Most popular digital integral interpolation

2022-08-08
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Digital integration interpolation

digital integration interpolation is a kind of pulse incremental interpolation. It uses the method of digital integration to calculate the movement of the tool along each coordinate axis, so as to make the tool move along the set curve. The device that realizes digital integral interpolation calculation is called digital integrator, or digital differential analyzer (DDA), which can be realized by software. The digital integrator has fast operation speed, uniform pulse distribution, can realize the interpolation of primary and quadratic curves and various function operations, and is easy to realize multi coordinate linkage. However, the traditional DDA Interpolation method also has the disadvantages of inconvenient speed adjustment, and the interpolation accuracy needs to take certain measures to meet the requirements. However, the above shortcomings can be easily overcome when the software is used to realize DDA Interpolation in the CNC system at present, Therefore, DDA Interpolation is a widely used interpolation method at present. Its basic principle can be changed by the bone screw shown in Figure 4.1. The host of the experimental machine adopts the function integral representation of the new measurement and control system independently developed by our company. From the concept of differential geometry, when calculating the area surrounded by the function y=f (T) curve from time 0 to time t, the integral formula can be used:

(1)

if the time from 0 to t is divided into time intervals of Δ The finite interval of T, when Δ When t is small enough, an approximate formula can be obtained:

(2)

in the formula, yi-1 is the value of F (T) when t=ti-1. This formula explains that the integral can be approximately replaced by the accumulation of numbers, and its geometric meaning is to use the sum of a series of small rectangular areas to approximately represent the area product under the function f (T).

if in numerical operation, use Δ T is the basic unit "1", then equation (2) can be simplified as:

(3)

if the basic unit of the system Δ If t is set small enough, it can meet the accuracy we need

generally, each coordinate direction requires an integrand function register and an accumulator, and its working process can be shown in Figure 4.2:

the integrand function register is used to store the coordinate value f (T), and the accumulator, also known as the remainder register, is used to store the accumulated value of the coordinates used in more convenient scenarios. whenever Δ Once t occurs, the value of F (T) in the integrand function register is added to the value in the accumulator once, and the accumulation result is stored in the accumulator. If the capacity of the accumulator is a unit area, and the capacity of the integrand function register is the same as that of the accumulator, then there will be overflow for every more unit area accumulator in the accumulation process. When the accumulation times reach the capacity of the accumulator, The total amount of overflow generated is the total area required, that is, the integral value

we know that 2. Pressure testing machine, the frequency of overflow pulse of digital integrator is directly proportional to the number of memories in the integrand register, that is, the overflow base value, that is, each program segment should complete the same number of accumulation operations, so the time used by each program segment is fixed regardless of the length of processing stroke. Therefore, the feed speed of each program segment is inconsistent, which affects the surface quality of the data to be processed, especially the low productivity of the program segment with short stroke. In order to overcome this shortcoming and make the overflow pulse uniform and the overflow speed improve, the left shift normalization is usually used. The so-called "left shift normalization" is that when the value of the integrand is small, such as there are I first zeros in the integrand function register, if it is iterated directly, it needs at least 2I iterations to output an overflow pulse, resulting in a decrease in the output pulse rate. Therefore, in the actual digital integrator, it is necessary to remove the first zero in the integrand function register, that is, to realize the "left shift normalization" processing of the integrand function. After left shift normalization, the integrator will overflow every two times, so it not only improves the overflow speed, but also makes the overflow pulse more uniform

current CNC systems generally use software to realize digital integration interpolation [27], so that the concept of left shift normalization of hardware digital integration and the concept of feed pulse due to carry can be completely abandoned. Because in software digital integration, we can easily set a base value. After completing the addition operation of the integrand value and the accumulated value, we can compare the accumulated result with the base value, and judge which coordinate axis direction there is pulse output through the comparison instruction

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