Evaluation of influence of elastic properties of slide bearing of ship stern gear on stiffness coefficient

The article considers the ship shaft line as a complex dynamic system influencing the operation of the ship. There has been given a diagram of the shaft line with one stern bearing and one remote bearing of the propeller shaft. The shaft line service life depends on the material of the slide bearing of the stern gear (lignum vitae, babbitt, textolite, caprolon, bronze, polyurethanes, rubber). The analysis of the research of static and dynamic calculations of ship shafting has been carried out. The design scheme of the ship shafting on elastic point supports is presented. It has been referred to consider feasibility of the elastic and mechanical properties of stern bearings at the stage of designing a ship shaft line. The method of calculating the transverse vibrations of the shaft line is studied, the purpose of which is to determine the natural frequency. The formula for calculating the lowest natural frequency of bending vibrations is given. The results of experimental studies at the KMV-200 stand based on uneven distribution of loads along the stern bearings are considered. It has been suggested that the greater the wear, the lower the stiffness coefficient. At a certain degree of wear of stern bearings, a resonance phenomenon occurs at the lowest operating frequencies. The value of the stiffness coefficient is studied depending on the modulus of elasticity of the stern bearing material. Static analysis of the ship shaft line was made taking into account the stiffness coefficient of the stern bearing. The universal equation of the curved axis of the beam is used according to the initial parameters method. As it has been found, the greater the deflection at the propeller attachment point, the lower the natural frequency of the transverse vibrations of the shaft line. In calculations it is necessary to take into account the separation of the shaft line from the stern bearing, since it helps to reduce the natural frequency and the appearing resonance during transverse vibrations.

Operating Parameters of a Slide Bearing with Parabolic-Shaped Slide Surfaces with Consideration of the Stochastic Changes in the Lubrication Gap Height

In this article, the authors present the equations of the hydrodynamic theory for a slide bearing with parabolic-shaped slide surfaces. The lubricating oil is characterized by non-Newtonian properties, i.e. an oil for which, apart from the classic oil viscosity dependence on pressure and temperature, also an effect of the shear rate is taken into account. The first order constitutive equation was adopted for considerations, where the apparent viscosity was described by the Cross equation. The analytical solution uses stochastic equations of the momentum conservation law, the stream continuity and the energy conservation law. The solution takes into account the expected values of the hydrodynamic pressure EX[p(ϕ,ζ)], of the temperature EX[T(ϕ,y,ζ)], of the velocity value of lubricating oil EX[vi(ϕ,y,ζ)], of the viscosity of lubricating oil EX[ηT(ϕ,y,ζ)] and of the lubrication gap height EX[εT(ϕ,ζ)]. It was assumed, that the oil is incompressible and the changes in its density and thermal conductivity were omitted. A flow of lubricating oil was laminar and non-isothermal. The research concerned the parabolic slide bearing of finite length, with a smooth sleeve surface, with a full wrap angle. The aim of this work is to derive the stochastic equations, that allow to determine the temperature distribution, hydrodynamic pressure distribution, velocity vector components, load carrying capacity, friction force and friction coefficient, in the parabolic sliding bearing, lubricated with non-Newton (Cross) oil, including the stochastic changes in the lubrication gap height. The paper presents the results of analytical and numerical calculation of flow and operating parameters in parabolic sliding bearings, taking into account the stochastic height of the lubrication gap. Numerical calculations were performed using the method of successive approximations and finite differences, with own calculation procedures and the Mathcad 15 software.

Simulations of the Influence of the Heat Flux at the Shaft Surface of the Conical Slide Bearing on Its Hydrodynamic Lubrication and Operating Parameters

The aim of this work is to investigate, how in the adopted model of hydrodynamic lubrication of a conical slide bearing, the change of the heat flux value at the bearing shaft, affects bearing operating parameters. In this research, the authors use, the known from the literature, Reynolds type equation, describing the stationary hydrodynamic lubrication process of a conical slide bearing. The analytical, solutions, that determine the components of the lubricating oil velocity vector and the equation (analytical solution of energy equation) determining the three-dimensional temperature distribution in the lubrication gap, was also adopted from previous works. In order to obtain numerical solutions, the Newton’s method was used, and the derivatives in the Reynolds type equation were approximated by the finite differences. An application of the method of subsequent approximations allowed considering the influence of temperature, pressure and shearing rate on the viscosity of lubricating oil. The considerations were performed by adopting the Reynolds condition of the hydrodynamic oil film. It was tested, how the assumed value of the heat flux on the bearing shaft surface affects the values of the obtained operating parameters, i.e. the transverse and longitudinal component of the load carrying capacity, friction force and coefficient of friction.

Calculation of lubricant flow in the slide bearing of the aviation engine reducer

A method has been developed for calculating the pressure distribution in a cylindrical slide bearing. We present the process of designing a heavy-duty slide bearing as a component of the reduction gearbox of a bypass turbojet engine as the object of our investigation. The process comprises the following stages: specification of the supporting structure; calculation of pressure distribution in the slide bearing for different eccentricities and angles of rotation of the shaft journal; calculation of the effect of shaft journal precession on pressure distribution; calculation of pressure distribution taking into account the channels of oil supply to the bearing. The results obtained in the experimental activities are given. The analysis carried out shows that the calculation helps to predict the location and size of pressure and rarefaction areas, to position the holes for oil supply, which will significantly improve the conditions of lubricant flow in the bearing.

INFLUENCE OF INCONSTANT DISTRIBUTION OF DEADWOOD BEARING STIFFNESS COEFFICIENTON NATURAL FREQUENCY OF THE SHAFT TRANSVERSE VIBRATIONS

One of the most significant factors affecting the natural frequency of transverse vibrations of shaft-slide bearing systems is the stiffness coefficient of the slide bearing. The need to consider the influence of heterogeneity of stiffness coefficient of the bearing on its natural frequency is caused by the fact that when the bearing is worn, the modulus of longitudinal elasticity of the material changes, and since the bearing wears unevenly, the non-uniform distribution of the stiffness coefficient occurs. The problem of determining the natural frequency of transverse vibrations of a ship propeller shaft based on the foundation with a variable stiffness coefficient along the length has been studied. The differential equation of the propeller shaft vibrations written taking into account the stiffness coefficient variable along the shaft length is considered. It has been noted that, in the general case, this equation is a fourth-order partial differential equation and cannot be integrated in quadratures for an arbitrary stiffness distribution function along the shaft length. A numerical-analytical method for determining the natural frequency of a system based on approximation of the stiffness distribution function by a piecewise-linear function is proposed. The method is applied to calculate the natural frequencies of the pipeline section taking into account the functions describing the change in the stiffness coefficient. The proposed method allows to consider the section of the shafting enclosed in the stern bearing, subject to the non-uniform distribution of the stiffness coefficient of the bearing, and is the basis for improving the accuracy of finding the true natural frequency of transverse vibrations of the shafting.

Marine Propulsion System Vibration Sensor Heads

Vibration symptoms are the main symptoms used for diagnosing machines. This applies mainly to vibrations of non-rotating machines. Symptoms of rotating element vibrations are used in a limited scope, while mostly used are the symptoms of radial vibrations of rotating shafts. Across industries, the use of technical vibration diagnosis varies. Marine propulsion systems are poorly equipped with diagnostic equipment of that type. One of the main reasons is lack of appropriate sensors. The study presents two solutions of sensor heads. One solution applies to a sensor head built into the free end of the crankshaft of a reciprocating machine. The shaft free end sensor allows measurement of torsional and longitudinal vibration accelerations of the free end as a function of shaft rotation. The other solution refers to a sensor head built into sealed slide bearing of a straight shaft. The slide bearing head enables measurement of the eccentricity to the journal relative to the shell. Sensor heads under consideration are particularly suitable to be built in the ship’s propulsion system and integrated with the ship’s maintenance system. Sensors of the ship’s maintenance system equipped with these heads will allow the operator to draw conclusions concerning the wear margins of the propulsion engine and that of the tail shaft.