Estimation of the tangential transverse vibrations effect on the friction force with the use of LuGre model

In this work, a novel dynamic computational model developed for the purpose of modelling the phenomenon of friction force reduction in a sliding motion at tangential transverse vibrations of elastic support is presented. In contrast to the currently used so-called kinematic models, this model takes into account the mass of a sliding and simultaneously subjected to vibrations body. It is based on the dynamic equations of motion of this body. For the description of the friction force, the LuGre model was used which considers both the compliance of the contact zone and its damping. Considered in this model are also compliance and damping of the drive. The model assumes that vibrations are not imposed directly on the shifting body but are transferred to it from the vibrating elastic support. The developed model has been implemented in the Matlab/Simulink environment and subsequently utilised in simulating analyses. The results of these were compared with the results of experiments which were carried out using a designated, in-house built, experimental rig. An excellent compliance has been achieved.

NONLINEAR TRANSVERSE VIBRATIONS OF COMPOSITE RODS UNDER THE ACTION OF A STATICALLY APPLIED TRANSVERSE LOAD

Nonlinear transverse vibrations of composite rods pre-loaded with lagging arranged symmetrically on both sides of the axis of the composite rod under the action of a statically applied transverse load are investigat-ed. The cases of attaching the lagging only to the ends of the composite rod, as well as when the laggings are continuously attached to the composite rod along its entire length, are considered. The results of the study of nonlinear transverse vibrations of composite rods under the action of a statically applied transverse load are presented. When conducting studies of transverse vibrations of composite rods, solutions of differential equations of vibration of prestressed through beams and stiffening cores of high-rise buildings are obtained. The obtained differential equations of vibration of composite rods allow us to determine the dynamic char-acteristics of prestressed through beams under various linear and boundary conditions. A method for com-posing differential equations of free and forced oscillations of prestressed through beams and stiffening cores of high-rise buildings and solving differential equations under various linear and nonlinear boundary conditions is developed. Expressions are given for determining the longitudinal forces and torques at the ends of the rod at any lo-cation of the lagging from the axis and at any different stiffness of the lagging

Analysis of influence of elastic properties of deadwood bearings on shaft line operability

The paper considers the ship shafting and its design. Depending on the constructive features, operating conditions, effects of continuous, dynamic, variable and random loads the operation of the shaft line is accompanied by wear of the shafting structure and auxiliary parts. The formulas for calculating the maximum permissible clearances during operation in stern bearings of propeller shafts are given, according to the norms and technical and operational requirements. A graph of the maximum permissible clearances in metal stern bearings is presented. There has been carried out a dynamic design of the shaft line in order to define the influence of rigid characteristics of the stern bearings on eigen frequency of transverse vibrations. It is noted that the service life of the shaft line depends on the material of bushings or liners of the bearings (bakout, babbit, textolite, caprolon, bronze, polyurethanes, rubber) and their wear degree. The design scheme of the ship shaft line on elastic supports with a coefficient of rigidity is presented. To assess the influence of the elastic properties of deadwood bearings, the method of initial parameters was used. According to the researchers’ opinion, the greater the wear, the lower their stiffness coefficient. At a certain wear degree of deadwood bearings, there occurs resonance at the lowest operating frequencies. It has been proved that the greater the deflection at the attachment point of the propeller, the lower the eigen frequency of transverse vibrations of the shaft line. It has been pointed out that the calculations should include the separation of the shaft line from the deadwood bearing, since it contributes to a decrease in eigen frequency and causes a resonance during transverse vibrations.