The objective of this chapter is to determine an optimal trailing edge flap configuration and flap location to achieve minimum hub vibration levels and flap actuation power simultaneously. An aeroelastic analysis of a soft in-plane four-bladed rotor is performed in conjunction with optimal control. A second-order polynomial response surface based on an orthogonal array (OA) with 3-level design describes both the objectives adequately. Two new orthogonal arrays called MGB2P-OA and MGB4P-OA are proposed to generate nonlinear response surfaces with all interaction terms for two and four parameters, respectively. A multi-objective bat algorithm (MOBA) approach is used to obtain the optimal design point for the mutually conflicting objectives. MOBA is a recently developed nature-inspired metaheuristic optimization algorithm that is based on the echolocation behaviour of bats. It is found that MOBA inspired Pareto optimal trailing edge flap design reduces vibration levels by 73% and flap actuation power by 27% in comparison with the baseline design.
Top1. Introduction
The helicopter is a versatile vehicle because of its unique capabilities, such as hover, forward and backward manoeuvres, and vertical take-off and landing, which makes it an inevitable machine of choice for defence and civilian operations. The helicopter rotor is a complex dynamical system which experiences asymmetric aerodynamic loading over the rotor disc during forward flight. This asymmetry in lift induces severe vibrations in the rotor system which is usually rich in harmonic content (Loewy, 1984). High vibration levels lead to crew and passenger discomfort, affect avionics reliability, decrease the fatigue life of various structural components and hence lead to an increase in maintenance costs. The helicopter rotor system is also an efficient mechanical filter that filters out all the forces and moments and only allows frequency content that is an integer multiple of the number of blades (or the blade passing frequency, Nb). Here, Nb represents the number of rotor blades and is the rotor rotational speed. In the past, a consider-able effort has been expended on vibration suppression research using passive vibration control devices such as vibration isolators or vibration absorbers. Passive devices demonstrate vibration alleviation but possess significant drawbacks as they incur a large weight penalty, increase drag forces and also their performance degrades from the tuned flight condition (Pearson, Goodall, & Lyndon, 1994).
Figure 1. Schematic of rotor blade section with dual flaps.
With the advent of smart materials, active vibration control techniques have caught the attention of researchers (Friedmann and Millott, 1995). In the last two decades, various active approaches were tested numerically (Milgram, Chopra, & Straub, 1998; Cesnik, Opoku, Nitzsche, & Cheng, 2004; Lim & Lee, 2009) and experimentally (Noboru, Kobiki, Saito, Fukami, & Komura, 2007; Konstanzer, Peter, Enenkl, Aubourg, & Cranga, 2008; Sinapius, Michael, Monner, Kintscher, & Riemenschneider, 2014). Piezo actuated active control flap (ACF) methods have emerged as the best potential candidates to alleviate helicopter vibration (Konstanzer, Peter, Enenkl, Aubourg, & P. Cranga, 2008). Figure 1 shows a schematic of the rotor blade section with dual trailing edge flaps. Multiple on-blade plain trailing edge flaps (TEFs) are capable of achieving better vibration reduction in comparison to a single TEF. Most of the studies available in the literature use parametric studies to find the best design of trailing edge flaps (Shen & Chopra, 2004). Although active methods are promising, they suffer from high cost and have reliability issues.