Coupled Vibration And Transferring Characteristics Of Flexible Supported Geared System Based On Impedance

As an indispensable and important part of marine power system,the geared transmission system has a significant contribution to the mechanical noise of marine ships.In order to reduce the vibration transmitted to the ship foundation,marine gear housings are usually flexibly installed on the rafts or ship hulls through isolators.The vibration isolation system will not only influence the vibration transmitted to the foundation,but also affect the system vibration and noise through changing the gear meshing process and the housing's boundary conditions.During the design and analysis of geared system,the only available parameters for isolation system and foundation are the impedance/mobility parameters.Therefore,it is very helpful to reasonably considerate the impedance parameters in the analysis of gear dynamics and the vibration and noise analysis of housing,for the quantitative prediction of vibration and noise and vibration transfer control of marine gears.In this study,a loaded tooth contact analysis model considering the flexible support condition of housing is established,and a general impedance dynamics modeling method for geared system with different isolation types is proposed.The influence of flexible support of housing and isolator on vibration and noise of geared system is studied,and the transfer characteristics of vibration power flow in geared system are analyzed.The main research work and achievements are as follows:1.A loaded tooth contact analysis model considering the flexible support of housing is proposed.The global bending-shearing deformation flexibility coefficient of gear teeth is extracted by the finite element substructure method,and the local contact deformation is calculated by the elastic contact theory.Three types of manufacturing error are determined according to the quality grade of gear.The mesh misalignment error induced by flexible support of housing is included in the model.Finally,the gear mesh stiffness is obtained by solving the non-linear contact equation with iterative algorithm.The influence of flexible support on mesh stiffness and gear excitation force is studied.Results show that: flexible support of housing will induce gear mesh misalignment,which will lead to obvious load bias,and then affect gear mesh stiffness and transmission error excitation force.2.A general impedance modeling method for flexible supported geared system is proposed,and a coupled gear-housing-foundation impedance model is established.This model overcomes the disadvantage of independence between traditional gear dynamic system and vibration isolation system,can take into consideration the flexibility of each subsystem and the coupling relationships between different degree of freedom,and can use mixed theoretical-experimental parameters.The effectiveness of the impedance model is verified by comparison with the finite element model and the lumped parameters model.3.The influence of housing flexibility on vibration and noise of geared system at different operating speeds is analyzed.The results show that the housing flexibility has little effect on gear vibration,but it decreases the vibration of bearing and vibration and noise of housing at low frequency.Decrease the housing stiffness or increase the bearing stiffness will enlarge this influence.Decrease the housing stiffness not always increases its vibration,but always increases the air-borne noise.The influence of isolator flexibility on system vibration and noise is also studied.Results show that the low stiffness isolator will increase the gear excitation force,but has little influence on the system natural frequencies;while the high stiffness isolator has little effect on the gear mesh process,but will affect the system modes.Decrease the stiffness of isolator will increase the vibration acceleration of housing foot.4.The transferring characteristics of vibratory power flow in geared system are systematically studied.Results show that,in general,the vibratory power of gears attenuates layer by layer in the transferring process from shaft,bearing,housing and isolation system to foundation,but there may be back power flow in some specific paths.The vibration of gear pair,shaft,bearing and bearing hole of the housing are dominated by the high-speed shaft part,but vibration of isolator and foundation are not very prominent at the high-speed shaft side.The influence of system parameters on foundation vibration is analyzed.Results show that decrease the bearing stiffness or increase the housing damping and isolator damping will decrease the vibration of foundation;increase the mesh damping only decrease vibration at some special speed;increase the foundation damping will decrease the vibration amplitude at resonance speeds but will increase vibration at non-resonance regions.5.A mechanical power closed vibration and noise test rig with herringbone gear is built.The free modes of housing and base are identified by the orthogonal polynomial fitting method,and the results are compared with the analysis model.The mobility parameters of foundation are obtained by experiment measurement,which are further used in the impedance model.The vibration and noise of geared system under flexible installation condition are measured and compared with the analysis model.Finally,some conclusions are given and further research works are pointed out.