圆柱齿轮传动非线性动力学键合图建模研究
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摘要
键合图方法提供了一种统一处理多种能量范畴的工程系统的动态分析方法,可以用来模拟多输入、多输出系统,线性和非线性系统,键合图中的状态变量均为物理变量,可深入地描述系统内部状态的变化过程。但是键合图法的不足是对机械系统中的非线性参数,如摩擦、间隙等因素建模时不是很方便。针对键合图建模方法的不足,本文的主要工作包括：
(1)通过对摩擦力运动特性的分析,引入功率结型结构,建立了能够全面反映摩擦力动态特性的通用键合图模型,该模型不仅能够反映摩擦力在静摩擦状态和动摩擦状态下的运动特性,而且还可以反映摩擦力的耗能特性。
(2)对典型的间隙接触动力学进行了分析,根据相对位移与间隙的关系,把接触力划分为三个状态,建立了间隙接触的通用键合图模型,采用20-sim仿真软件对所建立的模型进行了仿真分析,仿真结果与实际情况相符,验证了模型的正确性。
(3)以齿轮系统为研究对象,分别建立了齿面摩擦的键合图模型、间隙和时变刚度的键合图模型以及静态传递误差的键合图模型,在此基础上,建立了包含齿面摩擦、间隙、时变刚度和静态传递误差等非线性因素的齿轮传动系统非线性键合图模型,并运用20-sim和Matlab仿真软件对模型进行了对比仿真研究,结果验证了模型的正确性。
(4)采用实验的方法测到了一对实验齿轮的静态传递误差和动态传递误差曲线,并将动态传递误差与采用本文建立的齿轮键合图模型计算得到的传递误差曲线进行了对比,两者的啮合频率基本一致,但是幅值有一定的误差,基本验证了本文建立的齿轮系统键合图模型的正确性。
Bond graph provides a multiple energy domain coupling analytical method, which can be used to simulate the multiple input and multiple output systems, linear and nonlinear systems. The state variables of bond graph are physical variables that can be in-depth described the process of state changes within the system. But it is hard to use bond graph model to express a micro mechanical system parameters, such as friction and clearance. In order to solve these problems, this paper has completed the following research work.
(1) On the base of theory analysis, this paper established a common bond graph model that could reflect the dynamic characteristics of friction through introducing the concept of switched power junction. This model not only could comprehensive reflect the characteristics of friction both in the static state and in the dynamic motion, but also reflect the consume energy characteristics of friction.
(2) According to the relationship between relative displacement and clearance, the contact force along the meshing line is divided into three statuses, and then presented the bond graph model of contact with clearance.20-sim is employed to studying the modeling.
(3) Taking a gear system as study object, established bond graph model of friction, bond graph model of time-varying stiffness with clearance and bond graph model of static transmission error, respectively. On this base, a comprehensive bond graph model of gear system that including friction, clearance, time-varying stiffness and static transmission error is presented. Applying advanced software 20-sim to simulate the model. The results are compared with those from Matlab to check the bond graph model and verity its credibility.
(4) Using experimental method measured the static gear transmission error and dynamic transmission error curve of a pair of gear, the results have been compared with values of theoretical calculation that based on bond graph model of this paper established. The results indicated that they have the same mesh frequency, but the amplitude has a little error, the conclusion verifies the accuracy and the possibility of the bond graph model.
(1)通过对摩擦力运动特性的分析,引入功率结型结构,建立了能够全面反映摩擦力动态特性的通用键合图模型,该模型不仅能够反映摩擦力在静摩擦状态和动摩擦状态下的运动特性,而且还可以反映摩擦力的耗能特性。
(2)对典型的间隙接触动力学进行了分析,根据相对位移与间隙的关系,把接触力划分为三个状态,建立了间隙接触的通用键合图模型,采用20-sim仿真软件对所建立的模型进行了仿真分析,仿真结果与实际情况相符,验证了模型的正确性。
(3)以齿轮系统为研究对象,分别建立了齿面摩擦的键合图模型、间隙和时变刚度的键合图模型以及静态传递误差的键合图模型,在此基础上,建立了包含齿面摩擦、间隙、时变刚度和静态传递误差等非线性因素的齿轮传动系统非线性键合图模型,并运用20-sim和Matlab仿真软件对模型进行了对比仿真研究,结果验证了模型的正确性。
(4)采用实验的方法测到了一对实验齿轮的静态传递误差和动态传递误差曲线,并将动态传递误差与采用本文建立的齿轮键合图模型计算得到的传递误差曲线进行了对比,两者的啮合频率基本一致,但是幅值有一定的误差,基本验证了本文建立的齿轮系统键合图模型的正确性。
Bond graph provides a multiple energy domain coupling analytical method, which can be used to simulate the multiple input and multiple output systems, linear and nonlinear systems. The state variables of bond graph are physical variables that can be in-depth described the process of state changes within the system. But it is hard to use bond graph model to express a micro mechanical system parameters, such as friction and clearance. In order to solve these problems, this paper has completed the following research work.
(1) On the base of theory analysis, this paper established a common bond graph model that could reflect the dynamic characteristics of friction through introducing the concept of switched power junction. This model not only could comprehensive reflect the characteristics of friction both in the static state and in the dynamic motion, but also reflect the consume energy characteristics of friction.
(2) According to the relationship between relative displacement and clearance, the contact force along the meshing line is divided into three statuses, and then presented the bond graph model of contact with clearance.20-sim is employed to studying the modeling.
(3) Taking a gear system as study object, established bond graph model of friction, bond graph model of time-varying stiffness with clearance and bond graph model of static transmission error, respectively. On this base, a comprehensive bond graph model of gear system that including friction, clearance, time-varying stiffness and static transmission error is presented. Applying advanced software 20-sim to simulate the model. The results are compared with those from Matlab to check the bond graph model and verity its credibility.
(4) Using experimental method measured the static gear transmission error and dynamic transmission error curve of a pair of gear, the results have been compared with values of theoretical calculation that based on bond graph model of this paper established. The results indicated that they have the same mesh frequency, but the amplitude has a little error, the conclusion verifies the accuracy and the possibility of the bond graph model.
引文
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