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In the process of high-speed machining, there are sharp corners at the joint of short lines. The vibration of cutting tools at the sharp corners will be severe, which will reduce the quality of machining surface and machining efficiency. For this problem, impulse response technology is proposed and applied. However, there is inevitable time delay in impulse response technology, which leads to the uncertainty of the maximum contour error of the corner. In order to further generate accurate reference motion trajectories, an accurate interpolation and contouring control algorithm based on FIR filters for the corner transition is proposed in this paper. According to the continuous short lines information in the CNC system, the rectangular velocity pulse signal of the short line is obtained. Initial rectangular velocity pulse is filtered to obtain third-order trajectory. In order to realize the continuous feed motion of short lines, the maximum feed velocity of short lines is constrained. Under the constraint of the maximum velocity limited, the maximum contour error of the corner is controlled by changing the overlapping time, and the accurate mathematical expression of the maximum contour error is reached. By using the FIR filters, the acceleration and jerk curves are generated from velocity pulse profiles. Through the experiment and simulation analysis, the algorithm proposed in this paper can determine the maximum contour error of the corner to realize smooth transition and reduce the machining path time by 7–10%. The proposed algorithm is proposed to achieve G1 continuous acceleration and effectively improve the processing quality. [ABSTRACT FROM AUTHOR]

The five-axis tool path generated by CAM software usually consists of a series of linear paths. The tangent direction at the corner of the adjacent line segment will suddenly change, and the curvature is also discontinuous, which will cause vibration and shock during the machining process. Thus, a global corner smoothing algorithm based on cubic NURBS interpolation is proposed to smooth the linear paths in this paper, so as to achieve G2 continuous for five-axis linear paths. The algorithm proposed does not require matrix operations to solve the control points, and it can also reduce the number of control points while satisfying the interpolation error. The algorithm is then used to generate smooth NURBS path for ceramic core burrs and blockage repair. The simulation and experiment show that the algorithm proposed can satisfy the error constraints, reduce the vibration of the motion axis, and improve the surface quality of laser cutting. [ABSTRACT FROM AUTHOR]

A typical interpolation strategy for line segments consists of a transition scheme, a Look-ahead ACC/DEC scheduling, and an interpolation algorithm. In these three parts, the main computation occurs in the first and second part. Some research work has been carried out to decrease the computation in the previous literatures, but these methods occupy a lot of computing resources for the optimization process during the calculation of transition curve parameters and feed rates. Consequently, the computational efficiency of interpolation strategy is greatly reduced. To deal with the issue, a real-time interpolation strategy is proposed in this paper. In the transition scheme, a Bézier curve is utilized to smooth the line segments. Based on the relationship among the approximation error, the approximation radius, and the transition curve, the curve can be directly generated when the approximation error is given. In the ACC/DEC scheduling, a 3-segment feed rate profile with jerk continuity is constructed. Meanwhile, a Look-ahead planning based on Backward Scanning and Forward Revision (BSFR) algorithm is utilized to eliminate redundant computation. Compared with Zhao’s and Shi’s strategy, the proposed strategy has the merits of C2 and G2 continuity for the tool path, jerk continuity for the tool movement, and distinguished real-time performance for interpolation. The experiments of 3D pentagram and 2D butterfly are carried out with different strategies and their results demonstrate that the interpolation efficiency can be greatly improved with the proposed strategy. [ABSTRACT FROM AUTHOR]

In order to improve the surface quality and dynamics for 5-axis finish machining, new algorithms to construct smooth tool orientation field function are proposed in this paper. Given several surface points and corresponding key tool axes, two methods are studied for open surfaces and half-open surfaces: (a) radial basis function (RBF) interpolation algorithm and (b) RBF-spline approximation algorithm. The two methods can ensure smoothness of all tool axes on the whole surface instead of a single tool path. Finally, several cases are studied to verify algorithms' effectiveness. [ABSTRACT FROM AUTHOR]

To alleviate the feed fluctuation and to maintain a smooth feed in conventional five-axis machining, an optimal feed interpolation algorithm (look-ahead) is proposed. However, the problem arises where the segment usually cannot be interpolated exactly in an integer period because of the nonzero joint feed at the junction. To overcome this problem, and to achieve faster machining speed and higher quality parts, this paper presents an optimal feed interpolation algorithm for high-speed, five-axis machining having the function of “look-ahead”, i.e., variable-period linear interpolation algorithm. In real applications, the proposed algorithm results in: (1) constant speed; (2) high machining accuracy. Moreover, in this paper, an efficient method for acceleration and deceleration control is presented to achieve the highest-quality feed profiles and to shorten machining times. The precision and speed of machining is improved greatly. Experimental results verify the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

Free form surfaces are primarily designed and manufactured by CAD/CAM/CNC system. In traditional way, toolpath generation approaches always consider machining precision and efficiency by constraining scallop height and toolpath lengths. However, toolpath lengths do not exactly reflect the actual machining time because the feedrate usually fluctuates along different toolpath during CNC interpolating period, which indicates that the total machining efficiency is coupled with both toolpath generation and interpolation. Therefore, the toolpath generation and interpolation systems should not be independent, and the conventional unidirectional information flow from CAM to CNC should be replaced by a new mechanism with information exchange and mutual optimization. This paper proposes an inverse evaluation mechanism with feedback information from CNC to CAM system. The feedback information is obtained by off-line interpolation simulation for each toolpath and evaluation of the total machining time for the entire surface. With the feedback information, CAM is able to optimize the toolpath or choose the best one among candidate solutions. As the evaluation mechanism should be under the same interpolation algorithm, an interpolation algorithm with axis kinematic/dynamic constraints is also introduced. The simulation results with different free form surfaces show that the proposed mechanism can economically improve the machining efficiency without increasing system cost. [ABSTRACT FROM AUTHOR]

This paper proposes a novel B-spline interpolation based on CL points preprocessing algorithm and on u- S modeling, aiming to overcome the shortages of linear and circular interpolations. A B-spline toolpath trajectory is generated by fitting a given set of CL points. CL points are preprocessed by chord distance to reduce computation load, thus using fewer feature CL points to generate a B-spline toolpath trajectory. As for disadvantages due to parameter updating for B-spline interpolation, a fifth order polynomial based on u- S modeling is constructed to map the desired curve length S to the corresponding spline parameter u, cutting the real-time computation load. Simulation results are provided to verify the feasibility and effectiveness of the proposed interpolation algorithm. [ABSTRACT FROM AUTHOR]

Speed control is a very important factor to machining quality. In order to get high dynamic performance at the time of the machining speed changing, many kinds of algorithm for the acceleration/deceleration control have been proposed. The techniques which employ polynomial functions or digital convolution to generate velocity profile have been widely used and achieved good performance in motion control system. However, the control cycle of all these methods is one interpolation interval at least, and the velocity jump between two adjacent interpolation intervals during the acceleration/deceleration stage cannot be avoided. In this paper, a hardware fine acceleration/deceleration algorithm inside a single interpolation cycle is proposed to make the velocity change smoothly all the time even inside the interpolation interval. Based on this approach, an acceleration/deceleration fine interpolation circuit is designed with Verilog hardware description language and implemented in field programmable gate array. At last, the algorithm is applied in a three-axes motion controller and achieves a better machining performance than the one without this algorithm. [ABSTRACT FROM AUTHOR]

As a key technique in CNC machining, nonuniform rational B-spline (NURBS) interpolator has been proposed to overcome the drawbacks caused by linear and circular interpolator, such as large data size, velocity discontinuity, shocks or variations in mechanical systems, and low machining efficiency. To improve machining quality and efficiency, an adaptive off-line interpolator was developed for NURBS curves in this paper. Both the chord accuracy and the acceleration/deceleration capability of machine tool are considered in the algorithm. There are four modules in the algorithm, adaptive feed rate adjustment, acceleration/deceleration disposal, feed rate modification, and S-type velocity generation. The acceleration/deceleration around the sharp corners is carefully calculated by those modules. A case study was provided to evaluate the feasibility of the interpolator. [ABSTRACT FROM AUTHOR]

This paper proposes an efficient algorithm to generate tool posture collision-free area for the whole free-form surface during five-axis CNC finishing period. The algorithm is consisted of two phases: sampling and interpolation. In the first phase, a few points are picked on the surface and the admissible area of tool posture is calculated at each point. The admissible area is a two-dimensional figure on the plane. Base on the assumption that the admissible area of adjacent surface points should transform continuously, so in the second phase, the admissible area of the sampling points are interpolated with cubic B-surface interpolation technique, forming an expression as ℚ( u, v), through which when the parameters u and v are assigned, the global collision-free area for the corresponding surface point can be easily calculated. The proposed algorithm is efficient because only a few surface points are needed to get the expression. The proposed algorithm is programmed and tested. Results show that the algorithm is relatively precise and efficient while considering the whole surface. [ABSTRACT FROM AUTHOR]

This paper presents an algorithm for improving the interpolation accuracy in turning operations. The parts considered are formed by revolving a free-form profile which is implemented in terms of Bézier formulation around a center linear axis. The demand for the manufacturing of such geometric shapes is frequently met in parts produced by casting and forging methods. The method employs a computer numerical control (CNC) turning machine and is based on the locus tracing concept. The algorithm described utilizes a real-time CNC interpolator providing the highest possible accuracy of which the turning machine is capable. The whole machining task can be programmed as a canned cycle, essentially extending the feature generating capabilities of the existing G70/G73 CNC turning fixed cycles. [ABSTRACT FROM AUTHOR]

Various methods for parametric interpolation of non-uniform rational B-spline (NURBS) curves have been proposed in the past. However, the errors caused by the approximate nature of the NURBS interpolator were rarely taken into account. This paper proposes an integrated look-ahead algorithm for parametric interpolation along NURBS curves. The algorithm interpolates the sharp corners on the curve with the Pythagorean-hodograph (PH) interpolation. This will minimize the geometric and interpolator approximation errors simultaneously. The algorithm consists of four different modules: a sharp corner detection module, a PH construction module, a feedrate planning module, and a dynamics module. Simulations are performed to show correctness of the proposed algorithm. Experiments on an X- Y table confirm that the developed method improves tracking and contour accuracies significantly compared to previously proposed algorithms. [ABSTRACT FROM AUTHOR]

Modern motion control adopts acceleration/deceleration before interpolation (ADBI) motion planning to eliminate path command errors. However, the individual velocity profiles might not be continuous at the junction of the blocks. Acceleration/deceleration after interpolation (ADAI) method may provide an alternative for solving the discontinuous problems, but it causes path command errors. In this paper, an integrated acceleration/deceleration interpolation (IAD) scheme which integrates the ADBI and ADAI modules is proposed. The ADBI provides a look-ahead function which plans the feedrate profiles based on chord errors, command errors, curvatures, and acceleration limits. Within the look-ahead function, the command error equation is utilized to determine the feedrate at the junction of adjacent blocks. Then the ADBI performs non-uniform rational B-spline (NURBS) interpolation using the planned feedrate profile and outputs the position points to the ADAI module. The ADAI module processes the points by a digital convolution technique such that the continuity of the block junction velocity is ensured. Finally, the IAD is applied to the multi-block NURBS interpolation to validate its effectiveness. Simulations and experiments are conducted to demonstrate the IAD scheme. It is shown that the IAD scheme can reduce the acceleration significantly at the junctions of the blocks under the given tolerance of the command error. Furthermore, the proposed algorithm can improve tracking and contour accuracies as compared to the hybrid multi-blocks look-ahead approach. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

The mechanical digitizers are robust and accurate but they have the disadvantage of not providing the digitized surface directly. Moreover, the information provided is often presented as a cloud of points, which makes the surface interpolation process difficult. Presented in the paper there is an algorithm that virtually reproduces the digitalization process of traditional mechanical copiers. The reconstructed surface is computed from a 'virtually digitised' model of the external cloud of points provided by digitizer. The algorithm is then analysed in terms of computing cost and accuracy. The proposed algorithm has been successfully implemented in a commercial CAD/CAM system specialized in shoe last design and machining. Finally, some illustrative examples are shown. [ABSTRACT FROM AUTHOR]

Continuous micro-line segments having micron magnitude are also used to approach complicated trajectories in computer numerical control (CNC) machining. Traditional linear interpolation processes micro-line segments separately. The rather small lengths of the segments result in low machining efficiency, and the frequent acceleration and deceleration also reduce the lifetime of the motor. To solve the problems, in this paper, we present an interpolation algorithm that is based on the look-ahead function. The look-ahead-based feedrate planning is elaborated from the aspects of trajectory feedrate description, feedrate preplanning, and feedrate planning. With the function of feedrate planning, CNC systems can predict the variation of the curvature of the coming trajectory so that adaptively determining whether accelerates interpolation feedrate to enhance machining efficiency or decelerates the feedrate to guarantee the machining precision. In addition, the trajectory interpolation for micro-line segment trajectories is analyzed as well, which realizes the generalization of the coordinates for each interpolation step. The implementation of the proposed algorithm in our CNC system is also studied. Finally, two machining experiments are provided to verify the accuracy and efficiency of the proposed interpolation algorithm. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

Many factors affect machining quality such as feedrate fluctuations, chord errors, machining time, machine characteristics, and unreasonable planning. Compared with traditional interpolations, parametric interpolations perform better at reducing feedrate fluctuations, chord errors, and it can save interpolation time. Reasonable feedrate planning and dynamic motion control are also necessary for precision improving. In this paper, NURBS interpolation is employed and feedrate is planned on basis of curve geometry and machine dynamic characters. Furthermore, a synthesized control algorithm is applied in control system to refine following accuracy. Simulation and experimental results demonstrate that the proposed approach can significantly reduce the machining error for biaxial following task. [ABSTRACT FROM AUTHOR]

In shoe-last high-speed numerical machining, the key step is to generate CNC machining tool path by data sampled from the shoe last rapidly and accurately. By analyzing the characteristics of helical line and the model of the shoe last expressed in cylindrical-polar coordination system, an algorithm for generating spiral tool path of shoe last with varying pitch was presented. By sample data interpolation, mathematic models with different pitch of helical line were built, and the tool paths with different machining parameters were determined. The effectiveness is verified by the emulation and experimental results represented in the paper. [ABSTRACT FROM AUTHOR]

Parametric interpolation has many advantages over the traditional linear or circular interpolation in computer numerical control (CNC) machining. The existing work in this regard is reported to have achieved constant feedrate, confined chord error and limited acceleration/deceleration in one interpolator. However, the excessive jerk still exists due to abrupt change in acceleration profile, which will cause shock to the machine as well as deteriorate the surface accuracy. In this paper, an adaptive interpolation scheme incorporating machine’s dynamics capability consideration is proposed and illustrated in details. In the proposed algorithm, the commanded feedrate is maintained at most of the time and adaptively reduced in large curvature areas to meet the demand of the machining accuracy requirement, while at the same time, the acceleration and jerk values are limited within the machine’s capabilities during the whole interpolation process. It ensures a high machining accuracy, eliminates the phenomenon of overshoot/undershoot and reduces mechanical shock to the machine tools. The real-time performance of this interpolator is also measured to demonstrate its practical application. Two non-uniform rational B-spline (NURBS) curve interpolation experiments are provided to verify the feasibility and advantages of the proposed scheme. [ABSTRACT FROM AUTHOR]

With the rapid development of the information/image system and aero-space industries, high quality optic aspheric surface lenses play an increasingly important role for completion of the functionalities. Aspheric lenses are non-spherical surfaces having rotation symmetry about the lens axis. The aspheric lens has various shapes according to its application and often requires tens nanometer order form accuracy since surface roughness and form accuracy play essential roles in the functional performance of the optical products. Interpolation of the aspherical surface path must precisely meet the allowable tolerance. Linear interpolation of the aspheric surface path for CNC machining generates an enormous amount of NC code to satisfy the extremely small tolerance, and produces scallops on the machined surface due to the acceleration and deceleration of the tool during every linear motion. Alternatively, interpolations with bi-arcs are used. In this paper, in order to minimize the error induced by the cutting tool path and to shorten the calculation time of interpolation, a precise -arc interpolation method is proposed. The developed algorithm of bi-arc interpolation meets the given tolerance precisely. This is guaranteed by an analytical proof and error maps. Another advantage is its ability to calculate about five times faster than the existing arc interpolation, since iterative calculations for the maximum error can be omitted. The developed algorithm has been used for the precise aspheric machining. [ABSTRACT FROM AUTHOR]

This paper deals with the real-time NURBS interpolation method in which the interpolation error between the ideal curve and the interpolated curve is compensated within the machine basic length unit (BLU). Parametric curve interpolation methods are based on the Taylor series expansion of curve parameters and an approximation. This approach enables effective feed command generation following the target curve. However, the interpolation error caused by the curve segmentation cannot be controlled. In this research, a two-stage interpolation method that compensates for interpolation errors within machine BLU is proposed. The interpolation result was filtered by an acceleration/jerk limitation equation. Through this two-stage interpolation, both the interpolation error condition and the motion dynamics can be satisfied. Using computer simulations in which interpolation results are revaluated by a numerical iteration method, it is shown that the two-stage interpolation algorithm can interpolate target curves precisely with geometric and dynamic contentment. The proposed algorithm was implemented in the CNC simulator system and an experimental run was conducted to identify the real-time adaptation. [ABSTRACT FROM AUTHOR]