Foundational Research On Application Of Lightweight Multistage Locally Resonant Structure Shaft In Gear Unit

Gear unit is an important mechanical equipment which is widely used to transfer motion and power.Research on its vibration and noise reduction has attracted much attention.Traditional methods of vibration and noise reduction for gear unit include structural optimization design and improving processing and installation accuracy,etc.However,there are major difficulties in the control of low-frequency vibration and noise.The locally resonant(LR)structure is a new type of artificial periodic structure with unique low-frequency band gap characteristics,which presents a huge potential application in structural design of gear unit for vibration and noise reduction.The noise characteristics of gear unit,the structural design and band gap algorithm of lightweight multistage LR structure shaft are studied for the objective of low noise of gear unit.In addition,the mechanism of low-frequency multi-band flexural vibration characteristics is analyzed,and the engineering application is further explored.Firstly,the noise characteristics of the gear unit are thoroughly studied.Based on in-depth analysis of generation mechanism,the noise is divided into acceleration noise and ringing noise to study.The theoretical analysis,the finite element method,multi-body dynamics method and boundary element method are used to calculate and analyze the noise of the gear unit.The experiment is carried out to verify the simulation results.The characteristic of the noise is analyzed,which provide theoretical support for the use of LR theory in structural design of gear unit for the noise reduction.Secondly,for larger errors caused by neglecting the rubber mass when calculating the band gap of the lightweight structure in the traditional transfer matrix method,an improved novel transfer matrix method based on discretization of mass is proposed.The algorithm separates the rubber into multistage mass-spring system that has a clear physical meaning and has high accuracy with good convergence when calculating the band gap characteristics of the lightweight structure,which lays the foundation for the following research on band gap characteristics.Thirdly,according to the noise characteristics of the gear unit,a lightweight multistage LR structure shaft is designed.The flexural vibration band gap characteristics of lightweight multistage structure calculated by the proposed algorithm and the influence of material parameters such as the Young's modulus of the shaft,the shear modulus of the rubber,and the density of the shaft and the scattering on the band gap characteristics are analyzed.The research shows that,the designed lightweight multistage structure can make the band gap move to low frequency compared with the one-stage structure,and its multi-band characteristics are more suitable for the noise control of gear unit.When focusing on the low-frequency first band gap,scatterings can be replaced with a less dense material except for the outermost scattering,which further reduces the additional mass and enables the additional structure to be lightweight providing theoretical guidance for its application design in engineering.Finally,fundamental application of lightweight multistage LR structure in gear unit is explored.Finite element method is employed to study the effect of constrained conditions on the gap characteristics of the lightweight two-stage LR structure.The constrained conditions do not change the attenuation position of the band gap but change the attenuation amplitude,providing theoretical support for the feasibility of its application in engineering.A prediction model for beginning frequency of the band gap of the lightweight multistage LR structure shaft is proposed to help engineering applications,which has higher accuracy and lower degree of simplification laying the foundation for further exploration of the engineering application of the lightweight multistage LR shaft in the gear unit.