Displacement Excitation Research Articles

Frequency and amplitude dependence of nuclear displacement and phase delay in mechanical vibrations for determining cellular natural frequency

Cultured cells biochemically respond to mechanical vibrations. However, the mechanisms of sensing mechanical vibrations and transducing biochemical responses remain unclear. A previous study reported that the expression of the alkaline phosphatase gene of osteoblastic cell under mechanical vibrations peaks at 50 Hz, which seems like a resonance curve in the mechanical vibration theory. Since forced displacement excitation is a dynamic mechanical stimulus that differs from other static mechanical stimuli in that an external force is equivalent to inertia, force is apparently exerted on the mass element by considering the equation of motion. In this study, the method for obtaining the change of a nucleus’s relative displacement to an excited dish was refined, and the frequency and acceleration amplitude dependence of the nucleus’s relative displacement and phase delay under mechanical vibrations were demonstrated by regarding a cell model as a vibration system. The change of the relative displacement of a HeLa nucleus to an excited dish decreases with increasing frequency in the 12.5–100 Hz range at 0.5 G and increases with increasing acceleration amplitude in the 0.5–2.0 G range at 50 Hz. Phase reversal occurs between 12.5 Hz and 50 Hz, which suggests the existence of the natural frequency of the cell between 12.5 Hz and 50 Hz. The tension estimated from the nucleus’s relative displacement change in this method was 2.3–10 pN and can be a biochemical response of the mechanotransducer. These findings can contribute to clarifying the mechanism of cell mechanotransduction in dynamic mechanical stimuli.

Time-varying displacement excitation and dynamic modeling of angular contact ball bearing with local defects

Angular contact ball bearings will produce fault damage when working for a long time, thus affecting the normal operation of the system. This paper takes angular contact ball bearings with local defects on the outer ring as the research object, proposes a method to distinguish different local defect profiles, establishes a generalized characterization model of time-varying displacement excitation of local defects in angular contact ball bearings, and studies the evolution process of local defects and their displacement excitation mechanism. On this basis, considering the influence of time-varying displacement caused by bearing defects on dynamic characteristics, based on Hertz contact theory, a fault dynamics model of angular contact ball bearings is established, and the correctness of the established model is verified by experiments. In addition, the analysis results show that rectangular local defects will eventually evolve into trapezoidal shapes; the displacement excitation change trends induced by different defect morphologies are different; compared with the length of local defects, the width has a greater impact on displacement excitation. The research results provide a theoretical basis for bearing optimization design and fault diagnosis.

Dynamic Modeling of Angular Contact Ball Bearing with Local Defects under EHL Considering Impact Force

In order to analyze the operating status of angular contact ball bearings(ACBBs) with local defects in more detail, a dynamic model of ACBB with local defects considering impact force under elastohydrodynamic lubrication conditions is proposed. Firstly, an elastohydrodynamic lubrication model for defective bearings considering spin is established, the film thickness and film stiffness of the defective bearings are calculated, and then time-varying displacement excitation model and time-varying stiffness model for local defects in angular contact ball bearings is presented. Based on this, an instantaneous impact force function related to defect size and bearing speed is established. Secondly, based on Hertz contact theory and impact force function, a dynamic calculation method for ACBBs with local defects on the outer ring is proposed. Finally, the vibration characteristics of ball bearings with faults are investigated, and the influence of different parameters on the dynamic response of the bearings is analyzed. The calculation results show that under lubrication conditions, the impact force on the vibration of the bearing is significantly weakened. With the increase of defect size and load, the frequency of bearing fault characteristics remain unchanged, but its amplitude increases. As the bearing speed increases, the characteristic frequency and amplitude of bearing faults increase.

Numerical investigation on a precast bridge using GPC and BFRP reinforcements subjected to cross-fault rupture and fling step excitation

This study investigates the seismic performances of a precast bridge made of geopolymer concrete (GPC) with fibre-reinforced polymer (FRP) reinforcements subjected to cross-fault ground motions. A numerical model was developed and verified against experimental results from a previous study and then used to evaluate the bridge's performances under earthquake excitations. The study found that a simplified model was able to reliably capture the failure pattern and displacement response of the bridge, reducing simulation time significantly. Additionally, the numerical results indicated the combination of torsional and flexural cracks was the primarily damage mode of the columns, which was not observed in the experimental test. This study also revealed that while the performances of the bridge using ordinary Portland cement (OPC) and GPC were similar under low ground excitations, GPC columns were more susceptible to brittle failure under higher ground excitations due to their brittleness. The use of FRP reinforcements led to similar displacement response as steel reinforcements under low ground displacement excitation, although severe flexural and shear damages on the column of Bent 2 were observed due to the lower elastic modulus and shear resistance of Basalt FRP material than steel. To address the disadvantages of brittle GPC and low-modulus of basalt FRP reinforcements, it is suggested to reinforce GPC with fibres and/or increase stirrup ratios if green GPC and corrosion-resistant basalt FRP reinforcements are used to construct bridges for seismic resistance.

Experimental study on the matching relationship of gas wave oscillation tube under liquid-carrying condition

The gas wave oscillation tube (GWOT) transfers energy directly between gases of varying pressures using non-constant motion waves, and its low rotational speed operation offers a broader application potential in two-phase refrigeration compared to turbomachinery. The GWOTs achieve a high performance by optimizing the relationship between tube length, deflection displacement, rotational speed, and incident excitation wave (S1) velocity. However, under the liquid-carrying conditions, the optimizing matching relationship of the GWOTs deviates, leading to a decline in performance, so it is necessary to explore the matching relationship of the high performance of the GWOTs under the liquid-carrying conditions. This study focuses on "spoon" GWOTs, analyzing the impact of rotational speed, liquid-carrying capacity, and deflection displacement on their refrigeration performance under a fixed tube length through experimental analysis. It is found that the refrigeration efficiency at the design parameters of the GWOTs decreases by a maximum of about 25 % with the increase in the amount of liquid-carrying capacity within the study area of this paper, while the refrigeration efficiency can be improved by a maximum of about 8 % by varying the rotational speed. The findings provide valuable insights for enhancing the liquid-carrying performance of the GWOTs and promoting the application expansion of GWOTs in the field of gas-liquid two-phase.

Real‐Time Detection of Coherent Vibrational Dynamics in TiN Films

AbstractTitanium nitride (TiN) has recently gained considerable interest because of its remarkable plasmonic properties and for its strong electron–phonon (e–ph) coupling, leading to extremely fast (<100 fs) electron‐lattice cooling. Here, the generation of coherent phonons in TiN films is reported, along with their real‐time detection by means of broadband transient reflection spectroscopy with sub‐15‐fs temporal resolution. The measurements show damped oscillations, superimposed to excited state electronic decay. A coherent vibrational mode is revealed, with ≈10 THz frequency ascribed to defect‐activated normal modes, consistent with spontaneous Raman scattering data, and a dephasing time of ≈250 fs. Two π‐phase flips are also observed located at photon energies corresponding to interband optical transitions (at 3.2 and 2.5 eV), ascribed to selective coupling of the vibrational mode to these transitions; the energy modulation induced by the vibrational coherence is evaluated. It is shown that the displacive excitation of coherent phonons model describes the coherent response in terms of temporal behavior and of spectral amplitude profile. Overall, a comprehensive and detailed analysis of coherent phonons in TiN films, so far undected, is provided and relevant information on TiN photo‐physical properties, potentially useful for its applications, is given.

Dynamic characteristics of high-speed angular contact ball bearings considering the coupling of outer race waviness and local defects

This paper proposes a novel four degrees of freedom model of angular contact ball bearings (ACBBs) under high-speed effect, in order to characterize the dynamic behavior of rolling bearings with coupling waviness and local defects on the outer race in detail. Firstly, based on bearing quasi-static model, considering centrifugal force, gyroscope moment, the bearing contact stiffness is calculated. Then, the representation model of outer race waviness and the time-varying displacement excitation expression of the bearing with local defects are put forward respectively. On the basis, a dynamic model of ACBBs with coupling factors is built. Finally, the vibration characteristics of the bearing with faults are investigated, the model is verified by the existing experimental results and the influence of different parameters on the bearing dynamics is analyzed. The results show that the bearing fault characteristic frequency is unchanged when the high-speed effect is considered, but the vibration amplitude is smaller than that without the high-speed effect. With the increase of speed, the bearing fault characteristic frequency and vibration amplitude increase. When considering the coupling of outer race waviness and local defects, with the increase of the two factors, the bearing fault characteristic frequency remains unchanged but the vibration amplitude increase.

Dynamic modeling and vibration characteristics analysis of cylinder with local defects in axial piston pump

The piston/cylinder pair suffers from excessive wear during the operation of axial piston pumps, and the local defects usually occur in the brass bush in the cylinder bore. Generally, the wear of cylinder is the main source of failure that affects the reliability of axial piston pumps. Thus, it is necessary to conduct an in-depth study on the vibration generated by the cylinder with local defects. Considering the effect of defect dimension, a novel time-varying displacement excitation model of the axial piston pump cylinder defect is proposed and establishes a 13 degrees of freedom lumped parameter dynamic model for cylinder fault. Then, investigating the effects of length and depth of the defect on the spectral amplitude and exploring the fault characteristic frequency of cylinder. Lastly, the model was validated on a test rig. The results demonstrate that the constructed model can predict the vibration caused by a locally defective cylinder with a frequency domain error of 0.69% and the fault characteristic frequency of cylinder is the same as its rotational frequency. Moreover, the defect length will influence the amplitude and duration of the cylinder-defect pulse waveform. The fault excitation amplitudes increase with the increase of defect depths.

Tornado‐induced vibration assessment of construction elevator attached to high‐rise buildings

SummaryAs one of major construction facilities, the safety concern about elevator outer‐attached to slender high‐rise buildings during construction needs to be seriously addressed. To specifically identify the risk of such slender building–elevator systems in extreme tornado wind field, a safety assessment strategy using the critical velocity envelope is systematically developed. To overcome the difficulties in modeling such building–elevator system, a modified generalized flexural‐shear model developed previously was employed to reach an efficient estimate on the response of a case high‐rise building under simulated tornado wind excitations. To account for the effect of the flexibility of high‐rise building on the response of its attached construction elevator, the response of the elevator was obtained by finite element analysis with applied wind forces, as well as the displacement excitations at its supports with the building. To simulate the typical failure modes of elevator in all states, some critical reference velocity‐based envelopes were generated for the safety assessment where the factors of wind velocity, wind direction, and cage level are systematically addressed. The safety envelopes of the building–elevator system were proved to be instinctively efficient for the assessment of its wind resistance under various scenarios.

Influence of adhesion on oscillatory indentations of viscoelastic biomaterials by a rigid cone

Abstract Steady-state responses in oscillatory indentation tests are widely adopted to evaluate the viscoelastic behavior of cells and tissues. In such tests, the adhesion of biomaterials is commonly neglected, which leads to significant inaccuracy in extracting the mechanical properties. In this article, by introducing the interfacial adhesion described by Lennard-Jones potential, we develop a finite element method to simulate the oscillatory indentation on a viscoelastic half-space. Under a sinusoidal displacement excitation by a rigid cone, it is found that the reaction force evolves sinusoidally at the same frequency but having some phase shift. Interfacial adhesion magnifies the amplitude of force vibration while weakens the average strength. The phase shift is eased in the case of weak adhesion, but turns aggravated once the strength of adhesion exceeds a critical value. The present study can provide guidance for the development of oscillatory indentation tests on viscoelastic materials, and extract more precisely their mechanical properties.

Wide quasi-zero stiffness region isolator with decoupled high static and low dynamic stiffness

Quasi-zero stiffness (QZS) isolators can achieve the two goals of relatively high static and low dynamic stiffness (HSLDS). However, the static and dynamic stiffness of most QZS isolators remains coupled, causing conflicts in optimizing these dual objectives, especially in the case of large displacement excitations and heavy loads, leading to limited performance. To overcome these limitations, this paper presents an isolator with an extended QZS region that allows for the independent design of HSLDS. The positive stiffness provided by the cantilever beam with curve fixture (CBCF) precisely counteracts the negative stiffness offered by a pair of inclined springs, thereby achieving continuous and extensive QZS characteristics from a point to a region. Dynamic equations are established based on the Lagrangian principle and swiftly solved utilizing the Runge-Kutta-4 method. The proposed isolator exhibits a low resonance frequency, and superior performance when exposed to large displacement excitations compared to alternative isolators. Both static and dynamic experiments confirm a QZS region of 0.023 m and resonance frequencies of below 1 Hz. The proposed isolator facilitates effective vibration isolation for ultra-low-frequency and large displacement excitations.

Experiment, Simulation, and Theoretical Investigation of a New Type of Interlayer Connections Enhanced Viscoelastic Damper

A conventional plate-type viscoelastic damper (VED) can easily crack at the interfaces of steel plates and viscoelastic components. In the present work, grooved VEDs, which are a new type of interfacial enhanced VEDs with interfacial grooves, are designed to improve the damping capacity and anti-cracking ability of conventional dampers. The dynamic property experiments of the normal and grooved VEDs are carried out and the interfacial cracking failure of the VEDs are simulated and analyzed by using bilayer cohesive constitutive model with ABAQUS. The grooved VED exhibits excellent dynamic performance and energy dissipation capacity at different temperatures, frequencies, and displacement amplitudes. Experiments and finite element analysis prove that the energy dissipation performance and interfacial bonding strength of the grooved VED are effectively improved. A modified fractional standard linear solid model, in which the Payne effect and temperature–frequency equivalent principle are combined and implemented, is proposed. This model can portray the influence of the excitation displacement, surrounding temperature and external excitation frequency on damper properties at the same time. The fillers and molecular chains affections at micro- and meso-scale are also taken into account. The model’s numerical calculations and experimental results comparisons present that the modified fractional standard linear solid model has sufficient accuracy and performs well in depicting the dynamic properties of the interfacial grooved VED. The errors between the theoretical and experimental values of [Formula: see text] and [Formula: see text] for the grooved VED are mostly within 20% at representative conditions. The interfacial groove structures can well enhance the interfacial bonding and improve the service life of conventional dampers. The modified fractional standard linear solid model is simple and has clear physical meanings for each macro/micro parameters, making it convenient for application in engineering practice. The present research is of great significance in improving the work stability of VEDs and promoting the application of viscoelastic damping technology.

Dual-stage theoretical model of magnetorheological dampers and experimental verification

The theoretical model for predicting the damping characteristics of magnetorheological dampers (MRDs) not only facilitates the optimization of MRD parameters, but also provides assistance for the theoretical design of MRDs. However, some existing models have limitations in fully characterizing the damping characteristics of MRDs. In this paper, the working stage of MRDs was categorized into yield and pre-yield stages based on whether the internal magnetorheological fluid attains the dynamic shear yield state or not, and the Herschel–Bulkley model with pre-yield viscosity (HBPV) and improved polynomial model (IPOL) were employed to respectively characterize the yield and pre-yield stages of MRDs. Subsequently, the HBPV-IPOL model was proposed to characterize the complete damping characteristics of MRDs in low-frequency vibration conditions, with considering the local loss effect of the fluid in the model. To accurately characterize the magnetic induction intensity in the MRD damping channel, employing the steady-state finite element method for magnetic field analysis; on this basis, dividing the damping channel to investigate the variation trends of the magnetic induction intensity in different regions. Simultaneously, the zero-field region hypothesis was proposed to quantitatively consider the influence of minute magnetic induction intensity in the traditional zero-field regions on the damping characteristics of MRDs. Finally, integrating the impact trends of currents in different regions, and employing the HBPV model to determine the impact magnitude of each region within the damping channel on the damping characteristics of the MRD in the yield stage. In the pre-yield stage, polynomial curves were fitted to experimental damping force–velocity curves, and the obtained polynomials were employed to predict the damping characteristics. Extensive experiments have been conducted on MRD samples to assess the predictive performance of the model on MRD damping characteristics under sinusoidal displacement excitation vibration conditions with different excitation currents, vibration frequencies and vibration amplitudes.

Dynamic modeling and force-vibration mapping mechanism construction of rolling bearings considering cage flexibility and local faults

Rolling bearings are one of important components of rotating machinery transmissions and thus its health condition is important for the safety of machinery. Thus, rolling bearing vibration analysis is critical for bearing health condition monitoring. Current bearing vibration analysis ignores multiple compound influencing factors for dynamic modeling. Hence, a more accurate bearing dynamic model, considering multiple factors including cage flexibility, time-varying displacement excitations caused by local defects and elastohydrodynamic (EHD) lubrication, is proposed to accurately reflect force states among bearing elements and vibration responses of bearings. Furthermore, the force states and vibration responses of bearings with localized defects in the proposed model are analyzed in details: (1) the main excitation source of the dynamic model under faulty conditions is identified as the contact force between the rolling element and the raceway by analyzing the vibration signals and main physical variables (the contact forces and the friction forces) in numerical values and change trends; (2) the mapping mechanism between the main excitation source and the vibration response is constructed. The force states among bearing elements are detailedly analyzed in the proposed model and the relationship between the forces and bearing vibration responses is revealed, facilitating the bearing health condition monitoring and vibration control of machinery.

Three-Dimensional Dynamic Modelling and Analysis of a Dual-Cable Winding Hoisting System

In this paper, a three-dimensional dynamic model of a dual-cable winding hoisting system is presented to simulate and analyze its coupled vibrations. The equations of motion of this system are derived based on a substructure method and Lagrange’s equations of the first kind, in which the longitudinal–torsional coupled mechanical characteristics of the hoisting cables are considered. Longitudinal and transverse natural frequencies of the system are obtained and studied, and its dynamic responses due to some assumed displacement excitations are calculated. Numerical results agree well with those from ADAMS simulation, and the results have shown that longitudinal and transverse resonances are inevitable, but the transverse resonance has little effect on the conveyance; Slow longitudinal excitations should be avoided, thus avoiding the first-order longitudinal resonance since the system longitudinal vibration is dominated by its first-order mode; the torque in the hoisting cable is mainly induced by its tension under longitudinal–torsional coupled mechanical characteristics of the cable, and a torque release device is suggested to protect the hoisting cable from torsion failure; Torsional and transverse vibrations of the conveyance are been well restricted by the guiding cables even when the guiding cable pre-tension is zero. The results of this paper can be used to improve the parameter design of the ultra-deep shaft hoisting systems.

Model verification and vibration analysis of the four-disk hollow flexible shaft rotor system

Rotor unbalances failure due to various factors such as manufacturing defects, mounting errors, and material inhomogeneity is inevitable, and will be aggravated by bearing pulse displacement excitation caused by maneuvering flight. Therefore, the purpose of this paper is to study the vibration of the rotor system under disk unbalance forces and bearing pulse displacement excitation. Firstly, the differential equation of motion for four-disk flexible hollow shaft rotor system modeling with a simple finite element model(SFEM) is established by the Lagrangian method in non-inertial systems, and the shaft is modeled using Timoshenko beam theory. Then, the dynamic characteristics of the four-disk flexible hollow shaft rotor are analyzed and compared with the 3D finite element model(3D FEM) to verify the accuracy of the model. To analyze the effects of different disk unbalanced positions and pulse displacement excitation on the vibration characteristics of the rotor, the characteristic vector method and the Runge–Kutta method are used to obtain the steady-state solution and the transient solution, respectively. In addition, the simulation results show that suitable in-shaft damping has a stable effect on the rotor during the start-up. Disk2 and Disk3 are more sensitive to synchronous harmonic excitation and pulse displacement excitation than Disk1 and Disk4. The research of this paper provides an important basis for vibration monitoring and control, and vibration transmission analysis of aero-engine rotor system.

RESEARCH ON FRACTAL HEAT FLOW CHARACTERIZATION OF FINGER SEAL CONSIDERING THE HEAT TRANSFER EFFECT OF CONTACT GAPS ON ROUGH SURFACES

Finger seal is a new flexible dynamic sealing technology, and its heat transfer characteristics and seepage characteristics are one of the main research hotspots. In this paper, based on the fractal theory, a fractal model of the total thermal conductance of the finger seal considering the heat transfer effect of the contact gap of the rough surface is established, a fractal model of the effective gas permeability of the adjacent finger seals annulus considering the gas slip effect and the temperature change is established, and a finite element calculation method of the two-way thermo-mechanical coupling for the finger seal is proposed. The results show that the solid-phase thermal conductance decreases with the increase of the scale coefficient. When the axial pressure difference is greater than 0.4[Formula: see text]MPa, the rotor speed is greater than 11,000[Formula: see text]r/min, the radial displacement excitation is [0.03[Formula: see text]mm, 0.09[Formula: see text]mm], and the temperature is less than 600[Formula: see text]K, the gas-phase thermal conductance between the finger seal and the rotor shows an increasing trend. The gas-phase thermal conductance of the finger seal and the rotor is always the main position under different working conditions. Under different fractal dimensions, the solid-phase thermal conductance gradually occupies the dominant position. Temperature has a certain effect on the effective gas permeability, and fractal dimension, scale coefficient, and axial pressure difference have less effect on the effective gas permeability. At an axial pressure difference of 0.08[Formula: see text]MPa, the numerical calculation results of the two-way thermo-mechanical coupling calculation method for finger seal are closer to the experimental results, with a maximum error rate of 1.96%. The above results further improve the theoretical research system of the heat transfer characteristics of the finger seal.

Cross-well dynamics for vibration energy harvesting of base-excited antisymmetric bi-stable laminate with a point being fixed

The cross-well dynamic of the bi-stable laminates triggered by ambient vibration is a typical nonlinear dynamic, the larger deformation makes the bi-stable laminates attract much attention in vibration energy harvesting. To obtain the performance of cross-well dynamics and vibration energy harvesting of the bi-stable laminate theoretically, a 4-layer harmonic base-excited antisymmetric cross-ply bi-stable laminates with d31 type Marco fiber composite (MFC) for vibration energy harvesting is proposed. The bi-stable laminate is fixed at a chosen point where a base excitation is applied as displacement excitation. The first order shear deformation laminated plate theory (FSDT), geometric nonlinear, and the energy principle are employed to obtain the governing equation of the system in terms of the polynomial coefficients of configuration functions. Two stable configurations are calculated by the principle of minimum potential energy, which is used as the initial state for the energy harvesting analysis. The stable configurations are predicted, and evaluated by comparing them with ABAQUS. The cross-well nonlinear dynamic behaviors and the performance of energy harvesting are analyzed. The effects of excitation level, excitation frequency, and the position of the fixed point on the cross-well dynamics and energy harvest characteristics of the antisymmetric bi-stable laminates are investigated in-depth, and some new aspects are revealed. It demonstrates that the base displacement harmonic excitation can induce chaotic cross-well vibration in a high-frequency band when the fixed point is far away from the center point, the various cross-well vibration of the system is more likely to occur in the dominate-frequency resonant band.

Numerical and experimental investigations on quasi-static component generation of longitudinal wave propagation in isotropic pipes

In this paper, the quasi-static component (QSC) generation of longitudinal waves propagating in an isotropic pipe is investigated numerically and experimentally. The three-dimensional (3D) finite element (FE) simulations are first carried out to gain physical insights into the characteristics of QSC generation from longitudinal wave travelling in an isotropic pipe with weak material nonlinearity. By applying the axial displacement excitation in the FE model, L(0, 1) mode and L(0, 2) mode are excited simultaneously. Then, the generated QSC pulses are extracted using the phase reversal approach for analysis. It is found that the QSC pulses generated by L(0, 2) mode and L(0, 1) mode are L(0, 1) mode. Meanwhile, the shapes of QSC pulses at different locations are extracted and compared. In this study, a data pre-processing method is proposed to handle numerically calculated and subsequent experimentally measured displacement signals, and a nonlinear acoustic parameter is defined to evaluate the incipient damages. After that, an experiment is conducted to measure the QSCs induced by the propagation of longitudinal waves in an aluminum pipe. The experimental results indicate that the propagation of longitudinal waves in the aluminum pipe can induce the QSCs. Different levels of corrosion are created on the surface of the aluminum pipe and are assessed by the generated QSCs. The results show that the nonlinear acoustic parameter has a monotonically increasing trend with the growing severity of corrosion. The QSCs generated by longitudinal wave can be used to detect and evaluate the early-stage surface corrosion in the aluminum pipe.

Influences of inclined crack defects on vibration characteristics of cylindrical roller bearings

Crack initiation and propagation directions on the raceway surface of cylindrical roller bearings (CRBs) can generate different forms of excitation patterns and affect the vibration level of CRBs. For inclined crack defects on the raceway surface, the direction of a roller passing through the cracked raceway determines the order and amplitude of time-varying displacement (TVD) excitation and time-varying stiffness (TVS) excitation. In this study, two different excitation modes are proposed to simulate the interactions between the roller and the raceway. Then, the excitation modes are integrated into the dynamic model of CRB and used to study the effects of crack inclination and propagation direction on the vibration characteristics of CRBs. The results show that the bearing vibration acceleration caused by excitation mode I is greater than that caused by excitation mode II. The distribution direction of the inclined crack defect on the CRB raceway has a great influence on its vibration level. It can provide useful guidance for early bearing fault detection and diagnosis.