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The rotor system supported by the cylindrical roller bearings is widely used in various fields such as aviation, space and machinery due to its importance. In the study of the dynamic characteristics of the cylindrical roller bearings, it is important to accurately calculate the stiffness of the cylindrical roller bearings. The stiffness of the cylindrical roller bearings is very important in the analysis of the vibration characteristics of the rotor system. Therefore, in this paper, the method of creating a comprehensive stiffness model of the cylindrical roller bearing is mentioned. The purpose of this study is to improve the dynamic stability of the rotor system supported by the cylindrical roller bearing by accurately establishing the comprehensive stiffness calculation model of the cylindrical roller bearings.

In consideration of the radial clearance of the cylindrical roller bearing, the radial load acting on the cylindrical roller bearing was derived, and based on this, a model for calculating the Hertz contact stiffness of the cylindrical roller bearing was created. Based on the load considering the radial clearance, an oil film stiffness model of the cylindrical roller bearing was created under the elastohydrodynamic lubrication (EHL) theory. Then, the comprehensive stiffness was calculated by combining Hertz contact stiffness and the oil film stiffness of the cylindrical roller bearing, and the dynamic parameters are calculated by using the MATLAB program.

When the radial clearance of the cylindrical roller bearing is considered, the comprehensive stiffness is larger than when the radial clearance is not taken into account, and the radial clearance of the cylindrical roller bearing is an important factor that directly affects the comprehensive stiffness of the cylindrical roller bearing.

In this paper, based on Hertz contact theory and the EHL theory, the authors investigated the method of creating a comprehensive stiffness model of the cylindrical roller bearing considering the radial clearance. These results will contribute to the theoretical basis for studying the mechanics of cylindrical roller bearings and optimizing their structures, and they will provide an important theoretical basis for analyzing the dynamic characteristics of the rotor system supported by the cylindrical roller bearing.

This study examines two distinct bearing stiffness calculation methods, both of which are based on the displacement-load function. Previous research typically incorporated one type of bearing stiffness into their system mechanics or vibration analysis. However, these two methods of calculating stiffness lead to different vibration models. This implies that the choice for vibration investigation is not merely about selecting one of the two types of stiffness, but also about how to appropriately implement that chosen stiffness within a model. The primary objective of this work is to compare these two methods of bearing calculation and to discuss the suitable applications of each method in both static and dynamic analyses.

This study compares two distinct methods for calculating bearing stiffness. It explores the relationships between varying bearing stiffnesses, their internal structures, and contact features. Furthermore, it examines the impact of external loads on the static properties and dynamic characteristics of different bearing stiffnesses. Finally, based on the outcomes observed under various operating conditions, the study discusses the suitability of each method for static and dynamic analysis.

Mean stiffness is more suitable for calculating load transmissibility in a static state or capturing the delivery performance at instantaneous equilibrium positions in a dynamic state. Since the variation of the equilibrium positions is ignored, the alternating stiffness model is better suited for capturing the fluctuating properties of the vibration behaviors, especially under variable external load conditions.

We compare the two bearing calculation methods and discuss the appropriate applications of each method for static and dynamic analysis.

Gives a bibliographical review of the finite element methods (FEMs) applied for the linear and nonlinear, static and dynamic analyses of basic structural elements from the theoretical as well as practical points of view. The range of applications of FEMs in this area is wide and cannot be presented in a single paper; therefore aims to give the reader an encyclopaedic view on the subject. The bibliography at the end of the paper contains 2,025 references to papers, conference proceedings and theses/dissertations dealing with the analysis of beams, columns, rods, bars, cables, discs, blades, shafts, membranes, plates and shells that were published in 1992‐1995.

The purpose of this paper is to calculate the meshing stiffness of nutation face gear considering the roughness, establish the calculation method of time-varying meshing stiffness of rough tooth surface and analyze the influence of roughness, load and other factors on the meshing stiffness of tooth surface.

The Weierstrass–Mandelbrot (W-M) function in the Majumdar–Bhushan model is used to characterize the rough contact line of the tooth surface, the normal height and radius of the micro convex body are calculated and the contact flexibility of the contact point of the tooth surface is obtained. The contact flexibility and the bending shear deformation flexibility obtained previously are substituted into the improved deformation compatibility equation for iterative calculation, and the time-varying meshing stiffness of the nutation face gear considering the roughness is obtained.

Compared with ABAQUS finite element simulation results, it is found that the meshing stiffness curve of rough tooth surface is more gentle than that of smooth tooth surface, the meshing stiffness value is smaller and the meshing stiffness change is smaller at the position where the number of gear teeth coincide changes.

In the process of calculating contact deformation, the fractal theory W-M function is used to characterize the contact line of the rough nutation face gear, and the deformation coordination condition considering roughness is improved. Therefore, the method of time-varying meshing stiffness considering roughness can obtain more accurate results, which provides theory and data for the subsequent dynamics analysis of the nutation face gear transmission.

The purpose of this paper is to obtain the single-tooth stiffness, single-tooth time-varying meshing stiffness and comprehensive meshing stiffness of the internal and external face gears and to analyze the influence of the modulus, pressure angle and tooth width of each face gear on the single-tooth stiffness of the gear in nutation face gear transmission.

From the point of view of material mechanics, the gear teeth of nutation face gear are simplified as spacial variable cross-section beams. The shear deformation of gear teeth, the bending deformation of tooth root and the additional elastic deformation caused by the base deformation are gotten by simplified trapezoidal section method, thus the stiffness of nutation face gear teeth can be obtained. The comparison with finite element method results verifies the rationality of simplified trapezoidal section method for calculating the tooth stiffness of nutation face gear.

The variation of stiffness of internal and external face gears along the meshing line and tooth height in nutation face gear transmission is studied, and the variation laws of single tooth stiffness, single-tooth-pair mesh stiffness and single tooth time-varying meshing stiffness of nutation face gear teeth are obtained.

Nutation face gear transmission is a new type of transmission. The stiffness of face gear teeth is analyzed, and the variation rules of single tooth stiffness, single-tooth-pair mesh stiffness and single tooth time-varying meshing stiffness of nutation face gear teeth are obtained, which not only enriches the research of nutation face gear transmission but also has important guiding significance for the application of nutation face gear in engineering practice.

The purpose of this paper is to propose a two-degrees-of-freedom wire-driven 4SPS/U rigid‒flexible parallel trunk joint mechanism based on spring, in order to improve the robot’s athletic ability, load capacity and rigidity, and to ensure the coordination of multi-modal motion.

First, based on the rotation transformation matrix and closed-loop constraint equation of the parallel trunk joint mechanism, the mathematical model of its inverse position solution is constructed. Then, the Jacobian matrix of velocity and acceleration is derived by time derivative method. On this basis, the stiffness matrix of the parallel trunk joint mechanism is derived on the basis of the principle of virtual work and combined with the deformation effect of the rope driving pair and the spring elastic restraint pair. Then, the eigenvalue distribution of the stiffness matrix and the global stiffness performance index are used as the stiffness evaluation index of the mechanism. In addition, the performance index of athletic dexterity is analyzed. Finally, the distribution map of kinematic dexterity and stiffness is drawn in the workspace by numerical simulation, and the influence of the introduced spring on the stiffness distribution of the parallel trunk joint mechanism is compared and analyzed. It is concluded that the stiffness in the specific direction of the parallel trunk joint mechanism can be improved, and the stiffness distribution can be improved by adjusting the spring elastic structure parameters of the rope-driven branch chain.

Studies have shown that the wire-driven 4SPS/U rigid‒flexible parallel trunk joint mechanism based on spring has a great kinematic dexterity, load-carrying capacity and stiffness performance.

The soft-mixed structure is not mature, and there are few new materials for the soft-mixed mixture; the rope and the rigid structure are driven together with a large amount of friction and hindrance factors, etc.

It ensures that the multi-motion mode hexapod mobile robot can meet the requirement of sufficient different stiffness for different motion postures through the parallel trunk joint mechanism, and it ensures that the multi-motion mode hexapod mobile robot in multi-motion mode can meet the performance requirement of global stiffness change at different pose points of different motion postures through the parallel trunk joint mechanism.

The trunk structure is a very critical mechanism for animals. Animals in the movement to achieve smooth climbing, overturning and other different postures, such as centipede, starfish, giant salamander and other multi-legged animals, not only rely on the unique leg mechanism, but also must have a unique trunk joint mechanism. Based on the cooperation of these two mechanisms, the animal can achieve a stable, flexible and flexible variety of motion characteristics. Therefore, the trunk joint mechanism has an important significance for the coordinated movement of the whole body of the multi-sport mode mobile robot (Huang Hu-lin, 2016).

In this paper, based on the idea of combining rigid parallel mechanism with wire-driven mechanism, a trunk mechanism is designed, which is composed of four spring-based wire-driven 4SPS/U rigid‒flexible parallel trunk joint mechanism in series. Its spring-based wire-driven 4SPS/U rigid‒flexible parallel trunk joint mechanism can make the multi-motion mode mobile robot have better load capacity, mobility and stiffness performance (Qi-zhi et al., 2018; Cong-hao et al., 2018), thus improving the environmental adaptability and reliability of the multi-motion mode mobile robot.

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.

Fused deposition modeling (FDM) has become an increasingly important process among the available additive manufacturing technologies in various industries. Although there are many advantages of FDM process, a downside of its industrial application is the attainable dimensional accuracy with tight tolerance without compromising the mechanical performance. This paper aims to study the effects of six FDM operating parameters on two conflicting responses, namely, dynamic stiffness and dimensional stability of FDM produced PC-ABS parts. This study also aims to determine the optimal process settings using graphical optimization that satisfy the dynamic mechanical properties without compromising the dimensional accuracy.

The regression models based upon IV-optimal response surface methodology are developed to study the variation of dimensional accuracy and dynamic mechanical properties with changes in process parameter settings. Statistical analysis was conducted to establish the relationships between process variables and dimensional accuracy and dynamic stiffness. Analysis of variance is used to define the level of significance of the FDM operating parameters. Scanning electron microscope and Leica MZ6 optical microscope are used to examine and characterize the morphology of the structures for some specimens.

Experimental results highlight the individual and interaction effects of processing conditions on the dynamic stiffness and part accuracy. The results showed that layer thickness (slice height), raster-to-raster air gap and number of outlines have the largest effect on the dynamic stiffness and dimensional accuracy. The results also showed an interesting phenomenon of the effect of number of contours and the influence of other process parameters. The optimal process conditions for highest mechanical performance and part accuracy are obtained.

The effect of FDM processing parameters on the properties under dynamic and cyclic loading conditions has not been studied in the previous published work. Furthermore, simultaneous optimization of dynamic mechanical properties without compromising the dimensional accuracy has also been investigated. On the basis of experimental findings, it is possible to provide practical suggestions to set the optimal FDM process parameters in relation to dynamic mechanical performance, as well as the dimensional accuracy.

Presents an alternative lower bound to the elastic buckling collapse of thin shells of revolution, in comparison with results from geometrically non‐linear elastic analysis. The numerical finite element method is based on axisymmetric rotational shell elements whose strain‐displacement relations are described by Koiter’s small finite deflection theory, with displacements expanded circumferentially using a Fourier series. First, compares the reduced stiffness linear analysis, based on the buckling equation without incremental linear in‐plane energy components corresponding to the lowest eigenmode (for a particular cylindrical shell under external pressure), with the results obtained by Batista and Croll. Second, the non‐linear astatic (quasi‐static) elastic analysis to clamped spherical caps under uniform external pressure is carried out in order to compare the results from a reduced stiffness analysis from viewpoints of not only buckling loads, but also total potential energy. Argues that the astatic buckling loads may relate to reductions due to a specific imperfection effect on elastic buckling collapses.

This paper aims to present the results of calculations that checked how the longerons and frames arrangement affects the stiffness of a conventional structure. The paper focuses only on first stage of research – analysis of small displacement. Main goal was to compare different structures under static loads. These results are also compared with the results obtained for a geodetic structure fuselage model of the same dimensions subjected to the same internal and external loads.

The finite element method analysis was carried out for a section of the fuselage with a diameter of 6.3 m and a length equal to 10 m. A conventional and lattice structure – known as geodetic – was used.

Finite element analyses of the fuselage model with conventional and geodetic structures showed that with comparable stiffness, the weight of the geodetic fuselage is almost 20 per cent lower than that of the conventional one.

This analysis is limited to small displacements, as the linear version of finite element method was used. Research and articles planned for the future will focus on nonlinear finite element method (FEM) analysis such as buckling, structure stability and limit cycles.

The increasing maturity of composite structures manufacturing technology offers great opportunities for aircraft designers. The use of carbon fibers with advanced resin systems and application of the geodetic fuselage concept gives the opportunity to obtain advanced structures with excellent mechanical properties and low weight.

This paper presents very efficient method of assessing and comparison of the stiffness and weight of geodetic and conventional fuselage structure. Geodetic fuselage design in combination with advanced composite materials yields an additional fuselage weight reduction of approximately 10 per cent. The additional weight reduction is achieved by reducing the number of rivets needed for joining the elements. A fuselage with a geodetic structure compared to the classic fuselage with the same outer diameter has a larger inner diameter, which gives a larger usable space in the cabin. The approach applied in this paper consisting in analyzing of main parameters of geodetic structure (hoop ribs, helical ribs and angle between the helical ribs) on fuselage stiffness and weight is original.