Manufacturing variation models in multi-station machining systems

  • José Vicente Abellán-NebotEmail author
  • Fernando Romero Subirón
  • Julio Serrano Mira
Original Article


In product design and quality improvement fields, the development of reliable 3D machining variation models for multi-station machining processes is a key issue to estimate the resulting geometrical and dimensional quality of manufactured parts, generate robust process plans, eliminate downstream manufacturing problems, and reduce ramp-up times. In the literature, two main 3D machining variation models have been studied: the stream of variation model, oriented to product quality improvement (fault diagnosis, process planning evaluation and selection, etc.), and the model of the manufactured part, oriented to product and manufacturing design activities (manufacturing and product tolerance analysis and synthesis). This paper reviews the fundamentals of each model and describes step by step how to derive them using a simple case study. The paper analyzes both models and compares their main characteristics and applications. A discussion about the drawbacks and limitations of each model and some potential research lines in this field are also presented.


Multi-station machining processes Part quality SoV MoMP Manufacturing variation model 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Ceglarek D, Huang W, Zhou S, Ding Y, Kumar R, Zhou Y (2004) Time-based competition in multistage manufacturing: stream-of-variation analysis (SOVA) methodology—review. Int J Flex Manuf Syst 16:11–44zbMATHCrossRefGoogle Scholar
  2. 2.
    Shi J (2007) Stream of variation modeling and analysis for multistage manufacturing systems. CRC, Boca RatonGoogle Scholar
  3. 3.
    Ogata K (2001) Modern control engineering, 4th edn. Prentice Hall, Upper Saddle RiverGoogle Scholar
  4. 4.
    Zhou S, Huang Q, Shi J (2003) State space modeling of dimensional variation propagation in multistage machining process using differential motion vectors. IEEE Trans Robot Autom 19:296–309CrossRefGoogle Scholar
  5. 5.
    Huang Q, Shi J, Yuan J (2003) Part dimensional error and its propagation modeling in multi-operational machining processes. J Manuf Sci Eng 125:255–262CrossRefGoogle Scholar
  6. 6.
    Djurdjanovic D, Ni J (2003) Dimensional errors of fixtures, locating and measurement datum features in the stream of variation modeling in machining. J Manuf Sci Eng Trans ASME 125:716–730CrossRefGoogle Scholar
  7. 7.
    Loose JP, Zhou S, Ceglarek D (2007) Kinematic analysis of dimensional variation propagation for multistage machining processes with general fixture layouts. IEEE Trans Autom Sci Eng 4:141–152CrossRefGoogle Scholar
  8. 8.
    Abellan-Nebot JV, Liu J, Romero F (2012) State space modeling of variation propagation in multi-station machining processes considering machining-induced variations. J Manuf Sci Eng. doi: 10.1115/1.4005790 Google Scholar
  9. 9.
    Zhang M, Djurdjanovic D, Ni J (2007) Diagnosibility and sensitivity analysis for multi-station machining processes. Int J Mach Tools Manuf 47:646–657CrossRefGoogle Scholar
  10. 10.
    Liu J, Shi J, Hu SJ (2009) Quality-assured setup planning based on the stream-of-variation model for multi-stage machining processes. IIE Trans 41:323–334(12)CrossRefGoogle Scholar
  11. 11.
    Abellan-Nebot JV, Liu J, Subiron FR (2011) Design of multi-station manufacturing processes by integrating the stream-of-variation model and shop-floor data. J Manuf Syst 30:70–82CrossRefGoogle Scholar
  12. 12.
    Wang H, Huang Q, Katz R (2005) Multi-operational machining processes modeling for sequential root cause identification and measurement reduction. J Manuf Sci Eng 127:512–521CrossRefGoogle Scholar
  13. 13.
    Ding Y, Shi J, Ceglarek D (2002) Diagnosability analysis of multi-station manufacturing processes. J Dyn Syst Meas Control 124:1–13CrossRefGoogle Scholar
  14. 14.
    Zhou S, Chen Y, Ding Y, Shi J (2003) Diagnosability study of multistage manufacturing processes based on linear mixed-effects models. Technometrics 45:312–325MathSciNetCrossRefGoogle Scholar
  15. 15.
    Zhou SY, Chen Y, Shi J (2004) Statistical estimation and testing for variation root-cause identification of multistage manufacturing processes. IEEE Trans Autom Sci Eng 1:73–83CrossRefGoogle Scholar
  16. 16.
    Li ZG, Zhou SY, Ding Y (2007) Pattern matching for variation-source identification in manufacturing processes in the presence of unstructured noise. IIE Trans 39:251–263CrossRefGoogle Scholar
  17. 17.
    Djurdjanovic D, Ni J (2003) Bayesian approach to measurement scheme analysis in multistation machining systems. Proc Inst Mech Eng B J Eng Manuf 217:1117–1130CrossRefGoogle Scholar
  18. 18.
    Ding Y, Kim P, Ceglarek D, Jin J (2003) Optimal sensor distribution for variation diagnosis in multistation assembly processes. IEEE Trans Robot Autom 19:543–556CrossRefGoogle Scholar
  19. 19.
    Djurdjanovic D, Ni J (2004) Measurement scheme synthesis in multi-station machining systems. J Manuf Sci Eng 126:178–188CrossRefGoogle Scholar
  20. 20.
    Djurdjanovic D, Ni J (2006) Stream-of-variation (SoV)-based measurement scheme analysis in multistation machining systems. IEEE Trans Autom Sci Eng 3:407–422CrossRefGoogle Scholar
  21. 21.
    Izquierdo L, Shi J, Hu S, Wampler C (2007) Feedforward control of multistage assembly processes using programmable tooling. NAMRI/SME Trans 35:295–302Google Scholar
  22. 22.
    Djurdjanovic D, Zhu J (2005) Stream of variation based error compensation strategy in multi-stage manufacturing processes. ASME Conference ProceedingsGoogle Scholar
  23. 23.
    Djurdjanovic D, Ni J (2007) Online stochastic control of dimensional quality in multistation manufacturing systems. Proc Inst Mech Eng B J Eng Manuf 221:865–880CrossRefGoogle Scholar
  24. 24.
    Jiao Y, Djurdjanovic D (2008) Allocation of flexible tooling for optimal stochastic multistation manufacturing process quality control. ASME Conference Proceedings 2008, pp 161–169Google Scholar
  25. 25.
    Jiao Y, Djurdjanovic D (2010) Joint allocation of measurement points and controllable tooling machines in multistage manufacturing processes. IIE Trans 42:703–720CrossRefGoogle Scholar
  26. 26.
    Abellan-Nebot JV, Liu J, Subiron FR (2012) Quality prediction and compensation in multi-station machining processes using sensor-based fixtures. Robot Comput-Integr Manuf 28:208–219CrossRefGoogle Scholar
  27. 27.
    Chen Y, Ding Y, Jin J, Ceglarek D (2006) Integration of process-oriented tolerancing and maintenance planning in design of multistation manufacturing processes. IEEE Trans Autom Sci Eng 3:440–453CrossRefGoogle Scholar
  28. 28.
    Ding Y, Jin JH, Ceglarek D, Shi J (2005) Process-oriented tolerancing for multi-station assembly systems. IIE Trans 37:493–508CrossRefGoogle Scholar
  29. 29.
    Shirinzadeh B (2002) Flexible fixturing for workpiece positioning and constraining. Assem Autom 22:112–120CrossRefGoogle Scholar
  30. 30.
    Ding Y, Ceglarek D, Jin JH, Shi JJ (2000) Process-oriented tolerance synthesis for multistage manufacturing systems. In: Proceedings of the international mechanical engineering congress and exposition, Orlando, FL, pp 15–22Google Scholar
  31. 31.
    Ballot E, Bourdet P (1997) A computational method for the consequences of geometric errors in mechanisms. In: Proceedings of the 4th CIRP seminar on computer aided tolerancing, Tokyo, Japan, pp 137–148Google Scholar
  32. 32.
    Chase KW, Gao J, Magleby SP (1995) General 2-D tolerance analysis of mechanical assemblies with small kinematic adjustments. J Des Manuf 5:263–274CrossRefGoogle Scholar
  33. 33.
    Chase KW, Gao J, Magleby SP, Sorensen CD (1996) Including geometric feature variations in tolerance analysis of mechanical assemblies. IIE Trans 28:795–807Google Scholar
  34. 34.
    Davidson JK, Mujezinovic A, Shah JJ (2002) A new mathematical model for geometric tolerances as applied to round faces. J Mech Des 124:609–622CrossRefGoogle Scholar
  35. 35.
    Villeneuve F, Legoff O, Landon Y (2001) Tolerancing for manufacturing: a three-dimensional model. Int J Prod Res 39:1625–1648zbMATHCrossRefGoogle Scholar
  36. 36.
    Desrochers A (1999) Modeling three-dimensional tolerance zones using screw parameters. In: CD-ROM proceedings of ASME 25th design automation conference, DAC-8587, Las-VegasGoogle Scholar
  37. 37.
    Desrochers A, Ghie W, Laperriere L (2003) Application of a unified Jacobian–torsor model for tolerance analysis. J Comput Inf Sci Eng 3:2–14CrossRefGoogle Scholar
  38. 38.
    Villeneuve F, Vignat F (2007) Simulation of the manufacturing process in a tolerancing point of view: generic resolution of the positioning problem. In: Models for computer aided tolerancing in design and manufacturing, pp 179–189Google Scholar
  39. 39.
    Vignat F, Villeneuve F (2003) 3D transfer of tolerances using a SDT approach: application to turning process. J Comput Inf Sci Eng 3:45–53CrossRefGoogle Scholar
  40. 40.
    Nejad MK, Vignat F, Desrochers A, Villeneuve F (2010) 3D simulation of manufacturing defects for tolerance analysis. J Comput Inf Sci Eng 10:021001CrossRefGoogle Scholar
  41. 41.
    Ghie W, Laperriére L, Desrochers A (2007) Re-design of mechanical assemblies using the unified Jacobian–torsor model for tolerance analysis. In: Models for computer aided tolerancing in design and manufacturing, pp 95–104Google Scholar
  42. 42.
    Nejad MK, Vignat F, Villeneuve F (2009) Simulation of the geometrical defects of manufacturing. Int J Adv Manuf Technol 45:631–648CrossRefGoogle Scholar
  43. 43.
    Villeneuve F, Vignat F (2005) Manufacturing process simulation for tolerance analysis and synthesis. In: Advances in integrated design and manufacturing in mechanical engineering, pp 189–200Google Scholar
  44. 44.
    Nejad MK (2010) Propositions de résolution numérique des problèmes d’analyse de tolérance en fabrication: approche 3D. Dissertation, Université Joseph FourierGoogle Scholar
  45. 45.
    Ayadi B, Anselmetti B, Bouaziz Z, Zghal A (2008) Three-dimensional modelling of manufacturing tolerancing using the ascendant approach. Int J Adv Manuf Technol 39:279–290CrossRefGoogle Scholar
  46. 46.
    Louati J, Ayadi B, Bouaziz Z, Haddar M (2006) Three-dimensional modelling of geometric defaults to optimize a manufactured part setting. Int J Adv Manuf Technol 29:342–348CrossRefGoogle Scholar
  47. 47.
    Tichadou S, Legoff O, Hascoet JY (2005) 3D geometrical manufacturing simulation. In: Advances in integrated design and manufacturing in mechanical engineering, pp 201–214Google Scholar
  48. 48.
    Kamali Nejad M, Vignat F, Villeneuve F (2012) Tolerance analysis in machining using the model of manufactured part (MMP)—comparison and evaluation of three different approaches. Int J Comput Integr Manuf 25:136–149CrossRefGoogle Scholar
  49. 49.
    Anselmetti B, Louati H (2005) Generation of manufacturing tolerancing with ISO standards. Int J Mach Tools Manuf 45:1124–1131CrossRefGoogle Scholar
  50. 50.
    Vignat F, Villeneuve F (2007) A numerical approach for 3D manufacturing tolerances synthesis. In: 10th CIRP conference on computer aided tolerancing, Erlangen, GermanyGoogle Scholar
  51. 51.
    Tichadou S, Kamalinejad M, Vignat F, Legoff O (2007) 3-d manufacturing dispersions: two experimental applications. In: 10th CIRP international conference on computer aided tolerancing, Erlangen, GermanyGoogle Scholar
  52. 52.
    Sergent A, Bui MH, Favreliere H, Duret D, Samper S, Villeneuve F (2010) Identification of machining defects by small displacement torsor and form parameterization method. In: IDMME international conference, Bordeaux, FranceGoogle Scholar
  53. 53.
    Loose J, Zhou Q, Zhou S, Ceglarek D (2010) Integrating GD&T into dimensional variation models for multistage machining processes. Int J Prod Res 48:3129–3149zbMATHCrossRefGoogle Scholar
  54. 54.
    Kong Z, Huang W, Oztekin A (2009) Variation propagation analysis for multistation assembly process with consideration of GD&T factors. J Manuf Sci Eng 131:051010CrossRefGoogle Scholar
  55. 55.
    Bourdet P, Ballot E (1995) Geometrical behaviour laws for computer aided tolerancing. In: 4th CIRP seminars on computer aided tolerancing, Tokyo, pp 143–154Google Scholar
  56. 56.
    Liu J, Shi J, Hu SJ (2008) Engineering-driven factor analysis for variation source identification in multistage manufacturing processes. J Manuf Sci Eng 130:041009CrossRefGoogle Scholar

Copyright information

© Springer-Verlag London Limited 2012

Authors and Affiliations

  • José Vicente Abellán-Nebot
    • 1
    Email author
  • Fernando Romero Subirón
    • 1
  • Julio Serrano Mira
    • 1
  1. 1.Department of Industrial Systems Engineering and DesignUniversitat Jaume ICastellón de la PlanaSpain

Personalised recommendations