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  • 标题:Influence of kinematic parameters on the deterministic vibrations of the viscoelastic linear connecting rod: part of a rod lug mechanism.
  • 作者:Stanescu, Marius-Marinel ; Chelu, Angela ; Nanu, Gheorghe
  • 期刊名称:Annals of DAAAM & Proceedings
  • 印刷版ISSN:1726-9679
  • 出版年度:2009
  • 期号:January
  • 语种:English
  • 出版社:DAAAM International Vienna
  • 摘要:The researches that were done until now by several authors determined only the transversal displacements for vibrating beams, but which do not move. This involves restrictions of the conditions.
  • 关键词:Connecting rods (Motor vehicles);Kinematics;Vibration;Vibration (Physics);Viscoelasticity

Influence of kinematic parameters on the deterministic vibrations of the viscoelastic linear connecting rod: part of a rod lug mechanism.


Stanescu, Marius-Marinel ; Chelu, Angela ; Nanu, Gheorghe 等


1. INTRODUCTION

The researches that were done until now by several authors determined only the transversal displacements for vibrating beams, but which do not move. This involves restrictions of the conditions.

We propose an original method, based on an iterative method of determining the field of transversal displacements of the linear-viscoelastic rod of a rod lug.mechanism. In our future studies, for the same problem we analyze now, we will determine the influence of the aleatoary vibrations.

2. THEORETICAL RESULTS

Let us consider the mathematic model of free vibrations, in a first approximation (Bagnaru, 1998), in the form:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII], (1)

Applying to equation (1) Laplace unilateral transform depending on time, and replacing module E with [??](s), it results the matricial equation of the first approximation (in Laplace images), of the vibrations of the viscoelastic connecting rod OA of mechanism R(RRT) (Harrison, 1997) in Fig. 1., in the form:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (2)

where:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

The solution of equation (1) is series type and has the following form:

[u.sup.(1).sub.2] (x,t) = 2/L [[infinity].summation over (n=1)] [u.sup.(1).sub.2,s] (n,t) x sin ([[alpha].sub.n] x x), (3)

where [u.sup.(1).sub.2,s] (n, t) is the Fourier transforms finite in sine, of the transversal elastic displacement. The relation (3) shows the effect of the kinematical parameters of the movement on the vibration modes.

[FIGURE 1 OMITTED]

3. NUMERICAL APPLICATION

Let us consider the concrete case of the textolite connecting rod with:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII].

From relation (3) it results the numerical values of transversal displacement (in the middle of the connecting rod) presented in tab. 1.

These errors are accepted in techniques, and therefore the theoretical results are verified by the experimental tests.

4. EXPERIMENTAL TESTS

The experimental tests were conducted on a stand, using the electronic measurement system Spider 8.

[FIGURE 2 OMITTED]

[FIGURE 3 OMITTED]

[FIGURE 4 OMITTED]

5. CONCLUSIONS

The displacement fields of some viscoelastic bars, especially the transversal ones, constitute the support of the afterwords determination of the stress and deformation states which are usefull in the design of the mechanisms used in the manufacturing engineering.

We insisted on the transversal displacement field because the influence of the longitudinal displacements on the stress or displacements state is insignificant.

The values in table 1 are comparable with those experimentally obtained in figures 2, 3, 4 and 5, the error being in the first and second case 10,3 %, and 5% respectively.

These errors are accepted in techniques, so that, in fact, the theoretical results are verified by the experimental tests.

The vibration energy is mainly contained in the fundamental harmonic. The rheological materials have the advantage of the existence of some forces and reduced inertia couples due to the specific mass which is lower than in the case of metallic materials in comparable rigidity conditions (Routh, 2003), the displacements being also comparable with those of the latter.

6. REFERENCES

Bagnaru, D. (1998). About the dynamic response of the viscoelastic bars of the plane mecanisms PRASIC 98, 5-7 XI 1998, Brasov, pp. 15-18

Bagnaru, D., Marghitu, D.B. (2000). Linear Vibrations of Viscoelastic Links, 20th Southeastern Conference on Theoretical and Applied Mechanics (SECTAM-XX), April 16-18, 2000, Callaway Gardens and Resort, Pine Mountain, Georgia, USA, pp. 1-7

Fu, K.S., Gonzalez, R.C. & Lee, C.S.G. (1997). Robotics, McGraw-Hill

Harrison, H.R. (1997). Advanced Engineering Dynamics, John Wiley & Sons Inc., New York

Routh, E.J. (2003). Dynamics of a system of rigid bodies, Part l & Part 2, Macmillan
Tab. 1. The numerical values of transversal displacement

Transversal Frequency Frequency 1,5381 1,3916
movement on 2,6184 3.2776 (Hz) 1,391 1,8860
the direction (Hz) [Hz] [Hz]

OT [mm] -- -- 0,24 5
V[mm] 15 15,01 -- --
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