A formulation of the Jacobian matrixfor 3D numerical friction contact model applied to turbine blade shroud contact

• 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.

Ämnesord

TEKNIK OCH TEKNOLOGIER  -- Maskinteknik -- Teknisk mekanik (hsv//swe)

ENGINEERING AND TECHNOLOGY  -- Mechanical Engineering -- Applied Mechanics (hsv//eng)

Nyckelord

Jacobian matrix

friction damping

shroud contact

cyclic symmetry

alternate frequency time domain method

multiharmonic balance method

Engineering Mechanics

Teknisk mekanik

Vehicle and Maritime Engineering

Farkostteknik

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