Dynamic answer modeling of a mechanism from the mowers machine structure.

Dumitru, Nicolae ; Ungureanu, Alin ; Catrina, Gheorghe 等

1. INTRODUCTION

Aspects concerning the dynamic answer analysis of the mobile mechanical systems are presented in the researches of many authors. The dynamic analysis is presented in two variants, respectively with the dynamic models method and with Newton-Euler method, completed with the Lagrange multipliers (Dumitru & Nanu, 2008).

In figure 1 are presented some mechanism models kinematic schemes, used in the mowers cut-off systems: a-balancing mechanism, b-oscillatory washer mechanism, (Dugaesescu, 2005).

[FIGURE 1 OMITTED]

2. KINEMATICAL ANALYSIS

2.1 The mechanism structure

In figure 2 we present the proposed mechanism kinematic scheme, for the mowers machine cut-off system. The mechanism dimensions are obtained trough geometric synthesis, problem presented by authors: (Dibakar & Vyankatesh, 2004) and (Kevin & Raj, 2005).

[FIGURE 2 OMITTED]

As it is observed from the kinematic scheme presented in figure 2, the mechanism has 5 kinematic elements and 7 kinematic joints. So we have the degree of mobility of the mechanism: M=3 x 5 x 2 x 7=1.

3. THE DYNAMIC ANSWER ANALYSIS OF THE MECHANISM USING THE DYNAMICS MODELS METHOD

3.1 The reduced moment and reduced inertia moment Is made from the condition: [P.sub.model] = [P.sub.mechanism]

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (1)

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (2)

Where: [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] is the angular speed of the motor element.

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

If we neglect the inertia moments we have:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (3)

The calculus of the reduced inertia moment is made from the condition: [T.sub.model] = [T.sub.mechanism]

[J.sub.red] x [[omega].sup.2]/2 = [3.summation over (i=1)]([m.sub.i] x [v.sub.Ci.sup.2]/2 + J[DELTA][c.sub.i.sup.2] x [[omega].sup.2.sub.i]/2) (4)

Where [omega] = [??] is the angular speed of the element 1.

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

We apply the kinetic energy theorem:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]. (5)

The angular speed for the motor element is give by the relation:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (6)

3.2 Graphical results

The force are represented in newton, angle are in radian. Graphics' for the kinematics parameters calculated in dynamic regime:

[FIGURE 3 OMITTED]

[FIGURE 4 OMITTED]

[FIGURE 5 OMITTED]

4. EXPERIMENTAL RESULTS

In figure 6 is presented the mechanism experimental model mounted on the essay stand.

[FIGURE 6 OMITTED]

[FIGURE 7 OMITTED]

[FIGURE 8 OMITTED]

For the experimental research the mechanism was mounted on a test stand, equipped with an electric motor (see figure 6). Also the stand offers the possibility to modify the angular velocity by means of a conical variable speed drive. We made tests for 3 technological forces, which have been determined whit the force transducer. Also have been determined the displacements [S.sub.1]--displacement of the slide 1, [S.sub.2]--displacement of the slide 2, and [S.sub.3]--displacement of the knife, the motor moment and the resistance force.

The finite element dynamic analyze results are presented in figure 8.

5. CONCLUSIONS

We realised the dynamic analysis of the mechanism, using the dynamic models method and we determined the time variation law of the motor element angular velocity (fig. 3). The graphics of dynamic parameters are represented upon phi1 (t), for a complete rotation of the motor element (6.28 rad). We determined by experimental research the motor element torque variation, and we used the experimental dates for the finite element analysis in dynamic regim with MSC.visual. Nastran software.

The future research plans are to study the flexible mechanism, as it is well know that the elastic deformation has a significant effect on the dynamic behavior.

6. REFERENCES

Dibakar S. & Vyankatesh J. (2004). Issues in geometric synthesis of mechanisms, Mechanism and Machine Theory vol. 39, pp 1321-1330

Dugaes.escu D. (2005). Contributions concerning the analysis and optimal control of mechanisms from harvester's machine, PhD Thesis, University ,J?olitehnica" Bucharest

Dumitru N. & Cherciu M. (2007). Theoretical and Experimental Modeling of the Dynamic Response of the Mechanisms with Deformable Kinematics Elements, Proceedings of IFToMM Congress, Besancon, France, june 2007

Dumitru, N. & Nanu, Ghe. (2008). Mechanisms and mechanical transmisions, E.D.P., Bucharest, ISBN 978-973-30-1882-7

Kevin R. & Raj S. (2005). On the design of slider-crank mechanisms, Mechanism and Machine Theory vol. 40 pp 301-317