Research On High-speed And High-precision NURBS Curve Interpolation Algorithm And Construction Of Motion Platform

In the trend of industrial production gradually moving towards high-end intelligence,high-speed and high-precision are the direction of machine tool technology development and the goals pursued by manufacturers.The Non Uniform Rational B-spline(NURBS)interpolation has the advantages of high accuracy,fast acceleration,and the ability to process complex curves and surfaces,making it a representative of high-tech CNC systems.Further improving the interpolation function of NURBS is an effective means to promote the development of CNC machine tools towards high-speed and high-precision.Therefore,this article studies NURBS interpolation technology to improve and implement the calculation of interpolation parameters and feed rates scheduling scheme of NURBS interpolation,which improve the efficiency and accuracy of interpolation.The main research content is as follows:(1)In order to solve insufficient accuracy of the method of second-order Taylor and differential equation in the calculation of NURBS curve interpolation parameters,and the complexity of traditional Newton’s method in correction calculation,the correction method without derivation is proposed to calculate the interpolation parameters.The effectiveness of the proposed algorithm is verified by simulation.The results show that the proposed method can improve the interpolation accuracy by up to 10~4 times compared to other methods without significantly increasing the calculation time.(2)In response to the problem of S-shaped feed rates scheduling scheme not being able to continuously satisfy constraints while maintaining maximum machining efficiency,this paper analyzes the advantages and disadvantages of cubic and quartic S-shaped profiles and proposes a feed rates scheduling scheme that couples cubic and quartic S-shaped profiles.Firstly,determine the slope of jerk of quartic S-shaped profiles to ensure that the feed rates meet the constraints.Then,use the iterative method to find the optimal processing time allocation between the cubic and quartic S-shaped profiles to achieve a balance between processing accuracy and efficiency.Finally,the solution method for obtaining the new maximum feed rates under feed rate interference was discussed in a classified manner.Simulation and experiments by motion platform have shown that compared to other methods,the processing time,running time,and acceleration distance required for the machine tools have been reduced by39.48%,118.34%,and 101%,respectively,which verify the effectiveness and efficiency of the proposed method.(3)To enhance the application value of the proposed method,we independently build a physical motion platform and construct a controller for the proposed feed rates scheduling scheme.The platform uses STM32 as the main control chip,stepper motor and ball screw as the feed system,grating ruler as the position measurement,FPGA to process the input displacement signal for subdivision,sensing and counting,and BP neural network is used to adjust the parameters of PID controller in real time,so that it can adjust the position as far as possible according to the given feed rates scheduling scheme in the movement.Finally,the constructed controller was validated through simulation,and the results showed that compared to the traditional PID method,there was almost no overshoot and fewer vibrations.