A real-time look-ahead interpolation methodology with curvature-continuous B-spline transition scheme for CNC machining of short line segments

Straight lines, or G01 blocks, are the most widespread representation form for the tool path in CNC machining. At the junctions between consecutive segments, the tangency and curvature discontinuities may lead to feedrate fluctuation and acceleration oscillation, which would deteriorate the machining efficiency and quality. To solve this problem, a real-time path-smoothing method is proposed, which adopts a curvature-continuous B-spline with five control points to blend the adjacent straight lines. The advantage of the transition scheme is that, G² continuity, analytical calculation of the curvature extrema, approximation error control and real-time performance are considered simultaneously. Then, a bidirectional scanning algorithm for jerk limited S-shape feedrate profile is proposed to evaluate the feedrate constraints. On this basis, a real-time look-ahead scheme, which comprises of path-smoothing, bidirectional scanning and feedrate scheduling, is developed to acquire a feedrate profile with smooth acceleration. Also, an arc-length based interpolation algorithm for mixed linear and parametric segments is proposed to overcome the difficulty of crossing different segments. With these schemes, the smoothness of both tool path and feedrate is guaranteed. Simulation and experiments on an X–Y–Z platform are conducted. The results demonstrate the feasibility and efficiency of the present algorithms.     

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.     

Feedrate optimization for freeform milling considering constraints from the feed drive system and process mechanics

This paper presents a new and comprehensive strategy for planning minimum cycle time tool trajectories subject to both machining process related constraints, and also limitations of the feed drive control system. The machining process is considered by computing the workpiece-tool engagement along the toolpath and setting local feed limits to maintain a specified resultant cutting force. The drive constraints are considered by limiting the velocity, acceleration, and jerk magnitudes commanded to each actuator. Feed profiling is realized with uninterrupted acceleration transitions, capable of spanning multiple toolpath segments. Effectiveness of the proposed strategy is demonstrated in sculptured surface machining experiments.     

High speed CNC system design. Part I: jerk limited trajectory generation and quintic spline interpolation

Reference trajectory generation plays a key role in the computer control of machine tools. Generated trajectories must not only describe the desired tool path accurately, but must also have smooth kinematic profiles in order to maintain high tracking accuracy, and avoid exciting the natural modes of the mechanical structure or servo control system. Spline trajectory generation techniques have become widely adopted in machining aerospace parts, dies, and molds for this reason; they provide a more continuous feed motion compared to multiple linear or circular segments and result in shorter machining time, as well as better surface geometry. This paper presents a quintic spline trajectory generation algorithm that produces continuous position, velocity, and acceleration profiles. The spline interpolation is realized with a novel approach that eliminates feedrate fluctuations due to parametrization errors. Smooth accelerations and decelerations are obtained by imposing limits on the first and second time derivatives of feedrate, resulting in trapezoidal acceleration profiles along the toolpath. Finally, the reference trajectory generated with varying interpolation period is re-sampled at the servo loop closure period using fifth order polynomials, which enable the original kinematic profiles to be preserved. The proposed trajectory generation algorithm has been tested in machining a wing surface on a three axis milling machine, controlled with an in house developed open architecture CNC.     

Integrated post-processor for 5-axis machine tools with geometric errors compensation

Geometric errors of 5-axis machine tools introduce great deviation in real workpiece manufacture and on-machine measurement like touch-trigger probe measurement. Compensation of those errors by toolpath modification is an effective and distinguished method considering the machine calibration costs and productivity. Development of kinematic transformation model is involved in this paper to clarify the negative influences caused by those errors at first. The deviation of the designed toolpath and the real implemented toolpath in workpiece coordinate system is calculated by this model. An iterative compensation algorithm is then developed through NC code modification. The differential relationship between the NC code and the corresponding real toolpath can be expressed by Jacobi matrix. The optimal linear approximation of the compensated NC code is calculated by utilizing the Newton method. Iteratively applying this approximation progress until the deviation between the nominal and real toolpath satisfies the given tolerance. The variations of the geometric errors at different positions are also taken into account. To this end, the nominal toolpath and the geometric errors of the specific 5-axis machine tool are considered as the input. The new compensated NC code is generated as the output. The methodology can be directly utilized as the post-processor. Experimental results demonstrate the sensibility and effectiveness of the compensation method established in this study.     

Improving tool wear and surface covering in polishing via toolpath optimization

Polishing operations are commonly carried out manually, thus inducing variability on the surface quality. The aim of this paper is to automate the polishing of free-form surfaces in order to obtain high quality surfaces. Tool wear and toolpath surface covering have a great impact on surface properties. The current work proposes therefore a toolpath which optimizes both tool wear and surface covering. This toolpath is composed of an optimized elementary pattern repeated along a 5-axis carrier trajectory. Usually, trochoid patterns are used. Non uniform wear of the tool and uneven probability density function of the surface covering are the main inconvenients of such pattern. So, this paper proposes two optimized patterns: Spade and Triangular. Both of them lead to uniform tool wear. Our paper also demonstrates that the second solution provides a uniform probability density function. All presented computations are validated experimentally.     

A new acceleration-based methodology for micro/meso-scale machine tool performance evaluation

Micro-machining and micro/meso-scale machine tools (mMTs) use substantially different motion parameters than those used at the macro-scale. A new acceleration-based mMT performance evaluation methodology is developed based on an assessment of motion parameters, and in particular, unique acceleration requirements at the micro-scale. Performance evaluations using the new methodology are carried out on two prototype mMTs. Following errors are found for the most part to increase linearly with acceleration. The closed loop bandwidth is found to be the current major factor affecting acceleration capability for the machines tested. A linear model linking servo-update frequency, closed-loop bandwidth, acceleration and following error is proposed. The model results provide a basis for prescribing maximum acceleration values to maintain 10⁻²–10⁻³ relative accuracy. Future mMT component performance requirements are explored.     

The effect of axis coupling on machine tool dynamics determined by tool deviation

High acceleration forces of machine tool with kinetic coupling as the dominating coupling forces may deform the machine structure and result in the tool deviation. In this paper, a dynamic model of a three-axis gantry milling machine tool considering axis coupling effects is proposed to model the varying dynamic behavior and evaluate the Tool Center Point (TCP) position deviations. The effect of axis coupling force on the stiffness changes of kinematic joints is analyzed. The variations of the frequencies and frequency response functions with respect to position parameters are calculated. And the TCP deviation affected by axial coupling in real-time motion state is discussed in detail. The results show that it is able to obtain an excellent match between the simulations and the measurements. The simulation and experimental results show that: (1) the natural frequencies and the receptance are greatly changed when the TCP is moving along the X-axis or the Z-axis, where the maximum changing of natural frequencies is up to 10% and response magnitude up to 2 times; (2) the elastic deformation and vibration of machine tool are caused by the coupling forces in acceleration and braking, which detrimentally affect dynamic response of the TCP. Thus, the model proposed in this paper represents the important effects for comprehension of machine dynamic behavior and for further compensation in future.     

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。     

Real-Time NURBS Interpolator for Distributed Motion Control

Off-line toolpath planning for machine tools inevitably leads to suboptimal use of the given equipment and, even more important, excludes the possibility to accommodate for unforeseen or unmodelled effects. Online path planning however requires the availability of real-time interpolators which are both numerically efficient and deterministic and which do not depend on global information on the path to interpolate. Continuity of the interpolant up to higher derivatives is highly desirable.This paper presents an interpolation scheme that meets all these requirements. The algorithm generates a third-order, C²-continuous Non Uniform Rational B-Spline curve from a series of exactly interpolated position and velocity setpoints. This curve is at all instants completely determined from the first up to the last available setpoint. It is shown that a new setpoint affects only the last control points and the end of the knot vector of the interpolant. A graphical interpretation of the algorithm and a discussion on numerical issues and start conditions are presented.     

Linear-rotary direct drive for multi-functional machine tools

By combining linear and rotary movement in one single drive, the overall dynamics of machine axes can be enhanced, and the installation space can be reduced. Existing concepts for linear-rotary drives either have low power density or load capacity, and the installation space of the guideways are not sufficient for applications in machine tools. Thus, this paper presents a novel linear-rotary direct drive for machine tools. The electromagnetic coupling between the linear and rotary direction is analyzed, and the control performance is evaluated. The developed drive is characterized by stiffness of up to 205 N/µm, acceleration dynamics of 3,100 mm/s² in linear and 24,100 °/s² in rotary direction, and fine positioning in 0.2 µm and 3.6″ steps.     

直线电机在机床工业中的最新应用及技术分析

直线电机在机床进给驱动上的应用日益广泛,比起传统的进给驱动方式,它能提供非常高的速度、加速度和位置精度,大大提高了生产率和加工件表面质量。文章介绍了直线电机在机床上的最新应用情况,并就应用中的关键技术问题进行了分析。     

Corner rounding of linear five-axis tool path by dual PH curves blending

The widespread linear five-axis tool path (G01 blocks) is usually described by two trajectories. One trajectory describes the position of the tool tip point, and the other one describes the position of the second point on the tool axis. The inherent disadvantages of linear tool path are tangential and curvature discontinuities at the corners in five-axis tool path, which will result in feedrate fluctuation and decrease due to the kinematic constraints of the machine tools. In this paper, by using a pair of quintic PH curves, a smoothing method is proposed to round the corners. There are two steps involved in our method. Firstly, according to the accuracy requirements of the tool tip contour and tool orientation tolerances, the corner is rounded with a pair of PH curves directly. Then, the control polygon lengths of PH curves are adjusted simply to guarantee the continuous variation of the tool orientation at the junctions between the transition curves and the remainder linear segments. Because the PH curves for corner rounding can be constructed without any iteration, and those two rounded trajectories are synchronized linearly in interpolation, which makes this smoothing method can be applied in a high efficiency way. Its high computational efficiency allows it to be implemented in real-time applications. This method has been integrated into a CNC system with an open architecture to implement on-line linear five-axis tool path smoothing. Simulations and experiments validate its practicability and reliability.     

Analytical curvature-continuous dual-Bézier corner transition for five-axis linear tool path

A novel analytical five-axis path-smoothing algorithm is developed for the high speed machining of a linear five-axis tool path. Segment junctions of the linear tool path in the machine tool coordinate system, which are tangent-discontinuous points, are all blended by two transition cubic Bézier curves. One cubic Bézier curve is used to smooth the segment junction of the translational path, and the other Bézier curve is used to smooth the segment junction of the rotational path. The tangency and curvature continuities are both guaranteed in the new path. The dual-Bézier transition algorithm has three advantages: (1) Compared with the path-smoothing method in the workpiece coordinate system, the new dual-Bézier transition method directly and simultaneously smooths the machine tool axis trajectories of both translational path and rotational path. The feed speed and stability will both be improved because the tool path discontinuities are the most important source of feed fluctuation. (2) The constraints of approximation error and the synchronization of parametrization of two smoothed curves, which are the most challenging problems in the smoothing of 5-axis tool path, are both considered. (3) The transition cubic Bézier curve pair has an analytical solution and can be easily integrated in the real-time interpolator. Computational examples and the cutting experiment of an impeller blade show that the novel path-smoothing method has obvious advantages in both feed smoothness and cutting efficiency over the original linear interpolator.     

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.     

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-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.     

Development of micro milling tool made of single crystalline diamond for ceramic cutting

In order to machine micro aspheric ceramic molds precisely and efficiently, micro milling tools made of single crystalline diamond (SCD) are developed. Many cutting edges are fabricated 3-dimensionally on the edge of a cylindrical SCD by a laser beam. Flat binderless tungsten carbide mold was cut with the developed tool to evaluate the tool wear rate and its life. Some micro aspheric molds of tungsten carbide were cut with the tool at a rotational speed of 50,000 min⁻¹. The molds were cut in the ductile mode. The form accuracy obtained was about 100 nm P–V and the surface roughness 12 nm R_z.     

Hierarchical Predictive Control within an Open Architecture Virtual Machine Tool

The proposed hierarchical structure, based on the a priori knowledge of the toolpath and using the receding horizon principle, aims at reducing the degradation of tracking performances due to control signals saturation. Starting with the predictive feed drives control as first level, a second one, called trajectory supervisor, modifies in a predictive way as well the axial setpoints in order to minimize the impact of control signals saturation on the tracking accuracy. The third level, called trajectory regenerator, acts with an anticipative effect when the modified setpoints are too distant from the original ones and recomputes the entire toolpath. This strategy is further tested within an open architecture virtual machine tool.     

The effect of stress on grain boundary interdiffusion in a semi-infinite bicrystal

Chemical interdiffusion along a grain boundary in a semi-infinite bicrystal subjected to external stress normal to the boundary plane is considered. Plating out of diffusing atoms in the grain boundary partially relaxes the applied stress and modifies the driving force for diffusion. The resulting diffusion wedge formed at the grain boundary exhibits a time-independent shape, with all its linear dimensions growing with annealing time t, according to the t^1/3 law. The diffusion zone formed in the vicinity of the grain boundary is a combined result of the grain boundary diffusion and lattice drift, and is characterized by concentration discontinuities at its borders. The proposed model is applied to the analysis of liquid metal embrittlement in the Fe–In and Cu–Bi systems.