In order to increase the efficiency in the machining of the sculptured surfaces, the contact principle of differential geometry is applied to the 5-axis NC machining; The best contact condition between tool and the su...In order to increase the efficiency in the machining of the sculptured surfaces, the contact principle of differential geometry is applied to the 5-axis NC machining; The best contact condition between tool and the surfaces is researched. Through analysis the contact degree of the intersection line of the cutter and the surfaces is known. In comparison to previous studies, the theory is more restricted and accurate by going beyond the second-order parameters into the third-order, suiting both the primary surfaces of analytical geometry and the computer-generated surfaces of the computation geometry. It has definite procedure of calculation, and the equations are easy to solve. The thought process is very clear： First, suppose that there is a surface of third-order, the coefficients of which are arbitrary; Then find out the best posture of the circle in order that the circle and the surface will most closely contact with each other at the origin position; Finally, develop the surface into a third-order surface at every point of machining and employ the results mentioned above to find the best cutter posture at every point of machining. As a result, the equations are easy to solve, and the concept is clear.展开更多
Although most of the 5-axis NC milling machine tool producers declare that their machine poses the function of 5-axis simultaneous machining, and most of the commercialized CAD/CAM software was reported it can support...Although most of the 5-axis NC milling machine tool producers declare that their machine poses the function of 5-axis simultaneous machining, and most of the commercialized CAD/CAM software was reported it can support the 5-axis simultaneous machining, but there are very few analyses about their machining efficiency. I hope that the reader would be interested to know how the new method is?highly effective. The paper did a good job in motivating the problem mentioned here. The model of this paper is extremely efficient ant. This is a highly effective way of surface machining. There are also some areas that need improving. The mathematic presentation is not clear, but much more pages are needed, if the authors like to make it clearer. In the resent paper “The Extreme Efficiency of the New Model in Milling of Complicated Surfaces” we discussed the extreme efficiency of the new model in milling of complicated surfaces in 5-axis machining for 2-dimensional contact. While this time let’s discuss the same problem but much complicated one, 5-axis machining for 3-dimensional contact. As the research activities conducted by Dr. Liu Huran opened a new field and wide horizons in 5-axis machining of sculptured complicated surfaces using mathematical theories, and according to the interesting results presented in paper, Dr. Liu Huran is strongly encouraged if he can submit a similar work but this time with a new title that corresponds to the purpose [1].展开更多
In this paper, the geometric properties of a pair of line contact surfaces are investigated. Then, based on the observation that the cutter envelope surface contacts with the cutter surface and design surface along th...In this paper, the geometric properties of a pair of line contact surfaces are investigated. Then, based on the observation that the cutter envelope surface contacts with the cutter surface and design surface along the characteristic curve and cutter contact (CC) path, respectively, a mathematical model describing the third-order approximation of the cutter envelope surface according to just one given cutter location (CL) is developed. It is shown that at the CC point both the normal curvature of the normal section of the cutter envelope surface and its derivative with respect to the arc length of the normal section can be determined by those of the cutter surface and design surface. This model characterizes the intrinsic relationship among the cutter surface, cutter envelope surface and design surface in the neighborhood of the CC point, and yields the mathematical foundation for optimally approximating the cutter envelope surface to the design surface by adjusting the cutter location.展开更多
基金This project is supported by Provincial Basic Science Research Foundation of Hunan, China(No.02-jxz3011)Research Foundation of Railway Department, China(No.J98Z102).
文摘In order to increase the efficiency in the machining of the sculptured surfaces, the contact principle of differential geometry is applied to the 5-axis NC machining; The best contact condition between tool and the surfaces is researched. Through analysis the contact degree of the intersection line of the cutter and the surfaces is known. In comparison to previous studies, the theory is more restricted and accurate by going beyond the second-order parameters into the third-order, suiting both the primary surfaces of analytical geometry and the computer-generated surfaces of the computation geometry. It has definite procedure of calculation, and the equations are easy to solve. The thought process is very clear： First, suppose that there is a surface of third-order, the coefficients of which are arbitrary; Then find out the best posture of the circle in order that the circle and the surface will most closely contact with each other at the origin position; Finally, develop the surface into a third-order surface at every point of machining and employ the results mentioned above to find the best cutter posture at every point of machining. As a result, the equations are easy to solve, and the concept is clear.
文摘Although most of the 5-axis NC milling machine tool producers declare that their machine poses the function of 5-axis simultaneous machining, and most of the commercialized CAD/CAM software was reported it can support the 5-axis simultaneous machining, but there are very few analyses about their machining efficiency. I hope that the reader would be interested to know how the new method is?highly effective. The paper did a good job in motivating the problem mentioned here. The model of this paper is extremely efficient ant. This is a highly effective way of surface machining. There are also some areas that need improving. The mathematic presentation is not clear, but much more pages are needed, if the authors like to make it clearer. In the resent paper “The Extreme Efficiency of the New Model in Milling of Complicated Surfaces” we discussed the extreme efficiency of the new model in milling of complicated surfaces in 5-axis machining for 2-dimensional contact. While this time let’s discuss the same problem but much complicated one, 5-axis machining for 3-dimensional contact. As the research activities conducted by Dr. Liu Huran opened a new field and wide horizons in 5-axis machining of sculptured complicated surfaces using mathematical theories, and according to the interesting results presented in paper, Dr. Liu Huran is strongly encouraged if he can submit a similar work but this time with a new title that corresponds to the purpose [1].
基金supported by the National Natural Science Foundation of China (Grant Nos. 50835004, 50775147)the National Basic Research Program of China ("973" Program) (Grant No. 2005CB724103)the Science & Technology Commission of Shanghai Municipality (Grant No. 07JC14028)
文摘In this paper, the geometric properties of a pair of line contact surfaces are investigated. Then, based on the observation that the cutter envelope surface contacts with the cutter surface and design surface along the characteristic curve and cutter contact (CC) path, respectively, a mathematical model describing the third-order approximation of the cutter envelope surface according to just one given cutter location (CL) is developed. It is shown that at the CC point both the normal curvature of the normal section of the cutter envelope surface and its derivative with respect to the arc length of the normal section can be determined by those of the cutter surface and design surface. This model characterizes the intrinsic relationship among the cutter surface, cutter envelope surface and design surface in the neighborhood of the CC point, and yields the mathematical foundation for optimally approximating the cutter envelope surface to the design surface by adjusting the cutter location.
