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The purpose of this paper is to discuss the asymptotic models of different parts with a pitting fault in rolling bearings.

For rolling bearings with a pitting fault, the displacement deviation between raceways and rolling elements is usually considered to vary instantaneously. However, the deviation should change gradually. Based on this shortcoming, the variation rule and calculation method of the displacement deviation are explored. Asymptotic models of different parts with a pitting fault are discussed, respectively. Besides, rolling bearing systems have prominent fractional characteristics unconsidered in the traditional models. Therefore, fractional calculus is introduced into the modeling of rolling bearings. New dynamic asymptotic models of different parts with a pitting fault are proposed based on fractional damping. The numerical simulation is performed based on the proposed model, and the dynamic characteristics are analyzed through the bifurcation diagrams, trajectory diagrams and frequency spectrograms.

Compared with the model based on integral calculus, the proposed model can better reflect the periodic characteristics and fault characteristics of rolling bearings. Finally, the proposed model is verified by the experiment. The dynamic characteristics of rolling bearings at different rotating speeds are analyzed. The experimental results are consistent with the simulation results. Therefore, the proposed model is effective.

(1) The above models are idealized, i.e. the local pitting fault is treated as a rectangle. When a component comes into contact with the fault, the displacement deviation between the component and the fault component immediately releases if the component enters the fault area and restores if the component leaves. However, the displacement deviation should change gradually. Only when the component touches the fault bottom, the displacement deviation reaches the maximum. (2) Due to the material's memory and fluid viscoelasticity, rolling bearing systems exhibit significant fractional characteristics. However, the above models are all proposed based on integral calculus. Integral calculus has some local characteristics and is not suitable for describing historical dependent processes. Fractional calculus can better describe the essential characteristics of the system.

Face contact has a strong impact on the service life of non-contacting gas face seals; the current research which mainly focuses on the face contact had appeared during the startup or shutdown operation. This paper aims to present a closed-form contact model of a gas face seal during the opened operation.

Referring to the axial rub-impact model of rotor dynamics, a closed-form contact model is developed under a nonparallel plane contact condition that corresponds to the local face contact of sealing rings arising from some disturbances during the opened operation. The closed-form contact model and a direct numerical contact model are performed on Gaussian surfaces to compare the contact behavior.

The closed-form contact model is in a good agreement with the direct numerical contact model. However, the closed-form contact model cannot involve the influence of grooves on the sealing ends. The error is eliminated in some other types of gas face seals such as coned gas face seals. Besides non-contacting face seals, the closed-form model can be applied to the axial rub impact of rotor dynamics.

A closed-form contact model of a gas face seal is established during the opened operation. The closed-form contact model is validated by a direct numerical contact model. The closed-form contact model also suits for axial rub-impact of rotor dynamics.

This paper aims to analyse the conceptual bases of the related terms of “host” and “guest” in Chinese and reveal essential, though overlooked, cultural differences that relate to “hospitality” in Western and Chinese cultural contexts.

A presupposition of this conceptual investigation is that culture manifests itself linguistically. The analytic approach used here is textual analysis. Confucian classical texts are the main source of evidence for examining the conceptual commitments of the Chinese characters 主 and 客 and their corresponding practical expressions.

Cross-cultural comparison reveals asymmetries between the term “hospitality” and its Chinese translations, etymologically and culturally. This study demonstrates how the Chinese 主–客 paradigm is both hierarchal in nature and centred on the role and interests of the host. It further compares this paradigm with its Western counterpart along five different dimensions.

The specific Chinese norms for the host–guest paradigm synthesized here could prompt both academicians and operators to question the cultural attachments associated with hospitality by participants and the cultural differences in hospitality transactions and management. The cultural sensitivity modelled here is intended to facilitate harmony between a hospitality setting and the culture in which it is embedded.

This conceptual paper is the first in the Anglophone literature to explore the Chinese cultural roots of the concepts “host” and “guest”. The linguistic perspective used in this study allows the concept of “hospitality” to be studied cross-culturally and in an interdisciplinary way, addressing a blind spot in the extant hospitality literature.