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Interpretation of errors from inspection results
Computer httegrated Manufacturing Systems 1994 7(3) 173-178
Interpretation of errors from inspection results A H Rentoul, G Mullineux and A J Medland Centre for Geometric Modelling and Design, Manufacturing and Engineering Systems, Brunel University, Uxbridge. Middlesex UB8 3PH, UK
This paper looks at ways in which inferences about errors in manufacturing can be made by comparing inspection points with a solid model of the desired component. The approach is to form a hierarchy of stages within a typical manufacturing process, and to try to match the inspected points associated with each with the computer model. This requires 'best fit' transforms to be found. Keywords: automatic inspection, manufacturing errors, solid modelling
Increasingly, automatic inspection technique are being used to provide feedback during the overall design and manufacturing process. Sometimes this is in the form of in-process gauging; alternatively a component is tested after manufacture or after some significant stage. In the latter case, a coordinate measuring machine (CMM) is often used. The basic technique with a CMM is to probe a number of points on the physical component. These are done in groups so that simple geometric entities such as lines and circles can be established. The results are then usually printed to a hard-copy device as a report for the human operator. Recently, links between C A D and automatic inspection systems have begun to be established. The C A D system provides a model of the component to be measured. From this a probing path for a CMM can be generated, perhaps interactively with a human operator. Such connections also open the way for more automatic handling of inspection results. If all the measured points lie correctly in relation to the C A D model, then it can be deduced that the physical part has been made correctly. (Care is required here to check that the various tolerances are satisfied appropriately.) In this paper, we look at how inferences about errors in manufacture operations can be made on the basis of finding invalid results during inspection. The approach relies on finding transform which map a given set of inspection points onto the C A D model. When an error has occurred it is necessary to search for a 'best compromise' transform. We illustrate the ideas by use of a software system called R A S O R , which allows the constraints of any application to be defined and possible solutions sought. Here the constraints are that the inspected points should map appropriately onto the C A D model. In the next section, an overview is provided of the R A S O R environment and of its ability to use the ACIS
solid modeller to create a model of the component in question. After this, we look at the use of R A S O R to establish best compromise transforms. This idea is applied in the later sections. A decomposition of a manufacturing process into set-ups, tools and features is proposed, which allows the inspected points to be handled hierarchically. Some examples of this are provided. Background When coordinate measuring machines (CMM) were first used, the programming of them was carried out via a 'teaching mode '1'2. The probe was manually taken through the steps required, and these were recorded by the machine to be reproduced at subsequent times. The next stage in the development was to allow the programming to be carried out off-line, and use made of a description of the component held in some sort of C A D system 3~. The path required was developed and checked within the C A D environment, and then the instructions sent to the CMM. In particular, this led to the establishment of standard languages such as DMIS 7 for describing measurement operations. Once inspection has taken place, the normal way to obtain the results is via a print-out from the CMM itself. Recently, attempts have been made to capture the results and use them for decision-making within a computer system. For example, the results can be passed back to the C A D system used to establish the probing path. The geometric features determined during inspection can then be superimposed on the original C A D model for visual checking 8. If necessary, the differences between the original and measured geometry can be magnified to make any errors more apparent to the human eye. The interpretation of the results is still left to the user. In this paper, we look at ways in which the
0951-5240/94/03/0173-06(~ 1994 Butterworth-Heinemann Ltd 173
Interpretation of errors from inspection results: A H Rentoul et al. interpretation can be carried out more automatically. By 'interpretation' here, we mean deciding whether a part has been made correctly, or if errors have occurred, trying to identify at which stage the manufacturing process has gone wrong. To investigate these ideas, a computer system called R A S O R has been used 9. This allows the constraint rules of a problem to be specified, and it can then automatically search for a configuration of the problem variables in which these are all satisfied (or in which a best compromise is obtained). The search is made iteratively using an optimization technique to try to minimize composite 'falseness' of all the imposed constraints. The R A S O R system was originally created for looking at the overall design process so that the constraints would represent the limits on the range of possible designs. It has also been applied to the design and analysis of mechanisms 9, in which the constraints specify how the parts of a mechanism assemble and what function they are to perform. In this case, the constraints are used to compare the original component data with the results of inspection. To facilitate this comparison, the ACIS solid modeller library 1° has been integrated into the R A S O R software. R A S O R itself is driven by a user command language, and to this language have been added commands to create solid objects and combine them using the standard Boolean operations. In the integrated system, components can be generated using instructions similar to those for normal NC machining operations 11. This provides a method for creating a computer model of the intended component. The results of inspection can be compared against it.
Basic comparisons In this section, we look at the problems of comparing two sets of points in three-dimensional space, and of comparing one set against a solid object. In each case, one set of points represents the results of an inspection using a CMM. In a sense, this is not making use of all the facilities available from a CMM system, which would normally try to fit geometry (such as circles, lines and planes) to the points and pass these back as its results. However, the advantage of using the original points is that no information is lost (and corruption by the CMM control progam is avoided). The disadvantage is that no offset allowance for the probe size can be made by the CMM software. As an initial example, consider two sets of points which are identical except that one set has been displaced with respect to another. This represents the case where points are taken on a particular feature on the physical component which has been positioned incorrectly. (Allowance for probing offsetting is assumed to have been made.) These two sets of points can be manipulated by the R A S O R system. The basic constraint rules are that each point from one set should agree with the
174 Computer Integrated Manufacturing Systems Volume 7 Number 3
corresponding one from the other. In the R A S O R language, if p l and p2 are two points then the command: rul p l on p2 specifies that these should be coincident. In fact, the binary function on evaluates the distance between the two points. When the constraint rules are solved, the system tries to minimize all the associated values, and so moves p l and p2 together. Whether or not the two sets of points match can be determined by evaluating all these rules and seeing if the result is zero. If it is then the points are superimposed; if not, then some adjustment needs to be made, and R A S O R does this by trying to minimize the sum of the squares of the rule values. Only one set to points needs to be moved to obtain a match. To ensure that they move together, they are e m b e d d e d into a 'model space '9. This means that each is associated with a three dimensional transformation matrix. If the translation and rotation components of this matrix are allowed to vary, then the whole set of points move together, and R A S O R is allowed to adjust these to try to reduce the distances between corresponding points to zero. Figure 1 shows 20 points distributed around five of the sides of a cube. As a test, these points are translated and rotated some distance from the original ones. The change used is far too large to represent a manufacturing error; however, it is a useful test case to demonstrate the ideas of matching. If the constraints are applied, then the model space for the transformed set is adjusted and the two sets of points match. Figure 2 shows some of the manipulations through which the transformed set passes as it converges onto the original set. The number of iterations taken to obtain the match is 7, which is large, and the time taken is noticeable (of the order of 30 seconds) using a Sun workstation. This
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the original points are not explicitly given. Instead, the information is presented in terms of a solid body. The ACIS software allows the distance to be found between any face of a solid object and any given point. This has been incorporated within the R A S O R code. The rule for a point lying on a body called 'cube' is as follows: rul point__body2(cube, p l ) - radius
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is because of the large distances between corresponding points. The technique can be improved quite simply. Two corresponding points are taken, and the movable set of points is translated to bring the two together to form a local origin. Then another two pairs of corresponding points are used to establish a rotation about the local origin. This can be done in terms of R A S O R rules; the difference now is that only two rules are used and only the rotation components of the transformation need to be adjusted. (It is necessary to ensure that neither set of three points used here is collinear.) The result is an initial estimate of the match between the points. If the sets are indeed identical then the appropriate transform is found directly. If not, then the full set of rules can be applied now starting with a good approximation to the 'best' transform. The points shown in Figure 1 are used again, except that now the second set does not match the original set exactly. Instead, they are displaced by a small distance away from the cube in a direction perpendicular to the relevant face. This is the situation that occurs when the inspection points represent the centre of a probe measuring the outside of a square protrusion with no allowance for the probe size. Again, the second set of points is moved well way from the original ones. The rules that need to be applied now have the following form:
When rules of this form are applied using the data of the last example, starting from a close approximate configuration, the same results (shown in Figure 3) are again obtained. This time six iterations are used, and this takes 120 seconds. However, if these rules are applied starting with the large displacement between the two sets of data, then the same problems are encountered as before. There is now an additional difficulty. The form of the rule given above only involves the distance between a point and a body. It is better to identify the actual face close to which the point should lie and write the rule in terms of the distance between this face and the point. This approach is not adopted here, since it is easier for a user to work in terms of a single body rather than have to identify and/or name individual faces. This has proved to be satisfactory in practice, since normally a reasonable good initial match between sets of points is available. Inference
strategy
Consider the case in which we have a solid model of a particular component and a number of points probed on a physical component (possibly without an offset allowance for the probe size). The techniques discussed in the previous section can be applied to see if the points correctly relate to the solid model. If they do not then the transform to obtain the best match between them can be determined. Note that in practice there is likely to be a good initial match, since otherwise it
rul (pl on p2) - radius H e r e the distance between two corresponding points is found using the on function, and the radius of the probe is subtracted. This value is then zero if the points are at the appropriate distance apart. The alignment is now accomplished in 35 seconds and takes nine iterations; it results in the situation shown in Figure 3. Finally in this section, we consider the case in which
I Figure 3 Inspection points fitted outside cube
Computer Integrated Manufacturing Systems Volume 7 Number 3 175
Interpretation of errors from inspection results: A H Rentoul ct al. would be obvious visually that there were errors. Thus the iterative matching has a good start point. If there is no immediate match, this suggests that errors have occurred. It is probable that some (perhaps the majority) of the measured points are correct. To make inferences about the location of the error, a decomposition of the points needs to be made. The decomposition used here is illustrated in Figure 4. This is in the form of a tree diagram representing a simple hierarchy in the manufacturing process. The 'root' of the tree is the full manufacturing process itself. At the next level appear the various set-ups used. In particular, these represent stages at which the workpiece is repositioned. The next level corresponds to the various tools used within each set-up. There is something of an over-simplification here, since if a tool is used in more than one set-up it is necessary to treat it as a different tool each time. The last level refers to the individual 'features' made with the various tools. There is much current interest in the ideas of features, and as yet a formal fully agreed definition of what a feature is has yet to appear ~2-~5. For the purposes of this paper, it is a part of a full component that can be measured and that (normally) has been produced by a simple tool. Thus, for example, holes and slots are regarded as 'manufacturing feature '~6. It is also assumed here that each measured point corresponds to a particular feature. We can use the hierarchy in several different ways. That suggested at the start of this section is the 'topdown' approach. We begin at the 'root' and compare all the measured points against the full solid model. If there is agreement then the physical component is correct. If not, then we look at the subset points corresponding to each set-up and try matching each subset. An exact match for each cannot be obtained (or else the full component would be correct). For any setup for which no match is obtained, we look at the tools. Similarly, we look at the individual features associated with any tool that does not match. If the points for all the features for a given tool do
not agree, this suggests that the tool (or the set-up which contains it) is incorrect. If a transform can be found which successfully matches them, then this provides information on the error in the tool. Similarly, if all the tools within a set-up are invalid, it suggests that the set-up itself is wrong. Again, if all the points associated with a single set-up can be matched by a transform, this shows what the error in the set-up was. Alternatively, the investigation can proceed 'bottomup'. H e r e the individual features are first checked. If there is agreement between the points then the feature is assumed to have been made correctly. (Note that there is an assumption that sufficient points on each feature have been probed.) If features have been made incorrectly, again a transform can be sought to try to match the two sets of points associated with it. If a single feature within a group made by a single probe is incorrect, it suggests that the fault was only at this one place. Again, if all the features for a single tool are incorrect the tool may have been at fault. Thus we move up the hierarchy and now investigate what has happened at the tool level. There appear to be advantages in both the top-down and bottom-up approaches, and indeed, any investigation is always going to be a combination of both. If a manufacturing process is well established, the attraction of the top-down technique is that one single comparison is likely to indicate a match between expected and inspected data. If there is scope for analysing some inspection results while others are still being obtained, then the bottom-up approach is attractive and allows inspection and analysis to be carried out in parallel. In particular, in some cases, it may be possible to abort the further inspection of a part which has already proved to be faulty. In the next two sections we illustrate the two approaches by some examples using a single model. Top-down approach The component used here is shown in Figure 5. On the upper surface is a circular boss with a circular hole
Part
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Figure 4 Hierarchy within overall manufacturing process
176 Computer Integrated Manufacturing Systems Volume 7 Number 3
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Interpretation of errors from inspection results: A H Rentoul et al.
Figure 5 Test component passing into it. There is also a rectangular slot. These are formed in one set-up and two different tools are used. Along one side and passing through the body are a number of parallel holes. These are of two different sizes and they are made in a second set-up. The hierarchy for manufacture of this part is shown in Figure 6. Inspection of the part is carried out by probing points around the boss and within the slot and all the holes. For each feature points at two levels are taken. The probe points are shown in Figure 7 from various view points. If comparison is made between all the points and the solid model of the component, then errors are observed. When a move down is made to the set-up level, there is disagreement between the points for each one. Consider first the set-up used for the boss and the slot. Looking at the tools, it is found that the tool used for the outside of the boss and the slot gives sets of points which are in agreement. However, the tool for the hole in the boss gives points which do not agree, hence we can infer that one error in manufacture is the wrong tool used to form the hole in the boss. Within the second set-up we find that all the tools appear to be incorrect. If we moved down to the individual features these are also all incorrect. However, if we now try to match all the inspection points for this set-up with the original solid model, it is found that a match can be achieved with a simple translation. Thus the set-up itself is invalid, and at this stage the component was positioned incorrectly.
the curved sides of the holes, we cannot infer information about the position along the axis of the hole or rotation about this axis. These components in the transforms are not allowed to vary during the solution of the constraints. It is found that the best transform for the hole in the boss is the identity, and this suggests that the hole is correctly positioned but the size is wrong. By also adjusting a scale factor within the matching transform, search could be made to establish the change in radius. This indicates that a tool of the wrong radius has been used. The holes along the side can be matched by imposing the same transform. Since they are all formed by tools within a single set-up, from this can be deduced that the set-up itself was incorrect. Alternatively, we can make this deduction by passing up the hierarchy and obtain the transform to match at the set-up, as in the previous section.
Conclusions The problem has been considered of making inferences about possible errors in manufacturing on the basis of inspection results. For simplicity, the case in which a coordinate measuring machine (CMM) returns point data has been used. These have been compared against a solid model representation of the required component. Clearly, when the points lie correctly in relation to the solid model, the inference can be made that the physical component is correct. (This assumes that the probe points are sufficient to define the object.) It has been seen that it is possible to apply constraints about how the inspection points relate to the solid object to establish transforms to produce 'best possible' matches. Ways in which to speed the convergence of the iterative search required here have been considered. Two possible approaches to handling the mass of data points required have been discussed and illustrated. In the 'top-down' approach, all the inspected points are considered. If these disagree with the solid model then they are subdivided, firstly into those corresponding to a manufacturing set-up, then to those for a tool, and then down to the feature level. In the 'bottom-up' approach, the process starts with the individual features and then moves to groups of these. Points in the
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Bottom-up approach The same component (Figure 5) with the same errors is again used here. Working at the feature level to start with, we find that the slot and the outer wall of the boss have been made correctly. There are errors in the holes in the boss and in each of the holes in the side. We can try to match the inspection points for each feature with the solid model by finding suitable transforms for each. Since the probe points are only on
Figure 6 Hierarchy for manufacture of test component
Computer Integrated Manufacturing Systems Volume 7 Number 3 177
Interpretation of errors from inspection results: A H Rentoul et al.
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Figure 7 Inspected points for test component hierarchy at which some items at one level are correct and others are incorrect indicate where manufacturing errors have possibly occurred. Acknowledgements The work discussed in the paper has been carried out in a research project sponsored by the ACME Directorate of the Science and Engineering Research Council (SERC) and a small group of collaborating companies. The financial funding is gratefully acknowledged along with the support and cooperation of all the personnel involved.
6 7 8
9
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References
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1 Anthony, D M Engineering Metrology, Pergamon Press, Oxford (1986) 2 Kunzmann, H and Waldele, F 'Performance of CMMs', Ann. CIRP, Vol 37 (1988) pp 633-640 3 Yau, H-T and Menq, C-H 'An automated dimensional inspection environment for manufactured parts using coordinate measuring machines', Int. J. Prod. Res, Vol 30 (1992) pp 1517-1536 4 Anon Valisys, McDonnell Douglas Information Systems Ltd., Woking, Surrey, UK (1990) 5 Takeuchi, Y, Shimizu, H and Mukai, I 'Automatic measurement
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of 3-dimensional coordinate measuring machine by means of CAD and image data', Ann. CIRP, Vol 39 (1990) pp 565-568 Duffle, N, Feng, S and Kann, J 'CAD-directed inspection, error analysis and manufacturing process compensation using tricubic solid databases', Ann. CIRP, Vol 37 (1988) pp 149-151 Anon Dimensional Measuring Interface Specification - DMIS 2. I, Specification CAM-I Standard 101, CAM-I, Arlington, TX (1988) Hassan, J H, Medland, A J, Mullineux, G and Sittas, E 'An intelligent link between CAD and automatic inspection', Proc. 29th Int. M A T A D O R Conf., Manchester, UK (1992) Leigh, R D, Medland, A J and Mullineux, G 'Model spaces and their use in mechanism simulation', Proc. I. Mech. E., Part B - J . Eng. Manuf, Vol 203 (1989) pp 167-174 Anon ACIS Technical Overview, Spatial Technology Inc., Boulder, CO (1992) Medland, A J, Mullineux, G and Rentoul, A H 'Integration of constraint and solid modellers', Proc. 30th Int. M A T A D O R Conf., Manchester, UK (1993) Catania, G 'Form features for mechanical design and manufacture', J. Eng. Des., Vol 2 (1991) pp 21-44 Shah, J J and Mathew, A 'Experimental investigation of the STEP form-feature information model', Comput.-Aided Des., Vol 23 (1989) pp 282-296 Shah, J J 'Assessment of features technology', Comput.-Aided Des., Vol 23 (1989) pp 331-343 Wade, J and Colton, J S 'A framework for feature-based representation of the design process', Eng. with Computers, Vol 6 (1990) pp 185-192 Medland, A J and Mullineux, G 'A constraint approach to feature-based design', Int. J. Comput. Integrated Manuf., Vol 6 (1993) 24-38
Interpretation of errors from inspection results A H Rentoul, G Mullineux and A J Medland Centre for Geometric Modelling and Design, Manufacturing and Engineering Systems, Brunel University, Uxbridge. Middlesex UB8 3PH, UK
This paper looks at ways in which inferences about errors in manufacturing can be made by comparing inspection points with a solid model of the desired component. The approach is to form a hierarchy of stages within a typical manufacturing process, and to try to match the inspected points associated with each with the computer model. This requires 'best fit' transforms to be found. Keywords: automatic inspection, manufacturing errors, solid modelling
Increasingly, automatic inspection technique are being used to provide feedback during the overall design and manufacturing process. Sometimes this is in the form of in-process gauging; alternatively a component is tested after manufacture or after some significant stage. In the latter case, a coordinate measuring machine (CMM) is often used. The basic technique with a CMM is to probe a number of points on the physical component. These are done in groups so that simple geometric entities such as lines and circles can be established. The results are then usually printed to a hard-copy device as a report for the human operator. Recently, links between C A D and automatic inspection systems have begun to be established. The C A D system provides a model of the component to be measured. From this a probing path for a CMM can be generated, perhaps interactively with a human operator. Such connections also open the way for more automatic handling of inspection results. If all the measured points lie correctly in relation to the C A D model, then it can be deduced that the physical part has been made correctly. (Care is required here to check that the various tolerances are satisfied appropriately.) In this paper, we look at how inferences about errors in manufacture operations can be made on the basis of finding invalid results during inspection. The approach relies on finding transform which map a given set of inspection points onto the C A D model. When an error has occurred it is necessary to search for a 'best compromise' transform. We illustrate the ideas by use of a software system called R A S O R , which allows the constraints of any application to be defined and possible solutions sought. Here the constraints are that the inspected points should map appropriately onto the C A D model. In the next section, an overview is provided of the R A S O R environment and of its ability to use the ACIS
solid modeller to create a model of the component in question. After this, we look at the use of R A S O R to establish best compromise transforms. This idea is applied in the later sections. A decomposition of a manufacturing process into set-ups, tools and features is proposed, which allows the inspected points to be handled hierarchically. Some examples of this are provided. Background When coordinate measuring machines (CMM) were first used, the programming of them was carried out via a 'teaching mode '1'2. The probe was manually taken through the steps required, and these were recorded by the machine to be reproduced at subsequent times. The next stage in the development was to allow the programming to be carried out off-line, and use made of a description of the component held in some sort of C A D system 3~. The path required was developed and checked within the C A D environment, and then the instructions sent to the CMM. In particular, this led to the establishment of standard languages such as DMIS 7 for describing measurement operations. Once inspection has taken place, the normal way to obtain the results is via a print-out from the CMM itself. Recently, attempts have been made to capture the results and use them for decision-making within a computer system. For example, the results can be passed back to the C A D system used to establish the probing path. The geometric features determined during inspection can then be superimposed on the original C A D model for visual checking 8. If necessary, the differences between the original and measured geometry can be magnified to make any errors more apparent to the human eye. The interpretation of the results is still left to the user. In this paper, we look at ways in which the
0951-5240/94/03/0173-06(~ 1994 Butterworth-Heinemann Ltd 173
Interpretation of errors from inspection results: A H Rentoul et al. interpretation can be carried out more automatically. By 'interpretation' here, we mean deciding whether a part has been made correctly, or if errors have occurred, trying to identify at which stage the manufacturing process has gone wrong. To investigate these ideas, a computer system called R A S O R has been used 9. This allows the constraint rules of a problem to be specified, and it can then automatically search for a configuration of the problem variables in which these are all satisfied (or in which a best compromise is obtained). The search is made iteratively using an optimization technique to try to minimize composite 'falseness' of all the imposed constraints. The R A S O R system was originally created for looking at the overall design process so that the constraints would represent the limits on the range of possible designs. It has also been applied to the design and analysis of mechanisms 9, in which the constraints specify how the parts of a mechanism assemble and what function they are to perform. In this case, the constraints are used to compare the original component data with the results of inspection. To facilitate this comparison, the ACIS solid modeller library 1° has been integrated into the R A S O R software. R A S O R itself is driven by a user command language, and to this language have been added commands to create solid objects and combine them using the standard Boolean operations. In the integrated system, components can be generated using instructions similar to those for normal NC machining operations 11. This provides a method for creating a computer model of the intended component. The results of inspection can be compared against it.
Basic comparisons In this section, we look at the problems of comparing two sets of points in three-dimensional space, and of comparing one set against a solid object. In each case, one set of points represents the results of an inspection using a CMM. In a sense, this is not making use of all the facilities available from a CMM system, which would normally try to fit geometry (such as circles, lines and planes) to the points and pass these back as its results. However, the advantage of using the original points is that no information is lost (and corruption by the CMM control progam is avoided). The disadvantage is that no offset allowance for the probe size can be made by the CMM software. As an initial example, consider two sets of points which are identical except that one set has been displaced with respect to another. This represents the case where points are taken on a particular feature on the physical component which has been positioned incorrectly. (Allowance for probing offsetting is assumed to have been made.) These two sets of points can be manipulated by the R A S O R system. The basic constraint rules are that each point from one set should agree with the
174 Computer Integrated Manufacturing Systems Volume 7 Number 3
corresponding one from the other. In the R A S O R language, if p l and p2 are two points then the command: rul p l on p2 specifies that these should be coincident. In fact, the binary function on evaluates the distance between the two points. When the constraint rules are solved, the system tries to minimize all the associated values, and so moves p l and p2 together. Whether or not the two sets of points match can be determined by evaluating all these rules and seeing if the result is zero. If it is then the points are superimposed; if not, then some adjustment needs to be made, and R A S O R does this by trying to minimize the sum of the squares of the rule values. Only one set to points needs to be moved to obtain a match. To ensure that they move together, they are e m b e d d e d into a 'model space '9. This means that each is associated with a three dimensional transformation matrix. If the translation and rotation components of this matrix are allowed to vary, then the whole set of points move together, and R A S O R is allowed to adjust these to try to reduce the distances between corresponding points to zero. Figure 1 shows 20 points distributed around five of the sides of a cube. As a test, these points are translated and rotated some distance from the original ones. The change used is far too large to represent a manufacturing error; however, it is a useful test case to demonstrate the ideas of matching. If the constraints are applied, then the model space for the transformed set is adjusted and the two sets of points match. Figure 2 shows some of the manipulations through which the transformed set passes as it converges onto the original set. The number of iterations taken to obtain the match is 7, which is large, and the time taken is noticeable (of the order of 30 seconds) using a Sun workstation. This
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the original points are not explicitly given. Instead, the information is presented in terms of a solid body. The ACIS software allows the distance to be found between any face of a solid object and any given point. This has been incorporated within the R A S O R code. The rule for a point lying on a body called 'cube' is as follows: rul point__body2(cube, p l ) - radius
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Figure 2 Stages during determination of transform to match
points
is because of the large distances between corresponding points. The technique can be improved quite simply. Two corresponding points are taken, and the movable set of points is translated to bring the two together to form a local origin. Then another two pairs of corresponding points are used to establish a rotation about the local origin. This can be done in terms of R A S O R rules; the difference now is that only two rules are used and only the rotation components of the transformation need to be adjusted. (It is necessary to ensure that neither set of three points used here is collinear.) The result is an initial estimate of the match between the points. If the sets are indeed identical then the appropriate transform is found directly. If not, then the full set of rules can be applied now starting with a good approximation to the 'best' transform. The points shown in Figure 1 are used again, except that now the second set does not match the original set exactly. Instead, they are displaced by a small distance away from the cube in a direction perpendicular to the relevant face. This is the situation that occurs when the inspection points represent the centre of a probe measuring the outside of a square protrusion with no allowance for the probe size. Again, the second set of points is moved well way from the original ones. The rules that need to be applied now have the following form:
When rules of this form are applied using the data of the last example, starting from a close approximate configuration, the same results (shown in Figure 3) are again obtained. This time six iterations are used, and this takes 120 seconds. However, if these rules are applied starting with the large displacement between the two sets of data, then the same problems are encountered as before. There is now an additional difficulty. The form of the rule given above only involves the distance between a point and a body. It is better to identify the actual face close to which the point should lie and write the rule in terms of the distance between this face and the point. This approach is not adopted here, since it is easier for a user to work in terms of a single body rather than have to identify and/or name individual faces. This has proved to be satisfactory in practice, since normally a reasonable good initial match between sets of points is available. Inference
strategy
Consider the case in which we have a solid model of a particular component and a number of points probed on a physical component (possibly without an offset allowance for the probe size). The techniques discussed in the previous section can be applied to see if the points correctly relate to the solid model. If they do not then the transform to obtain the best match between them can be determined. Note that in practice there is likely to be a good initial match, since otherwise it
rul (pl on p2) - radius H e r e the distance between two corresponding points is found using the on function, and the radius of the probe is subtracted. This value is then zero if the points are at the appropriate distance apart. The alignment is now accomplished in 35 seconds and takes nine iterations; it results in the situation shown in Figure 3. Finally in this section, we consider the case in which
I Figure 3 Inspection points fitted outside cube
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Interpretation of errors from inspection results: A H Rentoul ct al. would be obvious visually that there were errors. Thus the iterative matching has a good start point. If there is no immediate match, this suggests that errors have occurred. It is probable that some (perhaps the majority) of the measured points are correct. To make inferences about the location of the error, a decomposition of the points needs to be made. The decomposition used here is illustrated in Figure 4. This is in the form of a tree diagram representing a simple hierarchy in the manufacturing process. The 'root' of the tree is the full manufacturing process itself. At the next level appear the various set-ups used. In particular, these represent stages at which the workpiece is repositioned. The next level corresponds to the various tools used within each set-up. There is something of an over-simplification here, since if a tool is used in more than one set-up it is necessary to treat it as a different tool each time. The last level refers to the individual 'features' made with the various tools. There is much current interest in the ideas of features, and as yet a formal fully agreed definition of what a feature is has yet to appear ~2-~5. For the purposes of this paper, it is a part of a full component that can be measured and that (normally) has been produced by a simple tool. Thus, for example, holes and slots are regarded as 'manufacturing feature '~6. It is also assumed here that each measured point corresponds to a particular feature. We can use the hierarchy in several different ways. That suggested at the start of this section is the 'topdown' approach. We begin at the 'root' and compare all the measured points against the full solid model. If there is agreement then the physical component is correct. If not, then we look at the subset points corresponding to each set-up and try matching each subset. An exact match for each cannot be obtained (or else the full component would be correct). For any setup for which no match is obtained, we look at the tools. Similarly, we look at the individual features associated with any tool that does not match. If the points for all the features for a given tool do
not agree, this suggests that the tool (or the set-up which contains it) is incorrect. If a transform can be found which successfully matches them, then this provides information on the error in the tool. Similarly, if all the tools within a set-up are invalid, it suggests that the set-up itself is wrong. Again, if all the points associated with a single set-up can be matched by a transform, this shows what the error in the set-up was. Alternatively, the investigation can proceed 'bottomup'. H e r e the individual features are first checked. If there is agreement between the points then the feature is assumed to have been made correctly. (Note that there is an assumption that sufficient points on each feature have been probed.) If features have been made incorrectly, again a transform can be sought to try to match the two sets of points associated with it. If a single feature within a group made by a single probe is incorrect, it suggests that the fault was only at this one place. Again, if all the features for a single tool are incorrect the tool may have been at fault. Thus we move up the hierarchy and now investigate what has happened at the tool level. There appear to be advantages in both the top-down and bottom-up approaches, and indeed, any investigation is always going to be a combination of both. If a manufacturing process is well established, the attraction of the top-down technique is that one single comparison is likely to indicate a match between expected and inspected data. If there is scope for analysing some inspection results while others are still being obtained, then the bottom-up approach is attractive and allows inspection and analysis to be carried out in parallel. In particular, in some cases, it may be possible to abort the further inspection of a part which has already proved to be faulty. In the next two sections we illustrate the two approaches by some examples using a single model. Top-down approach The component used here is shown in Figure 5. On the upper surface is a circular boss with a circular hole
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Figure 4 Hierarchy within overall manufacturing process
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Interpretation of errors from inspection results: A H Rentoul et al.
Figure 5 Test component passing into it. There is also a rectangular slot. These are formed in one set-up and two different tools are used. Along one side and passing through the body are a number of parallel holes. These are of two different sizes and they are made in a second set-up. The hierarchy for manufacture of this part is shown in Figure 6. Inspection of the part is carried out by probing points around the boss and within the slot and all the holes. For each feature points at two levels are taken. The probe points are shown in Figure 7 from various view points. If comparison is made between all the points and the solid model of the component, then errors are observed. When a move down is made to the set-up level, there is disagreement between the points for each one. Consider first the set-up used for the boss and the slot. Looking at the tools, it is found that the tool used for the outside of the boss and the slot gives sets of points which are in agreement. However, the tool for the hole in the boss gives points which do not agree, hence we can infer that one error in manufacture is the wrong tool used to form the hole in the boss. Within the second set-up we find that all the tools appear to be incorrect. If we moved down to the individual features these are also all incorrect. However, if we now try to match all the inspection points for this set-up with the original solid model, it is found that a match can be achieved with a simple translation. Thus the set-up itself is invalid, and at this stage the component was positioned incorrectly.
the curved sides of the holes, we cannot infer information about the position along the axis of the hole or rotation about this axis. These components in the transforms are not allowed to vary during the solution of the constraints. It is found that the best transform for the hole in the boss is the identity, and this suggests that the hole is correctly positioned but the size is wrong. By also adjusting a scale factor within the matching transform, search could be made to establish the change in radius. This indicates that a tool of the wrong radius has been used. The holes along the side can be matched by imposing the same transform. Since they are all formed by tools within a single set-up, from this can be deduced that the set-up itself was incorrect. Alternatively, we can make this deduction by passing up the hierarchy and obtain the transform to match at the set-up, as in the previous section.
Conclusions The problem has been considered of making inferences about possible errors in manufacturing on the basis of inspection results. For simplicity, the case in which a coordinate measuring machine (CMM) returns point data has been used. These have been compared against a solid model representation of the required component. Clearly, when the points lie correctly in relation to the solid model, the inference can be made that the physical component is correct. (This assumes that the probe points are sufficient to define the object.) It has been seen that it is possible to apply constraints about how the inspection points relate to the solid object to establish transforms to produce 'best possible' matches. Ways in which to speed the convergence of the iterative search required here have been considered. Two possible approaches to handling the mass of data points required have been discussed and illustrated. In the 'top-down' approach, all the inspected points are considered. If these disagree with the solid model then they are subdivided, firstly into those corresponding to a manufacturing set-up, then to those for a tool, and then down to the feature level. In the 'bottom-up' approach, the process starts with the individual features and then moves to groups of these. Points in the
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Bottom-up approach The same component (Figure 5) with the same errors is again used here. Working at the feature level to start with, we find that the slot and the outer wall of the boss have been made correctly. There are errors in the holes in the boss and in each of the holes in the side. We can try to match the inspection points for each feature with the solid model by finding suitable transforms for each. Since the probe points are only on
Figure 6 Hierarchy for manufacture of test component
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Interpretation of errors from inspection results: A H Rentoul et al.
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Figure 7 Inspected points for test component hierarchy at which some items at one level are correct and others are incorrect indicate where manufacturing errors have possibly occurred. Acknowledgements The work discussed in the paper has been carried out in a research project sponsored by the ACME Directorate of the Science and Engineering Research Council (SERC) and a small group of collaborating companies. The financial funding is gratefully acknowledged along with the support and cooperation of all the personnel involved.
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References
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1 Anthony, D M Engineering Metrology, Pergamon Press, Oxford (1986) 2 Kunzmann, H and Waldele, F 'Performance of CMMs', Ann. CIRP, Vol 37 (1988) pp 633-640 3 Yau, H-T and Menq, C-H 'An automated dimensional inspection environment for manufactured parts using coordinate measuring machines', Int. J. Prod. Res, Vol 30 (1992) pp 1517-1536 4 Anon Valisys, McDonnell Douglas Information Systems Ltd., Woking, Surrey, UK (1990) 5 Takeuchi, Y, Shimizu, H and Mukai, I 'Automatic measurement
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of 3-dimensional coordinate measuring machine by means of CAD and image data', Ann. CIRP, Vol 39 (1990) pp 565-568 Duffle, N, Feng, S and Kann, J 'CAD-directed inspection, error analysis and manufacturing process compensation using tricubic solid databases', Ann. CIRP, Vol 37 (1988) pp 149-151 Anon Dimensional Measuring Interface Specification - DMIS 2. I, Specification CAM-I Standard 101, CAM-I, Arlington, TX (1988) Hassan, J H, Medland, A J, Mullineux, G and Sittas, E 'An intelligent link between CAD and automatic inspection', Proc. 29th Int. M A T A D O R Conf., Manchester, UK (1992) Leigh, R D, Medland, A J and Mullineux, G 'Model spaces and their use in mechanism simulation', Proc. I. Mech. E., Part B - J . Eng. Manuf, Vol 203 (1989) pp 167-174 Anon ACIS Technical Overview, Spatial Technology Inc., Boulder, CO (1992) Medland, A J, Mullineux, G and Rentoul, A H 'Integration of constraint and solid modellers', Proc. 30th Int. M A T A D O R Conf., Manchester, UK (1993) Catania, G 'Form features for mechanical design and manufacture', J. Eng. Des., Vol 2 (1991) pp 21-44 Shah, J J and Mathew, A 'Experimental investigation of the STEP form-feature information model', Comput.-Aided Des., Vol 23 (1989) pp 282-296 Shah, J J 'Assessment of features technology', Comput.-Aided Des., Vol 23 (1989) pp 331-343 Wade, J and Colton, J S 'A framework for feature-based representation of the design process', Eng. with Computers, Vol 6 (1990) pp 185-192 Medland, A J and Mullineux, G 'A constraint approach to feature-based design', Int. J. Comput. Integrated Manuf., Vol 6 (1993) 24-38