倾转旋翼机多模态耦合动力学建模和气弹稳定性参数影响

郑礼雄; 王博; 招启军; 马砾

doi:10.13224/j.cnki.jasp.20230445

倾转旋翼机多模态耦合动力学建模和气弹稳定性参数影响

doi: 10.13224/j.cnki.jasp.20230445

南京航空航天大学直升机动力学全国重点实验室，南京 210016

基金项目: 国家自然科学基金（12032012）；航空科学基金（20200057052006）；江苏高校优势学科建设工程资助项目

详细信息

作者简介:
郑礼雄（1999-），男，硕士生，主要从事直升机动力学研究。E-mail：zhenglx@nuaa.edu.cn

通讯作者:
马砾（1991-），男，博士，主要从事直升机气弹动力学研究。E-mail：lim@nuaa.edu.cn

中图分类号: V215.34
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出版历程
- 收稿日期: 2023-07-09
- 网络出版日期: 2024-07-01

Multi-mode coupling dynamic modeling and influence of aeroelastic stability parameters of tiltrotor aircraft

National Key Laboratory of Helicopter Aeromechanics，Nanjing University of Aeronautics and Astronautics，Nanjing 210016，China

摘要

摘要:
基于Hamilton原理及多体动力学方法，通过建立坐标系准确地描述出旋翼/机翼/短舱等动部件的空间位置及运动关系，充分考虑不同偏置以及气动、结构和惯性耦合，保留了部件弹性变形引起的耦合效应，推导出非旋转坐标系下的质量、刚度和阻尼矩阵，建立了一套倾转旋翼机的旋翼/机翼多模态耦合气弹稳定性分析模型。在此基础上开展了倾转旋翼机多模态耦合气弹稳定性参数影响分析，包括机翼挥舞弯曲、弦向弯曲和扭转刚度、机翼前掠角、桅杆高度、桨毂预锥角、旋翼挥舞刚度、挥舞变距系数等参数，结果表明：机翼三个方向刚度中，系统稳定性对扭转刚度最敏感，机翼前掠和挥舞变距调节系数均不利于抑制回转颤振，增大桅杆高度的同时需增大机翼扭转刚度可保持回转颤振边界不变，倾转铰靠近弹性轴后缘和增大旋翼挥舞刚度可提高回转颤振边界，桨毂预锥角和悬挂高度综合考虑可更高效地增大回转颤振边界。
- 倾转旋翼机 /
- 多体动力学 /
- 多模态耦合 /
- 回转颤振 /
- 气弹稳定性 /
- 参数分析
Abstract:
Based on Hamilton’s principle and the multi-body dynamics method, a coordinated system was established to accurately describe the spatial position and motion relationship of the rotor, wing, pylon, and other moving parts. Various offsets and the coupling effects of aerodynamics, structural deformations, and inertial forces were fully considered. The influence of the coupling effects resulting from the elastic deformation of components was retained. For the necessary analytical framework, mass, stiffness, and damping matrices were derived in non-rotating coordinates. Subsequently, a sophisticated rotor/wing multi-mode coupled aeroelastic stability analysis model for tiltrotor aircraft was formulated. Utilizing this model, the impact of various parameters on the multi-mode coupling aeroelastic stability of tiltrotor aircraft was analyzed. These parameters included vertical bending, chord bending, and torsional stiffness of the wing, as well as the wing forward sweep, mast height, hub pre-cone angle, rotor flapping stiffness, and pitch-flap coupling coefficient. The results indicated that the system’s stability was most sensitive to the torsional stiffness in three directions of wing stiffness. Furthermore, the wing forward sweep and the pitch-flap coupling coefficient did not effectively suppress whirl flutter. Increasing the mast height and the wing torsional stiffness can keep the whirl flutter boundary unchanged. Additionally, placing the tilting hinge closer to the rear of the elastic shaft and increasing the rotor flapping stiffness can enhance the whirl flutter stability margin. Moreover, comprehensive consideration of the hub pre-cone angle and suspension height can increase the whirl flutter stability margin in a more efficient manner.
- tiltrotor aircraft /
- multi-body dynamics /
- multi-mode coupling /
- whirl flutter /
- aeroelastic stability /
- parameter analysis

HTML

图 1 简化模型及坐标转换图

Figure 1. Simplified model and coordinate conversion diagram

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图 2 桨叶剖面气动力

Figure 2. Aerodynamic force of blade profile

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图 3 机翼有限单元体自由度示意图

Figure 3. Schematic diagram of the degree of freedom of the wing finite element body

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图 4 模态频率随前飞速度变化曲线图

Figure 4. Curves of mode frequency changing with forward flight speed

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图 5 模态阻尼比随前飞速度变化曲线图

Figure 5. Curves of mode ratio changing with forward flight speed

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图 6 机翼刚度对回转颤振边界的影响

Figure 6. Effect of wing stiffness on the boundary of whirl flutter

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图 7 不同机翼扭转刚度下模态阻尼比随前飞速度变化

Figure 7. Mode damping ratio changing with the forward flight speed under different wing torsional stiffness

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图 8 机翼前掠角对回转颤振边界的影响

Figure 8. Effect of wing forward sweep on the boundary of whirl flutter

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图 9 桅杆高度对回转颤振边界的影响

Figure 9. Effect of mast height on the boundary of whirl flutter

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图 10 不同桅杆高度下模态频率随前飞速度变化

Figure 10. Mode frequency changing with the forward flight speed under different mast heights

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图 11 不同桅杆高度下模态阻尼比随前飞速度变化

Figure 11. Mode damping ratio changing with the forward flight speed under different mast heights

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图 12 倾转铰与弹性轴偏置对回转颤振边界的影响

Figure 12. Effect of the offset between the tilting hinge and the elastic axis on the boundary of whirl flutter

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图 13 不同挥舞刚度下模态频率随前飞速度变化

Figure 13. Mode frequency changing with the forward flight speed under different flapping stiffness

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图 14 不同挥舞刚度下模态阻尼比随前飞速度变化

Figure 14. Mode damping ratio changing with the forward flight speed under different flapping stiffness

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图 15 挥舞变距调节系数对回转颤振边界的影响

Figure 15. Effect of pitch-flap coupling coefficient on the boundary of whirl flutter

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图 16 预锥角对回转颤振边界的影响

Figure 16. Influence of pre-cone angle on the boundary of whirl flutter

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图 17 桨毂悬挂高度对回转颤振边界的影响

Figure 17. Effect of hub suspension height on the boundary of whirl flutter

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表 1 坐标系定义

Table 1. Coordinate system definition

符号表示	坐标系定义方式
$ \left( {{I_{\text{i}}},{J_{\text{i}}},{{K}_{\text{i}}}} \right) $	惯性坐标系
$ \left( {{I_{\text{p}}},{J_{\text{p}}},{K_{\text{p}}}} \right) $	短舱坐标系
$ \left( {{I_{\text{h}}},{J_{\text{h}}},{K_{\text{h}}}} \right) $	桨毂坐标系，桨毂中心为原点
$ \left( {{I_{\text{r}}},{J_{\text{r}}},{K_{\text{r}}}} \right) $	旋转坐标系，绕$ {K_{\text{h}}} $轴旋转$ \psi $角
$ \left( {{I_{\beta}},{J_{\beta}},{K_{\beta}}} \right) $	挥舞坐标系，挥舞铰为原点
$ \left( {{I_{\zeta}},{J_{\zeta}},{K_{\zeta}}} \right) $	摆振坐标系，摆振铰为原点
$ \left( {{I_{\theta}},{J_{\theta}},{K_{\theta}}} \right) $	变距坐标系

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表 2 Bell倾转旋翼机模型基本参数

Table 2. Basic parameters of Bell tiltrotor model

参数	数据
桨叶片数$ {N_{\text{b}}} $	3
旋翼半径$ R $/m	3.82
挥舞变距调节系数$ {K_{\text{pf}}} $	−0.268
旋翼桨叶翼型升力线斜率$ {a_{\alpha}} $	5.7
巡航转速$ \varOmega $/（rad/s）	48
桨叶挥舞惯量$ {I_{\text{b}}} $/（kg∙m²）	142
机翼展长$ {Y_{{\rm{tw}}}} $/m	5.09
机翼弦长$ {C_{\text{w}}} $/m	1.58
桅杆高度$ H $/m	1.31
短舱重心偏置$ {e_{\text{p}}} $/m	0.191
短舱质量$ {m_{\text{p}}} $/kg	655
短舱偏航惯矩$ {I_{{\rm{p}}{\textit{z}}}} $/（kg∙m²）	231
短舱俯仰惯矩$ {I_{{\rm{p}}y}} $/（kg∙m²）	257
机翼前掠角$ {w_3} $/（°）	6.5
机翼翼型升力线斜率$ {a_{{{\alpha{\mathrm{w}}}}}} $	4.2
机翼垂向刚度$ {k_{{{{q}}_{\text{1}}}}} $/10⁶ （N∙m²）	9.2
机翼弦向刚度$ {k_{{{{q}}_{\text{2}}}}} $/10⁷ （N∙m²）	2.5
机翼扭转刚度$ {k_\varPhi } $/10⁶ （N∙m²）	1.77
机翼垂向阻尼$ {C_{{{{q}}_{\text{1}}}}} $/（kg∙m²/s）	9030
机翼弦向阻尼$ {C_{{{{q}}_{\text{2}}}}} $/（kg∙m²/s）	27300
机翼扭转阻尼$ {C_{\text{p}}} $/（kg∙m²/s）	955

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