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14 pages, 5944 KiB

Open AccessArticle

Visualized Stacked Denoising Auto-Encoder Model for Extracting and Evaluating the State Features of Rolling Bearings

by Qing Zhang, Junshen Zhang, Ye Wang and Lie Chen

Machines 2022, 10(10), 849; https://doi.org/10.3390/machines10100849 - 23 Sep 2022

Cited by 2 | Viewed by 1482

Abstract

Extracting intuitive operating state features from vibration signals without prior knowledge is a prospective requirement for health monitoring and fault diagnosis in bearings. In this paper, a visualized stacked denoising auto-encoder (VSDAE) model is proposed for the unsupervised extraction and quantitative evaluation of [...] Read more.

Extracting intuitive operating state features from vibration signals without prior knowledge is a prospective requirement for health monitoring and fault diagnosis in bearings. In this paper, a visualized stacked denoising auto-encoder (VSDAE) model is proposed for the unsupervised extraction and quantitative evaluation of bearings’ state features. First, the stacked denoising auto-encoder (SDAE) was used to reconstruct vibration signals. The intermediate vector of the SDAE, which is a high-information-density representation of vibration signals, was regarded as the pending state feature. Then, the dimension of the intermediate vector was reduced by the t-distributed stochastic neighbor embedding (t-SNE) method to the two-dimensional visualization space. Finally, the silhouette coefficient of feature distribution was calculated to quantitatively evaluate the extracted features. The proposed model was evaluated using experimental bearing signals simulating various operating states. The results proved that the features, extracted and evaluated by the VSDAE, allowed the recognition of the operating states of the examined bearings. Full article

(This article belongs to the Special Issue Rolling Bearing and Rotor System Modeling and Simulation, Monitoring and Control, and Performance Diagnosis)

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12 pages, 6030 KiB

Open AccessArticle

Investigation on the Cage Whirl State of Cylindrical Roller Bearings under High Speed and Light Load

by Jiaming Zhang, Ming Qiu, Yanfang Dong, Xiaoxu Pang, Junxing Li and Chuanmeng Yang

Machines 2022, 10(9), 768; https://doi.org/10.3390/machines10090768 - 2 Sep 2022

Cited by 5 | Viewed by 1902

Abstract

This paper explores the cage whirl state under different operating conditions based on the cylindrical roller bearing dynamics model. The stability and whirl characteristics of the cage whirl are evaluated by considering the rotation and force of the cage and roller. The results [...] Read more.

This paper explores the cage whirl state under different operating conditions based on the cylindrical roller bearing dynamics model. The stability and whirl characteristics of the cage whirl are evaluated by considering the rotation and force of the cage and roller. The results demonstrate that the cage whirl state is divided into three types according to the cage whirl orbit: disordered whirl, local periodic whirl and regular circular whirl. With disordered whirl, the whirl speed and whirl radius of the cage are unpredictable, and the force of the cage changes frequently. With local periodic whirl, the rotation speed, whirl speed and the force on the cage change periodically or stay constant. In the case of a regular circular whirl, the force on the cage should be considered to evaluate the stability of the cage whirl. In addition, the collision force between the roller and cage determines whether the cage whirl speed is stable or not, and the bearing slipping has no obvious effect on cage whirl stability. Full article

(This article belongs to the Special Issue Rolling Bearing and Rotor System Modeling and Simulation, Monitoring and Control, and Performance Diagnosis)

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19 pages, 4756 KiB

Open AccessArticle

Fault Diagnosis of Rolling Bearings Based on Variational Mode Decomposition and Genetic Algorithm-Optimized Wavelet Threshold Denoising

by Can Hu, Futang Xing, Shuhan Pan, Rui Yuan and Yong Lv

Machines 2022, 10(8), 649; https://doi.org/10.3390/machines10080649 - 4 Aug 2022

Cited by 14 | Viewed by 1933

Abstract

Fault diagnosis of rolling bearings can be a serious challenge, as rolling bearings often work under complex conditions and their vibration signals are typically nonlinear and nonstationary. This paper proposes a novel approach to diagnosing faults of rolling bearings based on variational mode [...] Read more.

Fault diagnosis of rolling bearings can be a serious challenge, as rolling bearings often work under complex conditions and their vibration signals are typically nonlinear and nonstationary. This paper proposes a novel approach to diagnosing faults of rolling bearings based on variational mode decomposition (VMD) and genetic algorithm-optimized wavelet threshold denoising. First, VMD was used to decompose the vibration signals of faulty rolling bearings into a series of band-limited intrinsic mode functions (BLIMFs). During the decomposition, the parameters of VMD were selected by Kullback–Leibler (K–L) divergence. Then, the effective BLIMFs were determined by the analysis of their correlation coefficients and variance contributions. Finally, genetic algorithm-optimized wavelet threshold denoising was proposed to optimize the selection of important parameters, and the optimized threshold function used not only ensures the continuity of the threshold function but also avoids the fixed deviation of the soft threshold. The validity and superiority of the proposed approach were verified by theoretical calculations, numerical simulations and application studies. The results indicate that the proposed approach is promising in fault diagnosis of rotary machinery. Full article

(This article belongs to the Special Issue Rolling Bearing and Rotor System Modeling and Simulation, Monitoring and Control, and Performance Diagnosis)

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17 pages, 4027 KiB

Open AccessArticle

Modeling and Fault Size Estimation for Non-Penetrating Damage in the Outer Raceway of Tapered Roller Bearing

by Wei Kang, Yongsheng Zhu, Ke Yan, Yuwei Liu, Dawei Gao and Zhijun Ren

Machines 2022, 10(7), 516; https://doi.org/10.3390/machines10070516 - 26 Jun 2022

Cited by 2 | Viewed by 1975

Abstract

The fault quantification of a tapered roller bearing (TRB) can provide a reliable guide for predictive maintenance. Currently, damage size estimation based on vibration signals has been proposed and developed. However, most approaches are focused on the theory of ball bearings. Unlike the [...] Read more.

The fault quantification of a tapered roller bearing (TRB) can provide a reliable guide for predictive maintenance. Currently, damage size estimation based on vibration signals has been proposed and developed. However, most approaches are focused on the theory of ball bearings. Unlike the point contact of a ball bearing, the contact between the tapered roller and the raceway is a line contact. So, the current practices based on the micro-motion theory of ball bearings are limited when estimating the TRB’s fault. To accurately estimate the TRB’s damage size, a dynamic model of non-penetrating damaged TRB was established to research the vibration response mechanism and explain the influence. The model takes the deflection factor of a tapered roller into consideration and uses the elastohydrodynamic lubrication model to simulate the influence of the lubrication factor. Then, a revised formula for estimating the TRBs’ fault size is proposed by uncovering the relationship between the impact time and the damage location. Simulation analysis and experimental analysis prove the correctness of the dynamic model and the effectiveness of the size estimation formula. Full article

(This article belongs to the Special Issue Rolling Bearing and Rotor System Modeling and Simulation, Monitoring and Control, and Performance Diagnosis)

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14 pages, 13588 KiB

Open AccessArticle

Effect of Strain Hardening and Ellipticity on Elastic–Plastic Contact Behaviour between Ellipsoids and Rigid Planes

by Jian Chen, Wangyang Zhang, Chenglong Wang, Di Liu and Linbo Zhu

Machines 2022, 10(6), 488; https://doi.org/10.3390/machines10060488 - 17 Jun 2022

Cited by 4 | Viewed by 2341

Abstract

The contact behaviour between an ellipsoid and a rigid plane is significant in research on bearing and assembly joint surfaces. However, an empirical relationship between an elastic–plastic ellipsoid and a rigid plane has not been established. In this study, the elastic–plastic contact behaviour [...] Read more.

The contact behaviour between an ellipsoid and a rigid plane is significant in research on bearing and assembly joint surfaces. However, an empirical relationship between an elastic–plastic ellipsoid and a rigid plane has not been established. In this study, the elastic–plastic contact behaviour between a deformable ellipsoid and a rigid plane was investigated by establishing a new finite element model. The proposed elastic–plastic ellipsoid contact model was designed considering the effects of the ellipticity and strain-hardening rate of the ellipsoid. The strain-hardening rate and ellipticity of the ellipsoid affected the contact area, load and mean pressure. Furthermore, the effect gradually increased with an increase in interference. New dimensionless empirical formulas for determining the contact load and contact area were proposed based on the analysis. The proposed model was validated by comparing the obtained results with previous experimental results and those of theoretical models. This study can be used to predict the elastic–plastic contact parameters between a single ellipsoid and a rigid body, such as bearings, gears and cams. It can also be used to investigate the elastic–plastic contact behaviour between anisotropic rough surfaces composed of asperities with different radii of curvature. Full article

(This article belongs to the Special Issue Rolling Bearing and Rotor System Modeling and Simulation, Monitoring and Control, and Performance Diagnosis)

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19 pages, 6976 KiB

Open AccessArticle

Improved DBSCAN Spindle Bearing Condition Monitoring Method Based on Kurtosis and Sample Entropy

by Yanfei Zhang, Yunhao Li, Lingfei Kong, Qingbo Niu and Yu Bai

Machines 2022, 10(5), 363; https://doi.org/10.3390/machines10050363 - 10 May 2022

Cited by 6 | Viewed by 1933

Abstract

An improved density-based spatial clustering of applications with noise (IDBSCAN) analysis approach based on kurtosis and sample entropy (SE) is presented for the identification of operational state in order to provide accurate monitoring of spindle operation condition. This is because of the low [...] Read more.

An improved density-based spatial clustering of applications with noise (IDBSCAN) analysis approach based on kurtosis and sample entropy (SE) is presented for the identification of operational state in order to provide accurate monitoring of spindle operation condition. This is because of the low strength of the shock signal created by bearing of precision spindle of misalignment or imbalanced load, and the difficulties in extracting shock features. Wavelet noise reduction begins by dividing the recorded vibration data into equal lengths. Features like kurtosis and entropy in the frequency domain are used to generate feature vectors that indicate the bearing operation state. IDBSCAN cluster analysis is then utilized to establish the ideal neighborhood radius (Eps) and the minimum number of objects contained within the neighborhood radius (MinPts) of the vector set, which are combined to identify the bearing operating condition features. Finally, utilizing data from the University of Cincinnati, the approach was validated and assessed, attaining a condition detection accuracy of 99.2%. As a follow-up, the spindle’s vibration characteristics were studied utilizing an unbalanced bearing’s load bench. Bearing state recognition accuracy was 98.4%, 98.4%, and 96.7%, respectively, under mild, medium, and overload circumstances, according to the results of the experimental investigation. Moreover, it shows that conditions of bearings under various unbalanced loads can be precisely monitored using the proposed method without picking up on specific sorts of failures. Full article

(This article belongs to the Special Issue Rolling Bearing and Rotor System Modeling and Simulation, Monitoring and Control, and Performance Diagnosis)

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19 pages, 15382 KiB

Open AccessArticle

Influence of Fit Clearance and Tightening Torque on Contact Characteristics of Spindle–Grinding Wheel Flange Interface

by Qianqian Yuan, Yongsheng Zhu, Ke Yan and Xinzhuo Zhang

Machines 2022, 10(5), 298; https://doi.org/10.3390/machines10050298 - 22 Apr 2022

Viewed by 2442

Abstract

The spindle and grinding wheel flange (GWF) adopt double positioning of a tapered surface and end face. Due to the processing quality, the contact state of the spindle–GWF interface cannot be determined accurately. Based on the theory of finite element and the Yoshimura [...] Read more.

The spindle and grinding wheel flange (GWF) adopt double positioning of a tapered surface and end face. Due to the processing quality, the contact state of the spindle–GWF interface cannot be determined accurately. Based on the theory of finite element and the Yoshimura integral method, an analysis method for the contact stiffness of the spindle–GWF interface was established. In addition, the effects of the spindle–GWF interface’s original clearance and tightening torque on the contact pressure, final contact state and contact stiffness of the spindle–GWF interface were investigated and experimentally verified. It was found that the final contact state of the spindle–GWF changed when the tightening torque increased, especially when the original contact state was tapered contact, and the final contact state changed significantly after assembly. The contact pressure and contact stiffness of the spindle–GWF interface are increased by increasing the tightening torque. The radial stiffness is more affected by the end clearance variation compared to the axial and angular stiffness. When the original contact state is tapered contact, the radial stiffness of the interface is at maximum in three contact states. This research provides theoretical guidance for GWF assembly on gear-grinding machines. Full article

(This article belongs to the Special Issue Rolling Bearing and Rotor System Modeling and Simulation, Monitoring and Control, and Performance Diagnosis)

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21 pages, 5279 KiB

Open AccessEditor’s ChoiceArticle

Analytical Determination and Influence Analysis of Stiffness Matrix of Ball Bearing under Different Load Conditions

by Qingbo Niu, Yeteng Li, Yongsheng Zhu, Shiyuan Pei, Yanjing Yin and Dongfeng Wang

Machines 2022, 10(4), 238; https://doi.org/10.3390/machines10040238 - 28 Mar 2022

Cited by 3 | Viewed by 3707

Abstract

Bearing stiffness, as one of the most important service characteristics for ball bearing, plays a crucial role in the bearing design and rotor dynamic analysis. To rapidly and accurately calculate the stiffness matrix of ball bearing under the arbitrary load conditions, a 5-DOF [...] Read more.

Bearing stiffness, as one of the most important service characteristics for ball bearing, plays a crucial role in the bearing design and rotor dynamic analysis. To rapidly and accurately calculate the stiffness matrix of ball bearing under the arbitrary load conditions, a 5-DOF analytical model for bearing stiffness matrix analysis has been established by the ball–raceway contact analysis, implicit/explicit differential method, and matrix operations. The model has been validated comparing with the previous methods and experimental results. Based on this, the model has been used to investigate the influences of the load and operation conditions, the structural parameters variation on stiffness of ball bearing. The results show that property increasing axial preload can inhibit the attenuation of speed-varying stiffness, and the contact states between balls and raceways also have significant influence on the change in the stiffness of ball bearings. Besides, a larger curvature coefficient of inner raceway and a small curvature coefficient of outer raceway can effectively improve the stiffness of ball bearing at high speed. Therefore, the proposed method can be a useful tool in bearing optimize design and performance analysis of ball and rotor system under various load conditions. Full article

(This article belongs to the Special Issue Rolling Bearing and Rotor System Modeling and Simulation, Monitoring and Control, and Performance Diagnosis)

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Review

Jump to: Research

23 pages, 2828 KiB

Open AccessReview

A Review of Key Technologies for High-Speed Motorized Spindles of CNC Machine Tools

by Ye Dai, Xueshi Tao, Zhaolong Li, Shiqiang Zhan, Yang Li and Yanhua Gao

Machines 2022, 10(2), 145; https://doi.org/10.3390/machines10020145 - 17 Feb 2022

Cited by 14 | Viewed by 9846

Abstract

The high-speed and high-precision motorized spindle is the future development trend of the CNC machine tool field, and has become the focus of research in the world. High-speed motorized spindles tend to develop in the direction of high precision, high speed, low energy [...] Read more.

The high-speed and high-precision motorized spindle is the future development trend of the CNC machine tool field, and has become the focus of research in the world. High-speed motorized spindles tend to develop in the direction of high precision, high speed, low energy consumption, high efficiency, and high reliability. We undertake a through, systematic review of the development history perspective of the research on precision bearing technology, dynamic balancing technology, thermal error measurement and compensation technology with regard to the key technologies of high-speed motorized spindles. On this basis, the current level of development of key technologies for high-speed motorized spindles is analyzed, and the objective advantages and disadvantages of existing technologies are summarized. Finally, the development tendency of high-speed motorized spindle technology is predicted and foreseen. Full article

(This article belongs to the Special Issue Rolling Bearing and Rotor System Modeling and Simulation, Monitoring and Control, and Performance Diagnosis)

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