Research On Key Technologies Of High-Quality Machining Based On Spline Interpolation

Along with the universal application of spline interpolation high-speed and high-accuracy machining have become the new requests in modern manufacturing fields. In some high-end commercial CNC systems, the spline interpolators could fit the data points into many parametric curves. Compared with conventional linear and circular interpolation, spline interpolation could reduce the transfer load between CAD/CAM and CNC, improve processing quality by avoiding the acceleration discontinuity and excessive jerk in high-speed machining. However, developed countries of the west have limited technological information and access of spline interpolation within our country. Consequently, research on the key techniques of spline interpolation has great theoretical and practical significance to improve and advance our national high-end CNC technology.Based on the theories of spline interpolation and velocity planning, in connection with the problem of high-speed, high-accuracy and high-quality machining, the research presented in this dissertation is focused mainly on the key techniques in spline interpolation: spline fitting, real-time interpolation and velocity scheduling.(1) Spline curve fitting conditions and methods. In order to improve the processing speed and quality of tabulated curve, this paper presents an Akima interpolation method to fit the continuous data point into smooth spline curve. This research mainly studies the fitting criteria and method of Akima curve. And the bi-chord error test and the tangent-chord error test are adopted to identify those continuous Akima blocks, then the five-point Akima method is applied to fit the continuous data points into spline curve. Simulations and experiments show that the Akima interpolation algorithm could make the processing path more continuous and improve processing accuracy. Moreover, the mathematical calculation of Akima curve is relatively time-saving, so the Akima interpolation algorithm could improve the processing efficiency and quality of tabulated curve.(2) Real-time spline interpolation technique based on approaching chord. To solve the problem of feedrate fluctuation of widely-used Taylor series expansion methods in real-time interpolation, this paper presents the strategy of actual chord approaching theoretical chord. And the Newton iteration method, secant method, and parabola interpolation combined with Newton iteration method are respectively adopted to calculate the parameters in real-time. The experiment results dominate that the proposed algorithm has advanced features of excellent stability and high precision. And the proposed algorithm can meet with the real-time interpolation requirements and reduce the feedrate fluctuation to idea level.(3) Flexible acceleration and deceleration control algorithms. By analyzing widely used speed scheduling algorithm in CNC machining, aiming at the CNC machine tool’s vibration due to unsmoothed velocity,acceleration and jerk during high-speed machining, this paper proposes a quartic polynomial speed control method and a linear-trigonometric velocity scheduling method. Both of the two methods could realize continuous change of jerk. And the research also simplifies the widely-used five-stage S-curve method, cubic polynomial method and trigonometric method. Simulation and experimental results shows the proposed quartic polynomial speed control method and linear-trigonometric velocity scheduling method could achieve flexible acceleration and deceleration control and realize high-quality CNC processing.(4) Spline interpolation algorithm based on look-ahead interpolation. To improve the real-time nature during velocity scheduling, this paper presents two spline interpolation methods based on look-ahead process. For tabulated curve, a real-time look-ahead interpolation algorithm based on Akima curve fitting is proposed, which could guarantee the processing accuracy by look-ahead interpolation. For the process of parametric curves like NURBS curve and B-spline curve, this paper presents a velocity scheduling algorithm based on two-time look-ahead interpolation. And the method considers the constraints of chord error, acceleration and jerk. Simulation and experimental tests demonstrate two methods could relieve intense vibration in high-speed machining, and could be used in high-quality CNC processing.The paper mainly focuses on key techniques in improving the processing quality of spline interpolation. For the process of tabulated curve, this paper proposes the fitting criteria and fitting method of Akima curve, and realizes a look-ahead interpolation algorithm based on Akima curve fitting. The strategy of actual chord approaching theoretical chord is presented in real-time interpolation part. And the Newton iteration method, secant method, and parabola interpolation combined with Newton method are adopted to calculate the parameters in their respective fields. Then three widely-used velocity scheduling methods are simplified in the research. Moreover, this paper presents quartic polynomial and linear-trigonometric velocity method, which could realize continuous change of velocity, acceleration and jerk at the same time. Finally, this paper proposes a velocity scheduling algorithm based on two-time look-ahead interpolation. Simulation and experimental tests demonstrate the effectiveness of the proposed algorithms.