| Gear ratio is stable.transmission accuracy of gear is high.transmission efficiency of gear is high,and application range is wide.Gear is widely used in industrial machinery,automotive applications,aerospace engineering,and other fields,and is a key component of power transmission.Therefore,it is necessary to study gear related indicators.In gear research,previous scholars have almost always analyzed the micro morphology of the gear tooth surface from the macro level,and considered the gear center distance as a constant value when conducting dynamic analysis of the gear system.In gear system transmission,this obviously does not conform to authenticity.Based on this,the following research content has been done in the paper:(1)Establishment of gear model and calculation of dynamic stiffness: In this paper,based on the standard involute spur cylindrical gear,the gear tooth is equivalent to a cantilever beam,and the Beam54 element is selected in the finite element software ANSYS,and a parametric programming language is used for finite element modeling of the gear;In FORTRAN language environment,parametric programming language is used for theoretical modeling of gears.According to the proposed dynamic stiffness calculation model,the Newmark method is used to solve the dynamic displacement at any time,and then the stiffness definition formula is used to solve the gear dynamic stiffness.The solution process requires assembling the global mass matrix,global stiffness matrix,and global damping matrix,and solving the time step.The finite element method and the energy method were used to compare and verify the rationality of the dynamic stiffness model.(2)Consider the micromorphology of the tooth surface and the time-varying center distance: simultaneously consider the micromorphology(surface roughness)of the gear tooth surface and the change in center distance of the gear system.This paper focuses on the influence of tooth surface roughness and time-varying center distance on the backlash of gear systems.The fractal theory is used to simulate the micro morphology of the tooth surface.The surface roughness height formula(fractal backlash)and the time-varying center distance formula of the gear system based on fractal theory are derived.Previous scholars’ modifications to the W-M function almost did not consider the periodic physical significance of the gear meshing process,but simply calculated the gear tooth surface roughness based on the total time or displacement.Based on this,we introduced the mod function into the fractal theory formula to fill this gap.(3)Establishment of gear dynamics model: In order to study the dynamic characteristics of gear transmission systems,considering factors such as constant driving torque excitation,constant load torque excitation,gear backlash,support bearings,support damping,and gravity,based on the energy principle and using Lagrange’s theorem,a nonlinear dynamic model for torsional vibration of gear systems with five degrees of freedom and six degrees of freedom considering gear backlash is derived and established.The assumed conditions for the research and analysis are given,and the meshing damping of the gear pair is considered.For the convenience of calculation,the tooth surface friction is ignored.The nonlinear dynamic model is solved using the Runge Kutta method with a fixed time step.(4)Research on the dynamic characteristics of gear systems: Based on the above nonlinear dynamic models,the effects of different stiffness models and different fractal backlash on the dynamic characteristics of gear systems were compared in the time and frequency domains,respectively.It is mainly represented by a frequency sweep diagram of the dynamic transmission error(DTE)of the gear system,a bifurcation diagram of the DTE,a DTE diagram of a specific rotational speed,a DTE change rate diagram,a pinion vibration response diagram,a frequency domain diagram,and a phase diagram.The results show that the dynamic stiffness model has a greater impact on the dynamic characteristics of the gear system as a whole than the static stiffness model;Due to the existence of gear backlash,the gear system will experience a jumping phenomenon,and this phenomenon is that the static stiffness model lags behind the dynamic stiffness model;The higher the rotational speed,the less the number of periodic motions of the gear system;The greater the rotational speed,the more significant the vibration response of the pinion is;At low rotational speeds,the fractal backlash has a significant impact on the gear system DTE,and as the fractal backlash increases,the system DTE increases;At high speeds,the fractal backlash has almost no effect.Based on the five degree of freedom dynamic model,the influence diagrams of different fluctuation coefficients DD on the model DTE were also explored.It was found that the fluctuation coefficient DD has a significant impact on the gear system DTE,and as the fluctuation coefficient DD increases,the fluctuation amplitude of the system DTE also increases. |
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