摘要
摆振是轮子行走机构动力学研究的重要问题之一。本文从简单的单转向轮系统入手,建立不同复杂程度单转向轮系统的线性与非线性动力学模型；搭建了参数可调的单转向轮摆振实验装置,验证了转向轮系统动力学系统模型的有效性；应用线性常微分方程稳定性理论与非线性动力学Hopf分岔理论,研究转向轮系统的稳定性；提出了防范摆振的方法；对实际轮椅车转向轮系统参数进行优化设计；解决了杠杆驱动式轮椅车转向轮的摆振问题。其具体研究工作如下：
从单自由度转向轮系统出发,分别探讨了单自由度垂直旋转枢轴、非垂直旋转枢轴转向轮动力学系统的数学模型与稳定性；建立了单自由度、二自由度典型单转向轮系统的线性动力学模型,分析了系统中阻尼参数、质量参数、几何参数与陀螺仪效应对稳定性的影响；基于线性稳定性理论对单轮、双轮、单自由度和二自由度典型单转向轮动力学系统进行稳定性分析；并从频域角度对摆振的机理进行进一步的解释。
以杠杆驱动式轮椅车的转向轮系统为研究对象,将系统适当简化,利用分析力学方法,建立了转向轮三自由度非线性动力学系统模型,以及分解的两种二自由度和单自由度转向轮动力学系统模型。讨论了转向轮动力学系统中主要参数对其稳定性的影响。
搭建了可调节主要参数的转向轮摆振实验装置,构造了一种全新的转向轮摆振实验台。此外,通过对三个自由度以及分解的二自由度和单自由度转向轮摆振实验装置的实验研究,用来检验理论上所建立的转向轮非线性动力学系统模型的可靠性。
在二自由度转向轮系统动力学模型的基础上,应用非线性动力学Hopf分岔理论和常微分方程稳定性理论,对二自由度有、无阻尼转向轮系统的自激型摆振分岔特性进行了分析。阐明了,转向轮系统在一组特定的参数组合下,会表现出自激型摆振的性质,即自激型摆振是一种非线性动力学Hopf分岔后出现的稳定极限环振动现象；通过对摆振振幅及摆振发生时的速度的分析表明,由于转向轮系统中质量参数、几何参数及阻尼参数的改变,能够引起转向轮系统稳定性的变化,间接影响了摆振振幅和频率的变化,而摆振的强烈程度也反映了轮子行走装置的稳定性。
通过研究转向轮系统参数变化对摆振的影响规律,提出了预防摆振的方法,获得了几条新的具有实用价值的结论。例如,通过增加拖距长度、合理的选择质量参数或者增加系统的阻尼都可以减小甚至消除摆振。利用遗传优化算法对轮椅车转向轮系统进行结构优化,针对实验研究的转向轮摆振实验装置进行稳定性分析,并采用增加阻尼轴承的方法改善实验中转向轮系统的稳定性。应用稳定性分析和结构优化设计的方法和结论,解决杠杆驱动式轮椅车转向轮摆振问题。
The steering wheel shimmy is a serious problem of wheeled device dynamics system. The mechanism of shimmy and stability analysis of different dynamics models were developed by simplified single steering wheel system. Meanwhile the mathematic steering wheel models were valid by shimmy test bench. The linear and nonlinear stability characters of steering wheel model were analyzed by stability theory of ordinary differential equation and Hopf bifurcation theory of nonlinear dynamics. The methods that can avoid shimmy were summed up from engineering viewpoints. The shimmy problem of steering wheel in a lever propulsion wheelchair has been solved based on the methods and conclusions of analysis of stability and optimization design. The main researches are as follows:
The single Degree of Freedom (DoF) model of the typical steering wheel with vertical axis and inclined axis was established and their stability analyses were conducted respectively. The linear dynamics model of the typical steering wheel system was established to study the stability effect with different parameters. In particular, an analytical solution has been found for a system where the wheel has a mechanical trail and both the yaw and lateral damping of the hinge point are taken into account. The stability analysis of one and two DoFs typical steering wheel model was conducted using root locus theory and Routh Criterion. Furthermore we are applying control theory to explain the mechanism of shimmy in frequency domain.
Lever propulsion wheelchair steering wheel dynamics model of3DoFs was established by analytic mechanics. This model is derived from Lagrange equation and its numerical solutions are solved by Ordinary Differential Equation (ODE) method. And the derivatives models are introduced by simplifying the3DoFs caster wheel model. Its different stability characters were given by changing the geometry, mass and damping parameters of the steering wheel system.
In the experimental stage, a new steering wheel shimmy test bench was established. The whole structure and the working process of the test bench were introduced. Vibration measurements successfully verified the theoretical results obtained from mathematical model as well as the dynamics behavior of towed wheels within different cases.
Steering wheel model bifurcation character of the self-excited shimmy was analyzed by Hopf bifurcation theory of nonlinear dynamics and by stability theory of ordinary differential equation. The computation results indicate that the self-excited shimmy is a stable limit cycle occurring after Hopf bifurcation and it can occur on the wheelchair with a certain set of parameters. The shimmy angle and the range of critical velocities of the wheelchair have effects on shimmy and the intensity of shimmy is also able to represent good or bad stability characters.
To avoid and eliminate shimmy, some new practical suggestions are offered due to the effects of system parameters on shimmy, for instance, by increasing length of the trail, applying a damped bearing and adopting reasonable parameters of geometry and mass.
To avoid the shimmy in the design stage, the genetic algorithm was applied to optimization design of the steering wheel system. According to the results obtained from the experiment to analyze the stability characters. Shimmy can be avoided after replacing a damping bearing with a set of reasonable parameters. Using the same method, the optimization of a real wheel chair was conducted. Base on the stability analysis and optimization design conclusion to solve the shimmy problem of steering wheel in a lever propulsion wheelchair.
引文
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