机械外文翻译

Optimization design of spur gear reducer based on genetic algorithm

Zhang Xiao-qin1 21 College of Mechanical Engineering Yan Shan University 2 College of Mechanical and Electrical Engineering Hebei Normal University of Science & Technology

Qinhuangdao China Hu Zhan-qi College of Mechanical Engineering Yan Shan University Qinhuangdao China

Lun Cui-fen Yu Jing-jing College of Mechanical and Electrical Engineering Hebei Normal University of Science & Technology Qinhuangdao China

Abstract—Gear reducer is one of the most widely used methods in mechanical transmission, optimization of which is of great significance in improving the bearing capacity, prolonging service life and reducing its size and quality. By Visual Basic programming mixed with MATLAB, automatic optimization design for gear reducer is realized in the paper, design efficiency and quality greatly improved. Genetic algorithm and genetic toolbox of MATLAB is used when calculating, with the advantages of simple programming, good reliability and high efficiency.

Keywords-reducer; optimization of design; genetic algrithm; MATLAB

I.INTRODUCTION

Gear reducer is one of the most widely used methods in mechanical transmission, which has many advantages, such as accuracy ratio, high efficiency, stable and accurate. With the rapid development of science and technology it will make continuous progress. So it is of great economic significance to improve the bearing capacity, prolong the service life and decrease its size and quality. Optimized design of gear reducer, choosing the best parameters is a kind of important ways to improve the bearing capacity, reduce weight and cost[1][2][3].

Optimization design of gear reducer includes the continuous variables and discrete variables. The traditional method is to round the optimal design to the adjacent discrete points. Thus, design point might run out of the feasible region, besides traditional optimization method is mostly based on gradient algorithm, which is likely trapped into local minimum search. Many studies indicate that the genetic algorithm has strong ability of general optimization, which is very effective in treating optimization problem containing continuous and discrete variables[4][5].

Based on single spur gear reducer, the paper establishes the mathematical model for optimization design of gear reducer, with the purpose of minimum volume or quality. By using

genetic algorithm and genetic toolbox of MATLAB to get optimum solution quickly and accurately, the efficiency and quality of gear design is greatly improved and the production cycle is shorten.

II.MATHEMATICAL MODEL FOR OPTIMIZATION DESIGN

Optimization design of gear reducer is usually given power P, gear ratio i, input speed n1 and other technical conditions and requirements, to seek a group of design parameters that achieve technical and economic indexes of a reducer optimum.

A single spur gears reducer transmission diagram and gear structure is shown in Fig 1. Assume that the gear ratio is known as i, the input power P(kW), active gear speed n1(r/min), it’s required to figure out various design parameters to make the reducer as light as possible under the condition that the strength and stiffness are guaranteed.

Figure 1. Single spur gear reducer and gear structure Since the size of the gear and axis is to determine the size and quality of reducer assembly, the objective function is the sum of their value, without considering cabinet and bearing volume or quality. According to the fig 1, the sum of the

978-1-4244-7161-4/10/$26.00 ©2010 IEEEvolume of gears and shafts can be approximately expressed as follows:

())1(42.14)(3.04)(421221222222jjjjjnjnjwjwjojldbddbddbddV×+»¼º«¬ª×−+×−+−=¦¦

==π

πππ

Where d01=mz1;d02=mz1i;dw1=mz1-8m;dw2=mz1i-8m;dn1=1.6d1;dn2=1.6d2.

From above equation, it can be seen that if i have been given beforehand, the volume of gear and shaft is determined only by face width b, the number of pinion teeth z1, modulus m, shaft diameter d1 and d2 and distance l between two bearings, i.e. V is the function of these parameters: V=f(b,z1,m,d1,d2,l1,l2).

Take these variables as design variables and expressed as: X=[x1,x2,x3,x4,x5,x6]= [b,z1,m,d1,d2,l] (2) Thus the objective function can be expressed as: f(X)=V=f(x1,x2,x3,x4,x5,x6) (3)The constraint conditions can be given by follows [1][2]: •Avoiding undercut condition z1 should be greater than the smallest number 17, i.e. g1(X)=-x2󰂔-17 (4)