| Gears are the most widely used transmission parts.The vibration and noise in gear meshing is the important component of the mechanical equipment's vibration and noise.It is significant to improve machine's performance,even fatigue life by reducing the vibration and noise of the gears.The gear transmission with a contact ratio greater than 2 is effective to reduce the load on single tooth,which plays a significant role in weight loss,vibration reduction and noise suppression of transmission system.However,the high contact ratio(HCR)gear has a greater relative sliding velocity than normal contact ratio(NCR)gear.In addition,HCR gear is more sensitive to precision parameter.For this reason,this dissertation propose the idea to establish HCR gear's parameter design theory by conducting the research on HCR gear's nonlinear dynamic performance with the considering of influence of rough surface.The precise profile equations for involute gear are obtained by generating processing principle.The time-varying parameters,such as relative sliding velocity,radius of curvature and Hertz pressure are deduced according to the equations.A friction coefficient model for HCR gear is proposed by considering the load mutation from double-triple teeth contact alternately based on former parameters and EHL-based model.The M-B fractal function is introduced to the characterization of rough surface.The mathematic model of static transmission error including surface roughness is established for the first time.The basic principle of traditional potential energy method for stiffness calculation is expounded.The calculation results are verified by the finite element method and experiment method.The shortcoming of traditional method which ignoring the influence of backlash and friction in dynamic meshing process on stiffness is clarified.An improved potential energy method is proposed.The difference between HCR gear's stiffness and NCR gear's is studied.The recommended single tooth stiffness and average value of timevarying mesh stiffness for general HCR gears are presented.Based on the time-varying friction coefficient model,static transmission error model and improved energy method,the multi-degree of freedom(MDOF)nonlinear dynamic model for HCR gear system is established.Dynamic performances between HCR gear and NCR gear under various working conditions are compared.Comparison results reveal the advantages of HCR gear in dynamic characteristics.At the same time,the influence of addendum coefficient and pressure angle on HCR gear's dynamic response is explored.Analysis results show that the dynamic features become worse first and then turn better as contact ratio increases from 2 to 3.The effect of system damping ratio,rotation speed,input torque and tooth surface finish on nonlinear dynamic vibration responses of HCR gear is investigated.The specific influence rules of various parameters on system's response amplitude,vibration stability,jump phenomena and bifurcation behavior are understood.System parameters for different working conditions,which can meet the requirement of vibration performance,as well as can decrease the processing cost and difficulty,can be acquired through nonlinear dynamic analysis.Then the dynamic parameters design theory for HCR gear can be established,which can provide theoretical support for the gear design and processing. |
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