A subtractive manufacturing constraint for level set topology optimization

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.