三自由度齒輪轉子系統的周期運動及其穩定性

  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(zhuan)子系(xi)統的共(gong)存的周期(qi)運動(dong)，并判(pan)(pan)斷了各周期(qi)的穩(wen)定(ding)性；通(tong)過延續(xu)追蹤發判(pan)(pan)斷了不(bu)同轉(zhuan)速(su)下系(xi)統周期(qi)軌道的穩(wen)定(ding)性；研(yan)究了齒(chi)輪(lun)轉(zhuan)子系(xi)統隨無量綱轉(zhuan)速(su)變(bian)化的分岔特(te)性。結果發現(xian)，齒(chi)輪(lun)轉(zhuan)子非線性系(xi)統在某些(xie)參(can)數組合下多個穩(wen)定(ding)和不(bu)穩(wen)定(ding)周期(qi)軌道共(gong)存；轉(zhuan)速(su)在1.54-1.42變(bian)化時，齒(chi)輪(lun)轉(zhuan)子系(xi)統通(tong)過倍周期(qi)分岔的形式終通(tong)向餛(hun)飩運動(dong)。

  齒(chi)(chi)(chi)輪(lun)因傳動(dong)(dong)效率、結構(gou)緊(jin)湊、使(shi)用范圍廣的特點(dian)，而(er)被應用在機械工程當中(zhong)、含間隙和時變嚙合(he)剛(gang)度的齒(chi)(chi)(chi)輪(lun)傳動(dong)(dong)系(xi)統(tong)(tong)的周期(qi)運動(dong)(dong)是(shi)其(qi)非(fei)線(xian)性(xing)(xing)動(dong)(dong)力(li)學特性(xing)(xing)研(yan)究的一個(ge)重要分支。KAHRAMNA等(deng)建立了(le)直齒(chi)(chi)(chi)圓柱齒(chi)(chi)(chi)輪(lun)副的非(fei)線(xian)性(xing)(xing)動(dong)(dong)力(li)學模(mo)型(xing)。Chosh S.S等(deng)采用諧波(bo)平(ping)衡(heng)(heng)發研(yan)究了(le)含摩擦的六自由度扭(niu)轉-平(ping)移(yi)齒(chi)(chi)(chi)輪(lun)副的穩(wen)定性(xing)(xing)問題，并(bing)找出了(le)其(qi)穩(wen)定運行(xing)區域。在非(fei)線(xian)性(xing)(xing)齒(chi)(chi)(chi)輪(lun)傳動(dong)(dong)系(xi)統(tong)(tong)同組參(can)數條件下，可能共存(cun)多(duo)個(ge)穩(wen)定或不穩(wen)定的周期(qi)軌道，這是(shi)造成非(fei)線(xian)性(xing)(xing)動(dong)(dong)力(li)系(xi)統(tong)(tong)遠(yuan)遠(yuan)復(fu)雜于(yu)線(xian)性(xing)(xing)系(xi)統(tong)(tong)的重要原因之一。目前研(yan)究非(fei)線(xian)性(xing)(xing)系(xi)統(tong)(tong)周期(qi)軌道的主要方法(fa)有PNF法(fa)、打標法(fa)、諧波(bo)平(ping)衡(heng)(heng)閥、不動(dong)(dong)點(dian)法(fa)以及(ji)增(zeng)量諧波(bo)發等(deng)幾(ji)種。