caa a22 4500 445361700 CHVBK 20180317142917.0 cr unu---uuuuu 170323e20111201xx s 000 0 eng 10.1007/s11071-010-9924-y doi (NATIONALLICENCE)springer-10.1007/s11071-010-9924-y Nonlinear analysis of chatter vibration in a cylindrical transverse grinding process with two time delays usinganonlinear time transformation method [Elektronische Daten] [Kwok-wai Chung, Zhaoheng Liu] A nonlinear dynamic system of cylindrical transverse grinding process is studied in this paper. The system consists of a grinding wheel and a workpiece, which are connected to the base by spring-damper elements, interacting with nonlinear normal forces. This two DOF model includes two time delays originated from the regenerative effects of the workpiece and the grinding wheel. Bifurcation points are located using a numerical algorithm by which we can find all the eigenvalues in a given rectangular region on the complex plane for the delayed differential equations. Supercritical bifurcation has been found for some sets of system parameter values. The amplitudes of the limit cycles are predicted using a nonlinear time transformation method, which is similar to the harmonic balance approach in that a periodic solution is approximated by a Fourier series. However, the main difference is that a nonlinear time ϕ is introduced in the Fourier series rather than the physical timet. The analytical solutions of stable limit cycles up to the third harmonics are compared with numerical simulations for the retarded system. It is shown that the proposed method gives accurate approximate solutions. Springer Science+Business Media B.V., 2011 Differential equations nationallicence Two time delays nationallicence Grinding system nationallicence Chatter vibration nationallicence Limit cycles nationallicence Nonlinear time transformation nationallicence Chung Kwok-wai Department of Mathematics, City University of Hong Kong, 83 Tat Chee Avenue, Kowloon Tong, Hong Kong aut Liu Zhaoheng Department of Mechanical Engineering, École de technologie supérieure, Université du Québec, H3C 1K3, Montreal, QC, Canada aut Nonlinear Dynamics Springer Netherlands 66/4(2011-12-01), 441-456 0924-090X 66:4<441 2011 66 11071 https://doi.org/10.1007/s11071-010-9924-y text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s11071-010-9924-y text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Chung Kwok-wai Department of Mathematics, City University of Hong Kong, 83 Tat Chee Avenue, Kowloon Tong, Hong Kong aut NATIONALLICENCE 700 1- Liu Zhaoheng Department of Mechanical Engineering, École de technologie supérieure, Université du Québec, H3C 1K3, Montreal, QC, Canada aut NATIONALLICENCE 773 0- Nonlinear Dynamics Springer Netherlands 66/4(2011-12-01), 441-456 0924-090X 66:4<441 2011 66 11071 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer