An improved feedrate scheduling method for NURBS interpolation in five-axis machining

Five-axis machining plays an important role in manufacturing by dint of its high efficiency and accuracy. While two rotation axes benefit the flexibility of machining, it also brings limitations and challenges. In order to further balance machining precision and efficiency, an improved feedrate scheduling method is presented considering geometric error and kinematic constraints for the Non Uniform Rational B-Spline (NURBS) interpolation in five-axis machining. A simplification method is proposed to calculate the geometric error which describes the deviation between the ideal tool path and the real tool path induced by the non-linear movement. A linear relation between geometric error and feedrate is built to limit the feedrate. The constraints determined by single axis kinematic performance and tangential kinematic performance are also considered. Under these constraints, a constrained feedrate profile is determined. Aiming to get more constant feedrate in the difficult-to-machine areas, this work proposes a scheduling method which combines morphological filtering and S-shape acceleration/deceleration (acc/dec) mode. Simulations and experiments are performed to compare the proposed feedrate scheduling method with two previous feedrate scheduling method and the results prove that the proposed feedrate scheduling method is reliable and effective.     

A robust method for axis identification

The present paper proposes a new method for axis identification in discrete axially symmetrical geometric models. This method is based on-a-never-used-before property of the axially symmetrical surfaces for which the symmetry line of any section curve of the surface (or of a portion of it in the case of an incomplete axially symmetrical surface) always intersects the axis of symmetry of the surface. Thus the working principle of the method makes it very robust to local defectiveness, measurement noise and outliers.In order to compare it with the most cited methods presented in literature, several types of tests have been designed and performed. The robustness of those methods, on the one hand, has been evaluated by defining the Statistical Confidence Boundary at 1σ confidence level. The trueness of the method, on the other hand, has been evaluated on geometric models obtained by measuring real objects. The high robustness, which characterizes the proposed method, makes it particularly suitable for product geometric inspection where high accuracy is required.     

磁浸没透镜的宽束曲轴像差分析的微分代数方法研究

微分代数是计算机数值分析领域中的一个非常有效的方法,可以实现任意高阶微分的准确计算.本文根据微分代数方法的基本原理,将其引入到磁浸没透镜的宽束曲轴像差的分析计算中,得到了任意阶曲轴像差的微分代数表达式.文中针对轴上磁场具有某种解析表达式的一个实际的磁浸没透镜系统,利用微分代数的曲轴像差分析方法,计算了它的曲轴像差,并给出了全部二阶和三阶几何像差的分布图形.     

The influence of the fabrication process on the buckling of thin-walled steel box sections

Steel box sections are usually fabricated from flat plates which are welded at the corners. The welding process can introduce residual stresses and geometric imperfections into the sections which can influence their strength. For some thin-walled sections, large periodic geometric imperfections have been observed in manufactured sections. Subsequent investigations have indicated that the imperfections are in fact buckling deformations i.e. the box section has buckled due to welding residual stresses prior to any application of external load. The welding procedure and the behaviour of the box sections under load has been modelled using a finite element analysis that accounts for both geometric and material non-linearities. Tests have been carried out on box sections with a range of width to thickness ratios for the plate elements. Modelling has been shown to give good correlation with the test results. The conditions for buckling to take place as a result of the welding process have been established. A design method has been proposed.     

二维谐振子与二维氢原子的能量及波函数

借助于ＳＵ(１,１)代数,找出了二维谐振子与二维氢原子的能量及波函数间的关系．     

Cryptosporidium Log-inactivation with Ozone Using Effluent CT10, Geometric Mean CT10, Extended Integrated CT10 and Extended CSTR Calculations

The draft Long-Term 2 Enhanced Surface Water Treatment Rule (LT2ESWTR) contains Cryptosporidium log-inactivation CT tables (ozone-in-water concentration [residual], “C” times contact time, T). Depending on water temperature, Cryptosporidium CT values that are listed are 15 to 25 times greater than CT values for equivalent Giardia log-inactivation credit. The elevated operating dose required for Cryptosporidium log-inactivation credit has the potential to increase disinfection by-product (DBP) formation (e.g., bromate). Calculating CT value accurately will minimize ozone dose, which will decrease operating cost and lower DBP formation, and at the same time maintain disinfection protection through implementation of scientifically based safety factors. Various methods are available for calculating CT value. The method chosen depends largely on the available information concerning ozone residual characteristics and hydrodynamic features of the ozone contactor, plus local regulatory requirements. Four methods are discussed in this paper. Each method can be used to calculate Giardia, virus, and Cryptosporidium log-inactivation credit.     

Controllability of One Spin and Two Interacting Spins

Mathematics of Control, Signals, and Systems - ?We consider the problem of steering control for the systems of one spin ½ particle and two interacting spin ½ particles in an...