We present a method for enforcing manufacturability constraints in generated parts such that they will be automatically ready for fabrication using a subtractive approach. We primarily target multi-axis CNC milling approaches but the method should generalize to other subtractive methods as well. To this end, we take as user input: the radius of curvature of the tool bit, a coarse model of the tool head and optionally a set of milling directions. This allows us to enforce the following manufacturability conditions: 1) surface smoothness such that the radius of curvature of the part does not exceed the milling bit radius, 2) orientation such that every part of the surface to be milled is visible from at least one milling direction, 3) accessibility such that every surface patch can be reached by the tool bit without interference with the tool or head mount. We will show how to efficiently enforce the constraint during level set-based topology optimization modifying the advection velocity such that at each iteration the topology optimization maintains a descent optimization direction and does not violate any of the manufacturability conditions. This approach models the actual subtractive process by carving away material accessible to the machine at each iteration until a local optimum is achieved.

中文翻译：

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水平集拓扑优化的减法制造约束

我们提出了一种在生成的零件中强制执行可制造性约束的方法，以便它们可以使用减法方法自动准备好进行制造。我们主要针对多轴 CNC 铣削方法，但该方法也应推广到其他减法方法。为此，我们将用户输入作为用户输入：刀头的曲率半径、刀头的粗略模型以及可选的一组铣削方向。这使我们能够强制执行以下可制造性条件：1) 表面光滑度，使得零件的曲率半径不超过铣削钻头半径，2) 定向，以便从至少一个角度可以看到待铣削表面的每个部分铣削方向，3) 可接近性，使得工具钻头可以到达每个表面补丁，而不会干扰工具或头架。我们将展示如何在基于水平集的拓扑优化修改平流速度期间有效地强制执行约束，以便在每次迭代时拓扑优化保持下降优化方向并且不违反任何可制造性条件。这种方法通过在每次迭代中去除机器可访问的材料来模拟实际的减法过程，直到实现局部最优。我们将展示如何在基于水平集的拓扑优化修改平流速度期间有效地强制执行约束，以便在每次迭代时拓扑优化保持下降优化方向并且不违反任何可制造性条件。这种方法通过在每次迭代中去除机器可访问的材料来模拟实际的减法过程，直到实现局部最优。我们将展示如何在基于水平集的拓扑优化修改平流速度期间有效地强制执行约束，以便在每次迭代时拓扑优化保持下降优化方向并且不违反任何可制造性条件。这种方法通过在每次迭代中去除机器可访问的材料来模拟实际的减法过程，直到实现局部最优。