Development of cutting simulator using polygon representation -Applying and extending Vatti clipping-
Development of cutting simulator using polygon representation -Applying and extending Vatti clipping-
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使用多边形表示的切割模拟器的开发 -应用和扩展华帝剪裁-
DOI：
10.1016/j.precisioneng.2020.09.005
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发表时间：
2020
期刊：
影响因子：
--
通讯作者：
Mizutani Takahiko
中科院分区：
文献类型：
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作者：
Kito Ryota;Takasugi Keigo;Asakawa Naoki;Mizutani Takahiko
近年来，产品设计、刀具轨迹生成和切削仿真可以在PC上进行，并具有扩展的三维（3D）CAD/CAM工具套件。切削仿真可以在加工过程中检查工件的形状，检测刀具和夹具之间即将发生的碰撞，并进一步预测切削力。然而，因为空间和时间分辨率的增加导致计算时间增加，所以具有高分辨率的切削模拟器不能真实的实时地计算操作。商业上可获得的切割模拟器通过使用图形库（诸如OpenGL）的着色技术来表达伪切割过程。因此，这种方法不能验证包括切削力计算在内的详细切削过程的有效性。因此，人们研究了各种有效的切削模拟器[[1]，[2]，[3]，[4]，[5]]。体素表示是切削仿真领域中最常用的三维模型表示技术，它是基于微小立方体的叠加。当体素表示刀具和工件的3D模型的形状时，切削过程由布尔运算表示。体素表示主要有两个优点：表示三维模型和计算切割体积的算法简单。[2019 - 09 - 19][2019 - 09 - 19][2019 - 09][2019 - 09 - 19][2019 - 09 - 19][2019 - 09][2019 - 09 - 19][2019 - 09][2019 - 09][2019 - 0例如，Wou等人开发了一种使用体素表示和计算机图形光线投射的切割力模拟器[12]。Noguchi等人使用机械结构和主轴驱动的数学模型开发了体素切削力模拟器[13]。Nishida等人开发了一种考虑静态切削刀具偏转的立铣刀加工模拟器[14]。Joy等人开发了一种帧切片体素表示，并实现了比传统体素表示更高的精度[15]。另一方面，体素表示具有以下缺点。体素表示中的空间分辨率是体素大小本身。例如，当用0.1 mm的空间分辨率表示体积为10 mm 3的立方体时，需要1百万个体素。如果空间分辨率变为0.01 mm，则需要10亿体素。因此，增加空间分辨率与表示立方体的体素的数量成比例。因此，八叉树结构已被提出作为加速仿真过程和减少内存消耗的方法[16]。然而，在体素表示中，必须减小体素尺寸以增加空间分辨率。因此，即使采用八叉树结构，也必须增加存储器消耗和计算时间。例如，如图1所示，当用最大体素尺寸1 mm表示直径4 mm和高度1 mm的圆柱体时，尽管当空间分辨率为0.25 mm时体素的总数为180，但当空间分辨率增加到1 μm时体素的总数将约为1167万。因此，体素的数量随着空间分辨率呈指数增加，这对体素表示的空间分辨率施加了限制。
In recent years, product design, tool path generation, and cutting simulation can be performed on a PC with a broadening suite of three-dimensional (3D) CAD/CAM tools. Cutting simulation can check the shape of the workpiece during processing, detect impending collisions between the cutting tool and jigs, and furthermore predict the cutting force. However, because an increase in spatial and temporal resolutions leads to increased calculation time, a cutting simulator with high resolution cannot calculate operations in real time. Commercially available cutting simulators express pseudo cutting processes by shading technology using graphics libraries such as OpenGL. Therefore, this method cannot verify the validity of the detailed cutting process including calculation of the cutting force.Thus, various efficient cutting simulators have been studied [[1],[2],[3],[4],[5]]. Voxel representation is the most popular technology to represent 3D models in the cutting simulator filed, which is based on stacks of minute cubes. When voxels represent the shapes of 3D models of cutting tools and workpieces, the cutting process is represented by Boolean operations. Voxel representation has mainly two advantages: simple algorithm to represent 3D models and calculate the cutting volume. Therefore, various studies have examined voxel representation [[6],[7],[8],[9],[10],[11],[12],[13],[14],[15],[16]]. For example, Wou et al. developed a cutting force simulator using voxel representation and ray casting with computer graphics [12]. Noguchi et al. developed a voxel cutting force simulator using a mathematical model of the mechanical structure and the spindle drive [13]. Nishida et al. developed an endmill processing simulator that considered static cutting tool deflection [14]. Joy et al. developed a frame-sliced voxel representation and achieved higher accuracy than conventional voxel representation [15]. On the other hand, the voxel representation has a following disadvantage. The spatial resolution in the voxel representation is the voxel size itself. For example, when a cube with a volume of 10 mm 3 is expressed with a spatial resolution of 0.1 mm, 1 million voxels are required. If the spatial resolution is changed to 0.01 mm, 1 billion voxels are required. Therefore, increasing the spatial resolution is proportional to the number of voxels representing the cubes. Therefore, the octree structure has been proposed as a method for accelerating the simulation process and reducing memory consumption [16]. However, in the voxel representation, voxel size must be reduced to increase the spatial resolution. Thus, even if the octree structure is adopted, memory consumption and calculation time must be increased. For example, when a cylinder 4 mm in diameter and 1 mm in height is represented with a maximum voxel size of 1 mm, as shown in Fig. 1, although the total number of voxels is 180 when the spatial resolution is 0.25 mm, the total number of voxels will be approximately 11.67 million when the spatial resolution is increased to 1 μm. Therefore, the number of voxels increases exponentially with the spatial resolution, which imposes a limit on the spatial resolution with voxel representation.