A subtractive manufacturing constraint for level set topology optimization
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RESEARCH PAPER
A subtractive manufacturing constraint for level set topology optimization Nigel Morris1
· Adrian Butscher1 · Francesco Iorio1
Received: 25 January 2019 / Revised: 30 August 2019 / Accepted: 15 October 2019 © Springer-Verlag GmbH Germany, part of Springer Nature 2020
Abstract 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. Keywords Manufacturability · CNC milling · Advection
1 Introduction The aim of this work is to optimally synthesize the geometry of a mechanical part under a specified set of loading conditions and constraints such that the part can be successfully and accurately manufactured using a subtractive process. This process typically begins with a solid block of stock material and gradually removes material from the block until the remaining material has the shape of the designed part. One of the most common subtractive approaches is called “milling” and uses rotary cutters otherwise known as “tools,” “end-mills,” or “bits” to remove the material (Brown and Sharpe Manufacturing Company 1914). This process inherently limits the types of shapes that can be manufactured, since the milling machine must be able to hold the part rigidly and the rotary bit must be able
Responsible Editor: Ole Sigmund Nigel Morris
[email protected]; [email protected] 1
Autodesk Research, Toronto, Ontario, Canada
to access the material surface without interference. Other important considerations must also be taken into account such as vibration of the part during material removal and stresses on the bit itself by the milling process. We focus the scope of this work on the problem of synthesizing optimal shapes whose surface is entirely accessible by a user-specified milling machine and tool. The process of synthesizing optimal shapes given specified b
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