements for validation purposes. The point of the boundary layer detachment from the cylinder surface and the lengths of primary and secondary separation regions occurring around the cylinder are determined numerically and compared with those obtained experimentally. From these comparisons it is found that the numerical modeling using either of k-ω and SST turbulence models is reasonably successful. Using the results of numerical solutions, the drag and lift coefficients, C_d and C_l, are also calculated and compared with the measured values.

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A new causal dynamic end-effector inversion method for a single flexible link manipulator is introduced. Contrary to the available non-causal inversion technique, this method does not lead to pre-actuation and works even in the presence of the purely imaginary zeros for the transfer function. Based on this approach, the desired end-effector trajectory is divided into a finite number of segments. In each segment, the desired trajectory is redefined so that a bounded continuous torque through causal dynamic inversion is obtained. The redefinition of the desired trajectory at each segment employs summation of stable exponential functions. This leads to a family of answers for the redefined trajectory, which is an advantage for control engineers. The results of the simulation and experimental studies show the feasibility and effectiveness of this new technique.

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This paper analyzes the optimal configuration and operating parameters of a heat exchanger in a geothermal district heating system. An optimization algorithm is presented for the nonlinear constrained problem to maximize the annual net profit for a system of counter-flow heat exchangers. Several parameters that affect the net profit are examined, including the mass flow rates of working fluids and heat transfer area, which both directly affect the outgoing temperatures. The performance of the heat exchanger and fuel savings by reducing fuel consumption to generate heat are modeled within the problem formulation. Also, power input to the pump for fluid circulation is included. By formulating these multiple parameters over a wide range of design conditions, the algorithm presents a useful new design tool for the improvement of heat exchanger networks in geothermal systems.

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A mathematical model which minimizes the production cost of an automatic and networktype multiple-order-production (MOP) system with restriction of time-phased order completion is presented. A step-by-step algorithm is described to find the minimal cost of production. In order to solve the combinatorial problems of the production rate, the machine cost, and numerous machines in parallel at each workstation of the production line, a feedback approach is also applied in the algorithm. An example of a large number of orders which is subdivided into different deadlines is shown to demonstrate the application of the algorithm that results in decreased production cost, enhanced production rate, improved efficiency of the production schedule, and on-time completion of production.

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The performances of three different ramjet inlets and an entire ramjet are numerically studied in this paper. The fluid is assumed to be inviscid. Inlet 1 is a SCRAMJET inlet and is chosen from the literature. Inlets 2 and 3 are instead designed based on the Oswatitsch principle. Inlets 2 and 3 produce a series of oblique shocks merging at the engine cowl lip followed by a terminating normal shock just downstream of the inlet throat. In ramjet, the combustion is modeled using a non-uniform volumetric heat source distributed in the combustor area. The position of the terminating normal shock in Inlets 2 and 3 is controlled via the inlet’s back pressure. Instead, in ramjet it is bounded by the amount of heat rate added in combustor and the exhaust nozzle throat area. For the numerical simulations, the Roe (1981) and MacCormack (1969) schemes are used. To prevent the spurious numerical oscillations in high resolution computations by Roe scheme the van Albada flux limiter (1982) is used, while in MacCormack scheme artificial viscosity terms are added to damp the oscillations. To double check the accuracy of the computations, the Fluent software package has also been used. Comparisons show very good agreement.

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This study applies computational geometric algebra based on a 4×4 homogeneous transformation matrix and Snell’s law of geometrical optics to analyze skew rays and the errors of a light ray’s path as it passes through a cylindrical lens. The author addresses two important topics: (1) the determination of the direction of a reflected or refracted ray by Snell’s law and (2) the expression of the combination of two principal sources of light path error using error analysis. In topic (2), one of the sources is the translational errors Δd_ix, Δd_iy, and Δd_iz and the rotational errors Δω_ix, Δω_iy, and Δω_iz that determine the deviation of the light path at each boundary surface, while the other source is the differential changes induced in the incident point position and the unit directional vector of the refracted/reflected ray as a result of differential changes in the position and unit directional vector of the light source. The methodology presented in this study provides a comprehensive and robust approach for evaluating the error of a light ray path as it passes through a cylindrical lens.

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This paper investigates worm coil distribution and load-carrying ability for a toroidal drive. The lead angle equations for the worm groove are given for different coil distributions. The center curve of the worm groove is obtained using coordinate transformation. A 3D worm model is constructed using Pro/Engineer software and the average output torque is presented to compare load-carrying ability for the drive with different worm coil distributions. As the number of the planet teeth increases, the output torque of the drive first increases then decreases. Large output torque requires an optimum number of planet teeth and a larger number of pole pairs and stator teeth.

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This paper proposes a novel concept of active balancer for reducing the input torque fluctuations of mechanisms. A differential gear train is used in this active balancer and one of its two input shafts is driven and controlled by a servomotor. From the structural point of view, it is designed as an independent device that can be assembled and disassembled easily; from the functional point of view, it can minimize the torque fluctuations in a variety of working conditions. At first, an exact control function of the servomotor that can totally eliminate the input torque fluctuations of the mechanism is gained by an analytical method; in what follows, an optimization approach is developed to select appropriate control functions for the servomotor to balance the input torque of the working mechanism with consideration of the servomotor’s own input torque minimization; finally, an integrated method is presented for optimizing both the control function of the servomotor and the structure parameters of the differential gear train. Two numerical examples are given to illustrate the design procedure and to show its feasibility.