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Interpolation principle of numerical control

interpolation principle: in actual machining, the connotation of environment and conditions changes significantly. The contour shapes of the machined workpiece vary greatly. Strictly speaking, in order to meet the requirements of geometric dimension accuracy, the tool center path should be accurately generated according to the contour shape of the workpiece. It can be easily realized for simple curve CNC systems, but for more complex shapes, If directly generated, the algorithm will become very complex, and the workload of the computer will be greatly increased. Therefore, in practical applications, a small segment of straight line or arc is often used for fitting to meet the accuracy requirements (there are also cases where parabola and high-order curve fitting are required). This fitting method is "interpolation", which is essentially a process of data encryption. The task of interpolation is to calculate the coordinate values of several intermediate points between the starting point and the end point of the contour according to the requirements of the feed speed. The time required for the calculation of each intermediate point directly affects the control speed of the system, and the calculation accuracy of the coordinate values of the interpolation intermediate points affects the control accuracy of the CNC system. Therefore, the interpolation algorithm is the core of the control of the entire CNC system. After decades of development, interpolation algorithms have become more and more mature, and there are many kinds of interpolation algorithms. Generally speaking, according to the generated mathematical model, there are mainly linear interpolation, conic interpolation, etc; From the numerical form of interpolation calculation output, there are mainly pulse incremental interpolation (also known as reference pulse interpolation) and data sampling interpolation [26]. Pulse incremental interpolation and data sampling interpolation have their own characteristics. According to different applications, this paper issued pulse incremental interpolation and data sampling interpolation in the cooperation with Chery automobile

1. Digital integral interpolation is a kind of pulse increment interpolation. The following will first explain the working principle of pulse incremental interpolation. 2. pulse incremental interpolation is stroke scalar interpolation. Each interpolation end generates a stroke increment, which is output in the form of pulse. This interpolation algorithm is mainly used in open-loop CNC system. In the process of interpolation calculation, coordinated feed pulses are continuously sent to each coordinate axis to drive the motor. The amount of axis movement produced by a pulse is called pulse equivalent. Pulse equivalent is the basic unit of pulse distribution. It is selected according to the machining accuracy designed by the machine tool. Generally, the pulse equivalent is taken as 0.01mm for machine tools with ordinary accuracy, and 1 or 0.5 for more precise machine tools. In the numerical control system with pulse incremental interpolation algorithm, the feed speed of the coordinate axis is mainly limited by the running time of the interpolation program, which is generally 1~3m/min. Pulse incremental interpolation mainly includes point by point comparison method, data integral interpolation method, etc. The point by point comparison method was originally called the region discrimination method, or the algebraic operation method, or the drunken step approximation method. The principle of this method is: in the process of controlling machining, the computer can calculate and judge the machining deviation point by point, control the coordinate feeding, and process the required workpiece according to the specified graphics. The machine tool is dragged by a stepping motor or an electro-hydraulic pulse motor. The feeding mode is stepping, and the machine tool is controlled by an interpolator. The point by point comparison method can realize both linear interpolation and circular interpolation. It is characterized by intuitive operation, interpolation error less than one pulse equivalent, uniform output pulse, small speed change and convenient adjustment. Therefore, it is widely used in two coordinate open-loop CNC systems. However, this method can not realize multi axis linkage, and its application range is greatly limited

interpolation principle of digital integration method: as mentioned earlier, digital integration method interpolation is a kind of pulse incremental interpolation. It uses the digital integration method 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). The digital integrator 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 CNC systems, So DDA Interpolation is a widely used interpolation method at present. The integrand function register is used to store the coordinate value f (T), and the accumulator, also known as remainder memory, is used to store the accumulated value of the coordinate. 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, there will be overflow for every unit area accumulator in the accumulation process. When the accumulation times reach the capacity of the accumulator, The total number of spills generated is the total area required, i.e. the integral value

we know that the frequency of the overflow pulse of the digital integrator is proportional to the number of memories in the integrand function register, i.e. the overflow base value. That is, each program segment has to complete the same number of accumulation operations. Therefore, the time spent in each program segment is fixed regardless of the length of the processing stroke. Therefore, the feed speed of each program segment is inconsistent, which affects the surface quality of machining, 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 higher, the left shift normalization is usually used. The so-called "left shift normalization" means that when the value of the integrand function is small, for example, there are I first zeros in the integrand function register, if the integrand function 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" of the integrand function. After left shift normalization, the integrator will overflow once every two accumulations, so it not only improves the overflow speed, but also makes the overflow pulse more uniform. At present, 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 the software digital integration, we can easily set a base value. After the addition of the integrand function value and the accumulated value is completed, the accumulated result is compared with the base value. Through the comparison instruction, we can judge which coordinate axis direction there is a pulse and our plastic matrix is a renewable biopolymer output

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