A Reduced-Order Integrated Design Synthesis for the Three-Dimensional Tailored Vibration Response and Flutter Control of High-Bypass Shroudless Fans
Authors: McGee O. G. , Fang C. 
Published: August 2009

A new reduced-order design synthesis technology has been developed for vibration response and flutter control of cold-stream, high-bypass ratio, shroudless fans. To simplify the design synthesis (optimization) of the fan, a significant order reduction of the mechanical response and stiffness-shape design synthesis has been achieved. The assumed cyclic symmetric baseline fan is modeled as a cascade of tuned, shroudless, arbitrarily-shaped, wide-chord blades, each with a reduced-order of degrees of freedom using a three-dimensional (3-D) elasticity-based, meshless energy model [Fang, (2002); McGee et al (2008); Fang et al (2008)]. The convergence accuracy and mechanical response error of the present 3-D predictions were estimated nearly one percent above the exact mechanical response of the baseline fan. In off-design operation, the frequency margins of the lower flex-torsion modes of a fan may be dangerously close to integral-order resonant and empirical stall flutter boundaries. It is shown that an optimized mechanical stiffness through material properties (via. symmetric angle-ply orientations) and an optimized fan shape (via. variation of blade thickness from hub-to-mid-radial height) can be found to reduce the likelihood of resonant response and flutter on a Campbell diagram. A baseline fan is numerically optimized using a first-of-its-kind reduced-order design synthesis technology involving a solution of simultaneous nonlinear partial differential equations determining the necessary and sufficient Kuhn-Tucker conditions of optimality of constrained minimization. Solution accuracy and validity of the reduced-order design synthesis technology is benchmarked against a widely-used conventional method of nonlinear programming (via. sequential unconstrained minimization technique). Fan design optima is obtained that (1) achieves multiple frequency margins and satisfies multiple empirical stall flutter constraints, (2) controls the twist-flex vibratory response in the lowest (fundamental) mode, and (3) ensures the mechanical strength integrity of the optimized angle-ply lay-up under steady centrifugal tension and gas bending stresses. Baseline and optimally-restructured Campbell diagrams and design sensitivity calculations are presented. Design histories of fan stiffness and shape and nondimensional constraints (i.e., frequency margins, reduced frequencies, twist-flex vibratory response, first-ply failure principal stress limits, and hub-to-mid-blade height thickness distribution) show that a proper implementation of fan stiffness tailoring and shape (thickness) optimization of the fan assembly produces a feasible Campbell diagram that satisfies all design goals. An off-design analysis of the optimized fan shows little sensitivity to twist-flex coupling response and flutter with respect to small variability or errors in optimum design construction. Industry manufacturing processes may introduce these small errors. Finally, the developed reduced-ordered technology of fan design is shown to be highly cost-effective and accurate, when its predictive mechanical response capability is compared to general-purpose finite element technology widely-used by industry.