非线性齿轮系统单齿故障动力学特性

针对齿轮系统运行过程中具有非线性动力学特性,借鉴混沌振子检测理论中根据系统相轨变化检测信号的原理,分析了齿轮单齿故障冲击信号出现的成因及其出现故障后非线性动力学特性的变化,建立了基于冲击分析的非线性齿轮系统单齿故障动力学模型。通过分析发现,齿轮系统模型在一定的参数条件下,其动力学特性会进入混沌状态。而在相同参数条件下,出现单齿冲击故障并达到一定程度后,齿轮系统会在故障冲击的激励下进入大周期运动,从而表现出明显异于无故障条件下齿轮系统的动力学特性。仿真结果表明,该方法能有效区别齿轮系统单齿故障状态。     

Jeffcott转子-轴承系统的非线性动力学特性分析

为了深入地研究转子-轴承系统的分岔规律,揭示转子系统丰富的非线性动力学行为,采用短轴承非稳态非线性油膜力的一般数学模型获得圆柱轴承的非线性油膜力表达式。在一定参数条件下,采用非线性动力学理论和方法,对刚性Jeffcott转子系统的动力学特性进行了分析。通过计算得到了系统的分叉图、时间历程、轴心轨迹、相图及Poincare映射图。计算结果表明-在特定的参数域内系统存在丰富的非线性动力学行为。该方法收敛速度快、精度高,为定性控制转子-轴承系统的稳定运行状态提供了理论依据。     

履带车辆齿轮传动系统非线性振动特性研究

以齿轮系统动力学和非线性振动理论为基础,针对具有齿侧间隙和时变啮合刚度的某履带车辆齿轮传动系统,建立单自由度齿轮系统非线性振动模型,通过数值仿真方法求解并分析在不同档位下的振动特性,并对其在某些变量参数下进行了振动特性研究,所得结果既反映了动力学性能,又为下一步进行多自由度齿轮系统的非线性振动研究提供了有力的依据.     

不确定转子耦合系统的经验参数研究

提出用非线性动力学行为进行不确定转子-轴承-密封耦合系统经验参数的研究,结果旨在为选择重要经验参数和实际控制转子的稳定运行提供依据.基于Muszynska模型和Capone圆轴承非线性油膜力模型,推导建立密封流体激振力和油膜力共同作用下的参数不确定转子-密封-轴承系统非线性动力学方程,通过数值分析,研究了该系统在平均周向速比常数影响下的分岔特性以及影响规律,并分析了几个特定参数下系统随转速变化的分岔特性和非线性动力学行为.分析结果发现,平均周向速比常数对系统的非线性动力学行为影响很大,随着平均周向速比常数的增大,系统提前出现倍周期分叉,并且振幅增大,使得不稳定性增加.基于上述分析,给出了合理的平均周向速比常数取值范围.     

非线性振动系统基于频率俘获现象的谐振同步分析

基于单质体非线性振动系统的机电耦合动力学模型,在对非线性振动系统起动过程中出现的频率俘获现象定量描述的基础上,考虑非理想振动系统的激振源与系统非线性振动运动的相互影响,研究了双激振源非线性振动系统基于频率俘获作用,实现谐振同步的理论条件。并依据激振电动机驱动系统与振动机械系统之间的耦合动力学模型及试验测定的试验台机械特性参数,通过数值仿真及试验,验证和解释了非线性振动系统频率俘获现象下,系统双激振源的谐振同步问题,指出非理想非线性振动系统的频率俘获现象,以及该现象下的多激振源谐振同步运动与振动系统的非线性强度、刚度、阻尼等参数之间的关系。研究结果对多激振源激励非线性振动系统的谐振同步运动现象分析,提供一定的理论支持和试验依据。     

故障参数下齿轮系统非线性动力学行为

为分析齿轮系统在故障条件下的非线性动力学变化机理,对不同故障参数下非线性齿轮系统的动力学行为进行了研究;建立了单齿冲击、单齿刚度、单齿磨损及全齿磨损的非线性动力学模型,采用齿轮混沌振子方法对其进行了分析;探讨了上述4种故障激励产生后齿轮系统吸引子的变化.研究表明,利用齿轮混沌振子能够较好地区分故障信号的大小,为更好地进行故障诊断提供了理论支持,也为旋转机械的故障诊断提供了一种新方法.     

非线性橡胶弹簧减振系统的数值分析与设计方法

针对非线性减振器的分析与设计问题,通过数值方法建立非线性减振系统的动力学模型,提出一种具有一般适用性的非线性减振系统设计方法,并进行验证。首先,通过对某型非线性橡胶弹簧进行仿真分析,并利用数值方法建立非线性橡胶弹簧减振系统的动力学方程;其次,提出一种包括系统线性特征设计,非线性特征设计及参数设计在内的非线性减振系统数值设计方法,并以非线性橡胶弹簧减振系统为例进行分析与设计;最后,通过实验对设计结果进行验证。分析结果表明,非线性橡胶弹簧减振系统的数值分析及设计方法能够准确设计非线性减振系统的动力学特征,为更复杂的非线性减振系统提供了分析及设计方法。     

强非线性单级齿轮系统的周期运动与全局分岔

针对含间隙和时变啮合刚度的强非线性齿轮系统动力学模型，用4阶变步长Runge—Kutta法对系统行为进行数值计算，做出了系统在不同参数值下的全局分岔图，显示了动力学系统通过倍周期分岔走向混沌的道路，并且为实际系统进行参数优化提供理论依据。通过分析揭示了强非线性齿轮系统存在着复杂的分岔结构，并为进一步研究其非线性动力学性能及控制提供理论依据。     

轧机辊系滞后非线性垂直振动系统的振动特性

考虑轧件弹塑性变形的滞后非线性作用,建立一种轧机辊系滞后非线性垂直振动动力学模型.运用奇点稳定性理论分析该滞后非线性系统的稳定性,得到了系统出现各种不同奇点的条件.同时采用渐进法求解系统在主共振情况下的解析近似解,得到了系统的主共振幅频特性方程.最后以实际轧机参数为例,分析轧件的非线性刚度、阻尼等参数对轧机主共振幅频响应的影响,并研究轧机在不同外部扰动下的分岔行为,发现在不同的外部扰动下,轧机表现出周期、倍周期以及混沌等多种动力学行为,这为研究和抑制轧机振动问题提供了理论参考.     

工程车辆非线性橡胶悬架系统的动态仿真与试验研究

在对某工程车辆非线性橡胶悬架系统进行试验研究的基础上,建立其非线性动力学模型和Simulink动态仿真模型,采用Simulink集成的隆格库塔方法对复杂非线性动力学方程组进行求解,并进行时域的仿真分析,得到各个工况和测点下的动态响应结果与试验基本一致,验证动力学模型及Simulink仿真模型的正确性.该动态模型可用于分析和评价车辆悬架系统的减振性能,并为橡胶悬架系统的参数优化打下基础.     

谐波齿轮传动系统动力学特性研究概述

对70年代以来国内外学者研究谐波齿轮传动系统动力学的几种典型模型进行了评价,指出了全面地考虑谐波齿轮传动系统中的非线性因素是进行谐波齿轮传动系统非线性动力学研究的重要条件,为合理地建立谐波齿轮传动系统的非线性动力学模型打下了基础。     

Friction induced vibration for an aircraft brake system—Part 2: Non-linear dynamics

Non-linear dynamics due to friction induced vibrations in a complex aircraft brake model are investigated. This paper outlines a non-linear strategy, based on the center manifold concept and the rational in order to evaluate the non-linear dynamical behaviour of a system in the neighbourhood of a critical steady-state equilibrium point. In order to obtain time–history responses, the complete set of non-linear dynamic equations may be integrated numerically. But this procedure is both time consuming and costly to perform when parametric design studies are needed. So it is necessary to use non-linear analysis: the center manifold approach and the rational approximants are used to obtain the limit cycle of the non-linear system and to study the behaviour of the system in the unstable region. Results from these non-linear methods are compared with results obtained by integrating the full original system. These non-linear methods appear very interesting in regard to computational time and also necessitate very few computer resources.     

一类含间隙滞回动力系统周期运动和分岔

以振动破碎机为工程背景,研究一类含间隙滞回动力系统的动力学行为.首先根据三角型滞回特性确定恢复力拐点的数值计算方法,然后数值分析该类系统的周期运动和分岔.计算结果表明间隙是一个敏感动力学参数,随着间隙大小的改变,系统的动力学行为也随之发生复杂的变化.另外,在某一频率比范围内,系统具有同一周期不同相轨迹的运动轨道,这种运动的复杂性会直接影响破碎机的破碎效率.     

磁悬浮轴承-转子系统的分岔与混沌特性

研究磁悬浮轴承-转子系统主共振情形时的非线性动力学行为。由Taylor级数展开得到非线性电磁力的表达式。用Lung-Kutta法计算系统的运动响应。借助Poincare影射和Lyapunov指数对系统的运动形态进行分析。结果发现了在主共振情形下系统中由环面破裂产生的混沌现象及之后的由倍周期分岔导致的混沌现象。     

动态油膜―柔性转子系统混沌运动的控制

借助最优控制混沌动力特性的方法,仅通过最优过程中的可调小参数的瞬态干扰反馈。将非稳态非线性油膜力作用下的不平衡转子系统出现的混沌运动,引导到嵌入在混沌吸引子内无数不稳定周期轨中预期的一个轨,并使之稳定。数值结果表明动态油膜—转子系统中的混沌运动也是可以有效控制的。     

Asymptotic buckling analysis of imperfect shallow spherical shells on non-linear elastic foundation

An asymptotic solution is formulated for non-linear buckling of elastically restrained imperfect shallow spherical shells continuously supported on a non-linear elastic foundation. The asymptotic iteration method is introduced to result in a cubic non-linear analytical relation between the external load and central transverse displacement (deflection) of the structures incorporating the effects of geometrical imperfection, edge-restraint coefficients, moduli of foundation and characteristic geometrical parameter. The resulting expression can be used easily to evaluate the effects of these factors on buckling behaviors. Numerical examples are given, and comparisons of the available results show validity of the method suggested in the present work.     

Identification and control of dynamical systems using different architectures of recurrent fuzzy system

Fuzzy logic based systems are very widely used for modeling and control of complex non-linear, plants. Fuzzy systems require the knowledge about the structure of the dynamic plant in order to achieve fruitful results. Recurrent Fuzzy systems (RFS) are a variation of fuzzy systems and have the ability to model and control dynamic plants without using the information about the structure of the plant. This paper presents identification and control of non-linear dynamical systems using two different architectures of recurrent fuzzy system (RFS). It highlights the importance of RFS over the conventional type-1 fuzzy based system. The objective of system identification as well as control has been achieved using both the architectures of RFS and the simulation results clearly show their efficiency. This paper also highlights yet another advantage of RFS over the conventional type-1 fuzzy systems which comes into light when dealing with higher order systems. The paper explains how the computational complexity can be greatly reduced by using RFS for higher order dynamical systems. A comparative analysis between the conventional type-1 fuzzy system and the two recurrent fuzzy systems has also been performed.     

FRACTAL DIMENSION OF TIME SERIES APPLIED TO IDENTIFICATION OF CRITICAL SPEED OF JEFFCOTT ROTOR SYSTEM

0 INTRODUCTIONChaos and bifurcation are two important topics in nonlineascience. For a continuous dynamical system =f(x,t,α(where t is time parameter, α is variable parameter) or a discretdynamical system (where g is map g: Rn ×when parameter α change…     

Model updating of locally non-linear systems based on multi-harmonic extended constitutive relation error

Improving the fidelity of numerical simulations using available test data is an important activity in the overall process of model verification and validation. While model updating or calibration of linear elastodynamic behaviors has been extensively studied for both academic and industrial applications over the past three decades, methodologies capable of treating non-linear dynamics remain relatively immature. The authors propose a novel strategy for updating an important subclass of non-linear models characterized by globally linear stiffness and damping behaviors in the presence of local non-linear effects. The approach combines two well-known methods for structural dynamic analysis. The first is the multi-harmonic balance (MHB) method for solving the non-linear equations of motion of a mechanical system under periodic excitation. This approach has the advantage of being much faster than time domain integration procedures while allowing a wide range of non-linear effects to be taken into account. The second method is the extended constitutive relation error (ECRE) that has been used in the past for error localization and updating of linear elastodynamic models. The proposed updating strategy will be illustrated using academic examples.