储能飞轮优化设计理论与方法研究
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摘要
在能源和环境问题日益严峻的今天,节能和环保技术已成为国内外研究的前沿和热点。储能技术是实现能源高效利用的重要途径,深受能源界和工业界的重视。飞轮储能技术具有储能密度大、功率密度大、效率高、寿命长、低污染等优点,在航空航天、汽车、电力系统等领域具有非常广泛的应用前景。高速旋转的飞轮是飞轮储能系统最核心的储能部件,因此,飞轮设计问题是实现飞轮系统储能的关键技术,将直接决定飞轮系统的储能性能。本论文在吸收现有研究成果的基础上,深入研究了影响飞轮储能性能的关键因素,针对各向同性材料飞轮、纤维增强复合材料飞轮及功能梯度材料飞轮,提出和改进了提高飞轮储能性能的方法和措施,进一步完善了高速储能飞轮优化设计的理论与方法,为设计和研制性能可靠、性价比高的储能飞轮,提供了重要的理论依据和实现途径。
本文深入研究了各向同性材料飞轮的形状优化设计问题,分析了转速对飞轮形状的影响,通过将飞轮转速划分为低速、中速和高速三个阶段,采用最优控制理论,直接得到了飞轮最优形状的解析表达式,克服了飞轮一般形状优化方法效率低的缺点；通过比较实心、空心飞轮低速、中速和高速情况下的最优形状,揭示了各向同性材料实心和空心飞轮最优形状随转速改变呈阶段性变化的规律。最后,根据飞轮形状优化的研究结果,设计了低成本、低转速工况的金属材料飞轮的最优结构,并将其用作汽车碰撞试验系统的动力牵引装置,以仅30kW功率的电机,完成了某微型客车的实车正碰试验,验证了飞轮储能在汽车碰撞试验系统中应用的可行性。
本文在深入分析传统渐进结构拓扑优化方法存在的问题和不足的基础上,引入新的材料插值模型和新的性能收敛指标,改进了传统的基于von Mises应力的双向渐进结构优化(BESO)算法。并结合有限元软件Abaqus和编程语言Matlab实现了该改进的BESO算法。运用改进BESO算法,本文又进一步研究了各向同性材料飞轮的拓扑结构优化问题,并得到了结构合理、边界清晰的飞轮最优拓扑结构。最后,分析和总结了飞轮的最优拓扑结构随结构控制体积、旋转周期数改变的变化规律及特点。
本文指出并分析了多层过盈装配的混合复合材料飞轮可能产生的多种失效形式：除了离心力作用下复合材料飞轮沿环向被拉断和沿径向被拉裂以外,还有可能存在层问过盈压力过大把飞轮压坏或者层间过盈压力过小导致飞轮外层圆环脱落的失效现象。利用本文提出的可以解决约束非线性优化问题的且具有全局收敛性和较高计算效率的两阶段增广Lagrange粒子群优化算法(TS-ALPSO),研究了多层混合复合材料飞轮的成本优化问题。分析了飞轮材料价格不变时,材料次序、分层数及过盈量对飞轮储能性能的影响；最后,得到和总结了飞轮单位成本储能最大时,飞轮分层半径、层间过盈量及转速随飞轮材料价格改变的变化规律。
对于功能梯度材料(FGM)飞轮,本文首先修正和改进了轴对称平面应力理论,克服了飞轮轴向厚度较厚时,平面应力(PS)解误差大的问题,并推导了FGM材料飞轮的三维修正平面应力(MPS)解：其次,基于分段三次保形插值法,提出了自适应保形(ASP)插值算法,解决了飞轮形状优化时,形状控制点位置难选取、数量难确定的问题,提高了飞轮形状优化的精度；最后,采用基于ASP插值的序列二次规划(SQP)算法,同时优化设计了FGM材料飞轮的形状和材料分布,进一步均匀化了飞轮的应力分布,提高了飞轮材料的利用率。通过对计算结果的分析,总结了FGM材料飞轮的形状及材料参数对其储能性能的影响规律。
Today, with the environment and energy problems growing, techniques for energy saving and environment protectiing become the hotspots and frontiers in current researches. Energy storage technology is an important way to utilize the energy efficiently, and is paid more attention to by energy sectors and industrial circles. Flywheel is proved to be an ideal form of energy storage on account of its high energy density, high power density, high efficiency, long lifetime, low environmental impact, etc. It is finding increasing use in aerospace, vehicles and power system. A high-speed rotating flywheel is a key component in the flywheel energy storage system. So the design of the flywheel is very crucial and important, which will directly determine the energy storage ability of the flywheel system. Based on assimilating current research findings, factors that affect energy storage performances of the flywheel are fully researched in this paper. Approaches and measures for improving energy storage ability of isotropic material, composite and founctionally graded material (FGM) flywheels are proposed and modified respectively. Works in this paper further round out the optimization design theory and methods for high-speed flywheels for energy storage, and provide important theory basses and effective approaches for designing and manufacturing a reliable and cost-effective flywheel for energy storage.
In this paper, shape optimization of the isotropic material flywheel is researched. To overcome the shortcomings that the calculation efficiency of the ordinary method is low in the flywheel shape optimization, effects of rotating speed on the optimal shapes of the flywheel are analyzed, and brief analytic expressions of the flywheel optimal shapes are directly gained adopting the optimal control theory by dividing the rotating speed into low, medium and high speed intervals. Through comparing the optimal shapes of the isotropic solid and hollow flywheels at low, medium and high speed respectively, change rules of the optimal shapes with the rotating speed are revealed. Based on the research results above, a low cost, low speed metal flywheel is designed to use as the power traction device for automobile crash test system in this paper. At last, a microbus front crash test is conducted by this new power traction device using merely a30kW motor and validates the availability of applying the energy storage flywheel to the automobile crash test system.
After analyzing the problems and flaws in the previous evolutionary structural topology method, the previous bi-directional evolutional structural optimization (BESO) method based on von Mises stress is improved by introducing a new material interpolation model and a new performance convergence index in this paper. For the implementation of the modified BESO method, a combination of finite element software Abaqus with programming language Matlab is used. Adopting this modified BESO method, the topology optimization of the flywheel is further researched in this paper, and the optimized flywheels with rational structures and clear profiles are found. At last, variation characteristics of the flywheel optimal topology are analyzed and summarized as the structure volume and rotationally period are changing.
For the press-fit multi-rim composite flywheel, the possible material failures that except radial crack drawn by the centrifugal force, too high interference press may crush the composite and too low interference press may separate the outer rims while the flywheel is rotating are pointed out and analyzed in this paper. And then, using the two-stage Augmented Lagrange Particle Swarm Optimization (TS-ALPSO) algorithm proposed in this paper, which can solve nonlinear optimization problems with constraints and has global convergence and higher computational efficiency, cost optimization of the multi-rim hybrid composite flywheel is researched. For a certain material price, the influences of material sequence, rims number and interferences on the energy storage performance of flywheel are discussed. At last, as the prices of materials change continuously, variation rules of radius of each rim, interferences and rotating speed are revealed and summarized for the composite flywheel when its stored energy per unit cost is maximized.
For the functionally graded material flywheel, firstly, a modified plane stress theory is presented by extending the2D PS theory in order to make up for the shortcomings that with thickness of the flywheel increasing, the plane stress(PS) solution becomes inaccurate. Then, a3D modified plane stress (MPS) solution of the functionally graded material flywheel is derived. Secondly, based on the piecewise cubic shape-preserving interpolation method, an adaptive shape-preserving (ASP) interpolation method is proposed to solve the problem that in the shape optimization, the locations and number of the control points are difficult to determine. Using this interpolation method, the accuracy of shape optimization is improved significantly. At last, using the sequential quadratic programming (SQP) optimization method based on the ASP interpolation method, shape and material distribution of FGM flywheel is optimized simultaneously. Both of the shape and material optimization produces a really better flywheel in which the stress is more even and the material is made better use of. Through analyzing the optimization results, influences of the shape and material properties on the energy storage performance of FGM flywheel are summarized.
本文深入研究了各向同性材料飞轮的形状优化设计问题,分析了转速对飞轮形状的影响,通过将飞轮转速划分为低速、中速和高速三个阶段,采用最优控制理论,直接得到了飞轮最优形状的解析表达式,克服了飞轮一般形状优化方法效率低的缺点；通过比较实心、空心飞轮低速、中速和高速情况下的最优形状,揭示了各向同性材料实心和空心飞轮最优形状随转速改变呈阶段性变化的规律。最后,根据飞轮形状优化的研究结果,设计了低成本、低转速工况的金属材料飞轮的最优结构,并将其用作汽车碰撞试验系统的动力牵引装置,以仅30kW功率的电机,完成了某微型客车的实车正碰试验,验证了飞轮储能在汽车碰撞试验系统中应用的可行性。
本文在深入分析传统渐进结构拓扑优化方法存在的问题和不足的基础上,引入新的材料插值模型和新的性能收敛指标,改进了传统的基于von Mises应力的双向渐进结构优化(BESO)算法。并结合有限元软件Abaqus和编程语言Matlab实现了该改进的BESO算法。运用改进BESO算法,本文又进一步研究了各向同性材料飞轮的拓扑结构优化问题,并得到了结构合理、边界清晰的飞轮最优拓扑结构。最后,分析和总结了飞轮的最优拓扑结构随结构控制体积、旋转周期数改变的变化规律及特点。
本文指出并分析了多层过盈装配的混合复合材料飞轮可能产生的多种失效形式：除了离心力作用下复合材料飞轮沿环向被拉断和沿径向被拉裂以外,还有可能存在层问过盈压力过大把飞轮压坏或者层间过盈压力过小导致飞轮外层圆环脱落的失效现象。利用本文提出的可以解决约束非线性优化问题的且具有全局收敛性和较高计算效率的两阶段增广Lagrange粒子群优化算法(TS-ALPSO),研究了多层混合复合材料飞轮的成本优化问题。分析了飞轮材料价格不变时,材料次序、分层数及过盈量对飞轮储能性能的影响；最后,得到和总结了飞轮单位成本储能最大时,飞轮分层半径、层间过盈量及转速随飞轮材料价格改变的变化规律。
对于功能梯度材料(FGM)飞轮,本文首先修正和改进了轴对称平面应力理论,克服了飞轮轴向厚度较厚时,平面应力(PS)解误差大的问题,并推导了FGM材料飞轮的三维修正平面应力(MPS)解：其次,基于分段三次保形插值法,提出了自适应保形(ASP)插值算法,解决了飞轮形状优化时,形状控制点位置难选取、数量难确定的问题,提高了飞轮形状优化的精度；最后,采用基于ASP插值的序列二次规划(SQP)算法,同时优化设计了FGM材料飞轮的形状和材料分布,进一步均匀化了飞轮的应力分布,提高了飞轮材料的利用率。通过对计算结果的分析,总结了FGM材料飞轮的形状及材料参数对其储能性能的影响规律。
Today, with the environment and energy problems growing, techniques for energy saving and environment protectiing become the hotspots and frontiers in current researches. Energy storage technology is an important way to utilize the energy efficiently, and is paid more attention to by energy sectors and industrial circles. Flywheel is proved to be an ideal form of energy storage on account of its high energy density, high power density, high efficiency, long lifetime, low environmental impact, etc. It is finding increasing use in aerospace, vehicles and power system. A high-speed rotating flywheel is a key component in the flywheel energy storage system. So the design of the flywheel is very crucial and important, which will directly determine the energy storage ability of the flywheel system. Based on assimilating current research findings, factors that affect energy storage performances of the flywheel are fully researched in this paper. Approaches and measures for improving energy storage ability of isotropic material, composite and founctionally graded material (FGM) flywheels are proposed and modified respectively. Works in this paper further round out the optimization design theory and methods for high-speed flywheels for energy storage, and provide important theory basses and effective approaches for designing and manufacturing a reliable and cost-effective flywheel for energy storage.
In this paper, shape optimization of the isotropic material flywheel is researched. To overcome the shortcomings that the calculation efficiency of the ordinary method is low in the flywheel shape optimization, effects of rotating speed on the optimal shapes of the flywheel are analyzed, and brief analytic expressions of the flywheel optimal shapes are directly gained adopting the optimal control theory by dividing the rotating speed into low, medium and high speed intervals. Through comparing the optimal shapes of the isotropic solid and hollow flywheels at low, medium and high speed respectively, change rules of the optimal shapes with the rotating speed are revealed. Based on the research results above, a low cost, low speed metal flywheel is designed to use as the power traction device for automobile crash test system in this paper. At last, a microbus front crash test is conducted by this new power traction device using merely a30kW motor and validates the availability of applying the energy storage flywheel to the automobile crash test system.
After analyzing the problems and flaws in the previous evolutionary structural topology method, the previous bi-directional evolutional structural optimization (BESO) method based on von Mises stress is improved by introducing a new material interpolation model and a new performance convergence index in this paper. For the implementation of the modified BESO method, a combination of finite element software Abaqus with programming language Matlab is used. Adopting this modified BESO method, the topology optimization of the flywheel is further researched in this paper, and the optimized flywheels with rational structures and clear profiles are found. At last, variation characteristics of the flywheel optimal topology are analyzed and summarized as the structure volume and rotationally period are changing.
For the press-fit multi-rim composite flywheel, the possible material failures that except radial crack drawn by the centrifugal force, too high interference press may crush the composite and too low interference press may separate the outer rims while the flywheel is rotating are pointed out and analyzed in this paper. And then, using the two-stage Augmented Lagrange Particle Swarm Optimization (TS-ALPSO) algorithm proposed in this paper, which can solve nonlinear optimization problems with constraints and has global convergence and higher computational efficiency, cost optimization of the multi-rim hybrid composite flywheel is researched. For a certain material price, the influences of material sequence, rims number and interferences on the energy storage performance of flywheel are discussed. At last, as the prices of materials change continuously, variation rules of radius of each rim, interferences and rotating speed are revealed and summarized for the composite flywheel when its stored energy per unit cost is maximized.
For the functionally graded material flywheel, firstly, a modified plane stress theory is presented by extending the2D PS theory in order to make up for the shortcomings that with thickness of the flywheel increasing, the plane stress(PS) solution becomes inaccurate. Then, a3D modified plane stress (MPS) solution of the functionally graded material flywheel is derived. Secondly, based on the piecewise cubic shape-preserving interpolation method, an adaptive shape-preserving (ASP) interpolation method is proposed to solve the problem that in the shape optimization, the locations and number of the control points are difficult to determine. Using this interpolation method, the accuracy of shape optimization is improved significantly. At last, using the sequential quadratic programming (SQP) optimization method based on the ASP interpolation method, shape and material distribution of FGM flywheel is optimized simultaneously. Both of the shape and material optimization produces a really better flywheel in which the stress is more even and the material is made better use of. Through analyzing the optimization results, influences of the shape and material properties on the energy storage performance of FGM flywheel are summarized.
引文
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