【作者】 虞志浩；

【导师】 杨卫东；

【作者基本信息】 南京航空航天大学 ， 飞行器设计， 2012， 博士

【摘要】 柔性多体系统动力学方法在旋翼气弹动力学分析中的应用是当前国内外的一个研究热点，为能建立旋翼多体系统气弹动力学模型，不论是柔性多体系统动力学方法还是旋翼动力学和气动建模都需要作相应的改进。本文开展了旋翼多体系统动力学建模方法研究，发展了可用于气弹分析的旋翼多体系统气弹动力学分析方法与程序，对分析方法各部分的准确性进行了验证，并将旋翼多体系统动力学模型应用于旋翼气弹分析中。本文首先建立了一种能够在多体系统动力学模型中应用，且适合于气弹分析的高精度桨叶动力学模型，并对模型的准确性和计算精度进行了验证。模型修正了桨叶预扭引起的剖面坐标基矢量非正交对应变能的影响，采用了准确的变形运动非线性几何关系，应变、动能以隐式表达并可采用位移有限元离散。为便于在多体系统动力学模型中与其它构件组合，通过代入数值后逐级展开提取了质量矩阵。由于桨叶与其它构件对接时对接面处约束力做功的计算过程和气动载荷做功一致，将约束力直接作为Lagrange乘子，最终得到含有对接面约束力的桨叶构件动力学方程。此外在高精度桨叶动力学模型的基础上对各环节的表达式进行精度的截断，得到了一种计算量较小，在小变形等情况下也足够准确的二阶精度桨叶动力学模型，用于模拟变距摇臂等弹性变形较小的构件。通过对模型桨叶加载后非线性变形的计算，变形状态下模型桨叶的频率计算，复合材料异形桨叶固有模态的计算与试验测试，验证了本文建立的高精度桨叶动力学模型的准确性。通过合并构件动力学方程并以约束方程体现构件之间的连接关系，建立旋翼多体系统动力学控制方程，并将旋翼气动载荷处理为非约束力元，以非完整约束的形式并入控制方程。通过建立铰链动力学方程和含铰链构件动力学方程，使识别非独立自由度的过程简化，约束方程的列写形式统一。旋翼连续旋转造成角位移约束方程求解中出现奇点，选择在旋转坐标系中建立以Rodriguez参数表示的角位移约束方程，相对旋转坐标系的转动始终为小量，从而避免了奇点的出现。旋翼气动力的计算采用非定常与动态失速模型和自由尾迹模型，通过对分布载荷做功表达式的分析，将旋翼气动力转换为一种非约束力元，在多体系统动力学模型中体现为一组非完整约束，从而使气动力的计算过程独立于桨叶构件的动力学建模，便于气动力计算中根据自身模型的需求设定计算步长和求解格式。旋翼多体系统动力学控制方程以广义坐标分离法进行缩并，得到只含有独立自由度的非线性刚性微分方程，发展了一套适合于此类方程直接积分求解的局部间断有限元积分方法。方程缩并中加入了约束协调模块，解决了约束违约问题。研究了局部间断有限元积分方法用于刚性方程积分计算的稳定性、阻尼和周期延迟等问题，并在积分方法中嵌入了Newton-Broyden组合法，解决了隐式求解格式中反复求取切线矩阵及其逆矩阵造成计算量过大的问题，显著提高了计算效率的同时，尤其适合用于旋翼多体系统动力学控制方程这种难以得到关于状态量Jacobi矩阵的方程求解瞬态响应。针对旋翼气弹动力学分析的需求，建立旋翼动力学方程与气动力方程耦合求解的瞬态响应以及周期稳态响应计算流程，研究了气弹动力学瞬态响应分析法中，桨距激振方式、衰减信号处理与阻尼识别等问题。采用本文的旋翼多体系统动力学建模方法构建无铰式旋翼和无轴承旋翼模型，以瞬态响应分析法计算悬停和前飞状态气弹稳定性，通过与试验数据对比验证了本文的建模方法、求解流程等各环节的正确性。此外还对比和分析了桨叶动力学模型、旋翼入流模型、响应求解方法等因素对气弹稳定性分析精度的影响，以及旋翼结构设计参数对旋翼摆振阻尼变化趋势的影响。更多还原

【Abstract】 The rotor flexible multibody system dynamic model is a research focus in rotor aeroelasticdynamics field. To introduce the flexible multibody system dynamics method into the rotor dynamicsmodeling, corresponding improvement should be implemented for multibody system dynamics androtor dynamics modeling. The rotor flexible multibody system dynamical model and its solutionmetheod of dynamic response have been investigated. To verify the developed model and method, thetransient analysis of a model blade and the aeroelastic analysis of rotors are also presented in thisdissertation.A high accuracy component dynamic model of rotor blade is developed, which is suitable foraeroelasticity analysis of rotor and integrated into flexible multibody system dynamic model easily.The nonorthogonal of base vectors in a helix coordinates, caused by the pretwist of the blade, and itsinfluence on the finite deflection strain tensor of the blade dynamic model is correlated. The exactnonlinear deflection geometry is also adopted. The implicit expressions of strain energy and kineticenergy could be discreted by displacement finite element. For the convenience of integrating intoflexible multibody system dynamic model, mass matrix is extracted using recurrence method. As theexpression form of the work of airload and constraint loads are the same, the Lagrange multipliers inthe component dynamic equations are represented by the constraint force directly. Based on the highaccuracy component dynamic equations, a second order accuracy blade component model is alsoobtained, which is suitable for modeling the small deflection and with much lower computationalcomplexity than the accuracy component model. To verify the correctness of the analysis result, aspecial-shaped blade mode test is conducted. Correlations between the analysis results and theexperimental data from Princeton beam test and Minguet’s composite beam experiments are alsoimpelementd.The rotor multibody system dynamic control equations are composed of the component dynamicequations, holonomic constraint equations and nonholonomic constraint equations. Connectionsbetween the structural components of rotor system produce the holonomic constraint equations, andnonholonomic constraint equations are produced in force elements used for airloads modeling. Tosimplify the form of holonomic constraint equations, the joint dynamic equations are introduced, andthe dynamic equations of component containing a joint are deduced. To avoid singularities for largerotations of the rotor, the angular constraint equations, expressed by Rodriguez parameters, are modified by introduced a nominal motion. The rotor airloads are calculated from the unsteady airfoilaerodynamics with dynamic stall and free wake model. Force elements of rotor airloads are alsodeduced, and integrated into the rotor multibody system as the nonholonomic constraints, in order toseparate the solution procedure of the aerodynamic model from the solution of multibody systemdynamic control equations.Using the generalized coordinate partitioning algorithm, dynamic control equations of rotormultibody system, with differential algebraic form, are reduced to ordinary differencal equations, anda locoal discontinuous Galerkin (LDG) integration method is developed to solve the equations. Thespectral radius, algorithmic damping and period elongation of LDG method are investigated.According to the nonlinear implicit expression and high stiffness ratio of the system equations, theLDG method, which is an implicit integration algorithm, are modified by combining with theNewton-Broyden method. The LDG integration method exhibits excellent numerical stability, andwithout calculating the Jacobi matrices and their inverse matrices, the method also exhibits goodcomputational efficiency.To verify the correctness of the developed rotor flexible multibody system dynamic model andtransient intergration method, the transient analysis of model blade and the aeroelastic analysis ofmodel rotor are implemented. The influence study of stability analysis method, blade structure modeland inflow model is also implemented. It demonstrates that the developed method is useful forimproving computation precision of aeroelastic stability.更多还原