A METHOD OF REAL-TIME NURBS INTERPOLATION WITH CONFINED CHORD ERROR FOR CNC SYSTEMS

This paper presents a method of real-time CNC interpolation for free-form NURBS curves. The interpolation algorithm is based on second order Taylor’s expansion with the principle part being a formula for updating the parametric value u after each sampling period. With the updated value of u, a new interpolated point is calculated based on the DeBoor’s algorithm. In this paper, an efficient method of limiting chord error introduced by the interpolation algorithm is also presented with the basic idea of reducing machining feedrate at positions with a radius of curvature smaller than a critical value.

Development of Advanced CNC Interpolation Algorithm With Consideration of Command and Dynamic Errors

In this paper, an integrated acceleration/deceleration with dynamics interpolation scheme is proposed to confine the maximum contour error at the junction of linear junction. The dynamic contour error equation is derived analytically and then it is utilized for the interpolation design. Based on the derived formulations which could predict the command and dynamic errors, the advanced interpolation design could adjust the connecting velocity of the two blocks to confine the overall contour errors under the given tolerance. Simulation results validate the proposed algorithm can achieve higher accurate trajectory as compared to the other interpolation algorithm proposed in the past.

A Generic Approach to Modeling Geometry of Un-Deformed Chip by Mathematical Representing Envelopes of Swept Cutter in Five-Axis CNC Milling

To pursue high performance 5-axis CNC milling in industry, it is crucial to simulate each specific mill process in high fidelity beforehand, which should model the machined surfaces and predict the cutting forces in the process planning. However, the kernel technique, representation of the un-deformed chip geometry removed by cutter in 5-axis milling, is far from mature. Aiming to solve the problem, this paper presents a generic approach to representing un-deformed chip geometry mathematically in 5-axis CNC milling. The unique features of this research are: (1) the machine tool kinematics chain is investigated and a 5-axis CNC interpolation algorithm is adopted to establish the tool kinematics model, and (2) the closed-form equation of the un-deformed chip geometry representation is derived based on the machined shape being the envelope of a group of ellipses. This approach can model a machined surface with high accuracy and efficiently, and can be used to evaluate the machine surface quality and machining parameters. It can greatly promote the technique of high performance 5-axis CNC milling.

Study and Design of Feedrate Scheme in CNC Interpolation

In this paper, the usual feedrate control methods are introduced. The characters of them are analyzed. The shortcomings such as the discontinuity of acceleration and jerk in these methods will influence the accuracy of CNC. In order to overcome the weaknesses, a novel feedrate scheme based on fractional power polynomial is proposed. The constraint condition is discussed. The jerk-time curves, acceleration-time curves feedrate-time curves are contrasted. The simulation result shows that this feedrate scheme can fulfill the requirements of high-speed and high-accuracy through the interpolation process.

Reference Pulse CNC Interpolator Based on Enclosing Line for 2D Parametric Curve

Kertas kajian ini mengemukakan algoritma interpolasi CNC bagi lengkok parametrik umum 2D. Interpolasi yang dikemukakan ini menggunakan teknik rujukan-dedenyut ataupun teknik langkah-tambahan. Algoritma ini berasaskan kepada pencarian secara berterusan garisan-lingkungan yang bersilang dengan lengkok parametrik. Setelah garisan-lingkungan dikenalpasti, kawasan jarak-terdekat digunakan untuk memilih titik interpolasi tanpa melaksanakan pengiraan. Simulasi komputer secara real-time menunjukkan bahawa interpolasi yang dikemukakan ini telah meningkatkan halaju maksimum yang dibenarkan dan pada waktu yang sama mengekalkan kejituan yang tinggi. Kata kunci: interpolator; CNC; rujukan-dedenyut; peralatan mesin This paper proposes an efficient CNC interpolation algorithm for general 2D parametric curves. The proposed interpolator uses reference-pulse or incremental step technique. The algorithm is based upon finding the successive enclosing-lines that the parametric curve intersects. Once the intersected line is identified, the pre-defined closest distance region is used to select the interpolating point without resorting to calculation. Real-time computer simulations indicate that the proposed algorithm increases maximum allowable velocity while still maintaining high precision. Key words: interpolators, computerized numerical control (CNC), reference pulse, machine tools

Design and Implementation of Real-Time CNC Interpolation ASIC for Pythagorean Hodograph Curve Based on FPGA

In this paper, a novel architecture of a real-time CNC interpolation ASIC for Pythagorean Hodograph curve based on FPGA is proposed. The ASIC built on a single FPGA chip contains a NikosⅡprocessor core. It uses a two-stage interpolation scheme to reduce the computational burden of PH curve interpolation. Firstly, the 1st-stage interpolation program is operated on the NikosⅡprocessor. The FPGA hardware logic performs the 2nd-stage interpolation and outputs two groups of pulses for the motion control of actuators (two stepper motors)