Research On Optimization Theory And Method For V-belt And Gear Drive Design Under Complex Environment

V-belt drive and gear drive are two classes of fundamental and important mechanical transmissions with wide application in mechanism. It has outstanding significance in theory and application to find a globally optimal design scheme and make an optimal decision under a complex environment of uncertainty for the design of V-belt drive and gear drive. In this dissertation, on the basis of the analysis on the real-world complex design and working conditions, some deterministic global optimization methods for the two classes of mechanical transmissions are investigated and some polymorphic uncertain nonlinear programming methods are first proposed to solve the optimal design problem of V-belt under a complex environment of uncertainty from the viewpoint of the theory and the methods in modern optimization and uncertain mathematics. The main contribution in this dissertation is as follows.1. Two deterministic optimal design models for maximizing the transmission capacity of V-belt drive and maximizing the fatigue life of V-belt are constructed, respectively. The concavity, the monotonicity and the global optimality condition are investigated for the objective functions in the constructed models. It is proved that the feasible regions in the models are bounded, closed and convex under some design conditions. On the basis of these analyses, a solution method, called an optimal segment algorithm, is developed to find the global maximizer of the optimization models. The proposed method remedied the shortage in the existent researches. For example, for the employed heuristic algorithms in the optimal drive design, there is no convergence theory to be established, while all of the classical local optimization algorithms can only obtain local optimal design scheme for a noncovex problem.2. Polymorphic uncertain nonlinear programming (PUNP) models are respectively constructed to formulate the problem of maximizing the power transmission capacity and the fatigue life of V-belt under a complex environment of uncertainty which are involved with some uncertain parameters such as stochastic, fuzzy and interval ones,etc.. Then, some deterministic equivalent formulations for the PUNP models are obtained with given degrees of membership and levels of confidence.3. Based on the interval programming theory where the maximal and minimal range inequalities are obtained for an interval inequality, a two-step based sampling algorithm is developed to find interval optimal solutions for the problems of maximizing the transmission capacity of V-belt drive and maximizing the fatigue life of V-belt under polymorphic uncertainties. Both of them provide flexible design schemes for the practical engineering problems.4. Two types of sampling-based interactive algorithms are developed to find out robust optoimal solutions for the constructed nonlinear uncertain models, respectively. The concepts of satisfaction level and possibility degree are introduced respectively to describe an interval inequality. These algorithms are applied into case study in the optimal design of V-belt drive under polymorphic uncertain environment.5. Three global optimization metthods are presented for the problem of minimizing the gear's volume for a type of spur gear drives with fixed load coefficient. In the first approach, the original nonlinear optimization model is converted into a linear program with mixed discrete variables by a suitable variable transformation. By means of developing a class of global optimization methods for linear programming with mixed discrete variables, all global optimal solutions are found for the original problem both in continuous variable space and in mixed variables space. Furthermore, a special global optimization approach is provided to optimize the spur gear drive with soft tooth flank in continuous variable space by taking into account modification of the contact ratio factors in addition. The third global optimization method is based on enumerating the discrete variables and analyzing the monotonicity for the original problem. The effectiveness of the algorithm does not depend upon taking an account on the modification of the contact ration factors in the optimization model.