In this paper,we apply function parameters,introduced by Persson,to real interpolation of Lorentz martingale spaces.Some new interpolation theorems concerning Lorentz martingale spaces are formulated.The results that ...In this paper,we apply function parameters,introduced by Persson,to real interpolation of Lorentz martingale spaces.Some new interpolation theorems concerning Lorentz martingale spaces are formulated.The results that we obtain generalize some fundamental interpolation theorems in classical martingale Hp theory.展开更多
G01 code generated by a computer-aided manufacture （CAM） system is the most common form of tool trajeclory in computer numerical control （CNC） machining. A tool path composed of short line segments has discontinuo...G01 code generated by a computer-aided manufacture （CAM） system is the most common form of tool trajeclory in computer numerical control （CNC） machining. A tool path composed of short line segments has discontinuous tangenc t and curvature, generating large fluctuations of feedrate and acceleration, which in turn produces vibration in a machine tool. To obtain a smooth tool path, many methods on tool-path smoothing have been developed. However, the shortcomings i：1 these methods exist when they are employed in a CNC system. It is difficult to simultaneously to guarantee the following requirements of CNC machining： （1） chord error should be rigidly constrained; （2） G01 points should be interpolated; （3） cur,,ature should be continuous （G2）; （4） machining should be applicable to spatial cases; （5） real-time performance of computaEion is required.Based on these various requirements, this study proposes an interpolation scheme using CUDlC t^ezler curves anu mciuucb illl adjustment strategy to eliminate deficiencies in the tool path. The tool path generated is G2, chord-elror-constrained, G01-point-interpolated, loop-free, and optimized for both stretch and jerk energy. The method is applicable ：o 3D cases and involves only simple algebraic computations. Thus, the algorithm can be applied to real-time CNC machining. A simulation is conducted to validate the efficiency of the algorithm. In addition, an experiment reveals its advantage over Hermite interpola- tion in surface quality and machining efficiency.展开更多
基金supported by National Natural Science Foundation of China(Grant No. 11171015)
文摘In this paper,we apply function parameters,introduced by Persson,to real interpolation of Lorentz martingale spaces.Some new interpolation theorems concerning Lorentz martingale spaces are formulated.The results that we obtain generalize some fundamental interpolation theorems in classical martingale Hp theory.
基金supported by the National Science and Technology Major Projects(Grant Nos.2013ZX04007041 and 2012ZX04001012)General Financial Grant from the China Postdoctoral Science Foundation(Grant No.2014M552032)
文摘G01 code generated by a computer-aided manufacture （CAM） system is the most common form of tool trajeclory in computer numerical control （CNC） machining. A tool path composed of short line segments has discontinuous tangenc t and curvature, generating large fluctuations of feedrate and acceleration, which in turn produces vibration in a machine tool. To obtain a smooth tool path, many methods on tool-path smoothing have been developed. However, the shortcomings i：1 these methods exist when they are employed in a CNC system. It is difficult to simultaneously to guarantee the following requirements of CNC machining： （1） chord error should be rigidly constrained; （2） G01 points should be interpolated; （3） cur,,ature should be continuous （G2）; （4） machining should be applicable to spatial cases; （5） real-time performance of computaEion is required.Based on these various requirements, this study proposes an interpolation scheme using CUDlC t^ezler curves anu mciuucb illl adjustment strategy to eliminate deficiencies in the tool path. The tool path generated is G2, chord-elror-constrained, G01-point-interpolated, loop-free, and optimized for both stretch and jerk energy. The method is applicable ：o 3D cases and involves only simple algebraic computations. Thus, the algorithm can be applied to real-time CNC machining. A simulation is conducted to validate the efficiency of the algorithm. In addition, an experiment reveals its advantage over Hermite interpola- tion in surface quality and machining efficiency.
