研究了含間隙三自由度的齒輪轉子非線性系統的周期軌道及其穩定性。采用有限差分法近似替非光滑系統的Jacobi矩陣，改善了CPNF法在求解非線性動力學時需要系統必須光滑的缺陷。改進后的CPNF發對算例的計算結果與數值積分結果比較驗證其有效性。在給定參數下采用改進后的CPNF發研究了齒輪轉子系(xi)統(tong)(tong)的(de)(de)共(gong)存的(de)(de)周(zhou)期(qi)運(yun)動，并(bing)判斷了(le)各周(zhou)期(qi)的(de)(de)穩(wen)定性(xing)；通(tong)過延(yan)續追蹤(zong)發(fa)判斷了(le)不同轉速(su)下(xia)(xia)系(xi)統(tong)(tong)周(zhou)期(qi)軌(gui)道的(de)(de)穩(wen)定性(xing)；研究了(le)齒(chi)(chi)輪轉子系(xi)統(tong)(tong)隨無量綱轉速(su)變化的(de)(de)分岔(cha)特性(xing)。結果發(fa)現，齒(chi)(chi)輪轉子非線性(xing)系(xi)統(tong)(tong)在某些參數組合下(xia)(xia)多個穩(wen)定和不穩(wen)定周(zhou)期(qi)軌(gui)道共(gong)存；轉速(su)在1.54-1.42變化時，齒(chi)(chi)輪轉子系(xi)統(tong)(tong)通(tong)過倍周(zhou)期(qi)分岔(cha)的(de)(de)形式(shi)終通(tong)向餛飩運(yun)動。

  齒(chi)輪因驅動(dong)效(xiao)率(lv)、結構緊湊、使用范圍廣的(de)(de)(de)特點，而(er)被應用在機械工程當中、含間隙(xi)和時變嚙合剛(gang)度的(de)(de)(de)齒(chi)輪驅動(dong)系(xi)(xi)統(tong)(tong)的(de)(de)(de)周(zhou)期運(yun)動(dong)是其非(fei)線(xian)(xian)(xian)性(xing)動(dong)力(li)學特性(xing)研究的(de)(de)(de)一(yi)個重要(yao)分支(zhi)。KAHRAMNA等建立(li)了直(zhi)齒(chi)圓(yuan)柱齒(chi)輪副的(de)(de)(de)非(fei)線(xian)(xian)(xian)性(xing)動(dong)力(li)學模型。Chosh S.S等采用諧(xie)波平衡發研究了含摩擦的(de)(de)(de)六自由度扭轉-平移齒(chi)輪副的(de)(de)(de)穩(wen)定(ding)性(xing)問題，并找出了其穩(wen)定(ding)運(yun)行區域。在非(fei)線(xian)(xian)(xian)性(xing)齒(chi)輪驅動(dong)系(xi)(xi)統(tong)(tong)同組(zu)參數條件下，可能共存多個穩(wen)定(ding)或不穩(wen)定(ding)的(de)(de)(de)周(zhou)期軌(gui)道，這(zhe)是造(zao)成非(fei)線(xian)(xian)(xian)性(xing)動(dong)力(li)系(xi)(xi)統(tong)(tong)遠(yuan)遠(yuan)復雜于線(xian)(xian)(xian)性(xing)系(xi)(xi)統(tong)(tong)的(de)(de)(de)重要(yao)原因之(zhi)一(yi)。目(mu)前研究非(fei)線(xian)(xian)(xian)性(xing)系(xi)(xi)統(tong)(tong)周(zhou)期軌(gui)道的(de)(de)(de)主(zhu)要(yao)方法有PNF法、打標法、諧(xie)波平衡閥、不動(dong)點法以及增量諧(xie)波發等幾種。