Fast Real-time Interpolation of Parametric Surfaces

I. Off-line interpolation of CNC system In the CNC system, the traditional off-line interpolation method must first be modeled by the geometry modeling system. On this basis, the relevant processing technology information is input through manual interaction, and then the correlation is generated through offline mode. Tool location file, after which the machine tool code instruction sequence is generated through post-processing. It can be seen from this that the off-line method not only has many links, but also consumes a lot of manpower and machine time, and occupies more hardware and software resources. Moreover, due to the separation of tool path planning and trajectory, it is difficult to achieve three-dimensional real-time accurate compensation of tool dimensions. The processing and programming need to be carried out several times to extend the processing time. At the same time, the process needs to encode, decode, transfer, store, and process a large amount of data, greatly increasing the probability of errors and adversely affecting the reliability of the CNC. In order to avoid the inherent insufficiency of off-line programming, people proposed a real-time interpolation technology, that is, the numerical control system generates a non-interfering tool position trajectory and control instructions for generating tool motion in real time based on the information about the processed surface, thereby realizing the machining process. control. However, this method has a high requirement for interpolation technology, which requires that the interpolation algorithm has high efficiency. Because real-time interpolation is required, the interpolation system must calculate the coordinate of the next interpolation point in the interpolation cycle, and perform interference, etc. Related technology processing. Therefore, at present, many CNC machine tools can only directly interpolate straight lines and circular arcs and cannot perform real-time interpolation of surfaces. In order to improve the above situation, we carefully studied the related technologies of NC machining and surface real-time interpolation, and proposed a real-time interpolation algorithm for parametric surfaces. This algorithm has a unique idea, greatly shortens the time for real-time interpolation of parametric surfaces, and significantly improves the time. Real-time interpolation efficiency makes it possible to interpolate free-form surfaces in real time. Second, the basic principle of interpolation The current CNC machining system interpolation methods are mainly divided into two categories: one is the pulse incremental interpolation, which is the scalar interpolation travel; the other is the data sampling interpolation, that is, time scalar interpolation Make up. Pulse incremental interpolation is performed by using the stepper's pitch in each pulse time as an interpolation unit. This method is mainly used in open-loop numerical control systems for linear and arc interpolation and interpolation. The speed is generally slower. The data sampling interpolation is based on the distance that the tool travels in one interpolation cycle. This method can be used for interpolation of more complex curves and can achieve fast interpolation. Taking into account some inherent deficiencies of pulse incremental interpolation, this paper uses data sampling method for interpolation. The principle of this method is to calculate the feed amount of the tool in the direction of the composite speed in one interpolation cycle according to the feed speed and the interpolation cycle, and then to pass the difference between the real-time measured value and the theoretical value in the actual interpolation. The servo controls each motion axis for interpolation. Third, the parametric surface of the real-time interpolation The surface real-time interpolation proposed in this paper uses the cutting plane method. The method is divided into 3 parts. First, discretize the machined surfaces, then intercept them with a set of parallel surfaces, find the intersection lines, and obtain the initial interpolation points. Finally, the initial interpolation points are interferred to generate the toolpath parameters. Discretization of Surfaces There are many studies on the discretization of parametric surfaces. In this paper, the quadtree is used to adaptively discretize the surface, that is, the discrete precision allowed by the discrete time is first calculated according to the processing precision required by the surface, and then the surface is recursively subdivided according to the discrete precision. When the sub-surface is in the When it is determined in the recursive subdivision process that the local precision is within the accuracy of the discrete precision, it is further subdivided so that all sub-surface patches are localized flat. Afterwards, each sub-surface patch is converted into four triangular patches by taking the center of the four corner points of the partially flat sub-surface patch. In this way, after the discretization, the parametric surface will be replaced by a series of triangular plane patches. Interpolation of Plane and Surface Generates Initial Interpolation Points Currently, toolpaths are generated by isoparametric, truncated-plane, and ring-cut methods. Among them, the cutting plane method has a high quality of toolpath generation. Therefore, the method of cut plane is used in this paper. The truncated plane method uses a set of parallel planes perpendicular to the XY plane to cut the processed surfaces and use their intersecting lines to perform related processing to generate the tool path. Since the processing surface has been composed of a series of simple triangular planes through the discrete processing of the previous step, it is relatively simple to solve the intersection of the plane and the surface, and only the intersection of the plane and the related triangular plane sheet is required. However, it must be noted here that the discretization of the previous step may occur due to the different subdivision levels of the adjacent sub-surface patches, as shown in the attached drawings. Of course, this phenomenon can be eliminated by certain means, but this will greatly reduce the efficiency of the discontinuity and is not used in this paper. This article will only deal with the issue here. When the plane intercepts the triangular plane piece at the crack, an intersection line will be generated between the plane and the crack, such as the line segment AB in the figure. In fact, two points AB should be the same point of the curved surface, but due to the imperfection of the discrete method. produce. In order to eliminate this phenomenon, the method adopted in this paper is to take the midpoints of points A and B as the intersection of the plane and the boundary of the subsurface patch at the crack in this case.

Cracks appearing during discretization of drawings

Through the above process, the result of the interception of the plane and the surface will be a continuous polyline. Based on this, the real-time interpolation method proposed in this paper is presented below. As described above, in the time scalar interpolation, the feed amount in the speed synthesis direction during the interpolation cycle is first calculated according to the feed speed and the interpolation cycle. At the same time, in the course of the specific interpolation surface, at the same time, It must be judged whether interpolation with the feed amount will cause the machining accuracy to exceed the allowable machining error. This process is more troublesome and the interpolation efficiency is significantly reduced. For this reason, this paper avoids this judgment process and directly processes each segment of the polyline segment obtained above to solve the feed amount in the interpolation period. The specific process is: for one of the broken line segments, the length is compared with the feed amount calculated according to the feed speed and the interpolation cycle & the standard feed amount here, and the following judgments are made: The length of the fold line is less than or equal to the standard feed amount. The fold length is taken as the feed amount in the interpolation cycle; otherwise, the break line length/N is taken as the feed amount of the interpolation cycle, where: N=INT(fold length/standard Feed rate)+1. In this way, the initial interpolation point can be easily found, and the initial interpolation point thus obtained will definitely meet the requirements of machining accuracy. Because this method avoids the inspection of the machining accuracy, the interpolation efficiency is greatly improved, which is very important for real-time interpolation. Toolpath Interference Processing In CNC machining, the radius of the selected tool may be greater than the radius of curvature of the surface. In this way, if the tool path trajectory of the NC machining is generated directly by the contact point generated above, the tool moves along the center point during machining. The tool will interfere at other points. Therefore, the tool path trajectory that is actually applied must be checked for in-position trajectory interference when it is generated. In fact, the tool trajectory interference test is a key link in the trajectory generation in NC machining, and it is also a difficult and time-consuming step. Since the interpolation in this paper is real-time interpolation, it is required that the interference check be generated while generating the trajectory to generate the interference-free cutter position trajectory in real time. This article adopts the lifting tool position method to check the interference. The idea is: at some interpolation point, it is checked whether the tool interferes with the quadrilateral surface in the tool projection area, and some of the tools lift the tool until it is in the quadrangular shape in the projection area. The dough piece does not interfere. At this time, the center point of the tool is not the interference knife point, and all the trajectories without the interference point form the non-interfering tool position trajectory. IV. CONCLUSION In this paper, based on the discretization of the surface, the discontinuity of the discretized triangular plane slice and the line cutting plane directly determines and calculates the feed amount of the tool during the interpolation cycle, and the initial interpolation point is obtained accordingly. . In this way, the interpolation time is greatly shortened, the efficiency of interpolation is significantly improved, and a solid foundation is laid for real-time interpolation of free surfaces. At the same time, this method also provides a new idea for the free surface interpolation method.

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