Analytical Modeling and Mechanism Analysis of Time-Varying Excitation for Surface Defects in Rolling Element Bearings

Surface defects,including dents,spalls,and cracks,for rolling element bearings are the most common faults in rotating machinery.The accurate model for the time-varying excitation is the basis for the vibration mechanism analysis and fault feature extraction.However,in conventional investigations,this issue is not well and fully addressed from the perspective of theoretical analysis and physical derivation.In this study,an improved analytical model for time-varying displacement excitations(TVDEs)caused by surface defects is theoretically formulated.First and foremost,the physical mechanism for the effect of defect sizes on the physical process of rolling element-defect interaction is revealed.According to the physical interaction mechanism between the rolling element and different types of defects,the relationship between time-varying displacement pulse and defect sizes is further analytically derived.With the obtained time-varying displacement pulse,the dynamic model for the deep groove bearings considering the internal excitation caused by the surface defect is established.The nonlinear vibration responses and fault features induced by surface defects are analyzed using the proposed TVDE model.The results suggest that the presence of surface defects may result in the occurrence of the dual-impulse phenomenon,which can serve as indexes for surface-defect fault diagnosis.

Methods of analytical mechanics for solving differential equations of first order

A differential equation of first order can be expressed by the equation of motion of a mechanical system. In this paper, three methods of analytical mechanics, i.e. the Hamilton-Noether method, the Lagrange-Noether method and the Poisson method, are given to solve a differential equation of first order, of which the way may be called the mechanical methodology in mathematics.

THE THEORY OF RELATIVISTIC ANALYTICAL MECHANICS OF THE ROTATIONAL SYSTEMS

The theory of rotational relativistic mechanics is discussed and the theory of relativistic analytical mechanics' of the rotational systems is constructed. The relativistic generalized kinetic energy function for the rotational systems [GRAPHICS] and the generalized acceleration energy function [GRAPHICS] are constructed, and furthermore, the Hamilton principle and three kinds of D'Alembert principles are given. For the systems with holonomic constraints, the relativistic Lagrange equation, Nielsen equation, Appell equation and Hamilton canonical equation of the rotational systems are constructed; For the systems with nonholonomic constraints, the relativistic Routh equation, Chaplygin equation, Nielsen equation and Appell equation of the rotational systems are constructed; the relativistic Noether conservation law of the rotational systems are given too.

A new geometrical and mechanical relation in the respiratory system with airflow limitation—From the perspective of analytical respiratory mechanics

Classic respiratory mechanics is a branch of vectorial mechanics, which aims to recognize all forces acting on the respiratory system. Another branch of mechanics, analytical mechanics, has been used for analyzing the motions of complicated systems with constraints through equilibrium among scalar quantities such as kinetic energy and potential energy. However, until now, there have not been any studies concerning about analytical respiratory mechanics. In this paper, the author has obtained two types of motion equations (linear and nonlinear) for the airflow limitation from formulation of the analytical respiratory mechanics. Reconstructed flow-volume trajectories of the linear equation revealed a new relationship among the slope of the linear portion of trajectory, the coefficient of the dissipation function and the coefficient of the potential function. Reconstructed trajectories of the nonlinear equation suggested that a curved flow-volume trajectory would be caused by the emergence of regional hypoventilated clusters with airtrapped lobules. In conclusion, analytical respiratory mechanics will provide the basis for analyzing the mechanical properties of the respiratory system con cerning pulmonary functional images made by newly developed technologies.

Unified symmetry of nonholonomic mechanical systems with variable mass

Based on the total time derivative along the trajectory of the system the definition and the criterion for a unified symmetry of nonholonomic mechanical system with variable mass are presented in this paper. A new conserved quantity, as well as the Noether conserved quantity and the Hojman conserved quantity, deduced from the unified symmetry, are also obtained, An example is given to illustrate the application of the results.

A DIFFERENTIAL GEOMETRIC DESCRIPTION FOR TIME-INDEPENDENT CHETAEV'S NONHOLONOMIC MECHANICAL SYSTEM WITH UNILATERAL CONSTRAINTS

By applying the framework of the tangent bundle geometry to the method of Lagrange multi- pliers,a geometric description of Chetaev's nonholonomic systems subjected to unilateral nonholonomic con- straints trod unilateral holonomic constraints respectively in time-independent circumstances is presented.

Lie-form invariance of nonholonomic mechanical systems

The Lie-form invariance of a nonholonomic mechanaical system is studied. The definition and criterion of the Lie-form invariance of the nonholonomic mechaaical system are given. The Hojman conserved quantity and a new type of conserved quantity are obtained from the Lie-form invariance. An example is givea to illustrate the application of the results.

EQUATIONS OF MOTION FOR NONHOLONOMIC MECHANICAL SYSTEMS WITH UNILATERAL CONSTRAINTS

In this paper, the equations of motion for nonholonomic mechanical system with unilateral holonomic constraints and unilateral nonholonomic constraints are presented, and an example to illustrate the application of the result is given.

Perturbation and Adiabatic Invariants of Mei Symmetry for Nonholonomic Mechanical Systems

基于这个概念断热不变，不安和为 nonholonomic 的 Mei 对称的断热的 invariants 机械系统被学习。为没有不安的系统的 Mei 对称的准确 invariants 被给。到 Meisymmetry 的不安被讨论，为使不安的系统的 Mei 对称的断热的 invariants 被获得。

Mei Adiabatic Invariants Induced by Perturbation of Mei Symmetry for Nonholonomic Controllable Mechanical Systems

Two types of Mei adiabatic invariants induced by perturbation of Mei symmetry for nonholonomic controllablemechanical systems are reported.Criterion and restriction equations determining Mei symmetry after beingdisturbed of the system are established.Form and existence condition of Mei adiabatic invariants are obtained.

Mei Symmetries and Lie Symmetries for Nonholonomic Controllable Mechanical Systems with Relativistic Rotational Variable Mass

为 nonholonomic 的 Mei 对称和谎言对称有相对论的旋转可变质量的可控制的机械系统被学习。系统的运动的微分方程被建立。Mei 对称的定义和系统的谎言对称分别地被学习。Mei 对称是谎言对称的必要、足够的在下面条件被给。Mei 对称能在下面被导致的条件新有点保存的数量和保存数量的形式被获得。一个例子被给说明结果的申请。

Perturbation to Noether-Mei Symmetry and Adiabatic Invariants for Nonholonomic Mechanical Systems in Phase Space

基于这个概念断热不变，不安到 Noether Mei 对称和为 nonholonomic 的断热的 invariants 在阶段空间的机械系统被学习。到为系统的 Noether Mei 对称的不安的定义被介绍，并且到 Noether Mei 对称的不安的标准被给。同时， Noether 断热的 invariants 和 Mei 为使不安的系统的断热的 invariants 被获得。

New Conserved Quantities of Noether-Mei Symmetry for Nonholonomic Mechanical System

Two new types of conserved quantities deduced by Noether-Mei symmetry of nonholonomic mechanicalsystem are studied.The definition and criterion of Noether-Mei symmetry for the system are given.A coordinationfunction is introduced,and the conditions under which the Noether-Mei symmetry leads to the two types of conservedquantities and the forms of the two types of conserved quantities are obtained.An illustrative example is given.Thecoordination function can be selected according to the demand for finding the gauge function,and the choice of thecoordination function has multiformity,so more conserved quantities deduced from Noether-Mei symmetry of mechanicalsystem can be obtained.

Efficient concentration of trace analyte with ordered hotspot construction for a robust and sensitive SERS platform

Surface-enhanced Raman scattering(SERS)platform,which enables trace analyte detection,has important application prospects.By structuring/modifying the surface of the SERSsubstrate,analyte in highly diluted solutions can be concentrated into localized active areas for highly sensitive detection.However,subject to the difficulty of the fabrication process,itremains challenging to balance hot-spot construction and the concentration capacity of analyte simultaneously.Therefore,preparing SERS substrates with densely ordered hot spots andefficient concentration capacity is of great significance for highly sensitive detection.Herein,we propose an Ag and fluoroalkyl-modified hierarchical armour substrate(Ag/F-HA),which has a double-layer stacking design to combine analyte concentration with hotspot construction.The microarmour structure is fabricated by femtosecond-laser processing to serve as asuperhydrophobic and low-adhesive surface to concentrate analyte,while the anodic aluminium oxide(AAO)template creates a nanopillar array serving as dense and ordered hot spots.Under the synergistic action of hot spots and analyte concentration,Ag/F-HA achieves a detectionlimit down to 10^(-7)M doxorubicin(DOX)molecules with a RSD of 7.69%.Additionally,Ag/F-HA exhibits excellent robustness to resist external disturbances such as liquid splash or abrasion.Based on our strategy,SERS substrates with directional analyte concentrations are further explored by patterning microcone arrays with defects.This work opens a way to the realistic implementation of SERS in diverse scenarios.

Perturbation to symmetries and Hojman adiabatic invariant for nonholonomic controllable mechanical systems with non-Chetaev type constraints

This paper studies the perturbation to symmetries and adiabatic invariant for nonholonomic controllable mechanical systems with non-Chetaev type constraints. It gives the exact invariants introduced by the Lie symmetries of the nonholonomic controllable mechanical system with non-Chetaev type constraints without perturbation. Based on the definition of high-order adiabatic invarlants of mechanical system, the perturbation of Lie symmetries for nonholonomic controllable mechanical system with non-Chetaev type constraints with the action of small disturbances is investigated, and a new type of adiabatic invariant of system are obtained. In the end of this paper, an example is given to illustrate the application of the results.

A unified symmetry of nonholonomic mechanical systems in phase space

In this paper, we have studied the unified symmetry of a nonholonomic mechanical system in phase space. The definition and the criterion of a unified symmetry of the nonholonomic mechanical system in phase space are given under general infinitesimal transformations of groups in which time is variable. The Noether conserved quantity, the generalized Hojman conserved quantity and the Mei conserved quantity are obtained from the unified symmetry. An example is given to illustrate the application of the results.

Noether's theory of generalized linear nonholonomic mechanical systems

By introducing the quasi-symmetry of the infinitesimal transformation of the transformation group Gr, the Noether＇s theorem and the Noether＇s inverse theorem for generalized linear nonholonomic mechanical systems are obtained in a generalized compound derivative space. An example is given to illustrate the application of the result.

Noether-Form Invariance of Nonholonomic Controllable Mechanical Systems in Phase Space

In this paper,we study the Noether-form invariance of nonholonomic mechanical controllable systems inphase space.Equations of motion of the controllable mechanical systems in phase space are presented.The definitionand the criterion for this system are presented.A new conserved quantity and the Noether conserved quantity deducedfrom the Noether-form invariance are obtained.An example is given to illustrate the application of the results.