Transactions of the Canadian Society for Mechanical Engineering

Volume 31 (2007), Issue 2

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This paper applies a computational geometric algebra approach based on a 4 × 4 homogeneous transformation matrix to model optical systems and to evaluate their performance. In the proposed approach, the directions of the refracted/reflected rays at each boundary in the optical system are determined using skew ray tracing based upon Snell's law. The differential changes in the image coordinates caused by optical aberrations are derived for both polychromatic and monochromatic light by applying a sensitivity analysis approach. Finally, a merit function is constructed comprising five individual defect items in order to evaluate the overall performance of a generic optical system. The proposed analytical approach provides a comprehensive and robust approach for the modeling and evaluation of optical systems.

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This paper presents the results of a study on performance of flexible stab resistant ceramic-based composite body armour that our research group has initiated, designed, assembled, and tested. The test outcomes were characterized in terms of the kinetic energy of the stabbing weapon at impact and the depth of penetration of the stab into the armour. A neutral date fitting model that departs from the classical least square approach is proposed. The test results show that the flexible panels are especially suitable for medium and low protection levels and by comparison with rigid panels, the flexible panels allow a deeper penetration which increases with thrust energy.

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This paper proposed a novel concept of active balancer for dynamic balancing of planar mechanisms. Somewhat similar to a vibration absorber, the active balancer is designed as an independent device, which is placed outside of the mechanism to be balanced and can be installed easily. It consists of a two degree-of-freedom (DOF) linkage with two input shafts, one of which is connected to the output shaft of the mechanism to be balanced by a joint coupling, and the other one is driven by a controllable motor. Flexible dynamic balancing adapted to different working conditions can be achieved by varying speed trajectories of the control motor actively. A design method is developed for selecting suitable speed trajectories and link parameters of the two DOF linkage of the balancer to meet various design requirements and constraints. Numerical examples are given to demonstrate the design procedure and to verify the feasibility of the proposed concept.

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Analysis of the uniqueness of Filippov's solutions to non-smooth robotic control systems is important before the solutions can be sought. Such an analysis is extremely challenging when the discontinuity surface is the intersection of multiple discontinuity surfaces. The key step is to study the intersections of the convex sets from Filippov's inclusions and their associated sets containing vectors tangent to the discontinuity surfaces. For practical non-smooth robotic systems, due to their complexities, the determination of the intersections of these sets symbolically is extremely difficult if not impossible. In this paper, we propose a method such that the determinations of the intersections become feasible. Two examples of practical nonsmooth robotic control systems are presented to demonstrate the efficacy of the method. The work contributes significantly to the analysis of non-smooth systems where the proof of the uniqueness of Filippov's solution is crucial to keep the mathematical model relevant to physical systems and to ensure the numerical solutions can be sought.

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Inadequate noise simulation, identification, and strategy often cause dreadful plant layout. This unacceptable abatement results in the tremendous cost and inefficiency of noise reduction. To minimize the influence of machine noise along the plant boundary, the advances of optimal allocation planning and appropriate noise abatement on machine are then progressed in this paper. By using a sixteen-station sound monitoring system and the gradient numerical method - EPFM (Exterior Penalty Function Method), the numerical assessment is thus achieved, accordingly. Introducing the optimal design data of equipment's locations and noise reduction value into the ENM (Environmental Noise Model), a commercial sound simulation package, the predicted noise contour map of the plant is moreover accomplished. The noise check of noise map along plant's boundary is then furthermore approached to confirm the accuracy and acceptance of the numerical result. Noise control is important and essential in the process plant, where the noise level is restricted by both Occupational Safety and Health Act (OSHA) and local noise regulation. In mis paper; we (1) develop a mathematical model for economic plant noise control system, (2) give the proper allocation, (3) simulate the acoustic distribution within the plant, and (4) compare noise levels with local noise regulations. The numerical technique in both adjusting the optimal allocations and searching for the best noise reduction to the machine is fully demonstrated; thereafter, the verification of plant's noise is attained using ENM. With the simulated results, it is shown that this paper absolutely provides an approachable method, which is very effective, economical and applicable in plant's noise control with profound insight.

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A geometric model and a mathematical model of a PP-type single screw rotor with planar gate rotor are derived from the gate-rotor generation process and gear theory. The teeth of gate rotor are planar. Based on the inverse envelope concept, the cutter required for machining the single screw rotor can be obtained using an inverse envelope of a one-parameter family of screw surfaces. The surface of the proposed screw rotor is analyzed using the developed mathematical model. A surface analysis, including stress analysis, of the design and manufacture of the screw compressor is presented. Finally, a numerical example demonstrates the geometric model of the PP-type single screw rotor with a compression ratio of 11:6.

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A new method for averaging physical quantities is discovered. It is shown that the traditional method of finding the average value of a physical quantity gives the wrong results when calculating the average radius of a tapering tube, the average flow velocity in the tube and the volume of liquid flow through the tapering tube. The new method of averaging gives the correct results. The new formula is applicable to many other processes, for example, for calculating the flow through tubes of arbitrary form or with time-dependent radius. At present, a neutral radius is used which leads to big discrepancies.

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This study analyzes the internal irreversibility of a realistic refrigeration plant under the design constraint of a fixed total thermal conductance. The internal heat losses are determined using a heat by-pass model. The optimal thermal conductance allocation and optimal coefficient of performance are derived from a series of detailed analyses and formulations. The numerical results indicate that the optimal thermal conductance ratio of the hot end of a realistic refrigeration plant is slightly higher than 0.5.