Linköping Studies in Science and Technology. Dissertations No. 519

**Modelling Microslip Friction Damping
and its Influence on Turbine Blade Vibrations**

**Gabor Csaba**

**Akademisk avhandling**

som för avläggning av teknisk doktorsexamen vid Linköpings
Tekniska Högskola kommer att försvaras offentligt i sal C3, Hus
C, Linköpings Universitet, fredagen den 17:e april 1998, kl 10:15.

Fakultetsopponent är Dr. A. V. Srinivasan, Connecticut, USA.

**ABSTRACT**

A common failure mode for turbomachinery is high-cycle fatigue of compressor and turbine blades, due to high dynamic stresses caused by blade vibration resonance within the operating range of the machinery. A large number of engine shut-downs can be explained by blade failure caused by resonance vibration or flutter. One method of reducing the dynamic stress is to increase the damping by use of dry friction in general, and specially a device called a friction damper. It is a well-know fact that friction dampers may reduce the vibratory blade response at resonance. There is, however, a lack of theoretical models that can predict the performance of an actual damper.

This thesis concerns theoretical modelling, analysis and optimization of
friction dampers. Two models have been developed, one, named the *Bar
*model, is a development of an existing damper model, the other, named
the *Brush *model, is a new design. Both models have the ability to
account for microslip in the contact between blade and damper.

Dynamic systems with Coulomb friction, i.e. friction dampers, give rise to nonlinear differential equations. These can be solved either through numerical integration in the time domain or by linearizing the force-displacement relationship of the damper. Partly new theory for linearization and a numeric version of the Bar model have been developed. This results in forced response analysis being computed faster and more efficiently than before.

The Bar model is relatively simple, yet complete enough to show the most important properties of a microslip friction interface. The model was used to optimize the weight of a new commercially used damper. Comparing simulations with spin-pit tests with a completely bladed disk shows good qualitative agreement, but it was not possible to see if the right weight had been predicted because the rotor could not be excited up to the design point.

The Bar model allows only for slip motion in one direction, while the Brush model permits relative motion between blade and damper in all six degrees of freedom. The variables for the contact model are defined by damper geometry and material data, except coefficient of friction and a constant for the tangential stiffness, which have to be defined by measurements or a more advanced contact model. This type of complicated friction damper model has not previously been presented. Simulations and experiments have been compared for hysteresis curves and forced vibration analysis of a simplified blade-damper-blade system. The agreement is qualitatively good, although the results gave some questions that need more research.

Division of Machine Design

Department of Mechanical Engineering

Linköping University, S-581 83 Linköping, Sweden

Linköping 1998

ISBN 91-7219-168-6 ISSN 0345-7524