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This paper employs a hybrid numerical method combining the differential transformation method (DTM) and the finite difference method (FDM) to study the bifurcation and nonlinear behavior of a rigid rotor supported by a relative short gas lubricated journal bearing system with herringbone grooves. The analysis reveals a complex dynamic behavior comprising periodic, subharmonic and quasi‐periodic responses of the rotor center. The dynamic behavior of the bearing system varies with changes in the rotor mass and bearing number. The current analytical results are found to be in good agreement with those of other numerical methods. This paper discusses these issues.

In this paper, DT is used to deal Reynolds equation and is also one of the most widely used techniques for solving differential equations due to its rapid convergence rate and minimal calculation error. A further advantage of this method over the integral transformation approach is its ability to solve nonlinear differential equations. In solving the Reynolds equation for the current gas bearing system, DTM is used for taking transformation with respect to the time domain τ, and then the FDM is adopted to discretize with respect to the directions of coordinates.

From the Poincaré maps of the rotor center as calculated by the DTM&FDM method with different values of the time step, it can be seen that the rotor center orbits are in agreement to approximately four decimal places for the different time steps. The numerical studies also compare the results obtained by the SOR&FDM and DTM&FDM methods for the orbits of the rotor center. It is observed that the results calculated by DTM&FDM are more accurately than SOR&FDM. Therefore, the DTM&FDM method suits this gas bearing system and provides better convergence than SOR&FDM method.

This study utilizes a hybrid numerical scheme comprising the DTM and the FDM to analyze nonlinear dynamic behavior of a relative short gas lubricated journal bearing system with herringbone grooves. The system state trajectory, phase portraits, the Poincaré maps, the power spectra, and the bifurcation diagrams reveal the presence of a complex dynamic behavior comprising periodic, subharmonic and quasi‐periodic responses of the rotor center. Therefore, the proposed method provides an effective means of gaining insights into the nonlinear dynamics of relative short gas lubricated journal bearing systems with herringbone grooves.

The water-lubricated hydrodynamic herringbone groove journal bearing (HGJB) is capable of running at high speed. However, when running at a low speed, it suffers from a low load-carrying capacity due to the weak hydrodynamic effect. To overcome this problem, this study proposes a hybrid water-lubricated HGJB and aims to investigate its dynamic characteristics.

A hybrid lubrication model applicable to the hybrid water-lubricated HGJB is established based on the boundary fitted coordinate system, which considers the turbulent, thermal and tilting effects, and the finite difference method is used to calculate the dynamic characteristics of the hybrid water-lubricated HGJB.

The result shows that the hybrid HGJB has larger dynamic coefficients and better system stability compared with the hydrodynamic HGJB when running at low speed. Furthermore, the stiffness of hybrid HGJB are mainly governed by the hydrodynamic effect rather than the hydrostatic effect when running at high speed.

The proposed hybrid water-lubricated HGJB shows excellent dynamic characteristics at either low speed or high speed; and the hybrid water-lubricated HGJB has a large load-carrying capacity when running at low speed and has a good dynamic stability when running at high speed.

The peer review history for this article is available at: https://publons.com/publon/10.1108/ILT-06-2024-0233/

This study aims to develop a new method to treat the numerical singularity at the critical nodes of two skew coordinates, and optimize the leakage of micro herringbone grooved journal bearings (MHGJBs) with this method.

A side leakage numerical algorithm is proposed by using the skew meshes with a virtual node (SMVN) method to evaluate the effects of groove angle, bank/groove ratio, groove depth and groove number on load capacity, friction and side leakage of MHGJB.

The SMVN method is effective in treating the numerical singularity at the critical nodes of two skew coordinates. Besides, a group of optimized parameters of micro herringbone groove is obtained which can not only minimize the side leakage but also improve the load capacity and friction force.

A virtual node method was proposed, which can significantly improve the calculation accuracy in the side leakage model.

This paper aims to elucidate the effects of lubricant groove shape, vertical load, swing angle and grease injection cycle on the friction and wear performances of journal bearings under the grease lubrication condition.

Three different types of lubricant grooves, namely, numeral eight-shaped, axial straight line-shaped and circular blind hole-shaped, were designed and machined in the bearing bush of journal bearings. The tribological behaviors of these journal bearings were investigated on the self-developed reciprocating swing friction and wear tester. Experimental data including the friction coefficient, the friction temperature, the wear loss and wear time were analyzed in detail. The wear morphologies of friction pairs were observed by scanning electron microscope and confocal laser scanning microscope.

The load carrying capacity and service life of the journal bearing with circular blind hole-shaped lubricant grooves are not affected. However, the load carrying capacities of journal bearings with numeral eight-shaped and axial straight line-shaped lubricant grooves are declined. The coverage areas of lubricating grease in the bearing bush are associated with the swing angle. The smaller the swing angle is, the more limited the coverage areas of lubricating grease get. Among these journal bearings, the maintenance-free time of journal bearing with circular blind hole-shaped lubricant grooves is the longest because of its large grease storage capacity.

The journal bearing with circular blind hole-shaped lubricant grooves exhibits the excellent antifriction and wear-resistant properties, making it suitable for the application in the low-speed and heavy-load engineering conditions.

To enhance the load capacity and dynamic characteristics of gas foil conical bearings (GFCBs), two kinds of microgrooves (sector and Fibonacci-like shape) are arranged on the top foil surface.

The Reynolds equation considering gas rarefaction effect is solved by the finite difference method, in which the 2D plate element stiffness model is used for the grooved top foil. The influence of groove on the static characteristics is studied, and the dynamic characteristics of novel bearing are obtained by the perturbation method.

The results show that the gas rarefaction effect on the load capacities is negligible, and the novel GFCB with microgrooved top foil has higher load capacities. Moreover, the deeper groove is conductive to the dynamic stability improvement. The positive Fibonacci-like groove seems to be the most suitable shape, which can largely increase the axial load capacity with little additional torque cost. And the improvement of dynamic characteristics for the Fibonacci-like grooved GFCB is also more favorable.

As the low cost of groove processing, it is an effective way to improve GFCB’s performance and even can be used to upgrade the bearings in service.

The peer review history for this article is available at: https://publons.com/publon/10.1108/ILT-04-2024-0148/

The purpose of this paper is to improve the film stiffness of a dry gas seal (DGS) through the proper design of 3D macroscopic surface structures based on numerical study.

A novel generalized three-dimensional (3D) geometric model is proposed to characterize macroscopic surface structures of a DGS, including grooves, waviness, radial taper and step. The mathematical model is established to simulate film pressure distribution. The effect of the surface profile and groove bottom profile on the steady-state performance of DGSs at different working conditions is investigated.

The unidirectional groove surface has the largest film stiffness at different speed conditions and the largest opening force at medium and high speed, whereas the annular groove has the largest opening force at static pressure. For obtaining the maximum film stiffness, unidirectional combined variable depth groove surface when ns = 0.4 and k = 0.5 outperforms the other unidirectional groove surfaces, whereas circumferential waviness when ns = 1 and k = 1 is the best choice among annular groove surfaces.

This study proposes a novel generalized 3D geometric model to characterize macroscopic surface structures of a DGS. The optimal groove bottom profile for different surface profiles of DGS is presented.

This paper gives a review of the finite element techniques (FE) applied in the analysis and design of machine elements; bolts and screws, belts and chains, springs and dampers, brakes, gears, bearings, gaskets and seals are handled. The range of applications of finite elements on these subjects is extremely wide and cannot be presented in a single paper; therefore the aim of this paper is to give FE researchers/users only an encyclopaedic view of the different possibilities that exist today in the various fields mentioned above. An Appendix included at the end of the paper presents a bibliography on finite element applications in the analysis/design of machine elements for 1977‐1997.

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.

The spindle behavior of machines and systems depends largely on the choice and design quality of the mechanical components used for the displacement between different parts. As far as very high technology is concerned, air bearings are suitable, for instance, for machining a telescope mirror or for systems used in medical applications that require a micro and nanometric resolution in displacement. Therefore, air bearings play a crucial role in ensuring spindle stability in machines and systems. The static and dynamic behavior of air spindles is dependent on several parameters, such as external load, dimensions, supply pressure, manufacturing capability and fluid properties.

This paper presents a methodology for the calculation and analysis of the stability and reliability of machine and system spindles supported by air hemispherical bearings. The static and dynamic characteristics of air spindles are calculated using the finite element method (FEM). The stochastic Response Surface Method (SRSM) is used for the approximation of the performance function, and the reliability is assessed by Monte Carlo Simulation (MCS) and the First Order Reliability Method (FORM).

The static and dynamic characteristics of air spindles are calculated using the finite element method (FEM). Stochastic Response Surface Method (SRSM) is used for the approximation of the performance function, and the reliability is assessed by Monte Carlo Simulation (MCS) and First Order Reliability Method (FORM).

The article presents an original approach for the behavior analysis of machines and systems spindles supported by hemispherical fluid bearings. The methodology based on the finite element method and the principle of structural reliability, allows studying the influence of physical and geometrical parameters on the static and dynamic characteristics and the failure probability of a spindle. Thus, the optimum behavior of a spindle can be predicted for different configurations of a bearing design taking into account the reliability evaluation.

The purpose of this paper is to study tilt angle effects as design parameters of noncircular bearings, on the linear dynamic analyses of micropolar lubricated circular, two, three and four lobe journal bearings.

Reynolds equation in dynamic state is modified considering the micropolarity characteristics of lubricant, and it is solved using generalized differential quadrature method. The perturbed components of the dynamic pressure are extracted based on the linear dynamic model. To explain the transient state of the governing equation, through the linear dynamic approach, the whirling motion of rotor around the steady state position is assumed to be harmonic.

It is observed from the results that tilt angle has significant effects on the steady state and stability performance of lobed journal bearings. It may be selected suitably to improve the performance of rotor-bearing system, while all other lubricant properties and noncircular bearing design parameters are kept fixed. Results show that among the three types of bearings considered, the dynamic performance of two lobe bearings are more affected by the variation of tilt angle.

The present study is mainly concerned with the effects of tilt angle as a design parameter on the stability performance of a hydrodynamic noncircular journal bearing lubricated with micropolar fluid.