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The transient loads on the spherical hybrid sliding bearings (SHSBs) rotor system during the process of accelerating to stable speed are related to time, which exhibits a complex transient response of the rotor dynamics. The current study of the shaft center trajectory of the SHSBs rotor system is based on the assumption that the rotational speed is constant, which cannot truly reflect the trajectory of the rotor during operation. The purpose of this paper truly reflects the trajectory of the rotor and further investigates the stability of the rotor system during acceleration of SHSBs.

The model for accelerated rotor dynamics of SHSBs is established. The model is efficiently solved based on the fourth-order Runge–Kutta method and then to obtain the shaft center trajectory of the rotor during acceleration.

Results show that the bearing should choose larger angular acceleration in the acceleration process from startup to the working speed; rotor system is more stable. With the target rotational speed increasing, the changes in the shaft trajectory of the acceleration process are becoming more complex, resulting in more time required for the bearing stability. When considering the stability of the rotor system during acceleration, the rotor equations of motion provide a feasible solution for the simulation of bearing rotor system.

The study can simulate the running stability of the shaft system from startup to the working speed in this process, which provides theoretical guidance for the stability of the rotor system of the SHSBs in the acceleration process.

The purpose of this paper is to explore the factors influencing customers’ willingness to participate in virtual brand community’s value co-creation and help companies better operating the virtual brand community.

Based on social cognitive theory and the features of the virtual brand community, this paper constructed a model of factors influencing customers’ willingness to participate in virtual brand community’s value co-creation. Then this paper quantitatively analyzed the mediating effect and the moderating effect.

The empirical analysis came to the following conclusions: first, in virtual brand communities, customers’ willingness to participate in value co-creation would be influenced by subject factors, environment factors, brand factors and perceived value factor. Second, customer involvement is an important moderator. The more involved the customer is, the more he/she will rely on the virtual brand community. Particularly, customer involvement has a positive moderating effect on the influence of subject factors, while it has a negative moderating effect on the influence of community experience and community trust. Third, perceived value plays a significant mediating role between subject factors and customers’ willingness to participate in value co-creation.

The results of this study can help companies better understand the influence of external factors like environment and brand so that they can better operate the virtual brand community and encourage customers to contribute to the development of the community and the brand.

Most of the existing studies focused on the formation of virtual brand communities and customers’ participation behaviors, but there is limited research focusing on what contributes to customers’ participation in value co-creation of virtual brand communities. This study, therefore, attempts to bridge the research gap.

Damage of engineering structures is a nonlinear evolutionary process that spans across both material and structural levels, from mesoscale to macroscale. This paper aims to provide a comprehensive review of damage analysis methods at both the material and structural levels.

This study provides an overview of multiscale damage analysis of engineering structures, including its definition and significance. Current status of damage analysis at both material and structural levels is investigated, by reviewing damage models and prediction methods from single-scale to multiscale perspectives. The discussion of prediction methods includes both model-based simulation approaches and data-driven techniques, emphasizing their roles and applications. Finally, summarize the main findings and discuss potential future research directions in this field.

In the material level, damage research primarily focuses on the degradation of material properties at the macroscale using continuum damage mechanics (CDM). In contrast, at the mesoscale, damage research involves analyzing material behavior in the meso-structural domain, focusing on defects like microcracks and void growth. In structural-level damage analysis, the macroscale is typically divided into component and structural scales. The component scale examines damage progression in individual structural elements, such as beams and columns, often using detailed finite element or mesoscale models. The structural scale evaluates the global behavior of the entire structure, typically using simplified models like beam or shell elements.

To achieve realistic simulations, it is essential to include as many mesoscale details as possible. However, this results in significant computational demands. To balance accuracy and efficiency, multiscale methods are employed. These methods are categorized into hierarchical approaches, where different scales are processed sequentially, and concurrent approaches, where multiple scales are solved simultaneously to capture complex interactions across scales.

The aim of this paper is to study the tribological performance and self-repairing performance of surface-modified nanoscale serpentine powders as lubricant additives in the mineral base oil (5-CST).

Fourier transform infrared spectroscopy spectra and thermo-gravimetric analysis of both modified and unmodified serpentine were performed to analyse their grafting ratio and suspension after modified using a long-chain naphthene aliphatic acid. The tribological properties of surface-modified serpentine as lubricant additives in 5-CST were evaluated and the worn surfaces were investigated by X-ray photoelectron spectroscopy (XPS) and X-ray absorption near edge structure (XANES).

The results show that the serpentine particles have high grafting ratio, improving the dispersity in 5-CST. When the serpentine concentration of 1.00 weight per cent is used as additives in 5-CST, friction coefficient reduces by 14.80 per cent under 294 N and wear scar diameter (WSD) decreases by 11.82 per cent. The results of X-ray absorption near edge structure and XANES show that the adsorption and tribochemical reactions occur to form self-repairing lubrication films.

The paper illustrates a tribofilm form on the rubbed surface, which is responsible for the decrease in friction and wear, mainly containing iron oxides, silicon oxides, magnesium oxides and organic compounds. The results are useful for further applications in advanced environmental friendly lubricating oils and additives.