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Design optimization of a wind tunnel force balance using stepwise response surface method


A force balance measures the forces being applied to an object in a wind tunnel test. The force balance needs to be optimized to generate an acceptable gauge reading while guaranteeing no structural failure by the wind tunnel loadings. This paper proposes a stepwise response surface method (RSM) for design optimization of a force balance. Three sampling techniques were tried in the RSM study, and finite element simulation was used for functional evaluation. The first trial was based on broad sampling, followed by a second trial based on narrow sampling. The data from these trials was then utilized in a final regression, in which a quadratic model was generated to identify the final optimum point. The final design of the force balance provides satisfactory gauge readings with decreased stress values even though the roll moment is greatly increased.

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K :

Gauge factor

V r :

Bridge reading output

ε i :

Strain gauge readings at ith strain gauge location

x i :

ith design variable

N :

Total number of design variables

β :

Coefficient in the response surface model

W :

Diagonal matrix for the weight values

y best :

The most desired observation

σ 0 :

Stress measured at the center point of sampling

ε 0 :

Gauge reading measured at the center point of sampling

y i :

ith value of the performance by variable set xi = {x1, x2, x3}i

f(x i):

Quadratic polynomial function used to predict yi

w σ :

Weight values for stress measure

w ε :

Weight values for strain reading measure

M :

Number of points used in the regression study


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This research was supported by the NASA Langley Research Center (Contract 17947, 18994) and the University of Maryland at Baltimore County, Department of Mechanical Engineering (Graduate Assistantship 3000633775).

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Correspondence to Soobum Lee.

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Thomas Chaisson received the M.S. in Mechanical Engineering, University of Maryland at Baltimore County, Baltimore MD, USA in 2021. He is currently a Manufacturing Engineer at Lockheed Martin, MD, USA. His main research interests include design optimization, design of experiment, computer aided design, and manufacturing.

Soobum Lee received the Ph.D. in Mechanical Engineering, Korea Advanced Institute of Science and Technology (KAIST), Daejeon, Korea, in 2007. He is currently an Associate Professor with the University of Maryland at Baltimore County, Baltimore, MD, USA. His main research interests include energy harvesting device design, structural topology optimization, and robust and reliability-based design optimization.

Devin E. Burns received the Ph.D. in Mechanical Engineering from Johns Hopkins University, Baltimore, Maryland in 2012. He is currently a Force Measurement Engineer at NASA’s Langley Research Center in Hampton, VA, USA. His interests include mechanics, mechanics of materials, sensors, and manufacturing.

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Chaisson, T., Lee, S. & Burns, D.E. Design optimization of a wind tunnel force balance using stepwise response surface method. J Mech Sci Technol 36, 3071–3079 (2022).

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  • Force balance
  • Response surface methodology
  • Optimization
  • Regression