PSI - Issue 75

Robert Goraj et al. / Procedia Structural Integrity 75 (2025) 691–708 Goraj/ Structural Integrity Procedia (2025)

695 5

1 ( ) = 1 2 + 1 + 1 2 ( ) = 2 2 + 2 + 2 1 ( ) = 1 + 1

(12)

The system damping is approximated using damping coefficients: ζ 1 for a steel and ζ 2 for a rubber as follows: 1 ≅2 1 1 √ 1 / 1 (13) 2 ≅2 2 2 √ 2 /( 1 + 2 ) (14) The equation system (11) is solved for the complex ratio ( X 1 - X 2 ) / U x referred as a transfer function G 3 . Restricting the study to a given damper configuration, in which 2 is a constant value one obtains a parametrical ( I y dependent) transfer function: 3 ( , )= 2 ( ) 1 ( , ) 2 ( ) + 1 2 1 ( , ) (15) 3. Structural analyses The SA parametric model derived in section 2 is used for a determination of the mechanical stress present in the bearing spoke. The stress is evaluated in a reference point located at: x =x 1 - H/ 2 , y = z = 0. In this location the mechanical stress consists of the normal component referred as the longitudinal stress σ zz . The evaluation is performed in the Software: MATLAB ® 2019b Update 6 for the parameters listed in Table 1.

Table 1. Input parameters for structural calculations Parameter

Symbol

Value

Unit

mass of rotating components mass of stationary components axial stiffness of a dumper max. propeller thrust propeller unbalance Young’s modulus prop. excitation frequency minimal second moment of area maximal second moment of area spoke length (radial dir.) spoke depth (axial dir.) spoke width (tangential dir.) web thickness of H-profile

m 1 m 2 k 2 F th F ub

54

kg kg

152 1968 8500

N/mm

N N

70

E L H f exc

200 110

GPa

Hz

2 8

cm 4 cm 4 mm mm mm mm

185 38 24 3.5

b a

period

2T

1

s - - - - -

damping ratio rubber damping ratio steel Poisson’s ratio number of spokes number of mounting pads

ζ 1 ζ 2 n 1 n 2 ν

0.05 0.008

0.3

4 4

3.1. Static analysis Dividing the bending moment M b by the section modulus W y one obtains the static value of the longitudinal stress σ static : ( )= = ℎ 2 / / (16) An increase of I y leads to a reduction of σ static but results in a higher structural mass. The evaluation of (16) is performed in a parameter range ∈ 〈 , 〉 (see Table 1). The obtained static longitudinal stress varies