Our goal is to develop a methodology which helps to guarantee that the intended tolerance specification is met as efficiently as possible. There are two crucial issues related to tolerance specifications:
The first of these is concerned primarily with the analysis of tolerance stack-up in assembly using geometries. The second of these involves sensor measurements either during the manufacturing phase or post-manufacture inspection, and is the subject of this paper. To ensure that the tolerance has been met, sensors are used to:
hole diameter), and
We propose to synthesize process monitoring and inspection strategies based on detailed knowledge of geometry, tolerance specification, manufacturing features and processes, and the sensors involved.
As an example, consider the laser spot or heat source tracker
currently being prototyped and manufactured as part of the ARPA Madefast program. Figure 1 shows the mirror part of the device; the box outlines a rough bump in the supposedly circular outer edge of the mirror. This is caused by the fact that the 3-axis mill sometimes performs differently during startup/slowdown which occurs at this point. We believe that this kind of systematic problem is a perfect example of something that our approach can help avoid or detect.
The question here is whether parts of uncertain shape fulfill certain functional specifications. The question is expressed as geometrical relationships between toleranced objects. Unfortunately, tolerance based relations are often inconsistent, unlike relations between exactly represented objects. We have presented elsewhere a survey of tolerance representation and analysis methods [6], and have derived an intuitionistic tolerance handling method for robust modeling [11][5][4].
Our methods allow us to simulate manufacturing tolerances, and thus simulate the validity of the design under these tolerances. For instance, we can find out whether a functional feature can be manufactured, and whether it has certain relationships with other features (within tolerance), and whether the relationships are logically consistent. The geometric operations that need to be carried out can be very similar to the solid modeling operations done in the design stage. We geometrically construct the object by machinable features (e.g., drilling a hole corresponds to a Boolean subtraction of a cylinder, etc.); however, for this we associate tolerances that correspond to the tool precision to the geometric elements, rather than the floating point, or design tolerances, used previously (see [6] for details).
After the geometric construction we can query relationships between geometric elements and features to test the validity of the functional features (e.g., to determine whether two holes manufactured by two independent drilling operations line up within the tolerance of the design specifications). The adaptive tolerance method of the intuitionistic geometry approach facilitates tolerance analysis and synthesis in that it can be used to determine whether certain relationships can be achieved unambiguously under the current tolerances, and it provides the necessary feedback, indicating that the precision of the individual objects in the relation need to be tightened in some cases, or that the features need to be manufactured with a more precise tool, or an additional finishing stage may become necessary. In other cases the analysis may tell us that the tolerances can be relaxed, or that the clearance needs to be increased.
To validate that tolerances have been achieved requires the allocation and management of sensing resources in order to monitor specific parts of the machining process and afterwards to measure particular features of the part. We can exploit earlier work in process monitoring [10][8], both to predict likely deviation from the process, as well as to determine the most appropriate sensing to detect such deviations. Furthermore, our technique provides the high-level goals (e.g., features to be inspected) to drive sensing strategies such as developed at Columbia [2][1] and others.
The usual approach to validation is to simply measure the geometry resulting from the manufacturing process and compare it to the nominal geometry from the CAD model. We believe that a stronger approach, exploiting knowledge of the process plan and the particular manufacturing process, is possible, and that this approach permits the automatic synthesis of sensing strategies.
To achieve this requires a tolerance specification which: