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Research Papers

Estimation of Axial Load in Tie-Rods Using Experimental and Operational Modal Analysis

[+] Author and Article Information
S. Campagnari, F. di Matteo, M. Scaccabarozzi

Department of Mechanical Engineering,
Politecnico di Milano,
Via La Masa, 34,
Milan 20156, Italy

S. Manzoni

Department of Mechanical Engineering,
Politecnico di Milano,
Via La Masa, 34,
Milan 20156, Italy
e-mail: stefano.manzoni@polimi.it

M. Vanali

Department of Engineering and Architecture,
Università degli Studi di Parma,
Parco Area delle Scienze, 181/A,
Parma 43124, Italy

1Corresponding author.

Manuscript received May 18, 2016; final manuscript received January 30, 2017; published online May 30, 2017. Assoc. Editor: Carole Mei.

J. Vib. Acoust 139(4), 041005 (May 30, 2017) (15 pages) Paper No: VIB-16-1253; doi: 10.1115/1.4036108 History: Received May 18, 2016; Revised January 30, 2017

This paper addresses a new method for estimating axial load in tie-rods using indirect measurements. This information is of great importance for assessing the health of the tie-rod itself and the health of the entire structure that the beam is inserted into. The method is based on dynamic measurements and requires the experimental estimation of the tie-rod eigenfrequencies and mode shapes at a limited number of points. Furthermore, the approach requires the development of a simple finite element model (FEM), which is then cross-correlated with the experimental data using a model update procedure. Extensive numerical simulations and experimental tests have demonstrated the ability of the new approach to yield accurate estimates of the tie-rod axial load and overcome various limitations of the methods currently available in the literature.

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References

Figures

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Fig. 1

Scheme of the tie-rod

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Fig. 2

Influence of N, k, l, E, and ρ on the lowest six eigenfrequencies of the tie-rod of Table 1

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Fig. 3

Trend of the lowest eigenfrequency for the tie-rod described in Table 1

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Fig. 4

Mode shape with generically scaled values of eigenvector components: for a fixed value of N and different values of k (a) and for a fixed value of k and different values of N (b). x is the coordinate along the tie-rod length, and x is thus between 0 and l.

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Fig. 5

Graphical definition of err and m. The points at 10% and 20% of the beam length were used to build this plot.

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Fig. 6

Maxima and minima values of the estimated k values with the bias values described in Table 3 (a) and the corresponding range rk with bounds rk1 and rk2 (b)

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Fig. 7

Influence of N, k, l, E, and ρ on the second, third, and fourth eigenfrequencies for the tie-rod of Table 1 and with bounds rk1 and rk2

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Fig. 8

Flowchart of the method for axial load assessment

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Fig. 10

Results for all the variables for the simulation with k = 25 and N = 0.2 Nsn (tie-rod 1)

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Fig. 9

Results for all the variables for the simulation with k = 70 and N = 0.8 Nsn (tie-rod 1)

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Fig. 11

Test setup (a) and rubber sheets used to lower the stiffness of the constraint (b)

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Fig. 12

Results (in terms of Nest) for: a nominal length of 4000 mm and measuring the force input (see Table 12) (a), a nominal length of 4000 mm without measuring the force input (see Table 13) (b), and a nominal length of 3836 mm and measuring the force input (see Table 14) (c). Δ (triangle) indicates the results before the update for tests without rubber, o (circle) indicates the results before the update for tests with rubber, □ (square) indicates the results after the update for tests without rubber, and * (asterisk) indicates the results after the update for tests with rubber.

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Fig. 13

Absolute value of the FRFs between the force given by the impact hammer and the response of the accelerometer at point y2 for three tests of Table 12 (the legend of the figure indicates the reference axial load (Nref (N)) and the presence/absence of rubber sheets)

Tables

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