| Gear is one of the mechanical components which the wheel rim has teeth for continuous meshing and could transfer motion and power. Gear is widely used in mechanical transmission systems. Gear mesh stiffness and transmission error are determined by the tooth profile modification, manufacturing and assembly errors which will affect the vibration characteristics and dynamic stress of a gear. This will further influence the degradation failure of a gear. For those problems, gear mesh stiffness and transmission error model, dynamic response and stress model are introduced in this paper. Then, the gear mesh stiffness, transmission error, dynamic response, dynamic stress and reliability of a gear are analyzed. The concentrates drawn from the study can be summarized as follows:(1) A model is developed for analyzing the influences of tooth shape deviations and assembly errors on the gear mesh stiffness, transmission error and load distribution. A gear is approximated as a series of independent spur gear slices along axial direction. The contact lines are determined by analyzing the mesh status of the sliced tooth pairs. From the equilibriums of the forces, the mesh stiffness model is developed. Finally, the gear mesh stiffness, transmission error, load distribution and effective stiffness distribution of a tooth are calculated. This research solves the gear mesh stiffness, transmission error and load distribution of a tooth with tooth profile errors.(2) A gear flexural-torsional-axial-swing coupling dynamic model is presented in which the gear mesh is represented by a pair of disks connected by a spring and the tooth profile error is ignored. The model incorporates the relative position angle of the gears, rotating direction of the gear, pressure angle, helix angle and direction of the helix angle. For the helical gear and the tooth with tooth profile errors, the load is non-uniform along axial direction. This will result in swing vibration of a gear. So a distribution dynamic model of a helical gear pair with tooth profile errors is developed. The gear mesh is represented by a pair of cylinders connected by a series of parallel springs. Finally, considering the supporting of bearings and shafts, the gear-rotor-bearing dynamic model is presented. The proposed model overcomes the accurate dynamic analysis of helical gear systems and the gear systems with tooth profile errors.(3) The finite element models of gear-rotor-bearing systems are developed by the single spring gear dynamic model and the distribution gear dynamic model. Then natural characteristics and dynamic responses of gear systems are studied to verify the correctness and applicability of gear mesh models in which the gear pair is a spur gear pair, a helical gear pair, a narrow-faced gear pair, a wide-faced gear pair, an ideal tooth profile gear pair and a gear pair with tooth profile errors, respectively.(4) Vibration of the gear, bearing and shaft in dynamic responses of a gear system will change tooth profile errors and the gear mesh force will be the dynamic mesh force. So a dynamic gear mesh stiffness model is presented. The effective stiffness distribution of a tooth and transmission error are studied. Then a gear-rotor-bearing finite element model is developed in which the gear mesh is represented by the distribution gear dynamic model. Dynamic responses and dynamic load distribution of a gear-rotor-bearing system are analyzed. Finally, gear dynamic contact stress and root stress are studied in which the contact stress is calculated by Hertzian theory and the root stress is calculated by the maximum stress of tooth root. This research proposes a gear dynamic effective stiffness, transmission error model and a gear dynamic responses and dynamic stress model with tooth profile errors.(5) Based on the finite element model of a gear-rotor-bearing system, the importance sampling method is used to analyze the gear dynamic contact stress and root stress distribution under the basic random variable distribution. Then the fatigue reliability and reliability sensitivity are studied by the stress-strength interference model. According to the results of reliability sensitivity and the tooth profile modification theory of "reverse deformation", the optimum gear profile modification is determined. |
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