The Optimization Design of Two Stages Helical Gear Reducer Based on GA and Nastran

Paper taking the volume of gear transmission system of two stages helical gear reducer as mathematical model and write a GA program based on MATLAB soft to get the relevant result. Next, paper draw gear model based on UG soft and analysis the gear’s bending stress in Nastran solver which contained in UG soft. The result shows that optimized gear transmission system can not only meet job requirement,also reduced the volume greatly. Introduction As a kind of power transfer device, gear reducer is widely used in aircraft automotive, machine tools,marine machinery etc[1],because of its simple structure, high transmission efficiency, good stability. Traditional reducer design method is combined with the experience and test way,which has many disadvantages,such as, results is reasonable, waste materials, tedious design work ,etc. Therefore, the optimum design of reducer has the important practical significance. Discussed problems The reducer of one type of band conveyors pass by 4.5kw power, total drive ratio is 7.53, the speed of high-speed spindle is 480r/min. The structure as shown in figure 1, the material of two small gears is 40Cr,two big gears’ material is 45 # steel. The design requirement is that volume of the reducer as small as possible under meet the condition of performance. Fig.1: Gear reducer structure diagram Optimal design of gear reducer Optimum design combined with the optimization theory in mathematics and computer technology, its aim is o seek the best design parameters under the given constraint conditions. Optimization design mainly consists of four steps[2]: requirement analysis, build mathematical modeling, choose optimization methods, write computer programming to solve the problem. 3.1 The selection of design variables. When selecting the design variables, we should make sure the variables little and sensitive, which means we should choose the variables has greater influence on the design requirements. The main optimizaion goal in the paper is volume of the reducer,which could be expressed in gear teeth counts, modulus, spiral angle and tooth width coefficient. After comprehensive consideration, paper choose normal module, teeth counts and helix angle of the two small gears and the ration between high-speed gear and middle-speed gear as the variables and gear width coefficient is 1. Relevant variables could be written as: International Conference on Information Sciences, Machinery, Materials and Energy (ICISMME 2015) © 2015. The authors Published by Atlantis Press 1462 T T i z m z m x x x x x x x X ] cos , cos , , , , , [ ] , , , , , , [ 2 1 2 2 1 1 7 6 5 4 3 2 1 β β = = (1) 3.2 The construction of objective function. Volume of the gear transmission system could be expressed as four gears’ volume up. Taking the variables into the expression and handle it, the object function can written as: ]} ) 53 . 7 ( 1 [ cos ) 1 ( cos { 4 3 5 7 3 3 4 3 3 3 5 6 3 3 2 3 1 x x x x x x x x F + × × + + × × × = π (2) 3.3 The structure of the constraint condition [3]. To prevent the gear tooth fracture, bending strength of gear shall not exceed the allowable value, we usually take tooth root as the dangerous section for checking: