236 C.W. Schwingshackl et al. 0 5 10 15 20 25 0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1 0 0.2 0.4 0.6 0.7 0.8 0.5 0.3 0.1 0.9 1 Force [N] Displacement [mHz] Normalised Frequency Amplitude control Displacement Force Fig. 21.12 Compressor blade test rig: (a) amplitude controlled signal (Displacement) and (b) corresponding excitation force 0.5 0.55 0.6 0.65 0.7 0.75 0.8 0.85 0.9 0.95 1 0 0.05 0.1 0.15 0.2 Normalised loss factor Tip displacement [mHz] Excitation control no control force control amplitude control Fig. 21.13 Compressor blade test rig: difference in the damping behaviour due to different control algorithms line-fit method as the real loss factor associated to the resonance. Due to a varying activation of the nonlinearity in the system, the damping varies through the frequency range but the line-fit method assumes a constant damping in the frequency range. The value can then only be referred to as an approximation of the loss factor over the frequency range, but not as an accurate damping parameter. A constant amplitude throughout the frequency range (see Fig. 21.12) leads to a linearisation of the system around the resonance which allows the application of traditional linear modal analysis methods to extract the damping. To investigate the influence of the different control methods on the compressor blade test rig all three methods have been implemented and the frequency response functions have been measured. The overall damping behaviour of all three investigated control methods in Fig. 21.13 looks relatively similar, but the absolute values vary strongly from each other. All three tests lead to similar damping values at low amplitudes where the nonlinearity is not really activated, but once slip is taking place in the root the uncontrolled and force controlled damping values are much lower than the amplitude controlled values. In the free and force controlled test the maximum damping is only reached at resonance and lower damping is present the rest of the time, leading to on average lower values, whereas in the amplitude test the maximum damping is present throughout the frequency range. For a reliable extraction of the damping values of a nonlinear system an amplitude controlled test must therefore be used. 21.6 Discussion Measuring the damping behaviour of a linear or nonlinear structure requires a careful planning of the test setup to minimise the influence of the test rig. When clamping a test specimen to a solid foundation and exciting it a large amplitudes, great care is required that the applied clamping load is evenly distributed over the clamping surface, and that an accurate control over the clamping load is maintained to ensure minimal slip in the clamping and repeatability of the tests. Two flat clamping surfaces and a very densely packed load introduction gave the best clamping results for the clamped beam test rig. When it comes to choosing the best foundation for a test rig, then either a soft foam bed, or better a free-free support should be used, since any other support shows a strong effect on the damping behaviour.
RkJQdWJsaXNoZXIy MTMzNzEzMQ==