1、 1 中文 4550字 HYDRODYNAMIC DAMPING OF THE TORSIONAL VIBRATIONS OF THE SYSTEM SHAFT-SHIPS PROPELLER For ships power plants with an internal combustion engine, whose important component is the propeller and shaft, a very topical question is the refinement of existing methods and the devising of new meth
2、ods of calculating torsional resonance vibrations. This will make it possible to accurately determine the state of dynamic stress of the installation, and consequently also to determine the possibility of fatigue failure of its most heavily loaded elements. At present, calculations of the torsional
3、vibrations of ships propeller shafts, amounting to obtaining the amplitude response of the system, are carried out by taking into account the damping which, as a rule, is due to friction in the internal combustion engine, in elastic couplings, and the friction of the propeller against the water 1. I
4、nvestigations in recent years showed that the damping of torsional vibrations in consequence of energy dissipation in the material of the propeller shafts is slight, and it is therefore usually neglected.Therefore, the prevalent role in the damping of the torsional vibrations of ships power plants b
5、elongs to structural and hydrodynamic damping, whose studyand refinement is at present the object of researchers ,endeavors. Damping of the propeller in the ships power plant is the most important form of damping outside the engine in all forms of vibrations, except the so-called motor vibrations at
6、 which the amplitudes of the free vibrations in the shaft section are small. However, it is very difficult to obtain a formula for calculating the damping effect of the propeller, because it depends on an entire complex of factors such as the geometry of the propeller, the number of blades, the vibr
7、ation frequency, etc. That is also the reason why the corresponding formulas determining the damping of the propeller were obtained experimentally on simulating installations, and they are not very accurate. Moreover, the formulas suggested by different authors yield different results when used in t
8、he same calculations. The methods used at present in the investigation and calculation of torsional vibrations 2 of ships propeller shafts are based, as a rule, on the approximate method worked out by Terskikh 2； this method entails the replacement of the real friction in the system by two nominal c
9、omponents, one of which has the properties of linear friction, and consequently, has a quadratic dependence of work on amplitude, and the other has the properties of dry friction with linear dependence of work on amplitude. In practice, friction in the elements of a ships propeller shaft is not line
10、ar； however, the nonlinear problem of the damping properties of different components of the ships power plant, especially of the propeller, led to difficulties in the solution of nonlinear differential equations, and in view of this, various approximate methods are used in practice, but they are not
11、 very accurate. Therefore, one of the ways of improving the accuracy of the calculations of torsional resonance vibrations is to continue the theoretical and experimental investigations, whose object would be to determine more accurately the elements of the propeller shaft and to solve the nonlinear
12、 problem of torsional resonance vibrations. The question of taking into account the energy dissipation due to hysteresis losses in the material in the calculation of mechanical vibrations has received sufficient attention； this included the elaboration of physically substantiated methods of calculat
13、ing the vibrations of systems, which was done very successfully by the use of asymptotic methods of nonlinear mechanics 3. Up to the present, however, there do not exist any reliable methods of calculating vibrations for other kinds of energy losses (structural and aerodynamic damping). Pisarenko 4
14、suggested a new approach which makes it possible to solve the problem of taking into account not only the hysteretic energy dissipation In the material, but also stnlctural as well as aerodynamic kinds of damping, on the basis of a single method whose essence is that all kinds of energy losses in th
15、e vibrating system, regardless of their origin, are represented in the form of some hysteresis loops, separately for each kind of loss, and the areas of the hysteresis loops then characterize the respective part of the energy out of the peak value of potential energy of a unit volume of cylically de
16、formed material of an elastic element of the vibrating system (spring) with the given amplitude of deformation (stress), Here we have to proceed from the following nonlinear correlations between stress and 3 relative deformation in any single cyclically deformed element (spring) with peak value of d
17、eformation afor the ascending and descending motion leading in a cycle to the formation of the hysteresis loop 5: 2nn3= E 28 (1) where E is the modulus of elasticity of the material； is the logarithmic decrement of the vibrations. Arrows pointing to the right refer to the ascending branch of the hys
18、teresis loop； arrows pointing to the left refer to the descending branch. By introducing into (1) the decrement as a function of the factor on which it depends, we can generalize the approach used in taking hysteresis losses in the material into account to the case of taking other energy losses into
19、 account, losses that are due to any arbitrary causes, because in all cases energy is dissipated which was integrally accumulated in the vibrating system and which consists of the sum of the energies of unit volumes of the cyclically deformed material of an elastic element of the system (spring), an
20、d the latter is a function of the amplitude of deformation (stress). llais approach therefore makes it possible to use a single method. By integrating with respect to the volume of the cyclically deformed material, we can take into account any energy losses, summing them as hysteresis loops having t
21、he same shape whose magnitude depends on the level of the vibration decrements contained in the equation of the loop and obtained experimentally as a function of some factor. The above-mentioned hysteresis loops characterizing the energy losses in a unit volume of cyclically deformed mate； rial with
22、 deformation amplitude a may, generalized and schematically, be represented in the form 2nn3= E 28 M K a d (2) where M is the vibration decrement characterizing the energy dissipation in the cyclically deformed material itself, which, as was shown above, depends on the deformation amplitude； K is the vibrational decrement characterizing energy losses in fixed joints (structural damping), which, as a rule, depends on the magnitude of the reactive moment acting in the
