Analysis of working performances at damaged vibration isolation devices.

Nastac, Silviu

1. INTRODUCTION

The main purpose of this research, regarding the isolation performances of the passive systems, consist by the estimation of the deep connection between the structural and behavioural demotion, for antivibrational devices, and, on the other side, the diminishing of the isolation degree, for the same working conditions. During the measurements, both in the laboratory tests, and "in situ" behaviour evaluations, it was observed that the damages level growing up with the exploitation time period, and the damages especially appears at the elastic elements. Taking into account the major influence of these elements on the global isolation degree of the insulated ensemble, it was appear the idea of damage level evaluation based on the isolation degree (or transmissibility) of the dynamic system. The main advantages of this method are: non-destructive method, increased safety, reduced costs. Another major advantage of this method consist of the possibility of damages evaluation as a continuous process, and detection the begining of an important failure until these had a critical value and disturbed the dynamic and the integrity of the isolation system. It have to be said that this procedure could be framed into the Structural Health Monitoring Concept, that enables Conditions--Based Maintenance at structures through diagnosis of the status current health during exploitation (Johnson et al., 2002).

2. RESEARCH SUPPOSITIONS

In the Figure 1 is presented the schematic diagram of the basic model, a rigid bodies system with three DOF underpined to the ground and between them by the visco-elastic elements (Bratu, 1990; Bratu, 2000; Harris et al., 2002). This is a full basic model, with all the linkages, constants and loading forces. In this shape, the model could simulate a large area of technical systems, from the point of view of dynamical behaviour.

The dynamic equations of this model was developed with the approaching of the next hypothesis (Nastac, 2004)

[check] the entire system are supposed as a rigid bodies ensemble ([m.sub.i]), with vertical translations [x.sub.i](t) for each mass;

[check] the linkages from the masses to the ground are maded with the visco-elastic elements, with linear characteristics;

[check] the elastic linkages have the characteristic rigidities [k.sub.ij], and internal dampings [b.sub.ij],

[check] the dynamic external loads (excitations) have innertial type and is generated by the forces [F.sub.i];

[check] in the previous notations the indexes i, j denotes the masses (1, 2, 3) and the ground (0).

Taking into account the previous hypothesis, the dynamic equations of the model are

M[??] + B[??] +KX = F (1)

where [??] denote accelerations vector, [??] denote velocities vector, X denote displacements vector, M denote matrix of masses, B denote matrix of dampings, K denote matrix of stiffness, F denote external forces vector.

The transfer function matrix of the three DOF model, presented in Figure 1, is

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (2)

where the new terms have next expressions

[b.sub.1] = [b.sub.10] + [b.sub.12] + [b.sub.13]; [b.sub.2] = [b.sub.20] + [b.sub.12] + [b.sub.23]; [b.sub.3] = [b.sub.30] + [b.sub.13] + [b.sub.23]; [k.sub.1] = [k.sub.10] + [k.sub.12] + [k.sub.13]; [k.sub.2] = [k.sub.20] + [k.sub.12] + [k.sub.23]; [k.sub.3] = [k.sub.30] + [k.sub.13] + [k.sub.23]; (3)

The analysis of the damage influences about the spectral composition of the amplification functions for each degree of freedom--vertical translations of the [m.sub.i] masses--will be maded supposing only the direct linkages between the nearest rigid bodies. This kind of model answer to majority types of technical systems.

[FIGURE 1 OMITTED]

3. TEST APPLICATION

For the first approach of numerical simulation, it was computed the FRFs of the three DOFs system. Even if the transmissibility functions are most sensitives to changes in mass, damping, and stiffness like a frequency response functions, the last are prefered because it's more facilely to evaluate. In the Figure 2 it is depicted the frequency response functions for the three degree of freedom of the system presented in Figure 1. In the Table 1 it is presented the basic values of the model constants for the numerical application.

[FIGURE 2 OMITTED]

[FIGURE 3 OMITTED]

[FIGURE 4 OMITTED]

[FIGURE 5 OMITTED]

The analysis was developed for damages influences identification on the system dynamic characteristics (i.e. FRFs). As a damaged element it was proposed the visco-elastic linkage between [m.sub.1] and [m.sub.2]. This element has [k.sub.12] stiffness and [b.sub.12] damping. In this paper it was presented only the analysis cases for constant dampings of all the linkages. Thus that, for the braked element, it was varied only the stiffness values. It was assume three main cases, which are 0.1%, 1%, and respectively 10%, losses in [k.sub.12] stiffness.

In Figures 3 ... 5 it is depicted only the relative changes of the FRFs, separately for each of the three DOFs system. Every figure contain two set of diagrams, with the next significations: (a) the FRF changes for 1% loss in [k.sub.12], and (b) the FRF changes for 10% loss in [k.sub.12]. The case of 0.1% loss in [k.sub.12] was not depicted because the real changes of the FRFs were not significant. In the Table 2 it was presented the values of the FRFs relative changes, evaluated for the three cases, at the reference frequency--this value was adopted after a qualitative and quantitative evaluation of the FRFs magnitudes of the original system. This value derived from the excitation pulsation value of 30 rad/sec.

4. CONCLUSION

Comparative analyses of the diagrams from Figures 3 ... 5, denote a certain sensitivity of the system DOFs frequency response functions. This sensitivity could be observed both at the natural frequency shift, and at the maximum values on these frequencies. If the shift of the natural frequencies is very small, the relative increasing or decreasing of the FRF magnitude at these frequencies acquire high values even for the low values of stiffness losses. The values from the Table 2, and the diagrams from Figures 3 ... 5, show that the maximum sensitivity is on the resonance frequencies area. From the Table 2 result that outside the resonance area, the relative changes acquires low and very low values - under a size order comparative with the stiffness loss value, but supposing a reference value of frequency, it could be evaluate the rigidity demotion degree, by means of FRFs measuring. After this step of the study, it will be analysed the dampings losses influences, separately and together with the stiffness losses. The entire data sets will be re-evaluate, tunning and validate on the instrumental laboratory tests, on the structures with damage level control.

5. REFERENCES

Bratu, P. (1990). Insulation Elastic Systems for Machines and Equipments, Editura Tehnica, ISBN 973-31-0234-2, Bucharest, Romania

Bratu, P. (2000). Elastic Systems Vibrations, Editura Tehnica, ISBN 973-31-1418-9, Bucharest, Romania

Harris, C.M. & Piersol, A.G. (2002). Shock and Vibration Handbook, 5th Edition, McGraw Hill

Johnson, T.; Adams, D. & Schiefer, M. (2002). An Analitical and Experimental Study to Assess Structural Damage and Integrity Using Dynamic Transmissibility, The Proceedings of the 20th International Modal Analysis Conference, pp. 472-476

Nastac, S. (2004). Contributions for Dynamic Behaviour of the Antivibrational and Antiseismical Passive Isolation Elastic Systems, A Dissertation submitted to the University "Dunarea de Jos" of Galati, Romania, for the Master of Science in Mechanical Engineering Degree

Tab 1. The basic values for the numerical application.

 Parameters Values Units

[m.sub.1]; [m.sub.2]; [m.sub.3] 12; 12; 12; [kg]
[k.sub.10]; [k.sub.12]; [k.sub.13];
 [k.sub.20]; [k.sub.23]; [k.sub.30] 0;1000;0;0;1000;1000; [N/m]
[b.sub.10]; [b.sub.12]; [b.sub.13];
 [b.sub.20]; [b.sub.23]; [b.sub.30] 0; 1; 0; 0; 1; 1; [N s/m]
[F.sub.10]; [F.sub.20]; [F.sub.30] 1; 0; 0; [N]

Tab 2. The relative changes of the FRFs at the reference
frequency ([omega] = 30 rad / s).

Analysis Damages level Ref. Frequency Differences
 [Hz] [%]

 case I 0,1% loss in [k.sub.12] 4.774789113 0.0128346204

case II 1% loss in [k.sub.12] 0.12806582

case III 10 % loss in [k.sub.12] 1.253263361