振动与冲击
振動與遲擊
진동여충격
JOURNAL OF VIBRATION AND SHOCK
2014年
19期
116-122
,共7页
盛冬平%朱如鹏%陆凤霞%靳广虎
盛鼕平%硃如鵬%陸鳳霞%靳廣虎
성동평%주여붕%륙봉하%근엄호
弯扭耦合%非线性振动%分岔%多间隙
彎扭耦閤%非線性振動%分岔%多間隙
만뉴우합%비선성진동%분차%다간극
bending-torsional coupling%non-linear vibration%bifurcation%multi-clearance
采用集中质量法，建立了齿轮转子轴承系统的四自由度的弯扭耦合的非线性振动模型，模型考虑了齿轮副间的时变啮合刚度、齿侧间隙、支承间隙以及综合传递误差等非线性因素；推导出系统的量纲一振动微分方程，采用数值积分方法研究多间隙弯扭耦合齿轮传动的运动随转速、齿侧间隙、支承间隙以及阻尼等参数的分岔特性，同时结合Poincaré截面图，全面系统的分析了转速、啮合阻尼、齿侧间隙以及支承间隙等参数对系统分岔特性的影响。结果发现，在一定的齿侧间隙和啮合阻尼下，随着转速的逐渐增加，系统进入混沌的途径包括激变和拟周期分岔，且随着阻尼系数的增加，系统的分岔和混沌运动被抑制，表现为其混沌区域宽度逐渐降低；在一定的转速和啮合阻尼下，而随着齿侧间隙的逐渐增加，系统会从通过激变进入混沌的途径转变成由倍周期分岔途径进入到混沌，且系统在不同的啮合阻尼下最终锁相为混沌、周期四、周期二和周期一运动；在满足一定的转速和啮合阻尼条件下，随着齿侧间隙的增加，系统可通过倍周期分岔进入并锁定为Naimark-sacker分岔。在满足一定的转速、啮合阻尼和齿侧间隙的条件下，随着支承间隙的增加，系统运动进入狭窄的周期五窗口后锁相为周期一运动，且从系统的控制方程和数值解可以发现支承间隙对系统的运动的影响较弱。
採用集中質量法，建立瞭齒輪轉子軸承繫統的四自由度的彎扭耦閤的非線性振動模型，模型攷慮瞭齒輪副間的時變齧閤剛度、齒側間隙、支承間隙以及綜閤傳遞誤差等非線性因素；推導齣繫統的量綱一振動微分方程，採用數值積分方法研究多間隙彎扭耦閤齒輪傳動的運動隨轉速、齒側間隙、支承間隙以及阻尼等參數的分岔特性，同時結閤Poincaré截麵圖，全麵繫統的分析瞭轉速、齧閤阻尼、齒側間隙以及支承間隙等參數對繫統分岔特性的影響。結果髮現，在一定的齒側間隙和齧閤阻尼下，隨著轉速的逐漸增加，繫統進入混沌的途徑包括激變和擬週期分岔，且隨著阻尼繫數的增加，繫統的分岔和混沌運動被抑製，錶現為其混沌區域寬度逐漸降低；在一定的轉速和齧閤阻尼下，而隨著齒側間隙的逐漸增加，繫統會從通過激變進入混沌的途徑轉變成由倍週期分岔途徑進入到混沌，且繫統在不同的齧閤阻尼下最終鎖相為混沌、週期四、週期二和週期一運動；在滿足一定的轉速和齧閤阻尼條件下，隨著齒側間隙的增加，繫統可通過倍週期分岔進入併鎖定為Naimark-sacker分岔。在滿足一定的轉速、齧閤阻尼和齒側間隙的條件下，隨著支承間隙的增加，繫統運動進入狹窄的週期五窗口後鎖相為週期一運動，且從繫統的控製方程和數值解可以髮現支承間隙對繫統的運動的影響較弱。
채용집중질량법，건립료치륜전자축승계통적사자유도적만뉴우합적비선성진동모형，모형고필료치륜부간적시변교합강도、치측간극、지승간극이급종합전체오차등비선성인소；추도출계통적량강일진동미분방정，채용수치적분방법연구다간극만뉴우합치륜전동적운동수전속、치측간극、지승간극이급조니등삼수적분차특성，동시결합Poincaré절면도，전면계통적분석료전속、교합조니、치측간극이급지승간극등삼수대계통분차특성적영향。결과발현，재일정적치측간극화교합조니하，수착전속적축점증가，계통진입혼돈적도경포괄격변화의주기분차，차수착조니계수적증가，계통적분차화혼돈운동피억제，표현위기혼돈구역관도축점강저；재일정적전속화교합조니하，이수착치측간극적축점증가，계통회종통과격변진입혼돈적도경전변성유배주기분차도경진입도혼돈，차계통재불동적교합조니하최종쇄상위혼돈、주기사、주기이화주기일운동；재만족일정적전속화교합조니조건하，수착치측간극적증가，계통가통과배주기분차진입병쇄정위Naimark-sacker분차。재만족일정적전속、교합조니화치측간극적조건하，수착지승간극적증가，계통운동진입협착적주기오창구후쇄상위주기일운동，차종계통적공제방정화수치해가이발현지승간극대계통적운동적영향교약。
Using the lumped mass method,a multi-clearance nonlinear gear-rotor-bearing coupled bending-torsional vibration model with 4-DOF was established and dimensionless dynamic equations of the system were derived,and transmission errors,time varying meshing stiffness and gear backlashes were considered in this model.By studying Poincaré maps and bifurcation diagrams,the bifurcation properties of the system were obtained.The influences of some bifurcation parameters,such as,rotation speed,damping coefficient and gear backlashes on the bifurcation features of the system were analyzed.It was shown that under a certain gear backlash and mesh damping and with increase in rotating speed,the way of the system entering chaos changes from abrupt varying to period doubling bifurcation,then the system phase is locked and the system enters period-four,period-two and period motion states under different mesh damping coefficients;under a certain rotation speed and mesh damping,the motion state of the system changes from period doubling bifurcation into Naimark-sacker bifurcation;under a certain rotation speed,mesh damping and gear backlash, the system enters a period-five motion,then its phase is locked and the system enters a periodic motion rapidly;bearing rolling clearance has a weak interaction with the system motion.
