在数控编程中应用的一种简单的三次样条拟合

本文提出了一种简单的三次样条拟合方式，其特点是方法简单，程序通用，对大小挠度的处理采用同一程序，解决了三次样条应用于数控编程中的数学问题，为数控编程中非圆曲线的拟合提供了一种新的拟合方式。文中作了实例计算，并在数控铣床上加工零件，验证了其方法的正确性。     

复杂曲面高效加工的环切刀具路径生成方法

提出一种适用于复杂曲面高效加工的环切刀具路径生成方法,该方法以平面封闭三次B样条曲线族作为导引线,运用复杂曲面笔式加工插补算法实现曲面局部区域的加工.导引曲线由封闭控制多边形顶点,通过逐层内等距,得到内偏置控制多边形的顶点,进而生成B样条导引曲线环.该方法提高了复杂曲面局部加工的效率,而且用B样条曲线描述刀具路径,为实现复杂曲面高效、高精度加工奠定了理论基础,并通过实例验证了算法的有效性.     

对等间距法逼近三次样条曲线的再研究

数控加工列表曲线时,通常先求出列表曲线样本点的三次样条插值方程,然后再利用直线或圆弧进行逼近。针对传统的三次样条曲线的直线逼近方法进行了再研究,提出了一种改进的等间距法,实现了三次样条曲线的直线逼近。该方法具有计算简捷,产生的数控代码较少,逼近误差可控等优点。在VC++环境下开发了基于此方法的列表曲线加工的数控系统,通过实例验证了该方法的有效性。     

组合有理二次Bezier曲线及其在数控弯管加工仿真中的应用

根据推导所得出的有理二次Bezier曲线表示圆弧曲线的表达式，给出了描述一类由直线和圆弧曲线构成的组合曲线分段参数方程，采用该方法能够自动保证圆弧曲线与直线达到G^1连续，并将其应用于数控弯管加工仿真中导管的动态成形，使用结果表明，该方法能够显著提高数控弯管加工仿真系统的运行效率。     

42CrMo钢CT图的数值计算方法

利用3次样条插值的方法对42CrMo钢的IT曲线进行了数值化处理。通过对IT曲线进行多项式拟合,利用孕育期迭加原理,建立了由IT图计算CT图的数学模型,并基于Matlab商业数学软件,计算出了一系列连续冷却的转变点,绘制出42CrMo钢的CT图。得到的IT图与实际IT图十分吻合。所建立的CT图与实际CT图进行了对比分析,二者吻合较好。     

基于UGNX的航空发动机叶片造型方法研究

对航空发动机的关键元部件之一——涡轮叶片进行了三维空间造型方法的研究。基于UGNX的自由曲面造型功能，采用双三次B样条拟合方式建立了叶片型面的空间样条曲线模型，由此来构造叶片空间型面。同时对叶片曲面造型中的几个关键问题从数学上进行了分析和探讨，验证了其造型方法的可行性，这为后续叶片加工精度分析和误差补偿提供了理论依据。     

G73指令在非圆曲线内轮廓加工中的应用

数控车床轮廓复合循环指令G73在车削加工、尤其仿形轴类零件加工中经常用到,适合加工锻件、铸件的加工编程。G73指令运行的精加工程序段中允许出现宏程序。本文就G73指令在非圆曲线内轮廓加工中的应用进行分析。     

巧用宏程序和调用子程序与G10在数车加工中实现一车多件

用补偿量的编程输入数据设置命令G10编制宏程序并配合子程序调用,可以实现在数控车床一次装夹中加工多个相同零件,程序简单,安全可靠,加工效率高.     

B样条曲线拟合技术处理波动代码的研究

针对NC代码中异常波动代码带来的机床抖动、进给速度受限制、工件表面留下划痕等问题,提出了一种三次均匀B样条曲线拟合技术处理波动代码的方法.通过对波动代码判别,在夹角平分线上控制最大误差实行曲线拟合,B样条曲线实时插补等对波动代码进行重新轨迹规划,实现有波动嫌疑的代码转角由曲线圆滑光顺过渡.该方法已在调试平台上证明了其可行性,并通过实际加工半球实验验证了该方法有效地提高了机床的平稳性和工件的表面质量.     

高硬度镍基喷熔层切削加工工艺参数的选定及刀具磨损研究

本文通过试验优选了精车、半精车高硬度镍基G112氧－乙炔焰喷熔层的刀具材料；建立了较优刀具材料的耐用度一切削速度（t－V）关系曲线；求出了精车、半精车条件下刀具耐用度与切削用量之间的关系表达式，并确定了合适的切削用量范围；最后，对刀具的磨损机理进行了研究。     

涡轮叶片造型方法的研究

对涡轮片进行精确的数学描述是对其进行数控加工的前提，本文讨论了在给定叶片沿叶高方向上截面数据的情况下，采用双三次B样条拟合法和三次NURBS曲面插值法构造叶片曲面的具体算法，分析了两种方法的优缺点，并给出了具体的算法和公式，深入探讨了叶片构造过程中遇到的部分网格确定，插值曲面构造，圆弧的二次NURBS曲线精确表示，NURBS曲线节点插入算法及其升降阶等关键性技术问题。     

三次NURBS曲线轮廓数控加工刀位数据计算

在给定具体型值点的条件下，通过平方根法计算得NURBS曲线的节点矢量；采用de Boor—Cox递推公式分别计算得一次、二次和三次基函数；构造边界条件反求得控制顶点。构造出三次NURBS曲线的参数方程。采用等距离位移计算得曲线轮廓加工刀位轨迹，为NC代码的生成提供数据。     

Bézier polygons for the linearization of dual NURBS curve in five-axis sculptured surface machining

Motivated by the excellent performance of three-axis NURBS interpolation, this paper presents a numerically efficient and accuracy controllable five-axis sculptured surface machining method with dual NURBS curve. Unlike the traditional three-axis NURBS interpolation, a dual NURBS format of the five-axis toolpath is developed to accurately and smoothly describe the tool movement in the part coordinate system. Different from the subdivision methods using the Taylor series expansion or inverse function, a piece-wise Bézier curve method is implemented to fast subdivide the NURBS curve within the user-defined tolerance. A generic rotation tool center point management module is also designed to realize the coordinate transformation and adaptive nonlinear error control for major five-axis machine tools. The overall effectiveness of the proposed five-axis NURBS machining scheme is demonstrated by the five-axis machining of an impeller’s flow channel.     

基于复合路径的连续纤维熔丝挤出成形轨迹优化研究

轨迹规划技术在复合材料熔丝挤出成形中非常关键,合理的轨迹可以提高增材制造成形零件的表面质量和强度。针对复合材料熔丝挤出成形的特点,结合多种路径规划算法,提出一种复合路径填充算法。引入NURBS曲线生成轮廓偏置路径,以保持切片轮廓的精度;在切片层的内部区域生成Zigzag填充路径,并在路径转折处进行圆弧优化,减少了约85%空行程,提高了成形效率;然后,基于生成的路径构建时间分析数学模型,以提前对整个制造过程所需的总体时间进行预估及分析,达到对制造过程的前馈控制;最后,使用复合路径填充算法对典型结构体进行模拟制造,相较传统算法减少了28.3%~36.2%制造时间,提高了制造效率。     

基于NURBS的复杂曲线多轴运动控制轨迹生成的研究

为了提高具有复杂曲线形状产品的设计和加工水平,在NURBS曲线建模理论的基础上,借助于MATLAB数学计算软件建立了复杂曲线的数学模型,并对生成的复杂曲线进行了多轴控制轨迹生成的研究。结果表明:生成的复杂曲线具有较高的精度和生成速度,能够对实际产品的数控加工起到一定的指导作用。     

Wear model in turning of hardened steel with PCBN tool

In this study a mathematical–computational model of tool wear of PCBN (polycrystalline cubic boron nitride) was developed in turning of quenched and tempered AISI D6 steel (57 HRC) using experimental planning and statistic techniques. On the experimental trials many parameters are important such as: surface roughness, cutting force and tool wear. These parameters were evaluated according to their statistical significance using Statistica^® and Matlab^® softwares. Through a multiple-regression analysis, it was possible to establish a mathematical model for estimating tool wear as a function of the cutting parameters. This model enhanced estimation of the ideal cutting conditions for turning hardened steel, i.e., those that generate minimum damage on the PCBN tool without compromising productivity.     

逆向工程中回转面特征参数的提取

从某种意义上说,逆向工程是从已有实物的测量数据点中提取特征参数进行模型重建的过程。回转面是机械零件中常见的几何特征,文章首先介绍了任意位置回转面特征参数的提取原理,然后采用极小惯量法运用MAT-LAB语言求出截面点云数据的对称轴及其垂线,通过截面点云对称轴并以其垂线为法矢量构造平面,该平面与数据点云求交,即得到回转面的母线数据点,运用NURBS曲线拟合得到母线,再应用极小惯量法求出母线数据点云对称轴,即回转轴线,从而实现了回转面的构建,最后用实例验证了该方法的正确性。     

Design of a NURBS interpolator with minimal feed fluctuation and continuous feed modulation capability

With the growing demands to machine complex dies, moulds, aerospace, automotive, and biomedical parts in shorter cycle time, the utilization of Non-Uniform Rational B-Spline (NURBS) toolpaths has become more important than ever before. There are two challenges associated with realizing a successful NURBS trajectory generator—minimizing feedrate fluctuations and being able to modulate the feed continuously. This paper presents a robust and numerically efficient NURBS interpolation strategy. Unwanted feed fluctuations and sensitivity to round-off errors are avoided by applying the feed correction polynomial concept to NURBS toolpaths in an adaptive manner. A numerically efficient feedrate modulation strategy is developed, based on the trapezoidal acceleration profile, which guarantees that the final trajectory is jerk limited in all axes and kinematic continuity is achieved between connecting segments throughout the long toolpaths. The feed modulation strategy can be integrated with various feed optimization techniques as well. Effectiveness of the overall NURBS interpolation scheme is demonstrated in 3-axis machining of a complex sculptured surface.     

Development and implementation of a NURBS interpolator with smooth feedrate scheduling for CNC machine tools

Parametric interpolation for Non-Uniform Rational B-Spline (NURBS) curve has become more important than ever before in the control of CNC machine tools. An effective NURBS interpolator not only can obtain accurate contour trajectories, but also have smooth dynamics performance. This paper proposes a numerically efficient NURBS interpolation scheme which consists of two stages namely preprocessing and interpolating. In the stage of pre-processing, the parameter interval is split into several blocks at breakpoints and an iterative numerical quadrature method is applied for each block. By means of the iterative quadrature method, the initial parameter intervals of each block are divided into several subintervals according to the arc length approximation error. Meanwhile, the curvature of each knot and the cubic polynomial coefficients of each subinterval are obtained. Then the critical points with large curvature of each block are found from the candidate points and the tolerated speed of each critical point is calculated according to the constraints of chord error and centripetal acceleration. Hence, the feedrate scheduling based on the S-shaped acceleration profile for each block can be preplanned via the approximate arc length of each subinterval, the tolerated speed of each critical point and kinematics characteristics such as acceleration/deceleration and jerk limits of the machine tools. In the stage of interpolating, the parameter of the next interpolation point can be calculated directly using the cumulative arc length and the cubic polynomial coefficients of each subinterval. Finally, a series of numerical simulations and real machining experiments are conducted, and the simulation and experimental results have showed the good performance of the proposed NURBS interpolator both in efficiency and accuracy.