Real-time Interpolation Research Articles

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.

Development of a STEP-NC Controller for 5-Axis Machining of NURBS Surfaces

In conventional machining of free form surfaces, incomplete information exchange between CNC and CAD/CAM results in many limitations need to be rectified. In the paper, a new structure of CNC based on STEP-NC is proposed. A 5-axis real-time interpolator for NURBS surfaces machining is realized. A STEP-NC controller has been developed, which is a software modular CNC system. The CNC system has been installed on a tilt-rotary type 5-axis machine tool. The milling experiment has been performed.

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

High speed interpolation for micro-line trajectory and adaptive real-time look-ahead scheme in CNC machining

CNC machining plays an important role in mechanical manufacturing. A key issue is to improve the machining feedrate while keeping the machining precision and satisfying the acceleration constraints of the CNC machine. For the consecutive micro-line segments interpolation, the velocities at the junction of two segments are the bottlenecks for the machining efficiency. This paper proposes a multi-period turning method to improve the feedrate at the junctions using the linear acceleration and deceleration mode, which utilizes the maximal acceleration capabilities of the NC machine while satisfying the machining precision. A new and more efficient look-ahead method and a feedrate override method are also proposed to boast the global machining speed. The proposed algorithm has been implemented on Blue Sky NC System, and experimented in real material manufacturing. Compared with several existing algorithms, the current algorithm can improve the manufacturing time ranging from 50% to 180%, depending on the machining parameters, and also results in better machining quality. In addition, the algorithm also satisfies the need of real-time interpolation.

5-axis Interpolation and Synchronous Servo Process with NURBS Method

Abstract Nowadays, NURBS (Non-Uniform Rational B-Spline) method is widely used in CAD/CAM (Computer-Aided Design/Computer-Aided Manufacturing) to represent sculptured curves or surfaces. In this paper, we develop a 5-axis NURBS real-time interpolator and realize it in our developing CNC(Computer Numerical Control) system. At first, we use two NURBS curves to represent tool-tip and tool-axis path respectively. According to feedrate and Taylor series extension, servo-controlling signals of 5 axes are obtained for each interpolating cycle. Then, generation procedure of NC(Numerical Control) code with the presented method is introduced and the method how to integrate the interpolator into our developing CNC system is given. And also, the servo-controlling structure of the CNC system is introduced. Through the illustration, it has been indicated that the proposed method can enhance the machining accuracy and the spline interpolator is feasible for 5-axis CNC system.

A new adaptive interpolation scheme of NURBS based on axis dynamics

A new interpolation scheme for 2D NURBS curve is proposed in this paper. The scheme contains two steps, pre-processing and real-time interpolation, which are bridged by circular buffer and table look-up method in order to improve the data utilization and simplify the calculation process. The pre-processing divides the curve into segments by dangerous points, then real-time interpolation is implemented within the segment unit. During this process, adaptive interpolation algorithm adjusts the feed rate according to the curvature which guarantees the contour accuracy; meanwhile, the axis dynamics module confines the dynamics parameters of every axis within limits, without requiring look-ahead and backtracking strategy. At the end, experiments verify the high efficiency and reliability of the algorithm.

Wind speed interpolation in the vicinity of the Panama Canal

AbstractA simplified boundary layer (SBL) model formulation is tested against the mesoscale meteorological model MM5 with respect to the 2 km interpolation of hourly surface wind station data for stations in the close vicinity of the Panama Canal. The required short computation time for the real time interpolation of the wind during air pollution incidents involving crossing cargo ships makes the use of simplified wind models an alternative to the full implementation of mesoscale models. The SBL model does take into consideration the land cover of the ground surface, which exhibits substantial variability in the study region. The SBL model produces features of wind speed that are similar to those of the MM5 simulation along the better‐observed Canal centreline. The presence of orographic features makes the applicability of the simplified formulation reasonable only near the Canal where the terrain has small undulations. The simulated wind fields show that the dry season (January to April) is more spatially and temporally coherent than the wet season and that it also has higher wind speeds than the wet season. The evening hours have higher wind speeds than the morning hours in both seasons. The simulated wind exhibits higher average wind speeds and higher frequencies of exceeding 5 m s−1 within the Gatun Lake on the Caribbean side of the Isthmus and the entrance/exit of the Canal on the Caribbean and Pacific coasts. These results are useful for the development of effective disaster mitigation strategies for air pollution events in the region. Copyright © 2011 Royal Meteorological Society

Spline Real-time Interpolation Algorithm for High-speed Machining

Spline Real-time Interpolation Algorithm for High-speed Machining

Optimal-Feedrate Interpolation for Machining Parametric Curves

Abstract In high-speed precision machining systems, trajectory requires very small feedrate fluctuation and contour error, which can be achieved with pazametric interpolation. This paper proposes aspeed-controlled interpolation method based on optimal-feedrate algorithm. The real-time interpolation method was taken full its advantages, the chord error and the difference between the orientation of tangent vector of the curve at current point and previous point were repeatedly checked through the whole interpolation process. If either chord error exceeded the prescribed tolerance or sharp corner was detected, the feedrate in the proposed interpolation method was automatically adjusted in order to confine the chord error within the prescribed tolerance. A parametric curve, determined by the non-uniform rational B-spline (NiJRBS), was employed to test the feasibility and precision of the proposed interpolation method.

Real-Time B-Spline Interpolator with Look-Ahead Scheme for High-Speed CNC Machine Tools

NC tool paths of digital CAD models are currently generated as a set of discrete data points. The CNC interpolator must convert these points into continuous machine tool axis motions. In order to achieve high-speed and high-accuracy machining, the development of a real-time interpolation algorithm is really indispensable, which can deal with a large number of short blocks and still maintain smooth interpolation with an optimal speed. In this paper, a real-time local cubic B-spline interpolator with look-ahead scheme is proposed for consecutive micro-line blocks interpolation. First, the consecutive micro-line blocks that satisfy the bi-chord error constraints are fitted into a C1 continuous cubic B-spline curve. Second, machining dynamics and tool path contour constrains are taken into consideration. Third, local cubic B-spline interpolator with an optimal look-ahead scheme is proposed to generate the optimal speed profile. Simulation and experiment are performed in real-time environment to verify the effectiveness of the proposed method. Compared with the conventional interpolation algorithm, the proposed algorithm reduces the machining time by 70%.

Real-time NURBS curve interpolator based on section

Parameter interpolation is more capable of modern computer numerical control (CNC) than traditional linear/circular interpolation with higher speed and higher precision. Most of non-uniform rational B-spline (NURBS) interpolation algorithms were developed based on the chord error and machines capability, where interpolation points are calculated beforehand to overcome acceleration/deceleration (acc/dec) and jerk problem, which needs large memory. In this paper, a NURBS interpolator based on feedrate section is proposed. Instead of a single interpolation point, this interpolator aims to feedrate section, which makes it possible to run on a digital signal processor or field programmable gate array (FPGA) whose memory is limited. Experiment on FPGA showed the performance of interpolation. A mould experiment verifies the feasibility of application.

A real-time high-precision interpolation algorithm for general-typed parametric curves in CNC machine tools

The machining accuracy of computer numerical control (CNC) machine tools largely depends on the interpolation algorithms implemented. In this paper, a real-time high-precision interpolation algorithm for a general-typed parametric curve is proposed. As with other time-partition interpolation algorithms, the linear motion trajectory (employed to approximate the real trajectory) in a sampling cycle is determined from the current position of the tool to another point (target point) on the target trajectory. To determine the target point in a sampling cycle, a neighbourhood interval containing the point is first determined, the target point is then iteratively approached by means of the bi-section or secant method for equation resolutions. Simulation results show that the order of magnitude of the maximum feedrate relative errors (the relative deviation of the computed feedrate from the desired one) is −8 or less, while the order of magnitude of the maximum chord errors in the unit of meter is −6 or less. The performance indices can be further improved with more computation iteration in each sampling cycle. The algorithm is general, and applicable to any smooth curve that can be formulated in parametric equations.

Research on Reconstruction and Recursion Interpolation of Curve with High-speed and High-precision

Aiming at low recursion-rate and poor approximation accuracy of polynomial-basis Hermite curve, which is commonly used in real-time interpolation of middle and top grade computer numerical control(CNC), a new kind of splines based on algebraic-exponential space, which takes full advantage of high recursion-rate and convergence-rate of exponential function e–t, is reconstructed. The experiment shows that the recursion rate of new curve is 1.7～2.1 times that of Hermite curve, and at the same time, the approximation precision is improved by one order of magnitude. The result indicates that the interpolation-algorithm based on new curve not only promotes machining precision of profile, but also improves machining efficiency simultaneously, thereby meeting the construction requirement of spline curve in middle and top grade CNC.

An adaptive parametric interpolator for trajectory planning

A real-time interpolation algorithm for trajectory planning is studied in this paper. The NURBS interpolation algorithm is proposed to confine contour errors and feedrate fluctuations. The feedrate is adjusted adaptively according to the specified acceleration/deceleration values and jerk value. A direct digital convolution method is also introduced into velocity planning for NURBS interpolator, and it is more efficient than the traditional method of polynomial functions. The feedrate at the sharp corner is smoothed by imposing limitations on the acceleration and jerk values generated in the machining process. Since the computation of the total length of NURBS curve is required for the digital convolution method, a numerical adaptive quadrature algorithm is used to approximate the integrand. Simulation results demonstrate the effectiveness of the proposed interpolator for machining curved paths.

On the Modeling and Analysis of an Improved CNC Interpolation Algorithm

An improved interpolation method is presented based on B-spline curve back calculation which regards data points as control points. First, a B-spline surface reconstruction is done, and a favorable condition for real-time interpolation can be provided for NC machining. Then, by prejudging the trajectory feedrate, the tangent vectors of spline curve junction can be calculated, which can be used to establish the spline curve equations based on time. At last, with the equations mentioned above, the trajectory and feedrate profile can be generated simultaneously by the improved interpolation algorithm. An error analysis is also discussed and the feasibility of the improved algorithm is verified by the simulation results.

Real-Time NURBS Interpolator with an Optimal Feed for High-Speed Machining

NURBS interpolation has many advantages over the traditional linear or circular interpolation in high-speed machining. The existing work in this regard focuses on adaptive feed interpolation considering the chord error constraints and tangent acceleration limits. However, regardless of the dynamic characteristics of individual axis, performance will inevitably suffer when the system is called upon to execute a complex trajectory beyond the range of its capabilities. The intent of the present work is to provide an optimal feed interpolation method respecting both the chord error constraint and the drive constraint of each axis. A look-ahead scheme is applied with a moving window to augment the calculation efficiency for real-time application. Simulations are performed to verify the resulting feedrate, acc/dec profiles and the real-time performance of the proposed interpolator.

An improved image interpolation algorithm

The paper sets forth an improved edge-directed image interpolation algorithm with low time complexity which is the combination of Newton's method and edge-directed method. It first partitions images into homogeneous areas and edge areas by setting a preset threshold value based on the local structure characteristics, and then specified algorithms are assigned to interpolate each classified areas, respectively. In this way, it achieves the goals of real-time interpolation and good subjective quality. The interpolated images have higher peak signal noise ratios (PSNR) and better visual effects using proposed method than that of using other algorithms referred to in this paper. Experimental results show that proposed method is highly performed in image interpolation.

Adaptive Prospective Interpolation Method for High Speed Machining of Micro Line Blocks Based on the Cubic Polynomial Model

An adaptive prospective interpolation method for high speed machining of micro line blocks, including interpolation preprocess and real time parametric interpolation, is proposed, which is based on the cubic polynomial model. During interpolation preprocess, the high speed adaptive prospective control strategy is established by using path transfer point maximum velocity confirming, adaptive predetermination of deceleration point position and stride segment transfer point speed checking. During real time interpolation, stride multi-path parametric interpolation algorithm is set up based on the cubic polynomial acceleration and deceleration control model. The results demonstrate the proposed method realizes high speed machining of consecutive micro line blocks and determination of deceleration point position in advance. The method achieves high speed machining and the productivity is improved significantly. It has been applied in multi-axis high speed micro machining system successfully.

Real-Time Interpolator and Contour Tracking in Link-Space for a 3 DOF Parallel Mechanism

Parallel mechanisms could be hardly used in contour tracking because of their mechanism features. This study proposed a link-space real time contour tracking for a 3 DOF (Z、α and β) hydraulic parallel mechanism. The essence of this approach is to convert control points of command trajectory to link space by inverse kinematics. A real-time interpolator was created and the multi-axis cross-coupled pre-compensation control (MCCPM) was constructed for link-space contour tracking. It was shown that a contour-accurate trajectory tracking could be performed which was impossible in the original Z-α-β space. Other advantages of this link-space approach were time efficiency and the uniform tracking velocity.

NURBS curve interpolation algorithm adaptive to the machine's kinetic characteristics

NURBS curve interpolation algorithm for high speed NC machining, which can fit diverse machine tool's kinetic characteristics and has the function of look-ahead control, is proposed. By integrating curve geometry features and machine tool dynamic characteristics, the look-ahead control information can be obtained. The interpolating process can be divided into two phases: getting the look-ahead control information including the particular points in the curve and their suitable max feed rate, modifying the real-time interpolation feed rate all the time according to the look-ahead control information. This algorithm has advantages over others on three aspects: wide adaptation to machine tool, high profile precision, and small feed rate vibration.