Influence of kinematic parameters on the deterministic vibrations of the linear-elastic connecting rod: component of a rod lug mechanism.

Bagnaru, Dan Gheorghe ; Grozea, Marius-Alexandru ; 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

By distributing the coupling terms between the longitudinal and transversal vibrations (Bagnaru, 2005), as well as the terms which confer to the mathematical model the quality of an invariant model in time, it results the model as the matrix:

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

As a result of an iterative process, it results the mathematic model in 'j' approximation, in the form:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]. (2)

The solution in 'j' approximation will be:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII],

where [u.sup.(j).sub.1,c])(n,t) and [u.sup.(j).sub.2,s] (n,t) are the Fourier transforms finite in cosine and sine respectively, of the longitudinal elastic displacement, and transversal respectively.

The process of successive approximations is considered completed when, for ([for all])n, [parallel]{[u.sup.(j)]}-{[u.sup.(j-1)]}[parallel] [less than or equal to] [epsilon] occurs, where [epsilon] > 0 and small enough depending on the required calculation precision, and

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII].

With {F} = {0}, {f } = {0} and m = 0 in equation (1), it results the mathematic model of the free vibrations, in a first approximation, having the form:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII].

We will only present the transversal displacement, solution of equation ([1.sup.(1)]

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (3)

[FIGURE 1 OMITTED]

3. NUMERICAL APPLICATION

If we situate ourselves in the concrete case when the lengths of the connecting rod in OL45 and the lug are: L = [L.sub.b] = 1 [m], r = 0,075 [m], and the width and thickness of the connecting rod are b = 0,04 [m], h = 0,005 [m] respectively, we obtain, by using relation (3), the numerical values of the transversal elastic displacement (in the middle of the connecting rod), presented in table 1 These values are comparable with those experimentally obtained (see figures 2-5), the error being around 6,695% .

4. EXPERIMENTAL TESTS

The experimental tests were made on a stand, using a device composed of the acquisition electronic system Spider 8 for the numeric measurement of the analogical data, the signal conditioner NEXUS 2692-A-0I4, accelerometers Bruel & Kjaer 4382, the inductive linear translator WA300 and Notebook IBM ThinkPad R51.

We analysed the dynamic response (Harrison, 1997) to variable strains of the connecting rod made of OL 45 universal iron.

The mechanism connecting rod lung was driven by a three-phase alternating current engine of 25 KW power, with constant turation of 1500 [rot/min]m, with the aid of a friction variator, so that variable turations of 60 ... 240 [rot/min] could be achieved at the level of the connecting rod.

[FIGURE 2 OMITTED]

[FIGURE 3 OMITTED]

In order to determine the dynamic response (Routh, 2003), we used an accelerometer Bruel & Kjaer 4391 successively installed in the middle of the connecting rod (pt. 2) on vertical and longitudinally horizontal directions reported to the plane of the connecting rod. The run/stroke was determined at the level of the slide by the inductive translator WA 300, the slide having the value of 140[mm].

In the middle of the connecting rod, the fundamental harmonic has the major contribution. The contribution of the harmonics of order 4 and 5 increases with the turation speed growth.

5. CONCLUSIONS

The field of the longitudinal displacements has an insignifiant influence on the stress or deformation states. That is why we did not give the solution of the ecuation ([1.sup.(1)]) as a function which characterize this field, too.

The paper is extremely important for blueprint activity where one must take into consideration the influence of dynamic parameters upon the vibrations (Bagnaru & Marghitu, 2000) to which the connecting road of this system is submitted, a constitutive part of, say, an internal combustion engine.

6. REFERENCES

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

Bagnaru, D. (2005). The influence of the vibrations upon the stress and deformation states in case of the linear-elastic connecting rod for a slider crank machanism R(RRT), Annals of the Oradea University. Fascicle of Management and Tehnological Enginering, pp 97-104, ISSN 1583-0691.

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 the transversal elastic
displacement

Transversal Frequency Frequency 1,5381 1,3916
displacement 2,8198 3,0030 (Hz) [Hz] [Hz]
 on the (Hz)
 direction

 OT [mm] -- -- 0,14 0,13
 V[mm] 21 20 -- --