Minimum vicinity interpolation algorithms for calculation of trajectory processing for a model of CNC machine tool (original) (raw)
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Direct trajectory interpolation on the surface using an open CNC
The International Journal of Advanced Manufacturing Technology, 2014
Free-form surfaces are used for many industrial applications from aeronautical parts, to molds or biomedical implants. In the common machining process, CAM software generates approximated tool paths because of the limitation induced by the input tool path format of the industrial CNC. Then, during the tool path interpolation, marks on finished surfaces can appear induced by non smooth feedrate planning. Managing the geometry of the tool path as well as the kinematical parameters of the machine tool are two key factors for quality and productivity improvements. The aim of this paper is to present a unified method to compute the trajectory directly on the surface to be machined avoiding CAM approximations and producing a smoother trajectory. This paper proposes an interpolation of the trajectory based on the free form surface mathematical model while considering the kinematical limitations of a high speed milling machine (velocity, acceleration and jerk). The amelioration of the data exchange between CAD/CAM and CNC opens new ways to optimize the manufacturing process. The Direct Trajectory Interpolation on the Surface (DTIS) method allows to obtain both a higher productivity and a better surface quality. Machining experiments carried out with an Open CNC on a 5-axis high speed milling machine show the benefits of the proposed method compared to the classical strategies available with an industrial CNC.
Precision Engineering-journal of The International Societies for Precision Engineering and Nanotechnology, 2019
A computationally efficient FIR-filtering based path-smoothing algorithm which simultaneously realizes vibration avoidance, high accuracy, and short machining time is proposed in this paper. Unlike the case of long G-line blocks where only the adjacent blocks affect the cornering error of a specific corner, more than two blocks affect the error in the case of short-segmented blocks. To satisfy the tolerance error, point-to-point (P2P) technique can be applied, but its machining time will be excessively elongated due to full stops at each corner. Alternatively, motions with the delay times of FIR filters fully-overlapped, which are available on commercially-installed NC systems, can realize short machining time, but they cannot satisfy the tolerance error due to the filtered trajectories accompanies by high speed. Other methods such as spline fitting may satisfy the tolerance error and realize short machining time, but they will allow vibration of the machine tool structure since these motions are not allowed to be filtered for satisfaction of the tolerance. Therefore, no method exists which realizes vibration avoidance, high accuracy, and short machining time all at the same time. For the first time in the literature, a method is proposed which realizes all of the above requirements. The proposed algorithm bases on a kinematic smoothing scheme where no spline-fitting based geometric smoothing is required, and the blended path geometry is only controlled by optimizing the feedrate (speed) profiles along a span of short G01 and G02/G03 moves. FIR filtering is applied to avoid the inertial excitation of the machine tool structure, and a novel "block splitting" method is proposed to keep elongation time of the G-line blocks the minimum. The effectiveness of the proposed method is validated through a series of experiments by comparison with conventional methods.
Accurate interpolation of machining tool-paths based on FIR filtering
Precision Engineering-journal of The International Societies for Precision Engineering and Nanotechnology, 2018
A novel online trajectory generation scheme is developed for motion systems using FIR filters. It enables generation of non-stop contouring motion along machining tool-paths. Both contour errors and frequency spectrum of reference trajectories are controlled. The method is computationally efficient for real-time implementation.
Improvement of toolpath quality combining polynomial interpolation with reduction of toolpath points
The International Journal of Advanced Manufacturing Technology, 2014
The aim of this study is to propose a five-axis toolpath smoothing method in order to improve the quality of machined surfaces. Currently, toolpaths are commonly computed from CAD models presenting small geometrical discontinuities. These discontinuities may be caused by an insufficient quality of the CAD model (geometrical discontinuities) and the use of meshed surfaces (e.g., stereolithography (STL) files). Normally, CAM systems generate linearly interpolated toolpaths. CNC options are then used on the machine to smooth the toolpath. The geometrical discontinuities of CAD models and linear toolpath interpolation may induce an unsmooth toolpath. This type of toolpath causes marks on the machined workpiece even if classical enhanced CNC options are used. Generally, these marks are unacceptable for the functionality of the workpiece. To reduce this problem, this study proposes a method to efficiently smooth toolpaths and consequently improve the obtained surface quality. The proposed method may be employed with high-end controllers commonly used on five-axis CNC machines. First, a five-degree polynomial interpolation method is presented. This interpolation is computed to ensure geometrical continuity in the slope and curvature of the obtained toolpath. Next, a concatenation method is proposed to reduce the size of the CNC program and to improve the toolpath smoothness. Moreover, the purpose of this concatenation is to obtain an optimized repartition of points along the toolpath. Furthermore, in a reverse engineering process, this method avoids surface reconstruction, decreasing the process time and improving the quality of the obtained surface. The efficiency of these methods is validated by the machining of biomedical prostheses. The CAD model used for the test is a meshed surface.
A parametric interpolator with confined chord errors, acceleration and deceleration for NC machining
Computer-aided Design, 2003
Parametric interpolation has many advantages over linear interpolation in machining curves. Real time parametric interpolation research so far has addressed achieving a uniform feed rate, confined chord errors and jerk limited trajectory planning. However, simultaneous consideration of confined chord errors that respect the acceleration and deceleration capabilities of the machine has not been attempted. In this paper, the offline detection of feed rate sensitive corners is proposed. The velocity profile in these zones is planned so that chord errors are satisfied while simultaneously accommodating the machine's acceleration and deceleration limits. Outside the zone of the feed rate sensitive corners, the feed rate is planned using the Taylor approximation. Simulation results indicate that the offline detection of feed rate sensitive corners improves parametric interpolation. For real time interpolation, the parametric curve information can be augmented with the detected feed rate sensitive corners that are stored in 2 £ 2 matrices. q
Development of a CNC interpolation scheme for CNC controller based on Runge-Kutta method
The parametric interpolators of modern CNC machines use Taylor’s series approximation to generate successive parameter values for the calculation of x, y, z coordinates of tool positions. In order to achieve greater accuracy, higher order derivatives are required at every sampling period which complicates the calculation for contours represented by NURBS curve. In addition, this method calculates the chordal error in a given segment through estimation of the curvature neglecting a fraction of the error. In order to avoid calculating higher derivatives and make the calculations simpler, this paper proposes the classical fourth-order Runge-Kutta (RK) method for the determination of successive tool positions requiring the calculation of the first derivatives only. Furthermore, a method of estimating the chordal error on the average value of parameters at the end points of a given curve segment is proposed here that does not require the calculation of curvature at every segment. Finally, a variable feedrate interpolation scheme is designed combining the RK method of parameter calculation and the proposed method of chordal error calculation. Results show that reduced chordal error and feedrate fluctuations are achievable with the proposed interpolator compared to the conventional interpolator based on Taylor’s approximation with higher order terms.
Ideal Selection of Circular Interpolation for CNC Turning Centers
INTERNATIONAL JOURNAL OF DESIGN AND MANUFACTURING TECHNOLOGY
A circular interpolation algorithm used to determine the parameters of separate circular paths was used to generate round shapes on a computer-controlled numeric (CNC) turning machine. It is suggested that this calculation should be included in the CNC lathes ' resident software program. This would decrease the amount of blocks of data required for part of the program. In a single block, a complete circular interpolation cycle for the number of passes could be specified. The suggested algorithm is optimized for minimal machining time and enhanced surface roughness. The programming of the new interpolation scheme, using circular and linear segments, must be applied to the specific part.
Reference-Word Circular Interpolators for CNC Systems
Journal of Engineering for Industry, 1982
Interpolation techniques for CNC manufacturing systems are either of the Reference-Pulse or Reference-Word type. Reference-Pulse interpolators have been discussed in a previous paper [2]. The present paper provides an analysis of a selected number of Reference-Word circular interpolation techniques that are useful in CNC systems. These interpolators function in an on-line iterative mode and generate binary words which are supplied as references to the control loops in Sampled-Data CNC systems. The various methods are evaluated in terms of accuracy, maximum permitted radius, and number of required iterations to complete a circular arc.
CNC Interpolators: Algorithms and Analysis
1993
CAD systems today interpolate general curves by dividing each curve into many straight-line segments which are downloaded to the CNC. Determining the number of lines to be transferred from the CAD to the CNC poses a conflict between the desired precision of the part and the feedrate fidelity. The current method results in severe variations in the feedrate, leading, in turn, to variations in the surface smoothness and a substantial increase in machining time. These problems are caused by the acceleration/deceleration at the ends of each segment. Moreover, the problems are inherent in the CNC interpolator, as is thoroughly discussed in this paper. These problems can be solved by the development of curve interpolation algorithms for CNC. In this paper, a real-time interpolation algorithm for curves presented in their parametric forms is proposed and compared with the existing CAD interpolators. Analysis shows that with this new interpolator, a constant feed is maintained along the cut and the machining time is as expected. In addition, the amount of geometric information transferred from the CAD system to the CNC is reduced by orders of magnitude. Moreover, the contour errors caused by the new interpolator are much smaller than those caused by conventional CAD interpolators.
A locus tracing algorithm for cutter offsetting in CNC machining
Robotics and Computer-Integrated Manufacturing, 2004
This paper presents a new interpolation algorithm for tool motion generation along planar offset curves, an important manufacturing problem in CNC machining. The development of the algorithm is based on a locus tracing concept. The main advantage of the concept is the fact that is applicable not only when an analytic expression of the desired path is available but also in situations where, although the path is geometrically defined, its analytic description is either impossible to compute, or too cumbersome to work with. The presented locus tracing algorithm, uses the locus defining geometric property to generate a succession of points on the desired path (the offset), through repeated application of two analytically implemented construction operations. These operations are formulated on the basis of the direction and proximity criteria introduced by Danielson, which guarantee a locus position error of at most one step. The effectiveness and simplicity of the algorithm is demonstrated by two representative examples. The first example uses an ellipse as the generator curve while the second example treats with a more complex case such is the case of a free-form curve implemented in terms of a Bezier curve.