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yflK 621.43
DETERMINATION OF THE INFLUENCE COEFFICIENTS DURING FORMATION OF AXIAL VIBRATIONS WITH THE HELP OF THE METHOD OF IDENTIFICATION OF MECHANICAL SYSTEMS BY CALIBRATION EFFECT
N. Ivanov, Seniour Assistant, Dr-Eng., Z. Ivanov, Seniour Assistant, Dr-Eng., Technical University - Varna, Bulgaria
Summary. The calculation of axial vibrations of internal combustion engine crankshafts caused by the gas and inertia forces acting in it takes into account the influence of the normal forces in the neighboring shafts as well as the influence of tangential forces applied to them. The described technology can be used for the defining of theoretical algorithms for calculation of crankshaft axial vibrations.
Key words: crankshaft, vibration, force, vibro-record, frequency
Introduction
The axial vibrations of the crank shaft line units of internal combustion engines are often a cause for various failures and other occurrences, that have minor or heavy consequences: breaking of the crank shaft, breaking of balance weights, destruction of the antifriction alloy of the fixing and main support ship bearings and their body, fretting-corrosion of the outer surface of the main bearings shells and the conic surface in the pap of the propeller. Besides, the axial vibrations can cause ship hull vibrations and breaking of some types of clutches. That is why they are a subject of series of theoretical and experimental researches.
In the published works on axial vibrations the basic focus is on the strength of the crank shaft and the thrust bearing and the cause of the vibration forces. . Only those forces are taken into consideration, that effect a taken crank, without calculation of the neighbouring cranks influences [4, 5, 6], etc. In [2, 3] as well as the normal force toward a crank, the forces, effecting the neighbouring cranks are given an account. Due to the complexity of the crank shaft the calculation formulas for stimulation forces have theoretical-empiric characteristic. Experimental method is used to register the half-covering of the basic and rod journal and the "effective" lengths of basic, crank and rod journal. The calculation of the accessibility of the main bearings requires quite complex algorithms [3] for calculation, in which however it is resorted to a simplification of the vary crank model (consisting of consecutively connected elastic and solid areas).
Background
So far it becomes clear, that the experimental determination of the formation forces has great significance for defining the theoretical-empiric relations for a certain engine and for applicability check of the complex algorithms for calculation on [2, 3].
I—I P, P.
" 111 111 [if
Fig. 1 Pj
Experimental research on the stimulation forces is reduced to the determination of the radial to equivalent axial force transformation coefficient [4, 5] or determination of the radial fusion coefficient (determined as a relation between the axial and radial deformation). The measurements are taken on crank shaft models or on real installed ones. The last case, although more accurate due to the account of the crank shaft bearings pliability, there is a significant results distortion [6] because of a presence of clearances between the main journals and the main bearings. This method has another disadvantage - it does not take account of the oil cotter pliability in the main bearings, created by the rotation of the crank shaft, and it is known that its pliability is equal or even higher of the main bearing pliability [8].
Therefore there is a need of an experimental research method, which allows the determination of axial vibrations formation at real working conditions of the crank shaft, i.e. at working engine. This opportunity
FiS.2
gives the method of identification of mechanical systems parameters by calibration influence, analyzed in [1]. The basics of the method are the following: the structural scheme of machine unit is available and with possibility for registration of the basic elements movement laws, but we don't have preliminary information about the model parameters. If we insert some calibration change in one of the unit parameters, we will come to a new law for the movement of the basic elements. The number of the calibration influences is determined by the system itself. The main goal is by the determined experimentally laws for movement and the known calibration influences to determine the parameters of the structural scheme of the machine unit.
Let's take a closer look of one crank shaft with 'n' in number cranks (fig. 1), on each crank of which there are applied the forces p, i = 1,2,...,n . Except this
we can register the "breathing" of the 'i' th crank under influence of these forces. Between the forces P; and the movement8j, j = 1,2,...,n, the following dependence exists:
P1 -Kj + P2 "^j +- + Pj "j +- + Pn ■ Mn, j =8j , (1)
where My - is the coefficient of influence of the ith force on the jth crank.
If the system (1) is lineal by a change of the forces Pt and measurement of the movements 5j we can build system of lineal algebraic equations, concerning the unknown My. It is clear that 'n' in number sets of
forces Pi, lineally independent, are needed. Thus the described problem is static, i.e. equations (1) are true only at static load on the crank shaft. If the deformation 8j is measured at the rotation of the shaft, it becomes clear that as the outcome equations must be taken the differential equations, describing the vibration processes in the whole crank shaft line. However, building the identification system of equations will require acquaintance of all the movements' 8j which in practice is hardly realized, because of the fact that it is needed to examine a multisupport shaft. Is it possible then to use (1)? It comes out possible, but only at certain rates. Let's clear out the last statement. By the theory of the vibrations is known, that the dynamism of the system is shown in an area around the resonance. In an area, distant enough from the resonance and before it, i.e. when the frequency of the formation force is smaller than the system frequency itself, the movements in the system, caused by this force are approximately equal to the static ones. Besides, the dephase between force and movement is almost equal to zero. The influence of the dampening is excluded. At the internal combustion engines the vibrations formation has multiharmoni-ous character. The formation forces appear to be the inertia ones from the backward-advancing moving masses and gas forces. From the inertia forces significant importance have the first 4-6 harmonious components, and for the gas force - the first 15-20 harmonious components from the Furies row. The rest practically have zero amplitude. The resonance rate depends, except by the harmonious order of the formation force, and the frequency spectrum of the own frequencies of the system. The high frequency
spectrum become in resonance with the harmonious components of the vibrations formation force from a higher rate in the revolution range of engine work. From all the mentioned issues comes out that it can be found the frequency range of the engine (usually it's the lower rev. frequencies), where the dynamic effect on the vibration processes in the crank shaft line is inessential. Knowing the frequency range (it is enough to know the first two frequencies) and with the experimental amplitude-frequency characteristic of the engine available (experimental axiogram), can be determined the revolutions range, for which identification system of algebraic equations will be worked out.
The created methods will be illustrated with the conducted experimental determination of the coefficients of influence | y, carried out in the laboratory on "Dynamics and vibrations of ICE" at department TTT in Technical University Varna. The experimental laboratory is described in [7]. It must be mentioned that the measurement of the axle contraction (breathing) of the crank shaft is taken out by the help of tense resistors, sticked on the arms of the crank. The way of calibration and their connection is illustrated in [7]. The breathing of the fifth and sixth crank of the crank shaft. For the first end is considered the opposite end of the flywheel.
On fig. 2 is illustrated a vibrorecord, representing the "breathing" of the fifth crank (curve 1). Curve 2 is an indicator diagram, taken from the second cylinder. Under the vibrorecord, with curve 3 is given the alteration of the sum force, normal to the fifth crank, received from the gas and inertia forces, acting in the fifth crank-connecting rod mechanism. The top death centers of the appropriate cylinders, at the moment of their work, are drawn. It is clearly pointed that the difference of curve 1 from curve 3 is due to the influence of the forces, applied on the separate cranks on the "breathing of the fifth crank.
On fig. 3 is given the scheme of one crank and drawn the forces, which are applied to it. The force P is the sum of the gas force, acting in the cylinder, and the inertia one from the backward-advancing moving masses:
P = Pg + P,
(2)
where Pg - is the gas force; Pj - inertia force backward-advancing moving masses,
Pj =-mb - R -ra2
cos (a + p) cos2 a
--+ k--
cos p
cos3 p
mb - mass of the piston group; R - radius of the piston; œ - frequency of the crank shaft rotation; a -angle of the crank shaft rotation; p - angle of connecting rod deflection; X - constant of the crank-connecting rod mechanism.
As the direction of the sum force P (2) depends on the position of the crank, it is suitable to examine its components: the normal and the tangential forces towards the crank Z and T:
Z = P. cos(a + P) + P T = P - sm(a + P) ^
cos p
cos p
where Pc = - mARa - centrifugal force of the mass mA of the unbalanced parts of the crank and the part of the connecting rod, concentrated in the connecting rod neck.
If we measure the "breathing" of the fifth crank the identification system of algebraic equations the following is the result:
7 Z
5 + Zi,2 ^ 2,5 + - + Zi,6^,5 +
+T'X5 + T',2^2,5 + - + Ti,6 ^6,5 = Si,
(4)
where i = 1,2,.. .12 for six cylinder in line engine and
51>5 is the breathing of fifth crank at the i forces.
set of
The set Pi, respectively Zi and Ti, we receive by the following way: The gas force is taken from the second cylinder via its indicating (it is supposed that in all cylinders of the engine we have the same working process) with the help of piezoquartz indicator. Calibration influence is achieved through the change of the cycle fuel supply, and therefore to the gas force. After that we calculate the real forces on [2 and 3] for each crank giving an account of the dephase of the working processes in the separate cylinders and the angles between the cranks of the engine. As the engine is a four-stroke one, for one and the same position of the crank shaft (like the first crank in TDC) we have a possibility for direct measure of the two values of the gas force. Therefore six types of cycle supply are needed: idle, 20%, 40%, 60%, 80% and 100% load of the engine. The cycle portion of fuel is changed because of the load characteristic of the chosen frequency regime. For the same position of the crank, for which we render an account of the forces, we do for the axe breathing as well. On fig.2 with thick lines is given one experimentally resulted diagram. With dotted lines are given the supposed indicator diagrams in the rest of the cylinders on the line
of engine work. The figure clearly enough illustrates the building of an identification system of algebraic equations (4). The results of the experimental vi-brorecords and their processing are given in table 1 at 900 rpm of the engine.
The processing of the vibrorecords is conducted on electronic processing unit. The identification system of algebraic equations is not well subjected. This difficulty can be overcome as some iteration methods are used as well as the Gauss_elimination method with double precision (32 taken numbers) and with following improvement of the solution. Regarding the influence of the variability of the basic bearings' strength, we can work out the identification system for different positions of the crank shaft at one and same rotation frequencies (for instance by the top death centers of the separate cylinders). In this case the system comes out to be well subjected and conditioned. The number of identification equations can be reduced, if we take into consideration that in TDC of a given crank-connecting rod mechanism the tangential force T is zero .In this case at the first described set of forces ten equations will be needed (for the first and sixth cylinder force T is zero).
References
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Рецензент: Ф.И. Абрамчук, профессор, д.т.н., ХНАДУ.
Статья поступила в редакцию 20 апреля 2005 г.
