For the CNC machining of degree coordinates, generally only linear interpolation or linear interpolation is used. Therefore, we discuss the principle of multi coordinate linear interpolation.
The task of linear interpolation is to calculate the coordinate values of several intermediate points between the starting point and the end point of tool movement according to the requirements of feed speed. Because the time required for the calculation of each intermediate point directly affects the control speed of the CNC system, and the calculation degree of the interpolation intermediate point affects the control accuracy of the whole CNC system, the interpolation algorithm is very important to the performance index of the whole CNC system. For many years, people have been trying to explore a simple and effective linear interpolation algorithm.
At present, in the multi coordinate CNC system, the linear interpolation algorithm with good interpolation performance and widely used is the CNC sampling interpolation algorithm.
The numerical control sampling interpolation algorithm is suitable for closed-loop and semi closed-loop position sampling control systems with DC or AC servo motors as driving devices. Coarse interpolation calculates the coordinate position increment value in each interpolation cycle, while fine interpolation samples the closed-loop and semi closed-loop feedback position increment value and the quality position increment value of the interpolation output in each sampling cycle. Then calculate the corresponding interpolation command position increment value of each coordinate axis. Then calculate the corresponding difference between the command position and the actual feedback position of each coordinate, and compare them to obtain the following error.
According to the obtained follow-up error, the feed speed command of the corresponding axis is calculated and output to the driving device. In use, rough interpolation is generally called interpolation, which is usually realized by software. Fine interpolation can be realized by software or hardware. The interpolation period and the sampling period can be equal or unequal. Usually, the interpolation period can be a positive multiple of the sampling period.
The selection of interpolation cycle of CNC machine tools is related to three aspects: first, operation time; Second, position feedback sampling; Third, accuracy and speed.
Relationship between interpolation cycle and interpolation operation time: once the interpolation algorithm is selected, the maximum number of instructions required to complete the algorithm is also determined. The interpolation period must be greater than the sum of the interpolation operation time and the time required to complete other real-time tasks.
Relationship between interpolation period and position feedback sampling: interpolation period and sampling period can be the same or different. If different, the interpolation period is generally an integral multiple of the sampling period.
Relationship between interpolation period and accuracy and speed: in linear interpolation, each small segment formed by interpolation coincides with the given straight line, which will not cause trajectory error, that is, the interpolation period is independent of interpolation accuracy and tool moving speed.