Prohl传递矩阵法在非线性转子系统中的应用研究
发布时间：2019-05-18 07:14
【摘要】：传递矩阵技术是国际上工程技术界近数十年来发展起来的一种效率非常高、非常可靠的链式结构系统计算分析工具。理论基础首先是将一个完整的复杂结构系统离散成一系列子单元或子结构,然后针对离散后的每一个结构子单元建立该单元左右两端状态变量的传递矩阵,最后在计算机的协助下利用矩阵的简单传递原理对结构进行动静态分析以及稳定性分析。由于传递矩阵技术相比有限单元法等分析方法具有简便实用,传递矩阵阶数低,无需预知振型,且对计算机性能要求不高,计算机时短,易为一般工程技术人员所掌握等优点,近年来特别受到工程技术人员的青睐。传递矩阵技术已经在建筑结构、航空航天、石油勘探、电力机械、火炮火箭等很多领域得到十分广泛应用。其中在这些领域中的线性系统应用较多、也比较成熟,但在大型复杂非线性系统中的应用研究才刚刚开始、还非常初步。对转子-轴承系统的动力响应研究和其他体系的研究一样,都是从线弹性范围开始,逐步增加约束条件和边界条件,过渡到局部非线性系统,然后是整体非线性系统等等。严格来讲,线性系统是理想化的、忽略次要因素简化后的系统,非线性系统才是物理现象的本质属性。本文研究的主要内容是对传统的Prohl传递矩阵技术进行改进,使其能够有效的应用于非线性链式结构系统中。主要研究内容如下:1、深入学习和研究了传递矩阵技术,综述了传递矩阵技术在建筑机械结构等领域的线性系统以及非线性系统中的应用;2、本文基于Prohl传递矩阵技术,提出借助Wilson-θ法建立传递矩阵关系,利用Rugge-kutta法计算传递矩阵中的非线性项,使改进后的Prohl传递矩阵技术能应用于非线性链式结构系统的分析计算;3、针对传递矩阵技术在每一时刻各个站位的状态变量的传递,本文采用加速度作为传递变量,这样避免了使用位移作为传递变量时带来的数值不稳定现象,提高了本文方法的数值稳定性。4、最后用改进后的Prohl传递矩阵技术,实例分析计算了一个非线性双转子系统的瞬态响应和稳态响应,通过与有限元法分析计算结果比较,验证了本文方法的正确性和有效性。
[Abstract]:Transfer matrix technology is a very efficient and reliable tool for the calculation and analysis of chain structure system, which has been developed in the field of engineering technology in recent decades. The theoretical basis is that a complete complex structural system is discretized into a series of subunits or substructures, and then the transfer matrix of the state variables at the left and right ends of the element is established for each discrete structural subsystem. Finally, with the assistance of computer, the static analysis and stability analysis of structural advance are carried out by using the simple transfer principle of matrix. Compared with the finite element method, the transfer matrix technique is simple and practical, the order of the transfer matrix is low, there is no need to predict the vibration mode, and the performance of the computer is not high, the computer time is short, and it is easy to be mastered by the general engineers and technicians. In recent years, it has been especially favored by engineers and technicians. Transfer matrix technology has been widely used in many fields, such as building structure, aerospace, oil exploration, power machinery, artillery and rocket and so on. Among them, there are many applications and mature linear systems in these fields, but the research on the application of linear systems in large and complex nonlinear systems has only just begun and is still very preliminary. The dynamic response of rotor-bearing system is the same as that of other systems, starting from the linear elastic range, gradually increasing the constraint and boundary conditions, transitioning to the local nonlinear system, and then the global nonlinear system and so on. Strictly speaking, the linear system is idealized, and the nonlinear system is the essential attribute of the physical phenomenon by neglecting the simplified system with secondary factors. The main content of this paper is to improve the traditional Prohl transfer matrix technology so that it can be effectively applied to nonlinear chain structure systems. The main research contents are as follows: 1. The transfer matrix technology is deeply studied and studied, and the application of transfer matrix technology in linear systems and nonlinear systems in the field of construction machinery structure is reviewed. 2. Based on the Prohl transfer matrix technique, this paper proposes to establish the transfer matrix relation with the help of Wilson- 胃 method, and to calculate the nonlinear terms in the transfer matrix by Rugge-kutta method. The improved Prohl transfer matrix technique can be applied to the analysis and calculation of nonlinear chain structure systems. 3. In view of the transfer of the state variables of each station at each time, the acceleration is used as the transfer variable, which avoids the numerical instability caused by the use of displacement as the transfer variable. The numerical stability of the proposed method is improved. 4. Finally, the transient response and steady state response of a nonlinear double rotor system are analyzed and calculated by using the improved Prohl transfer matrix technique, and the results are compared with those of the finite element method. The correctness and effectiveness of the proposed method are verified.
【学位授予单位】：西安工业大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：TH113
本文编号：2479782
[Abstract]:Transfer matrix technology is a very efficient and reliable tool for the calculation and analysis of chain structure system, which has been developed in the field of engineering technology in recent decades. The theoretical basis is that a complete complex structural system is discretized into a series of subunits or substructures, and then the transfer matrix of the state variables at the left and right ends of the element is established for each discrete structural subsystem. Finally, with the assistance of computer, the static analysis and stability analysis of structural advance are carried out by using the simple transfer principle of matrix. Compared with the finite element method, the transfer matrix technique is simple and practical, the order of the transfer matrix is low, there is no need to predict the vibration mode, and the performance of the computer is not high, the computer time is short, and it is easy to be mastered by the general engineers and technicians. In recent years, it has been especially favored by engineers and technicians. Transfer matrix technology has been widely used in many fields, such as building structure, aerospace, oil exploration, power machinery, artillery and rocket and so on. Among them, there are many applications and mature linear systems in these fields, but the research on the application of linear systems in large and complex nonlinear systems has only just begun and is still very preliminary. The dynamic response of rotor-bearing system is the same as that of other systems, starting from the linear elastic range, gradually increasing the constraint and boundary conditions, transitioning to the local nonlinear system, and then the global nonlinear system and so on. Strictly speaking, the linear system is idealized, and the nonlinear system is the essential attribute of the physical phenomenon by neglecting the simplified system with secondary factors. The main content of this paper is to improve the traditional Prohl transfer matrix technology so that it can be effectively applied to nonlinear chain structure systems. The main research contents are as follows: 1. The transfer matrix technology is deeply studied and studied, and the application of transfer matrix technology in linear systems and nonlinear systems in the field of construction machinery structure is reviewed. 2. Based on the Prohl transfer matrix technique, this paper proposes to establish the transfer matrix relation with the help of Wilson- 胃 method, and to calculate the nonlinear terms in the transfer matrix by Rugge-kutta method. The improved Prohl transfer matrix technique can be applied to the analysis and calculation of nonlinear chain structure systems. 3. In view of the transfer of the state variables of each station at each time, the acceleration is used as the transfer variable, which avoids the numerical instability caused by the use of displacement as the transfer variable. The numerical stability of the proposed method is improved. 4. Finally, the transient response and steady state response of a nonlinear double rotor system are analyzed and calculated by using the improved Prohl transfer matrix technique, and the results are compared with those of the finite element method. The correctness and effectiveness of the proposed method are verified.
【学位授予单位】：西安工业大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：TH113
【引证文献】
相关硕士学位论文 前1条
1 周元伟;磁悬浮储能飞轮转子系统的临界转速分析[D];哈尔滨工程大学;2018年
，本文编号：2479782
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