Briefly introduce the interpolation method of Shenyang CNC machine tools

The early CNC machine tool numerical control system used digital pulse multiplier interpolation method. After years of development, the interpolation principle has matured, and there are many types of interpolation methods. From the generated digital model, there are one (straight line) interpolation, quadratic (circle, parabola, etc.) interpolation and high-order curve interpolation; from the basic principles and calculation methods adopted, it is divided into regions. A point-by-point comparison interpolation that is characterized as a feature, a digital pulse multiplier interpolation characterized by proportional multiplication, a digital integral interpolation with a digital integral method, and a vector-based interpolation based on vector operation, at a speed The operation-based time division method, the comparative integral method interpolation with point-by-point comparison and digital integral features, and the extended integral method interpolation, and the like. At present, the most widely used interpolation algorithms can be divided into two categories: pulse incremental interpolation and data sampling interpolation.

(1) Pulse incremental interpolation

The interpolation algorithm is characterized in that only one stroke increment is generated at the end of each interpolation, and is outputted in a pulse manner. During the machining process, the numerical control device continuously outputs a reference pulse sequence to each motion coordinate, thereby making each coordinate The shaft is displaced accordingly. Each pulse represents the minimum displacement, so the number of pulse sequences determines the amount of displacement of the coordinate axes, and the frequency of the pulse sequence determines the speed of motion of the axes. The implementation of pulse-quantity interpolation is relatively simple. Usually, interpolation can be performed only by addition and shifting. Therefore, it is easier to implement in hardware, and the speed of performing such operations with hardware circuits is fast. Software is currently used to perform such algorithms, but only for some medium-precision (0.01mm) or medium-speed (1~3m/min) CNC systems.

(2) Data sampling interpolation

The feature of this type of interpolation algorithm is that the interpolation operation is completed in two steps. The first step is coarse interpolation, which inserts several points between the start and end points of a given curve, and uses several small straight line segments to approximate a given curve. The length L of each tiny straight line segment is equal, and Given the feed rate. The coarse interpolation is calculated once in each interpolation operation cycle, so the length L of each tiny straight line segment is related to the feed rate F and the interpolation period T, that is, L = FT. The characteristic of the coarse interpolation is given A curve is approximated by a set of straight segments. The second step is fine interpolation. It is the “densification of data points” on each tiny straight line segment calculated by the coarse interpolation. This step is equivalent to the pulse incremental interpolation of the straight line.

The data sampling interpolation method is suitable for the position control system of the closed loop and semi-closed loop with the direct and AC servo motor as the driving device. The coarse interpolation calculates the actual position increment of the coordinate in each interpolation cycle, and the fine interpolation corrects the position increment value fed back to the closed loop or semi-closed loop control system and the command position of the interpolation output in each sampling period. The incremental value is sampled. Then calculate the corresponding interpolation command position and actual feedback position of the coordinate axis, and compare the two to obtain the following error. The feedrate of the corresponding axis is calculated from the following error and drives the machine tool movement. In the CNC system, the general coarse interpolation methods are: linear function method, extended digital integration method, double digital integral interpolation method, and the like.