This paper presents a method for safe testing of aircraft models equipped with a nonlinear dynamic vibration damper in a wind tunnel. The nonlinearity of the tested vibration damper is provided by an elastic element consisting in a package of thin flat springs. Nonlinear dynamic dampers of various designs are presented, along with the results of their application. It is experimentally shown that improved dissipative properties of the proposed elastic fastening of the model under test to the wind tunnel surface have a positive effect on the expansion of the range of admissible attack angles.

Wind tunnel (WT) tests of aircraft (A/C) models are basically conducted to determine aerodynamic forces and moments acting on the aircraft. Generally, the aircraft model under test is mounted on a mechanism that allows to change the angle of attack α using a sting support (Fig. 1). A straingage balance for load measurement is installed between the model and the support. During experiments at transonic flow velocities, a challenging problem is sudden and typically fast-paced vibration of the model. Only emergency termination of the experiment can help prevent an accident in this situation.

The leading European Transonic Windtunnel (ETW) uses stationary active (automatically controlled) anti-vibration systems for vibration damping.

The TsAGI’s Т-128 industrial transonic wind tunnel features passive dynamic vibration dampers arranged inside the model (Fig. 1).

In Fig. 1, vector Y depicts the component of the total force acting on the aircraft model, which is perpendicular to the airflow. This component can be divided in two forces: Y = Ys + Yd, where Ys – static force, Yd – dynamic force. Fig. 2 shows red curves depicting dependencies Ys and Yd on the model’s angle of attack α without a dynamic vibration damper. The dependencies show that as angle α increases, force Ys regularly increases up to values Ys = max, while the vibration amplitude of force Yd demonstrates a rapid growth when getting closer to values Ys = max. Vibration amplitudes of force Yd and the model’s vibration amplitudes are interrelated and their unlimited growth inevitably leads to an accident.

This phenomenon is called the loss of dynamic stability of the “model/sting support” system under the impact of airflow at high values of angle α. Jacob Pieter Den Hartog was the first researcher who explained the phenomenon, analysing the swaying (or galloping) of overhead lines exposed to wind [1]. He proved that overhead lines swayed if the derivative of force Y by angle α was negative. He also introduced the following criterion of dynamic stability: < 0 – instability, > 0 – stability (it is assumed that there is no internal friction in the structure).

Work [2] proves that as angle α increases in the airflow, the loss of dynamic stability of an elastic system occurs before reaches negative values. At low but still positive values of , the derivative of lift force by the angle of attack rate (derivative ) begins to grow rapidly. This accelerates the occurrence of dynamic instability of the “model/sting support” system.

As a rule, the application of dynamic vibration dampers in the ADT-128 wind tunnel (see green lines in Fig. 2) allows to overcome the above-mentioned drawback of aerodynamic experiments with sting-mounted aircraft models. Actual experiment results are given below.

A dynamic vibration damper (DVD) transforms the initial dynamic “model/sting support” system, which is almost free of internal friction, into a new “model/DVD/sting support” system with internal fiction. The DVDs, which were previously widely in ADT-128 ([2] by Gozdek V. S., Koryakin A. N., TsAGI), are called linear dynamic vibration dampers because their characteristics are near to those of linear devices. The diagram of such a device is shown in Fig. 3. The integral components of the device are a moving mass, an elastic element, a damper, and a base. The effect of dynamic load on the model leads to vibrations of the damper’s moving mass in the linear (y) and angular (φ) directions. This, in its turn, causes vibrations of the damper rod and absorption of the model’s vibrational energy by the damper.

The analysis of stability of motion of the dynamic system “model/DVD/sting support” in the linear layout comes down to the determination of conformity of the model to the requirements of the Routh – Hurwitz criterion. Calculations prove that introduction of incidental internal friction into the “model/sting support” system” due to the application of DVD allows, at certain parameters of the DVD, to provide a sufficient dynamic stability margin [2]. Practical application proved the theoretical predictions, and, therefore, the DVDs became integral part of ADT-128 as countermeasures against dangerous vibrations of aircraft models. Their design was gradually improved with the efforts focused on enhanced performance along with more compact sizes. As a result, specialists now tend to use the DVDs with nonlinear parameters (nonlinear DVD [3]). The diagram of the device is shown in Fig. 4.

The base of a nonlienar DVD has a cantilevered elastic element that is a pack of thin flat springs. The surfaces of end springs of the pack touch sliding supports inside the moving mass while the pack is connected to the moving mass via the middle spring. When the moving mass moves, flat springs are bent and displaced relative to one another with friction against one another and against the moving mass. The work due to friction, which takes place when the packed springs are displaced, leads to conversion of the model’s vibrational energy to the heat energy, which dissipates in the environment. The advantage of the applicable elastic element is its compact sizes along with high performance in terms of flexibility, strength characteristics, and dissipative properties. The relevant engineering methods and design routines were developed to design nonlinear vibration dampers. The engineering design procedure is specified in [4]. Nonlinear DVDs provided for reliable stationary aerodynamic characteristics of aircraft models using ADT-128 at high values of angles of attack and sideslip and now they are the basic safety components of such experiments. Fig. 5 shows a drawing of the design version of such a vibration damper for a fighter aircraft model. This damper version has been used successfully for more than a decade.

The graphs shown in Fig. 6 demonstrate dissipative properties of the “model/DVD/sting support” system together with the device mentioned above. The figure represents the results of a ramp change of force Y acting in the vertical direction without the DVD (Fig. 6a) and with the DVD installed inside the model (Fig. 6b).

A ramp change of force was obtained by bending the system with the help of a lifting jack, the loading point of which was located near the centre of mass of the model. A lifting jack was fitted with a break shaft mounted on its end. We recorded changes of component Y of the straingage balance using standard measuring equipment of ADT-128 after breakdown of the lifting jack shaft and occurrence of model vibrations. Measurement results show that with the DVD installed, the logarithmic vibration decrement δ becomes 10 times higher than the previous value.

Design versions of the DVD able to prevent dangerous vibration in both vertical and horizontal planes of motion have been developed. For this purpose, the damper’s elastic link shall comprise two packs of thin flat springs with orthogonally oriented surfaces (Fig. 7).

The DVD moving masses are usually made of tungsten-based heavy alloy, but, wherever practicable, they may be made of lead.

All the represented DVDs were designed and prepared for experiments at the ADT-128 and were adjusted during tests by the author of the work.

The graphs shown in Fig. 8 prove that the DVD can provide safe measurement of aircraft model characteristics in ADT-128 in compliance with all requirements of the experiment program and within the required range of measured parameters, including values of derivatives Cyα≤ 0.

Successful operation of the DVD as a part of ADT-128 has confirmed the provisions stated in [2] that appropriate use of internal friction in the mounting assemblies of an aerodynamic model in order to ensure its dynamic stability in the airflow is effective. The work proposes that the sting support should be attached to the stand of mechanism α with the help of two hinges instead of a rigid connection. Moreover, the hinge nearest to the model is fixed to the stand while the outermost one is fastened on the elastic link with the damper. This design solution is shown in Fig. 9. When the model turns through angle α, the sting support turns accordingly on the hinge nearest to the model with linear deformation of the elastic link and displacement of the damper rod on its end. As a result, the model’s vibrational energy, just as in the dynamic damper, is converted in the damper to the heat energy to be dissipated in the environment. According to calculations [2], some reduction of the lowest vibration frequency of the model is comparable with its typical reduction during a real experiment due to installation of a dynamic vibration damper.

Long-time stable and successful operation of dynamic vibration dampers for aircraft models tested by means of the T-128 wind tunnel confirms that improvement of dissipative characteristics of a dynamic system consisting of a sting support and a model turns out to be the correct solution. In the future, it is possible to abandon mandatory use of dynamic vibration dampers by imparting the necessary dissipative properties to a stationary mounting of aircraft models.