Research Papers

Stochastic Modeling and Diagnosis of Leak Areas for Surface Assembly

[+] Author and Article Information
Jie Ren, Chiwoo Park

Department of Industrial and
Manufacturing Engineering,
Florida State University,
Tallahassee, FL 32310

Hui Wang

Department of Industrial and
Manufacturing Engineering,
Florida State University,
Tallahassee, FL 32310
e-mail: hwang10@fsu.edu

1Corresponding author.

Manuscript received April 11, 2017; final manuscript received December 10, 2017; published online February 13, 2018. Assoc. Editor: Laine Mears.

J. Manuf. Sci. Eng 140(4), 041011 (Feb 13, 2018) (10 pages) Paper No: MANU-17-1244; doi: 10.1115/1.4038889 History: Received April 11, 2017; Revised December 10, 2017

Assembly through mating a pair of machined surfaces plays a crucial role in many manufacturing processes such as automotive powertrain production, and the mating errors during the assembly (i.e., gaps between surfaces) can cause significant internal leakage and functional performance problems. The surface mating errors are difficult to diagnose because they are not measurable. Current in-plant quality control for surface mating focuses on controlling the surface flatness of each individual part before they are mated, and the mating errors are indirectly evaluated by a pressurized sealing test to check whether any pressure drop occurs. However, it does not provide any clue to engineers about the origins and the root cause of the internal leakage. To address these limitations, this paper presents a pressurized color-tracking method to directly measure internal leak areas. By using the measurements of leak areas and the profiles of surfaces mated as training data along with Hagen–Poiseuille law, this paper develops a novel diagnostic method to predict potential leak areas (leakage paths) given the measurements on the profiles of mating surfaces. The effectiveness and robustness of the proposed method are verified by a simulation study and an experiment. The approach provides practical guidance for the subsequent assembly process as well as troubleshooting in surface machining processes.

Copyright © 2018 by ASME
Your Session has timed out. Please sign back in to continue.


Arghavani, J. , Derenne, M. , and Marchand, L. , 2002, “ Prediction of Gasket Leakage Rate and Sealing Performance Through Fuzzy Logic,” Int. J. Adv. Manuf. Technol., 20(8), pp. 612–620. [CrossRef]
Nguyen, H. T. , Wang, H. , Tai, B. L. , Ren, J. , Hu, S. J. , and Shih, A. , 2015, “ High-Definition Metrology Enabled Surface Variation Control by Cutting Load Balancing,” ASME J. Manuf. Sci. Eng., 138(2), p. 021010. [CrossRef]
Du, S.-C. , Huang, D.-L. , and Wang, H. , 2015, “ An Adaptive Support Vector Machine-Based Workpiece Surface Classification System Using High-Definition Metrology,” IEEE Trans. Instrum. Meas., 64(10), pp. 2590–2604. [CrossRef]
Nguyen, H. T. , Wang, H. , and Hu, S. J. , 2013, “ Characterization of Cutting Force Induced Surface Shape Variation in Face Milling Using High-Definition Metrology,” ASME J. Manuf. Sci. Eng., 135(4), p. 041014. [CrossRef]
Zhou, L. , Wang, H. , Berry, C. , Weng, X. , and Hu, S. J. , 2012, “ Functional Morphing in Multistage Manufacturing and Its Applications in High-Definition Metrology-Based Process Control,” IEEE Trans. Autom. Sci. Eng., 9(1), pp. 124–136.
Suriano, S. , Wang, H. , Shao, C. , Hu, S. J. , and Sekhar, P. , 2015, “ Progressive Measurement and Monitoring for Multi-Resolution Data in Surface Manufacturing Considering Spatial and Cross Correlations,” IIE Trans., 47(10), pp. 1033–1052. [CrossRef]
Wang, M. Y. , 2004, “ Form Error Evaluation: An Iterative Reweighted Least Squares Algorithm,” ASME J. Manuf. Sci. Eng., 126(3), pp. 535–541. [CrossRef]
Lee, S. , Wolberg, G. , and Shin, S. Y. , 1997, “ Scattered Data Interpolation With Multilevel B-Splines,” IEEE Trans. Visualization Comput. Graph., 3(3), pp. 228–244. [CrossRef]
Valette, S. , and Prost, P. , 2004, “ Wavelet-Based Multiresolution Analysis of Irregular Surface Meshes,” IEEE Trans. Visualization Comput. Graph., 10(2), pp. 113–122. [CrossRef]
Yang, T.-H. , and Jackman, J. , 2000, “ Form Error Estimation Using Spatial Statistics,” ASME J. Manuf. Sci. Eng., 122(1), pp. 262–272. [CrossRef]
Xia, H. , Ding, Y. , and Wang, J. , 2008, “ Gaussian Process Method for Form Error Assessment Using Coordinate Measurements,” IIE Trans., 40(10), pp. 931–946. [CrossRef]
Qian, P. Z. , and Wu, C. J. , 2008, “ Bayesian Hierarchical Modeling for Integrating Low-Accuracy and High-Accuracy Experiments,” Technometrics, 50(2), pp. 192–204. [CrossRef]
Xia, H. , Ding, Y. , and Mallick, B. K. , 2011, “ Bayesian Hierarchical Model for Combining Misaligned Two-Resolution Metrology Data,” IIE Trans., 43(4), pp. 242–258. [CrossRef]
Jin, R. , Chang, C.-J. , and Shi, J. , 2012, “ Sequential Measurement Strategy for Wafer Geometric Profile Estimation,” IIE Trans., 44(1), pp. 1–12. [CrossRef]
Du, S. , and Fei, L. , 2015, “ Co-Kriging Method for Form Error Estimation Incorporating Condition Variable Measurements,” ASME J. Manuf. Sci. Eng., 138(4), p. 041003. [CrossRef]
Shao, C. , Ren, J. , Wang, H. , Jin, J. J. , and Hu, S. J. , 2017, “ Improving Machined Surface Shape Prediction by Integrating Multi-Task Learning With Cutting Force Variation Modeling,” ASME J. Manuf. Sci. Eng., 139(1), p. 011014. [CrossRef]
Ren, J. , and Wang, H. , 2016, “Surface Variation Modeling by Fusing Surface Measurement Data With Multiple Manufacturing Process Variables,” ASME Paper No. MSEC2016-8717.
Furrer, R. , Genton, M. G. , and Nychka, D. , 2006, “ Covariance Tapering for Interpolation of Large Spatial Datasets,” J. Comput. Graph. Stat., 15(3), pp. 502–523. [CrossRef]
Kaufman, C. G. , Schervish, M. J. , and Nychka, D. W. , 2008, “ Covariance Tapering for Likelihood-Based Estimation in Large Spatial Data Sets,” J. Am. Stat. Assoc., 103(484), pp. 1545–1555. [CrossRef]
Seeger, M. , Williams, C. , and Lawrence, N. , 2003, “Fast Forward Selection to Speed Up Sparse Gaussian Process Regression,” Ninth International Workshop on Artificial Intelligence and Statistics (AISTATS), Key West, FL, Jan. 3–6, Paper No. EPFL-CONF-161318. https://infoscience.epfl.ch/record/161318
Snelson, E. , and Ghahramani, Z. , 2006, “ Sparse Gaussian Processes Using Pseudo-Inputs,” 19th Annual Conference on Neural Information Processing Systems (NIPS), Vancouver, BC, Canada, Dec. 5–8, p. 1257. https://papers.nips.cc/paper/2857-sparse-gaussian-processes-using-pseudo-inputs
Rasmussen, C. E. , and Ghahramani, Z. , 2002, “ Infinite Mixtures of Gaussian Process Experts,” 15th Annual Conference on Neural Information Processing Systems (NIPS), Vancouver, BC, Canada, Dec. 9–14, pp. 881–888. https://papers.nips.cc/paper/2055-infinite-mixtures-of-gaussian-process-experts
Gramacy, R. B. , and Lee, H. K. H. , 2008, “ Bayesian Treed Gaussian Process Models With an Application to Computer Modeling,” J. Am. Stat. Assoc., 103(483), pp. 1119–1130. [CrossRef]
Park, C. , Huang, J. Z. , and Ding, Y. , 2011, “ Domain Decomposition Approach for Fast Gaussian Process Regression of Large Spatial Data Sets,” J. Mach. Learn. Res., 12, pp. 1697–1728. http://www.jmlr.org/papers/v12/park11a.html
Park, C. , and Huang, J. Z. , 2016, “ Efficient Computation of Gaussian Process Regression for Large Spatial Data Sets by Patching Local Gaussian Processes,” J. Mach. Learn. Res., 17(174), pp. 1–29. http://jmlr.org/papers/v17/15-327.html
Malburg, M. C. , 2003, “ Surface Profile Analysis for Conformable Interfaces,” ASME J. Manuf. Sci. Eng., 125(3), pp. 624–627. [CrossRef]
Yan, W. , and Komvopoulos, K. , 1998, “ Contact Analysis of Elastic-Plastic Fractal Surfaces,” J. Appl. Phys., 84(7), pp. 3617–3624. [CrossRef]
Persson, B. , Albohr, O. , Creton, C. , and Peveri, V. , 2004, “ Contact Area Between a Viscoelastic Solid and a Hard, Randomly Rough, Substrate,” J. Chem. Phys., 120(18), pp. 8779–8793. [CrossRef] [PubMed]
Xin, L. , and Gaoliang, P. , 2016, “ Research on Leakage Prediction Calculation Method for Static Seal Ring in Underground Equipments,” J. Mech. Sci. Technol., 30(6), pp. 2635–2641. [CrossRef]
Pfitzner, J. , 1976, “ Poiseuille and His Law,” Anaesthesia, 31(2), pp. 273–275. [CrossRef] [PubMed]
Dijkstra, E. W. , 1959, “ A Note on Two Problems in Connexion With Graphs,” Numer. Math., 1(1), pp. 269–271. [CrossRef]


Grahic Jump Location
Fig. 1

Sealing test demonstrating the insufficiency of qualified individual surface variation. Note: the color/gray scale represents the surface height, by which the dark color refers to a low height value while the bright color is the opposite.

Grahic Jump Location
Fig. 2

An example of surface measurement of different resolution from different metrology system [6]: (a) Coherix ShaPix surface measurement using laser holographic interferometry and (b) CMM measurement

Grahic Jump Location
Fig. 3

Void space of mating surfaces

Grahic Jump Location
Fig. 4

Isolated void areas with no leakage

Grahic Jump Location
Fig. 5

(a) Surface partition and (b) lattice graph of the mating area

Grahic Jump Location
Fig. 6

Framework of the leakage diagnosis

Grahic Jump Location
Fig. 7

Design of a surface mating testbed: (a) mini engine head, (b) mini engine block, and (c) surface assembly (unit: mm)

Grahic Jump Location
Fig. 8

Data acquisition of the testbed: (a) Coherix ShaPix3D metrology system and (b) leakage test

Grahic Jump Location
Fig. 9

Simulated void space and corresponding leak areas: (a) and (b) are training void space data with σ=0,0.05, respectively, (c) is training leak areas, (d) and (e) are test void space data with σ=0,0.05, respectively, and (f) is test leak areas (the color/gray scale bars in (a), (b), (d), and (e) reflect the magnitude of void space)

Grahic Jump Location
Fig. 10

Predicted probabilistic leak areas with different noise levels and their log-likelihood values: (a) predicted leak areas with σ = 0, (b) example of predicted leak areas with σ=0.05, (c) log-likelihood versus increasing noise level (the color/gray scale bars in (a) and (b) reflect the probability of leak at every grid point)

Grahic Jump Location
Fig. 11

Experimental data: (a) surface height measurement of block, (b) surface height measurement of head, and (c) measured leak areas (unit: mm)

Grahic Jump Location
Fig. 12

Subsamples and prediction results: (a) five equal sized subsamples and (b) predicted leak areas (color/gray scale bar reflects the probability of leak) (axial unit: mm)



Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In