Least-squares tool path approximation with Pythagorean-hodograph curves for high-speed CNC machining (original) (raw)
Related papers
Least--Squares Tool Path Approximation
Pythagorean{hodograph (PH) curves admit the formulation of real{time CNC interpolators that are extremely accurate, exible, and robust. Motivated by the practical bene ts of these algorithms in high{speed machining applications, we study the approximation of \traditional" (piecewise{linear/circular) G code part programs by PH curve tool paths. A least{squares tting approach, entailing the solution of a non{linear system of equations in four variables, is employed to accomplish this approximation. We discuss both the Newton{Raphson and simulated annealing methods for solving this system. We also address issues of tolerance computation, footpoint parameter re nement, penalization of the objective function by the absolute rotation numbers or bending energies of PH curves, and extension of the tting procedure to 3D tool paths.
Computer-aided Design, 1998
An NC system that machines a curved shape at fixed depth of cut experiences time-varying cutting forces due to the 'curvature effect'-the material removal rate is higher than nominal in concave regions, and lower in convex regions. A curvaturedependent feedrate function that automatically compensates for this effect is formulated, and it is shown that, for Pythagoreanhodograph (PH) curves, the periodic real time computation of reference points in accordance with this function can be analytically reduced to a sequence of root-finding problems for simple monotone functions. Empirical results from an implementation of this variable-feedrate interpolators on an open-architecture CNC milling machine are presented and compared with results from fixed-feedrate interpolators.
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.
2010 International Joint Conference on Computational Cybernetics and Technical Informatics, 2010
This article aims to present two interpolation algorithms (linear and circular) based on minimun vicinity method, developed and tested by the authors, required in the trajectory processing for CNC machine tools.The algorithms for linear and circular interpolation using the minimum vicinity method is part of the algorithms that calculate a function. The points that are chosen are the closest to the calculated circular or linear trajectory. Testing and validation of algorithms has been achieved by implementing a model of machine tool using a computing system that consists of a PC/104 computer type, a data acquisition system and control ADA1100 and for the model of machine tool was used an X-Y recorder.
The International Journal of Advanced Manufacturing Technology, 2018
The feedrate scheduling of parametric interpolator is one of the most important factors for a high-performance CNC machining, since it directly concerns the machining efficiency, machining accuracy, and cutting stability. In this paper, an adaptive feedrate scheduling method with limited contour error and axis jerks is proposed for free-form contour machining based on a strategy of moving knot sequence. The analytical relations between dynamic contour error and feedrate are first derived explicitly, and then the formula of maximum feedrate limit under confined contour error and axis jerks is yielded using a numerical decoupling scheme. Consequently, the maximum feedrate limit satisfying the above constraints is obtained for each predefined parametric segment of the tool path. Further, a bidirectional scanning algorithm is employed to globally adjust the local minimum feedrate values of all feedrate segments. On the basis of feedrate segments with local minimum value and maximum recommendation value, an exact knot sequence configuration method for the B-spline curve, which is used to express the initial feedrate profile, is proposed. Finally, a simple feedrate relaxation algorithm is performed to generate the final feedrate profile with entirely limited contour and axis jerks by utilizing a strategy of moving knot sequence. The proposed feedrate scheduling method is validated by several typical experimental tests, and the results demonstrate the effectiveness and reliability of the proposed method.
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.
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
A new format for 5-axis tool path computation, using Bspline curves
Computer-Aided Design, 2004
This article presents a new format of tool path polynomial interpolation in 5-axis machining. The linear interpolation usually used produces tangency discontinuities along the tool path, sources of decelerations of the machine tool whereas polynomial interpolation reduces the appearance of such discontinuities. The new format involves a faster tool path and a better surface quality. However, it imposes a modification of the process so as to take the interpolation format and the inverse kinematics transformation (necessary to 5-axis machining) into account. This article deals with the geometrical problem of tool path calculation. Validation tests are detailed. They show that profits concern the reduction of machining time as well as the quality of the machined surfaces. Indeed, the trajectory continuity avoids the appearance of marks and facets. q
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.