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A Parametric Dynamic Study on Hunting Stability of Full Dual-Bogie Railway Vehicle
김필기,정지현,석종원 한국정밀공학회 2011 International Journal of Precision Engineering and Vol.12 No.3
Analysis is performed on the hunting stability of a full railway vehicle system composed of a vehicle body, two bogie frames,and two wheelsets for each bogie frame. Incorporated into this analysis are the nonlinear heuristic creep and flange-rail contact models. The results show that the hunting speed is most sensitive to the primary longitudinal and lateral stiffnesses,and the nonlinear heuristic creep model plays a key role in confining the hunting speed within a physically reasonable range. Eigenanalysis is performed to investigate the dynamic behavior of the vehicle in the vicinity of the hunting speed. The results reveal that there exists not only the most dominant pair of complex conjugate roots, but also its shadowed roots. The roles of these two principal pairs of eigensolutions in the hunting motion are thoroughly explored via numerical studies using bifurcation analysis and an orbital representation. It is shown that the nonlinear hunting motions before the modal transition speed mainly refer to the principal mode, and those after the critical speed refer not only to the principal mode,but also to its shadowed mode, which supports the necessity of the dual-bogie railway vehicle model in the hunting analysis.
상태의존적 시간지연을 고려한 선삭시스템의 비선형 동특성 해석
김필기(Pilkee Kim),석종원(Jongwon Seok) 대한기계학회 2010 대한기계학회 춘추학술대회 Vol.2010 No.11
In this study, the stability and bifurcation analyses are performed on the orthogonal micro-turning process that has a cubic structural nonlinearity and a nonlinear cutting force including state dependent, large time delay. A multiple scale analysis is performed on the resulting state dependent delay differential equation, in which the scale of time delay is treated to be large compared to the time scale of cutting tool vibrations. The nonlinear forcing term in the form of non-integer power of state variables that include state dependent time delay is properly expanded up to the third order, and then stability boundaries are obtained, which are shown to be well matched with those obtained from a linear stability analysis. Numerical computation on the slow time scale modulation equations is also conducted and the results are compared to the numerical integration of original SD-DDEs. It is shown that the two results remarkably well match with each other and the reduction of dimensionality using center manifold can greatly enhance computational efficiency. A bifurcation analysis is performed on the basis of the asymptotic expansions for a couple of cases chosen for illustration purposes. Multiple bifurcation points including the Hopf bifurcation point are identified, which occur due to the existence of nonlinearities in the governing equations. The characteristics of the resulting bifurcation and the associated limit cycles are thoroughly examined and discussed.