The motion track of belt spindle is important for the radial error of belt spindle. An analytical modeling method for the motion track of belt spindle under the combined effects of bending moment-torque-thermal deform...The motion track of belt spindle is important for the radial error of belt spindle. An analytical modeling method for the motion track of belt spindle under the combined effects of bending moment-torque-thermal deformation is proposed in this paper. Three running phases of belt spindle have been analyzed and modeled: the start-up phase with leaping change due to the change in force and bending moment, the accelerating phase with axis deflection, and the constant speed phase with axis regression because of the combined effects of bending moment-torque-thermal deformation. The simulation and test were completed on the belt spindle of SKVM850 machine tool, which illustrates the variation law of the radial error of belt spindle during the whole running phases.展开更多
Simulations of bubble entrainment into a stationary Gaussian vortex are performed by using the combined particle tracking method(PTM)and boundary element method(BEM).Before the bubble is captured by the vortex core,os...Simulations of bubble entrainment into a stationary Gaussian vortex are performed by using the combined particle tracking method(PTM)and boundary element method(BEM).Before the bubble is captured by the vortex core,oscillation and migration of the quasi-spherical nucleus are solved by using improved RP equation and the momentum theorem in the Lagrangian reference frame simultaneously,and the trajectory of the nucleus presents a kind of reduced helix shape.After captured by the vortex core,the bubble grows immediately and moves and deforms along the vortex core axis.The non-spherical evolution and deformation of the bubble is simulated by adopting a mixed Eulerian-Lagrangian method.The output of quasi-spherical stage is taken as the input of non-spherical stage,and all the behaviors of the entrained bubble can be simulated such as inception,motion,deformation and split.Numerical results agree well with published experimental data.On this basis,the influences of various factors such as viscosity,surface tension,buoyancy are studied systemically.Hopefully the results from this paper would provide some insight into the control on vortex bubble entrainment.展开更多
基金Supported by the State S&T Projects for Upmarket NC Machine and Fundamental Manufacturing Equipments of China(No.2012ZX04012-031)
文摘The motion track of belt spindle is important for the radial error of belt spindle. An analytical modeling method for the motion track of belt spindle under the combined effects of bending moment-torque-thermal deformation is proposed in this paper. Three running phases of belt spindle have been analyzed and modeled: the start-up phase with leaping change due to the change in force and bending moment, the accelerating phase with axis deflection, and the constant speed phase with axis regression because of the combined effects of bending moment-torque-thermal deformation. The simulation and test were completed on the belt spindle of SKVM850 machine tool, which illustrates the variation law of the radial error of belt spindle during the whole running phases.
基金supported by the Excellent Young Scientists Fund(Grant No.51222904)the national natural science foundation of China(Grant No.11302056)
文摘Simulations of bubble entrainment into a stationary Gaussian vortex are performed by using the combined particle tracking method(PTM)and boundary element method(BEM).Before the bubble is captured by the vortex core,oscillation and migration of the quasi-spherical nucleus are solved by using improved RP equation and the momentum theorem in the Lagrangian reference frame simultaneously,and the trajectory of the nucleus presents a kind of reduced helix shape.After captured by the vortex core,the bubble grows immediately and moves and deforms along the vortex core axis.The non-spherical evolution and deformation of the bubble is simulated by adopting a mixed Eulerian-Lagrangian method.The output of quasi-spherical stage is taken as the input of non-spherical stage,and all the behaviors of the entrained bubble can be simulated such as inception,motion,deformation and split.Numerical results agree well with published experimental data.On this basis,the influences of various factors such as viscosity,surface tension,buoyancy are studied systemically.Hopefully the results from this paper would provide some insight into the control on vortex bubble entrainment.
