An adaptive feedrate scheduling method of dual NURBS curve interpolator for precision five-axis CNC machining

Non-uniform rational b-spline (NURBS) tool path is becoming more and more important due to the increasing requirement for machining geometrically complex parts. However, NURBS interpolators, particularly related to five-axis machining, are quite limited and still keep challenging. In this paper, an adaptive feedrate scheduling method of dual NURBS curve interpolator with geometric and kinematic constraints is proposed for precision five-axis machining. A surface expressed by dual NURBS curves, which can continuously and accurately describe cutter tip position and cutter axis orientation, is first used to define five-axis tool path. For the given machine configuration, the calculation formulas of angular feedrate and geometric error aroused by interpolation are given, and then, the adaptive feedrate along the tool path is scheduled with confined nonlinear geometric error and angular feedrate. Combined with the analytical relations of feed acceleration with respect to the arc length parameter and feedrate, the feed profiles of linear and angular feed acceleration sensitive regions are readjusted with corresponding formulas and bi-directional scan algorithm, respectively. Simulations are performed to validate the feasibility of the proposed feed scheduling method of dual NURBS curve interpolator. It shows that the proposed method is able to ensure the geometric accuracy and good machining performances in five-axis machining especially in flank machining.     

Adaptive feedrate interpolation with multiconstraints for five-axis parametric toolpath

A good adaptive feedrate will be helpful for improving machining accuracy and efficiency, as well as avoiding the excess of the machine’s physical capabilities and feed fluctuations during machining. Therefore, it is highly desirable to consider the constraints of geometric error, cutting performance, and drive constraints in the feedrate scheduling of the parametric curve interpolator for five-axis computer numerical control machining. In this paper, a novel multiconstraints feedrate scheduling method is proposed for the parametric curve interpolator in five-axis machining. In the method, the feed optimization model is first built with the constraints of geometric error, the maximum feedrate and acceleration of cutter tip, and the maximum feedrate and acceleration of five-drive axes. Then, the relations between each constraint and the cutter tip feedrate are derived by means of near arc length parameterization. After that, a linear programming algorithm is applied to obtain the optimal feed profile on the sampling positions of the given tool path. Finally, illustrated examples are given to validate the feasibility and applicability of the proposed feedrate scheduling method. The comparison results show that the proposed method has an ability of the simultaneous guarantees of geometric accuracy, cutting performance, and drive characters of machine tools.     

Time-optimal interpolation for five-axis CNC machining along parametric tool path based on linear programming

In this paper, the time-optimal velocity planning problem for five-axis computer numerical control machining along a given parametric tool path under chord error, acceleration, and jerk constraints is studied. The velocity planning problem under confined chord error, feedrate, and acceleration is reduced to an equivalent linear programming problem by discretizing the tool path and other quantities. As a consequence, a polynomial time algorithm with computational complexity O(N ^3.5) is given to find the optimal solution, where N is the number of discretized segments of the tool path. The velocity planning problem under confined chord error, feedrate, acceleration, and jerk is reduced to a linear programming program by using a linear function to approximate the nonlinear jerk constraint. As a consequence, a polynomial time algorithm is given to find the approximate time-optimal solution. Simulation results are used to show the efficiency and effectiveness of the algorithms.     

Optimal CNC plunge cutter selection and tool path generation for multi-axis roughing free-form surface impeller channel

Plunge milling is the most effective way for rough machining of impeller parts, but previous research had not considered the optimization of plunge cutter selection and tool path. In this paper, a new method for optimizing the plunge cutter selection and tool path generation in multi-axis plunge milling of free-form surface impeller channel is proposed in order to improve the efficiency in rough machining. Firstly, in the case of fixing a rotation axis at a certain angle in five-axis machine, a mathematical representation is formulated for the geometric model of the cutter interfering the impeller, and an optimization model of the cutter size is established at a cutter contact point on the impeller channel surface, so the largest tool could be determined. Secondly, by analyzing the machine tool movement characteristics, the geometric constraint model of the plunge tool path which relative to the largest tool, step distance, and row space is established, and a tool orientation calculation method of impeller channel machining is given, and then, the plunge tool path and tool orientation could be obtained. Finally, the generated tool path and tool orientation are simulated and verified in practical processing. Simulation and experimental result shows that the rough machining efficiency of the impeller part is improved up to 40 % with this method.     

五轴数控机床加工误差动态修正方法研究

为修正五轴数控机床加工误差,提高五轴数控机床加工质量,提出一种新的五轴数控机床加工误差动态修正方法.构建五轴数控机床加工误差计算模型,获取五轴数控机床加工的刀心方位、刀轴方位轮廓误差;锁定误差方位后,通过五轴数控机床误差的动态实时补偿方法,实现五轴数控机床加工误差动态修正.研究结果表明:所提方法可实现全方位、高效率的五...     

五轴数控加工中旋转轴运动引起的非线性误差分析及控制

五轴数控(Computer numerical control,CNC)加工中,刀具路径规划阶段与实际加工阶段对旋转轴运动采用的插补方式存在差异,其中刀具路径规划阶段是根据零件的几何信息进行插补,而实际加工中则根据机床信息进行插补,这种差异将引起原理性加工误差。针对五轴数控加工中旋转轴的运动,分析采用线性插补方式控制两个旋转轴进行加工时刀具姿态变化引起的原理性误差,进一步研究不同加工情况下由此产生的在垂直于走刀方向的平面内的非线性误差。通过分析旋转轴运动过程中线性插补引起的刀轴偏差角,证明刀具在相邻两刀位点运动过程的中间时刻处刀轴偏差角取得最大值,并得到由该最大值的显式表达式,在此基础上分析最大偏差角的影响因素。提出通过限制相邻两刀位点间刀轴夹角来控制此非线性误差的方法,并给出实例验证。     

基于机床运动学约束球头刀多轴加工刀轴矢量优化方法

针对目前航空发动机叶片进排气边加工精度和表面质量较差的问题,提出了一种基于机床运动学约束球头刀多轴加工刀轴矢量优化方法。建立刀位优化变量与刀位数据之间的关系方程,同时建立刀位数据与机床回转轴角度之间的运动变换方程,从而推导出刀位优化变量与机床回转轴角度之间的关系方程。通过求解上述方程得到球头刀多轴加工复杂曲面的刀轴矢量计算公式。在此基础上,给出球头刀多轴加工刀轴矢量优化方法和刀轨生成方法。同时,以某航空发动机叶片为例,分析了本文算法和Sturz算法对机床回转轴角度的影响。分别利用本文算法和Sturz算法生成该叶片进气边加工的刀轨,并在五轴数控机床上进行加工试验。试验结果表明,该算法能够避免加工过程中机床回转轴的大幅波动,使机床轴运动更加平稳和光滑,从而提高曲面的加工质量和加工效率,具有一定的实际应用价值。     

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.     

Interpolation of parametric CNC machining path under confined jounce

Aiming at reducing the computer numerically controlled (CNC) machining vibration and increasing machining quality, an interpolation method for parametric tool paths with confined jounce, jerk, acceleration, and speed is proposed. An acceleration/deceleration profile with confined jounce, jerk, acceleration, and speed is proposed, and it is shown that this profile is time optimal to change the speed from one value to another under the given constraints. For a given parametric tool path, the velocity function is obtained by first computing the critical points of the tool path where the radius of curvature reaches extremal values, then determining the feasible maximal speeds at the critical points, and finally using the jounce confined acceleration/deceleration profile to connect the speeds at the adjacent critical points. A vibration experiment is conducted, which shows that vibration of the CNC machine decreases significantly for motions under confined jounce than that under confined acceleration and jerk. Simulation for two real CNC models are given to show the feasibility of the method.     

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.     

Surface normal interpolation for five axis CNC milling

This paper presents an algorithm for five-axis CNC interpolation. The algorithm generates cutter location points by interpolating the surface normals along a desired path. The surface normals are represented by line coordinates which tie a orientation vector with a specific point in space. The algorithm uses line displacements to generate an approximation of the surface normals along a path. The main advantage of this method is that it relates the angular velocity of the tool to the feed rate requirement of the interpolation. An example is shown of the interpolation technique on a Bezier surface.     

Automatic selection of cutter orientation for preventing the collision problem on a five-axis machining

The rotation joints of a five-axis machine tool can offer freedom and appropriate rotation to prevent interference problem between workpiece and the cutter. However, to a five-axis machine tool, it is quite difficult to determine the collision-free cutter orientation. Over this problem, a two-stage cutting tool collision check method is proposed to prevent the collision problem during the cutting process on a five-axis machine tool. The proposed method is capable of determining the collision free ball-end cutter orientation automatically. The first stage is to obtain the tilting and collision-free angle range in the plane that is normal to the tool path obtained. Next, a checking cone generated from this collision-free tool axis range is used for the second collision check. The collision region is formed by the intersection of the neighboring surfaces. This implies a collision-free yaw angle range. The final cutting tool orientation is determined automatically by referring the original spindle axis and the least angular variation from the spindle axis. Finally, the implementation issue is discussed with example.     

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.     

隐曲线的线性和旋转插补

基于数控五轴刀具运动分析,提出了旋转插补的概念,给出了旋转插补的相关定义,在此基础上提出了隐曲线的线性和旋转插补原理和方法,并进一步提出了改进的插补方法。     

Five-axis tool path and feed rate optimization based on the cutting force–area quotient potential field

Feed rate assignment in five-axis surface machining is constrained by many factors, among which a particularly critical one is the deflection cutting force on the tool: while a larger feed rate increases the machining productivity by shortening the total machining time, it nevertheless inevitably enlarges the deflection cutting force as well, which will cause the tool to be more prone to bending and the machine more prone to vibration, thus adversely degrading the surface finish quality. In this paper, we present a new five-axis tool path generation algorithm that strives to globally maximize feed rate for an arbitrary free-form surface while respecting a given deflection cutting force threshold. The crux of the algorithm is a new concept of the (cutting) force–area quotient function—at any cutter contact point on the surface, the maximal effective material removal rate (with respect to the deflection cutting force threshold) is a continuous function of the feed direction. This function induces a potential field on the surface and based on which an efficient tool path generation algorithm is designed. Preliminary experiments show that substantial reduction in total machining time can often be achieved by the proposed algorithm.     

A novel kinematic model for five-axis machine tools and its CNC applications

In conventional five-axis CNC machining, the machine structure is treated as a single kinematic chain just like a robotic manipulator while the cutter is treated as an end effector. In this paper, besides the machine kinematic chain, a cutter kinematic chain is introduced, and the two subkinematic chains are combined to form one machine–cutter kinematic chain. Forward, inverse kinematics and constrained inverse kinematics for the proposed machine–cutter kinematic chain are further put forward. Two applications are presented to demonstrate the advantages and effectiveness of the proposed kinematic model. The proposed kinematic model unifies the structure of the machine and cutter; therefore, the flexibility of the five-axis machine tool can be fully explored.     

Optimisation of workpiece setup for continuous five-axis milling: application to a five-axis BC type machining centre

When machining complex geometries on five-axis machining centres, the orientation and positioning of the workpiece in the machine workspace are generally chosen arbitrarily by the operator from the Computer-Aided Manufacturing software. Nevertheless, these two factors have considerable influence on the machining time. The present article firstly studies the choice of workpiece orientation. Relying on analysis of the machine’s kinematic behaviour, orientations of the workpiece in the machine workspace are proposed minimising the overall distance travelled by the rotary axes. Secondly, choice of workpiece positioning in translation is studied. To this purpose, the work volume in five-axis machining is identified so as to avoid overshooting the machine travels when the program is executed. The optimum positioning is chosen to minimise the overall distance covered by the machine’s axes of translation. Finally, the proposed method provides for a workpiece setup to be adopted that minimises the distances covered by the machine axes. This leads to reduced machining time with concomitant gains in productivity and greater respect for the cutter/workpiece relative feed rate for enhanced quality.     

五轴加工刀具路径生成的有效加工域规划方法

为复杂曲面五轴数控加工的刀具路径优化生成问题提出一种新的有效加工域规划方法。在对工件被加工表面和刀具的几何特征进行分析的基础上,得到在加工件表面上各处的最优可加工域宽度和刀具切削方向。通过采用离散采样和插值计算生成优化的有效加工域集,得到最优化的初始刀具路径;同时建立一种迭代搜索算法,用于解决最优加工域的选择规划问题。采用此算法生成优化的后续刀具路径,使得有效加工域最终完全覆盖整个被加工表面。给出的示例显示相对于传统的五轴加工刀具路径生成算法,有效加工域规划方法可以减少刀具路径的总长度和加工时间,得到更为优化的刀具路径和更好的工件表面质量,因此有效加工域规划方法可以被用于五轴数控加工实践以降低加工成本和提高产品质量。     

基于MMR的三角网格曲面五轴加工刀轨生成算法

为了提高三角网格曲面五轴加工的加工效率,提出了基于最大材料去除率(maximal materialremoval rate,MMR)的平底刀五轴加工刀轨生成算法。首先计算无曲率干涉且具有最大材料去除率的网格曲面五轴加工的刀具方位角;然后在确定网格曲面可能干涉区域的基础上,提出刀触点处干涉性假设,并以最大材料去除率、刀具无曲率干涉和全局干涉为约束条件,采用二分法确定具有最大材料去除率的无干涉刀具方位角;最后采用截面线法生成三角网格曲面MMR平底刀五轴加工刀轨。通过实验验证了采用文中算法生成的刀轨进行加工能够获得较高的加工效率和表面质量。     

五轴微段平滑插补算法

在五轴加工编程中,计算机辅助制造系统对曲面加工通常采用以折代曲,采用大量的微小G01直线段来加工曲面,在曲率半径较大的工件表面会出现明显折痕,严重影响工件表面的加工质量。为提高五轴数控加工工件的表面质量,提出一种五轴微段平滑插补算法。该算法考虑五轴加工中刀位数据的量纲差异,根据相邻数据点间的线性轴长度、线性轴的夹角和旋转轴角度变化量识别五轴数控加工程序中非连续微段和连续微段加工区域。对非连续微段加工区域按照原始直线段和旋转轴直接插补,从而保证加工精度。对连续微段加工区域,先通过五维变量获取节点参数,采用最小二乘法对指令点在允许的精度范围内进行修正;对修正后的指令点采用4点构造法计算二阶切矢,根据连续微段的指令点修正值,节点参数值和对应的二阶切矢值获取二阶连续的三次样条曲线;在二阶连续平滑的曲线上进行实时插补计算,控制机床进行五轴加工。试验结果表明:通过提出的五轴微段平滑压缩算法拟合后的路径要更加接近原始的曲面模型,平滑处理过的实际工件加工表面也要优于未进行处理的工件加工表面,提高了五轴自由曲面的表面质量。