Transient Resonance Passage With Respect to Friction

Abstract

Gas and steam turbine applications are exposed to high vibration amplitudes. Friction damping elements are commonly used to prevent blades from fatigue failure. Most of the work done so far in this field is dealing with steady state vibration occurring due to harmonic excitation. Regarding the growing importance of renewable energy, the number of run-ups and rundowns in power plants is increasing continuously. Furthermore, also the speed of jet engines is changed regularly during operation. To give an analytical approach on how to calculate and create most effective friction damping during instationary excitation, this paper discusses the computation of transient nonlinear vibration. Following the description of a single-degree-of-freedom system comprising a friction contact, it is shown how to assemble the equation of motion using piecewise linear equations. An analytical ansatz is illustrated to solve the ODEs of the system. In the next step, two simple multi-body-systems are created that are coupled by a friction contact. To validate the analytical computation of the vibration response of the system, a numeric time integration of the system is done. The calculations are compared, and it is shown that the analytical ansatz is valid to compute the vibration of the system. Using the solution of the equation of motion of the multi-body-system, it is shown how the optimal friction damping of the system can be determined while varying important parameters like e.g. the normal force of the friction contact and the tangential stiffness of the contact model.

Transient Resonance Passage of a Mistuned Bladed Disk with and without Underplatform Dampers

“…The overall resonance shift by means of the underplatform dampers though can be easily detected when comparing these graphs with Figure 4. The impact of friction damping on the effects of a transient resonance passage is further demonstrated in Figure 7a,b, as it was previously stated by [12] as well. When comparing the graphs to the linear measurements in Figure 5, only marginal differences in the blade vibration responses with an increasing speed rate can be observed, as the amount of friction damping by means of the asymmetric underplatform dampers is inhibiting almost any kind of beating.…”

“…Friction damping through, e.g., adding underplatform dampers causes the blade vibrations to decrease in general and creates a shift of the resonance peak towards higher frequencies. A faster decay of vibration of each excited blade is expected to decrease the extent of both the ring-down and the transient frequency shift (see [12]). When yet again comparing the steady-state with the transient measurements in Figure 6, the effect of friction damping can be observed.…”

“…is solved by means of a time-step integration in Matlab that bases upon the Runge-Kutta method which is commonly used for this type of vibration problem (see [3,7]). Here, M,D and K respectively denote the system's mass, damping and stiffness matrices, and the excitation force F(t) is calculated for each DOF in accordance to Equation (2).…”

“…However, the effect of friction damping on the blade dynamics during a transient resonance passage has rarely been studied experimentally in this context. A time-step simulation performed by [7] shows a distinct reduction in the effects of a transient sweep by means of frictional damping.…”