Abstract
To find out the effect of eccentricity of a gear wheel on inherent characteristics of a gear-rotor system, this paper establishes a pair of general transverse-rotational-axial-swinging multi degrees of freedom coupling helical gear meshing dynamic model based on the finite element method (FEM). Considering the influence of the azimuth, the meshing angle, the helix angle and the rotation direction of driving shaft on mesh stiffness matrix, it analyzes the effect of mesh stiffness and mesh damping on the inherent characteristics and the transient response of the system. It obtains the displacement response curve and the dynamic meshing force curve of all nodes responding to the incentives of static transmission error and unbalance while considering mesh damping. It concludes that the effects of gear coupling and eccentricity of gear wheel should be taken into account in a multi-parallel-shaft gear meshing rotor system.
Highlights
For its high efficiency and reliable kinematic accuracy, gear transmission is used as one of the most common mechanical transmission types and has been widely adopted in many industrial fields
Research on dynamic analysis of a gear system can reveal the inner mechanism that causes a gear vibration and the controlling of vibration can make stable, high-speed, and accurate transmission possible. It almost exists in every rotor system and should be controlled strictly for its leading to inaccuracy and uncontrollability
For the single pair of gear meshing, references [1,2,3] developed dynamic models based on gear backlash, tooth modification and gear mesh impact respectively and dynamic analysis approved the validity of the method put forward
Summary
For its high efficiency and reliable kinematic accuracy, gear transmission is used as one of the most common mechanical transmission types and has been widely adopted in many industrial fields. Under the excitation of unbalance and static transmission error, Kahraman [6] analyzed the problems of forced vibration by constructing a lateral-torsional coupled model with 3 DOFs, and obtained calculated data curves of bearing stiffness and mesh stiffness to the dynamic response. This paper employed the numerical example of geared rotor system in reference [9] and developed a transverse-rotational-axial-swinging coupled dynamic model of helical gear with 12 DOFs under the excitation of unbalance by using the FEM. It considered the effect of every two DOFs’ coupling, gyroscopic moment, bearing stiffness, mesh stiffness and mesh damping. Comparing with the results in reference [9], we could learn that the influence degree of unbalance on dynamic characteristics was bigger than that of transmission error in geared rotor systems
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