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A calculation formulation of the Jacobian matrix for 3D numerical friction contact model applied to turbine blade shroud contact
KTH, School of Engineering Sciences (SCI), Aeronautical and Vehicle Engineering, MWL Structural and vibroacoustics. kth.ORCID iD: 0000-0003-4237-2630
KTH, School of Engineering Sciences (SCI), Aeronautical and Vehicle Engineering, MWL Structural and vibroacoustics. Eindhoven University of Technology, the Netherlands.ORCID iD: 0000-0002-3609-3005
KTH, School of Engineering Sciences (SCI), Aeronautical and Vehicle Engineering, MWL Structural and vibroacoustics.ORCID iD: 0000-0001-5760-3919
(English)Manuscript (preprint) (Other academic)
Abstract [en]

An analytical expression is formulated to compute the Jacobian matrix for 3D friction contact modelling that eciently evaluates the matrix while computing the friction contact forces in the time domain by means of the alternate frequency time domain approach. The developed expression is successfully used for thecalculation of the friction damping on a turbine blade with shroud contact interface having an arbitrary 3Drelative displacement. The analytical expression drastically reduces the computation time of the Jacobian matrix with respect to the classical finite dierence method, with many points at the contact interface. Therefore,it also significantly reduces the overall computation time for the solution of the equations of motion,since the formulation of the Jacobian matrix is the most time consuming step in solving the large set of nonlinear algebraic equations when a finite dierence approach is employed. The equations of motion are formulated in the frequency domain using the multiharmonic balance method to accurately capture the nonlinear contact forces and displacements. Moreover, the equations of motion of the full turbine blade model are reduced to a single sector model by exploiting the concept of cyclic symmetry boundary condition for aperiodic structure. Implementation of the developed scheme in solving the equations of motion is proved to be effective and significant reduction in time is achieved without loss of accuracy.

Keyword [en]
Jacobian matrix, friction damping, shroud contact, cyclic symmetry, alternate frequency time domain method, multiharmonic balance method
National Category
Applied Mechanics
Research subject
Engineering Mechanics; Vehicle and Maritime Engineering
Identifiers
URN: urn:nbn:se:kth:diva-177922DOI: 10.1016/j.compstruc.2016.08.014OAI: oai:DiVA.org:kth-177922DiVA: diva2:875065
Projects
TurboPower
Funder
Swedish Energy Agency, 26159
Note

QS 2015

Available from: 2015-11-30 Created: 2015-11-30 Last updated: 2016-10-26Bibliographically approved
In thesis
1. Numerical modelling and analysis of friction contact for turbine blades
Open this publication in new window or tab >>Numerical modelling and analysis of friction contact for turbine blades
2015 (English)Licentiate thesis, comprehensive summary (Other academic)
Abstract [en]

High cycle fatigue failure of turbine and compressor blades due to resonance in the operating frequency range is one of the main problems in the design of gas turbine engines. To suppress excessive vibrations in the blades and prevent high cycle fatigue, dry friction dampers are used by the engine manufacturers. However, due to the nonlinear nature of friction contact, analysis of such systems becomes complicated.

This work focuses on the numerical modelling of friction contact and a 3D friction contact model is developed. To reduce the computation time in the Newton-iteration steps, a method to compute the Jacobian matrix in parallel to the contact forces is proposed. The developed numerical scheme is successfully applied on turbine blades with shroud contact having an arbitrary 3D relative displacement. The equations of motion are formulated in the frequency domain using the multiharmonic balance method to accurately capture the nonlinear contact forces and displacements. Moreover, the equations of motion of the full turbine blade model are reduced to a single sector model by exploiting the concept of the cyclic symmetry boundary condition for a periodic structure.

The developed 3D coupled numerical contact model is compared with a 3D contact model having uncoupled tangential motion and drawback of the uncoupled contact model is discussed. Furthermore, presence of higher harmonics in the nonlinear contact forces is analyzed and their effect on the excitation of the different harmonic indices (nodal diameters) of the bladed disk are systematically presented. Moreover, due to the quasi-analytical computation of the Jacobian matrix, the developed scheme is proved to be effective in solving the equations of motion and significant reduction in time is achieved without loss of accuracy.

 

 

 

Place, publisher, year, edition, pages
Stockholm: KTH Royal Institute of Technology, 2015. x, 54 p.
Series
TRITA-AVE, ISSN 1651-7660 ; 2015:94
National Category
Energy Engineering Applied Mechanics
Research subject
Vehicle and Maritime Engineering
Identifiers
urn:nbn:se:kth:diva-177920 (URN)
Presentation
2015-12-03, Lab farkostteknik, Teknikringen 8, bv, KTH, Stockholm, 13:15 (English)
Opponent
Supervisors
Funder
Swedish Energy Agency
Note

QC 20151130

Available from: 2015-11-30 Created: 2015-11-30 Last updated: 2015-11-30Bibliographically approved

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Afzal, MohammadLopez Arteaga, InesKari, Leif
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