Design of Wind Tunnel Balance Structure Using Robust Topology Optimization Under Multiple Stress Constraints

This research studies a new design methodology for an internal wind tunnel balance structure using topology optimization. The internal wind tunnel balance structure is a 6-axis force sensor that measures aerodynamic forces and moments exerted on wind tunnel models during wind tunnel testing. The balance structure is composed of 6 separate sections that measure the three forces and three moments. Among them, designing an axial force measurement section is challenging because of the significantly high axial to normal force ratio (1:10+) that is investigated in this research. Stress is the most important performance measure when designing the balance structure. In the axial section, the stress subject to axial force needs to be amplified and the stress by other forces needs to be minimized. Typically, the strain gauges are attached to measure forces on the balance structure and the full Wheatstone bridge circuit is used to amplify the axial force signal and minimize the signal of other forces and moments by mutual cancellation.

Topology optimization obtains the material density distribution in a design domain and has been widely used for conceptual design of structures for various purposes. The topology optimization problem with a stress measure requires overcoming some challenges such as singularity and local measurement issues. In this work, the relaxation approach and global stress evaluation method are used to solve singularity and local measurement issues respectively. Also, two different stress evaluations are used in the design formulation. One is the normalized P-norm stress measurement to evaluate the structural safety under combined load – axial force, normal force, and pitching moment – and the other is directional stress measurement to sense the axial force.

To ensure manufacturability (e.g. 3D printing) by imposing the minimum length scale on the optimized design, the proposed formulation includes a robust approach based on Dilated, Intermediate, and Eroded projected design variables. Dilated, Intermediate, and Eroded variables are projected under different threshold points from density filtered variables. The robust topology optimization is developed to consider over- or under-edging manufacturing uncertainty. The three projected design variables in the robust topology optimization also support eliminating one node connections which are not manufacturable and require additional postprocessing to define the structure and ensure the design constraints are satisfied. Aforementioned two stress measures – normalized P-norm stress and directional stress – are evaluated by using each of three projected design variables (Dilated, Intermediate, and Eroded). Using this proposed formulation, we obtain a flexure structure for the axial section of an internal wind tunnel balance that is manufacturable subject to the high normal to axial force ratio. This solution satisfies all constraints and no one node connections are observed.