CAJ | 학술논문

综合考虑由扭矩波动引起的低频外激励和齿轮阻尼比、齿侧间隙、啮合频率、啮合刚度的随机扰动等因素，基于牛顿定律建立了单对三自由度直齿齿轮系统的随机振动方程，利用Runge-Kutta法对运动微分方程进行了求解，采用系统的分岔图、相图、时间历程图和Poincaré映射图分析了齿轮系统在啮合频率变化下的分岔特性与稳定性，并分析了啮合频率的随机扰动对系统分岔特性的影响．数值仿真表明：随机非光滑齿轮系统存在丰富的倍周期分岔现象，随着齿轮啮合频率的减小，齿轮系统通过周期倍化分岔从周期运动通向混沌运动；通过剔除6处不稳定转速区段，可获得无量纲啮合频率在0．1～6．0之间的稳定速度区段；系统的运动对啮合频率的随机扰动极其敏感，建模时要考虑其大小的影响．
종합고필유뉴구파동인기적저빈외격려화치륜조니비、치측간극、교합빈솔、교합강도적수궤우동등인소，기우우돈정률건립료단대삼자유도직치치륜계통적수궤진동방정，이용Runge-Kutta법대운동미분방정진행료구해，채용계통적분차도、상도、시간역정도화Poincaré영사도분석료치륜계통재교합빈솔변화하적분차특성여은정성，병분석료교합빈솔적수궤우동대계통분차특성적영향．수치방진표명：수궤비광활치륜계통존재봉부적배주기분차현상，수착치륜교합빈솔적감소，치륜계통통과주기배화분차종주기운동통향혼돈운동；통과척제6처불은정전속구단，가획득무량강교합빈솔재0．1～6．0지간적은정속도구단；계통적운동대교합빈솔적수궤우동겁기민감，건모시요고필기대소적영향．
By considering the random disturbances caused by the low-frequency internal excitation of torque fluctua-tion,damping ratio,gear backlash,meshing frequency and meshing stiffness,the random vibration equations of a single pair of spur gear system with three degrees of freedom are established based on Newton's law.Then,the mo-tion differential equations are solved by means of the Runge-Kutta method,and the bifurcation and stability of the gear system with varying gear meshing frequency are analyzed according to the bifurcation diagram,phase diagram, time course diagram and Poincaré mapping graph of the system.Finally,the effect of the random disturbance of meshing frequency on the system dynamics is investigated.Numerical simulation results show that (1 )there exists abundant period-doubling bifurcation in the random non-smooth gear system;(2)with the decrease of meshing fre-quency,the periodic motion of gear system becomes chaotic via the period-doubling bifurcation;(3)by eliminating 6 unstable speed sections,a stable speed section can be obtained in a dimensionless meshing frequency range from 0.1 to 6.0;and (4)as the system motion is extremely sensitive to the random disturbance of meshing frequency, the influence degree should be taken into consideration during the system modeling.