旋转周期结构动力学研究
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摘要
工程实际中广泛存在一类旋转周期结构。为保证该类结构安全可靠地工作并提高其动态特性,需要深入研究该类结构的动力学问题,揭示基本参数与动力学响应之间的映射关系,进而为其动态设计提供理论依据。本文工作为国家自然科学基金《基于相位调谐的永磁电机减振降噪机理研究》(编号:50705062)的一部分。论文以永磁电机定子为基本原型,系统研究了旋转周期结构的动力学响应特征,主要内容如下:
1.采用哈密顿原理建立了环状旋转周期结构的通用动力学模型,其中结构的基本对称单元可为点单元或面单元。论文采用弹性结构的质量及刚度算子描述结构的模态,进而提出了模态摄动分析的两种一般方法,还给出了各自的适用范围。2.研究了含点对称单元的环状周期结构的模态解析问题,揭示了基本参数与模态特性之间的映射关系,并对其进行了仿真验证。还研究了该类结构的随机失谐问题,并给出了模态特性的统计分布规律和解析形式的数字特征。
3.分析了含面对称单元的环状旋转周期结构的模态特性。采用单位阶跃函数表示面对称单元构型,应用摄动法分析了固有频率分裂和振型耦合规律,并分析了单元周向几何尺寸对模态的影响。还研究了多重旋转周期结构的模态问题,揭示了单元之间的夹角及单元个数等特征参数与动力学响应之间的映射关系。
4.探讨了环状旋转周期结构的受迫振动响应问题。采用摄动方法得到了系统稳态响应的解析结果,分析了共振响应的波动性质,并给出了抑制响应的一般方法。还借助现有文献提供的实验数据对其进行验证。最后以永磁电机的齿槽配合为例,给出了基于旋转周期结构动力学理论的齿槽配合基本原则。
There exist a large number of rotationally periodic structures in engineering. The relationships between the basic parameters and the dynamics of the structures should be studied to present the theoretical foundation for the dynamic design of the structures. This work is a part of the National Natural Science Foundation of China (Investigations on the mechanism of noise and vibration reduction of permanent machines based on phase tuning, Grant No. 50705062). Motivated by the magnetic motor stators, the thesis studied the dynamic response of the rotational periodic structures. And the main contents are:
1. The general dynamic model of the annular-rotational-periodic structures (ARPS) was developed by the Hamilton's principle, in which the basic symmetric element can be point or area element. Two methods for the perturbation analysis of the mode properties were presented according to the mass and stiffness operators, and the application range of the two methods are also given.
2. Closed-form solution to the ARPS with point element was presented. The relationships between the basic parameters and the modal properties are given. The simulation analysis was also carried out to verify the relationships. In addition, the random mistuning of this structure was investigated, and the statistical distribution and the closed-form statistics characteristics of the modal response were also obtained.
3. The modal properties of the ARPS with area element modeled as unit step function were studied. The natural frequency splitting and the mode contamination were analyzed by using the perturbation analysis. And the relationship between the configuration of the area element and the modal response was investigated. Furthermore, the modal properties of the multi-rotationally periodic structures were also studied, and the corresponding relationship between the basic parameters, such as the element number and the position angle between two adjacent elements, and the dynamic response was presented.
4. The closed-form solution to the forced vibration of the ARPS was obtained by using the perturbation method. The method for the wave vibration suppression was also given. The main results were verified by the experimental results given by existing literature. Finally, the basic principle of the slot/pole combination of the magnetic motors was presented based on the rotationally periodic structure dynamics.
1.采用哈密顿原理建立了环状旋转周期结构的通用动力学模型,其中结构的基本对称单元可为点单元或面单元。论文采用弹性结构的质量及刚度算子描述结构的模态,进而提出了模态摄动分析的两种一般方法,还给出了各自的适用范围。2.研究了含点对称单元的环状周期结构的模态解析问题,揭示了基本参数与模态特性之间的映射关系,并对其进行了仿真验证。还研究了该类结构的随机失谐问题,并给出了模态特性的统计分布规律和解析形式的数字特征。
3.分析了含面对称单元的环状旋转周期结构的模态特性。采用单位阶跃函数表示面对称单元构型,应用摄动法分析了固有频率分裂和振型耦合规律,并分析了单元周向几何尺寸对模态的影响。还研究了多重旋转周期结构的模态问题,揭示了单元之间的夹角及单元个数等特征参数与动力学响应之间的映射关系。
4.探讨了环状旋转周期结构的受迫振动响应问题。采用摄动方法得到了系统稳态响应的解析结果,分析了共振响应的波动性质,并给出了抑制响应的一般方法。还借助现有文献提供的实验数据对其进行验证。最后以永磁电机的齿槽配合为例,给出了基于旋转周期结构动力学理论的齿槽配合基本原则。
There exist a large number of rotationally periodic structures in engineering. The relationships between the basic parameters and the dynamics of the structures should be studied to present the theoretical foundation for the dynamic design of the structures. This work is a part of the National Natural Science Foundation of China (Investigations on the mechanism of noise and vibration reduction of permanent machines based on phase tuning, Grant No. 50705062). Motivated by the magnetic motor stators, the thesis studied the dynamic response of the rotational periodic structures. And the main contents are:
1. The general dynamic model of the annular-rotational-periodic structures (ARPS) was developed by the Hamilton's principle, in which the basic symmetric element can be point or area element. Two methods for the perturbation analysis of the mode properties were presented according to the mass and stiffness operators, and the application range of the two methods are also given.
2. Closed-form solution to the ARPS with point element was presented. The relationships between the basic parameters and the modal properties are given. The simulation analysis was also carried out to verify the relationships. In addition, the random mistuning of this structure was investigated, and the statistical distribution and the closed-form statistics characteristics of the modal response were also obtained.
3. The modal properties of the ARPS with area element modeled as unit step function were studied. The natural frequency splitting and the mode contamination were analyzed by using the perturbation analysis. And the relationship between the configuration of the area element and the modal response was investigated. Furthermore, the modal properties of the multi-rotationally periodic structures were also studied, and the corresponding relationship between the basic parameters, such as the element number and the position angle between two adjacent elements, and the dynamic response was presented.
4. The closed-form solution to the forced vibration of the ARPS was obtained by using the perturbation method. The method for the wave vibration suppression was also given. The main results were verified by the experimental results given by existing literature. Finally, the basic principle of the slot/pole combination of the magnetic motors was presented based on the rotationally periodic structure dynamics.
引文
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