Aerodynamic control surfaces, with excessive free-play, can cause limit cycle oscillations (LCO), a sustained vibration of constant amplitude. The LCO is caused by a combination of aeroservoelastic effects and free-play. If the amplitude is sufficiently large, it can impact handling qualities, ride quality, and can cause structural fatigue, ultimately leading to structural failure. Free-play is typically distributed throughout the actuator and control surface, with contributions from actuator mounting bearings as well as the surface hinge.

Figure 1: The Free-Play Problem.
Due to the negative impacts of LCO, absolute free-play limits have been established by the Joint Services Guidance Military specification. The FAA has also adopted these military specifications for commercial aircraft. These stringent requirements can be overly conservative, making them very difficult and costly to meet. The existing free-play amount (control surface deflection angle) must also be constantly monitored throughout the life of the aircraft to ensure that the specification is not violated. Currently, this monitoring method is labor intensive and involves statically loading the surface and measuring the control surface deflection while on the ground. This adds additional costs associated with inspection. Typical locations of free-play on an aircraft actuator are shown in Figure 1(a). A measurement setup and typical result are shown, respectively, in Figure 1(b) and (c).

As such, a reliable analytical technique to analyze the effect of control surface free-play is highly desirable. Reliable analytical techniques can be used in early design phases, relaxing the free-play requirement and, ultimately, aircraft weight as well as manufacturing and inspection costs.

Figure 2: Free-Play Prediction and Validation.
To address this need, an age-old quasilinear describing function approach was applied. Describing function analysis is a classical approach for analyzing nonlinearities in dynamic systems. Using describing functions, nonlinearities can be represented by a quasi-linear system element that produces near-equivalent output response due to a prescribed input. It was shown that free-play can be accurately represented via describing function analysis and analyzed as part of a larger aeroservoelastic system. The effect of free-play in the system (i.e., the presence of LCO as well as LCO amplitude and frequency) can then be accurately estimated analytically using the describing function definition without the need to perform any simulations.

This technique was demonstrated using a generic aeroservoelastic stabilator model with free-play at the control surface hinge. Nonlinearities in the form of free-play were separated from the model via a linear fractional transformation (LFT) to cast the problem into a structure of significant generality. It was shown that the occurrence and behavior of the LCO could be estimated accurately using this describing function approach by comparing the LCO amplitude and frequency estimate to the results of a nonlinear simulation that modeled the free-play exactly (Figure 2).

This work was done by Brian Danowsky and Peter Thompson of Systems Technology, Inc. for Armstrong Flight Research Center. DRC-010-028