摘要
利用拉格朗日方程建立了含间隙直齿圆柱齿轮副的动力学模型，通过齿轮轮齿弹性变形的原理数值计算建立了时变刚度的数学模型。利用4~5阶Runge-Kutta数值积分法对系统进行了数值求解。结合Poincar＆#233;映射图、相图、FFT频谱图、系统分岔图分析了系统随激励频率和阻尼变化时的动力学行为，发现了其稳定周期运动和倍周期运动及混沌运动。通过齿轮冲击模型数值计算，找出了不同初值情况下的冲击状态。
A nonlinear dynamic modeling for spur gear pair with the clearance is established by La-grange equation.The time-varying stiffness＆#39;mathematical model is established by the numerical calculation for principle of gear tooth deformation.The nonlinear dynamic equations are solved by employing variable step size 4~5 order Runge-kutta integration method and the bifurcation dia-grams are obtained.The nonlinear dynamics characteristics of the system are discussed for the variation of the exciting frequency or damping and classified based on bifurcation diagrams,phase portraits,Poincar＆#233;maps and FFT spectrum.The stable period motion,double period motion and chaotic motion are found.The gear impact state under different initial values is found by the nu-merical calculated for gear impact model.
出处
《兰州交通大学学报》
CAS
2014年第4期196-202,共7页
Journal of Lanzhou Jiaotong University
基金
甘肃省自然科学基金(1208RJZA111)
关键词
非线性动力学
分岔
冲击状态
齿轮副
nonlinear dynamics
bifurcation
gear impact state
gear pair
