In this paper, two new interpolation algorithms lot CNC machining along curve^l tom pathes are proposed： a time-optimal interpolation algorithm under chord error, feedrate, and tangential acceleration bounds, and a g...In this paper, two new interpolation algorithms lot CNC machining along curve^l tom pathes are proposed： a time-optimal interpolation algorithm under chord error, feedrate, and tangential acceleration bounds, and a greedy interpolation algorithm under the chord error and tangential jerk bounds. The key idea is to reduce the chord error bound to a centripetal acceleration bound which leads to a velocity limit curve, called the chord error velocity limit curve. Then, the velocity planning is to find the proper velocity curve governed by the acceleration or jerk bounds ＇~under＂ the chord error velocity limit curve. For two types of simple tool pathes, explicit formulas for the velocity curve are given and the methods are implemented in commercial CNC controllers.展开更多
Abstract. In this paper, we discuss the limit behaviour of solutious to equivalued surfaceboundary value problem for parabolic equations when the equivalued surface boundaryshrinks to a point and the space dimension o...Abstract. In this paper, we discuss the limit behaviour of solutious to equivalued surfaceboundary value problem for parabolic equations when the equivalued surface boundaryshrinks to a point and the space dimension of the domain is two or more.展开更多
基金supported by a National Key Basic Research Project of China under Grant No.2011CB302400the National Natural Science Foundation of China under Grant No.60821002
文摘In this paper, two new interpolation algorithms lot CNC machining along curve^l tom pathes are proposed： a time-optimal interpolation algorithm under chord error, feedrate, and tangential acceleration bounds, and a greedy interpolation algorithm under the chord error and tangential jerk bounds. The key idea is to reduce the chord error bound to a centripetal acceleration bound which leads to a velocity limit curve, called the chord error velocity limit curve. Then, the velocity planning is to find the proper velocity curve governed by the acceleration or jerk bounds ＇~under＂ the chord error velocity limit curve. For two types of simple tool pathes, explicit formulas for the velocity curve are given and the methods are implemented in commercial CNC controllers.
基金NSF of Shandong Province (No.Y98A09012, No. Q99A05.)
文摘Abstract. In this paper, we discuss the limit behaviour of solutious to equivalued surfaceboundary value problem for parabolic equations when the equivalued surface boundaryshrinks to a point and the space dimension of the domain is two or more.
