A Unifying Framework
Previous: Introduction
The traditional approach to structuring sensing strategies and tolerance computation for the inspection of machine parts has been to utilize the sensed data (range, image, and/or touch) and the recovered geometries of the sensed objects for guiding the sensors to get more data and to do better fittings at the ``relevant'' or ``uncertain'' regions. We propose an approach that is based on the knowledge of the actual manufacturing process for the parts to be inspected, as opposed to only the sensed data points and the recovered geometric CAD model. Our approach utilizes the knowledge of the process plan and the subsequent toolpath of the milling machines and the errors, uncertainties, and tolerances associated with that process to achieve an optimal sensing strategy at the relevant regions, features, and manufacturing path on the parts to be inspected. We anticipate that this approach will not only permit us to answer questions concerning design and manufacturing processes, but also gives a way to determine places in the process and on the part where sensing is useful to ensuring that tolerances are met.
We propose toolpaths with tolerances as an instance of the manufacturing process (process plan) that provides a unifying approach to dealing with tolerance and sensing issues across design, manufacturing and inspection. We give examples of tolerance-based techniques for manufacturing features and for inspection purposes. The relation between part error models and tolerance specifications is outlined. The initial design of a unified framework for manufacturing-based sensing strategies for manufacture and inspection is given; the key is to tag tolerances to the manufacturing process itself (e.g., we use the toolpath and tolerance for NC milling).
The importance of quantifying tolerance in the specification, design, manufacturing and inspection process is obvious. Unfortunately, adequate representations of tolerance do not exist which permit dialog between these various aspects of the manufacturing process. This lack is particularly acute in systems which tightly integrate all of the aspects of prototyping (i.e, Manufacturing, Design, and Sensing for inspection). We use the tolerance specification in conjunction with knowledge of the manufacturing process plans to determine more optimized sensing strategies. We propose to avoid the use of weak methods (e.g., comparing nominal geometry to dense range data from the actual part), and to synthesize strong process monitoring and inspection strategies based on detailed knowledge of geometry, tolerance specification, manufacturing features and processes, and the sensors involved.
The use of interval Bezier curves for a complete description of approximation errors was proposed by Sederberg and Farouki[5] (see paper for details). The basic idea is to extend splines to polynomials whose coefficients are intervals with well defined arithmetic operations. Such splines define a region in space rather than a curve. This notion captures very nicely the semantics of a tolerance specification. We have developed interval curves for both 2D and 3D and algorithms based on interval splines for machine toolpath representation. We have also implemented toolpath-based algorithms for answering tolerance questions in inspection of parts, and for structuring coarse-to-fine sensing strategies based on tolerance regions around sensed data.
Our goal is to develop a methodology which helps to guarantee that the intended tolerance specification is met as efficiently as possible. There issue we address in our framework is to validate that the tolerances have been achieved in the actual part that is inspected. This process involves sensor measurements either during the manufacturing phase or post-manufacture inspection. To ensure that the tolerance has been met, sensors are used to:
In order to structure the analysis process, we focus here on NC milling, and
use the toolpath as the basis upon which design and manufacturing tolerance and
sensor measurements will be compared. Much as operational semantics allows
the meaning of a high level program to be defined in terms of the particular
architecture upon which it executes, so can the CAD specification of a part be
defined in terms of the machining operations which produce its shape.
Given the CAD geometry for a part, a tolerance specification, and a class of
NC mill to be used, then generic knowledge about such mills can be used to
generate a desired toolpath with its associated tolerance (call it .
Once a specific mill is selected, then the nominal toolpath from
together with the accuracy of the mill determine the actual toolpath (call this
These two toolpaths allow us to determine a great deal about the
efficiency and uncertainty regions of the process.
First, if
is true, then we know that the tolerance
should, in principle, be achieved. If
is large, then the
selected machine may be too precise, and therefore, too expensive. If the
boundary of
is close to that of
, this signals places where
sensing may be necessary to guarantee the inclusion relation. This also gives
insight into how accurate the sensing needs to be. Even if
is not
contained in
, this approach allows us to estimate what percentage
of milled parts will be out of spec, and thus an informed decision can be
made whether to tighten the accuracy of the machine, or where to sense with
high probability of part error. Thus, the toolpath representation allows
insight into design, manufacture and inspection in a common framework.
A Unifying Framework
Previous: Introduction