Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Blade Envelopes Part I: Concept and Methodology   Blades manufactured through flank and point milling will likely exhibit
geometric variability. Gauging the aerodynamic repercussions of such
variability, prior to manufacturing a component, is challenging enough, let
alone trying to predict what the amplified impact of any in-service degradation
will be. While rules of thumb that govern the tolerance band can be devised
based on expected boundary layer characteristics at known regions and levels of
degradation, it remains a challenge to translate these insights into
quantitative bounds for manufacturing. In this work, we tackle this challenge
by leveraging ideas from dimension reduction to construct low-dimensional
representations of aerodynamic performance metrics. These low-dimensional
models can identify a subspace which contains designs that are invariant in
performance -- the inactive subspace. By sampling within this subspace, we
design techniques for drafting manufacturing tolerances and for quantifying
whether a scanned component should be used or scrapped. We introduce the blade
envelope as a computational manufacturing guide for a blade that is also
amenable to qualitative visualizations. In this paper, the first of two parts,
we discuss its underlying concept and detail its computational methodology,
assuming one is interested only in the single objective of ensuring that the
loss of all manufactured blades remains constant. To demonstrate the utility of
our ideas we devise a series of computational experiments with the Von Karman
Institute's LS89 turbine blade.

8
The categories of this paper are: hep-ex
13
The categories of this paper are: quant-ph
18
The categories of this paper are: econ
21
The categories of this paper are: adap-org
19
The categories of this paper are: eess
29
The categories of this paper are: funct-an
2
The categories of this paper are: math
9
The categories of this paper are: nlin
34
The categories of this paper are: chem-ph
32
The categories of this paper are: atom-ph
11
The categories of this paper are: hep-lat
35
The categories of this paper are: mtrl-th
17
The categories of this paper are: q-fin
36
The categories of this paper are: cmp-lg
30
The categories of this paper are: q-alg
37
The categories of this paper are: supr-con