基于切比雪夫多项式展开的转子动力特性区间分析

基于切比雪夫多项式展开,建立了转子系统临界转速和稳态响应区间分析方法,能在仅具有参数上下界的情况下获得结果分布区间。针对临界转速区间分析问题,将支承刚度、密度和弹性模量视为区间变量,建立转子系统固有频率的切比雪夫多项式表达式,最终获得临界转速区间,临界转速误差不超过0.07%。在固有特性分析基础上,应用切比雪夫方法求解转子系统的稳态响应,并由模态叠加原理对响应区间进行修正,解决了固有特性不确定性较大时稳态响应求解精度不足的问题。与蒙特卡洛插值结果相比,响应上界误差不超过8%。基于切比雪夫展开的非确定分析方法,不需修改原结构的振动微分方程。结果表明该方法结合商业有限元软件后,应用简单,并具有理想的精度。

Interval analysis of rotor dynamic characteristics based on ,Chebyshev polynomials expansion

Interval analysis method on critical speeds and steady response was established to acquire accurate results with the bounds of parameters based on Chebyshev expansion. Critical speeds were expressed as Chebyshev polynomials expansion to calculate the interval results when support stiffness, density or elastic modulus were interval parameters. The comparison between Chebyshev method, perturbation method and combination method illustrated that the maximum error was less than 0.07%. The Chebyshev method on steady response was proposed while modal superposition was applied to correct the bounds. The defect of the original method arising from the large uncertainty of critical speeds was fixed. The comparison with Monte Carlo method illustrated that the maximum error of response upper bound was less than 8%. The differential equations of the original system do not need to be modified in Chebyshev method. The results illustrate that combined with commercial finite element software, the method has good applicability and advantages of high accuracy.