少齿差齿轮传动承载能力分析及体积优化
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摘要
在少齿差内啮合传动中,由于齿廓间隙较小,易出现多齿啮合使其实际承载能力大大超过设计值。这是因为在以往的少齿差传动轮齿强度计算中,未考虑该类型传动的多齿啮合特性,致使少齿差减速器的强度裕量过大。为减小强度值浪费,从承载能力系数优化和求解最大承载两个角度予以分析。采用多目标优化思想得到主齿对所承受的最大载荷,再利用少齿差内啮合齿轮传动多齿啮合载荷分配的数学模型,求解少齿差传动的法向总载荷,通过实例对比计算,得到考虑多齿啮合与不考虑多齿啮合时少齿差传动所能承受的载荷具有显著差别。利用该计算方法既避免了强度浪费又减小了减速器体积,为少齿差传动轮齿强度更为准确的分析提供了理论依据。
Considering the gearing with few teeth number difference inner meshing transmission,usually the tooth profile clearance is not enough,which causes multi-teeth meshing,as a result,the actual load-bearing capacity exceeds the value expected vastly,which is because during the conventional calculation of the strength of gear teeth,the multi-teeth meshing properties have been ignored,leading to an inordinate increment of the strength margin of the few teeth difference reducer.In order to decrease the waste of strength,analyzing from the perspectives of optimizing the load-bearing capacity coefficient and solving the maximum load,a methodology that getting the maximum load of main gear pair through multi-objective optimization,followed by solving the total normal load through the mathematical model of load sharing between teeth has been put forward.After the comparison of real cases,obvious difference occurs.The method here is available to avoid wasting strength;meanwhile,the volume of decelerator could drop to some extent,which could be regarded as the theoretical foundation while analyzing the strength of gear teeth in few teeth number difference accurately.
Considering the gearing with few teeth number difference inner meshing transmission,usually the tooth profile clearance is not enough,which causes multi-teeth meshing,as a result,the actual load-bearing capacity exceeds the value expected vastly,which is because during the conventional calculation of the strength of gear teeth,the multi-teeth meshing properties have been ignored,leading to an inordinate increment of the strength margin of the few teeth difference reducer.In order to decrease the waste of strength,analyzing from the perspectives of optimizing the load-bearing capacity coefficient and solving the maximum load,a methodology that getting the maximum load of main gear pair through multi-objective optimization,followed by solving the total normal load through the mathematical model of load sharing between teeth has been put forward.After the comparison of real cases,obvious difference occurs.The method here is available to avoid wasting strength;meanwhile,the volume of decelerator could drop to some extent,which could be regarded as the theoretical foundation while analyzing the strength of gear teeth in few teeth number difference accurately.
引文
[1]应广驰,张策,宋轶民,等.三环传动的弹性啮合、载荷分配和强度计算[J].机械设计,2004,21(8):12-15.
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[6]李玥.基于多目标遗传算法的航空发动机多目标优化控制[D].南京:南京航空航天大学,2007:8-20.
[7]Kollat J B,Reed P M.The Value of Online Adaptive Search:A PerformanceComparsion of NSGAⅡ,∈NSGAⅡand∈MOEA[C].Proc of the3rd IntConf on Evolutionary Multi-criterion Optimization.Mexico,2005:386-398.
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[9]时丽娜.进化多目标优化算法及其应用研究[D].桂林:广西师范大学,2010:20-23.
[2]舒小龙,夏齐霄.少齿数差内啮合齿轮的强度计算[J].机械设计,2002(10):35-37.
[3]余跃海.少齿差内啮合齿轮的计算机辅助几何设计及参数优化[D].天津:天津大学,2005:42-48.
[4]田红亮,朱大林,方子帆.三环减速器齿廓间隙角啮合刚度和载荷分配的计算[J].机械设计与制造,2005(9):19-21.
[5]杨锡和.关于少齿差内啮合实际接触齿数及承载能力的研究[J].雷达与对抗,1990(1):11-19.
[6]李玥.基于多目标遗传算法的航空发动机多目标优化控制[D].南京:南京航空航天大学,2007:8-20.
[7]Kollat J B,Reed P M.The Value of Online Adaptive Search:A PerformanceComparsion of NSGAⅡ,∈NSGAⅡand∈MOEA[C].Proc of the3rd IntConf on Evolutionary Multi-criterion Optimization.Mexico,2005:386-398.
[8]Sierra M R,Coello C A C.Improving PSO-based Multi-objectiveOptimization Using Crowding,Mutation and∈-dominance[C].Proc ofthe3rd Int Conf on Evolutionary Multi-criterion Optimization.Mexico,2005:505-519.
[9]时丽娜.进化多目标优化算法及其应用研究[D].桂林:广西师范大学,2010:20-23.