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1. 北京航空航天大学 能源与动力工程学院, 北京 100191;
2. 先进航空发动机协同创新中心, 北京 100191

Constraint model and vibration response analysis of rotor rub-impact
ZHANG Li1, MA Yanhong1,2, LIANG Zhichao1, HONG Jie1,2
1. School of Energy and Power Engineering, Beijing University of Aeronautics and Astronautics, Beijing 100191, China;
2. Collaborative Innovation Center of Advanced Aero-Engine, Beijing 100191, China
Abstract: Considering the additional constraints induced by rub-impact, a mechanical model was proposed for typical mechanical characteristic of rub-impact. Based on the constraint model, some characteristics in response such as resonant interval extending, amplitude jumping and contact instability were analyzed. Impact of typical mechanical characteristic parameters on rotor response during rub-impact process was studied. It is found that additional constraint stiffness will cause the extension of the resonant range and instable contact region, while greater friction coefficient between rotor and stator causes the decrease of the vibration response and resonant range. A rub-impact analytical model with structure features of aero-engine was built, numerical simulation shows that in addition to the resonance range extension caused by additional constraints, characteristics of rotor response are closely related to rub location and mode shapes. System's response shows characteristics of quasi-periodic in soft rub-impact, while rotor movement tends unstable and closer to the mechanical model in heavy rub-impact.
Key words: rub-impact     mechanical model     typical parameters     response characteristics     numerical simulation

1 转子碰摩力学模型与机理 1.1 碰摩约束模型

 图 1 碰摩约束力学模型 Fig. 1 Constraint mechanical model for rub-impact

1.2 碰摩约束条件下转子振动响应特征

|z|＜c时,由式(1)推导得出有关B的方程:

Δ<0,方程无实数解,当

 图 2 转子振动响应随转速变化曲线 Fig. 2 Response curve of rotor with speed variation

0-1-3-5反映了升速过程中的转子系统响应特征,当振动响应大于1时,转子静子发生碰摩,与无碰摩响应相比,碰摩产生的附加约束使得响应一定程度降低,随着碰摩的进行,约束刚度增加,使得一定转速范围转子始终处于共振区间,转子发生持续的碰摩.碰摩进行至2-3区间时,系统响应出现了两个振动响应解(2-3与4-3段),物理过程上对应着不稳定的碰摩接触过程,转子在该工作转速区间可能失稳.当相对响应值到达点3时,转速继续上升,式(4)将不存在正实数解,此时转静子接触分离,响应振幅从点3突跃到点5.5-4-2-1-0反映了发动机的减速过程,当到达点4时碰摩发生,系统振动响应值发生了响应突跃,与加速过程不同,减速过程中没有出现接触不稳定现象.

1.3 力学特征参数对转子振动特性的影响

 图 3 约束刚度对碰摩响应的影响 Fig. 3 Influence of constraint stiffness on rub-impact response

 图 4 摩擦系数对碰摩响应的影响 Fig. 4 Influence of friction coefficient on rub-impact response

2 碰摩约束下复杂转子系统响应 2.1 转静件弹性碰摩方程

1.1节中提出的力学模型,忽略了转静子的结构特征.对于具有结构特征的复杂转子系统,进行碰摩动力响应分析时,需要基于结构特征,并考虑对转静件的弹性体特性进行碰摩过程的分析.图 5所示为航空发动机转静件碰摩的动力学简化模型,包含转子、叶片以及机匣结构,相应的碰摩动力学基本方程为

 图 5 航空发动机转静碰摩简化模型 Fig. 5 Simplified model for rotor and stator rub-impact in aero-engine

1) 对求解域离散化,采用位移格式构造插值函数,并形成系统动力方程系数矩阵M、C、K,给定系统的初值条件Zt(0), t(0),Zt(0),T(0)(转速和不平衡力).

2) 根据给定初值条件通过隐式求解得到系统静态响应,将结果作为初值条件对系统运动方程刚度项进行修正,随后采用显式中心差分进行数值积分求解得到系统时域响应. 2.2 风扇叶片机匣碰摩响应特征 2.2.1 有限元模型

 图 6 碰摩有限元模型 Fig. 6 Finite element model for rub-impact
2.2.2 稳态响应

 图 7 碰摩约束时转子不平衡响应 Fig. 7 Unbalance response considering rub-impact constraint

 图 8 碰摩作用下共振响应区扩张 Fig. 8 Expansion of resonance area considering rub-impact

2.2.3 瞬态响应

 图 9 转子轻微碰摩时域响应 Fig. 9 Time-domain curve of soft rub-impact

 图 10 轻微碰摩转子轴心轨迹 Fig. 10 Rotor orbit of soft rub

 图 11 转子严重碰摩时域曲线 Fig. 11 Rotor time-domain curve of heavy rub-impact
 图 12 严重碰摩转子轴心轨迹 Fig. 12 Rotor orbit of heavy rub-impact
3 结论

1) 碰摩时静子等效于对转子产生了附加的约束,该约束具有时变与突变特性.碰摩产生的附加约束改变了转子的固有特性,使得转子系统共振区域扩展.在特定参数范围,系统可能出现多个振动响应解,振动响应曲线表现出接触不稳定与振幅跃迁等特征.

2) 附加约束刚度越大,共振响应区间越宽,不稳定接触区间越大.转静件接触摩擦系数越大,共振响应区间越窄,不稳定接触区间越小.约束刚度与摩擦系数的增大都会造成响应幅值的降低.

3) 对于具有航空发动机结构特征的碰摩系统,转子系统的响应还与碰摩位置及转子模态密切相关,碰摩约束对以碰摩部件变形为主的模态对应振动响应影响较大,而对其余模态影响较小.碰摩程度较轻微时,叶片位于弹性变形区,响应表现出拟周期特征,轴心轨迹为多边形,转子运行较稳定.碰摩严重时,叶片产生塑性变形,响应幅值在一定时间范围内于固定值附近波动,转子稳定性变差.

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#### 文章信息

ZHANG Li, MA Yanhong, LIANG Zhichao, HONG Jie

Constraint model and vibration response analysis of rotor rub-impact

Journal of Beijing University of Aeronautics and Astronsutics, 2015, 41(9): 1631-1637.
http://dx.doi.org/10.13700/j.bh.1001-5965.2014.0647