Dynamics of a Rigid Unbalanced Rotor with Nonlinear Elastic Restoring Forces. Part I: Theoretical Analysis

In a previous paper, the dynamic behaviour of a Jeffcott rotor was studied in the presence of pure static unbalance and nonlinear elastic restoring forces. The present paper extends the analysis to a rigid rotor with an axial length such as to make the transverse moment of inertia greater than the axial one. As in the previous investigation, the elastic restoring forces are assumed to be nonlinear and the effects of couple unbalance are also included but, unlike the Jeffcott rotor, the system exhibits six degrees-of-freedom. The Lagrangian coordinates were fixed so as to coincide with the three coordinates of the centre of mass of the rotor and the three angular coordinates needed in order to express the rotor's rotations with respect to a reference frame having its origin in the centre of mass. The precession motions of such a rotor turn out to be cylindrical at low angular speeds and exhibit a conical aspect when operating at higher speeds. The motion equations of the rotor were written with reference to a system that was subsequently adopted for the experimental analysis. The particular feature of this system was the use of a steel wire (piano wire) for the rotor shaft, suitably constrained and with the possibility of regulating the tension of the wire itself, in order to increase or reduce the nonlinear character of the system. The numerical analysis performed with integration of the motion equations made it possible to point out that chaotic solutions were manifested only when the tension in the wire was given the lowest values – i.e. when the system was strongly nonlinear – in the presence of considerable damping and rotor unbalance values that were so high as to lose any practical significance. Under conditions commonly shared by analogous real systems characterised by poor damping, where the contribution to nonlinearity is almost entirely due to elastic restoring forces, the analysis pointed out that precession motions may be manifested with a periodic character, whether synchronous or not, or a quasi-periodic character, but in no case is the solution chaotic.     

变速转子准稳态主动平衡系统的增益调度控制

在现代高速旋转机械中,不平衡引起的振动是机器性能降低甚至损坏的重要原因。对变速转子准稳态主动平衡系统,可按一定时间步长把变转速离散成有限个转动角速度。针对每个离散角速度,依据影响系数法,采用包含残余振动值和校正不平衡的广义线性二次型目标性能函数推导出控制律。通过每个离散转速下影响系数的估计和增益矩阵的计算,形成对应于各离散转速的增益表,从而实现变速转子准稳态主动平衡系统的增益调度控制。数值模拟验证了增益调度控制能很好地抑制不平衡振动。与传统的加权二乘法(WLS)相比,数值模拟显示,该法对校正不平衡的惩罚可提高系统的稳定性,也可增强控制的鲁棒性。     

具有局部非线性动力系统周期解及稳定性方法

对于具有局部非线性的多自由度动力系统，提出一种分析周期解的稳定性及其分岔的方法该方法基于模态综合技术，将线性自由度转换到模态空间中，并对其进行缩减，而非线性自由度仍保留在物理空间中在分析缩减后系统的动力特性时，基于Ｎｅｗｍａｒｋ法的预估－校正－局部迭代的求解方法，与Ｐｏｉｎｃａｒé映射法相结合，推导出一种确定周期解，并使用Ｆｌｏｑｕｅｔ乘子判定其稳定性及分岔的方法     

旋翼尾流与地面干扰时地面涡现象的研究

用Ｎ－Ｓ方程对近地飞行时旋翼尾流与地面干扰时产生的地面涡现象进行了数值计算旋翼对流场的作用由分布在特定区域内的动量源项模拟结果表明，旋翼尾流撞到地面后的卷起和轴向流动的拉伸作用是形成地面涡的原因；地面边界层形成的二次分离涡向地面涡内输入（与尾流所携带的涡量）相反的涡量，而使地面涡保持平衡；地面涡的存在和运动使旋翼附近流场大大改变     

转子振动的灰色Verhuslt预测优化控制研究

以灰色预测控制理论为基础，首次将非线性GM模型引入到转子振动主动控制中，并采用现代控制理论中的二次型优化原理，以控制力和响应加权最小为目标函数，设计了转子系统振动的灰色Verhuslt预测优化控制方案。将该方案应用于带电磁阻尼器转子轴承系统的转子振动控制中，仿真结果显示转子振动的灰色预测Verhuslt优化控制是有效的、可行的。     

Effect of parameters on the rubbing condition of an unbalanced rotor system with initial permanent deflection

A rotor-stator rubbing Jeffcott model of a rotor system with mass unbalance including the mass eccentricity and the initial permanent deflection was set up and the corresponding governing motion equation was derived by d’Alembert principle. Through the analytical method, the rubbing condition was analyzed. Whether the rub would happen and when the rub would happen were well solved. The amplitude of the rotor center was calculated, and the rubbing factor was introduced to determine whether the rub would happen or not for all rotating speeds. Rubbing speeds when rub began to happen were obtained. Parameters such as the mass eccentricity, the initial permanent deflection, damping coefficients, and the phase angle between the mass eccentricity and the permanent deflection were used to analyze their effect on the rubbing condition. Results were obtained and could be used to prevent the rubbing fault or decrease the damage of the rub and diagnose or balance the initial permanent deflection fault.     

Rotor wake capture improvement based on high-order spatially accurate schemes and chimera grids

A high-order upwind scheme has been developed to capture the vortex wake of a helicopter rotor in the hover based on chimera grids. In this paper, an improved fifth-order weighted essentially non-oscillatory (WENO) scheme is adopted to interpolate the higher-order left and right states across a cell interface with the Roe Riemann solver updating inviscid flux, and is compared with the monotone upwind scheme for scalar conservation laws (MUSCL). For profitably capturing the wake and enforcing the period boun...     

Combined resonance of low pressure cylinder-generator rotor system with bending-torsion coupling

A nonlinear model of a low pressure cylinder-generator rotor system is presented to study sub-synchronous resonance and combined resonance. Analytical results are obtained by an averaging method. Transition sets and bifurcation diagrams are obtained based on the singularity theory for the two-state variable system. The bifurcation characteristics are analyzed to provide a basis for the optimal design and fault diagnosis of the rotor system. Finally, the theoretical results are verified with the numerical results.     

Using a pseudo-functionally graded interlayer in order to improve the static and dynamic behavior of wind turbine blade T-bolt root joints

The large wind turbines blades with multi-ton composite structures are mostly connected to the peach-bearings flanges using T-bolt joints which induce shear and bearing stress fields around the cross bolts. The significant differences between the modulus of elasticity of metallic bolts and composite surrounding materials cause stress concentration around interfaced zones and, also, limit the load capacity of the joints. In the present research, a pseudo functionally graded material (PFGM) as an interlayer is used around the cross bolts to examine the reduction of the stress concentration. Some radial variation of the mechanical properties would be considered for this interlayer. The finite element method is used to analyze the structures. Loadings are applied to the center of the cross bolts analogous to the real cases. Both the static and dynamic loadings are studied. For the finite element of the functionally graded material interlayer, a multilayer alternative material with constant properties in each layer is used. The results show that using an isotropic single layer with an average modulus of elasticity and specific thickness decreases the stress concentration of the composite part up to 47%. The various property models for the interlayer also show that an appropriated model can decrease the stress concentration up to 55%. Dynamic transient analyses would be implemented over the joint structure and improved considering to the practical cases. Using the PFGM interlayer decreases the constant and variable parts of the stresses up to 55% and also causes significant increasing of the joint fatigue life.     

Analysis of unsteady wave processes in a rotating channel

The impact of passage rotation on the gasdynamic wave processes is analyzed through a numerical simulation of ideal shock-tube flow in a closed rotating-channel containing a gas in an initial state of homentropic solid-body rotation. Relevant parameters of the problem such as wheel Mach number, hub-to-tip radius ratio, length-to-tip radius ratio, diaphragm temperature ratio, and diaphragm pressure ratio are varied. It is shown that for a fixed geometry and initial conditions, the contact interface acquires a distorted three-dimensional time-dependent orientation at non-zero wheel Mach numbers. At a fixed wheel Mach number, the level of distortion depends primarily on the density ratio across the interface and also the hub-to-tip radius ratio. The nature of the rarefaction and shock wave propagation is one-dimensional, although the acoustic waves are diffracted due to the radially varying propagation speed. Under conditions of initially homentropic solid-body rotation, a degree of similarity exists between rotating and stationary shock-tube flows. This similarity is exploited to arrive at an approximate analytical solution to the Riemann problem in a rotating shock-tube.