Influence of Dry Friction on the Dynamics of Cantilevered Pipes Conveying Fluid

A cantilevered pipe conveying fluid can lose stability via flutter when the flow velocity becomes sufficiently high. In this paper, a dry friction restraint is introduced for the first time, to evaluate the possibility of improving the stability of cantilevered pipes conveying fluid. First, a dynamical model of the cantilevered pipe system with dry friction is established based on the generalized Hamilton’s principle. Then the Galerkin method is utilized to discretize the model of the pipe and to obtain the nonlinear dynamic responses of the pipe. Finally, by changing the values of the friction force and the installation position of the dry friction restraint, the effect of dry friction parameters on the flutter instability of the pipe is evaluated. The results show that the critical flow velocity of the pipe increases with the increment of the friction force. Installing a dry friction restraint near the middle of the pipe can significantly improve the stability of the pipe system. The vibration of the pipe can also be suppressed to some extent by setting reasonable dry friction parameters.

Selection of Nanostructured Zirconium Dioxide Crystals under Dry Friction against Molybdenum

The article considers the issues of contact interaction of nanostructured zirconium dioxide crystals with molybdenum coating on titanium-based alloy ВТ9. The following statement is substantiated: the best mechanical properties of crystals correspond to the total amount of 2.8% additives of stabilizing and doping rare earths elements. Antifriction properties of crystals under dry friction against molybdenum are investigated. Tribological testing was performed on a reciprocating friction gauge simulating the operation of a plunger in a cylinder. The high scoring resistance of the friction couple under study was experimentally proved; the friction coefficient did not exceed 0.07. On the basis of the study performed, the friction couple is defined as promising for increasing the lifetime and reliability of friction units for hydraulic equipment and fuel pumps.

Tribological Properties of Sapphire under Dry Friction against Chromium and Zirconium Ceramics

The issues of sapphire friction and wear in contact with chrome steel and zirconium ceramics are discussed in this article. The kinetic microindentation method is used to study the mechanical properties of sapphire in frictional contact in modelling experiments on the indentation of a Vickers indent. Taking into account the anisotropy of the mechanical properties of sapphire, the influence of the load and orientation of the indent on the modulus of elasticity and hardness is analyzed. It has been established that, under dry friction conditions it is promising the use of zirconium ceramics in the supports of devices operating under conditions in which the use of lubricants is impossible. The possibility of using a friction couple of sapphire-zirconium ceramics in friction units operating in open space is noted.

Non-stationary oscillations of an instantly loaded oscillator under conditions of nonlinear resistance

The motion of an oscillator instantaneously loaded with a constant force under conditions of nonlinear external resistance, the components of which are quadratic viscous resistance, dry and positional friction, are considered. Using the first integral of the equation of motion and the Lambert function, compact formulas for calculating the ranges of oscillations are derived. In order to simplify the search for the values of the Lambert function, asymptotic formulas are given that, with an error of less than one percent, express this special function in terms of elementary functions. It is shown that as a result of the action of the resistance force, including dry friction, the oscillation process has a finite number of cycles and is limited in time, since the oscillator enters the stagnation region, which is located in the vicinity of the static deviation of the oscillator caused by the applied external force. The system dynamic factor is less than two. Examples of calculations that illustrate the possibilities of the stated theory are considered. In addition to analytical research, numerical computer integration of the differential equation of motion was carried out. The complete convergence of the results obtained using the derived formulas and numerical integration is established, which confirms that using analytical solutions it is possible to determine the extreme displacements of the oscillator without numerical integration of the nonlinear differential equation. To simplify the calculations, the literature is also recommended, where tables of the Lambert function are printed, allowing you to find its value for interpolating tabular data. Under conditions of nonlinear external resistance, the components of which are quadratic viscous resistance, dry and positional friction, the process of oscillations of an instantly loaded oscillator has a limited number of cycles. The dependences obtained in this work using the Lambert function make it possible to determine the range of oscillations without numerical integration of the nonlinear differential equation of motion both for an oscillator with quadratic viscous resistance and dry friction, and for an oscillator with quadratic resistance and positional and dry friction. Keywords: nonlinear oscillator, instantaneous loading, quadratic viscous resistance, Lambert function, oscillation amplitude.

Gas film lubrication method on rotation shaft seal based on contact design

Purpose Wear failure happens frequently in rubber seal of high-speed rotating shaft because of the dry friction. Some traditional lubrication methods are not effective because of the restrictions on the relative high speed, temperature and others. This paper aims to present a new method of lubrication with gas film for the rotation shaft seal based on the contact design. Design/methodology/approach To obtain the generation condition of gas film and good effect of lubrication in the contact gap between the shaft and its seal, a series of micro-spiral grooves are designed on the contact surface of rubber seal so as to obtain a continuous dynamic pressure difference. Findings The result is that the distribution of the gas film in the micro-gap is continuous under the design of the spiral grooves and the contact with eccentricity because of the deformation of rubber seal, which is verified through the simulation calculation and experiment test. It is confirmed that the lubrication method with gas film through designing micro-spiral grooves on the contact surface is effective, and can achieve self-adaptive air lubrication for the high-speed shaft under the premise of the reliable sealing. Originality/value The method of gas film lubrication is realized through designing a microstructure of spiral grooves on the rubber surface to change the contact status, which can form a mechanism of adaptive lubrication to reduce the dry friction automatically in the contact gap. For the cross-scale difference between the rubber seal and gas film, a new modeling method is presented by building the mapping relation for the split blocks and repairing technique with integrated computer engineering and manufacturing, to reduce the possibility of nonconvergence and improve the efficiency and accuracy of calculation.

Tribotechnical Properties of Sintered Antifriction Aluminum-Based Composite under Dry Friction against Steel

The disadvantage of antifriction Al–Sn alloys with high tin content is their low bearing capacity. To improve this property, the aluminum matrix of the alloys was alloyed with zinc. The powder of Al–10Zn alloy was blended with the powder of pure tin in the proportion of 40/60 (wt.%). The resulting mixture of the powders was compacted in briquettes and sintered in a vacuum furnace. The sintered briquettes were subjected to subsequent pressing in the closed press mold at an elevated temperature. After this processing, the yield strength of the sintered (Al–10Zn)–40Sn composite was 1.6 times higher than that of the two-phase Al–40Sn one. The tribological tests of the composites were carried out according to the pin-on-disk scheme without lubrication at pressures of 1–5 MPa. It was established that the (Al–10Zn)–40Sn composite has higher wear resistance compared with the Al–40Sn one. However, this advantage becomes insignificant with an increase in the pressure. It was found that the main wear mechanism of the investigated composites under the dry friction process is a delamination of their highly deformed matrix grains.

Mathematical models of the gyrostabilizer in different modes of its operation

The article considers the development of a mathematical model of the stabilization and rotation system in the modes of stabilization, targeting, auto-tracking of the target and electrical arrest. The output signals shall be signals proportional to the components of the angular velocities of the line of sight, the angles of pitch and dash of deviation around the axes of the gyrosystem and the angles of inconsistency of the line of sight relative to the optical axis of the homing head. The system of cardan suspension of the stabilization and rotation system is considered, where the actuators are located on the axes of rotation of the outer and inner frames of the cardan suspension. The homing head is mounted on the inner frame. The inner frame is a gyrostabilized platform. Depending on the mode of operation of the stabilization and rotation system: in the stabilization mode, the coordinate system that is stabilized is assumed to be stationary in inertial space; in the auto-tracking mode of the target, the coordinate system that is stabilized by Oxyz is returned according to the change of direction to the target; in the mode of electrical locking, the axes of the coordinate system which is stabilized by Oxyz coincide with the axes of Oxoyozo connected to the body of the main product. To obtain differential equations, the projections of the total vector of the kinetic moment of the inner and outer frames on the axis of the outer frame are taken and written according to the theorem on the change of the kinetic moment of the considered system relative to the axes of suspensions. The total moments of external forces applied to the outer and inner frames around their axes of rotation, which have the following components: moments of actuators, moments of viscous and dry friction, imbalance and other unaccounted for factors around the axes of the outer and inner frames . The moments of the forces of viscous and dry friction are presented in the classical form, taking into account the signs when changing the direction of movement. The mass of the inner frame with all devices mounted on it, and the mass of the entire movable system (outer and inner frames), as well as the radius vector characterizing the displacement of the center of mass, give a static imbalance of the movable system relative to the suspension axis of the i-th frame are components imbalance. The scientific novelty of the work is to obtain a mathematical model for a particular product, as well as the practical feasibility of their application. The result is a differential equation that fully describes this system of stabilization and rotation, takes into account the parameters of actuators, turbulent moments, as well as random effects and can be used depending on the tasks.