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.     

Circular tests for HSM machine tools: Bore machining application

Today's High-Speed Machining (HSM) machine tool combines productivity and part quality. The difficulty inherent in HSM operations lies in understanding the impact of machine tool behaviour on machining time and part quality. Analysis of some of the relevant ISO standards [230. Acceptance code for machine tools. Part 4, Circular tests for numerically controlled machine-tools, April 1998, 10791. Test conditions for machining centres. Part 6, Accuracy of feeds, speeds and interpolation, September 1998, 10791. Test conditions for machining centres. Part 7, Accuracy of feeds, speeds and interpolation, September 1998] and a complementary protocol for better understanding HSM technology are presented in the first part of this paper. These ISO standards are devoted to the procedures implemented in order to study the behaviour of machine tool. As these procedures do not integrate HSM technology, the need for HSM machine tool tests becomes critical to improving the trade-off between machining time and part quality. A new protocol for analysing the HSM technology impact during circular interpolation is presented in the second part of the paper. This protocol, which allows evaluating kinematic machine tool behaviour during circular interpolation, was designed from tests without machining. These tests are discussed and their results analysed in the paper. During the circular interpolation, axis capacities (such as acceleration or Jerk) related to certain setting parameters of the numerical control unit have a significant impact on the value of the feed rate. Consequently, a kinematic model for a circular-interpolated trajectory was developed on the basis of these parameters. Moreover, the link between part accuracy and kinematic machine tool behaviour was established. The kinematic model was ultimately validated on a bore machining simulation.     

A real-time look-ahead interpolation algorithm based on Akima curve fitting

To process the complex geometric-shapes consisting of discrete data points, this paper presents a real-time look-ahead interpolation algorithm based on Akima curve fitting. The algorithm consists of two modules: pretreatment module and real-time interpolation module. The pretreatment module firstly adopts the bi-chord and tangent-chord criteria to identify those continuous Akima blocks and calculates the linking velocity between two adjacent blocks according to the required machining accuracy. Then the five-point Akima method is used to fit the continuous blocks into a Akima spline curve. In the real-time interpolation module, the look-ahead interpolation is executed to ensure that the processing error is limited in a satisfying range, and the Newton iteration method is employed to calculate the parameters when interpolating Akima spline blocks. Simulations and experimental results demonstrate that the Akima spline is more suitable when processing discrete data points. And the proposed look-ahead interpolation algorithm could reduce the feedrate fluctuation to satisfactory level and implement high-quality CNC processing.     

Adaptive interpolation scheme for NURBS curves with the integration of machining dynamics

This paper develops a comprehensive interpolation scheme for non-uniform rational B-spline (NURBS) curves, which does not only simultaneously meet the requirements of both constant feedrate and chord accuracy, but also real-time integrates machining dynamics in the interpolation stage. Although the existing work in this regard has realized the importance to simultaneously consider chord error and machining dynamics, none has really incorporated these in one complete interpolation scheme. In this paper, machining dynamics is considered for three aspects: sharp corners or feedrate sensitive corners on the curves, components with high frequencies or frequencies matching machine natural ones and high jerks. A look-ahead module was developed for detecting and adaptively adjusting the feedrate at the sharp corners. By Fast Fourier Transform (FFT) analysis with a moving window in the interpolation stage identified were some special frequency components such as those containing high frequencies or with frequencies matching machine natural ones. Then, the notch filtering or time spacing method was used to eliminate these components. To more completely reduce feedrate and acceleration fluctuations, the jerk-limited algorithm was also developed. Finally, the interpolated feedrate was further smoothened with B-spline fitting method and the NURBS curves were re-interpolated with the smoothened feedrate. During the interpolation, the chord error was repeatedly checked and confined in the prescribed tolerance. Two NURBS curves were used as examples to test the feasibility of the developed interpolation scheme.     

Design of trigonometric velocity scheduling algorithm based on pre-interpolation and look-ahead interpolation

To generate continuous velocity, acceleration and jerk curves of parametric interpolation in high-speed and high-accuracy machining, this paper presents a trigonometric velocity scheduling algorithm based on two-time look-ahead interpolation (pre-interpolation and look-ahead interpolation). The algorithm consists of three modules: pre-interpolation, look-ahead interpolation and real-time interpolation. The pre-interpolation module aims to explore and record the information of the path to be machined. The look-ahead interpolation module firstly calculates the velocity scheduling functions according to the data recorded by pre-interpolation, and then tests and adjusts the feedrate scheduling schemes constantly. The real-time interpolation module adapts the method of beforehand deceleration or delaying acceleration according to the signals received from pre-interpolation and look-ahead interpolation to guarantee the processing accuracy. Simulation and experimental tests demonstrate the availability, effectiveness and advantages of the trigonometric velocity scheduling algorithm. And the proposed trigonometric velocity scheduling algorithm based on pre-interpolation and look-ahead interpolation could realize smooth velocity, acceleration and jerk control with restricted chord error and implement high-quality CNC processing.     

5-Axis tool path smoothing based on drive constraints

In high speed machining, the real feedrate is often lower than the programmed one. This reduction of the feedrate is mainly due to the physical limits of the drives, and affects machining time as well as the quality of the machined surface. Indeed, if the tool path presents sharp geometrical variations the feedrate has to be decreased to respect the drive constraints in terms of velocity, acceleration and jerk. Thus, the aim of this paper is to smooth 5-axis tool paths in order to maximize the real feedrate and to reduce the machining time.Velocity, acceleration and jerk limits of each drive allow to compute an evaluation of the maximum reachable feedrate which is then used to localize the areas where the tool path has to be smoothed. So starting from a given tool path, the proposed algorithm iteratively smoothes the joint motions in order to raise the real feedrate. This algorithm has been tested in 5-axis end milling of an airfoil and in flank milling of an impeller for which a N-buffer algorithm is used to control the geometrical deviations. An important reduction of the measured machining time is demonstrated in both examples.     

Feed-rate optimization with jerk constraints for generating minimum-time trajectories

Competitive pressure requires manufacturers to simultaneously address increasingly stringent constraints on both productivity and quality. From the perspective of numerically controlled (NC) machine tools, this means higher machining performance in terms of speed and accuracy. Conventional approaches to programming NC operations involve selecting a constant feedrate for a given operation to produce acceptable performance (operation time and contouring accuracy).In this paper, we examine the possibility of scheduling or varying the feedrate by taking into consideration the geometry of the contour that the machine is expected to follow and the physical capabilities of the machine (i.e., its maximum velocity, acceleration and jerk constraints). Previous work by the authors has addressed the efficient, off-line computation of time-optimal trajectories with constraints on velocity and acceleration. This paper introduces additional constraints on the permissible jerk (rate of change of acceleration) on the machine's axis. From a practical perspective, excessive jerk leads to excitation of vibrations in components in the machine assembly, accelerated wear in the transmission and bearing elements, noisy operations and large contouring errors at discontinuities (such as corners) in the machining path.The introduction of jerk into the feedrate scheduling problem makes generating computationally efficient solutions while simultaneously guaranteeing optimality a challenging problem. This paper approaches this problem as an extension of our previous bi-directional scan algorithm [23] and [29]. A new acceleration-continuation procedure is added to the feedrate optimization algorithm to address jerk constraints and remove discontinuities in the acceleration profile. The algorithm maintains computational efficiency and supports the incorporation of a variety of state-dependent (such as position, velocity, acceleration and jerk) constraints. By carefully organizing the local search and acceleration continuity enforcing steps, a globally optimal solution is achieved. Singularities, or critical points, and critical curves on the trajectory, which are difficult to deal within optimal control approaches, are treated in a natural way in this algorithm. Several application examples and tests are performed to verify the effectiveness of this approach for high-speed contouring.     

基于HPGL的数控裁床加工系统方案设计与实现

为提高数控裁床自动化生产水平,设计一种数控裁床加工系统方案。围绕数控裁床运动速度控制和轨迹插补算法等关键技术点,根据HPGL协议的数据特性,提出数控裁床CNC加工数据生成方法,设计一种基于线段分段的速度控制方法来生成速度列表,并基于微软基础类库MFC开发上位机,实现处理曲线中各线段的运动速度控制的功能。设计将加工插补算法与数据栈相结合的应用方法,并运用STM32F103开发下位机,实现计算各线段的插补步进量并进行轨迹控制的功能。通过样片测试,验证了所设计的数控裁床系统具有用于实际加工的可行性和高效准确性,能有效满足生产需要。     

梯形速度控制变插补周期的实时插补算法研究

提出了基于梯形速度控制的变插补周期实时插补算法.在固定插补步长条件下,依据直线加减速算法,确定出加速段、恒速段和减速段的插补次数,进而生成变化的进给速度和相应的插补周期;同时,形成各坐标轴的运动增量.仿真实例结果表明,该算法可有效地控制加工精度,充分发挥联动各轴的加速能力,有效缩短加减速过程时间,且易于在CNC系统中实现.     

Modeling and improvement of dynamic contour errors for five-axis machine tools under synchronous measuring paths

In this paper, a contour error model of the tool center point (TCP) for a five-axis machine tool is proposed to estimate dynamic contour errors on three types of measuring paths. A servo tuning approach to achieve five-axis dynamic matching is utilized to improve contouring performance of the cutting trajectory. The TCP control function is developed to generate measuring trajectories where five axes are controlled simultaneously to keep the TCP at a fixed point. The interpolation method of the rotary axes with S-shape acceleration/deceleration (ACC/DEC) is applied to plan smooth five-axis velocity profiles. The contour error model for five axes is derived by substituting five-axis motion commands into servo dynamics models. The steady state contour error (SSCE) model is demonstrated to illustrate three particular dynamic behaviors: the single-circle with amplitude modulation, double-circle effect and offset behavior. Furthermore, the model is also utilized to investigate the behaviors of dynamic contour errors change in 3D space. The factors that affect dynamic contour errors, including the initial setup position, feedrate and five-axis servo gains, are analyzed. With the developed servo tuning process under the measuring paths (CK1, CK2 and CK4), the contour errors caused by servo mismatch are reduced remarkably. Finally, experiments are conducted on a desktop five-axis engraving machine to verify the proposed methodology can improve dynamic contouring accuracy of the TCP significantly.     

基于多轴运动控制方法的高速切削复合轨迹研究

为了解决复杂曲面数控加工中的高速数控加工问题,从过程集成控制的角度构建了多轴平滑运动模型、插补控制、位置跟踪等。速度优化模型采用数学方法,构造了加、减速控制。速度预处理中通过简化优化模型,提出了柔性加减速控制算法,并对其进行了优化设计。为了克服高速进给系统的非线性影响,通过引入新的加速度和速度的前馈控制,提出了高速位置跟踪算法;实现了基于双核处理器的嵌入式数控系统,且该结构能保证六轴插补周期的要求。现场数据显示该系统在高速运动平稳性好,能满足叶轮复杂轨迹控制要求等。     

Spline interpolation with optimal frequency spectrum for vibration avoidance

A major source of inaccuracy in CNC machines is unwanted vibrations induced by the frequency spectra of reference motion trajectory. This paper presents a novel approach where instead of filtering techniques, axis motion commands are generated with optimal frequency spectra in the first place. Tangential feedrate profile is defined as parametric spline, and its frequency spectrum is optimized with respect to structural dynamics of the machine. The optimization problem is solved efficiently using Quadratic Programming. Experimental results confirm that proposed technique can greatly improve surface finish during machining spline tool-paths without sacrificing from cycle time and contouring performance.     

Real-time trajectory generation for 5-axis machine tools with singularity avoidance

This paper presents a novel trajectory generation method to exceed limitations of 5-axis machine tools. 3 key deficiencies are addressed. Synchronous and accurate interpolation of tool's translational (TCP) and rotational (ORI) motion is achieved by Finite Impulse Response (FIR) filtering of velocity commands in cartesian and spherical coordinates. The long-lasting feedrate optimization problem is solved analytically to plan rapid feed motion within kinematic limits of drives. A tool-path modification strategy is developed to interpolate around kinematic singularity within part tolerances and while minimizing rapid traverse of rotary axes. Simultaneous 5-axis contouring experiments confirm significant cycle time and accuracy improvement.     

Guide curve based interpolation scheme of parametric curves for precision CNC machining

Real-time parametric interpolation has played a key role in the computer control of machine tools. To achieve highest quality parts, generated trajectories not only describe the desired toolpath accurately, but also have smooth dynamics profiles. This paper presents a novel parametric interpolator based on guide curve. The relationships between geometric properties and kinematic properties are firstly discussed. Then, with a consideration of the important effect of the curvature of curvilinear path on the machining dynamics, a corresponding formula, which describes the relation of the maximum allowed feed acceleration/deceleration and the maximum allowed rate of change of curvature radius of paths, is built. Thus, based on a near arc parameterization and through modifying the curvature radius curve to deal with corners, key regions and other cases, adaptive feedrate schedule is completed according to the reconstructed smooth curvature radius curve. Consequently, confined chord errors, corners on the path and the acceleration/deceleration capabilities of the machine tool are simultaneously considered and incorporated into the guide curve based parametric interpolation system without using look-ahead scheme. Simulation results indicate the feasibility and precision of the proposed interpolation method.     

Real-time generation and control of cutter path for 5-axis CNC machining

This paper presents a new approach to real-time generation and control of the cutter path for 5-axis machining applications. The cutter path generation method comprises real-time algorithms for cutter-contact path interpolation, cutter offsetting, and coordinate conversion. In addition, a global feedback loop is closed by the CNC interpolator so as to augment the controlled accuracy in practical cutter path generation. An error compensation algorithm and a feedrate adaptation algorithm for the control loop are developed, respectively.     

局部刀具轨迹平滑过渡方法的研究

当三轴机床沿线性轨迹运动时,其速度、加速度以及跃度在过渡点是不连续的,直接影响刀具的运动状态,从而降低曲面的精度。提出一种优化方法,通过在刀尖点相邻的线性位置插入三次B样条,从而获得满足误差限制条件、能够实现在连接点三阶连续的的最优刀具位置点样条曲线。通过该方法,可以使刀具在拐角处圆滑过渡,同时保持速度、加速度连续,避免刀具在拐角处产生接刀痕迹。最后通过一大拐角的实验证明该方法相对于传统的线性插补可以提高产品的加工质量。     

A smooth curve evolution approach to the feedrate planning on five-axis toolpath with geometric and kinematic constraints

Feedrate planning with geometric and kinematic constraints is crucial for sculptured surface machining. Due to the non-linear relationship between the Cartesian space and the joint space, the feedrate planning method for a given five-axis toolpath is very limited compared with that in three-axis machining. To achieve the exact control of the chord error and the kinematic characteristics of cutter and machine tool, this paper presents a new feedrate planning method for five-axis parametric path using a smooth curve evolution strategy. The constraints in feedrate planning are first classified as two types of neighbor-independent (NI) constraints and neighbor-dependent (ND) constraints. Then for constraint violated region, the detailed formulas of determining the update feedrates of violated sampling points are given using a decoupled manner. As a result, NI and ND constraints are satisfied respectively with one step and multi-step smooth curve evolution technique, which can smoothly deform the target feedrate profile to the desired update positions. Simulations and experiments are performed on the given tool path to validate the effectiveness of the proposed feed planning method. The results show that the proposed method is robust and effective in the exact control of constraints in the feedrate planning on complex five-axis toolpath.     

Feed optimization for five-axis CNC machine tools with drive constraints

Real time control of five-axis machine tools requires smooth generation of feed, acceleration and jerk in CNC systems without violating the physical limits of the drives. This paper presents a feed scheduling algorithm for CNC systems to minimize the machining time for five-axis contour machining of sculptured surfaces. The variation of the feed along the five-axis tool-path is expressed in a cubic B-spline form. The velocity, acceleration and jerk limits of the five axes are considered in finding the most optimal feed along the tool-path in order to ensure smooth and linear operation of the servo drives with minimal tracking error. The time optimal feed motion is obtained by iteratively modulating the feed control points of the B-spline to maximize the feed along the tool-path without violating the programmed feed and the drives’ physical limits. Long tool-paths are handled efficiently by applying a moving window technique. The improvement in the productivity and linear operation of the five drives is demonstrated with five-axis simulations and experiments on a CNC machine tool.     

Smooth feedrate planning for continuous short line tool path with contour error constraint

In the machining program for free form surfaces, the tool path is usually represented as continuous short lines. For the computer numerical control, the feedrate profile for short line tool path should be smooth and optimized in order to achieve high machining quality and high speed. In high speed machining, the feedrate profile also has a strong influence on contour accuracy. This paper presents a new real-time smooth feedrate planning algorithm for short line tool path, in which the contour error constraint is included. To realize contour error control, the feedrate is adaptively adjusted based on the curvature radius of the tool path, which is directly estimated from the short lines. The 7-phase jerk-limited look-ahead planning is employed to generate a smooth feedrate profile. The target feedrate filter (TFF) and planning units merging techniques are developed to improve the smoothness of the feedrate profile and reduce the overhead on look-ahead. The advantage of the proposed algorithm is that it is not only convenient to achieve the balance among accuracy, smoothness and productivity by adjusting parameters, but also efficient in design, which makes it possible to be implemented on low cost hardware platforms. Experiment results demonstrate the feasibility of the proposed algorithm on smooth feedrate planning and contour error control for continuous short line tool path.     

A realtime curvature-smooth interpolation scheme and motion planning for CNC machining of short line segments

G01 codes generated by CAM (Computer Aided Manufacturing) system are the most common form of tool path in CNC (Computer Numerical Control) machining. For the piecewise linear path, tangential and curvature discontinuities bring about large fluctuation of feedrate and acceleration, which produces vibration of machine tool. In recent studies, the methods for G² (curvature-continuous) tool-path smoothing and jerk-limiting feedrate scheduling were developed. However there still exist the deficiencies when these methods are employed in CNC machining. It is difficult to simultaneously ensure that the tool path is chord-error-constrained and G01-point-interpolated in real time. In addition, heavy computational load hinders realtime processing in CNC system. Recently the scholars experimentally found the potential of G³ (curvature-smooth) trajectory and jerk-continuous motion in reducing the vibration of machinery. This work proposes a realtime tool-path smoothing algorithm, generating G³ interpolative tool path composed by mixed linear and quartic Bezier segments. The purpose of the smoothing scheme is the simultaneous considerations of G³ continuity, confined chord error, G01 points interpolated, and realtime performance. And the tool path generated is optimized in curvature variation energy (CVE) and analytical curvature extrema is available. To reduce the vibration, a high-efficient algorithm of jerk-continuous (JC) feedrate scheduling for G³ tool path is provided. Finally, a realtime tool-path processing scheme is developed, including G³ interpolation and motion planning functions. As shown in the simulation, the contour error, curvature of tool path, feedrate fluctuation and machining time are reduced compared with G² transition scheme. The experiment on a machine tool is conducted to demonstrate the advantages of the proposed algorithm in vibration reduction and surface quality, compared with G² transition scheme.