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In this study, the dynamic characteristics of the water-lubricated rubber bearing considering asperity contact are numerically studied, including water-film stiffness and damping coefficients and plastic-elastic contact stiffness coefficient.

The Kogut-Etsion elastic-plastic contact model is applied to calculate the contact stiffness coefficient at the bearing-bush interface and the perturbed method is used to calculate the stiffness and damping coefficients of water-film. In addition, the rubber deformation is determined by the finite element method (FEM) during the simulation. Parametric studies are conducted to assess the effects of the radial clearance, rubber thickness and elastic modulus on the dynamic characteristic of water-lubricated rubber bearing.

Numerical results indicate that stiffness and damping coefficients of water film and the contact stiffness of asperity are increased with the decreasing of the radial clearance and the dynamic coefficients are less sensitive to the rubber thickness compared with the elastic modulus of rubber. Furthermore, due to the existed groove, a sudden change of the water film direct stiffness and damping coefficients is observed when the eccentricity ratio ranges from 0.6 to 1.0.

It is expected this study can provide more information to establish a dynamic equation of water-lubricated rubber bearings exposed to mixed lubrication conditions.

To meet the high stiffness requirement of bearings used in high-precision spindles, this paper aims to propose a novel kind of bearing composited by hydrostatic cavities and tilting pads with preload.

Cavities are cut on the oil seal surface of a hybrid bearing, in which the tilting pads are set up. The load of the bearing is carried by the hydrostatic cavities and tilting pads. The structural features of this compound bearing and the controlling variables of the main stiffness coefficient are presented. Two basic design principles are proposed on the basis of equal machining clearance (EMC) and equal installation clearance (EIC).

The theoretical analysis indicates that the stiffness of compound bearings under the EMC condition increases to infinity monotonously when the preload coefficient of the tilting pad tends to 1, while the stiffness under the EIC condition has a peak value. Therefore, a synthetic design principle is proposed by synthetically using the above-mentioned two principles. The applicable range of the three principles is discussed through an example.

The study about technological combination of hydrostatic cavity and tilting pad in this paper can provide suggestions for the design of a high-stiffness bearing in a precision spindle.

The purpose of this paper is to enhance film stiffness and control seal leakage of conventional spiral groove dry gas seal (S-DGS) at a high-speed condition by introducing a new type superellipse surface groove.

The steady-state performance and dynamic characteristics of superellipse groove dry gas seal and S-DGS are compared numerically at a high-speed condition. The optimized superellipse grooves for maximum steady-state film stiffness and dynamic stiffness coefficient are obtained.

Properly designed superellipse groove dry gas seal provides remarkable larger steady-state film stiffness, dynamic stiffness coefficient and lower leakage rate at a high-speed condition compared to a typical S-DGS. The optimal values of first superellipse coefficient for maximum steady and dynamic stiffness are 1.3 and 1.4, whereas the optimal values of second superellipse coefficient for which are 1.4 and 2.0, respectively.

A new type of molded line, namely, superellipse curve, is proposed to act as the boundary lines of surface groove of dry gas seal, as an alternative of typical logarithm helix. The conclusions provide references for surface groove design with larger stiffness and lower leakage rate at a high-speed condition.

The purposes of the present study are to ensure higher sustainability of journal bearings under different applied loads and to observe bearing performances such as elastic strain, total deformation and stress formation.

A journal bearing test rig was used to determine the effect of the applied load on the bearing friction, film thickness, lubricant film pressure, etc. A steady-state analysis was performed to obtain the bearing performance.

An efficient aspect ratio (L/D) range was obtained to increase the durability or the stability of the bearing while the bearing is in the working condition by using SAE 5W-30 oil. The results from the study were compared with previous studies in which different types of oil and water, such as Newtonian fluid (NF), magnetorheological fluid (MRF) and nonmagnetorheological fluid (NMRF), were used as the lubricant. To ensure a preferable aspect ratio range (0.25-0.50), a computational fluid dynamics (CFD) analysis was conducted by ANSYS; the results show a lower elastic strain and deformation within the preferable aspect ratio (0.25-0.50) rather than a higher aspect ratio using the SAE 5W-30 oil.

It is expected that the findings of this study will contribute to the improvement of the bearing design and the bearing lubricating system.

The purpose of this paper is to introduce a method for stiffness modeling, identification and updating of collaborative robots (cobots). This method operates in real-time and with high precision and can eliminate the modeling error between the actual stiffness model and the theoretical stiffness model.

To simultaneously ensure the computational efficiency and modeling accuracy of the stiffness model, this method introduces the finite element substructure method (FESM) into the virtual joint method (VJM). The stiffness model of the cobots is built by integrating several 6-degree of freedom virtual joints that represent the elastic deformation of the cobot modules, and the stiffness matrices of these modules can be identified and obtained by the FESM. A model-updating method is proposed to identify stiffness influence coefficients, which can eliminate the modeling error between the actual prototype model and the theoretical finite element model.

The average relative error and the cycle time of the proposed method are approximately 6.14% and 1.31 ms, respectively. Compared with other stiffness modeling methods, this method not only has high modeling accuracy in high dexterity poses but also in low dexterity poses.

A hybrid stiffness modeling method is introduced to integrate the modeling accuracy of the FESM into the VJM. Stiffness influence coefficients are proposed to eliminate the modeling error between the theoretical and actual stiffness models.

The prediction model to estimate the stability of a rotor-bearing system is established, which can predict the stability of gas bearings by applying Routh–Hurwitz stability criterion. This paper aims to provide the theoretical foundation for controlling actively the bearing running stiffness and damping and stemming the instability of a gas film.

The nonlinear dynamic lubrication analysis mathematical model of spherical hybrid gas bearings is established. Perturbation control equation is derived by the partial derivative method. The finite difference method is used to discrete the perturbation control equation in generalized coordinate system, and the difference expression of perturbation pressure is derived. The relational expression which involves the relationship between the dynamic characteristic coefficients of HSGHGB systems and perturbation pressure is deduced. So, the transient perturbation pressure distribution of a three-dimensional micro gas film, nonlinear gas film force, dynamic stiffness and dynamic damping coefficients of bearings are numerically computed using VC++6.0 programs.

The results show that the influence of supply pressure, speed and eccentricity on the dynamic characteristics of bearings is significant.

The influence law of supply pressure, speed and eccentricity ratio on the dynamic stiffness and damping coefficients of HSGHGB systems is researched. The prediction model to estimate the stability of rotor-bearing system is established, which can predict the stability of gas bearings by applying the Routh–Hurwitz stability criterion.

This study aims to understand how the texture shape, number of textures and addition of nanoparticle additives in lubricants impact the dynamic characteristics of journal bearing by comparing six different texture shapes like triangle, chevron, arc, circle, rectangle and elliptical applied in pressure-increasing region under various geometrical and operating conditions.

The finite element method approach has been employed to solve governing Reynold’s equation, assuming iso-viscous Newtonian fluid, for computation of performance parameters like stiffness and damping coefficient, threshold speed, etc. By using a regression model, the impact of adding nanoparticles Al₂O₃ and CuO to the base lubricant on viscosity variation is calculated for selected temperature ranges and weight fractions of nanoparticles.

The arc-shaped texture with an area density of 28.27%, eccentricity ratio of 0.2 and texture depth of 0.6 exhibited 35.22% higher direct stiffness and 41.4% higher damping coefficient compared to the lowest value in the circle-shaped texture. Increasing the number of arc-shaped textures on the bearing surface with low area density led to declining stiffness and damping parameters. However, with nanoparticle additives, the arc-shaped texture further showed 10.75% and 8.11% improvement in stiffness and 9.99% and 4.87% enhancement in damping coefficient for Al₂O₃ and CuO, respectively, at 90 °C temperature and 0.5% weight fraction.

By understanding the influence of texture shapes on the dynamic characteristics, engineers can design bearings that exhibit improved stability and enhance overall performance.

IN Part I wc saw how structural flexibility could introduce aerodynamic forces which might eventually lead to instability, or to the complete nullification of a desired aerodynamic effect. The phenomenon of flutter presents another problem in stability, but in this case an oscillatory instability is threatened. It must be realized at the outset that flutter is no mere resonance phenomenon such as the bad vibrations a motor‐car may exhibit at a particular engine speed. Flutter is a vibration in which energy is extracted from the airstrcam to help build up the amplitude, and a catastrophic failure can easily occur within a second of the start of the flutter.

A method is presented for calculating influence coefficients in multispar wings of any plan form. Shear deflexion, chordwise bending and taper are taken into account. All the bending material is concentrated at the rib and spar booms and the skin is assumed to carry only shear. The method is particularly useful in the early stages of design as it is rapid and gives a good internal load distribution. The choice of the method, the assumptions made, and the idealization of the structure are discussed. The structure is reduced to a system of beams and torque boxes, the latter connected to the beams by vertical shear at their corner nodes. The internal forces are first expressed as functions of the displacements at the nodes by means of stiffness coefficients. Next the equations of equilibrium, at each node, are established. Finally the conditions of compatibility are brought in. The solution of this system of equations gives the matrix of influence coefficients. Wherever vertical loads only are applied it is possible to solve for the moment equations of straight beams separately from the remainder of the structure, hence from the stiffness matrix. For convenience, these straight beams are organized into sub‐matrices whose moment equations are ‘reduced’. The specific end conditions also allow further reductions. The internal loads can be obtained by substituting the influence coefficients back into the sub‐matrices and by considering the equilibrium of the beams. The angular displacements of the nodes may also be calculated in a similar manner by using the ‘reduced’ rows from the sub‐matrices.

The purpose of this paper is to equip damping performance of frame structure with viscoelastic dampers connected to supports is studied, the influence of the damper supports and the damping parameters on the damping performance of the structure is analyzed, the practical economical arrangement of viscoelastic dampers on each floor is researched and the calculation method of the seismic effect of the damping structure is presented.

In this paper, Fourier transform is applied to the vibration equation of the structure equipped with viscoelastic dampers, the frequency domain solution of the vibration equation is solved and the time-domain solution of the equation is obtained by Fourier inverse transform, from which effects of the support coefficient and the relaxing time coefficient on the seismic response of the structure are analyzed.

The seismic effect of each floor and the bottom shear force of each vibration mode of a structure are analyzed, which indicates that the relaxing time coefficient of the damper should be controlled reasonably.

In this paper, the vibration equation is solved in the frequency domain for frame structure equipped with viscoelastic dampers. The time-domain solution of the equation is obtained by Fourier inverse transform, from which the seismic response of frame structure equipped with viscoelastic damper connected to supports is studied.