A novel adaptive-feedrate interpolation method for NURBS tool path with drive constraints

Feedrate scheduling is crucial for CNC systems to generate a smooth movement which is able to satisfy increasing requirements on machining quality and efficiency. In this paper, a novel adaptive feedrate interpolation method is proposed for NURBS tool path with drive constraints. The tool path is first expressed in NURBS form, and then the satisfaction conditions of drive constraints are derived according to the kinematic and geometric characteristics of the NURBS tool path. On this base, a proportional adjustment algorithm, which can quantitatively reduce the accelerations and jerks of drive axes at the sensitive regions of feed profile, is proposed to achieve the new positions of violated sampling points. After each adjustment, a curve evolution strategy is used to ensure the feed profile is locally or globally deformed to the target positions with a good smoothness of path curve and the avoidance of re-interpolation. Through the iterative adjustment, a smooth feed profile with limited velocities, accelerations and jerks of drive axes is thus yielded along the entire tool path. Finally, performances of the proposed method are validated by performing both simulations and experiments on two freeform NURBS curves. The results show the effectiveness and reliability of the proposed feedrate interpolation method.     

The feedrate scheduling of parametric interpolator with geometry,process and drive constraints for multi-axis CNC machine tools

Parametric interpolator has been widely adopted in machining sculptured parts. Accordingly, the feedrate scheduling of parametric interpolator plays a role in CNC machine tools especially for multi-axis machines with linear and rotary axes, since a smooth movement is beneficial for achieving better surface geometry as well as shorter machining time. This paper presents a new feedrate scheduling method for the five-axis machining of geometrically complex part with geometry, process and drive constraints. The satisfaction conditions of constraints are first built and the proportional adjustment of feedrate sensitive regions is proved to be suitable for simultaneously reducing the magnitudes of constraints such as angular acceleration, linear acceleration, axis accelerations and jerks. The initial feedrate profile is first constructed with confined chord error, angular velocity and axis velocities owing to the independence of these constraints. Then, for each iterative adjustment a curve evolution strategy is used to deform the target feedrate profile to the adjusted positions instead of the re-interpolation of feedrate profile, until the final desired feedrate profile is achieved without violated constraints. Simulations and experiments are conducted and the results validate the performances of the proposed method.     

Machining accuracy improvement in five-axis flank milling of ruled surfaces

The aim of this study is to develop a new adjustment method for improving machining accuracy of tool path in five-axis flank milling of ruled surfaces. This method considers interpolation sampling time of the five-axis machine tools controller in NC tool path planning. The actual interpolation position and orientation between G01 commands are estimated with the first differential approximation of Taylor expansion. The tool swept volume is modeled using the envelope surface and compared with the design surface to determine the deviation, which corresponds to the machining error induced by the linear interpolation. We propose a feedrate adjustment rule that automatically controls the tool motion at feedrate-sensitive corners based on a bisection method, thus limiting the maximum machining errors and improving the machining accuracy. Experimental cuts are conducted on different ruled surfaces to verify the effectiveness of the proposed method. The result shows that it can enhance the machining quality in five-axis flank milling in both simulation and practical operation.     

An accurate,efficient envelope approach to modeling the geometric deviation of the machined surface for a specific five-axis CNC machine tool

Geometric deviation, defined as the difference between the nominal surface and the simulation model of the machined surface, is the fundamental concern of five-axis tool path planning. Since the machined surface is part of the cutter envelope surface generated by the cutter motion, it is necessary to calculate the envelope surface in order to obtain the geometric deviation. In the stage of tool path planning, current approaches calculate the cutter envelope surface by using the cutter motion along the given tool path. However, the cutter motion of practical machining on a specific five-axis CNC machine tool is different from the given tool path. Moreover, the computation is very challenging when the accurate cutter motion of practical machining is applied to calculate the envelope surface. To overcome these two problems, a geometric envelope approach with two major distinctions is proposed in this paper. First, the envelope surface of the cutter undergoing a general motion is efficiently obtained as a closed-form vector expression. Second, the accurate cutter motion, which is determined by machine kinematic and interpolation scheme in practical machining, can be easily applied to calculate the accurate envelope surface. With the envelope surface, the geometric deviation is calculated to estimate the overcut or undercut in five-axis milling. An example is given to demonstrate the validity of the proposed method.     

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.     

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.     

Corner optimization for pocket machining

The aim of this paper is to propose a pocketing tool path improvement method by adapting the geometry of the tool path to the kinematic performance of high speed machining machine tools. The minimization of the machining time is a major objective, which should be taken into account for the tool path computation. In this way the tool path length can be reduced or the real feedrate increased. The described method proposes modification of the values of the corner radii in order to increase real feedrate. In the same way, this method checks the radial depth of cut variations along the tool path. The computed tool path presents a smaller length and the machine tool produces a higher average feedrate at the same time. In addition, the use of Bspline for the tool path computation is a significant improvement compared with straight lines and circle arcs for the machining time reduction. Several tests are realized on various machine tools in order to quantify the benefits: the proposed method can reduce the machining time by approximately 25% compared with classical tool paths computed using a CAM system.     

Optimized tool path generation based on dynamic programming for five-axis flank milling of rule surface

This paper presents a computation scheme that generates optimized tool path for five-axis flank milling of ruled surface. Tool path planning is transformed into a matching problem between two point sets in 3D space, sampled from the boundary curves of the machined surface. Each connection in the matching corresponds to a possible tool position. Dynamic programming techniques are applied to obtain the optimal combination of tool positions with the objective function as machining error. The error estimation considers both the deviation induced by the cutter at discrete positions and the one between them. The path planning problem is thus solved in a systematic manner by formulizing it as a mathematical programming task. In addition, the scheme incorporates several optimization parameters that allow generating new patterns of tool motion. Implementation results obtained from simulation and experiment indicate that our method produces better machining quality. This work provides a concise but effective approach for machining error control in five-axis flank milling.     

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.     

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.     

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.     

Spiral cutting operation strategy for machining of sculptured surfaces by conformal map approach

Although compound surfaces and polyhedral models are widely used in manufacturing industry, the tool path planning strategies are very limited for such surfaces in five-axis machining and high speed machining. In this paper, a novel conformal map based and planar spiral guided spiral tool path generation method is described for NC machining of complex surfaces. The method uses conformal map to establish a relationship between 3D physical surface and planar circular region. This enables NC operation to be performed as if the surface is plat. Then through inversely mapping a planar spiral defined by a mathematical function into 3D physical space, the spiral cutter contact paths are derived without inheriting any corners on the boundary in the subsequent interior paths. The main advantage of the proposed method is that a smoother, longer and boundary conformed spiral topography tool path is developed. Therefore, the machined surface can be cut continuously with minimum tool retractions during the cutting operations. And it allows both compound surfaces and triangular surfaces can be machined at high speed. Finally, experimental results are given to testify the proposed approach.     

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.     

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.     

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.     

Multibody dynamic modeling of five-axis machine tool vibrations and controller

A computationally efficient, reduced-order multibody dynamic model of a five-axis machine tool is presented. The machine tool is modeled by substructures assembled via flexible springs and damping elements at interfaces which affect the machining performance. NC tool path commands are processed by the linear acceleration-based motion trajectory filters and fed to the axis servo controllers through an inverse kinematic model of the machine. The computed motor torque commands are applied to the structural dynamic model of the machine at the motor connections. The experimentally validated model predicts the performance of the five-axis CNC machine's controller along the tool path.     

Tool path planning for five-axis machining using the principal axis method

A study of the effect of feed direction on five-axis tool paths generated using local surface properties for tool orientation and positioning is presented in this paper. The principal axis method for five-axis machining defines the placement of the cutting tool at a single point on the workpiece surface and assumes that a preferred feed direction will be maintained. This preferred direction may not represent a practical choice for tool path planning. In this work, numerical simulations are used to evaluate tool paths with different feed directions. Numerical simulations are then verified experimentally by machining two example surfaces. The results show that both gouging and the effective cutter profile will dictate the optimal choice of feed direction.     

雕刻表面球形铣削的分段变进给率加工

雕刻表面球形铣削加工中,根据刀头的受力模型,可以计算整个刀具路径上刀头的受力.刀具路径上加工深度变化时,若采用恒进给率,则刀具受力是变化的,为了安全保险起见,往往按最大受力来选择较低的恒进给率,整个加工效率很低.采用变进给率加工,即加工深度小时提高进给率,使刀具在整个路径上受力均匀.本文给出了路径上力的计算仿真方法,以及分段进给率的计算方法,可以指导实际的加工过程,这样既保证了加工过程的安全,又提高了生产率.     

Modeling and analysis of servo dynamics errors on measuring paths of five-axis machine tools

Dynamic error is one of the major error sources for five-axis machine tools in achieving high-speed machining. It can be estimated and compensated by means of servo dynamics modeling and servo control method. This paper presents a contour error model on five-axis measuring paths where the dynamics and contour errors of the tool center point (TCP) can be estimated accurately during five-axis synchronized motions. The forward and inverse kinematics equations are derived according to the kinematic configuration of a C-type five-axis machine. To generate smooth measuring paths, the S-shape acceleration/deceleration (ACC/DEC) method is applied on planning the motion trajectory. The contour error model of the TCP is derived by substituting the commands of the measuring trajectory into the servo dynamics models. To investigate how the contour charts of the TCP are affected by the dynamic gains of five-axis servo loops, twelve combinations under different gains are studied. It is shown that, for the CK2 path, the steady-state contour error consists of an offset and a double-circular trajectory which is quite different from that of two-axis contour path. By tuning the gains of the servo loops, the dynamics mismatch among five axes can be eliminated and the contour error of the TCP (CETCP) can be reduced. To validate the contour error equations, simulations and experiments are performed to demonstrate that the proposed method improves the contouring performance of the TCP significantly when performing five-axis synchronized motions.     

Five-axis milling mechanics for complex free form surfaces

Accurate and fast prediction of machining forces is important in high performance cutting of free form surfaces that are commonly used in aerospace, automotive, biomedical and die/mold industries. This paper presents a novel and generalized approach for prediction of cutting forces in five-axis machining of parts with complex free form surfaces. Engagement simulations between cutter and part are performed precisely along the tool path by a recently developed boundary representation method. Moreover, mathematical model for five-axis milling mechanics is developed for any given solid model of parts with complex free form surfaces. Theoretical simulations and experimental validations show that cutting forces are predicted fast and precisely for five-axis machining of complex free form surfaces.