We introduce CURDIS,a template for algorithms to discretize arcs of regular curves by incrementally producing a list of support pixels covering the arc.In this template,algorithms proceed by finding the tangent quadra...We introduce CURDIS,a template for algorithms to discretize arcs of regular curves by incrementally producing a list of support pixels covering the arc.In this template,algorithms proceed by finding the tangent quadrant at each point of the arc and determining which side the curve exits the pixel according to a tailored criterion.These two elements can be adapted for any type of curve,leading to algorithms dedicated to the shape of specific curves.While the calculation of the tangent quadrant for various curves,such as lines,conics,or cubics,is simple,it is more complex to analyze how pixels are traversed by the curve.In the case of conic arcs,we found a criterion for determining the pixel exit side.This leads us to present a new algorithm,called CURDIS-C,specific to the discretization of conics,for which we provide all the details.Surprisingly,the criterion for conics requires between one and three sign tests and four additions per pixel,making the algorithm efficient for resource-constrained systems and feasible for fixed-point or integer arithmetic implementations.Our algorithm also perfectly handles the pathological cases in which the conic intersects a pixel twice or changes quadrants multiple times within this pixel,achieving this generality at the cost of potentially computing up to two square roots per arc.We illustrate the use of CURDIS for the discretization of different curves,such as ellipses,hyperbolas,and parabolas,even when they degenerate into lines or corners.展开更多
This paper focuses on the analysis of running conditions and machining processes of conical cam with oscillating follower. We point out the common errors existing in the design and machining of the widely used plane e...This paper focuses on the analysis of running conditions and machining processes of conical cam with oscillating follower. We point out the common errors existing in the design and machining of the widely used plane expansion method of conical cam trough-out line. We show that the motion can be divided into two parts, i.e. the oscillating motion of oscillating bar and the rotary motion of oscillating bar relative to the conical cam. By increasing the rotary motion of oscillating bar, the motion path of tapered roller on oscillating bar (i.e. contour surface of conical cam) can be expanded on the cylinder. Based on these analyses, we present a creative and effective designing and machining method for 3D curve expansion of conical cam with oscillating follower.展开更多
The appriximation properties of generalized conic curves are studied in this paper. A generalized conic curve is defined as one of the following curves or their affine and translation e-quivalent curves:(i) conic curv...The appriximation properties of generalized conic curves are studied in this paper. A generalized conic curve is defined as one of the following curves or their affine and translation e-quivalent curves:(i) conic curves i including parabolas, hyperbolas and ellipses;(ii) generalized monomial curves, including curves of the form x=yr,.r R.r=0,1, in the x-y Cartesian coordinate system;(iii) exponential spiral curves of the form p=Apolar coordinate system.This type of curves has many important properties such as convexity , approximation property, effective numerical computation property and the subdivision property etc. Applications of these curves in both interpolation and approximations using piecewise generalized conic segment are also developed. It is shown that these generalized conic splines are very similar to the cubic polynomial splines and the best error of approximation is or at least in general provided appropriate procedures are used. Finally some numerical examples of interpolation and approximations with generalized conic splines are given.展开更多
In this paper,based on the mean value theorem of differential,a new method of generating conics such as circles and parabolas is given,and the related algorithm for generating conics is designed.
A two-pass annealing/quenching internal spinning process with small-end rotations is proposed to form a curved generatrix conical thin-walled shell.That is,annealing at 360°C for 2 h followed by the 1st pass spin...A two-pass annealing/quenching internal spinning process with small-end rotations is proposed to form a curved generatrix conical thin-walled shell.That is,annealing at 360°C for 2 h followed by the 1st pass spinning,and finally quenching in ice water after holding for 1 h at 498°C followed by the 2nd pass spinning.ABAQUS finite element software is used to simulate the internal spinning process of the products formed under different forming parameters.The distribution laws of spinning force,the stress and strain under different forming processes were compared and analyzed.The mechanical properties and microstructure of the products are subsequently analyzed.The results show that the strain and the residual stress in the skin area of the formed products under two-pass spinning process more uniform,and the hardness and the mechanical performance are improved.The microstructure of the products formed with the 0.15 mm thickness reduction at the 2nd pass is excellent.And the second phase grain size distributed uniformly in the range of 36μm.Whereas,the second phase particles are broken seriously and the size distribution inhomogeneity is increased when the thickness reduction in the skin area is greater than 0.20 mm at the 2nd pass spinning process.展开更多
The Joule-Thomson effect is one of the important thermodynamic properties in the system relevant to gas switching reforming with carbon capture and storage(CCS). In this work, a set of apparatus was set up to determin...The Joule-Thomson effect is one of the important thermodynamic properties in the system relevant to gas switching reforming with carbon capture and storage(CCS). In this work, a set of apparatus was set up to determine the Joule-Thomson effect of binary mixtures(CO_(2)+ H_(2)). The accuracy of the apparatus was verified by comparing with the experimental data of carbon dioxide. The Joule-Thomson coefficients(μ_(JT)) for(CO_(2)+ H_(2)) binary mixtures with mole fractions of carbon dioxide(x_(CO_(2))= 0.1, 0.26, 0.5,0.86, 0.94) along six isotherms at various pressures were measured. Five equations of state EOSs(PR,SRK, PR, BWR and GERG-2008 equation) were used to calculate the μ_(JT)for both pure systems and binary systems, among which the GERG-2008 predicted best with a wide range of pressure and temperature.Moreover, the Joule-Thomson inversion curves(JTIC) were calculated with five equations of state. A comparison was made between experimental data and predicted data for the inversion curve of CO_(2). The investigated EOSs show a similar prediction of the low-temperature branch of the JTIC for both pure and binary systems, except for the BWRS equation of state. Among all the equations, SRK has the most similar result to GERG-2008 for predicting JTIC.展开更多
Conical cam mechanism has been widely used in modern machinery and equipment.However,the commonly used planar expansion methods for the design of spatial cam contour produce significant errors,because these methods in...Conical cam mechanism has been widely used in modern machinery and equipment.However,the commonly used planar expansion methods for the design of spatial cam contour produce significant errors,because these methods incorrectly use the distance from the axis of the follower to the main conical cam to replace the corresponding arc length on the conical cam.HSIEH,et al,used analytical methods to achieve higher accuracy,but these analytical methods have their own drawbacks since they are too complicated for practical use.Through the analysis of the errors created during the generation of conical cam contour using the existing expansion methods,this paper proposes to include diverge angle in the calculation of conical cam rotation angle in the equation of conical cam contour expansion.This correction eliminates the error generated by the commonly used methods.Based on the expression of the follower＇s 3D trajectory and the spatial geometry of conical cam,this paper has deduced the planar polar curve equation for determining polar coordinates for the curve of planar expansion outline.Furthermore,this paper provides an example of conical cam contour design based on sinusoidal acceleration variation.According to polar coordinates and the movement of curve equation function expression,this paper applies MATLAB software to solve coordinates for the cam expansion curve and uses AutoCAD software to generate conical cam expansion contour that meets the requirement of the law of motion.The proposed method provides a design process that is simple,intuitive and easy to master and implement.It also avoids the design error in the traditional methods for generating contour of conical cam with oscillating follower that requires high precision.展开更多
In CAGD, the Said-Ball representation for a polynomial curve has two advantagesover the B′ezier representation, since the degrees of Said-Ball basis are distributed in a step type.One advantage is that the recursive ...In CAGD, the Said-Ball representation for a polynomial curve has two advantagesover the B′ezier representation, since the degrees of Said-Ball basis are distributed in a step type.One advantage is that the recursive algorithm of Said-Ball curve for evaluating a polynomialcurve runs twice as fast as the de Casteljau algorithm of B′ezier curve. Another is that theoperations of degree elevation and reduction for a polynomial curve in Said-Ball form are simplerand faster than in B′ezier form. However, Said-Ball curve can not exactly represent conics whichare usually used in aircraft and machine element design. To further extend the utilizationof Said-Ball curve, this paper deduces the representation theory of rational cubic and quarticSaid-Ball conics, according to the necessary and su？cient conditions for conic representation inrational low degree B′ezier form and the transformation formula from Bernstein basis to Said-Ballbasis. The results include the judging method for whether a rational quartic Said-Ball curve is aconic section and design method for presenting a given conic section in rational quartic Said-Ballform. Many experimental curves are given for confirming that our approaches are correct ande？ective.展开更多
We construct two conical surfaces which take non-coplanar lines as generatrix and rational Bezier curve as ridge-line, and prove that the intersecting line of conical surface has similar properties to Bezier curve. Th...We construct two conical surfaces which take non-coplanar lines as generatrix and rational Bezier curve as ridge-line, and prove that the intersecting line of conical surface has similar properties to Bezier curve. Then, the smoothly blending of two cylinders whose axes are non-coplanar is realized by taking intersecting line of conical surface as axes.展开更多
文摘We introduce CURDIS,a template for algorithms to discretize arcs of regular curves by incrementally producing a list of support pixels covering the arc.In this template,algorithms proceed by finding the tangent quadrant at each point of the arc and determining which side the curve exits the pixel according to a tailored criterion.These two elements can be adapted for any type of curve,leading to algorithms dedicated to the shape of specific curves.While the calculation of the tangent quadrant for various curves,such as lines,conics,or cubics,is simple,it is more complex to analyze how pixels are traversed by the curve.In the case of conic arcs,we found a criterion for determining the pixel exit side.This leads us to present a new algorithm,called CURDIS-C,specific to the discretization of conics,for which we provide all the details.Surprisingly,the criterion for conics requires between one and three sign tests and four additions per pixel,making the algorithm efficient for resource-constrained systems and feasible for fixed-point or integer arithmetic implementations.Our algorithm also perfectly handles the pathological cases in which the conic intersects a pixel twice or changes quadrants multiple times within this pixel,achieving this generality at the cost of potentially computing up to two square roots per arc.We illustrate the use of CURDIS for the discretization of different curves,such as ellipses,hyperbolas,and parabolas,even when they degenerate into lines or corners.
基金Project supported by the National Natural Science Foundation of China (No. 50575205)the HiTech Research and Development Program (863) of China (No. 2006AA04Z233)and the Natural Science Foundation of Zhejiang Province (Nos. Y104243 and Y105686), China
文摘This paper focuses on the analysis of running conditions and machining processes of conical cam with oscillating follower. We point out the common errors existing in the design and machining of the widely used plane expansion method of conical cam trough-out line. We show that the motion can be divided into two parts, i.e. the oscillating motion of oscillating bar and the rotary motion of oscillating bar relative to the conical cam. By increasing the rotary motion of oscillating bar, the motion path of tapered roller on oscillating bar (i.e. contour surface of conical cam) can be expanded on the cylinder. Based on these analyses, we present a creative and effective designing and machining method for 3D curve expansion of conical cam with oscillating follower.
文摘The appriximation properties of generalized conic curves are studied in this paper. A generalized conic curve is defined as one of the following curves or their affine and translation e-quivalent curves:(i) conic curves i including parabolas, hyperbolas and ellipses;(ii) generalized monomial curves, including curves of the form x=yr,.r R.r=0,1, in the x-y Cartesian coordinate system;(iii) exponential spiral curves of the form p=Apolar coordinate system.This type of curves has many important properties such as convexity , approximation property, effective numerical computation property and the subdivision property etc. Applications of these curves in both interpolation and approximations using piecewise generalized conic segment are also developed. It is shown that these generalized conic splines are very similar to the cubic polynomial splines and the best error of approximation is or at least in general provided appropriate procedures are used. Finally some numerical examples of interpolation and approximations with generalized conic splines are given.
文摘In this paper,based on the mean value theorem of differential,a new method of generating conics such as circles and parabolas is given,and the related algorithm for generating conics is designed.
基金Project(51775479)supported by the National Natural Science Foundation of ChinaProject(E2017203046)supported by the Natural Science Foundation of Hebei Province,China
文摘A two-pass annealing/quenching internal spinning process with small-end rotations is proposed to form a curved generatrix conical thin-walled shell.That is,annealing at 360°C for 2 h followed by the 1st pass spinning,and finally quenching in ice water after holding for 1 h at 498°C followed by the 2nd pass spinning.ABAQUS finite element software is used to simulate the internal spinning process of the products formed under different forming parameters.The distribution laws of spinning force,the stress and strain under different forming processes were compared and analyzed.The mechanical properties and microstructure of the products are subsequently analyzed.The results show that the strain and the residual stress in the skin area of the formed products under two-pass spinning process more uniform,and the hardness and the mechanical performance are improved.The microstructure of the products formed with the 0.15 mm thickness reduction at the 2nd pass is excellent.And the second phase grain size distributed uniformly in the range of 36μm.Whereas,the second phase particles are broken seriously and the size distribution inhomogeneity is increased when the thickness reduction in the skin area is greater than 0.20 mm at the 2nd pass spinning process.
基金supported by the National Natural Science Foundation of China (21878056)Key Laboratory of Petrochemical Resource Processing and Process Intensification Technology (2019Z002)。
文摘The Joule-Thomson effect is one of the important thermodynamic properties in the system relevant to gas switching reforming with carbon capture and storage(CCS). In this work, a set of apparatus was set up to determine the Joule-Thomson effect of binary mixtures(CO_(2)+ H_(2)). The accuracy of the apparatus was verified by comparing with the experimental data of carbon dioxide. The Joule-Thomson coefficients(μ_(JT)) for(CO_(2)+ H_(2)) binary mixtures with mole fractions of carbon dioxide(x_(CO_(2))= 0.1, 0.26, 0.5,0.86, 0.94) along six isotherms at various pressures were measured. Five equations of state EOSs(PR,SRK, PR, BWR and GERG-2008 equation) were used to calculate the μ_(JT)for both pure systems and binary systems, among which the GERG-2008 predicted best with a wide range of pressure and temperature.Moreover, the Joule-Thomson inversion curves(JTIC) were calculated with five equations of state. A comparison was made between experimental data and predicted data for the inversion curve of CO_(2). The investigated EOSs show a similar prediction of the low-temperature branch of the JTIC for both pure and binary systems, except for the BWRS equation of state. Among all the equations, SRK has the most similar result to GERG-2008 for predicting JTIC.
基金supported by National Natural Science Foundation of China(Grant No.50645032)Zhejiang Provincial Natural Science Foundation of China(Grant No.Y105686)Ningbo Municipal Natural Science Foundation of China(Grant No.2008A610038)
文摘Conical cam mechanism has been widely used in modern machinery and equipment.However,the commonly used planar expansion methods for the design of spatial cam contour produce significant errors,because these methods incorrectly use the distance from the axis of the follower to the main conical cam to replace the corresponding arc length on the conical cam.HSIEH,et al,used analytical methods to achieve higher accuracy,but these analytical methods have their own drawbacks since they are too complicated for practical use.Through the analysis of the errors created during the generation of conical cam contour using the existing expansion methods,this paper proposes to include diverge angle in the calculation of conical cam rotation angle in the equation of conical cam contour expansion.This correction eliminates the error generated by the commonly used methods.Based on the expression of the follower＇s 3D trajectory and the spatial geometry of conical cam,this paper has deduced the planar polar curve equation for determining polar coordinates for the curve of planar expansion outline.Furthermore,this paper provides an example of conical cam contour design based on sinusoidal acceleration variation.According to polar coordinates and the movement of curve equation function expression,this paper applies MATLAB software to solve coordinates for the cam expansion curve and uses AutoCAD software to generate conical cam expansion contour that meets the requirement of the law of motion.The proposed method provides a design process that is simple,intuitive and easy to master and implement.It also avoids the design error in the traditional methods for generating contour of conical cam with oscillating follower that requires high precision.
基金Supported by the National Natural Science Foundations of China(61070065, 60933007)the Zhejiang Provincial Natural Science Foundation of China(Y6090211)
文摘In CAGD, the Said-Ball representation for a polynomial curve has two advantagesover the B′ezier representation, since the degrees of Said-Ball basis are distributed in a step type.One advantage is that the recursive algorithm of Said-Ball curve for evaluating a polynomialcurve runs twice as fast as the de Casteljau algorithm of B′ezier curve. Another is that theoperations of degree elevation and reduction for a polynomial curve in Said-Ball form are simplerand faster than in B′ezier form. However, Said-Ball curve can not exactly represent conics whichare usually used in aircraft and machine element design. To further extend the utilizationof Said-Ball curve, this paper deduces the representation theory of rational cubic and quarticSaid-Ball conics, according to the necessary and su？cient conditions for conic representation inrational low degree B′ezier form and the transformation formula from Bernstein basis to Said-Ballbasis. The results include the judging method for whether a rational quartic Said-Ball curve is aconic section and design method for presenting a given conic section in rational quartic Said-Ballform. Many experimental curves are given for confirming that our approaches are correct ande？ective.
文摘We construct two conical surfaces which take non-coplanar lines as generatrix and rational Bezier curve as ridge-line, and prove that the intersecting line of conical surface has similar properties to Bezier curve. Then, the smoothly blending of two cylinders whose axes are non-coplanar is realized by taking intersecting line of conical surface as axes.
