In this paper,a new technique is introduced to construct higher-order iterative methods for solving nonlinear systems.The order of convergence of some iterative methods can be improved by three at the cost of introduc...In this paper,a new technique is introduced to construct higher-order iterative methods for solving nonlinear systems.The order of convergence of some iterative methods can be improved by three at the cost of introducing only one additional evaluation of the function in each step.Furthermore,some new efficient methods with a higher-order of convergence are obtained by using only a single matrix inversion in each iteration.Analyses of convergence properties and computational efficiency of these new methods are made and testified by several numerical problems.By comparison,the new schemes are more efficient than the corresponding existing ones,particularly for large problem sizes.展开更多
The worm wheel whose undercutting characteristic is researched is a member of offsetting normal arc-toothed cylindrical worm drive.The tooth profile of the worm in its offsetting normal section is a circular arc.The n...The worm wheel whose undercutting characteristic is researched is a member of offsetting normal arc-toothed cylindrical worm drive.The tooth profile of the worm in its offsetting normal section is a circular arc.The normal vector used to calculate the first-type limit function is determined in the natural frame without the aid of the curvature parameter of worm helicoid.The first-type limit line is ascertained via solving the nonlinear equations iteratively.It is discovered that one first-type limit line exists on the tooth surface of worm wheel by numerical simulation,and such a line is normally located out of the meshing zone.Only one intersection point exists between the first and second-types of limit lines,and this point is a lubrication weak point.The undercutting mechanism is essentially that a part of the meshing zone near the conjugated line of worm tooth crest will come into the undercutting area and will be cut off during machining the worm wheel.The machining simulation verifies the correctness of undercutting mechanism.Moreover,a convenient and practical characteristic quantity is proposed to judge whether the undercutting exists in the whole meshing zone via computing the first-type limit function values on the worm tooth crest.展开更多
Based on the Reynolds equation with Reynolds boundary conditions, the Castelli method was employed to solve the Reynolds equation for oil lubrication upon bearings. By doing so, a profile of nonlinear oil film force o...Based on the Reynolds equation with Reynolds boundary conditions, the Castelli method was employed to solve the Reynolds equation for oil lubrication upon bearings. By doing so, a profile of nonlinear oil film force of single-pad journal bearings is established. According to the structure of combination journal bearings, nonlinear oil film force of combination journal bearing is obtained by retrieval, interpolation and assembly techniques. As for symmetrical flexible Jeffcott rotor systems supported by combination journal bearings, the nonlinear motions of the center of the rotor are calculated by the self-adaptive Runge-Kutta method and Poincar6 mapping with different rotational speeds. The numerical results show that the system performance is slightly better when the pivot ratio changes from 0.5 to 0.6, and reveals nonlinear phenomena of periodic, period-doubing, quasi-periodic motion, etc.展开更多
基金Supported by the National Natural Science Foundation of China(12061048)NSF of Jiangxi Province(20232BAB201026,20232BAB201018)。
文摘In this paper,a new technique is introduced to construct higher-order iterative methods for solving nonlinear systems.The order of convergence of some iterative methods can be improved by three at the cost of introducing only one additional evaluation of the function in each step.Furthermore,some new efficient methods with a higher-order of convergence are obtained by using only a single matrix inversion in each iteration.Analyses of convergence properties and computational efficiency of these new methods are made and testified by several numerical problems.By comparison,the new schemes are more efficient than the corresponding existing ones,particularly for large problem sizes.
基金Projects(52205069,52075083,52304049)supported by the National Natural Science Foundation of ChinaProject(2021-BS-164)supported by the Liaoning Province Doctoral Research Startup Fund,China+2 种基金Project(LJKZ0264)supported by the Science and Technology Research Projects of Education Department of Liaoning Province,ChinaProject(G2022003010L)supported by the High-end Foreign Experts Recruitment Plan of ChinaProject(E2021203095)supported by the Natural Science Foundation for Young Scholars of Hebei Province,China。
文摘The worm wheel whose undercutting characteristic is researched is a member of offsetting normal arc-toothed cylindrical worm drive.The tooth profile of the worm in its offsetting normal section is a circular arc.The normal vector used to calculate the first-type limit function is determined in the natural frame without the aid of the curvature parameter of worm helicoid.The first-type limit line is ascertained via solving the nonlinear equations iteratively.It is discovered that one first-type limit line exists on the tooth surface of worm wheel by numerical simulation,and such a line is normally located out of the meshing zone.Only one intersection point exists between the first and second-types of limit lines,and this point is a lubrication weak point.The undercutting mechanism is essentially that a part of the meshing zone near the conjugated line of worm tooth crest will come into the undercutting area and will be cut off during machining the worm wheel.The machining simulation verifies the correctness of undercutting mechanism.Moreover,a convenient and practical characteristic quantity is proposed to judge whether the undercutting exists in the whole meshing zone via computing the first-type limit function values on the worm tooth crest.
基金Project(2007CB707706) supported by the National Basic Research Program of China Projects(51075327,10972179) supported by the National Natural Science Foundation of China+2 种基金 Project(SKLMT-KFKT-201011) supported by Open Foundation of State Key Laboratory of Mechanical Transmission,China Projects(2009JQ7006,2007E203) supported by the Natural Science Foundation of Shaanxi Province of China Projects(09JK680,07JK340) supported by the Natural Science Foundation of Department of Education of Shaanxi Province of China
文摘Based on the Reynolds equation with Reynolds boundary conditions, the Castelli method was employed to solve the Reynolds equation for oil lubrication upon bearings. By doing so, a profile of nonlinear oil film force of single-pad journal bearings is established. According to the structure of combination journal bearings, nonlinear oil film force of combination journal bearing is obtained by retrieval, interpolation and assembly techniques. As for symmetrical flexible Jeffcott rotor systems supported by combination journal bearings, the nonlinear motions of the center of the rotor are calculated by the self-adaptive Runge-Kutta method and Poincar6 mapping with different rotational speeds. The numerical results show that the system performance is slightly better when the pivot ratio changes from 0.5 to 0.6, and reveals nonlinear phenomena of periodic, period-doubing, quasi-periodic motion, etc.
