Convergence in Norm of Projection Regularized Krasnoselski-Mann Iterations for Fixed Points of Cutters

In this article, we introduce a projection regularized Krasnoselski-Mann iteration for cutters. The proposed algorithm ensures the strong convergence of the generated sequence toward the least norm element of the set of fixed points of the cutter. It is verified that the projection regularized Krasnoselski-Mann iteration converges locally faster than the regularized Krasnoselski-Mann iteration introduced by Maingé and Maruster [11 P. E. Maingé and S. Maruster ( 2011 ). Convergence in norm of modified Krasnoselski-Mann iterations for fixed points of demicontractive mappings . Appl. Math. Comput. 217 : 9864 – 9874 .[Crossref], [Web of Science ®] , [Google Scholar]]. Furthermore, we present projection regularized Krasnoselski-Mann iterations for quasi-nonexpansive and nonexpansive mappings in Hilbert spaces.     

Cookie-Cuter集的多重Fractal分解的Packing维数

直线上的Ｃｏｏｋｉｅ－Ｃｕｔｔｅｒ集是一个扩张动力系统的不变集，并且是一个Ｆｒａｃｔａｌ集合．本文得到Ｃｏｏｋｉｅ－Ｃｕｔｔｅｒ集的多重Ｆｒａｃｔａｌ分解的Ｐａｃｋｉｎｇ维数，从而证明其是Ｔａｙｌｏｒ意义下的Ｆｒａｃｔａｌ集合     

基于FPGA的实时Pythagorean Hodograph曲线运动控制器的设计

提出了一种采用SOPC技术在单个FPGA芯片上构建的新型实时PH曲线运动控制器的架构;该运动控制器在QuartusⅡ9.0中设计,由一个NiosⅡ软核处理器和多个功能模块构成;它通过采用二次插补方式以减少PH曲线插补的计算量;NiosⅡ处理器执行主控程序和PH曲线粗插补算法,FPGA硬件逻辑执行精插补算法并输出两组用于控制执行机构(XY工作台)的控制脉冲;实验数据表明,该运动控制器完成恒进给速度的单次PH曲线插补的平均耗时均小于2ms,终点坐标的定位误差均低于0.0079mm。     

A novel cutting force modelling method for cylindrical end mill

This paper proposes a new and simplified method for the calibration of cutting force coefficients and cutter runout parameters for cylindrical end milling using the instantaneous cutting forces measured instead of average ones. The calibration procedure is derived for a mechanistic cutting force model in which the cutting force coefficients are expressed as the power functions of instantaneous uncut chip thickness (IUCT). The derivations are firstly performed by establishing mathematical relationships between instantaneous cutting forces and IUCT. Then, nonlinear algorithms are proposed to solve the established nonlinear contradiction equations. The typical features of this new calibration method lie in twofold. On the one hand, all derivations are directly based on the tangential, radial and axial cutting force components transformed from the forces which are measured in the workpiece Cartesian coordinate system. This transformation makes the calibration procedure very simple and efficient. On the other hand, only a single cutting test is needed to be performed for calibrating the cutting force coefficients that are valid over a wide range of cutting conditions. The effectiveness of the proposed method in developing cutting force model is demonstrated experimentally with a series of verification cutting tests.     

Effect of cutter geometric configuration on aerodynamic noise generation in face milling cutters

Aerodynamic noise spectrum of rotary face milling cutters consists of a broad range of high frequencies and discrete tones. This paper aims to develop a method to calculate the aerodynamic noise generation and propagation by rotary face milling cutters. The effects of milling cutter geometry on the generation of aerodynamic noise are analyzed. Based on the computational fluid dynamics (CFD) method, the Ffowcs Williams–Hawkings (FW–H) equation is used to predict the sound pressure level (SPL) of aerodynamic noise in face milling cutters. The accurate calculation of time-varying flow variables along with the rotation of cutter is very important for the prediction of aerodynamic noise. In this case, the Navier–Stokes (N–S) equation is employed to evaluate the pressure and velocity fields around the milling cutters, first in a steady mode with the Multiple Reference Frames (MRF) model, and then in an unsteady mode with sliding mesh technique (SMT) by introducing the steady flow variables as its initial fields. It is found that both the overall aerodynamic noise due to the entire cutter and the aerodynamic noise only due to the cutter gullet regions are significantly affected by the number of cutter teeth/gullet regions. Moreover, six representative milling cutters with different tooth numbers and geometries of gullet regions are chosen to study the effects of gullet configuration on aerodynamic noise generation, and the characteristics of noise spectra generated by the cutters are analyzed. The aerodynamic noise generated only by the cutter gullet regions is found to be strongly dependent on the gullet design-volume and shape. The results also reveal that the gullet design advantage of Cutter C in reducing noise generation among the eight-tooth designs, and the gullet design advantage of Cutter A in reducing noise generation among the five and seven-tooth designs in this investigation.