Study On Vibration Modeling Of Blade Beam And Its Modal Sensing Design

As the key component of turbomachinery to achieve energy conversion,blades are widely used in various engineering occasions,such as gas turbines,helicopter rotors,propellers,wind turbines etc.With the increasing demand of modern industry for high power,high load and high efficiency power systems,blade damage and failure caused by vibration,high-low cycle fatigue has become more serious.Therefore,further study of the vibration problem of blade structure,a comprehensive understanding and mastery of its complex vibration characteristics and modal smart sensing mechanism is an important premise and foundation for the optimal design of blade,ensuring the blade safe and reliable operation as well as vibration control.Surrounding the blade beam vibration characteristic modeling and its modal sensing design with typical structural characteristics,the following research work is carried out:Aiming at the problem of complex elastic boundary constraints,the transverse vibration analysis model of a rotating blade beam is established by using the principle of boundary internal force balance and harmonic balance.Two types of boundary springs against translation and rotation are introduced to simulate the general boundary constraints.The elastic boundary of the blade structure is realized uniformly by introducing rotational constraint spring and translational displacement constraint spring.Fourier series expansion and superposition of boundary smoothing auxiliary terms are proposed firstly to solve the blade governing differential equation and its boundary conditions,and the exact solution of blade free vibration is obtained.In the numerical calculations,the influence of centrifugal stiffening effect on blade vibration characteristics with the variations of hub radii and rotating speeds is systematically discussed and analyzed.Moreover,the boundary constraint effect of the rotating blade beams is explored.Surrounding the modeling problem of the complex structure characteristics such as stagger angle,pretwisted angle and non-uniform variable section,a unified bending coupling vibration analysis model for the typical blade beam is established.In this analytical model,the Fourier series expansion with smooth boundary is used to characterize the flapwise and chordwise displacement of the rotating blades,and the spatial variation of the non-uniform section and moment of inertia are uniformly expanded into Fourier series.Based on the energy principle and Lagrange equation,the flapwise and chordwise coupled bending vibration characteristic equation of variable cross-section rotating blade is derived.The influence of key parameters,including the stagger angle,pretwisted angle and taper ratio,on modal characteristics of the rotating blade structure is investigated.Results show that stiffness softening and enhancement effects in the coupling zone may occur due to the stagger angle,pretwisted angle and rotational speed variation,the modal frequency loci veering phenomena as well as mode shape exchanging are found.Furthermore,critical eigenfrequencies occur with the variation of blade doubly taper ratios,which alters the trend of frequency and accompanies the shift of vibration deformation direction.Based on the energy principle and the Rayleigh Ritz method,the spatial second derivative of the modal shape in the profile function of a distributed PVDF modal smart sensor is obtained,and the modal sensor design model suitable for light and thin blade beam is established,the design problem of smart modal sensors with arbitrary boundary conditions is solved.Then,based on the Euler-Bernoulli beam model and the non-uniform elastic supported foundation beam model,blade and grouped blade-disk systems are established respectively.The effects of parameter variation on smart modal sensing and filtering of PVDF modal sensors are studied.The most significant advantage of the smart modal sensor is to solve the trouble of signal postprocessing and connections,and avoid the measurement detuning caused by discrete sensing.To overcome the problems of complex electrode shapes of irregular structures,boundary disturbance and target mode change need to be redesigned in shaped sensor,an array sensor based on modal sensing sensitivity coefficient and curvature mode shape function is proposed,and the smart modal sensing is realized by designing a set of weight coefficients of piezoelectric patches.The weight coefficient of the structure is calculated by the pseudo-inverse method combined with the truncated singular value.In numerical calculation,the optimization method of weight matrix and adjustment factor is used to overcome the defect of incomplete filtering of unwanted modal information in the frequency response curve.Moreover,the sensor numbers and random noise signals on the sensing and filtering performance of the array modal sensors are addressed.Based on the framework of the previous vibration characteristic modeling and investigation,the modal smart sensor design and its sensing characteristic analysis of the rotating blade beam are studied systematically for the first time.Meanwhile,the modal sensing experiment of a thin blade is carried out,including the added mass effect and boundary stiffness effect.All the results show that the piezoelectric smart modal sensor has good modal sensing characteristics.Finally,a relatively complete design,manufacturing and packaging criteria and sensing experimental scheme of the PVDF modal smart sensor is formed,which provides a new design method and technical reference for the development of sensor and experiment study.Investigation carried out in this thesis provides a comprehensive theoretical model for the dynamic analysis of typical blade beam.The influence of complex structure characteristics on the vibration characteristics of blade beam is revealed.Based on the vibration analysis model,the design and experimental research of piezoelectric modal smart sensing are carried out systematically.Corresponding study results can provide a model foundation and method reference for the subsequent study of the vibration analysis,optimization design,smart modal sensing and control of typical blade beam.