直升机飞行动力学模型与飞行品质评估
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摘要
我国新型直升机研制已采用美军航标ADS-33为飞行品质规范蓝本。因此，对ADS-33
及其应用的研究工作，具有十分重要的意义。本项研究针对新机研制过程必须解决的品
质评定、飞控系统设计等问题，按照ADS-33军用品质规范的要求，建立了一个较完整
的直升机非线性的、具有状态空间表达形式的飞行动力学模型，进行了模型验证工作，
并以某样例直升机为例，计算了ADS-33品质规范（3．3）节中悬停和小速度状态的各项
指标，得到了开环状态的品质参数。主要理论研究内容如下：
一．建立了适用于实时仿真计算的、高精度的旋翼流场计算模型和程序。
本模型以Peters-He有限状态尾迹理论为基础，修正了大尾迹倾斜角时的诱导速度影
响系数矩阵，并结合了王氏涡流理论，导出了旋翼诱导速度垂向分量和旋转分量的表达
式，可计算平尾、尾桨和垂尾气动中心处诱导速度各分量。该模型的计算结果分别经过
了经典试验数据和本实验室试验结果的检验；所编制的程序采用实时优化技术和并行编
程技术，能够以较细粒度进行并行计算。该程序不仅可用于对实时性要求高的飞行仿真
项目，还可应用到计算量比较大的旋翼动力学项目研究中。
二．采用了非定常、非线性的叶素气动力模型
旋翼气动力学模型以现代薄翼型理论为基础，改进了非定常的环量升力并作了简化，
以满足实时计算环量升力、非环量升力及阻力项的要求。同时，还设计了一种动态桨叶
分段方法，即根据当前飞行状态下诱导速度场的分布特征，动态地将桨叶划分为若干段，
这样既保证了计算精度，又提高了计算速度。对于后行桨叶的动态失速行为，引入了对
翼型实验数据不敏感，并也具有状态空间形式的ONERA动态失速模型。该表达式有利
于全机系统方程的求解。
三．建立了高精度、实时涡轮轴发动机数学模型
以T700发动机为样例，引入了一个涡轮轴发动机实时数学模型。该模型通过模拟常
规涡轮轴发动机的压气机、燃烧室、燃气发生器涡轮和功率涡轮等部件的工作状况，能
够较真实地计算发动机内发生的能量变换过程，因而能够较准确地表示发动机与旋翼之
间的功率匹配关系。
四．研究和对比了不同的配平计算方法，设计了算法程序
设计了具有反馈校正的自动配平算法（APT）进行旋翼配平的计算。该算法具有较
好的收敛性和较高的计算精度，也适合孤立旋翼系统配平研究。
南京航空航天大学博士学位论文
全机配平算法针对直升机旋翼的周期运动特点，采用了Galerkin方法的原理，将单
桨叶坐标系下的动力学方程变换到多桨叶坐标系下，之后采用经典非线性方程解法计算
具有周期特性的配平参数。本文的非线性方程求解分别采用了修正的Powell混合方法和
正割方法，并对比了这两种方法的优劣性。
五．研究和对比了不同的积分计算方法，编制了算法程序
针对直升机飞行动力学方程组状态变量多、变量之间量值差别大并混迭有代数方程
的特点，本文采用了四种不同的积分算法展开对比，包括代数／微分混合方程（DAE）算
祛DASSL、具有较高计算效率的Adams－MoUton：方法、Gearfs BDF方法，以及适合
刚性方程的五阶eungeXutta－verner方法，并分别衡量不同算法的计算效率、并行效率
等。
六．建立了品质评估方法，并编制了评估计算程序。
本文利用所建立的模型，根据 ADS－33规范要求，逐条计算了（3．3）节的内容，并
对样例直升机进行了开环状态下的部分品质等级的评估工作。
A mathematical model is developed for an articulated helicopter. It is especially suitable to flight quality analysis and flight control system design. This model is formulated as a non-linear state-space representation of helicopter flight dynamics, incorporating with blade element unsteady aerodynamics, a finite state dynamic inflow wake model, and flapping/lead-lag blade dynamic model. The formulation of the coupled rotor and fuselage equations enables the use of common solution techniques for trim and linearization in arbitrary steady flight condition as well as control response calculations. Besides, a flying quality evaluation code of the military rotorcraft is developed, and the quality levels in hover/low speed flightwere calculated according ADS-33D(3.3). The principal contributions of this dissertation are:
1. A high fidelity and real-time rotor wake inflow model was built up. Based on Peters-He finite states wake theory, a new influence coefficient matrix for high speed flight was derived, The modified wake model is better suitable for the flight state with a large wake skew angle.
2. An unsteady, nonlinear state-space airfoil aerodynamics model was developed with ONERA dynamic stall model.
3. A high fidelity real-time mathematical model of a turboshaft
engine was developed and included in the helicopter flight dynamics mathematical model.
4. An effective trim solution for first order state-space unsteady aerodynamics formulation was obtained.
5. The integration technology for solving the flight dynamics equations was investigated and applicable code was compiled.
6. The flight quality levels of the sample helicopter were caculated according to ADS-33D.
At first, the model validation work was done with the available experiment data from NASA and our key lab. Results and analysis are presented in chapter 2. For the validation of the total model, the comparison of trim results in hover/forward flight was made with the popular software of FLIGHTLAB, and linearization matrixes were compared with HELISIM, they both show the coordination results.
及其应用的研究工作，具有十分重要的意义。本项研究针对新机研制过程必须解决的品
质评定、飞控系统设计等问题，按照ADS-33军用品质规范的要求，建立了一个较完整
的直升机非线性的、具有状态空间表达形式的飞行动力学模型，进行了模型验证工作，
并以某样例直升机为例，计算了ADS-33品质规范（3．3）节中悬停和小速度状态的各项
指标，得到了开环状态的品质参数。主要理论研究内容如下：
一．建立了适用于实时仿真计算的、高精度的旋翼流场计算模型和程序。
本模型以Peters-He有限状态尾迹理论为基础，修正了大尾迹倾斜角时的诱导速度影
响系数矩阵，并结合了王氏涡流理论，导出了旋翼诱导速度垂向分量和旋转分量的表达
式，可计算平尾、尾桨和垂尾气动中心处诱导速度各分量。该模型的计算结果分别经过
了经典试验数据和本实验室试验结果的检验；所编制的程序采用实时优化技术和并行编
程技术，能够以较细粒度进行并行计算。该程序不仅可用于对实时性要求高的飞行仿真
项目，还可应用到计算量比较大的旋翼动力学项目研究中。
二．采用了非定常、非线性的叶素气动力模型
旋翼气动力学模型以现代薄翼型理论为基础，改进了非定常的环量升力并作了简化，
以满足实时计算环量升力、非环量升力及阻力项的要求。同时，还设计了一种动态桨叶
分段方法，即根据当前飞行状态下诱导速度场的分布特征，动态地将桨叶划分为若干段，
这样既保证了计算精度，又提高了计算速度。对于后行桨叶的动态失速行为，引入了对
翼型实验数据不敏感，并也具有状态空间形式的ONERA动态失速模型。该表达式有利
于全机系统方程的求解。
三．建立了高精度、实时涡轮轴发动机数学模型
以T700发动机为样例，引入了一个涡轮轴发动机实时数学模型。该模型通过模拟常
规涡轮轴发动机的压气机、燃烧室、燃气发生器涡轮和功率涡轮等部件的工作状况，能
够较真实地计算发动机内发生的能量变换过程，因而能够较准确地表示发动机与旋翼之
间的功率匹配关系。
四．研究和对比了不同的配平计算方法，设计了算法程序
设计了具有反馈校正的自动配平算法（APT）进行旋翼配平的计算。该算法具有较
好的收敛性和较高的计算精度，也适合孤立旋翼系统配平研究。
南京航空航天大学博士学位论文
全机配平算法针对直升机旋翼的周期运动特点，采用了Galerkin方法的原理，将单
桨叶坐标系下的动力学方程变换到多桨叶坐标系下，之后采用经典非线性方程解法计算
具有周期特性的配平参数。本文的非线性方程求解分别采用了修正的Powell混合方法和
正割方法，并对比了这两种方法的优劣性。
五．研究和对比了不同的积分计算方法，编制了算法程序
针对直升机飞行动力学方程组状态变量多、变量之间量值差别大并混迭有代数方程
的特点，本文采用了四种不同的积分算法展开对比，包括代数／微分混合方程（DAE）算
祛DASSL、具有较高计算效率的Adams－MoUton：方法、Gearfs BDF方法，以及适合
刚性方程的五阶eungeXutta－verner方法，并分别衡量不同算法的计算效率、并行效率
等。
六．建立了品质评估方法，并编制了评估计算程序。
本文利用所建立的模型，根据 ADS－33规范要求，逐条计算了（3．3）节的内容，并
对样例直升机进行了开环状态下的部分品质等级的评估工作。
A mathematical model is developed for an articulated helicopter. It is especially suitable to flight quality analysis and flight control system design. This model is formulated as a non-linear state-space representation of helicopter flight dynamics, incorporating with blade element unsteady aerodynamics, a finite state dynamic inflow wake model, and flapping/lead-lag blade dynamic model. The formulation of the coupled rotor and fuselage equations enables the use of common solution techniques for trim and linearization in arbitrary steady flight condition as well as control response calculations. Besides, a flying quality evaluation code of the military rotorcraft is developed, and the quality levels in hover/low speed flightwere calculated according ADS-33D(3.3). The principal contributions of this dissertation are:
1. A high fidelity and real-time rotor wake inflow model was built up. Based on Peters-He finite states wake theory, a new influence coefficient matrix for high speed flight was derived, The modified wake model is better suitable for the flight state with a large wake skew angle.
2. An unsteady, nonlinear state-space airfoil aerodynamics model was developed with ONERA dynamic stall model.
3. A high fidelity real-time mathematical model of a turboshaft
engine was developed and included in the helicopter flight dynamics mathematical model.
4. An effective trim solution for first order state-space unsteady aerodynamics formulation was obtained.
5. The integration technology for solving the flight dynamics equations was investigated and applicable code was compiled.
6. The flight quality levels of the sample helicopter were caculated according to ADS-33D.
At first, the model validation work was done with the available experiment data from NASA and our key lab. Results and analysis are presented in chapter 2. For the validation of the total model, the comparison of trim results in hover/forward flight was made with the popular software of FLIGHTLAB, and linearization matrixes were compared with HELISIM, they both show the coordination results.
引文
[0-1] Hoh, R.H., Mitchell, D.G., Aponso, B.L.. Key, D.L.. and Blanken, C.L., "Handling Qualities Requirements for Military Helicopters (ADS-33C)", STI Technical Report No. 1194-6．
[0-2] Howlett, J.J., " UH-60A Blackhawk Engineering Simulation Program-Volume II-Mathematical Model" , NASA CR-166309, Dec. 1981．
[0-3] Ballin, M.G., "Validation of a Real-Time Engineering Simulation of the UH-60A Helicopter", NASA TM-88360, Feb. 1987．
[0-4] Dirtier, M.A., "UH-60A Helicopter Stability Augmentation Study", Fourteenth European Rotorcraft Forum, Milano, Italy, Sept. 1988．
[0-5] Mansur, M.H., Tischler, M.B., Chaimovich, M., Rosen, A., and Rand, O., "Modeling Methods for High-Fidelity Rotorcraft Flight Mechanics Simulation", Sixteenth European Rotorcraft Forum, Glasgow, Scotland, Sept. 1990．
[0-6] DuVal, R., "A Real-Time Blade Element Helicopter Simulation for Handling Qualities Analysis", Fifteenth European Rotorcraft Forum, Amsterdam, Sep 1989．
[0-7] He, C., and Lewis, W.D. "A Parametric Study of Real Time Mathematical Modeling Incorporating. Dynamic Wake and Elastic Blades", Proceedings of the 48th Annual Forum of the American Helicopter Society, Washington D.C., June 1992, pp.1181-1196．
[0-8] Bauchau, O.A., and Kang, N.K., "A Multibody Formulation for Helicopter Structural Dynamic Analysis", Journal of the American Helicopter Society, Vol. 34, (4) , Oct. 1989． pp. 3-14．
[0-9] Ballin, M.G. and Dalang-Secretan, M.A., "Validation of the Dynamic Response of a Blade-Element UH-60 Simulation Model in Hovering Flight", Journal of the American Helicopter Society, Vol. 36, No. 4, 1991． pp. 77-88．
[0-10] Fletcher, J.W., "Identication of UH-60 Stability Derivative Models in Hover from Flight Test Data", American Helicopter Society 49th AnnualForum, St. Louis, MO, 1993．
[0-2] Howlett, J.J., " UH-60A Blackhawk Engineering Simulation Program-Volume II-Mathematical Model" , NASA CR-166309, Dec. 1981．
[0-3] Ballin, M.G., "Validation of a Real-Time Engineering Simulation of the UH-60A Helicopter", NASA TM-88360, Feb. 1987．
[0-4] Dirtier, M.A., "UH-60A Helicopter Stability Augmentation Study", Fourteenth European Rotorcraft Forum, Milano, Italy, Sept. 1988．
[0-5] Mansur, M.H., Tischler, M.B., Chaimovich, M., Rosen, A., and Rand, O., "Modeling Methods for High-Fidelity Rotorcraft Flight Mechanics Simulation", Sixteenth European Rotorcraft Forum, Glasgow, Scotland, Sept. 1990．
[0-6] DuVal, R., "A Real-Time Blade Element Helicopter Simulation for Handling Qualities Analysis", Fifteenth European Rotorcraft Forum, Amsterdam, Sep 1989．
[0-7] He, C., and Lewis, W.D. "A Parametric Study of Real Time Mathematical Modeling Incorporating. Dynamic Wake and Elastic Blades", Proceedings of the 48th Annual Forum of the American Helicopter Society, Washington D.C., June 1992, pp.1181-1196．
[0-8] Bauchau, O.A., and Kang, N.K., "A Multibody Formulation for Helicopter Structural Dynamic Analysis", Journal of the American Helicopter Society, Vol. 34, (4) , Oct. 1989． pp. 3-14．
[0-9] Ballin, M.G. and Dalang-Secretan, M.A., "Validation of the Dynamic Response of a Blade-Element UH-60 Simulation Model in Hovering Flight", Journal of the American Helicopter Society, Vol. 36, No. 4, 1991． pp. 77-88．
[0-10] Fletcher, J.W., "Identication of UH-60 Stability Derivative Models in Hover from Flight Test Data", American Helicopter Society 49th AnnualForum, St. Louis, MO, 1993．