This article studies bounded traveling wave solutions of variant Boussinesq equation with a dissipation term and dissipation effect on them. Firstly, we make qualitative analysis to the bounded traveling wave solution...This article studies bounded traveling wave solutions of variant Boussinesq equation with a dissipation term and dissipation effect on them. Firstly, we make qualitative analysis to the bounded traveling wave solutions for the above equation by the theory and method of planar dynamical systems, and obtain their existent conditions, number, and general shape. Secondly, we investigate the dissipation effect on the shape evolution of bounded traveling wave solutions. We find out a critical value r^＊ which can characterize the scale of dissipation effect, and prove that the bounded traveling wave solutions appear as kink profile waves if ｜r｜≥ r^＊; while they appear as damped oscillatory waves if ｜r｜ 〈 r^＊. We also obtain kink profile solitary wave solutions with and without dissipation effect. On the basis of the above discussion, we sensibly design the structure of the approximate damped oscillatory solutions according to the orbits evolution relation corresponding to the component u（ξ） in the global phase portraits, and then obtain the approximate solutions （u（ξ）, H（ξ））. Furthermore, by using homogenization principle, we give their error estimates by establishing the integral equation which reflects the relation between exact and approximate solutions. Finally, we discuss the dissipation effect on the amplitude, frequency, and energy decay of the bounded traveling wave solutions.展开更多
The current research of machine center accuracy in workspace mainly focuses on the poor geometric error subjected to thermal and gravity load while in operation, however, there are little researches focusing on the ef...The current research of machine center accuracy in workspace mainly focuses on the poor geometric error subjected to thermal and gravity load while in operation, however, there are little researches focusing on the effect of machine center elastic deformations on workspace volume. Therefore, a method called pre-deformation for assembly performance is presented. This method is technically based on the characteristics of machine tool assembly and collaborative computer-aided engineering （CAE） analysis. The research goal is to enhance assembly performance, including straightness, positioning, and angular errors, to realize the precision of the machine tool design. A vertical machine center is taken as an example to illustrate the proposed method. The concept of travel error is defined to obtain the law of the guide surface. The machine center assembly performance is analyzed under cold condition and thermal balance condition to establish the function of pre-deformation. Then, the guide surface in normal direction is processed with the pre-deformation function, and the machine tool assembly performance is measured using a laser interferometer. The measuring results show that the straightness deviation of the Z component in the Y-direction is 158.9% of the allowable value primarily because of the gravity of the spindle head, and the straightness of the X and Y components is minimal. When the machine tool is processed in pre-deformation, the straightness of the Z axis moving component is reduced to 91.2%. This research proposes a pre-deformation machine center assembly method which has sufficient capacity to improving assembly accuracy of machine centers.展开更多
基金supported by National Natural ScienceFoundation of China(11071164)Innovation Program of Shanghai Municipal Education Commission(13ZZ118)Shanghai Leading Academic Discipline Project(XTKX2012)
文摘This article studies bounded traveling wave solutions of variant Boussinesq equation with a dissipation term and dissipation effect on them. Firstly, we make qualitative analysis to the bounded traveling wave solutions for the above equation by the theory and method of planar dynamical systems, and obtain their existent conditions, number, and general shape. Secondly, we investigate the dissipation effect on the shape evolution of bounded traveling wave solutions. We find out a critical value r^＊ which can characterize the scale of dissipation effect, and prove that the bounded traveling wave solutions appear as kink profile waves if ｜r｜≥ r^＊; while they appear as damped oscillatory waves if ｜r｜ 〈 r^＊. We also obtain kink profile solitary wave solutions with and without dissipation effect. On the basis of the above discussion, we sensibly design the structure of the approximate damped oscillatory solutions according to the orbits evolution relation corresponding to the component u（ξ） in the global phase portraits, and then obtain the approximate solutions （u（ξ）, H（ξ））. Furthermore, by using homogenization principle, we give their error estimates by establishing the integral equation which reflects the relation between exact and approximate solutions. Finally, we discuss the dissipation effect on the amplitude, frequency, and energy decay of the bounded traveling wave solutions.
基金Supported by National Key Technology Support Program of China(Grant No.2011BAF11B03)National Science and Technology Major Projects of China(Grant No.2012ZX04010-011)
文摘The current research of machine center accuracy in workspace mainly focuses on the poor geometric error subjected to thermal and gravity load while in operation, however, there are little researches focusing on the effect of machine center elastic deformations on workspace volume. Therefore, a method called pre-deformation for assembly performance is presented. This method is technically based on the characteristics of machine tool assembly and collaborative computer-aided engineering （CAE） analysis. The research goal is to enhance assembly performance, including straightness, positioning, and angular errors, to realize the precision of the machine tool design. A vertical machine center is taken as an example to illustrate the proposed method. The concept of travel error is defined to obtain the law of the guide surface. The machine center assembly performance is analyzed under cold condition and thermal balance condition to establish the function of pre-deformation. Then, the guide surface in normal direction is processed with the pre-deformation function, and the machine tool assembly performance is measured using a laser interferometer. The measuring results show that the straightness deviation of the Z component in the Y-direction is 158.9% of the allowable value primarily because of the gravity of the spindle head, and the straightness of the X and Y components is minimal. When the machine tool is processed in pre-deformation, the straightness of the Z axis moving component is reduced to 91.2%. This research proposes a pre-deformation machine center assembly method which has sufficient capacity to improving assembly accuracy of machine centers.
