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An analytical calculation of the Jacobian matrix for 3D friction contact model applied to turbine blade shroud contact
KTH, School of Engineering Sciences (SCI), Aeronautical and Vehicle Engineering, Marcus Wallenberg Laboratory MWL.ORCID iD: 0000-0003-4237-2630
KTH, School of Engineering Sciences (SCI), Aeronautical and Vehicle Engineering, Marcus Wallenberg Laboratory MWL.ORCID iD: 0000-0002-3609-3005
KTH, School of Engineering Sciences (SCI), Aeronautical and Vehicle Engineering, Marcus Wallenberg Laboratory MWL.ORCID iD: 0000-0001-5760-3919
2016 (English)In: Computers & structures, ISSN 0045-7949, E-ISSN 1879-2243, Vol. 177, 204-217 p.Article in journal (Refereed) Published
Abstract [en]

An analytical expression is formulated to compute the Jacobian matrix for 3D friction contact modeling that efficiently 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 the calculation of the friction damping on a turbine blade with shroud contact interface having an arbitrary 3D relative displacement. The analytical expression drastically reduces the computation time of the Jacobian matrix with respect to the classical finite difference 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 difference 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 a periodic 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.

Place, publisher, year, edition, pages
Elsevier, 2016. Vol. 177, 204-217 p.
Keyword [en]
Jacobian matrix, Friction damping, Shroud contact, Cyclic symmetry, Alternate frequency time domain method, Multiharmonic balance method
National Category
Applied Mechanics
Identifiers
URN: urn:nbn:se:kth:diva-198949DOI: 10.1016/j.compstruc.2016.08.014ISI: 000386989300016Scopus ID: 2-s2.0-8499173727OAI: oai:DiVA.org:kth-198949DiVA: diva2:1063791
Note

QC 20170111

Available from: 2017-01-11 Created: 2016-12-22 Last updated: 2017-06-28Bibliographically approved
In thesis
1. On efficient and adaptive modelling of friction damping in bladed disks
Open this publication in new window or tab >>On efficient and adaptive modelling of friction damping in bladed disks
2017 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

This work focuses on efficient modelling and adaptive control of friction damping in bladed disks. To efficiently simulate the friction contact, a full-3D time-discrete contact model is reformulated and an analytical expression for the Jacobian matrix is derived that reduces the computation time drastically with respect to the classical finite difference method. The developed numerical solver is applied on bladed disks with shroud contact and the advantage of full-3D contact model compared to a quasi-3D contact model is presented. The developed numerical solver is also applied on bladed disks with strip damper and multiple friction contacts and obtained results are discussed. Furthermore, presence of higher harmonics in the nonlinear contact forces is analyzed and their effect on the excitation of the different nodal diameters of the bladed disk are systematically presented. The main parameters that influence the effectiveness of friction damping in bladed disks are engine excitation order,  contact stiffnesses,  friction coefficient, relative motion at the friction interface and the normal contact load. Due to variation in these parameters during operation, the obtained friction damping in practice may differ from the optimum value. Therefore, to control the normal load adaptively that will lead to an optimum damping in the system despite these variations, use of magnetostrictive actuator is proposed. The magnetostrictive material that develops an internal strain under the influence of an external magnetic field is employed to increase and decrease the normal contact load. A linearized model of the magnetostrictive actuator is used to characterize the magnetoelastic behavior of the actuator.  A nonlinear static contact analysis of the bladed disk reveals that a change of normal load more than 700 N can be achieved using a reasonable size of the actuator. This will give a very good control on friction damping once applied in practice.

Place, publisher, year, edition, pages
Stockholm: KTH Royal Institute of Technology, 2017. 70 p.
Series
TRITA-AVE, ISSN 1651-7660 ; 2017:10
Keyword
High cycle fatigue, Friction contact, Jacobian matrix, Shroud contact, Strip damper, Multiharmonic balance method, Contact stiffness, Cyclic symmetry, Nodal diameter, Magnetostrictive actuator, Magnetic field
National Category
Applied Mechanics Energy Engineering
Research subject
Engineering Mechanics
Identifiers
urn:nbn:se:kth:diva-202978 (URN)978-91-7729-292-0 (ISBN)
Public defence
2017-04-12, F3, Lindstedtsvägen 26, Stockholm, 10:00 (English)
Opponent
Supervisors
Projects
TurboPower
Funder
Swedish Energy Agency, 26159
Note

QC 20170310

Available from: 2017-03-13 Created: 2017-03-10 Last updated: 2017-03-13Bibliographically approved

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