前轮非线性摆振稳定性分析

飞机前起落架支柱上的几个非线性项,例如扭转间隙、库仑摩擦以及速度平方阻尼等,对前轮摆振稳定区域有着重要的影响.文中假设前起落架支柱上端固支,并且给出了用以描述五自由度的前轮摆振运动的非线性微分方程组,使用描述函数法研究了上述三个非线性项对前轮摆振稳定区域的影响,将准线性化的方程组代入状态空间内,利用优化特征值实部的方法确定摆振系统的极限环幅值、摆振频率以及临界参数曲线,这种方法可以免去以往摆振稳定性分析时冗长的代数推导.作为比较,文中还计算了前轮线性摆振系统的临界频率以及临界参数曲线,两种结果比较分析表明,支柱内的几个非线性项对前轮摆振稳定区域有着重要的影响,由于扭转间隙的存在,使得飞机临界滑跑速度大大降低.

The Stability Analysis of the Nonlinear Shimmy

Several nonlinear terms, such as backlash, Coulomb friction and velocity-squared damping in the nonlinear shimmy system, have the significant effect on stability. This paper assumes that the top of nose wheel strut is fixed and gives the complete nonlinear equations used to describe the shimmy system with five degrees of freedom. The describing function method is used to analyse the contribution of the above nonlinear terms to the shimmy stability region. The nonlinear equations are transferred into the state space. The amplitude of limit cycle, frequency and the critical parameter curves are determined by optimizing the real part of complex eigenvalues. Meanwhile, this method can extricate designers from the tedious algebraical derivation in the early shimmy stability analysis. For comparison, the corresponding linear shimmy stability is also analysed. It is shown that the influence of several nonlinear terms in the strut on the shimmy stability region is significant. Because of backlash, the critical taxiing speed of aircraft decreases greatly.