ABSTRACT OF THE MASTER WORK'S THEME
Table of contents:
Table of contents:
1. Actuality of theme
2. Analysis of publications
3. Aim and research tasks
4. A physical model of resonator is with a branch
5. Mathematical model of new hydraulic of oscillation contour
Conclusions
List of literature
1. Actuality of theme
Further development and technical level of hydraulic apparatuses are indissolubly related to the improvement of them dynamic descriptions. Application of existent hydraulic apparatuses is in technological machines, does not allow to provide permanent reliability of work of hydraulic driver of vcelom.
The known lacks of hydraulic apparatuses with valvular or slide-valve distributive elements are a presence of hydrodynamic forces, nonlinear friction, possibility of the hydrostatical jamming.
One of effective ways of fight against the noted defects there is application of hydraulic apparatuses with oscillation which registers in works of Т.М. Bashta, Г.А. Nikitina, other researchers. However, working processes which take place in hydraulic apparatuses with a hydraulic management and with hydraulic oscillation are not investigational and a simple and effective hydraulic oscillation contour is not worked out.
Hydroelectric generators which are used in industry are characterized by the variety of elements which are included in their composition, presence of difficult working processes which take place in the process of their functioning. The methods of their calculation and planning have a row of features from the account of which it is possible to improve them dynamic descriptions: complex account at mathematical description of hydraulic apparatuses of unstationarity of hydraulic mechanic processes and descriptions of working liquid, which change in the process of his functioning; improvement of schematics of гідроапаратури and томпоновки of his elements; an increase of exactness of calculation of sources is in the mobile elements of гідроапаратури; forces of friction are on the осцилюючому slide-valve of гідророзподільиика, which promote exactness of mathematical model of hydraulic apparatuses.
Taking into account transferred, count the theme of master's degree work, sent to the decision scientifically, - practical task, related to the increase of technical level of hydroelectric generators by the use of pulsation of pressure of working liquid for revealing to of oscillation motion the mobile elements of hydraulic apparatuses is timely and actual.
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2. Analysis of publications
To the methods of planning of resonator with a branch, which to it was used as гасник, the small amount of works is devoted. Yes, in [3, 4] they over are brought fundamental charts and dependences for determination of volume of chamber and sizes of channels. In [5] a design technique over, which is based on an electro-analogy at the use of which the row of limitations is laid on, is brought, tying up with the sizes of resonator with a branch and sometimes passing of hydrodynamic transients. In addition, the use of this methodology requires realization of previous experimental researches, that complicates her use considerably. In [6] the brought mathematical models over of resonator with a branch, built with the use of method of Euler, but in them absent recommendations in relation to determination of them rational, structural and working parameters. In addition, the use of these mathematical models is labour intensive enough. More complete reflection of this problem found in [7], where mathematical models over of such devices, built with the use of transformations of Fourier, which can be used for certain them rational, structural and working parameters, are brought. However in her more attention is spared гасникам pulsations of pressure. Thus, determination of structural and working parameters of resonator with a branch on the basis of realization of comprehensive analytical researches is an actual scientific and technical task.
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3. Aim and research tasks
The aim of work is a construction of mathematical model resonator with a branch, analysis of influence of him structural and working parameters on a transmitivity.
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4. A physical model is a resonator with a branch
In a cylindrical corps 3(capacity element) the cylindrical narrowed union coupling is placed 2 (inertia element), which through the union coupling 1 it is connected to the highway of feed (sources of pulsations of pressure). It is realized shaking loose resonance contour. Union coupling 4 connects a resonator with a branch with the chamber of management of hydrodistributor. The pulsations of pressure of working liquid enter capacity through the union coupling 1 and 2. In case of presence of change of phases of pulsating stream of working liquid and eigenfrequency a resonator is with a branch, there is strengthening of pulsations of pressure which acts to the chamber of management of hydrodistributor. Gathering additionally corresponding capacities, crossing and length of the narrowed union coupling 2, it is possible to get different amplification factors.
Picture 1 - Chart of resonator from by a branch: 1 - an entrance pipeline; 2 - the entrance narrowed union coupling; 3 - chamber of new hydraulic oscillation contour; 4 - chamber of hydrodistributor.
Picture 2 – Interaction of the hydrodistributor with the volume pump
(animation: volume - 254 Кб; size - 450х422; consists of a 22 shot; delay between shots - 1с; delay between the last and first shots - 7с; amount of cycles of reiteration - 25)
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5. Mathematical model of new hydraulic of oscillation contour
At the stowage of mathematical model of new hydraulic oscillation contour will do such suppositions:
– consider that there are withstand hydrodynamic processes in a new hydraulic oscillation contour. Does not examine transients, related to the dramatic change of parameters on his entrance. Examine batch hydrodynamic processes, conditioned by the pulsation of pressure of working liquid on an exit from a pump;
– possibly, that the type of distribution of speed of working liquid on the cut of channels of new hydraulic oscillation contour is formed;
– consider that in hydraulic sistem, and thus and in a new hydraulic oscillation contour, absents resonance, kavitacion of working liquid and water-hammer;
– speed of sound of working liquid is a size permanent, considerably anymore from her speed in hydraulic system;
– a temperature of working liquid is permanent and is in a range 50-55?С. Permanent also there is газовміст of working liquid, which is taken into account at the calculation of the module of by volume resiliency of working liquid, which take permanent and expect taking into account resilient properties of pipeline;
– equalization of unbreak of working liquid is executed on all areas of hydraulic sistem;
– ignore mass forces of working liquid. Will notice that analogical supposition is taken by most researchers [14, 15];
– consider a working liquid newtonian, and flow isothermal;
– the flow of working liquid is unidimensional axisymmetrical.
Taking into account the accepted suppositions, motion of working liquid in hydraulic sistem can be described by means of wave equalization as a system of two differential equalizations of first-order, which taking into account hydraulic resistance of pipeline can write down as [8]
 ,(1)
where ; λ - is a coefficient of hydraulic resistance; dт – is a diameter of pipeline; ρ - it is a closeness of working liquid; V - - is speed of working liquid; а -is speed of sound in a works liquid; р -is pressure ; х -is distance from the beginning of pipeline to the cut, where pressure (speed) of working liquid is determined
As an expense absents through a new hydraulic oscillation contour, it is possible a member which takes into account the losses of pressure in equalization (1) to scorn. A ground over of this supposition is brought in [9,10].
A decision (1) will conduct the method of frequency analysis, namely by the method of standing waves, offered Lytcem for the calculation of wave processes. In accordance with this method, a decision (1) can be writtenin in a hyperbolical form [8]
 ,(2)
where - became distribution of wave process; φ - it is a wave-number; l - - it is length of area of pipeline (to the channel);  - - it is an area of transversal cut of pipeline;  - it is circular frequency of vibrations.
Setting maximum terms as an impedor (to the impedance) of Zг and value of amplitude of speed and pressure in one cut of pipeline for help (2), it is possible to find the value of their amplitudes in any other cut. It is thus necessary also to set maximum terms which are determined by character of loading on the end of pipeline. Namely a presence of expense in гідросистемі is throttles, snuffled, attachments et al. Absence of expense is permanent or variable volumes on the end of the muffled pipeline.
For the linear area of pipeline at the set impedor of loading of Zн and the brought impedance over of Z0. Upshots (1) can be writtenin as [1,2] .
 ,(3)
where for hydraulic system in which absent expense of work liquids:
 ,(4)
 ,(5)
Taking into account (4) and (5) equalization (3) will purchase a kind:
 ,(6)
Will mark, that (3) allows to define amplitudes of pressures and speed in any point of hydraulic system and for any types of loading.
For harmonic vibrations at  , and  ,decision (1) can be also written down in a kind (3) [8], where Z0 in default of internal friction it is determined from expression
 ,
At consideration of hydrodynamic processes which take place in a new hydraulic oscillation contour, the waves of pressure spread in his channels with eventual speed, what considerably less to speed of sound. Therefore the change of parametres in any part of new hydraulic oscillation contour at times does not have time to influence on the change of parametres of other parts. Such supposition, going out the physical model of processes which take place in a new hydraulic oscillation contour, answers reality.
As all elements of new hydraulic oscillation contour show by itself the short union coupling, consider that they are all linear, and maximum terms are permanent (on included harmonic influences were set in a new hydraulic oscillation contour). At mathematical description of hydrodynamic processes in short pipelines such supposition is accepted by most researchers and it is confirmed by numerous experimental researches, for example [22]. Then the flow diagramme of new hydraulic oscillation contour can be given in a kind.
Picture 3 - Flow diagramme of new hydraulic oscillation contour: 1 - is an entrance pipeline; 2 - is the entrance narrowed union coupling; 3 - is a chamber of new hydraulic oscillation contour; 4 - is a chamber of hydrodistributor.
For the calculation of size of pressure in any structural element of new hydraulic oscillation contour will enter a transmitivity under which will understand the relation of pressure on the entrance of channel (union coupling) to his value on an output:
 ,(7)
Thus, (7) allows to define, on how many the size of pressure will increase (will diminish) on the output of pipeline in comparing to his entrance. Thus the value of transmitivity of structural element can find from the first equalization (6).
 ,(8)
where
 ,
Equalization (7) can be used for the calculation of transmitivity of pulsations of pressure, then instead of pressure of entrance and output for him it is necessary to put amplitudes of pulsations. If the known transmitivities of separate structural elements of new hydraulic oscillation contour pulsations of pressure on his entrance, can find a transmitivity for him
НГВК=kп1kп2kп3kп4(9)
From equalization (8) and (9) will find kНГВК, which after presentation of hyperbolical functions [12], for a new hydraulic oscillation contour, can write down in a kind.
 ,(10)
где
 ,
As in the new hydraulic oscillation contour ?осц it is determined by description of source of feed (by a pump) and in general case is a size permanent, equalization (10) allows, changing length of the union coupling and size of area of him communicating cut, to execute the rational choice of transmitivity of new hydraulic oscillation contour. Will mark, that in general case his size must be more than 1.[13]
If it is known kНГВК in supposition, the change of pressure on an exit from a pump takes place by law by a sinewave, can find the pulsations of pressure in the initial chamber of new hydraulic oscillation contour:
 ,(11)
where and  - according to the pulsation of pressure in the chamber of new hydraulic oscillation contour and amplitude of pulsations of pressure on an entrance at a new hydraulic oscillation contour.
Equalization (11) is the mathematical model of new hydraulic oscillation contour. It allows to define force, which operates on the slide-valve of hydrodistributor, and parametres of his oscillation. Thus the choice of d3 and l3, coming from that after physical essence the entrance narrowed union coupling and chamber 3 new hydraulic oscillation contour is the resonator of Helmholtz, it must do, using dependence [8]:
 ,(12)
where V3- is a volume of chamber 3 new hydraulic oscillation contour.
Analysis of dependences (10) and (12) allowed to set that with the increase of length of chamber 3 the transmitivity of new hydraulic oscillation contour increases. Thus, length of chamber 3 it follows to choose as possible anymore taking into account overall limitations of new hydraulic oscillation contour[11].
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CONCLUSIONS
It is set that for the construction of mathematical model of new hydraulic oscillation contour it is expedient to use the method of spectrology.
With the use of this method the mathematical model of new hydraulic oscillation contour is got.
The conducted analytical researches allowed to set that most influence on a transmitivity the diameters of chamber of resonator have a from відглажуванням and the constricted union coupling. For the receipt of desirable transmitivities of new hydraulic oscillation contour length of chamber of resonator from ironed it follows to choose as possible anymore.
 ,(a) ,(b)
 ,(c) ,(d)
 ,(e)
Picture 4 - Chang of sumarnoy inflexibility of spring of hydrodistributor with a hydraulic oscillation contour depending on moving of him plug-forming – regulative element: a – at izminenii amplitudes of oscilyaciy; a, b, c, d – for different types plug-forming – regulative element: 1 - sharp drosseliruyuschaya edge, 2 - conical drosseliruyuschaya edge, 3 - drosseliruyuschaya edge with triugol'nym incarceration, 4 - drosseliruyuschaya edge with incarceration as a segment of circle, 5 - drosseliruyuschaya edge sharp with a half-round ditch.
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