Optimization in Design of Multiunit Mechanical Transmission Systems A. DOLGUI * , N. GUSCHINSKY † , G. LEVIN † * Industrial Engineering Department University of Technology of Troyes 12, rue Marie Curie, B.P. 2060 - 10010 Troyes FRANCE † Institute of Engineering Cybernetics National Academy of Sciences of Belarus Surganov St., 6, 220012 Minsk BELARUS Abstract: - This work presents mathematical models and optimization methods for computer-aided design of mechanical transmission systems. The problem of decision making in transmission design is formulated as a multicriteria optimization problem. To solve it, we propose an iterative man-machine procedure. The procedure is based on multilevel decomposition scheme and involves methods of quadratic, dynamic and nonlinear programming. It is oriented to active participation of competent designer in decision making. The application of our approach to an industrial case study is presented. Key-Words: - Multilevel decomposition, Multicriteria optimization, Transmission design 1 Introduction Many computer-aided packages exist for power transmissions design. However, in most cases they are capable to design only separate elements of transmissions such as gears, shafts and bearings, see for example [1, 2, 3]. Some results were obtained in structural and parametric synthesis for certain type of transmission systems [4, 5, 6]. The expert systems are widely used in order to take in account engineering experience and to integrate the partial optimization models in design process [7, 8, 9]. An approach dealing with hierarchical decomposition of mathematical model of design problem was proposed in [10, 11]. The optimization model is decomposed and solved as a set of smaller, coordinated sub-problems. In our previous works, a multi-criteria optimization approach was proposed for automation of the initial stage of multiunit transmission systems design [12, 13]. The considered transmission systems can be composed of tens shafts and gears, and the number of kinematic chains (different speeds of output shaft) can be greater than 20. Such transmission systems are typical for tractors. The design problem is formulated as non-linear multi- criteria optimization problem with discrete, combinatorial and continuous variables. It is solved using iterative man-machine procedure with active participation of competent designer. This procedure consists of two stages and is based on a multilevel parametric decomposition [14, 15]. In our approach, at the first stage, the problem of preliminary kinematic calculation is solved. The problem is to find a set of output shaft speeds nearest to desired values that can be realized by the given structural scheme of the transmission system within the framework of the specified kinematic constraints. At the second stage, the problem of strength optimization calculation is solved. The problem is to determine design parameters of