基于模糊可靠性的新型行星变速箱多目标优化设计研究
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摘要
行星变速箱由于传动效率高、体积小、传动比大、运动平稳、抗冲击和振动的能力较强等优点被广泛用在石油、矿山、工程机械、汽车等众多的工业生产领域。
应用常规的设计方法和以往设计者的经验,可以设计出符合要求的变速箱。但是随着社会的发展,对变速箱的可靠性、传动效率以及振动噪音提出了更高的要求,且行星轮系结构复杂,行星架是一个不规则的实体,其受力变形后会对整个行星轮系产生影响。常规的可靠性设计假设部件处于完全正常或者失效的状态试图精确的描述部件的运行状态,但实际运行中存在大量模糊的随机的现象。为了准确的计算产品的可靠性将常规的可靠性设计与模糊数学结合起来,应用现代设计方法综合优化设计以及有限元分析,以提高行星传动系统效率和增大系统可靠性并尽量减轻整机的重量为目标函数,通过线性加权函数法确定目标函数的数学模型,采用设计变量规格化的方法确定加权因子,基于模糊数学理论的可靠性约束条件以及功能约束几何约束,运用MATLAB优化工具箱进行优化,对三个局部最优解叠加计算,保证了优化参数是满足目标函数的全局最优解。优化结果表明运用多目标可靠性设计优化方法后传递效率和系统的稳定性比初始设计方案提高了,轮系质量也有所减轻。其中整个行星轮系的质量较之前降低了2.43%,重合度和啮合效率分别提高了2.70%和2.84%。由此证明模糊可靠性多目标设计不仅能客观的反映产品设计和运行的真实情况,而且在设计阶段保证了产品在运行中的可靠性要求,是一种更具科学性更符合客观事实的设计方法,在工程实践中具有广泛的应用。
基于模糊可靠性多目标优化设计得到的结果,建立整个行星轮系的三维模型,在产品的设计阶段进行装配干涉检查,保证了零件设计的正确性。
行星架是行星齿轮传动主要的受力部件,其变形的大小对整个轮系齿轮的啮合影响情况,且设计完成之后需要校核检验齿轮啮合情况。因此,须对行星架做ANSYS有限元分析,得到行星架的受力情况和变形情况,利用有限元接触分析计算行星架的变形对太阳轮-行星轮间的啮合力的影响情况,防止轮齿失效。由于行星轮的旋转速度比较高,为防止行星轮系在旋转过程中产生共振,有必要对行星轮进行模态分析。通过设计、校核、分析,保证了产品的可靠性。
Planetary gear drive is widely applied in petroleum, mines, engineering machinery, automobiles and many industrial production fields because of its high transmission efficiency, small volume, smooth movement and strong ability of resistance to impact and vibration.
Use of routine design methods or past designers experiences could be meet the requirements. But along with the development of society, the user put higher request with the reliability of gearbox, transmission efficiency and vibration noise.For the structure of planetary gear train is complex, and the planet carrier is an irregular entity, its deformation will impact the whole planet gear train. The conventional reliability design assumptions components is completely normal or failure, trying to accurate description of the state of components, but there are a lot of fuzzy, random phenomenon in actual condition. In order to accurately calculating the reliability of the products, we combined the conventional reliability design with fuzzy mathematics. Application of modern design method integrated optimizing design and finite element analysis in order to improve the transmission efficiency and increasing the planetary system reliability and try our best to reduce the weight, through the linear weighted function method to establish the objective function.Adopt the method of design variables normalization to determine the weighting factors, based on the fuzzy mathematics theory of reliability constraints and geometric constraint. Then, the optimal design is conducted by using optimization toolbox in MATLAB. To ensure the optimal parameter to meet the the global optimal solution of objective function, stack calculation the three local optimal solution. The optimization results show that using multi-objective optimization method of fuzzy reliability design, the transfer efficiency and stability of the system improved, the weight of the planet gear train also reduced. For the weight of planetary gear train decreased 2.43%, Coincidence degree and the meshing efficiency improved 2.70% and 2.84% respectively. This indicates the fuzzy reliability of multi-objective design not only reflect the real situation of product design and operation in the design phase, and guarantee the reliability of the products, it is a kind of more scientific and more accord with the objective facts design method.Its has wide application in engineering practice.
Based on the results obtained from the fuzzy reliability multi-objective optimization, than establish the 3d models of whole planet gear train.In the product design phase assembly interference and guarantee the parts design calculation is correct.
In planetary gear transmission planet carrier is the main parts to transfer force and torque, its deformation affects the meshing gears of entire gear train. After Design completed we must check the gear stress. To get planet shelf stress and deformation we must do finite element analysis with planet carrier. Using finite element contact analysis to calculation how the deformation of planet carrier influence of the gearing force of the planet to sun gear. The planet wheel rotation speed is higher, in order to prevent the resonance of planetary gear train in rotating process, it is necessary to do modal analysis of the planet gear. Through the design, checking, analysis, to ensure the reliability of the product.
应用常规的设计方法和以往设计者的经验,可以设计出符合要求的变速箱。但是随着社会的发展,对变速箱的可靠性、传动效率以及振动噪音提出了更高的要求,且行星轮系结构复杂,行星架是一个不规则的实体,其受力变形后会对整个行星轮系产生影响。常规的可靠性设计假设部件处于完全正常或者失效的状态试图精确的描述部件的运行状态,但实际运行中存在大量模糊的随机的现象。为了准确的计算产品的可靠性将常规的可靠性设计与模糊数学结合起来,应用现代设计方法综合优化设计以及有限元分析,以提高行星传动系统效率和增大系统可靠性并尽量减轻整机的重量为目标函数,通过线性加权函数法确定目标函数的数学模型,采用设计变量规格化的方法确定加权因子,基于模糊数学理论的可靠性约束条件以及功能约束几何约束,运用MATLAB优化工具箱进行优化,对三个局部最优解叠加计算,保证了优化参数是满足目标函数的全局最优解。优化结果表明运用多目标可靠性设计优化方法后传递效率和系统的稳定性比初始设计方案提高了,轮系质量也有所减轻。其中整个行星轮系的质量较之前降低了2.43%,重合度和啮合效率分别提高了2.70%和2.84%。由此证明模糊可靠性多目标设计不仅能客观的反映产品设计和运行的真实情况,而且在设计阶段保证了产品在运行中的可靠性要求,是一种更具科学性更符合客观事实的设计方法,在工程实践中具有广泛的应用。
基于模糊可靠性多目标优化设计得到的结果,建立整个行星轮系的三维模型,在产品的设计阶段进行装配干涉检查,保证了零件设计的正确性。
行星架是行星齿轮传动主要的受力部件,其变形的大小对整个轮系齿轮的啮合影响情况,且设计完成之后需要校核检验齿轮啮合情况。因此,须对行星架做ANSYS有限元分析,得到行星架的受力情况和变形情况,利用有限元接触分析计算行星架的变形对太阳轮-行星轮间的啮合力的影响情况,防止轮齿失效。由于行星轮的旋转速度比较高,为防止行星轮系在旋转过程中产生共振,有必要对行星轮进行模态分析。通过设计、校核、分析,保证了产品的可靠性。
Planetary gear drive is widely applied in petroleum, mines, engineering machinery, automobiles and many industrial production fields because of its high transmission efficiency, small volume, smooth movement and strong ability of resistance to impact and vibration.
Use of routine design methods or past designers experiences could be meet the requirements. But along with the development of society, the user put higher request with the reliability of gearbox, transmission efficiency and vibration noise.For the structure of planetary gear train is complex, and the planet carrier is an irregular entity, its deformation will impact the whole planet gear train. The conventional reliability design assumptions components is completely normal or failure, trying to accurate description of the state of components, but there are a lot of fuzzy, random phenomenon in actual condition. In order to accurately calculating the reliability of the products, we combined the conventional reliability design with fuzzy mathematics. Application of modern design method integrated optimizing design and finite element analysis in order to improve the transmission efficiency and increasing the planetary system reliability and try our best to reduce the weight, through the linear weighted function method to establish the objective function.Adopt the method of design variables normalization to determine the weighting factors, based on the fuzzy mathematics theory of reliability constraints and geometric constraint. Then, the optimal design is conducted by using optimization toolbox in MATLAB. To ensure the optimal parameter to meet the the global optimal solution of objective function, stack calculation the three local optimal solution. The optimization results show that using multi-objective optimization method of fuzzy reliability design, the transfer efficiency and stability of the system improved, the weight of the planet gear train also reduced. For the weight of planetary gear train decreased 2.43%, Coincidence degree and the meshing efficiency improved 2.70% and 2.84% respectively. This indicates the fuzzy reliability of multi-objective design not only reflect the real situation of product design and operation in the design phase, and guarantee the reliability of the products, it is a kind of more scientific and more accord with the objective facts design method.Its has wide application in engineering practice.
Based on the results obtained from the fuzzy reliability multi-objective optimization, than establish the 3d models of whole planet gear train.In the product design phase assembly interference and guarantee the parts design calculation is correct.
In planetary gear transmission planet carrier is the main parts to transfer force and torque, its deformation affects the meshing gears of entire gear train. After Design completed we must check the gear stress. To get planet shelf stress and deformation we must do finite element analysis with planet carrier. Using finite element contact analysis to calculation how the deformation of planet carrier influence of the gearing force of the planet to sun gear. The planet wheel rotation speed is higher, in order to prevent the resonance of planetary gear train in rotating process, it is necessary to do modal analysis of the planet gear. Through the design, checking, analysis, to ensure the reliability of the product.
引文
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[4]China Association for Science and Technology.Report on advances of mechanical engineering(2008-2009)[M].Beijing:Press of Science and Technology of China,2009.
[5]赵青,刘长生Matlab优化工具箱在齿轮传动设计中的应用[J].机械研究与应用,2008,21(5)：78-80
[6]韩敏,高媛.基于Matlab优化工具箱的星齿行星传动的优化设计[J].机械设计与制造,2009,9：31-32
[7]耿兴春,林国湘,叶进宝.机械系统可靠性的动态优化设计[J].机械设计与制造,2009,09：109-110
[8]孟凡净,周哲波,黄道业.基于MATLAB的航空圆弧齿面齿轮的多目标优化设计,2009,10：78-91
[9]V. Savsani, R.V. Rao, D.P. Vakharia.Optimal weight design of a gear train using particle swarm optimization and simulated annealing algorithms[J].Mechanism and Machine Theory, Volume 45, Issue 3, March 2010, Pages 531-541
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