Optimization of Combined Scroll Profile Based on Multi-objective Genetic Algorithm

Abstract

This In the design of scroll compressor, in order to improve the performance of the combined profile by involute of circle and high order curve, the mathematical model was established which takes the stroke volume and area utilization coefficient as the objective function. Then optimize it by the MATLAB genetic algorithm toolbox and have a contrast of the original parameters with the optimized parameters. The optimal result shows that the result after optimization has higher stroke volume and area utilization coefficient. Introduction Scroll compressors are widely used in air conditioning and refrigeration because of its high efficiency, small volume, light weight, low noise and simple structure etc. . But the material utilization rate of uniform scroll part is low, in order to improve the material utilization rate of scroll plate, the variable cross section scroll profile by involute of circle and high order curve is put forward. To make it have higher utilization rate, we can optimize it. However, optimizations of combined profile of existing work [2] have limitations, because they are only based on the single objective to optimize. Therefore, this paper proposes to take the stroke volume and area utilization coefficient as the target function and then optimize the profile .Finally, make a comparison of the profiles between the original parameters and the optimized parameters. Mathematical model This paper chooses the profile composed by involute of circle and high order curve and then optimize it. Combined profile is shown in Fig1 and its equation is: 1 1 1 1 1 cos( ) sin( ) (0 ) sin( ) cos( ) g s g s x R R y R R φ φ φ φ φ φ = +  ≤ <  = −  (1) Where: Rg1=a, Rs1= aφ , a is the radius of base circle 2 2 1 2 2 2 cos( ) sin( ) ( ) sin( ) cos( ) g s g s x R R y R R φ φ φ φ φ φ φ = +  ≤ <  = −  (2) Fig .1 Combined profile International Conference on Information Sciences, Machinery, Materials and Energy (ICISMME 2015) © 2015. The authors Published by Atlantis Press 1162 Where: 2 2 1 2 3 2 ( ) 3 ( ) 2 2 g R c c c π π φ φ = + − + − 2 3 2 0 1 2 3 ( ) ( ) ( ) 2 2 2 s R c c c c π π π φ φ φ = + − + − + − When 1 2 2π, 4.5π, 2.25 a φ φ = = = 0 1 2 3 c 32.1464,c 11.8210,c 2.1066,c 0.0868 = = − = = − . The dynamic and static scroll meshing is shown in Fig 2. Fig .2 profile meshing diagram Objective function The stroke volume and area utilization coefficient are taken as the objective function. Calculate stroke volume [3] When the dynamic scroll plate angle θ=0, compression cavity is closed, the volume of first compression chamber is stroke volume and its formula is: 1 2 V S h = ⋅ (3) Where: S1— cross-sectional area of single compression cavity of the outer ring H—the height of scroll plate When θ=0, the length of the busbar of suction chamber is: ( ) ( ) 2 2 2 2 ' ' 2 2 2 2 2π = cos R sin sin R cos g s g s L R R d φ φ φ φ φ φ φ − + + − ∫ (4) The cross-sectional area of single compression cavity of the outer ring is: ( ) ( ) 1 2 2 2π or g g or S L R R R R φ φ   = ⋅ + − − ⋅   (5) The first objective function, namely stroke volume, is: ( ) 1 1 2 f X V S h = = ⋅ (6) In order to reflect the material utilization rate of scroll plate, defined area utilization coefficient. 2 4 π S r D = (7) Where: S—the cross-sectional area of the compression chamber D—scroll meshing diameter The length of the bus bar of second compression chamber is: ( ) ( ) ( ) ( ) 2