航空用微小型减速装置多目标优化设计及性能分析
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摘要
航空航天领域迫切需求开发出一种具有体积小、重量轻、回差小、输出扭矩大、动力学特性好、传动平稳和传动效率高等诸多优点的微小型减速装置,其技术指标要求近乎苛刻本文成功地开发出一种航空用微小型可调间隙变厚齿轮RV减速装置,并对其进行了理论研究和样机试验。
首先在对国内外现有减速装置的多种方案进行了全面深入分析,为了实现输入输出轴垂直和苛刻的技术要求确定了采用RV减速传动形式。确定了圆弧锥齿轮传动(高速级)和变齿厚齿轮传动(低速级)的可调隙RV减速装置方案。根据传统设计方法初步确定了减速装置的结构参数,运用有限元理论及ANSYS软件对其关键件进行了强度和模态分析,为此开发出少齿差变厚齿轮参数化设计软件,解决了变厚齿轮因各种截面变位系数不同、左右齿廓参数完全不同,使其公式复杂和参数计算量大等问题。
针对传统的多目标优化算法必须通过线性加权的方式处理目标函数,只能达到近似的优化问题。本文提出一种精确的多目标优化算法,即改进的双群体差分多层文化粒子群融合算法。在信仰空间的进化过程中,该算法采用“多层空间、择优选用”的策略,避免有时因信仰空间更新而导致算法陷入局部最优的缺点;又在群体空间的进化过程中,采用了改进的双群体进化差分的方式,避免丢弃了大量高适应度的不可行解,导致优化结果不理想的问题,实现了群体的多样性,并提高了算法的收敛速度。
本文对航空用微小型减速装置进行三目标优化设计,得到了该减速装置优化设计的最满意解。并采用改进后的算法解决了该装置优化设计时参数多、各参数间的相互制约条件多、计算复杂和设计繁琐等问题,为该微小型减速装置的结构设计奠定了基础。
论文以弧齿锥齿轮系统为研究对象,对高速级弧齿锥齿轮进行了动力学分析。在综合考虑齿侧间隙、时变啮合刚度、传递误差等多种非线性因素的情况下,建立了弧齿锥齿轮副的非线性动力学分析模型。针对齿轮传动过程中啮合刚度的时变性、刚度激励的周期性等特点,在计算的过程中提出了将啮合综合刚度按五次谐波展开,齿侧间隙非线性描述函数用七次多项式拟合,通过无量纲化处理简化了齿轮动力学分析的复杂非线性微分方程,并对其进行了数值仿真分析,得到系统的单周期简谐、多周期次谐、拟周期和混沌等多种稳态响应结果。结合响应的时间历程、相平面图、Poincaré映射图和FFT频谱图,对得到的各类响应结果进行了详细的分析和比较。
针对减速装置的传统可靠性分析方法计算量巨大、过程繁琐等问题,本文将改进的动态过程神经网络与Monte-Carlo方法相结合,应用于减速装置的可靠性分析中。提出了用改进的粒子群算法替换传统的BP算法,并将其应用在给定的全连接过程神经网络的训练过程中,优化了网络结构,提高了网络的收敛速度和精确度。本文以Henon系统仿真为例验证了改进的动态过程神经网络的有效性。在对减速装置故障树分析的基础上,将ICPDPNN和Monte-Carlo方法相结合,对航空用可调间隙变厚齿轮RV减速装置进行了可靠性研究。结果表明,该减速装置具有较高的可靠性,完全符合设计要求。
最后研制一台样机,并对其进行了效率和振动特性的试验,结果表明其性能指标已基本达到试验样机设计要求。
Aeronautical and space technologies actively get rid of the stale and bring forth the fresh and design a perfect micro device. The qualification laid down strict, almost harsh, requirements for the micro reducer- the developing tendency of reducer is toward the orientation of miniaturization, large torque, high speed, stable drive, low noise and high reliability. For the special requirement of the adjustment device of the tail lamina of the rocket the paper develops the micro reducer. A series of theoretical research work is presented in follow:
First, fix on adopting RV reducer after the entirely analysis of many kinds of device system. On the base of the study on some kinds of RV reducers, the Arc bevel gear transmission (high-speed level)and The adjustable gap thicken gear reducer device of variable thick tooth gear drive (low-speed level) are chosen. Conventional design methods are employed to determine primary structure parameters of reducer. Finite element theory and ANSYS software are adopted to force analysis and mode analysis of reducer key components and exploit the parametric design software for the Less thickening gear tooth difference, figure out the thickening gear problem of the complexity of the formula and the large quantity caused by the difference of coefficient, the vary of tooth profile factor.
For the reason that multi-objective optimization in traditional need to deal with the aim function by Linear-weighted, could only achieve optimize approximately. The paper put forward a kind of accurate multi-objective optimization—double populations differential multi-storey culture particle swarm fusion arithmetic after improving. In the evolution process of belief space, the algorithm uses the strategy”Multi-space, Merit-based selection”, avoid the shortcoming of local extremes which is caused by the dispatch of the belief space after updating. In the evolution process of the colony space. The algorithm uses the method of double populations differential multi-storey, avoid the shortcoming of the badly result caused by the discard of abundant high fitness feasible solution, improve the diversity of the colony and the convergence speed. It modify multi-objective optimization of culture particle swarm.
For the reason that the aeronautical micro reducer exists the shortcoming involving the excessive parameters, constraints multiply, the complexity calculation and the fussy design, the paper uses the double populations differential multi-storey culture particle swarm fusion arithmetic to design in three objective in the aeronautical micro reducer, achieve the best solution, comparing with the tradition solution, optimize the problem.
Using the spiral bevel gear as the research objective, the system put up the dynamic analysis of spiral bevel gear in the high level. After the integration consideration of the backlash, time-varying mesh stiffness, transmission error and other kinds of non-linear factors, establish the non-linear dynamic model of Spiral bevel gear pairs. Aim at the point of meshing stiffness, the periodicity of stiffness incentives in the transmission process, In this physical model, the time-varying stiffness has been expressed by a harmonic form with 5 orders and the nonlinear backlash function has been fitted by a polynomial of degree 7. The complicated nonlinear differential equations in dimensionless form has been presented in this dissertation. Using Gear method the reunification of the numerical simulation analysis in non-dimensional differential equations. The results of the various state are single-cycle harmonic, multi-cycle times harmonic, quasi-periodic and chaotic response, after the combination of history, floor plans, Poincare map and FFT spectrum map, the paper analysis and compares various types of detail.
For the reason that the traditional reliability is very difficult, the process is fussy, the paper combines the dynamic process neural networks and Monte-Carlo methods which apply in the reliability analyses in the reducer device. The paper bring forward using the PSO to replace the traditional BP algorithm and apply in the process of the whole connection neural networks, train its connection weights, delete redundant link and make it part of the process of connecting neural network, optimize the structure of the network and increase the speed of network convergence and accuracy. On the basis of the deceleration device fault tree analysis, combine the ICDPNN and Monte-Carlo methods, make reliability study on adjustable air space thickness RV gear deceleration device. The results show that the deceleration device has high reliability, full compliant with the design requirements.
Finally, all structure parameters of reducer sample machine are determined and the drawings of reducer are completed. The load capacity, transmission efficiency and vibration features of the prototype are investigated. The test of the sample machine indicates that it meets the demands of design completely.
首先在对国内外现有减速装置的多种方案进行了全面深入分析,为了实现输入输出轴垂直和苛刻的技术要求确定了采用RV减速传动形式。确定了圆弧锥齿轮传动(高速级)和变齿厚齿轮传动(低速级)的可调隙RV减速装置方案。根据传统设计方法初步确定了减速装置的结构参数,运用有限元理论及ANSYS软件对其关键件进行了强度和模态分析,为此开发出少齿差变厚齿轮参数化设计软件,解决了变厚齿轮因各种截面变位系数不同、左右齿廓参数完全不同,使其公式复杂和参数计算量大等问题。
针对传统的多目标优化算法必须通过线性加权的方式处理目标函数,只能达到近似的优化问题。本文提出一种精确的多目标优化算法,即改进的双群体差分多层文化粒子群融合算法。在信仰空间的进化过程中,该算法采用“多层空间、择优选用”的策略,避免有时因信仰空间更新而导致算法陷入局部最优的缺点;又在群体空间的进化过程中,采用了改进的双群体进化差分的方式,避免丢弃了大量高适应度的不可行解,导致优化结果不理想的问题,实现了群体的多样性,并提高了算法的收敛速度。
本文对航空用微小型减速装置进行三目标优化设计,得到了该减速装置优化设计的最满意解。并采用改进后的算法解决了该装置优化设计时参数多、各参数间的相互制约条件多、计算复杂和设计繁琐等问题,为该微小型减速装置的结构设计奠定了基础。
论文以弧齿锥齿轮系统为研究对象,对高速级弧齿锥齿轮进行了动力学分析。在综合考虑齿侧间隙、时变啮合刚度、传递误差等多种非线性因素的情况下,建立了弧齿锥齿轮副的非线性动力学分析模型。针对齿轮传动过程中啮合刚度的时变性、刚度激励的周期性等特点,在计算的过程中提出了将啮合综合刚度按五次谐波展开,齿侧间隙非线性描述函数用七次多项式拟合,通过无量纲化处理简化了齿轮动力学分析的复杂非线性微分方程,并对其进行了数值仿真分析,得到系统的单周期简谐、多周期次谐、拟周期和混沌等多种稳态响应结果。结合响应的时间历程、相平面图、Poincaré映射图和FFT频谱图,对得到的各类响应结果进行了详细的分析和比较。
针对减速装置的传统可靠性分析方法计算量巨大、过程繁琐等问题,本文将改进的动态过程神经网络与Monte-Carlo方法相结合,应用于减速装置的可靠性分析中。提出了用改进的粒子群算法替换传统的BP算法,并将其应用在给定的全连接过程神经网络的训练过程中,优化了网络结构,提高了网络的收敛速度和精确度。本文以Henon系统仿真为例验证了改进的动态过程神经网络的有效性。在对减速装置故障树分析的基础上,将ICPDPNN和Monte-Carlo方法相结合,对航空用可调间隙变厚齿轮RV减速装置进行了可靠性研究。结果表明,该减速装置具有较高的可靠性,完全符合设计要求。
最后研制一台样机,并对其进行了效率和振动特性的试验,结果表明其性能指标已基本达到试验样机设计要求。
Aeronautical and space technologies actively get rid of the stale and bring forth the fresh and design a perfect micro device. The qualification laid down strict, almost harsh, requirements for the micro reducer- the developing tendency of reducer is toward the orientation of miniaturization, large torque, high speed, stable drive, low noise and high reliability. For the special requirement of the adjustment device of the tail lamina of the rocket the paper develops the micro reducer. A series of theoretical research work is presented in follow:
First, fix on adopting RV reducer after the entirely analysis of many kinds of device system. On the base of the study on some kinds of RV reducers, the Arc bevel gear transmission (high-speed level)and The adjustable gap thicken gear reducer device of variable thick tooth gear drive (low-speed level) are chosen. Conventional design methods are employed to determine primary structure parameters of reducer. Finite element theory and ANSYS software are adopted to force analysis and mode analysis of reducer key components and exploit the parametric design software for the Less thickening gear tooth difference, figure out the thickening gear problem of the complexity of the formula and the large quantity caused by the difference of coefficient, the vary of tooth profile factor.
For the reason that multi-objective optimization in traditional need to deal with the aim function by Linear-weighted, could only achieve optimize approximately. The paper put forward a kind of accurate multi-objective optimization—double populations differential multi-storey culture particle swarm fusion arithmetic after improving. In the evolution process of belief space, the algorithm uses the strategy”Multi-space, Merit-based selection”, avoid the shortcoming of local extremes which is caused by the dispatch of the belief space after updating. In the evolution process of the colony space. The algorithm uses the method of double populations differential multi-storey, avoid the shortcoming of the badly result caused by the discard of abundant high fitness feasible solution, improve the diversity of the colony and the convergence speed. It modify multi-objective optimization of culture particle swarm.
For the reason that the aeronautical micro reducer exists the shortcoming involving the excessive parameters, constraints multiply, the complexity calculation and the fussy design, the paper uses the double populations differential multi-storey culture particle swarm fusion arithmetic to design in three objective in the aeronautical micro reducer, achieve the best solution, comparing with the tradition solution, optimize the problem.
Using the spiral bevel gear as the research objective, the system put up the dynamic analysis of spiral bevel gear in the high level. After the integration consideration of the backlash, time-varying mesh stiffness, transmission error and other kinds of non-linear factors, establish the non-linear dynamic model of Spiral bevel gear pairs. Aim at the point of meshing stiffness, the periodicity of stiffness incentives in the transmission process, In this physical model, the time-varying stiffness has been expressed by a harmonic form with 5 orders and the nonlinear backlash function has been fitted by a polynomial of degree 7. The complicated nonlinear differential equations in dimensionless form has been presented in this dissertation. Using Gear method the reunification of the numerical simulation analysis in non-dimensional differential equations. The results of the various state are single-cycle harmonic, multi-cycle times harmonic, quasi-periodic and chaotic response, after the combination of history, floor plans, Poincare map and FFT spectrum map, the paper analysis and compares various types of detail.
For the reason that the traditional reliability is very difficult, the process is fussy, the paper combines the dynamic process neural networks and Monte-Carlo methods which apply in the reliability analyses in the reducer device. The paper bring forward using the PSO to replace the traditional BP algorithm and apply in the process of the whole connection neural networks, train its connection weights, delete redundant link and make it part of the process of connecting neural network, optimize the structure of the network and increase the speed of network convergence and accuracy. On the basis of the deceleration device fault tree analysis, combine the ICDPNN and Monte-Carlo methods, make reliability study on adjustable air space thickness RV gear deceleration device. The results show that the deceleration device has high reliability, full compliant with the design requirements.
Finally, all structure parameters of reducer sample machine are determined and the drawings of reducer are completed. The load capacity, transmission efficiency and vibration features of the prototype are investigated. The test of the sample machine indicates that it meets the demands of design completely.
引文
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53 X.H.Shi, Y.C. Liang, H. P. Lee, C. Lu, Q. X. Wang. An Improved GA and a Novel PSO-GA-based Hybrid algorithm. Information Processing Letters. 2005, 93(5): 255~261
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56 Q. K. Pan, M. F. Tasgetiren, Y. C. Liang. A Discrete Particle Swarm Optimization Algorithm for the No-wait Flowshop Scheduling Problem. Computer & Optimizations Reserch. 2008(35): 2807~2839
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51 C.A .C. Coello, G .T.Pulido, M.S. Lechuga. Handing Multiple Objectives with Particle Swarm Optimization. IEEE Transactions on Evolutionary Computation, 2004,18(3):256~279
52 X.H.Shi, Y.C. Liang, H. P. Lee, C. Lu, Q. X. Wang. Particle swarm optimization-based algorithms for TSP and generalized TSP. Information Processing Letters. 2007, 103(5): 169~176
53 X.H.Shi, Y.C. Liang, H. P. Lee, C. Lu, Q. X. Wang. An Improved GA and a Novel PSO-GA-based Hybrid algorithm. Information Processing Letters. 2005, 93(5): 255~261
54金欣磊.基于PSO的多目标优化算法研究及应用.浙江大学博士学位论文. 2006: 6~10
55 B. Jiao, Z. Lian, X. Gu. A Dynamic Inertia Weight Particle Swarm Optimization Algorithm. Chaos, Solitons & Fractals. 2008,37(3): 698~705
56 Q. K. Pan, M. F. Tasgetiren, Y. C. Liang. A Discrete Particle Swarm Optimization Algorithm for the No-wait Flowshop Scheduling Problem. Computer & Optimizations Reserch. 2008(35): 2807~2839
57 A. Chatterjee, P. Siarry. Nonlinear Inertia Weight Variation for Dynamic Adaptation in Particle Swarm Optimization. Computers and Operations Research. 2006,33(3): 859~871
58 Hu.X, Eberhart.R:Multi-objective Optimization Using Dynamic Neighborhood Particle Swarm Optimization.In:Proceedings of the 2002 Congress on Evolutionary Computation, IEEE Press, 2002
59 S.Mostaghim and J.Teich.Strategies for finding good local guides in multi-objective particle swarm optimization In IEEE Swarm Intelligence Symposium, 2005 :26~33
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61高芳.智能粒子群优化算法研究.哈尔滨工业大学博士学位论文. 2008:
62 Vilfredo Pareto. Liang. Cours D’Economie Politique. volumeⅠandⅡ.F. rouge. Lansanne, 1986, 143~146
63 C.A . Coello, M.S. Lechuga. MOPSO: A Proposal for Multi-objective Particle Swarm Optimization. The IEEE Congress on Evolutionary Computation. Honolulu. Hawii, 2002: 1051~1056
64 C.A .C. Coello, G .T.Pulido, M.S. Lechuga. Handing Multiple Objectives with Particle Swarm Optimization. IEEE Transactions on Evolutionary Computation, 2004,18(3):256~279
65 Parsonpoulos K.E., Vrahatis M.N. Partiele Swarm Ontimization Method in Multiobjeetiv Problems. Proeeeding sof the 2002 ACM Symposium on Applied Computing (SAC202), 2002,18(3):603~607
66 X.Hu, Eberhart R.C. Multiobjeetive Optimization Using Dynamic Neighborhood Particle Swarm Optimization. In Proeeeding sof the IEEE World Congress on Computational Intelligence, Hawaii, USA, 2002, 1666~1670
67 Robert R G. An introduction to cultural algorithms. Proe of the 3th Annual Conf on Evolution Programming. Singapore : World Scientific Publishing , 1994, 131~136
68 Nguyen T T, Yao Xin. Hybridizing Cultural Algorithms and Local Search. IDEAL. 2006,4224:586～594.
69 Trung Thanh Nguyen, Xin Yao. Hybridizing cultural algorithms and local search. Lecture Notes in Computer Science , 2006 , 42(24) : 586-594
70 Reynolds R G, Peng B. Knowledge learning and social swarms in culture algorithms. J of Mathematical Sociology , 2005 , 29 (2) : 115～132
71 Gao Fang , Cui Gang , Liu Hong-wei. Integration of genetic algorithm and cultural algorithms for constrained optimization. Lecture Notes in Computer Science , 2006 , 4234 : 817～825
72 Reynolds R G. An Introduction to Cultural Al gorithms. Proceedings of the Third Annual Conference on Evolutionary Programming ,World Scientific. River Edge ,New Jersey,1994 :131～139
73齐仲纪,刘漫丹.文化算法研究.计算机技术与发展, 2008, 18(5): 126~130
74 Ricardo Landa Becerra , Carlos A , Coello Coello. A cultural algorithm with differential evolution to solve const rained optimization problems. LectureNotes in Computer Science , 2004 , 3315 : 881～891
75 Yuan X H , Yuan Y B. Application of culture algorithm to generation scheduling of hydrothermal systems .Energy Conversion and Management , 2006 , 47 : 2192～2201
76黄海燕,顾幸生.基于文化算法的神经网络及其在建模中的应用.控制与决策, 2008, 28(4): 477~480
77 Reynolds R ,Stefan J . Web Services ,Web Searches ,and Cultural Algorithms. Proc of IEEE Int’l Conf on Systems , Man and Cybernetics. 2003. 3982~3987
78黄海燕,柳桂国,顾幸生.基于文化算法的KPCA特征提取方法.华东理工大学学报(自然科学版).2008,34(2):256~260
79 Jin X, Reynolds R G. Using knowledge-based evolutionary computation to solve nonlinear constraint optimization problems: a cultural algorithm approach. In: Proceedings of 1999 Congress on Evolutionary Computation. Washington: IEEE, 1999. 1672~1678
80 Lin Yung-Chien, Hwang Kao2Shing, Wang Feng-Sheng. Hybrid differential evolution with multiplier updating method for nonlinear const rained optimization problems.Proceedings of the CEC′2002. Piscataway , New Jersey , 2002 , 1: 872~877
81 Gao F, Cui G, Liu H W. Integration of genetic algorithm and cultural algorithms for constrained optimization. Lecture Notes in Computer Science. Springer, 2006,4234:817~825
82 Lin Yung-Chien, Hwang Kao2Shing, Wang Feng-Sheng. Hybrid differential evolution with multiplier updating method for nonlinear const rained optimization problems.Proceedings of the CEC′2002. Piscataway , New Jersey , 2002 , 1: 872~877
83李炳宇,萧蕴诗,吴启迪.一种基于粒子群算法求解约束优化问题的混合算法.控制与决策, 2004, 19(7): 804~807
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