| Rotating disks are widely used in various rotating machinery,and their structures are developing towards lighter and thinner with the advancement of technology.As the main form of flexible disk vibration,transverse vibration seriously restricts the further improvement of the rotating machinery’s working performance.The asymmetric moment of inertia,the slider loading and fluctuant rotational speed on the disk,etc.will cause the parametric vibration of the rotating disk system,and even lead to the instability and destruction of the entire system.The occurrence of parametric vibration does not depend on whether the applied excitation’s frequency is close to the system’s natural frequency.This vibration can be induced as long as the excitation periodically changes the system’s parameters,and even a small excitation can produce a very large vibration response.Furthermore,the rotating disk is usually excited by more than one parametric excitation under normal circumstances.At present,there lacks dynamic analysis on rotating flexible disks under the combined action of multiple parameter excitations in relevant research at home and abroad,and the transverse vibration control method of flexible disks during rotating needs to be supplemented and improved.By taking the rotating flexible disk as the main research object,this dissertation puts forward a set of general dynamic characteristics solving methods for the basic common problems of the parametric excitation gyroscopic system.It can be used to solve the linear and nonlinear problems of gyroscopic systems under various parametric excitations,and has important scientific research significance.According to the unique phenomenon that the parametric vibration is affected by the excitation phase,a novel method of the parametric excitation phase adjustment vibration suppression method is proposed,which provides a new approach with obvious effect for the suppression of the gyroscopic systems’ parametric vibration.At the same time,through the three-level research work of theoretical analysis,experimental verification,and practical application,a convenient method for the vibration suppression of the rotating flexible disk by inner boundary temperature control is obtained.This method can achieve effective vibration suppression by using a heating device with a simple structure,and has important engineering value and good application prospects.The main research contents of this dissertation are as follows:Firstly,the physical model of the rotating flexible disk system under various parametric excitations is constructed,and a general solving method for the dynamic characteristics of the rotating disk system is formed.Considering that the parametric excitations of three different properties,namely speed fluctuation,slider loading,and electromagnetic attraction are applied to the disk system,a dynamic model of the rotating flexible disk including the initial deformation is constructed.The Galerkin method is used for the derivation and arrangement of the system dynamics equations.The hypothetic steady-state solution of the system equation is made according to the Floquet theory,and the steady-state response is solved by the harmonic balance method.The quadratic eigenvalue equation is obtained by the Hill method,then the natural frequency and instability parameter of the system are obtained by solving it.The effects of single parametric excitation alone,double parametric excitations coupled and triple parametric excitations combined on the stability and resonance of the disk system are analyzed,which could be used as the theoretical basis for the following study on the vibration control of the rotating flexible disk.Secondly,the system equations of the flexible disk and the flexible shaft under multiple parametric excitations are summarized and integrated,the existing solving process is perfected into a systemic method for solving the dynamic characteristics of the parametric excited gyroscopic system with a wider range of applications,and a vibration suppression method based on parametric excitation phase adjustment is proposed according to relevant analysis results.A nonlinear term is introduced into the system model and the nonlinear solution problem is solved by an iterative algorithm,and the system equations of the flexible shaft and the flexible disk under the action of multiple parametric excitations are combined and unified.Thus,a systematic method for solving the dynamic characteristic of parametric excitations excited gyroscopic system is improved.The effect of the parametric excitations’ position phase on the vibration of the flexible rotating disk system and the effect of the parametric excitations’ fluctuant phase on the vibration of the flexible rotating shaft system are analyzed after setting the vibration evaluation indexes.According to the obtained results,a method of applying extra parametric excitation and adjusting its phase to an appropriate value is proposed to achieve vibration suppression,and its suppression effect is tested.Thirdly,the working principle and application effect of the vibration suppression method by controlling the temperature at the rotating flexible disk’s inner boundary are investigated both theoretically and experimentally.This method increases the transverse deformation stiffness of the flexible disk by heating its inner boundary to generate in-plane thermal stress.Considering the loading effect of a mass-springdamper system,a dynamic model of a temperature-controlled rotating disk system is constructed,the stability,steady-state response,and natural frequency of the rotating disk system with the inner boundary temperature increment are obtained according to the analytical method.The thermal expansion of flexible disks with different modal shapes under the action of temperature increment at its inner boundary is analyzed by finite element simulation software.However,this thermal expansion deformation is often ignored in previous studies.After that,a set of special experimental device was designed to verify the theoretical analysis results of the temperature-controlled rotating flexible disk.Thus,the variation law of the disk’s natural frequency with the temperature increment at the inner boundary is determined,and the thermal expansion deformation of the flexible disk under real conditions is measured.By setting different slider loading types,it is verified that the appropriate inner boundary temperature increment can suppress the transverse vibration of the rotating flexible disk.Finally,a set of temperature-controlled circular saw device with simple structure and convenient operation is designed to carry out sample research on the application of the vibration suppression method by inner boundary temperature controlling for rotating flexible disk at steady state.The previous contact-type semiconductor heating is improved to non-contact infrared radiation heating,to simplify the installation of the heating unit in the temperature-controlled device.According to the simplified dynamic model of the temperature-controlled circular saw,the natural frequency of the circular saw blade under the action of different inner boundary temperature increments after assembly and the appropriate temperature increment for ensuring the whole system stay stable are obtained through analytical solutions.The two spindle speeds near and far from the resonance speed are set to saw a same beech bar stock at a same feed speed.A laser displacement sensor is used to monitor the transverse vibration of the rotating circular saw blade in real-time during the cutting process,and a three-dimensional surface profile measurement device is used to capture and construct the machined surface topography of the cut workpiece,for checking the transverse vibration suppression effect of the circular saw blade during the cutting process and the improvement of the workpiece surface’s quality by applying this inner boundary temperature controlled method. |
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