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On efficient and adaptive modelling of friction damping in bladed disks
KTH, School of Engineering Sciences (SCI), Aeronautical and Vehicle Engineering, Marcus Wallenberg Laboratory MWL. KTH.ORCID iD: 0000-0003-4237-2630
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. , p. 70
Series
TRITA-AVE, ISSN 1651-7660 ; 2017:10
Keyword [en]
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: urn:nbn:se:kth:diva-202978ISBN: 978-91-7729-292-0 (print)OAI: oai:DiVA.org:kth-202978DiVA, id: diva2:1080367
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
List of papers
1. An analytical calculation of the Jacobian matrix for 3D friction contact model applied to turbine blade shroud contact
Open this publication in new window or tab >>An analytical calculation of the Jacobian matrix for 3D friction contact model applied to turbine blade shroud contact
2016 (English)In: Computers & structures, ISSN 0045-7949, E-ISSN 1879-2243, Vol. 177, p. 204-217Article 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
Keyword
Jacobian matrix, Friction damping, Shroud contact, Cyclic symmetry, Alternate frequency time domain method, Multiharmonic balance method
National Category
Applied Mechanics
Identifiers
urn:nbn:se:kth:diva-198949 (URN)10.1016/j.compstruc.2016.08.014 (DOI)000386989300016 ()2-s2.0-8499173727 (Scopus ID)
Note

QC 20170111

Available from: 2017-01-11 Created: 2016-12-22 Last updated: 2017-06-28Bibliographically approved
2. INVESTIGATION OF DAMPING POTENTIAL OF STRIP DAMPER ON A REAL TURBINE BLADE
Open this publication in new window or tab >>INVESTIGATION OF DAMPING POTENTIAL OF STRIP DAMPER ON A REAL TURBINE BLADE
2016 (English)In: PROCEEDINGS OF THE ASME TURBO EXPO: TURBINE TECHNICAL CONFERENCE AND EXPOSITION, 2016, VOL 7A, AMER SOC MECHANICAL ENGINEERS , 2016Conference paper, Published paper (Refereed)
Abstract [en]

This paper investigates the damping potential of strip dampers on a real turbine bladed disk. A 3D numerical friction contact model is used to compute the contact forces by means of the Alternate Frequency Time domain method. The Jacobian matrix required during the iterative solution is computed in parallel with the contact forces, by a quasi-analytical method. A finite element model of the strip dampers, that allows for an accurate description of their dynamic properties, is included in the steady-state forced response analysis of the bladed disk. Cyclic symmetry boundary conditions and the multiharmonic balance method are applied in the formulation of the equations of motion in the frequency domain. The nonlinear forced response analysis is performed with two different types of boundary conditions on the strip: (a) free-five and (b) elastic, and their influence is analyzed. The effect of the strip mass, thickness and the excitation levels on the forced response curve is investigated in detail.

Place, publisher, year, edition, pages
AMER SOC MECHANICAL ENGINEERS, 2016
National Category
Mechanical Engineering
Identifiers
urn:nbn:se:kth:diva-196479 (URN)000385461600052 ()2-s2.0-84991693685 (Scopus ID)
Conference
ASME Turbo Expo: Turbine Technical Conference and Exposition
Note

QC 20161124

Available from: 2016-11-24 Created: 2016-11-14 Last updated: 2017-06-28Bibliographically approved
3. Numerical analysis of multiple friction contacts in bladed disks
Open this publication in new window or tab >>Numerical analysis of multiple friction contacts in bladed disks
(English)In: International Journal of Mechanical Sciences, ISSN 0020-7403, E-ISSN 1879-2162Article in journal (Other academic) Submitted
Abstract [en]

The damping potential of multiple friction contacts in a bladed disk, tip shroud and strip damper is investigated, showing that friction damping effectiveness can be potentially increased by using multiple friction contact interfaces. Friction damping depends on many parameters such as rotational speed, engine excitation order and mode family and therefore it is not possible to damp all the critical resonances using a single friction contact interface. For example, a strip damper is more effective for the low nodal diameters, where blade/disk coupling is strong. The equations of motion of the bladed disk with multiple friction contacts are derived in the frequency domain for a cyclic structure with rotating excitations and a highly accurate method is used to generate the frequency response function (FRF) matrix. Furthermore, a finite element contact analysis is performed to compute the normal contact load and the contact area of the shroud interface at operating rotational speed. The multiharmonic balance method is employed in combination with the alternate frequency time domain method to find the approximate steady state periodic solution. A low-pressure turbine bladed disk is considered and the effect of the engine excitation level, strip mass, thickness and the accuracy of FRF matrix on the nonlinear response curve are investigated in detail.

Keyword
Friction damping, Shroud contact, Strip damper, Cyclic symmetry, Alternate frequency time domain method, Multiharmonic balance method.
National Category
Applied Mechanics
Research subject
Engineering Mechanics
Identifiers
urn:nbn:se:kth:diva-202994 (URN)
Projects
TurboPower
Funder
Swedish Energy Agency, 26159
Note

QC 20170313

Available from: 2017-03-10 Created: 2017-03-10 Last updated: 2017-11-29Bibliographically approved
4. Adaptive control of normal load at the friction interface of bladed disks using giant magnetostrictive material
Open this publication in new window or tab >>Adaptive control of normal load at the friction interface of bladed disks using giant magnetostrictive material
(English)In: Journal of Vibration and Control, ISSN 1077-5463, E-ISSN 1741-2986Article in journal (Other academic) Submitted
Abstract [en]

A novel application of magnetostrictive actuators in underplatform dampers of bladed disks is proposed for adaptive control of the normal load at the friction interface in order to achieve the desired friction damping in the structure. Friction damping in a bladed disk depends on many parameters such as rotational speed, engine excitation order, nodal diameter, contact stiffness, friction coefficient and normal contact load. However, all these parameters have a fixed value at an operating point. On the other hand, the ability to vary some of these parameters such as the normal contact load is desirable in order to obtain an optimum damping in the bladed disk at different operating conditions. Under the influence of an external magnetic field, magnetostrictive materials develop an internal strain that can be exploited to vary the normal contact load at the friction interface, which makes them a potentially good candidate for this application. A commercially available magnetostrictive alloy, Terfenol-D is considered in this analysis that is capable of providing magnetostrain up to 0.002 under prestress and a blocked force over 1500 N. A linearized model of the magnetostrictive material, which is accurate enough for a DC application, is employed to compute the output displacement and the blocked force of the actuator. A nonlinear finite element contact analysis is performed to compute the normal contact load between the blade platform and the underplatform damper as a result of magnetostrictive actuation. The contact analysis is performed for different mounting configurations of the actuator and the obtained results are discussed. The proposed solution is potentially applicable to adaptively control vibratory stresses in bladed disks and consequently to reduce failure due to high-cycle fatigue. Finally, the practical challenges in employing magnetostrictive actuators in underplatform dampers are discussed.

Keyword
Giant magnetostrictive material, Terfenol-D, Actuators, Friction damping, High-cycle fatigue, Bladed disk
National Category
Applied Mechanics
Research subject
Engineering Mechanics
Identifiers
urn:nbn:se:kth:diva-202996 (URN)
Projects
TurboPower
Funder
Swedish Energy Agency, 26159
Note

QC 20170313

Available from: 2017-03-11 Created: 2017-03-11 Last updated: 2017-11-29Bibliographically approved

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