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주기적으로 운동하는 점탄성 지지대를 갖는 회전 보의 안정성 해석
김필기(Pilkee Kim),석종원(Jongwon Seok) 대한기계학회 2011 대한기계학회 춘추학술대회 Vol.2011 No.10
Dynamic analysis of burnishing process is performed using eigenanalysis and numerical simulation. The tool and workpiece are modeled as a 1-DOF oscillator and the clamped-hinged rotating beam, respectively, coupled in contact force. The system model of the burnishing process are appeared to be a rotating Rayleigh beam with a traveling support. The state space and modal analyses for the system model are carried out in this study. The resulting decoupled equations are shown to be a linear differential equations with time-varying coefficients. The eigensolutions of the system, under the quasi-static assumption, are obtained according to the position of the support and the corresponding stability of the system are discussed. The variations in the shape of the beam are also investigated with respect to the number of vibration mode included in the numerical simulation.
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.
주기적인 하중을 받는 중공 원통의 비선형 동적 거동 해석
이수영(Sooyoung Lee),김필기(Pilkee Kim),석종원(Jongwon Seok) 대한기계학회 2013 대한기계학회 춘추학술대회 Vol.2013 No.12
In this study, the dynamic behavior of a hollow cylinder under a periodic, consecutive moving force applied at the inner hole is investigated. The cylinder is assumed to deform large compared to the classical linear elastic material, so that the Neo-Hookean constitutive model is employed. The cylinder is fixed at the top and bottom surfaces in the present model. The resulting governing equation and the associated boundary conditions appear to be highly nonlinear in the cylinder’ s displacements. After performing the eigen analysis on the present system, an appropriate biorthogonality condition is obtained. Galerkin’ s method is applied, in conjunction with the eigen analysis results, to obtain the discretized equation of motion, which include the nonlinearity of both the governing field equation and boundary conditions. As a result of the successive nonlinear analysis, the cricical speed of the moving force could be derived and the influences of the nonlinearty on the dynamic behavior of the cylinder are examined. with the eigen analysis results, to obtain the discretized equation of motion, which include the nonlinearity of both the governing field equation and boundary conditions. As a result of the successive nonlinear analysis, the critical speed of the moving force could be derived and the influences of the nonlinearty on the dynamic behavior of the cylinder are examined.