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Modeling Machining Errors on a Transfer Line to Predict Quality
Journal ofJournal Manufacturing of Manufacturing Processes Processes Vol. 5/No.Vol. 1 5/No. 1 2003 2003
Modeling Machining Errors on a Transfer Line to Predict Quality John S. Agapiou, Eric Steinhilper, Fangming Gu, and Pulak Bandyopadhyay, Enterprise Systems Laboratory, General Motors R&D Center, Warren, Michigan, USA
Abstract
Research work in tolerancing that affects quality has taken place sporadically. During the early 1970s, many articles were published on how to assign tolerances to minimize costs (Speckhart 1972; Spotts 1973). In the late 1980s, some researchers emphasized the application of statistical tolerancing to reduce manufacturing costs (Chase et al. 1989; Lee and Woo 1990). Dimensional errors used in assembly and machining are addressed in geometric dimensioning and tolerancing (GD&T) (ASME 1994). Several methods of tolerance assignment are available based on linear stack-up analysis using the knowledge of the mean and the variance for the individual variations/errors. This linear stack-up can be obtained using a worst-case or calculus-based approach (Straight Stack), a statistical tolerance analysis method—root sum squares, or Monte Carlo simulation (Evans 1975; Kawira 1994). The Monte Carlo simulation works well for both linear and nonlinear stack-ups. Variation simulation techniques have been developed for tolerancing and dimensioning in process planning (Fainguelernt, Weill, Bourdet 1986). Such models take into account fixturing tolerances as well as machining tolerances. Another approach is error budgeting, which has been used to estimate overall workpiece accuracy (Slocum 1992; Soons, Theuws, Schellekens 1992; Frey, Otto, Pflager 1997). An error budget is a systematic account of all sources of error in a machine, including such effects as component accuracy, structural compliance, and thermally induced deflections. Linear state-space modeling of dimensional machining errors was also lately used to transform and accumulate machining errors as the workpiece is machined in a multistation process (Djurdjanovic and Ni 2001; Maier-Speredelozzi and Hu 2002). This approach requires the definition of a frame of reference for each machining station, fixture,
This paper introduces a methodology for predicting part quality based on the expected and measured process variations (geometric, static, and dynamic errors). Part quality in terms of dimensional (location), orientation, form, and profile tolerances can be predicted using a “stream of variation model” in a multistation machining system (serial, parallel, or hybrid) and validated on an engine cylinder head. The understanding gained from an application of this methodology to a machined component can help achieve substantial part-quality and process improvements.
Keywords: Quality, Predicting, Machining, Variation, Simulation, Modeling
Introduction Machining can involve a large number of stations, operations, and several locating datum changes, especially when machining engine blocks, heads, or transmission components. Part quality is affected by the variations or errors from each station and any reference datum frame changes between stations. Although quality prediction (variation simulation) has been used for product design and assembly (VSA 1998; DCS 2000), it has had very limited application for manufacturing system design. A manufacturing system consists of one or more machining or assembly stations through which the part travels and where dimensions or features are generated. Several locating datum changes may occur between operations and/or stations. Consequently, features are made with small part-to-part variations or errors. Generic models for analyzing product quality from machining systems are not yet available. Such models should include variations/errors for (or from) a manufacturing system. This paper is an original work and has not been previously published except in the Transactions of NAMRI/SME, Vol. 31, 2003.
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and part. The mathematical transformations between frames are then described and the geometric errors can be estimated. This approach is extremely time consuming because it is explicit. The above variation simulation approaches tend to neglect the influence of fixture positional errors on the geometric accuracy of a part. Another group of researchers concentrated on the analysis of a part’s geometric error due to fixture positional errors (Rong and Zhu 1999; Weill, Darel, Laloum 1991; Choudhuri and De Meter 1999; Chandra et al. 1997). These simulations include only geometric errors in their calculations of part accuracy. The static errors (introduced by part and spindle deflections due to clamping and cutting forces) were neglected in the latter analyses except in one case, where the static errors due to clamping and cutting forces were estimated in a very simple part using finite element analysis on the part and fixture (Zhang et al. 2001). Software companies have done significant work in variation simulation and tolerance analysis. Commercial versions of simple tolerance stack-up software are available from Variation Systems Analysis and Dimensional Control Systems, both in Michigan. Their software has been used to model the conform-
ance of assemblies (called capability) to their tolerances specified in the part geometry drawings. These software packages use the GD&T and Monte Carlo sampling techniques to estimate conformance of the assembly to part print tolerances. Most of the current available research as explained above is involved in the prediction of quality based on geometric errors for which the level of modeling difficulty is low. A complete quality model should include all of the types of machining errors and, specifically, the geometric (machine and fixture errors or GD&T tolerance), static (clamping, cutting, spindle, and workpiece errors), and dynamic (wear and thermal) errors and their interactions. Models for static and dynamic errors are more complicated and less widely available. The present modeling methodology, named QUALITY, includes not just geometric errors but also static errors and has the potential to include dynamic errors as well as interactions among errors. The objective of this work is to model these errors on a station-level basis and then show that station errors can be combined into a procedure that propagates errors to subsequent stations and thus predicts final part quality. The goal also includes the validation of these models with both laboratory and production data.
Figure 1 QUALITY Modeling Methodology for Propagation of Various Machining Errors Within and Between Station(s)
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Quality Modeling Methodologies Generic Concept The QUALITY modeling methodology propagates the various errors in machining a part from station to station. All of the station-level errors are modeled at each station, and they propagate through a machining line, as illustrated in Figure 1. The error at the final station is affected by the errors from all the stations in the manufacturing system. For example, the quality of the part feature i at station K is represented as Qik and is described in terms of a mean and six standard deviations, as illustrated in Figure 1. The quality, Qik, is the sum of the part quality coming from the previous operation or station, Qik-1, plus the quality or variability at station/ operation K, represented as Eik. The station-level variability (sometimes referred as an error), Eik, is a sum of the geometric, static, and dynamic variations/errors (Eg, Es, Ed). This methodology allows the user to evaluate the contribution of each operation and each component involved in the operation to part quality and hence identifies the major process and system components to reduce variations. Analytical Representation of Station-Level Quality There are several methods for determining the overall tolerance by performing tolerance stack-up analysis, as explained in the introduction. In all these methods, each operation or station is described so that the variation (or error) at each stage in the process is modeled as the sum of the variations from the system components that contribute to the total variation at that stage. Typical variation/error components are illustrated in Figure 2. Each variation/error is modeled separately. If there are N operations (stations) in the system (that is, k = 1, 2, …, K–1, K, …, N, as illustrated in Figure 1), the error for the jth feature and the ith quality characteristic, Qij, is represented by the following analytical form:
Figure 2 Sources of Variations and Influence Diagram for a Machining Station
where: Cx = 1 if the Ex type of error contributes to the error at the kth station; otherwise Cx = 0. Qijk = ith quality characteristic of jth feature at kth machining station. Exijk = type of xth error (Figure 2) at the kth station contributing to jth feature and ith quality characteristic.
N
Qij Qijk k 1
(1)
where the error at each station is:
The ith quality characteristic includes various types of tolerances, such as form (flatness, straightness, circularity, cylindricity), profile, orientation (perpendicularity, angularity, parallelism), location (position and
m
Qijk Cx Ex ijk X 1
(2)
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concentricity), and runout (circular and total) (Evans 1975). These errors are modeled separately for each feature. Let’s say that each error/variation, Exijk , has a distribution with mean xijk and variance 2xijk . Any stack-up tolerance analysis discussed in the introduction can be used in combination with Eq. (1) to define the ith quality-type error at the kth station for each feature j. The variations for each feature are summed at each station. Then the mean (ijk) and vari2 ance ( ijk) of the distribution for Qijk on the processed samples can be obtained at any station.
the relevant features are machined as well as black shading that highlights the feature machined at that station. Special treatment of the current 3DCS software is required to model a manufacturing process. Each station in the line is modeled. The model of the fixture is positioned in the machine, the model of the in-process part is placed on the fixture, and then the machining operation is performed by placing the machined feature on the in-process part. The modeler must know or select an appropriate station-level variation/error model to specify the variation (or tolerance) that occurs for each type of error, which can contribute to machining error at this station. In principle, these can be independently verified. If more than one machining operation is performed on a single fixture, this procedure is replicated in the model for each operation. Sometimes this means that a multispindle operation must be modeled, and other times it means that successive operations must be modeled. The formulation of accurate station-level error models for the machining operation is critical to the success of the QUALITY methodology. In 3DCS, each part, subassembly, and fixture is identified as an element in the correct assembly sequence, and each element in the assembly tree contains its associated moves and tolerances for quick assessment of the model. An element in the assembly tree may also contain the geometry information of a physical part. A physical part can be defined via DCS points and DCS entries such as lines, circles, slots, or
Station-Level Error Modeling Procedure The 3DCS software was selected to be used in QUALITY to propagate errors among the system manufacturing stations. The 3DCS software accepts multiple statistical distributions (for example, Gaussian, Weibull, Pearson, plant data, etc.) as errors (DCS 2000). 3DCS is a tolerance simulation software that allows the user to model the effect of variation on an assembly, determine the “robustness” of the design, and test alternative tolerance schemes. 3DCS displays the relationships between parts and subassemblies with an assembly tree. The basic approach of the methodology is to follow the manufacturing process sheets in constructing the model in 3DCS. For example, the process steps that contribute to variations in the deckface flatness of a cylinder head are shown in Figure 3. The figure contains annotations that indicate the station at which
Figure 3 Cylinder Head Process Steps Affecting Deckface Flatness
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even IGES geometry, as illustrated in Figure 4. Figure 4 shows the deckface and coverface of the cylinder head. It also shows machined features such as milled exhaust face and drilled primary locators that define the reference locations for the part in the subsequent operations. The DCS points are the basis of the 3DCS model, while DCS entries are primarily for visualization and verification of the assembly sequence. Figure 5 shows the structure of the propagation model for part quality, which is a rather complicated relationship between factors that affect part quality. These have been depicted as several levels. The Key Product Input Variables (KPIV) are the known Inputs, which describe the variability of the system setup parameters (shown on the top level). The group shown on the next level is the geometric, static, and dynamic models required at each station. The models comprise the generic Process Models, which are used to model the individual machining processes. The simplest process models can be used directly as the station-level error model, for example, a machine accuracy that might be specified as a mean, η, and a variance, σ. In complicated cases, such as clamping distortions, the process models be-
come the FEA, which must be run for a number of boundary conditions to generate an intermediate database. The station-level error model is an algorithm (which the user must create) that determines the part distortion as a function of the station-level process parameters such as variations in clamping force or part geometry as it affects fixturing. In the final or fourth level, the Key Product Output Variables (KPOV) or errors are tracked and accumulated on a station-by-station, process-by-process basis. This is done by the 3DCS software. Information such as variation in the depth of cut propagates from the 3DCS predictions for the current station into the error models for the following stations. Implementation in 3DCS The QUALITY procedure was implemented and validated, as illustrated in Figure 6, for an engine cylinder head, shown in Figure 7. The various functions performed to implement and validate the QUALITY methodology are: • The geometric errors of the machines and spindles were deduced from plant coordinate
Figure 4 Machine Feature(s) Representation in 3DCS
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Predictive algorithms based on the station-level error models were used by the 3DCS model to provide the variation of the static errors. The Monte Carlo variation simulation from 3DCS was used to propagate all these variations/errors between stations and to predict the final part quality. 3DCS Model Construction The manufacturing processes modeled in the 3DCS software were: (1) mill the locating pads, (2) drill and ream locator holes, (3) rough mill deckface, (4) drill, (5) counterbore, and (6) finish bore the exhaust seats and guides pockets; (7) drill, (8) counterbore, and (9) finish bore the intake seats and guides pockets; (10) press valve seats and guides; (11) finish mill deckface, (12a) (12b) (12c) (12d) finish bore exhaust seats and guides, and (13a) (13b) (13c) (13d) finish bore intake seats and guides. The deckface of the cylinder head was affected by five of the manufacturing stations (1, 2, 3, 10, and 11, shown in Figure 3), while the seats and guides were affected by all of the above stations. Typically, a 3DCS model of a manufacturing process is created as follows: 1. Import the CAD entities (points, lines, circles, etc.) for use as visual aids. 2. Based on the CAD entities, define a set of DCS points as needed. They are the basis of moves, tolerance assignments, and measurements. 3. Define the sequence in which the different operations in the process go together via 3DCS move functions. 4. Define the range of variations for significant errors via 3DCS tolerance functions. 5. Track the critical dimensions in the process that are affected by machine tool, fixture, cutting tool, and cutting process tolerances via 3DCS measurement functions.
Figure 5 Static-Level Propagation Model for Machining Part Quality Using 3DCS
• • • • •
•
measuring machine (CMM) data if available or defined based on experience. The tool/holder variation was estimated from previous experimental and collected data. The geometric variations of the part and fixture were modeled based on plant data for part geometry and prints for fixture geometry. Casting variation of the cylinder head was obtained from CMM data of the casting plant. The static errors for the part due to clamping and spindle deflection were determined from models based on FEA. The static error for the part due to cutting forces was determined from models based on FEA supplemented by models developed using metalcutting simulations. The static error models were validated in the lab using a fixture nearly identical to that in the plant.
The 3DCS software itself consists of a number of routines, which are used to track accumulating errors or tolerances for the factors of variations illustrated in Figure 6, as a part is machined at sequential stations. After a model of the process has been built, the tolerances are applied and the quality is simulated. The variation is provided either from a predictive algorithm or a suggested statistical distribution. The predictive algorithms are analytical or empirical models based on FEA results.
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Figure 6 QUALITY Information/Data Flow
Model Enhancement Possibilities It is essential that the largest contributors to variance, listed in Figure 2, are included in the model. In many cases, these must be estimated because of a lack of data. For example:
Application in 3DCS Simulation The Monte Carlo method was adapted in this method to stack up all anticipated and predicted deviations/errors during manufacturing of the selected part features. One advantage of the Monte Carlo method is that it lets the user enter a probability distribution for each feature error. The 3DCS model accepts multiple statistical distributions to define the variation for each KPIV or estimated KPOV. The feature errors are then “stacked up” in the computer using 3DCS software. The Monte Carlo simulation will run a specified number of parts, M. Each part travels from station to station through the machining process modeled in 3DCS software, and a random error (within its statistical distribution) for each KPOV can be assigned for each machined feature. After the desired number of the same features is manufactured (that is, M), standard statistics are used to determine the nominal and the variance (tolerance) values for the features. M = 3000 has been chosen, which gives an accuracy better than 2%.
• The positioning error of a CNC machine can be estimated, based on experience and OEM specifications, to be less than ±0.010 mm. This includes errors such as E4 – E8 and E15 – E17 in Figure 2. Machine tool performance (or geometric error components) could be also measured because it is mainly characterized by the positional and squareness errors of a machine relative to a fixture. • Likewise, tool wear (E18 in Figure 2) can be estimated to be uniformly distributed and, depending on the type of machining operation and size tolerance to be held, the tool would be changed after it affects the feature tolerance by 0.012 mm. • The measurement error of a gage (E21 in Figure 2) could also be considered when a prediction
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Figure 7 Case Study – Cylinder Head
is compared against actual plant data. The error in measured quality made by a gage is defined by a mean and variance, as follows: qijk = ijk + CMM
(3)
q2ijk = 2ijk + 2CMM
(4)
Figure 8 Comparison of Surface Deviation Predicted by QUALITY Model with Plant Measurements for Point 9 for Deckface at Station 11
parts. The height of 12 points on the deckface (shown in Figure 7) was measured by a CMM and also predicted by the QUALITY model. The distortion of these 12 points due to clamping and cutting (based on station-level error models) was estimated from FEA. The height variation of the primary machining locating pads and the fixture pad height deviation affects significantly the machined deckface surface height through the geometric and static errors. The height for one of the 12 points (point 9 in Figure 7) on the deckface after finish milling (station 11) is shown in Figure 8 for a controlled sample. The predicted values follow the same trend as the measured values in most cases. The predictions from this QUALITY model were satisfactory because, even though they did not match exactly the measurements, the trend for the eight parts was generally predicted. The actual production value for the surface height at each of the 12 points on the deckface is very difficult to predict using the currently available information. This is because the actual values of the geometric errors (machine accuracy, fixture variation, tooling variation, discussed in an earlier section and Figure 2) for the machines in production were not available and had to be estimated. The flatness error is defined for each part as the range (maximum minus the minimum value) of the height of the surface at 12 points. The comparison of the 3DCS predicted flatness versus the plant measurements for the 219 parts is shown in Figure 9 after
This gage error can be obtained from the gage repeatability and reproducibility (gage R&R) performance.
Quality Model Validation The scope of the investigation was limited to two measures of quality—flatness/profile and hole quality of a cylinder head, as illustrated in Figure 7. The QUALITY methodology was validated using quality data from production (based either on 219 part measurements in the CMM database or parts traced between stations) and experiments in the lab, as illustrated in Figure 6. A fixture similar to that in the production plant was made to validate some of the models used in QUALITY. Experiments were conducted under controlled conditions to validate the clamping and cutting distortion of the deckface results from FEM. The hole quality deformation was also validated. The pressing operation of the seats and guides was validated at the plant. Deckface Height and Flatness The deckface height and flatness were calculated in the QUALITY model (3DCS application) using the actual pad height distribution (CMM data) for 219
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the surface heights at individual points because flatness zeros out local variations caused by geometric and dynamic errors. Considering the limitations of the input data (values that had to be estimated), it is believed that the model provides fairly good agreement with the measured SPC data. Factors Dominating Mean Shift A sensitivity analysis was performed for the finish milling of deckface at station 11 in 3DCS to evaluate the contributions of the pad height error, clamping, cutting, and spindle tilt on the deckface height for nine points. The results are shown in Figure 10. The different patterns in the bar chart identify the individual contributions to changes in the surface profile from the various tolerances or factors. Figure 10 shows that the sensitivities are different at each different point. Nevertheless, some general trends can be identified, as follows:
Figure 9 Comparison of Flatness for All of the 219 heads after Finish Milling Operation
manufacturing station 11. The two distributions have about the same shape, but the 3DCS prediction is approximately 0.010 mm higher than the plant measurements. It is believed that one of the geometric errors estimated for the machine is larger than the actual machine error in the plant for station 11 and should be reduced. The agreement for the flatness prediction is much better than for the prediction of
1. The clamping contribution is very significant for most of the points. 2. The spindle tilt is significant at the points far from the centerline of the cutter (by the intake and exhaust sides) as expected. 3. The contribution from cutting deflection tends to be the smallest of the four factors.
Figure 10 Comparison of Mean Shift Contributions Predicted by QUALITY
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Factors Dominating Variation A number of different parameters have the potential to contribute to the part-to-part variation. These parameters were discussed in an earlier section. The variation is defined in terms of the square of the standard deviation. However, some errors, such as pad height, have a compounding effect on the measurement, clamping, cutting, and tilting effect. To examine the contribution from each effect, each one of the four variables is turned off individually, which means that four separate simulations must be run. The relative contributions to variance are shown in Figure 11. This figure shows that most of the contributions to the variation come from two sources, both of which are related to the variations in machining the locating pads. Figure 11 also shows that clamping distortion also can make a significant contribution to the part-to-part variations in the height of the deckface. At nearly all the points on the deckface, the clamping distortion is much larger than the cutting distortion. The other variations, such as the machine accuracy, tend to be relatively small, on the order of a few microns (assuming the machine is properly maintained), and do not contribute significantly to the variation. These are specific results. They apply to
this part, processed in this manner and fixtured in this manner. Changes to the part stiffness, the process, or the fixturing will alter the relative contributions to variance. Seats and Guides Concentricity The concentricity of the seats and guides was evaluated in the QUALITY model based on 219 parts. Figure 12 shows the concentricity for two valves machined in a single station with twin spindles. The QUALITY prediction is shown as well. A comparison of the part CMM data indicates how much the concentricity can vary from station to station. A detailed inspection of the results for all of the 16 valves and guides on a station-by-station basis shows that each station has its own unique distribution of concentricity because some of the errors, that is, runout between the tool and spindle, vary from station to station. The QUALITY model predicts the spread of the variation based on the statistical distribution for the errors. Some of the errors (concentricity, runout, and so on) could have small mean shifts between tool changes, resulting in wider distribution spread with all the data, which were not considered in the above model.
Figure 11 Comparison of Variance Contribution Predicted by QUALITY
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Figure 12 Concentricity of Inlet Seat and Guide #3 and #7
Summary and Conclusions
and flatness of the deckface and for form and location of the seats and guides of a cylinder head. An essential part of this methodology is the availability of models to predict the most significant contributors to errors or variations during the machining of the part. In the case of the cylinder head, these errors occurred during the clamping of the part and during the machining of the primary machining locating pads. Neither of these errors is included in the earlier, simple formulations of quality (Fainguelernt, Weill, Bourdet 1986; Slocum 1992; Soons, Theuws, Schellekens 1992; Frey, Otto, Pflager 1997; Djurdjanovic and Ni 2001; Maier-Speredelozzi and Hu 2002; Rong and Zhu 1999; Weill, Darel, Laloum 1991; Choudhuri and De Meter 1999; Chandra et al. 1997; Zhang et al. 2001), which are based only on geometry and tolerances specified on part prints. The operation of the software replicates the anticipated trends and sensitivities, producing confidence that the process model of the cylinder head has been implemented correctly and that the results are valid. Finally, the dynamic (thermal, tool wear, etc.) errors were not considered in the above procedure because such error models are not available for such complex phenomena.
• A QUALITY methodology has been established to predict the quality of machined parts. • The methodology determines deviations from nominal part dimensions based on geometric, static, and dynamic errors occurring at each station during the machining of certain features. • It is a methodology and tool for performing quantitative analysis and sensitivity analysis on machine tool systems. • The dynamic (thermal, tool wear, etc.) errors were not considered in the above procedure because such error models are not available for such complex phenomena. The methodology predicts process quality in terms of Cp and Cpk for a given part feature and manufacturing system. It can compare different manufacturing configurations based on the number of setups, reference planes, process layout, and so on. It provides an understanding of the major sources of variation on part quality and manufacturing system design. The total station errors at all stations are appropriately (vectorially) summed to predict the overall quality. The procedure was validated for the case of form
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Acknowledgments The authors would like to thank A. Anagonye, J. Alden, P. Bojda, P. Hilber, J. Xie, and W. Nguyen for helping with the analysis, modeling, and validation.
Soons, J.A.; Theuws, F.C.; and Schellekens, P.H. (1992). “Modeling the errors of multi-axis machines: a general methodology.” Precision Engg. (v14/1), pp5-19. Speckhart, F.H. (1972). “Calculation of tolerance based on minimum cost approach.” Journal of Engg. for Industry (v94, May 1972), pp447-453. Spotts, M.F. (1973). “Allocation of tolerances to minimize cost of assembly.” Journal of Engg. for Industry (v92, Aug. 1973), pp762-764. VSA (1998). VSAVSA-GDT/UG & VSA-3D/UG Training Manual. Variation Systems Analysis, Inc. Weill, R.; Darel, I.; and Laloum, M. (1991). “The influence of fixture positional errors on the geometric accuracy of mechanical parts.” Proc. of CIRP Conf. on PE & MS, Sept. 1991. Zhang, Y.; Hu, W.; Rong, Y.; and Yen, D.W. (2001). “Graph-based setup planning and tolerance decomposition for computer-Aided fixture design” (accepted).
References ASME (1994). ASME Y14.5M – 1994. American Society of Mechanical Engineers National Standards. Chandra, P.; Athavale, S.M.; Kapoor, S.G.; and DeVor, R.E. (1997). “Finite element based fixture analysis model for surface error predictions due to clamping and machining forces.” Mfg. Science and Technology (ASME MED-Vol. 2), pp245-252. Chase, K.W.; Greenwood, W.H.; Loosi, B.G.; and Hauglund, L.F. (1989). “Least cost tolerance allocation for mechanical assemblies with automated process selection.” Failure Prevention and Reliability (ASME, DE-Vol. 16), pp165-171. Choudhuri, S.A. and De Meter, E.C. (1999). “Tolerance analysis of machining fixture locators.” Journal of Mfg. Science and Engg. (v121, May 1999), pp273-281. DCS (2000). DCS Training Manual. Dimensional Control Systems Training Manual. Djurdjanovic, D. and Ni, J. (2001). “Linear space modeling of dimensional machining errors.” Trans. of the North American Mfg. Research Institution of SME (v29), pp541-547. Evans, D.H. (1975). “Statistical tolerancing: the state of the art – Part II. methods for estimating moments.” Journal of Quality Technology (v7, n1), pp1-12. Fainguelernt, D.; Weill, R.; and Bourdet, P. (1986). “Computer aided tolerancing and dimensioning in process planning.” Annals of the CIRP (v35/1), pp381-386. Frey, D.D.; Otto, K.N.; and Pflager, W. (1997). “Swept envelopes of cutting tools in integrated machine and workpiece error budgeting.” Annals of the CIRP (v46/1), pp475-480. Kawlra, R.K. (1994). “Development and application of a methodology for minimizing costs based on optimal tolerance allocation.” PhD thesis. Ann Arbor, MI: Univ. of Michigan. Lee, W.J. and Woo, T.C. (1990). “Tolerances: their analysis and synthesis.” Journal of Engg. for Industry (v112, May 1990), pp113-121. Maier-Speredelozzi, V. and Hu, J.S. (2002). “Selecting manufacturing system configurations based on performance using AHP.” Trans. of the North American Mfg. Research Institution of SME (v30), pp637-644. Rong, Y. and Zhu, Y. (1999). Computer-Aided Fixture Design. New York: Marcel Dekker. Slocum, A.H. (1992). Precision Machine Design. Englewood Cliffs, NJ: Prentice-Hall.
Authors’ Biographies John Agapiou received his PhD from the University of Wisconsin-Madison in 1985. He is currently a staff research engineer in the Manufacturing Systems Research Lab at the GM R&D Center. His research interests are optimization of metal cutting operations, including cutting tools and tool holders, agile/flexible manufacturing, modeling metal cutting operations, modeling manufacturing quality for machining lines, and high-speed machining. Eric Steinhilper received his PhD from the California Institute of Technology (CalTech) in 1972. He is currently a staff research engineer in the Manufacturing Systems Research Lab at the General Motors Research and Development Center. His areas of research include predicting part quality and predictive maintenance. Fangming Gu is a staff research engineer at Manufacturing Systems Research Lab at the GM R&D Center. He received his MS and PhD in mechanical engineering from the University of Illinois in UrbanaChampaign in 1991 and 1994, respectively. His research interests are computer-aided metal cutting process simulation/analysis and application of emerging information technology in manufacturing. Pulak Bandyopadhyay is currently a Lab Group Manager at the GM R&D Center’s Manufacturing Systems Research Laboratory. He has been working at the GM R&D Center for 19 years in the area of automotive manufacturing research. His research interests include math-based modeling of manufacturing processes and systems, agile/reconfigurable manufacturing system design, and real-time process control. Recently, his group has been involved in defining e-manufacturing R&D needs for GM. Dr. Bandyopadhyay has won several awards, including Outstanding Young Manufacturing Engineer Award from the Society of Manufacturing Engineers and GM’s most prestigious award, the Boss Kettering award. Dr. Bandyopadhyay is a senior member of SME and serves on the scientific committee of NAMRI/SME.
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Modeling Machining Errors on a Transfer Line to Predict Quality John S. Agapiou, Eric Steinhilper, Fangming Gu, and Pulak Bandyopadhyay, Enterprise Systems Laboratory, General Motors R&D Center, Warren, Michigan, USA
Abstract
Research work in tolerancing that affects quality has taken place sporadically. During the early 1970s, many articles were published on how to assign tolerances to minimize costs (Speckhart 1972; Spotts 1973). In the late 1980s, some researchers emphasized the application of statistical tolerancing to reduce manufacturing costs (Chase et al. 1989; Lee and Woo 1990). Dimensional errors used in assembly and machining are addressed in geometric dimensioning and tolerancing (GD&T) (ASME 1994). Several methods of tolerance assignment are available based on linear stack-up analysis using the knowledge of the mean and the variance for the individual variations/errors. This linear stack-up can be obtained using a worst-case or calculus-based approach (Straight Stack), a statistical tolerance analysis method—root sum squares, or Monte Carlo simulation (Evans 1975; Kawira 1994). The Monte Carlo simulation works well for both linear and nonlinear stack-ups. Variation simulation techniques have been developed for tolerancing and dimensioning in process planning (Fainguelernt, Weill, Bourdet 1986). Such models take into account fixturing tolerances as well as machining tolerances. Another approach is error budgeting, which has been used to estimate overall workpiece accuracy (Slocum 1992; Soons, Theuws, Schellekens 1992; Frey, Otto, Pflager 1997). An error budget is a systematic account of all sources of error in a machine, including such effects as component accuracy, structural compliance, and thermally induced deflections. Linear state-space modeling of dimensional machining errors was also lately used to transform and accumulate machining errors as the workpiece is machined in a multistation process (Djurdjanovic and Ni 2001; Maier-Speredelozzi and Hu 2002). This approach requires the definition of a frame of reference for each machining station, fixture,
This paper introduces a methodology for predicting part quality based on the expected and measured process variations (geometric, static, and dynamic errors). Part quality in terms of dimensional (location), orientation, form, and profile tolerances can be predicted using a “stream of variation model” in a multistation machining system (serial, parallel, or hybrid) and validated on an engine cylinder head. The understanding gained from an application of this methodology to a machined component can help achieve substantial part-quality and process improvements.
Keywords: Quality, Predicting, Machining, Variation, Simulation, Modeling
Introduction Machining can involve a large number of stations, operations, and several locating datum changes, especially when machining engine blocks, heads, or transmission components. Part quality is affected by the variations or errors from each station and any reference datum frame changes between stations. Although quality prediction (variation simulation) has been used for product design and assembly (VSA 1998; DCS 2000), it has had very limited application for manufacturing system design. A manufacturing system consists of one or more machining or assembly stations through which the part travels and where dimensions or features are generated. Several locating datum changes may occur between operations and/or stations. Consequently, features are made with small part-to-part variations or errors. Generic models for analyzing product quality from machining systems are not yet available. Such models should include variations/errors for (or from) a manufacturing system. This paper is an original work and has not been previously published except in the Transactions of NAMRI/SME, Vol. 31, 2003.
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and part. The mathematical transformations between frames are then described and the geometric errors can be estimated. This approach is extremely time consuming because it is explicit. The above variation simulation approaches tend to neglect the influence of fixture positional errors on the geometric accuracy of a part. Another group of researchers concentrated on the analysis of a part’s geometric error due to fixture positional errors (Rong and Zhu 1999; Weill, Darel, Laloum 1991; Choudhuri and De Meter 1999; Chandra et al. 1997). These simulations include only geometric errors in their calculations of part accuracy. The static errors (introduced by part and spindle deflections due to clamping and cutting forces) were neglected in the latter analyses except in one case, where the static errors due to clamping and cutting forces were estimated in a very simple part using finite element analysis on the part and fixture (Zhang et al. 2001). Software companies have done significant work in variation simulation and tolerance analysis. Commercial versions of simple tolerance stack-up software are available from Variation Systems Analysis and Dimensional Control Systems, both in Michigan. Their software has been used to model the conform-
ance of assemblies (called capability) to their tolerances specified in the part geometry drawings. These software packages use the GD&T and Monte Carlo sampling techniques to estimate conformance of the assembly to part print tolerances. Most of the current available research as explained above is involved in the prediction of quality based on geometric errors for which the level of modeling difficulty is low. A complete quality model should include all of the types of machining errors and, specifically, the geometric (machine and fixture errors or GD&T tolerance), static (clamping, cutting, spindle, and workpiece errors), and dynamic (wear and thermal) errors and their interactions. Models for static and dynamic errors are more complicated and less widely available. The present modeling methodology, named QUALITY, includes not just geometric errors but also static errors and has the potential to include dynamic errors as well as interactions among errors. The objective of this work is to model these errors on a station-level basis and then show that station errors can be combined into a procedure that propagates errors to subsequent stations and thus predicts final part quality. The goal also includes the validation of these models with both laboratory and production data.
Figure 1 QUALITY Modeling Methodology for Propagation of Various Machining Errors Within and Between Station(s)
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Quality Modeling Methodologies Generic Concept The QUALITY modeling methodology propagates the various errors in machining a part from station to station. All of the station-level errors are modeled at each station, and they propagate through a machining line, as illustrated in Figure 1. The error at the final station is affected by the errors from all the stations in the manufacturing system. For example, the quality of the part feature i at station K is represented as Qik and is described in terms of a mean and six standard deviations, as illustrated in Figure 1. The quality, Qik, is the sum of the part quality coming from the previous operation or station, Qik-1, plus the quality or variability at station/ operation K, represented as Eik. The station-level variability (sometimes referred as an error), Eik, is a sum of the geometric, static, and dynamic variations/errors (Eg, Es, Ed). This methodology allows the user to evaluate the contribution of each operation and each component involved in the operation to part quality and hence identifies the major process and system components to reduce variations. Analytical Representation of Station-Level Quality There are several methods for determining the overall tolerance by performing tolerance stack-up analysis, as explained in the introduction. In all these methods, each operation or station is described so that the variation (or error) at each stage in the process is modeled as the sum of the variations from the system components that contribute to the total variation at that stage. Typical variation/error components are illustrated in Figure 2. Each variation/error is modeled separately. If there are N operations (stations) in the system (that is, k = 1, 2, …, K–1, K, …, N, as illustrated in Figure 1), the error for the jth feature and the ith quality characteristic, Qij, is represented by the following analytical form:
Figure 2 Sources of Variations and Influence Diagram for a Machining Station
where: Cx = 1 if the Ex type of error contributes to the error at the kth station; otherwise Cx = 0. Qijk = ith quality characteristic of jth feature at kth machining station. Exijk = type of xth error (Figure 2) at the kth station contributing to jth feature and ith quality characteristic.
N
Qij Qijk k 1
(1)
where the error at each station is:
The ith quality characteristic includes various types of tolerances, such as form (flatness, straightness, circularity, cylindricity), profile, orientation (perpendicularity, angularity, parallelism), location (position and
m
Qijk Cx Ex ijk X 1
(2)
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concentricity), and runout (circular and total) (Evans 1975). These errors are modeled separately for each feature. Let’s say that each error/variation, Exijk , has a distribution with mean xijk and variance 2xijk . Any stack-up tolerance analysis discussed in the introduction can be used in combination with Eq. (1) to define the ith quality-type error at the kth station for each feature j. The variations for each feature are summed at each station. Then the mean (ijk) and vari2 ance ( ijk) of the distribution for Qijk on the processed samples can be obtained at any station.
the relevant features are machined as well as black shading that highlights the feature machined at that station. Special treatment of the current 3DCS software is required to model a manufacturing process. Each station in the line is modeled. The model of the fixture is positioned in the machine, the model of the in-process part is placed on the fixture, and then the machining operation is performed by placing the machined feature on the in-process part. The modeler must know or select an appropriate station-level variation/error model to specify the variation (or tolerance) that occurs for each type of error, which can contribute to machining error at this station. In principle, these can be independently verified. If more than one machining operation is performed on a single fixture, this procedure is replicated in the model for each operation. Sometimes this means that a multispindle operation must be modeled, and other times it means that successive operations must be modeled. The formulation of accurate station-level error models for the machining operation is critical to the success of the QUALITY methodology. In 3DCS, each part, subassembly, and fixture is identified as an element in the correct assembly sequence, and each element in the assembly tree contains its associated moves and tolerances for quick assessment of the model. An element in the assembly tree may also contain the geometry information of a physical part. A physical part can be defined via DCS points and DCS entries such as lines, circles, slots, or
Station-Level Error Modeling Procedure The 3DCS software was selected to be used in QUALITY to propagate errors among the system manufacturing stations. The 3DCS software accepts multiple statistical distributions (for example, Gaussian, Weibull, Pearson, plant data, etc.) as errors (DCS 2000). 3DCS is a tolerance simulation software that allows the user to model the effect of variation on an assembly, determine the “robustness” of the design, and test alternative tolerance schemes. 3DCS displays the relationships between parts and subassemblies with an assembly tree. The basic approach of the methodology is to follow the manufacturing process sheets in constructing the model in 3DCS. For example, the process steps that contribute to variations in the deckface flatness of a cylinder head are shown in Figure 3. The figure contains annotations that indicate the station at which
Figure 3 Cylinder Head Process Steps Affecting Deckface Flatness
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even IGES geometry, as illustrated in Figure 4. Figure 4 shows the deckface and coverface of the cylinder head. It also shows machined features such as milled exhaust face and drilled primary locators that define the reference locations for the part in the subsequent operations. The DCS points are the basis of the 3DCS model, while DCS entries are primarily for visualization and verification of the assembly sequence. Figure 5 shows the structure of the propagation model for part quality, which is a rather complicated relationship between factors that affect part quality. These have been depicted as several levels. The Key Product Input Variables (KPIV) are the known Inputs, which describe the variability of the system setup parameters (shown on the top level). The group shown on the next level is the geometric, static, and dynamic models required at each station. The models comprise the generic Process Models, which are used to model the individual machining processes. The simplest process models can be used directly as the station-level error model, for example, a machine accuracy that might be specified as a mean, η, and a variance, σ. In complicated cases, such as clamping distortions, the process models be-
come the FEA, which must be run for a number of boundary conditions to generate an intermediate database. The station-level error model is an algorithm (which the user must create) that determines the part distortion as a function of the station-level process parameters such as variations in clamping force or part geometry as it affects fixturing. In the final or fourth level, the Key Product Output Variables (KPOV) or errors are tracked and accumulated on a station-by-station, process-by-process basis. This is done by the 3DCS software. Information such as variation in the depth of cut propagates from the 3DCS predictions for the current station into the error models for the following stations. Implementation in 3DCS The QUALITY procedure was implemented and validated, as illustrated in Figure 6, for an engine cylinder head, shown in Figure 7. The various functions performed to implement and validate the QUALITY methodology are: • The geometric errors of the machines and spindles were deduced from plant coordinate
Figure 4 Machine Feature(s) Representation in 3DCS
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Predictive algorithms based on the station-level error models were used by the 3DCS model to provide the variation of the static errors. The Monte Carlo variation simulation from 3DCS was used to propagate all these variations/errors between stations and to predict the final part quality. 3DCS Model Construction The manufacturing processes modeled in the 3DCS software were: (1) mill the locating pads, (2) drill and ream locator holes, (3) rough mill deckface, (4) drill, (5) counterbore, and (6) finish bore the exhaust seats and guides pockets; (7) drill, (8) counterbore, and (9) finish bore the intake seats and guides pockets; (10) press valve seats and guides; (11) finish mill deckface, (12a) (12b) (12c) (12d) finish bore exhaust seats and guides, and (13a) (13b) (13c) (13d) finish bore intake seats and guides. The deckface of the cylinder head was affected by five of the manufacturing stations (1, 2, 3, 10, and 11, shown in Figure 3), while the seats and guides were affected by all of the above stations. Typically, a 3DCS model of a manufacturing process is created as follows: 1. Import the CAD entities (points, lines, circles, etc.) for use as visual aids. 2. Based on the CAD entities, define a set of DCS points as needed. They are the basis of moves, tolerance assignments, and measurements. 3. Define the sequence in which the different operations in the process go together via 3DCS move functions. 4. Define the range of variations for significant errors via 3DCS tolerance functions. 5. Track the critical dimensions in the process that are affected by machine tool, fixture, cutting tool, and cutting process tolerances via 3DCS measurement functions.
Figure 5 Static-Level Propagation Model for Machining Part Quality Using 3DCS
• • • • •
•
measuring machine (CMM) data if available or defined based on experience. The tool/holder variation was estimated from previous experimental and collected data. The geometric variations of the part and fixture were modeled based on plant data for part geometry and prints for fixture geometry. Casting variation of the cylinder head was obtained from CMM data of the casting plant. The static errors for the part due to clamping and spindle deflection were determined from models based on FEA. The static error for the part due to cutting forces was determined from models based on FEA supplemented by models developed using metalcutting simulations. The static error models were validated in the lab using a fixture nearly identical to that in the plant.
The 3DCS software itself consists of a number of routines, which are used to track accumulating errors or tolerances for the factors of variations illustrated in Figure 6, as a part is machined at sequential stations. After a model of the process has been built, the tolerances are applied and the quality is simulated. The variation is provided either from a predictive algorithm or a suggested statistical distribution. The predictive algorithms are analytical or empirical models based on FEA results.
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Figure 6 QUALITY Information/Data Flow
Model Enhancement Possibilities It is essential that the largest contributors to variance, listed in Figure 2, are included in the model. In many cases, these must be estimated because of a lack of data. For example:
Application in 3DCS Simulation The Monte Carlo method was adapted in this method to stack up all anticipated and predicted deviations/errors during manufacturing of the selected part features. One advantage of the Monte Carlo method is that it lets the user enter a probability distribution for each feature error. The 3DCS model accepts multiple statistical distributions to define the variation for each KPIV or estimated KPOV. The feature errors are then “stacked up” in the computer using 3DCS software. The Monte Carlo simulation will run a specified number of parts, M. Each part travels from station to station through the machining process modeled in 3DCS software, and a random error (within its statistical distribution) for each KPOV can be assigned for each machined feature. After the desired number of the same features is manufactured (that is, M), standard statistics are used to determine the nominal and the variance (tolerance) values for the features. M = 3000 has been chosen, which gives an accuracy better than 2%.
• The positioning error of a CNC machine can be estimated, based on experience and OEM specifications, to be less than ±0.010 mm. This includes errors such as E4 – E8 and E15 – E17 in Figure 2. Machine tool performance (or geometric error components) could be also measured because it is mainly characterized by the positional and squareness errors of a machine relative to a fixture. • Likewise, tool wear (E18 in Figure 2) can be estimated to be uniformly distributed and, depending on the type of machining operation and size tolerance to be held, the tool would be changed after it affects the feature tolerance by 0.012 mm. • The measurement error of a gage (E21 in Figure 2) could also be considered when a prediction
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Figure 7 Case Study – Cylinder Head
is compared against actual plant data. The error in measured quality made by a gage is defined by a mean and variance, as follows: qijk = ijk + CMM
(3)
q2ijk = 2ijk + 2CMM
(4)
Figure 8 Comparison of Surface Deviation Predicted by QUALITY Model with Plant Measurements for Point 9 for Deckface at Station 11
parts. The height of 12 points on the deckface (shown in Figure 7) was measured by a CMM and also predicted by the QUALITY model. The distortion of these 12 points due to clamping and cutting (based on station-level error models) was estimated from FEA. The height variation of the primary machining locating pads and the fixture pad height deviation affects significantly the machined deckface surface height through the geometric and static errors. The height for one of the 12 points (point 9 in Figure 7) on the deckface after finish milling (station 11) is shown in Figure 8 for a controlled sample. The predicted values follow the same trend as the measured values in most cases. The predictions from this QUALITY model were satisfactory because, even though they did not match exactly the measurements, the trend for the eight parts was generally predicted. The actual production value for the surface height at each of the 12 points on the deckface is very difficult to predict using the currently available information. This is because the actual values of the geometric errors (machine accuracy, fixture variation, tooling variation, discussed in an earlier section and Figure 2) for the machines in production were not available and had to be estimated. The flatness error is defined for each part as the range (maximum minus the minimum value) of the height of the surface at 12 points. The comparison of the 3DCS predicted flatness versus the plant measurements for the 219 parts is shown in Figure 9 after
This gage error can be obtained from the gage repeatability and reproducibility (gage R&R) performance.
Quality Model Validation The scope of the investigation was limited to two measures of quality—flatness/profile and hole quality of a cylinder head, as illustrated in Figure 7. The QUALITY methodology was validated using quality data from production (based either on 219 part measurements in the CMM database or parts traced between stations) and experiments in the lab, as illustrated in Figure 6. A fixture similar to that in the production plant was made to validate some of the models used in QUALITY. Experiments were conducted under controlled conditions to validate the clamping and cutting distortion of the deckface results from FEM. The hole quality deformation was also validated. The pressing operation of the seats and guides was validated at the plant. Deckface Height and Flatness The deckface height and flatness were calculated in the QUALITY model (3DCS application) using the actual pad height distribution (CMM data) for 219
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the surface heights at individual points because flatness zeros out local variations caused by geometric and dynamic errors. Considering the limitations of the input data (values that had to be estimated), it is believed that the model provides fairly good agreement with the measured SPC data. Factors Dominating Mean Shift A sensitivity analysis was performed for the finish milling of deckface at station 11 in 3DCS to evaluate the contributions of the pad height error, clamping, cutting, and spindle tilt on the deckface height for nine points. The results are shown in Figure 10. The different patterns in the bar chart identify the individual contributions to changes in the surface profile from the various tolerances or factors. Figure 10 shows that the sensitivities are different at each different point. Nevertheless, some general trends can be identified, as follows:
Figure 9 Comparison of Flatness for All of the 219 heads after Finish Milling Operation
manufacturing station 11. The two distributions have about the same shape, but the 3DCS prediction is approximately 0.010 mm higher than the plant measurements. It is believed that one of the geometric errors estimated for the machine is larger than the actual machine error in the plant for station 11 and should be reduced. The agreement for the flatness prediction is much better than for the prediction of
1. The clamping contribution is very significant for most of the points. 2. The spindle tilt is significant at the points far from the centerline of the cutter (by the intake and exhaust sides) as expected. 3. The contribution from cutting deflection tends to be the smallest of the four factors.
Figure 10 Comparison of Mean Shift Contributions Predicted by QUALITY
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Factors Dominating Variation A number of different parameters have the potential to contribute to the part-to-part variation. These parameters were discussed in an earlier section. The variation is defined in terms of the square of the standard deviation. However, some errors, such as pad height, have a compounding effect on the measurement, clamping, cutting, and tilting effect. To examine the contribution from each effect, each one of the four variables is turned off individually, which means that four separate simulations must be run. The relative contributions to variance are shown in Figure 11. This figure shows that most of the contributions to the variation come from two sources, both of which are related to the variations in machining the locating pads. Figure 11 also shows that clamping distortion also can make a significant contribution to the part-to-part variations in the height of the deckface. At nearly all the points on the deckface, the clamping distortion is much larger than the cutting distortion. The other variations, such as the machine accuracy, tend to be relatively small, on the order of a few microns (assuming the machine is properly maintained), and do not contribute significantly to the variation. These are specific results. They apply to
this part, processed in this manner and fixtured in this manner. Changes to the part stiffness, the process, or the fixturing will alter the relative contributions to variance. Seats and Guides Concentricity The concentricity of the seats and guides was evaluated in the QUALITY model based on 219 parts. Figure 12 shows the concentricity for two valves machined in a single station with twin spindles. The QUALITY prediction is shown as well. A comparison of the part CMM data indicates how much the concentricity can vary from station to station. A detailed inspection of the results for all of the 16 valves and guides on a station-by-station basis shows that each station has its own unique distribution of concentricity because some of the errors, that is, runout between the tool and spindle, vary from station to station. The QUALITY model predicts the spread of the variation based on the statistical distribution for the errors. Some of the errors (concentricity, runout, and so on) could have small mean shifts between tool changes, resulting in wider distribution spread with all the data, which were not considered in the above model.
Figure 11 Comparison of Variance Contribution Predicted by QUALITY
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Figure 12 Concentricity of Inlet Seat and Guide #3 and #7
Summary and Conclusions
and flatness of the deckface and for form and location of the seats and guides of a cylinder head. An essential part of this methodology is the availability of models to predict the most significant contributors to errors or variations during the machining of the part. In the case of the cylinder head, these errors occurred during the clamping of the part and during the machining of the primary machining locating pads. Neither of these errors is included in the earlier, simple formulations of quality (Fainguelernt, Weill, Bourdet 1986; Slocum 1992; Soons, Theuws, Schellekens 1992; Frey, Otto, Pflager 1997; Djurdjanovic and Ni 2001; Maier-Speredelozzi and Hu 2002; Rong and Zhu 1999; Weill, Darel, Laloum 1991; Choudhuri and De Meter 1999; Chandra et al. 1997; Zhang et al. 2001), which are based only on geometry and tolerances specified on part prints. The operation of the software replicates the anticipated trends and sensitivities, producing confidence that the process model of the cylinder head has been implemented correctly and that the results are valid. Finally, the dynamic (thermal, tool wear, etc.) errors were not considered in the above procedure because such error models are not available for such complex phenomena.
• A QUALITY methodology has been established to predict the quality of machined parts. • The methodology determines deviations from nominal part dimensions based on geometric, static, and dynamic errors occurring at each station during the machining of certain features. • It is a methodology and tool for performing quantitative analysis and sensitivity analysis on machine tool systems. • The dynamic (thermal, tool wear, etc.) errors were not considered in the above procedure because such error models are not available for such complex phenomena. The methodology predicts process quality in terms of Cp and Cpk for a given part feature and manufacturing system. It can compare different manufacturing configurations based on the number of setups, reference planes, process layout, and so on. It provides an understanding of the major sources of variation on part quality and manufacturing system design. The total station errors at all stations are appropriately (vectorially) summed to predict the overall quality. The procedure was validated for the case of form
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Acknowledgments The authors would like to thank A. Anagonye, J. Alden, P. Bojda, P. Hilber, J. Xie, and W. Nguyen for helping with the analysis, modeling, and validation.
Soons, J.A.; Theuws, F.C.; and Schellekens, P.H. (1992). “Modeling the errors of multi-axis machines: a general methodology.” Precision Engg. (v14/1), pp5-19. Speckhart, F.H. (1972). “Calculation of tolerance based on minimum cost approach.” Journal of Engg. for Industry (v94, May 1972), pp447-453. Spotts, M.F. (1973). “Allocation of tolerances to minimize cost of assembly.” Journal of Engg. for Industry (v92, Aug. 1973), pp762-764. VSA (1998). VSAVSA-GDT/UG & VSA-3D/UG Training Manual. Variation Systems Analysis, Inc. Weill, R.; Darel, I.; and Laloum, M. (1991). “The influence of fixture positional errors on the geometric accuracy of mechanical parts.” Proc. of CIRP Conf. on PE & MS, Sept. 1991. Zhang, Y.; Hu, W.; Rong, Y.; and Yen, D.W. (2001). “Graph-based setup planning and tolerance decomposition for computer-Aided fixture design” (accepted).
References ASME (1994). ASME Y14.5M – 1994. American Society of Mechanical Engineers National Standards. Chandra, P.; Athavale, S.M.; Kapoor, S.G.; and DeVor, R.E. (1997). “Finite element based fixture analysis model for surface error predictions due to clamping and machining forces.” Mfg. Science and Technology (ASME MED-Vol. 2), pp245-252. Chase, K.W.; Greenwood, W.H.; Loosi, B.G.; and Hauglund, L.F. (1989). “Least cost tolerance allocation for mechanical assemblies with automated process selection.” Failure Prevention and Reliability (ASME, DE-Vol. 16), pp165-171. Choudhuri, S.A. and De Meter, E.C. (1999). “Tolerance analysis of machining fixture locators.” Journal of Mfg. Science and Engg. (v121, May 1999), pp273-281. DCS (2000). DCS Training Manual. Dimensional Control Systems Training Manual. Djurdjanovic, D. and Ni, J. (2001). “Linear space modeling of dimensional machining errors.” Trans. of the North American Mfg. Research Institution of SME (v29), pp541-547. Evans, D.H. (1975). “Statistical tolerancing: the state of the art – Part II. methods for estimating moments.” Journal of Quality Technology (v7, n1), pp1-12. Fainguelernt, D.; Weill, R.; and Bourdet, P. (1986). “Computer aided tolerancing and dimensioning in process planning.” Annals of the CIRP (v35/1), pp381-386. Frey, D.D.; Otto, K.N.; and Pflager, W. (1997). “Swept envelopes of cutting tools in integrated machine and workpiece error budgeting.” Annals of the CIRP (v46/1), pp475-480. Kawlra, R.K. (1994). “Development and application of a methodology for minimizing costs based on optimal tolerance allocation.” PhD thesis. Ann Arbor, MI: Univ. of Michigan. Lee, W.J. and Woo, T.C. (1990). “Tolerances: their analysis and synthesis.” Journal of Engg. for Industry (v112, May 1990), pp113-121. Maier-Speredelozzi, V. and Hu, J.S. (2002). “Selecting manufacturing system configurations based on performance using AHP.” Trans. of the North American Mfg. Research Institution of SME (v30), pp637-644. Rong, Y. and Zhu, Y. (1999). Computer-Aided Fixture Design. New York: Marcel Dekker. Slocum, A.H. (1992). Precision Machine Design. Englewood Cliffs, NJ: Prentice-Hall.
Authors’ Biographies John Agapiou received his PhD from the University of Wisconsin-Madison in 1985. He is currently a staff research engineer in the Manufacturing Systems Research Lab at the GM R&D Center. His research interests are optimization of metal cutting operations, including cutting tools and tool holders, agile/flexible manufacturing, modeling metal cutting operations, modeling manufacturing quality for machining lines, and high-speed machining. Eric Steinhilper received his PhD from the California Institute of Technology (CalTech) in 1972. He is currently a staff research engineer in the Manufacturing Systems Research Lab at the General Motors Research and Development Center. His areas of research include predicting part quality and predictive maintenance. Fangming Gu is a staff research engineer at Manufacturing Systems Research Lab at the GM R&D Center. He received his MS and PhD in mechanical engineering from the University of Illinois in UrbanaChampaign in 1991 and 1994, respectively. His research interests are computer-aided metal cutting process simulation/analysis and application of emerging information technology in manufacturing. Pulak Bandyopadhyay is currently a Lab Group Manager at the GM R&D Center’s Manufacturing Systems Research Laboratory. He has been working at the GM R&D Center for 19 years in the area of automotive manufacturing research. His research interests include math-based modeling of manufacturing processes and systems, agile/reconfigurable manufacturing system design, and real-time process control. Recently, his group has been involved in defining e-manufacturing R&D needs for GM. Dr. Bandyopadhyay has won several awards, including Outstanding Young Manufacturing Engineer Award from the Society of Manufacturing Engineers and GM’s most prestigious award, the Boss Kettering award. Dr. Bandyopadhyay is a senior member of SME and serves on the scientific committee of NAMRI/SME.
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