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In modern industry, the application of free-form surfaces is becoming more widespread. These surfaces often have complex shapes that greatly increase the difficulty of machining. Five-axis CNC machining is one of the most effective ways to machine such surfaces. However, complex surface shapes and tool motion add to the difficulty of tool selection. Using large tooling can increase machining efficiency but may interfere with the machined surface, while using small tools requires longer machining times. With the advent of high-speed automatic tool change mechanisms on modern CNC machines, the use of a combination of multiple tools to machine the entire surface becomes quite attractive. The use of multiple tool combinations can significantly reduce machining time and processing costs while maintaining machining accuracy compared to machining processes that use a single tool.
Modern CAM systems allow the user to select the right tool, but it is almost impossible for the user to determine an optimal non-interfering tool combination based on his own experience. In addition, the published algorithms for automatically selecting multiple tool combinations focus on tool selection for three-axis machining. In order to ensure high efficiency and high quality cutting of five-axis CNC machine tools, this paper proposes a method to automatically select a set of non-interfering tool combinations. The method is based on our algorithm for automatically selecting a largest non-interfering tool to machine the entire surface. This problem can be summarized as "a well-designed free-form surface, a five-axis machine tool and a tool magazine, and an optimal set of tools to machine this surface". This method is divided into two steps: first determine the angular extent of each tool in the tool magazine at each point of contact with the surface, and the optimal tool combination consists of the largest feasible tool in each area.
2 Interference detection and calibration methods In the five-axis CNC machining, there are usually three types of knives: flat bottom knives, circular knives and spherical knives. The ring cutter is represented by three parameters: tool radius (R), ring radius (rf) and tool length (L). The ring cutter is representative because when rf is equal to zero, the knife is converted into a flat-bottomed knife; when R and rf are equal, the knife is converted into a spherical knife. NURBS surfaces are one of the most commonly used expressions for precise free-form surfaces. NURBS surfaces can be generated in most common 3D design software. Therefore, we study the ring cutter and NURBS surface.
In order to detect and check the interference of the tool and the surface, a coordinate system must first be established. This coordinate system consists of three coordinate systems: the world coordinate system (X WY WZ W), the local coordinate system (X LY LZ L), and the tool coordinate system (XTYTZT). At point P c , the coordinate origin of the local coordinate system (X LY LZ L) is at the point P c , the ZL axis is along the outer normal direction of the point at the point, and the XL axis and the YL axis are respectively along the curved surface. The maximum and minimum normal curvature directions of the point. The coordinate origin of the tool coordinate system (XTYTZT) is at the center point of the bottom surface of the tool, the ZT axis is along the tool axis, the XT axis is perpendicular to the ZT axis and points to the point Pc, and the YT axis is the right-hand rule of the ZT axis and the XT axis. determine. The tool can be positioned by a pair of azimuth angles (λ, θ), wherein the tilt angle λ and the side yaw angle θ are the angles at which the tool axis rotates counterclockwise about the XL axis and the ZL axis, respectively.
a ring knife and its parameter b coordinate system When performing interference detection, a set of discrete feature points are used to approximate the surface to be processed, and the original data of these feature points are represented in the world coordinate system.
For the convenience of calculation, the feature point data needs to be transformed from the world coordinate system to the local coordinate system, and then transformed from the local coordinate system into the tool coordinate system. At each point of the surface, the tool's interference is divided into four categories: local interference, knife rear interference, tool axis interference, and tool-machine interference. In five-axis machining, when any kind of interference occurs in the tool, the direction angle of the tool can be changed by rotating the tool to achieve interference-free machining. According to the occurrence conditions of the different interferences, the corresponding non-interference tool angle can be determined by applying the corresponding calibration method. The approximate method is as follows. Assume that the range of values ​​of θ and λ is [0° to 360°] and [0° to 90°], respectively. At each point of the surface, this range of values ​​of θ is equally divided for each θ value, find the λ range in which each interference detection and non-interference occurs after checking, and then obtain a common λ range, then the corresponding tool angle (λ, θ) does not appear in this λ range. Interference. If this range does not exist, it means that the current tool cannot be machined without interference. Figure 2b shows the non-interference (λ, θ) range at point P c on the surface.
3 Tool combination selection According to the tool interference detection method discussed above, at each point of the surface, if a tool has a non-empty angular range, it indicates that the knife can be processed without interference at this point. When selecting multiple tool combinations, our goal is to select the most efficient combination of tools. In the machining process using multiple tool combinations, the non-interference machining areas of two different tools may overlap. The usual method is to use a larger tool to machine all possible machining areas at high speed, and the smaller tool. It is then used to machine areas where larger tools cannot be machined. In this way, the effective machining area of ​​each knife may be smaller than the surface that can be processed without interference. In addition, in order to achieve maximum machining efficiency under the condition of ensuring machining accuracy, in the effective tool combination, we only retain one of the largest tools that can machine the entire surface without interference. All tools smaller than this knife are not considered. In order to avoid the disadvantages of surface discontinuities that may occur between adjacent areas of the two tool machining, and to reduce the time required for tool idling and positioning, unlike the traditional method of directly limiting the number of tools in the final combination, we A minimum reasonable ratio is pre-set to ensure that each knife has a large enough machining area. For each tool, if it has a non-interference-free effective area of ​​the surface that accounts for more than a predetermined ratio of the total area of ​​the surface, the tool is used to machine this area.
The entire tool combination selection process is roughly as follows. First, the surface is approximated as a series of discrete points, and the knives in the tool magazine are arranged in descending order of size (if the tool radii of the two knives are the same, the tool with a small radius is placed front). Starting from the first tool, calculate its position at each point. If the total area that can be machined exceeds the total area of ​​the surface by more than ζ, we use this knife to process these areas and mark these areas as Processed area. Repeat this process to select the remaining suitable tool to machine the remaining unprocessed surface. If the ratio of the remaining unprocessed surface area to the total surface area is less than ζ, then the largest tool that can process the entire surface without interference is selected. This selected tool forms the optimal tool combination to machine the entire surface without interference.
In order to verify the effectiveness of the method, we used processing time as the parameter for evaluation. By observing, the larger the surface area, the smaller the tool machining radius, and the larger the tool inclination angle λ, the larger the machining time required. Taking into account the inclination of the tool, the maximum cutting width per tool occurs at the position where the tool inclination angle is the smallest. Since the machining direction of the tool is not determined, we first find the λ minimum value corresponding to each θ at each point on the area where the tool is to be machined, and then find the average value λi-min of the λ minimum at that point, after which The average of all these λi-min is obtained.
According to these analyses, the machining time T of the tool can be approximated as: T = Area × (1 ni = 1 λi - min) R - rf × K (1) where Area is the area of ​​the machining area and n is the total number of effective points , k is a constant coefficient related to the feed amount and the like.
The whole algorithm process is as follows: (1) Approximate a given surface with discrete points. This point set is denoted as {P i}, and the area of ​​the calculated surface is recorded as Area({P i}).
(2) Record that the set of points for which the machining tool has not been determined is {S i-unmachined}, and set {S i-unmachined}={P i}.
(3) Arrange the tools in the tool magazine in order from largest to lowest, and record them as {C ​​i}. Let C i{S i-unmachined}=0, i=1.
(4) List C i as the current knife, and calculate its positioning at each point on {S i-unmachined} according to the four methods of interference detection and checking. If there is a non-interfering range of (λ, θ) at one point, the point is stored in C i{S i-unmachined} of the knife, and λi-min is recorded.
(5) If 1) C i{S i-unmachined}<{S i-unmachined}, calculate the area of ​​C i{S i-unmachined}, if AreaC i{S i-unmachined}Area({P i}) ≥ζ, we use this knife to machine these areas and {S i-unmachined}={S i-unmachined}-C i{S i-unmachined}. i=i+1, go to step 4.
2) C i{S i-unmachined}={S i-unmachined}, will be placed in the final selected optimal combination, go to step 6.
(6) Output tool combination and the effective machining point set C i{S i-unmachined} corresponding to each tool.
4 Example verification and conclusion The algorithm proposed above has been implemented in the Visual C++ environment. In order to confirm the feasibility of the proposed method, we will introduce an example below. First, Table 1 lists the tool parameters in the available tool magazines. P c θ λ no interference angle range The free surface in this example is as shown. By setting ζ=0.23, we get a set of optimal tool combinations: {1#,19#,26#}(1#:R=20.0mm, rf=1.
0 mm, L = 135 mm; 19#: R = 4.0 mm, rf = 0.5 mm, L = 50 mm; 26 #:: R = 1.5 mm, rf = 0.2 mm, L = 45 mm). Among them, the area of ​​the 1# knife can be processed to account for 76.42% of the total surface area, and the area of ​​the 19# knife can be processed to account for 99.54% of the total surface area; the 26# knife is the largest tool that can process the entire surface without interference. In other words, it can process 100% of the total area of ​​the surface. The actual effective surface area of ​​these three knives accounts for 76.42%, 23.12% and 0.46% of the total surface area, respectively. The effective processing area is shown in Figure 3d. According to equation (1), the time taken to machine the entire surface with this tool combination saves up to 58% compared to the time it takes to machine the entire surface with a conventional single tool (26# knife in this case).
This paper presents a new method for machining freeform surfaces with multiple tool combinations.
In this combination, each tool corresponds to a specific processing area. Compared with the traditional five-axis machining method using a single tool to machine the entire surface, the example proves that our proposed algorithm can achieve higher processing efficiency. Moreover, this algorithm can also be applied to the processing of three-axis free-form surfaces.
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