Managing Geometrical Variation through Optimization and Visualization
Doktorsavhandling, 2010

All manufacturing processes are afflicted by variation that causes deviations in critical dimensions in the final product. Geometrical variation results in form and size deviation in individual parts. Assembly variation comes from defects in assembly equipment, and influence how parts are mounted together. To secure and control the effects of variation, an efficient geometry assurance process is required. In this thesis, the research challenge was to develop methods and tools that increased the efficiency in managing geometrical variation in the virtual geometry assurance process. To fulfil this challenge, focus was set on optimization techniques and algorithm development. The research project was divided into three main areas: 1) Locating scheme optimization, 2) Tolerance allocation and 3) Visualization of variation. The focus in the first area was set on locating scheme optimization. The way parts in an assembly are located in relation to each other or to fixtures is critical for how geometrical variation will propagate and cause variation in critical product dimensions. The result from this part was a demonstrator that utilizes optimization to find the locator positions that maximise robustness in critical dimensions. The second area of the research investigated how tolerances on individual dimensions can be set automatically to fulfil tolerance requirements on critical product dimensions. Traditionally, tolerances are set based on engineering knowledge and earlier experiences from design projects. Here, demonstrators were developed for different tolerance allocation optimization strategies, based on either cost or geometric properties. Finally, in the third area of this research, the centre of interest was visualization of variation. Here, a new method was developed to calculate an envelope enclosing a total volume based on simulation or measurement data. The contribution of this research is enhanced knowledge of how to virtually manage geometrical variation within product development. It has also contributed to an increased understanding of research connected to the virtual geometry assurance process. In addition, contributions have been made in the area of demonstrator development for locating scheme optimization, tolerance allocation and visualization of variation. Finally, the results have been spread within both academia and industry.

variation simulation


Tolerance allocation

locating scheme optimization

geometry assurance

visualization of variation

tolerance analysis

HA2, Hörsalsvägen 4, Chalmers tekniska högskola
Opponent: Prof. Petter Krus, Institutionen för ekonomisk och industriell utveckling, Tekniska högskolan vid Linköpings universitet


Johan Lööf

Chalmers, Produkt- och produktionsutveckling, Produktutveckling

An Efficient Solution to the Discrete Least-Cost Tolerance Allocation Problem with General Loss Functions

Models for Computer Aided Tolerancing Design and Manufacturing,; (2007)

Kapitel i bok

Optimizing Locator Position to Maximize Robustness in Critical Product Dimensions

ASME 2009 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, IDETC/CIE2009; San Diego, CA; United States; 30 August 2009 through 2 September 2009,; Vol. 2(2010)p. 515-522

Paper i proceeding

Visualization of Variation in Early Design Phases: A Convex Hull Approach

Proceedings of The Design 2006 9th International Design Conference, May 15-18, Dubrovnik, Croatia,; Vol. 2(2006)p. 905-912

Paper i proceeding

Envelope of Rotating Parts Based on Motion and Variation Simulation Data

10th CIRP Conference on Computer Aided Tolerancing, Specification and Verification for Assemblies, March 21-23, Erlangen, Germany, 2007,; (2007)

Artikel i vetenskaplig tidskrift

Top-Down Decomposition of Multi-Product Requirements onto Locator Tolerances

Proceedings of IMECE2007, 2007 ASME International Mechanical Engineering Congress and Exposition, November 11-15, 2007, Seattle, Washington, USA.,; Vol. 3(2007)p. 247-255

Paper i proceeding

Secure Variation along a Robot Path using Discrete Tolerance Allocation Optimization

Proceedings of the 2nd CIRP Conference on Assembly Technologies and Systems, 21-23 September 2008, Toronto, Ontario, Canada,; (2008)

Paper i proceeding



Tillförlitlighets- och kvalitetsteknik



Doktorsavhandlingar vid Chalmers tekniska högskola. Ny serie: 3066

HA2, Hörsalsvägen 4, Chalmers tekniska högskola

Opponent: Prof. Petter Krus, Institutionen för ekonomisk och industriell utveckling, Tekniska högskolan vid Linköpings universitet

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