Tolerance is essential for integration of CAD and CAM. Unfortunately, the meaning of tolerances in the national standard is expressed in graphical and language forms and is not adaptable for expression, processing and...Tolerance is essential for integration of CAD and CAM. Unfortunately, the meaning of tolerances in the national standard is expressed in graphical and language forms and is not adaptable for expression, processing and data transferring with computers. How to interpret its semantics is becoming a focus of relevant studies. This work based on the mathematical definition of form tolerance in ANSI Y 14.5.1 M-1994, established the mathematical model of form tolerance for cylindrical feature. First, each tolerance in the national standard was established by vector equation. Then on the foundation of toler-ance's mathematical definition theory, each tolerance zone's mathematical model was established by inequality based on degrees of feature. At last the variance area of each tolerance zone is derived. This model can interpret the semantics of form tolerance exactly and completely.展开更多
An integrated approach for modeling the entire spray forming process is presented in this paper, and the program for the simulation is developed. The whole spray forming process can be divided into four calculation pr...An integrated approach for modeling the entire spray forming process is presented in this paper, and the program for the simulation is developed. The whole spray forming process can be divided into four calculation processes and the basis for the analysis is the classical k -ε turbulence model which was used to simulate the flow field of gas formed in the chamber. In the atomization model the flow field of gas is coupled with formation, velocity and location of droplet. By means of the above mathematical model, the process of spray forming was simulated.展开更多
With the help of skew-symmetric differential forms the hidden properties of the mathematical physics equations are revealed. It is shown that the equations of mathematical physics can describe the emergence of various...With the help of skew-symmetric differential forms the hidden properties of the mathematical physics equations are revealed. It is shown that the equations of mathematical physics can describe the emergence of various structures and formations such as waves, vortices, turbulent pulsations and others. Such properties of the mathematical physics equations, which are hidden (they appear only in the process of solving these equations), depend on the consistency of derivatives in partial differential equations and on the consistency of equations, if the equations of mathematical physics are a set of equations. This is due to the integrability of mathematical physics equations. It is shown that the equations of mathematical physics can have double solutions, namely, the solutions on the original coordinate space and the solutions on integrable structures that are realized discretely (due to any degrees of freedom). The transition from the solutions of the first type to one of the second type describes discrete transitions and the processes of origin of various structures and observable formations. Only mathematical physics equations, on what no additional conditions such as the integrability conditions are imposed, can possess such properties. The results of the present paper were obtained with the help of skew-symmetric differential forms.展开更多
Based on the Newtonian heat transfer formulation and classical heterogeneous nucleation theory, a mathematical model has been established to predict the profile of flight velocity, heat transfer coefficient, temperat...Based on the Newtonian heat transfer formulation and classical heterogeneous nucleation theory, a mathematical model has been established to predict the profile of flight velocity, heat transfer coefficient, temperature, solid fraction and cooling rate of atomizing droplets for a superalloy. The results indicated that above parameters change with different droplet size and flight distance. The changing trend as well as the mechanism for the change are described and discussed.展开更多
The simplest normal form of resonant double Hopf bifurcation was studied based on Lie operator. The coefficients of the simplest normal forms of resonant double Hopf bifurcation and the nonlinear transformations in te...The simplest normal form of resonant double Hopf bifurcation was studied based on Lie operator. The coefficients of the simplest normal forms of resonant double Hopf bifurcation and the nonlinear transformations in terms of the original system coefficients were given explicitly. The nonlinear transformations were used for reducing the lower- and higher-order normal forms, and the rank of system matrix was used to determine the coefficient of normal form which could be reduced. These make the gained normal form simpler than the traditional one. A general program was compiled with Mathematica. This program can compute the simplest normal form of resonant double Hopf bifurcation and the non-resonant form up to the 7th order.展开更多
The high-frequency components in the traditional multi-scale transform method are approximately sparse, which can represent different information of the details. But in the low-frequency component, the coefficients ar...The high-frequency components in the traditional multi-scale transform method are approximately sparse, which can represent different information of the details. But in the low-frequency component, the coefficients around the zero value are very few, so we cannot sparsely represent low-frequency image information. The low-frequency component contains the main energy of the image and depicts the profile of the image. Direct fusion of the low-frequency component will not be conducive to obtain highly accurate fusion result. Therefore, this paper presents an infrared and visible image fusion method combining the multi-scale and top-hat transforms. On one hand, the new top-hat-transform can effectively extract the salient features of the low-frequency component. On the other hand, the multi-scale transform can extract highfrequency detailed information in multiple scales and from diverse directions. The combination of the two methods is conducive to the acquisition of more characteristics and more accurate fusion results. Among them, for the low-frequency component, a new type of top-hat transform is used to extract low-frequency features, and then different fusion rules are applied to fuse the low-frequency features and low-frequency background; for high-frequency components, the product of characteristics method is used to integrate the detailed information in high-frequency. Experimental results show that the proposed algorithm can obtain more detailed information and clearer infrared target fusion results than the traditional multiscale transform methods. Compared with the state-of-the-art fusion methods based on sparse representation, the proposed algorithm is simple and efficacious, and the time consumption is significantly reduced.展开更多
Cold roll forming is a complicated metal processing, and its is very difficult to simulate the forming process. Based on the Updated-Lagrange method in the deformation mechanics, an elastic-plastic large deformation s...Cold roll forming is a complicated metal processing, and its is very difficult to simulate the forming process. Based on the Updated-Lagrange method in the deformation mechanics, an elastic-plastic large deformation spline finite strip method is developed to analyze cold roll forming of a thin channel section. The longitudinal membrane strain values on the edge of the deformed strip for four one-pass sequences in different fold angles are got. Simulated results are compared with the results from previously conducted experiments. The deviation of the simulated peak strain values is within 30% compared with the experimental results.展开更多
Orthogonal turn-milling is a high-efficiency and precision machining method.Its cutting layer directly affects chip formation,cutting forces,and chatter,and further affects tool life,machining quality,etc.We studied T...Orthogonal turn-milling is a high-efficiency and precision machining method.Its cutting layer directly affects chip formation,cutting forces,and chatter,and further affects tool life,machining quality,etc.We studied The cutting layer geometry(CLG)in orthogonal turn-milling with zero eccentricity(OTMZE)is studied to explore orthogonal turn-milling cutting layer formation process.OTMZE principles of motion and formation processes are analyzed statically without considering kinetic influences.Mathematical models of the entrance and exit angles,cutting thickness,and cutting depth are established.In addition,these models are validated experimentally and some influences of cutting parameters on the tool cutting layer are analyzed.The results show that OTMZE cutting layer formation can be divided into two stages,chip shapes are nearly consistent with the simulated CLGs,and the most influencial parameter in affecting the cutting layer is found to be the tool feed per revolation of workpiece fa,followed by the ratio of the tool and workpiece speedsλand the cutting depth ap.These models and results can provide theoretical guidance to clarify formation processes and quantitatively analyze changes in cutting layer geometry during OTMZE.In addition,they offer theoretical guidelines for cutting forces and chatter.展开更多
The metal goes into the plastic deformation after the application of external load. Most of the metal forming industries work on this principle of plastic deformation. Thus the understanding of plastic deformation in ...The metal goes into the plastic deformation after the application of external load. Most of the metal forming industries work on this principle of plastic deformation. Thus the understanding of plastic deformation in the metal forming industry is important. The research on the single material plastic deformation has been carried out from many centuries before the era of Tresca. In this study the two metals 0.05% C steel annealed (soft metal) and 0.6% C steel quenched and tempered (hard metal) were deformed plastically in the parallel combination in the composite form. This study has been carried out with simple mathematical theory and simulated numerical model. The comparison shows the exact match between the mathematical and numerical results. It is also observed that the individual metal thickness affects the deformation flow curve.展开更多
文摘Tolerance is essential for integration of CAD and CAM. Unfortunately, the meaning of tolerances in the national standard is expressed in graphical and language forms and is not adaptable for expression, processing and data transferring with computers. How to interpret its semantics is becoming a focus of relevant studies. This work based on the mathematical definition of form tolerance in ANSI Y 14.5.1 M-1994, established the mathematical model of form tolerance for cylindrical feature. First, each tolerance in the national standard was established by vector equation. Then on the foundation of toler-ance's mathematical definition theory, each tolerance zone's mathematical model was established by inequality based on degrees of feature. At last the variance area of each tolerance zone is derived. This model can interpret the semantics of form tolerance exactly and completely.
文摘An integrated approach for modeling the entire spray forming process is presented in this paper, and the program for the simulation is developed. The whole spray forming process can be divided into four calculation processes and the basis for the analysis is the classical k -ε turbulence model which was used to simulate the flow field of gas formed in the chamber. In the atomization model the flow field of gas is coupled with formation, velocity and location of droplet. By means of the above mathematical model, the process of spray forming was simulated.
文摘With the help of skew-symmetric differential forms the hidden properties of the mathematical physics equations are revealed. It is shown that the equations of mathematical physics can describe the emergence of various structures and formations such as waves, vortices, turbulent pulsations and others. Such properties of the mathematical physics equations, which are hidden (they appear only in the process of solving these equations), depend on the consistency of derivatives in partial differential equations and on the consistency of equations, if the equations of mathematical physics are a set of equations. This is due to the integrability of mathematical physics equations. It is shown that the equations of mathematical physics can have double solutions, namely, the solutions on the original coordinate space and the solutions on integrable structures that are realized discretely (due to any degrees of freedom). The transition from the solutions of the first type to one of the second type describes discrete transitions and the processes of origin of various structures and observable formations. Only mathematical physics equations, on what no additional conditions such as the integrability conditions are imposed, can possess such properties. The results of the present paper were obtained with the help of skew-symmetric differential forms.
文摘Based on the Newtonian heat transfer formulation and classical heterogeneous nucleation theory, a mathematical model has been established to predict the profile of flight velocity, heat transfer coefficient, temperature, solid fraction and cooling rate of atomizing droplets for a superalloy. The results indicated that above parameters change with different droplet size and flight distance. The changing trend as well as the mechanism for the change are described and discussed.
基金Supported by National Natural Science Foundation of China(No. 10372068).
文摘The simplest normal form of resonant double Hopf bifurcation was studied based on Lie operator. The coefficients of the simplest normal forms of resonant double Hopf bifurcation and the nonlinear transformations in terms of the original system coefficients were given explicitly. The nonlinear transformations were used for reducing the lower- and higher-order normal forms, and the rank of system matrix was used to determine the coefficient of normal form which could be reduced. These make the gained normal form simpler than the traditional one. A general program was compiled with Mathematica. This program can compute the simplest normal form of resonant double Hopf bifurcation and the non-resonant form up to the 7th order.
基金Project supported by the National Natural Science Foundation of China(Grant No.61402368)Aerospace Support Fund,China(Grant No.2017-HT-XGD)Aerospace Science and Technology Innovation Foundation,China(Grant No.2017 ZD 53047)
文摘The high-frequency components in the traditional multi-scale transform method are approximately sparse, which can represent different information of the details. But in the low-frequency component, the coefficients around the zero value are very few, so we cannot sparsely represent low-frequency image information. The low-frequency component contains the main energy of the image and depicts the profile of the image. Direct fusion of the low-frequency component will not be conducive to obtain highly accurate fusion result. Therefore, this paper presents an infrared and visible image fusion method combining the multi-scale and top-hat transforms. On one hand, the new top-hat-transform can effectively extract the salient features of the low-frequency component. On the other hand, the multi-scale transform can extract highfrequency detailed information in multiple scales and from diverse directions. The combination of the two methods is conducive to the acquisition of more characteristics and more accurate fusion results. Among them, for the low-frequency component, a new type of top-hat transform is used to extract low-frequency features, and then different fusion rules are applied to fuse the low-frequency features and low-frequency background; for high-frequency components, the product of characteristics method is used to integrate the detailed information in high-frequency. Experimental results show that the proposed algorithm can obtain more detailed information and clearer infrared target fusion results than the traditional multiscale transform methods. Compared with the state-of-the-art fusion methods based on sparse representation, the proposed algorithm is simple and efficacious, and the time consumption is significantly reduced.
基金Acknowledgements - This work was supported by the National Natural Science Foundation of Chin a (Grant No.59875075) and the Univ
文摘Cold roll forming is a complicated metal processing, and its is very difficult to simulate the forming process. Based on the Updated-Lagrange method in the deformation mechanics, an elastic-plastic large deformation spline finite strip method is developed to analyze cold roll forming of a thin channel section. The longitudinal membrane strain values on the edge of the deformed strip for four one-pass sequences in different fold angles are got. Simulated results are compared with the results from previously conducted experiments. The deviation of the simulated peak strain values is within 30% compared with the experimental results.
基金supported by the National Natural Science Foundation of China (No. 51475233)the Natural Science Foundation of Jiangsu Province(No. BK20171170)+2 种基金the Six Talent Peaks Project of Jiangsu Province(No. JXQC-049)the Major Program of the Natural Science Foundation for Colleges and Universities of Jiangsu Province(No. 19KJA560007)the Project of Jiangsu Key Laboratory of Large Engineering Equipment Detection and Control(No. JSKLEDC201512)
文摘Orthogonal turn-milling is a high-efficiency and precision machining method.Its cutting layer directly affects chip formation,cutting forces,and chatter,and further affects tool life,machining quality,etc.We studied The cutting layer geometry(CLG)in orthogonal turn-milling with zero eccentricity(OTMZE)is studied to explore orthogonal turn-milling cutting layer formation process.OTMZE principles of motion and formation processes are analyzed statically without considering kinetic influences.Mathematical models of the entrance and exit angles,cutting thickness,and cutting depth are established.In addition,these models are validated experimentally and some influences of cutting parameters on the tool cutting layer are analyzed.The results show that OTMZE cutting layer formation can be divided into two stages,chip shapes are nearly consistent with the simulated CLGs,and the most influencial parameter in affecting the cutting layer is found to be the tool feed per revolation of workpiece fa,followed by the ratio of the tool and workpiece speedsλand the cutting depth ap.These models and results can provide theoretical guidance to clarify formation processes and quantitatively analyze changes in cutting layer geometry during OTMZE.In addition,they offer theoretical guidelines for cutting forces and chatter.
文摘The metal goes into the plastic deformation after the application of external load. Most of the metal forming industries work on this principle of plastic deformation. Thus the understanding of plastic deformation in the metal forming industry is important. The research on the single material plastic deformation has been carried out from many centuries before the era of Tresca. In this study the two metals 0.05% C steel annealed (soft metal) and 0.6% C steel quenched and tempered (hard metal) were deformed plastically in the parallel combination in the composite form. This study has been carried out with simple mathematical theory and simulated numerical model. The comparison shows the exact match between the mathematical and numerical results. It is also observed that the individual metal thickness affects the deformation flow curve.
