以弧长为参数的快速NURBS插补研究

针对复杂零件的高速高精加工需要,提出了基于弧长为参数的快速NURBS插补。由于NURBS曲线参数u没有几何意义,与弧长是非线性映射关系。弧长难以直接用解析表达式计算,没有弧长信息难以对曲线进行速度规划。基于此,利用高斯积分计算曲线弧长,同时对参数u和弧长S进行五次多项式u-S建模,建立它们之间映射关系,在插补时既可以进行速度规划,又可以实时快速计算下一个插补点,保持小的速度波动。仿真与实验结果验证了该算法的有效性。     

提高曲面零件加工精度方法的分析与研究

零件的加工精度主要体现在零件加工尺寸精度和零件表面粗糙度两个方面,影响零件加工精度的主要因素是弦高误差。为了减少弦高误差,提高加工精度,分别研究了参数曲线、曲面插补中的弦高误差控制算法,并对其进行仿真和实时性验证。在传统控制算法的基础上,误差补偿值与参数曲面其高精度刀具轨迹规划的算法与之相结合,在满足实时性的基础上,将弦高误差可以控制在预定范围之内,以保证零件的加工精度。     

基于双圆弧步长伸缩数控插补非圆曲线算法的研究

为了加工出高质量的非球曲面器件,超精密非球曲面数控系统的数控插补算法非常重要。根据所要加工的非球曲面零件,采用了一种新的非圆曲线数控插补算法“双圆弧步长伸缩数控插补算法”。这种算法采用双圆弧段逼近方式,其双圆弧段彼此相切,一阶导数连续,并且步长可伸缩,其数控插补误差可进行控制。因此加工后的工件表面整体光滑,插补曲线的质量很高,而且适用性很广泛。最后用所研制的数控插补算法进行了大量的磨削加工试验,试验结果表明:该插补算法能加工出高质量的非球曲面零件,加工后的零件面形精度为O.30μm,其表面粗糙度Rrms=11.555nm,Ra=8.538 nm。     

辛普森积分法在双NURBS曲线随动插补中的应用

提出一种精确计算插补步长的双NURBS曲线随动插补算法。首先由曲面数控加工的离散刀位数据分别拟合出刀尖点和刀轴点NURBS曲线,并建立两条曲线插补参数间的随动关系模型;然后采用辛普森积分法计算出曲线的总弧长,进行插补运动的加减速规划;再以刀尖点NURBS曲线为基准确定插补参数,采用辛普森法确定各插补周期的进给步长及插补点坐标;最后依据随动关系模型获得刀轴点NURBS曲线对应的插补参数,完成曲面加工刀路规划的刀具位姿插补。仿真实验表明,与同一参数插补法相比,参数随动法可以获得更加稳定的等距效果,便于实时控制插补过程中的刀轴位置和姿态。     

基于三弯矩法的环曲面金刚石切削刀具路径规划及其仿真分析

为解决环曲面加工困难的问题,对环曲面金刚石切削方法进行研究。在刀具路径规划中,使用了刀触点综合离散方法,该方法结合了等角度离散与等弧长离散的优点;提出了通过控制相邻刀触点间Z向距离以减小刀具的Z向移动从而提高离散精度的方法。根据加工时刀位点插补的特点,应用三弯矩法计算插补入口参数,实现插值函数的二阶导数连续。仿真分析表明,综合离散方法能够减小离散误差,使用三弯矩法进行插补计算可将最大插值误差由Hermite插值的0.35 μm减小至0.001 2 μm,效果明显。加工试验结果表明,该路径规划方法可用于环曲面的加工,且能改善工件的加工质量。     

高速数控加工中NURBS曲线拟合及插补技术的研究

通过分析现代数控系统中自由曲面插补算法的特点,提出了基于最小二乘法的NURBS曲线拟合算法和基于弧长参数补偿的NURBS插补技术。采用最小二乘法拟合NURBS曲线,能获得光滑的刀具加工路径,并且在一定范围内能复原曲线的设计轮廓。参数补偿的NURBS插补方法,以泰勒展开法得到的插补参数作为临时插补点,利用该插补法能显著减小速度波动,可将速度控制在理想的范围内,可进一步提高加工精度并减小数控机床的振动。仿真实验表明：该算法简明高效、易于实现,能够满足现代数控系统的要求。     

曲线的三参数路径规划车削插补算法研究

为了保证数控加工中复杂曲线零件的车削加工精度,在普通二参数车削加工的基础上,提出了一种三参数路径规划车削插补算法。该算法将复杂曲面数控加工插补过程的路径规划分解为若干插补点之间的最优路径搜索和选取问题,根据不同加工要求设置决策变量,并进行取值判别,通过3个参数联动对曲线进行插补运算,优化加工过程中刀具的路径,并应用于相关的实例分析。研究结果表明,该优化算法能保证加工曲线的光滑性,有利于提高曲线的加工质量,并且该算法还具有计算规模小、求解迅速、数控加工插补误差小等优点。     

并联机床空间曲线等弦长插补算法研究

通过对空间隐式方程曲线、参数方程曲线的插补算法的研究,把等弦长插补算法用于并联机床,用微小直线段拟合曲线。首先根据弦长求出各离散点,并求出其对应杆长,根据相邻两点之间的杆长增量按比例进给。插补无累积误差,从而提高了插补算法的准确性和高效性。     

两类参数曲面的高精度刀具轨迹规划

在曲面加工参数线法的基础上,提出引入误差补偿值的参数曲面高精度刀具轨迹规划算法(HPTPPAC)。通过引入误差补偿值,HPTPPAC在满足插补运算实时性要求的前提下,使插补点的参数值计算精度得到极大提高,有利于降低进给速度波动,实现高速切削。在使用平底刀五座标加工的条件下,证明HPTPPAC算法对两类曲面的适用性。实例表明HPTPPAC可以提高曲面的加工精度。     

基于递归特征分析的NURBS曲线插补算法

在分析NURBS曲线公式中基函数递归特征的基础上,提出了一种新的NURBS曲线插补算法。该算法通过前一个参数增量值和前一段插补弦长来确定下一个参数增量值,进而实现对参数的密化。仿真实验结果表明,该算法在改善弦长误差和减小计算量方面优于Taylor展开插补算法。     

一种数据采样法圆弧插补误差的分析

分析了在数据采样法圆弧插补中以程编进给速度F与插补周期Ts的乘积作为微小直线段的长度△L来逼近待加工圆弧轮廓所引起的加工时间误差。具体以弦线法插补为分析对象,阐明引起误差的原因,分析误差程度,最后证明了该误差的收敛性。论证了在实际插补算法的研究中令△L=FTs的可行性。     

等弓高误差变步长的插补点求取方法优化

传统的等弓高误差求取插补点的方法是根据走刀步长来计算,并且假设步长内为等曲率半径。由于自由曲面的曲率半径不断变化,传统的插补方法并不能准确计算出下一个刀触点的位置。为了克服传统方法的不足,提出了一种新的等弓高误差变步长插补方法。采用该算法得到的两相邻刀触点之间的弓高误差值一致,可得到较高的加工表面精度;而且在保证表面加工质量的情况下,刀触点最少,提高了加工效率。最后,通过MATLAB对该方法的可行性和精度进行了验证。     

基于非均匀有理B样条的凸轮轴插补算法

针对高速加工高精度凸轮轴的需求，应用非均匀有理B样条的方法，提出了凸轮轴实时插补算法。该算法通过插补预处理，合理的近似计算，大大减小了插补计算时间；并且引入插补误差和进给步长自适应控制，从而实现了凸轮轴的高速高精度加工插补控制。     

Non-redundant tool trajectory generation for surface finish machining based on geodesic curvature matching

The increasing complexity of surface has put forward higher demands for CNC machining trajectory generation. The constant scallop height method has the disadvantage of point redundancy during trajectory discretization. Therefore, a non-redundant tool trajectory generation method for surface finish machining is put forward. The cutting row spacing is determined by the geodesic curvature according to scallop height and the convexity or concavity of the local surfaces. The adjacent cutter contact (CC) points with constant scallop height are expressed point by point from the present CC point. The redundant points are removed by maximizing each cutting step length through making the chord error equal to the machining allowable error. The dual NURBS ruled surface is constructed to realize smooth transition of the tool trajectories and tool axis vector. The prototype system taking ACIS R13 and HOOPS V11.0 as modeling kernel has been developed to verify the proposed method. The experiment results proved that the proposed method can realize non-redundant tool trajectory considering tool interference during surface finish machining.     

基于传动系统动力学的NURBS曲线插补算法

对机床传动系统、伺服驱动系统和数控插补模块进行动力学建模和求解。提出一种新的NURBS插补算法,按照进给率自适应轨迹规划算法进行当前插补周期的速度设定,并且根据曲线当前位置的曲率特性,进行基于曲率的最大速度限定,通过求解动力学模型,获得按照这一速度进行插补时系统需要的最大驱动力,若该驱动力超过系统能够提供的最大驱动力,则再次按照用户设定的加速度进行减速,获得的速度作为指令速度,按照一阶泰勒展开近似进行插补点的计算。该算法不仅在NURBS曲率较大的区域自动降低进给速度,保证要求的弦误差,而且使输出的插补速度指令区域平滑,保证不会出现插补输出的位置值系统无法进行位置控制造成更大的加工误差。     

An accurate surface error optimization for five-axis machining of freeform surfaces

This paper presents an accurate surface error interpolation algorithm for five-axis machining of freeform surfaces. One of the most important steps in the interpolation process is to calculate the next cutter contact (CC) point according to the present one. In this paper, the next CC point is calculated by an accurate chord evaluation method. This method is developed based on the cutting simulation process, which can be vividly described as firstly planting dense grasses on the tool path curve and then cutting them when the tool moves by. The left lengths of the grasses either positive or negative are considered to be the machining error. The method is accurate also because the tool geometry and the tool orientation changes during five-axis machining are taken into consideration. With this method, the chord errors between CC points are controlled uniform along the tool path. The proposed interpolation algorithm is compared with the commercial CAM systems like PowerMILL and UG. The results show that the proposed algorithm can significantly reduce the number of cutter locations meanwhile confine the chord error. A real cutting experiment is implemented, and the result indicates its promising value in industrial applications.     

机床加工误差补偿信号的实时测量系统

机床加工误差补偿是提高加工精度的重要途径.正确测量机床主轴误差运动是实现加工误差补偿的前提.然而,这一测试问题一直未得到很好解决.本文提出的用差动传感器直接相对主轴表面测量的系统比较简单,容易实现,且为实时测量.该方法已用于车削加工误差实时补偿系统之中,取得了较好的效果.     

蒙皮镜像加工误差实时补偿优化方法研究

针对传统的飞机蒙皮镜像加工误差补偿方法收敛速度慢,在大进给高速加工中很难完成较好的补偿效果的问题,提出了一种蒙皮镜像加工误差实时补偿优化方法。该方法基于双点弦截法,借助超声波测厚仪前两次获得的蒙皮壁厚与程序切削深度,计算下一点的补偿值,并通过控制镜像铣补偿轴运动实现加工误差补偿,有效的提升了飞机蒙皮镜像铣的补偿效果,减小了加工误差。最后通过有限元仿真和试验证明了该方法的优越性,最大加工误差降低了41.67%,总体加工误差降低了41.96%。     

A Cutter Orientation Modification Method for the Reduction of Non-linearity Errors in Five-Axis CNC Machining

In the machining of sculptured surfaces, five-axis CNC machine tools provide more flexibility to realize the cutter position as its axis orientation spatially changes. Conventional five-axis machining uses straight line segments to connect consecutive machining data points, and uses linear interpolation to generate command signals for positions between end points. Due to five-axis simultaneous and coupled rotary and linear movements, the actual machining motion trajectory is a non-linear path. The non-linear curve segments deviate from the linearly interpolated straight line segments, resulting in a non-linearity machining error in each machining step. These non-linearity errors, in addition to the linearity error, commonly create obstacles to the assurance of high machining precision. In this paper, a novel methodology for solving the non-linearity errors problem in five-axis CNC machining is presented. The proposed method is based on the machine type-specific kinematics and the machining motion trajectory. Non-linearity errors are reduced by modifying the cutter orientations without inserting additional machining data points. An off-line processing of a set of tool path data for machining a sculptured surface illustrates that the proposed method increases machining precision.     

Adaptive feedrate scheduling for NC machining along curvilinear paths with improved kinematic and geometric properties

In precision machining of free-form surfaces at high speed, it is very important to ensure part accuracy and machining properties. To achieve this, this paper develops a guide spline-based feedrate scheduling method for machining along curvilinear paths with simultaneous constraints of chord errors and ac/deceleration. Based on two metrics about feedrate scheduling from the view of geometric and kinematic properties, the nonlinear relationships between the arc-length parameter and path parameter are subsequently established with a parameter correction spline. Then a guide spline associated with the modified curvature radius of paths is constructed to the schedule feedrate. It is shown that determining the largest safe feedrate with constant chord error can be reduced to the issue of changing the feedrate proportionally with the square root of path curvature radii and ensuring the safe feed acceleration can be converted into the issue of presetting the largest slope of guide spline. The simulation results prove that the proposed feedrate scheme has potential applications in the field of finish machining.