Research Papers

Combining Variation Simulation With Thermal Expansion Simulation for Geometry Assurance

[+] Author and Article Information
Rikard Söderberg

Department of Product and
Production Development,
Chalmers University of Technology,
Gothenburg SE-412 96, Sweden

Robert Sandboge

Fraunhofer-Chalmers Centre for
Industrial Mathematics,
Chalmers Science Park,
Gothenburg SE-412 88, Sweden

Contributed by the Design Engineering Division of ASME for publication in the Journal of Computing and Information Science in Engineering. Manuscript received February 28, 2013; final manuscript received April 24, 2013; published online July 22, 2013. Editor: Bahram Ravani.

J. Comput. Inf. Sci. Eng 13(3), 031007 (Jul 22, 2013) (8 pages) Paper No: JCISE-13-1032; doi: 10.1115/1.4024655 History: Received February 28, 2013; Revised April 24, 2013

In every set of assembled products, there are geometrical variations and deviations from nominal dimensions. This can lead to products that are difficult to assemble or products not fulfilling functional or aesthetical requirements. In several industries, variation simulation is used to predict assembly variation in the development phase. This analysis is usually done under room temperature conditions only. However, for some materials, such as plastics, the thermal expansion can be significant in the intended environmental span of the product. In an assembly, this can lead to thermal stresses and parts that will deform. To avoid this problem, locating schemes need to be designed to allow for the right behavior while exposed to varying temperatures. In this work, the effect of thermal expansion is studied in the context of variation simulation. A virtual tool for this purpose is also presented. Two case studies from the automotive industry are used where the combined effect of thermal expansion and assembly variation is analyzed. It is shown that it may not be sufficient to simply add the result from thermal analysis to assembly variation. Hence, to assure the geometrical and functional quality of assembled products during usage variation simulations need to be combined with thermal expansion simulation.

Copyright © 2013 by ASME
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Fig. 1

Geometrical robustness studied at different levels of plastic design [3]

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Fig. 2

A 3-2-1 positioning system often used for rigid bodies

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Fig. 3

Relations between displacements, strain and stress

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Fig. 4

As a case study, the combined effect of thermal expansion and variation is studied on a plastic appliqué on the rear end of an automobile. The appliqué is the component under the rear windshield.

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Fig. 5

The gap between the appliqué and rear lamp is one critical measure that is of interest in different temperature

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Fig. 6

The result of the critical gap measure after 1000 MC-runs. Above, the temperature is −30 °C, in the middle 20 °C and below 90 °C

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Fig. 7

Above, the instantiation resulting in the maximal gap for the temperature −30 °C and below, the minimum gap in 90 °C between the appliqué (right) and the rear lamp (left)

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Fig. 8

Above, 6 standard deviations (mm) in x-direction in 20 °C. The circles are displaying the position of the additional support points to hinder expansion in the y-direction. Below are 6 standard deviations in 90 °C

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Fig. 9

Mean shift in x-direction (mm) caused by thermal expansion while hindered to expand in y-direction. The temperature is 90 °C

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Fig. 10

The distribution of the gap measure at 90 °C when the appliqué is hindered to expand in the y-direction

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Fig. 11

The position of 4 measures, to measure mean shift and variation in the x-direction

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Fig. 12

Above, the result of thermal expansion for 4 measures where 6 standard deviations have been added as vertical bars from a variation simulation. Below, thermal expansion and variation simulated combined



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