A class of quasi-cubic B-spline base functions by trigonometric polynomials are established which inherit properties similar to those of cubic B-spline bases. The corresponding curves with a shape parameter a, defined...A class of quasi-cubic B-spline base functions by trigonometric polynomials are established which inherit properties similar to those of cubic B-spline bases. The corresponding curves with a shape parameter a, defined by the introduced base functions, include the B-spline curves and can approximate the B-spline curves from both sides. The curves can be adjusted easily by using the shape parameter a, where dpi（a,t） is linear with respect to da for the fixed t. With the shape parameter chosen properly, the defined curves can be used to precisely represent straight line segments, parabola segments, circular arcs and some transcendental curves, and the corresponding tensor product surfaces can also represent spherical surfaces, cylindrical surfaces and some transcendental surfaces exactly. By abandoning positive property, this paper proposes a new C^2 continuous blended interpolation spline based on piecewise trigonometric polynomials associated with a sequence of local parameters. Illustration showed that the curves and surfaces constructed by the blended spline can be adjusted easily and freely. The blended interpolation spline curves can be shape-preserving with proper local parameters since these local parameters can be considered to be the magnification ratio to the length of tangent vectors at the interpolating points. The idea is extended to produce blended spline surfaces.展开更多
The present research on involute spline cold roll-beating forming is mainly about the principles and motion relations of cold roll-beating,the theory of roller design,and the stress and strain field analysis of cold r...The present research on involute spline cold roll-beating forming is mainly about the principles and motion relations of cold roll-beating,the theory of roller design,and the stress and strain field analysis of cold roll-beating,etc.However,the research on law of metal flow in the forming process of involute spline cold roll-beating is rare.According to the principle of involute spline cold roll-beating,the contact model between the rollers and the spline shaft blank in the process of cold roll-beating forming is established,and the theoretical analysis of metal flow in the cold roll-beating deforming region is proceeded.A finite element model of the spline cold roll-beating process is established,the formation mechanism of the involute spline tooth profile in cold roll-beating forming process is studied,and the node flow tracks of the deformation area are analyzed.The experimental research on the metal flow of cold roll-beating spline is conducted,and the metallographic structure variation,grain characteristics and metal flow line of the different tooth profile area are analyzed.The experimental results show that the particle flow directions of the deformable bodies in cold roll-beating deformation area are determined by the minimum moving resistance.There are five types of metal flow rules of the deforming region in the process of cold roll-beating forming.The characteristics of involute spline cold roll-beating forming are given,and the forming mechanism of involute spline cold roll-beating is revealed.This paper researches the law of metal flow in the forming process of involute spline cold roll-beating,which provides theoretical supports for solving the tooth profile forming quality problem.展开更多
基金Project supported by the National Natural Science Foundation of China (Nos. 10171026 and 60473114), the Research Funds forYoung Innovation Group, Education Department of Anhui Prov-ince (No. 2005TD03) and the Natural Science Foundation of An-hui Provincial Education Department (No. 2006KJ252B), China
文摘A class of quasi-cubic B-spline base functions by trigonometric polynomials are established which inherit properties similar to those of cubic B-spline bases. The corresponding curves with a shape parameter a, defined by the introduced base functions, include the B-spline curves and can approximate the B-spline curves from both sides. The curves can be adjusted easily by using the shape parameter a, where dpi（a,t） is linear with respect to da for the fixed t. With the shape parameter chosen properly, the defined curves can be used to precisely represent straight line segments, parabola segments, circular arcs and some transcendental curves, and the corresponding tensor product surfaces can also represent spherical surfaces, cylindrical surfaces and some transcendental surfaces exactly. By abandoning positive property, this paper proposes a new C^2 continuous blended interpolation spline based on piecewise trigonometric polynomials associated with a sequence of local parameters. Illustration showed that the curves and surfaces constructed by the blended spline can be adjusted easily and freely. The blended interpolation spline curves can be shape-preserving with proper local parameters since these local parameters can be considered to be the magnification ratio to the length of tangent vectors at the interpolating points. The idea is extended to produce blended spline surfaces.
基金supported by National Natural Science Foundation of China(Grant Nos.5107512450975229)Doctoral Foundation of Henan University of Science and Technology of China(Grant No.09001331)
文摘The present research on involute spline cold roll-beating forming is mainly about the principles and motion relations of cold roll-beating,the theory of roller design,and the stress and strain field analysis of cold roll-beating,etc.However,the research on law of metal flow in the forming process of involute spline cold roll-beating is rare.According to the principle of involute spline cold roll-beating,the contact model between the rollers and the spline shaft blank in the process of cold roll-beating forming is established,and the theoretical analysis of metal flow in the cold roll-beating deforming region is proceeded.A finite element model of the spline cold roll-beating process is established,the formation mechanism of the involute spline tooth profile in cold roll-beating forming process is studied,and the node flow tracks of the deformation area are analyzed.The experimental research on the metal flow of cold roll-beating spline is conducted,and the metallographic structure variation,grain characteristics and metal flow line of the different tooth profile area are analyzed.The experimental results show that the particle flow directions of the deformable bodies in cold roll-beating deformation area are determined by the minimum moving resistance.There are five types of metal flow rules of the deforming region in the process of cold roll-beating forming.The characteristics of involute spline cold roll-beating forming are given,and the forming mechanism of involute spline cold roll-beating is revealed.This paper researches the law of metal flow in the forming process of involute spline cold roll-beating,which provides theoretical supports for solving the tooth profile forming quality problem.
