Nonlinear Contact Dynamics Character Research For Cycloid Bevel Gear

Cycloid bevel gear (Klingelnberg) is one of the spiral bevel gear widely used atpresent, often working in complex conditions such as overloading, impact andvariable load, so the tooth surface failure, vibration and noise is the consequentproblems. The dynamics problem of cycloid bevel gear is particularly prominenttogether with its complex tooth surface structure and strongly nonlinear factors(time-varying meshing stiffness, time-varying meshing damping, transmission error,clearance, friction), so its dynamic characteristics has become a research hotspot athome and abroad.Based on the project funding of National Nature Science Foundation of China:Study and identification of damage mechanism of heavy-duty cycloid bevel gear undernon-steady state (Authorize No.:51075006), coupling vibration characteristics ofcycloid bevel gear and dynamics behavior when considering the friction and not isstudied, mainly contents as follows:(1) Bend-Twist-Shaft-Pendulum coupled vibration model of cycloid bevel geartransmission system is established by adopting lumped parameter method based onvibration mechanism of cycloid bevel gear, related excitation source of gear vibrationis introduced: meshing stiffness excitation, error excitation and meshing shockexcitation.(2) Vibration balance equation of cycloid bevel gear is derived by applicating theprinciple of Lagrange, gear dynamic equation is obtained by reduced order,decoupling and normalized. Mathematical model of meshing nonlinear factors, suchas time-varying meshing damping, time-varying meshing stiffness and clearance, areextracted, which lay the foundation for solving dynamic equation and response curveanalysis.(3) Dynamic equation is solved with the method of Runge-Kutta, the influencelaw of constant damping, harmonic damping, harmonic stiffness, excitation frequencyand external load on gear pair meshing dynamics characteristics is analysised underthe three conditions of-1<X<1, X≤-1and X≥1, based on the different relationshipbetween normal displacement of meshing point and clearance, and vibrationcharacteristic curve is plotted.(4) According to tooth surface friction existed in meshing gear, friction vector analysis of tooth surface is conducted for cycloid bevel gear, normal friction of toothsurfaces is solved adopting Coulomp friction model. The mathematical model withfriction of gear pair is established based on the foregoing theory, and the deriveddynamics equation is solved. For time-varying term in the equation: friction factor,constant damping, harmonic damping, harmonic stiffness, external load, transmissionerror and excitation frequency is analyzed respectively, and vibration characteristiccurve is given, and on this basis the influence law of time-varying term on gearvibration characteristics is contrasted when considering friction and not.