Real-time Interpolation Algorithm Research Articles

A real-time dual NURBS interpolator with optimised control of flexible acceleration and deceleration for five-axis CNC machining

The limited computing capacity makes it difficult to plan a suitable feedrate profile in real-time for high speed and high accuracy machining of five-axis parametric toolpaths. In this paper, a real-time interpolation algorithm with optimised control of flexible acceleration and deceleration (acc-dec) for the dual NURBS toolpath is proposed. The toolpath is marked as subsegments with similar geometric properties by introducing the five-axis curvature. Machine kinematic and toolpath geometry constraints are considered in the kinematic parameter constraint model. Initial feedrate profiles are solved in a dynamic 3D window which preserves the motion performance of machine tools to a great extent. Convolution is used to smooth the initial feedrate profile to achieve a higher order continuity over the global range. Feedrate fluctuations caused by imprecise parameter interpolation are eliminated through modifying each interpolation periods. Resampling adjusts the position of interpolation points and unify the interpolation periods. All operations mentioned are in series and real-time is strictly guaranteed. Effectiveness of the developed algorithm is validated in simulations and also experimentally on a Self-developed-NC controlled 5-axis machine tool.

A general framework for solving inverse dynamics problems in multi-axis motion control

An inverse dynamics compensation (IDC) scheme for the execution of curvilinear paths by multi-axis motion controllers is proposed. For a path specified by a parametric curve r(ξ), the IDC scheme computes a real-time path correction Δr(ξ) that (theoretically) eliminates path deviations incurred by the inertia and damping of the machine axes. To exploit the linear time-invariant nature of the dynamic equations, the correction term is computed as a function of elapsed time t, and the corresponding curve parameter values ξ are only determined as the final step of the IDC scheme, through a real-time interpolator algorithm. It is shown that, in general, the correction term for P, PI, and PID controllers consists of derivative, natural, and integral terms (the integrand of the latter involving only the path r(ξ), and not its derivatives). The use of lead segments to minimize transient effects associated with the initial conditions is also discussed, and the performance of the method is illustrated by simulation results. The IDC scheme is expressed in terms of a linear differential operator formalism to provide a clear, general, and systematic development, amenable to further adaptations and extensions.

Contour error–bounded parametric interpolator with minimum feedrate fluctuation for five-axis CNC machine tools

In this paper, a new generalized parametric interpolation method is proposed for optimized five-axis machining with the consideration of both the machine contour errors and the feedrate fluctuation elimination. An analytic processing is presented for linearization of contour errors with respect to feedrate limit. For machine configuration, explicit analytical modeling of the contour error and the tracking error with respect to feedrate is presented; thus, the error constraint problem is nicely converted to a kinematic constraint problem. On this basis, an accurate feedrate upper limit with confined contour errors is further determined by using a shifted Frenet frame with linear computational complexity. With the consideration of both the motion smoothness and machining efficiency, a time-based optimization algorithm is proposed for time-optimal feedrate scheduling. For eliminating the feedrate fluctuation, a new real-time interpolation algorithm is developed for free derivation between the path parameter and the arc length for smoothed five-axis tool path generation. Laboratory testing experiments were conducted for validation and were presented in the paper. And the experimental results indicate that the proposed feedrate interpolation method is capable of confining both the tool tip contour error and tool orientation contour error simultaneously, as well as maintaining a satisfactory interpolation performance in both computation efficiency and accuracy. The presented methods can be used for five-axis machining and the feedrate optimization of complex part machining.

A Real-Time Feedrate Planning Method and Efficient Interpolator With Minimal Feedrate Fluctuation for Parametric Toolpath

Different from linear and circular interpolation, feedrate fluctuation is inevitable for parametric toolpath, which is caused by the nonlinear relation between spline parameters and arc-length. In order to improve the accuracy and efficiency of real-time interpolation algorithm with minimal feedrate fluctuation, this thesis presents an iterative feedback interpolator to restrain the feedrate fluctuation. Estimator and corrector stage are two essential steps of our proposed method. The result of the first-order Taylor expansion is used for the iterative initial value in the estimator stage. Thereafter, based on Steffensen iterative accelerator method, the feedback of current feedrate and command feedrate will control to update parameters value repeatedly until feedrate fluctuation rate reaches the allowable value in the corrector stage. By means of the numerical method, it is proved that this iteration method can satisfy the high-order convergence and fast convergence theoretically. In the simulation, the third-degree B-spline curve is utilized to test the proposed method which is equipped with obvious effects on restraining the feedrate fluctuation and improving computation efficiency compared with four existing methods.

Acceleration smoothing algorithm for global motion in high-speed machining

When machining a series of short linear segments, the computer numerical control system interpolates the machining path with the pre-specified spline curve to obtain continuous feed motion. However, to obtain adequate smooth tool-paths to smooth the feed velocity and acceleration, the computer-aided manufacturing system needs to use a higher order spline curve, which will be limited by some technical bottlenecks. In this article, a new real-time interpolation algorithm is proposed from the perspective of kinematics to achieve uninterrupted feed motion throughout the global tool-path. At the same time, the acceleration profile achieves G2 continuous to avoid unnecessary feed frustration and inertial impact, reaching the balance between time-optimal and motion performance. First, the jounce-limited acceleration curve is blended at the corner of the machining path, and the optimal cornering transition velocity is obtained by adding the velocity, acceleration and contour error constraints to the corner transition motion. Then, according to the linear segments with different lengths between the corners, combined with the feed motion around the corner, a look-ahead interpolation algorithm is proposed to calculate the maximum feed rate with the constraint of the linear segment length and kinematic boundary conditions. At last, for the linear segments whose corner contours overlap with each other after interpolation, the smooth transition between the two corners can be realized by mixing the feed motion of the next corner. Compared with non-uniform rational B-spline interpolation algorithm, the proposed algorithm reduces the total machining time by 14% and the computer numerical control system improves the computational efficiency by 11%. It proves that the proposed algorithm has better application value in the manufacturing of complex parts.

Accurate interpolation of machining tool-paths based on FIR filtering

This paper presents a novel real-time (online) interpolation algorithm based on Finite Impulse Response (FIR) filters to generate smooth and accurate reference motion trajectories for machine tools and motion systems. Typically, reference tool-paths are composed of series of linear (G01) or circular (G02) segments. Basic point-to-point (P2P) feed motion can be generated by interpolating each segment with trapezoidal or S-curved velocity profile. However, smooth and accurate transitions between path segments are necessary to realize non-stop contouring motion. In this study, FIR filters are utilized, and the reference tool-path is filtered to interpolate a non-stop rapid feed motion. By using a chain of FIR filters, acceleration and jerk continuous motion profiles are generated from velocity pulse commands. A segment interpolation timing technique is developed to control the contour errors during non-stop real-time interpolation of tool-paths. Furthermore, by utilizing FIR filters for interpolation, frequency spectrum of the interpolated motion profiles is controlled. The time constant (delay) of the filter is tuned to create notches around the lightly damped vibration modes of the motion system, which allows mitigation of unwanted vibrations and thus enables delivering accurate feed motion. Simulation studies and industrial scale experimental validations are provided to illustrate effectiveness of the developed interpolation technique.

A smooth tool path generation and real-time interpolation algorithm based on B-spline curves

In the machining progress of free-form surface, tool path is presented as continuous small line segments. To achieve high machining speed and fine machining quality, the tool path needs to be smoothed. This study presents a smooth tool path generation algorithm based on B-spline curves for small line segments machining. The algorithm includes two modules: smooth tool path generation module and real-time look-ahead interpolation module. In the smooth tool path generation module, the tool path is divided into non-fitting regions and fitting regions by three conditions: the length of small line segments, the angle of adjacent small line segments, and the change rate of the length and angle. To control contour error and get fine machining quality, the fitting regions are corrected by circle correction method and fitted into B-spline curves, while the non-fitting regions are smoothed with B-spline curves. In this module, the gained tool path has continuous curvature. In the interpolation module, the seven-phase jerk-limited look-ahead planning is adopted to generate smooth machining velocity, while the calculation accuracy of interpolation point generated by the interpolation period crossing two adjacent tool path is controlled. Simulations and experimental results demonstrate that the proposed algorithm is able to reduce the amount of numerical control codes, achieve high machining speed, and improve machining quality.

Global tool-path smoothing for CNC machine tools with uninterrupted acceleration

Majority of tool-paths for high-speed machining is composed of series of short linear segments, so-called G01 moves. This discrete tool-path format limits the achievable speed and accuracy of CNC machines. To generate continuous feed motion along sharp cornered tool-paths, most NC systems smooth corners locally using a pre-specified curve or a spline and slow down to be able to change the feed direction within machine kinematic limits. Path speed is dramatically reduced for accuracy if sharp corners are within close vicinity. This paper proposes a new real-time interpolation algorithm for NC systems to generate continuous rapid feed motion along short segmented linear tool-paths by smoothing local and adjacent corners that are within close vicinity. Instead of locally modifying the corner geometry with a spline, the proposed algorithm directly blends axis velocities between consecutive linear segments based on the jerk limited acceleration profile (JLAP) and generates cornering trajectories within user-specified contour errors and kinematic limits of the drives. A novel Look-Ahead Windowing (LAW) technique is developed to plan tangential feed profile with uninterrupted acceleration to continuously smooth the path. The feed profile is optimized to generate rapid motion along overlapping adjacent corners. Simulation and experimental results demonstrate effectiveness of the proposed method to interpolate accurate Cartesian high-speed motion along short-segmented tool-paths for machining free-form surfaces found in dies, molds and aerospace parts.

A polynomial equation-based interpolation method of NURBS tool path with minimal feed fluctuation for high-quality machining

Due to the approximation errors of interpolation methods in non-uniform rational b-spline (NURBS) interpolation, feed fluctuation is inevitable, which has great effects on the machining quality and should be minimized. Based on the idea of zero feed fluctuation, a polynomial equation-based interpolation method of NURBS tool path is proposed in this paper. Firstly, a polynomial equation with respect to the curve parameter increment is formulized according to the sampling step size, which is determined by the scheduled feedrate, acceleration, and jerk. Then, Newton’s method is utilized to solve the high-degree polynomial equation with taking both convergence rate and computational load. In order to improve the computing efficiency in real-time interpolation, a fast-evaluation and derivation algorithm is proposed, which uses the Taylor series expansion to accelerate the calculation of any order derivatives of NURBS. Simulations are conducted among the proposed method and the chord-tracking algorithm (CTA) method, and the results of each method are compared on the basis of computing time and feed fluctuation, which shows that the proposed method is better than the CTA method. Experiment is also conducted to verify the feasibility and applicability of the proposed method in practical application.

Five-axis interpolation of continuous short linear trajectories for 3[PP]S-XY hybrid mechanism by dual Bezier blending

A novel five-axis real-time interpolation algorithm for 3[PP]S-XY hybrid mechanism is proposed in this paper. In the algorithm, the five-axis tool path for controlling this hybrid mechanism is separated into two sub-paths. One sub-path describes the movement of 3[PP]S parallel kinematic mechanism module, and the other one describes the movement of XY platform. A pair of cubic Bezier curves is employed to smooth the corners in those two sub-paths. Based on the homogenous Jacobian matrix of 3[PP]S mechanism, a relationship between the position errors of every driving joint in hybrid mechanism and the position deviation of the tool tip center point at the moving platform is established. This relationship is used to estimate the approximation error for the corners smoothing according to the accuracy requirement of tool tip center in interpolation. Due to the high computational efficiency of this corner smoothing method, it is integrated into the look-ahead module of computer numerical control (CNC) system to perform online tool path smoothing. By performing the speed planning based on a floating window scheme, a jerk limited S-shape speed profile can be generated efficiently. On this basis, a realtime look-ahead scheme, which is comprised of path-smoothing and feedrate scheduling, is developed to acquire a speed profile with smooth acceleration. A monotonic cubic spline is employed for synchronization between those two smoothed sub-paths in tool path interpolation. This interpolation algorithm has been integrated into our own developed CNC system to control a 3PRS-XY experimental instrument (P, R and S standing for prismatic, revolute and spherical, respectively). A club shaped trajectory is adopted to verify the smoothness and efficiency of the five-axis interpolator for hybrid mechanism control.

Hardware Development of CNC System Based on OMAPL138 and FPGA

In order to realize high speed, high precision, high reliability, miniaturization performance of the CNC (Computer numerical control) system, this paper proposed a hardware platform of embedded CNC system based on OMAPL138 and FPGA. OMAPL138 is a SOC using C6748 DSP kernel and ARM9 kernel dual-core structure, the kernel frequency can achieve up to 375/456 MHz. ARM kernel of the CNC system which runs the Linux operation system is responsible for task management, DSP kernel is in charge of real-time interpolation and look-ahead algorithm, and FPGA module generates pulses to control the movement of the servo motor. Firstly, the overall hardware architecture of the embedded CNC system was designed. Meanwhile the hardware circuit design of CPU core module based on OMAPL138, human-computer interaction module, EMIFA bus interface of the FPGA core module were emphasized in detail, and also the serial port, Ethernet, USB communication interface module were introduced. A serial test experiments have been conducted and the results have shown that this embedded CNC system is powerful and stable.

A CNC Manufacturing Method for Parts with Trochoidal Profile

AbstractThis paper presents a manufacturing method for parts with trochoidal profile on CNC milling machines. The method is based on a new real-time interpolation algorithm capable to drive the cutter along the offset of trochoid curves with precision equal to the resolution of the machine. The structure of the presented algorithm may be adapted accordingly so as to be used either for parts with an epitrochoidal or a hypotrochoidal profile. Both types of curves, known as trochoid curves, have important industrial applications such as gears with trochoidal tooth-profile, cams, trochoidal-shaped housings for rotary internal combustion engines and rotary piston pumps etc. The effectiveness and accuracy of the proposed method is verified by simulation tests of the generated tool path for the machining of two representative mechanical parts, an inner rotor of a hypogerotor pump and an epitrochoidal-shaped housing.

Space Trajectory On-Line Interpolation Technique of Six-DOF Robot

This paper presents a real-time interpolation algorithm of the space trajectory which based on the theory of coordinate transform. The algorithm can solve the path planning problem of six-DOF robot. According to the actual movement state of robot, the algorithm can obtain some key points for the robot motion path by teaching. Then it can realize the dimensional random trajectory interpolation by coordinate transformation after building a suitable dimensional coordinate. Finally it can obtain the corresponding joint angle though the inverse kinematics solution. The experimental results show that this algorithm has a good rapidity and practicality, it suit for the six-DOF robot real-time trajectory interpolation, so it is worth promoting.

Design and Implementation of an Interpolation Processor for CNC Machining

As the demand for high speed and high precision machining increases, the fast and accurate real-time interpolation is necessary in modern computerized numerical control (CNC) systems. However, the complexity of the interpolation algorithm is an obstacle for the embedded processor to achieve high performance control. In this paper, a novel interpolation processor is designed to accelerate the real-time interpolation algorithm. The processor features an advanced parallel architecture, including a 3-stage instruction pipeline, very long instruction word (VLIW) support, and asynchronous instruction execution mechanism. The architecture is aimed for accelerating the computing-intensive tasks in CNC systems. A prototype platform was built using a low-cost field programmable gate array (FPGA) chip to implementation the processor. Experimental result has verified the design and showed the good computing performance of the proposed architecture.

New CNC Programming Functions Based on Elliptical Motion

AbstractThis paper proposes a set of four elliptical features that can enhance the programming capabilities of a modern CNC system. Namely, a real-time interpolation algorithm for motion generation along an ellipse and its offset, machining of an elliptical pocket, and drilling a series of equidistant holes along an elliptical path. The paper analytically describes the implementation of the new functions while the G-codes, along with their complementary requisite data needed to be introduced in the CNC part program, are exemplified with simulation and actual machining tests for each feature.

The Research of Real-Time Trajectory Interpolation Based on Open Numerical Control System

This paper researches on Open Numerical Control System based on the PC platform, in which the motion controller works as the control core, can realize the multiaxis motion control in real time and the sequential logic control. This paper sets out from the hardware structure, use the Real-time trajectory interpolation algorithm, and choose the proper motion-control function. it can realize fast, stable and continuous movement with multistage path, and ensure that the system is open, real-time and reconfigurable.

Curvature-Based Real-Time NURBS Surface Interpolator with Look-Ahead ACC/DEC Control

Real-time parametric surface interpolation is very useful in high-performance machining. A curvature-based NURBS surface interpolator with look-ahead acceleration/deceleration (ACC/DEC) control has been developed. The cutter contact (CC) paths are planned through iso-parametric line method. The CC feedrate profile is optimized using global flexible control strategy and local adaptive ACC/DEC optimization strategy according to the look-ahead algorithm. The real-time surface interpolation algorithm was programmed on Windows XP platform. The stability and efficiency of the proposed interpolation method were verified by a NURBS curve and a NURBS surface. It is shown that the proposed parametric interpolation algorithm can satisfy the high speed and high precision requirements of high-speed CNC systems.

Optimal Interpolation Algorithm Research Based on Quasi-Hermite Space Curve

According to the principle of parametric curve paths CNC interpolating, a real-time interpolation algorithm based on algebraic index of the micro-segment spline is presented. It’s used to solve the problems of Hermite polynomial interpolation algorithm, which are commonly slow recursive algorithm, poor accuracy of approximation and the limitations of constant parameters increment interpolation. And the constant interpolation is achieved by fitting a first-order Taylor Formula. Simulation results show that the algorithm shortens the interpolation time and also improve the interpolation accuracy; meanwhile, it maintains the stability of the feed rate.

Research on Dimensional Variable Groove Cutting Machine of CNC H-Beam Wedge Head

H-beam wedge heads are traditionally cut by manual operation. Considering the complex operation, high labor intensity and poor quality of the manual operation, a dimensional variable groove cutting machine of CNC H-beam wedge head is developed in the research, which concerns mechanical components and numerical systems. The mechanical structure are introduced first, especially gradeless piercing gas line. In the CNC system, based on minimum deviation method, a real-time interpolation algorithm is adopted and successfully applied. The human-computer interface of CNC system is also represented. Some machinable typical work pieces are illustrated also

Spline Real-time Interpolation Algorithm for High-speed Machining

Spline Real-time Interpolation Algorithm for High-speed Machining