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A reduction of friction by vibrations has been observed in various experiments. This effect can be applied to actively control frictional forces by modulating vibrations. Moreover, common methods of controlling friction rely on lubricants and suitable material combinations. The superimposition of vibrations can further reduce the friction force. This study presents a theoretical approach based on the Dahl friction model that describes the friction reduction observed in the presence of the tangential vibrations at an arbitrary angle. Analysis results indicated that the tangential compliance should be considered in modeling the effect of vibrations in reducing friction. At any vibration angle, the tangential compliance of the contacts reduces the friction reduction effect. The vibrations parallel to the macroscopic velocity are most effective for friction reduction.

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SUMMARYThe use of multiobjective optimization techniques, which may be regarded as a systematic sensitivity analysis, for the selection and modification of system parameters is presented. A minimax multiobjective optimization model for structural optimization is proposed. Three typical multiobjective optimization techniques-goal programming, compromise programming and the surrogate worth trade-off method-are used to solve such a problem. The application of multiobjective optimization techniques to the selection of system parameters and large scale structural design optimization problems is the main purpose of this paper.

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A mathematical model of a modified helical gear train (MHGT), manufactured with a practical hobbing machine using a curved-template guide, and which takes considerations of center-distance variation and axial misalignment into account, is developed. Tooth contact analysis (TCA) and kinematic errors of a MHGT due to mis-assembly are investigated. A multiple optimization method is applied to reduce the level of MHGT kinematic errors, and to investigate optimal gear tooth modifications. Computer simulation programs for TCA and optimization are also developed. Two numerical examples are presented to illustrate the kinematic optimization of the proposed helical gear train. The results of this study are most helpful in designing and analyzing a MHGT.

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The branch-and-bound method was originally developed to cope with difficulties caused by discontinuous design variables in linear programming. When the branch-an~-bound method is applied to solve nonlinear programming (NLP) problems with a large number of mixed discontinuous and continuous design variables. the slow rate of convergence becomes a major drawback of the method. In thIs study. a number of enhancements are proposed to speed up the rate of convergence of the conventIOnal branch-an~~bound algorithm. Three NLP in the form of truss-design examples ar~tested to compare the capabilitIes and effIcIency of the proposed enhancements. It is shown that of the five CrIterIa for arranglllg the order III which the deSign variables are branched. the criterion of maximum cost difference dramatically reduces the number of branch nodes. thereby reducing the total number of continuous-optimization runs executed. Moreover. neighboring search. a branching procedure restricted in the neighborhood of the contllluous optImum. IS proven to be effective in speeding up the convergence. Investigation also shows that branching several deSign varIables simultaneously is not as efficient as sequentially branching one variable at a time. The proposed enhancements are incorporated along with a sequential quadratic programming algorithm mto a software package that IS shown to be very useful in the optimal design of engineering structures.