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The condition monitoring and fault diagnosis of the rolling bearings of the main fan in the mine are significant to the safety of coal mine production. The existing fault diagnosis methods of rolling bearing have the problems of insufficient training and accuracy when applied directly in actual working conditions. Moreover, the rolling bearings of the mine main fan are in normal operation for a long time, and the number of normal samples is much more than the faulty samples, so there is a sample imbalance problem. Therefore, this paper proposes a fault diagnosis method for rolling bearings of mine main fan based on transfer learning. The method takes the conventional rolling bearing data as the source domain data and the mine main fan rolling bearing data as the target domain data. Firstly, the one-dimensional vibration signal is converted into two-dimensional SDP images using the SDP method, and then the conventional rolling bearing fault diagnosis model is trained using sufficient source domain image samples. After training, the parameters of the diagnostic model are transferred to the mine main fan rolling bearing fault diagnosis model, and the lower layer network is locked and the higher layer network of the model is fine-tuned by the target domain image samples during the transfer process, and finally the mine main fan rolling bearing fault diagnosis model with optimized parameter weights is obtained. Meanwhile, in order to solve the sample imbalance problem, a weighted cross-entropy loss function is added to the model for training, so that the diagnosis model gives higher weights to the fault samples as a minority class and pays more attention to the fault samples in the diagnosis process, thus improving the diagnosis accuracy. In order to verify the effectiveness of the proposed method, this paper uses a conventional rolling bearing fault test bench and the rolling bearing data of the mine main fan fan in actual working conditions for experimental verification. The results show that the proposed method can accurately identify and classify the operating status of the mine main fan rolling bearings, and the accuracy rate is 99.28%.

Given that two-phase closed thermosiphons (TPCT) are a prevalent and efficacious means of heat transfer. However, non-condensable gas (NCG) may potentially impact the heat transfer performance of the aforementioned devices. Nevertheless, the theoretical analysis of heat transfer in TPCT containing NCG is not fully comprehensive and therefore requires further supplementation by means of relevant experiments. This paper presents the development and experimental investigation of a theoretical heat transfer model for a TPCT containing NCG. The research encompasses the optimal fluid-filling ratio of R22 and R410a working fluid and the impact of NCG on heat transfer in the condenser section of TPCT. Experimental findings indicate that TPCT with R22 and R410a working fluids at a fluid-filling ratio of 60% and 50%, respectively, demonstrate excellent isotherm and heat transfer efficiency. The presence of NCG affects the condenser section heat transfer process of the vapor, leading to a 2 °C decrease in the average temperature of the condenser section of the TPCT (Tca). In comparison with the TPCT without NCG, it was observed that an increase in the mass of NCG from 0.0097 to 0.0197 mol resulted in a reduction in the effective length of the condenser section (La) and effective heat transfer rate (κ) of R22 TPCT. The decrease in La was 75.1 mm, while the decrease in κ was 15.02%. Furthermore, at the same NCG mass, the effective heat transfer rate of R410a TPCT is evidently superior to that of R22 TPCT. The NCG in the TPCT can be removed by using a check valve. Nevertheless, this will result in a reduction in the fluid-filling ratio of the TPCT. The temperature of the R410a TPCT containing 0.0197 mol NCG with a fluid-filling ratio of 50% is comparable to that observed in fluid-filling ratio of 40% after the NCG is exhausted.

The large lateral displacement of tail ropes increases the risk of their wear and fracture, posing hidden dangers to the safety of the hoisting system. However, no suitable method is available to recognize the lateral swing of tail ropes online. A target-free visual measurement method, which includes the dual-branch SiamSeg, was proposed in this study. Considering the slender characteristics of tail ropes, the receptive field of the feature extraction network was enhanced via the Receptive Field Module (RFM), thereby strengthening the discriminability and integrity of tail rope features. The consistency loss constraints were added to the segmentation loss function to maximize the time sequence information of the video and further improve the accuracy of pixel-level displacement. Compared with other methods, the proposed approach achieved better segmentation effects. Comparison results synchronously measured by sensors revealed the effectiveness of this method and its potential for practical underground applications.

Rolling bearings are crucial parts of primary mine fans. In order to guarantee the safety of coal mine production, primary mine fans commonly work during regular operation and are immediately shut down for repair in case of failure. This causes the sample imbalance phenomenon in fault diagnosis (FD), i.e., there are many more normal state samples than faulty ones, seriously affecting the precision of FD. Therefore, the current study presents an FD approach for the rolling bearings of primary mine fans under sample imbalance conditions via symmetrized dot pattern (SDP) images, denoising diffusion probabilistic models (DDPMs), the image generation method, and a convolutional neural network (CNN). First, the 1D bearing vibration signal was transformed into an SDP image with significant characteristics, and the DDPM was employed to create a generated image with similar feature distributions to the real fault image of the minority class. Then, the generated images were supplemented into the imbalanced dataset for data augmentation to balance the minority class samples with the majority ones. Finally, a CNN was utilized as a fault diagnosis model to identify and detect the rolling bearings’ operating conditions. In order to assess the efficiency of the presented method, experiments were performed using the regular rolling bearing dataset and primary mine fan rolling bearing data under actual operating situations. The experimental results indicate that the presented method can more efficiently fit the real image samples’ feature distribution and generate image samples with higher similarity than other commonly used methods. Moreover, the diagnostic precision of the FD model can be effectively enhanced by gradually expanding and enhancing the unbalanced dataset.

Healthy operation of the tail rope is crucial to the stable and safe operation of a friction hoisting system. Failure of the tail rope will threaten the property and personnel. In this study, a fault diagnosis algorithm based on deep learning is proposed for the tail rope. Specifically, we add a spatial attention mechanism in the feature extraction stage to assign different weights to different regions in images. This way “guides” the model to focus on more important regions. A class-balance cross-entropy loss is introduced to alleviate the imbalanced data distribution in the actual conditions for enhancing the robustness of the algorithm and its transferability in practical applications. Experimental studies are conducted to validate the algorithm. The accuracy of the algorithm on the conducted dataset is 99.4819%. The accuracy of the provided algorithm is increased by 10% and 7% compared with those of the hand-crafted features, namely, scale-invariant feature transform with support vector machine and random forest, respectively. Results show that the proposed algorithm can meet the requirements of high accuracy and generalization in practical engineering applications.

A novel three-dimensional fractal model for normal contact stiffness is proposed in this paper. First of all, a hypothetical surface based on axisymmetric cosinusoidal asperity is established. Then, based on the hypothetical surface, the analytical expressions for the contact stiffness and contact load are derived by combining the three-dimensional fractal theory with the contact mechanics theory. In addition, the simulation results of the presented model and the Pan model are compared with the experimental results. The comparison results show that the maximum relative error of the Pan model is 29.58%, while the maximum relative error of the presented model is 4.35%. Ultimately, the influence of different fractal parameters on contact stiffness is discussed. Under the same contact load, the normal contact stiffness first increases and then decreases with the increase of the fractal dimension D, while the normal contact stiffness monotonically decreases with the increase of scale coefficient G. The results are explained from the perspective of the shape of the asperity. This study provides a novel model for the calculation of normal contact stiffness, which provides a model basis for the study of contact properties for the mechanical interface.

Rolling bearings are a vital component of mechanical equipment. It is crucial to implement rolling bearing fault diagnosis research to guarantee the stability of the long-term action of mechanical equipment. Conversion of rolling bearing vibration signals into images for fault diagnosis research has been a practical diagnostic approach. The current paper presents a rolling bearing fault diagnosis method using symmetrized dot pattern (SDP) images and a deep residual network with convolutional block attention module (CBAM-DRN). The rolling bearing vibration signal is first visualized and transformed into an SDP image with distinct fault characteristics. Then, CBAM-DRN is utilized to derive characteristics directly and detect faults from the input SDP images. In order to prevent conventional time-frequency images from being limited by their inherent flaws and avoid missing the fault features, the SDP technique is employed to convert vibration signals into images for visualization. DRN enables adequate extraction of rolling bearing fault characteristics and prevents training difficulties and gradient vanishing in deep level networks. CBAM assists the diagnostic model in concentrating on the image’s more distinctive parts and preventing the interference of non-featured parts. Finally, the method’s validity was tested with a composite fault dataset of motor bearings containing multiple loads and fault diameters. The experimental results reflect that the presented approach can attain a diagnostic precision of over 99% and good stability and generalization.

Permanent-magnet couplers are widely used in various industrial applications due to their high functionality and economy. The magnetic field of the magnetic circuit of a permanent-magnet coupler is divided by the segmentation method, by which the magnetoresistance of each area can be calculated. The magnetic resistance of the magnetic flux and the permanent-magnet coupler characteristics outside the magnetic circuit are obtained using the equivalent magnetic circuit model of permanent-magnet couplers. The working point of the permanent magnet is analyzed, and the skin effect is found to be equivalent to a conductor plate with an increase in its resistivity. According to the principle of electromagnetic induction, the ampere force received by each part is calculated. Finally, the theoretical calculation model of the transmitted torque of the permanent-magnet coupler is obtained, and its accuracy is verified by finite element simulation and experiments. This can significantly guide the design and engineering applications of permanent-magnet couplers.

With the continuous progress of modern industry, rotating machinery is gradually developing toward complexity and intelligence. The fault diagnosis technology of rotating machinery is one of the key means to ensure the normal operation of equipment and safe production, which has very important significance. Deep learning is a useful tool for analyzing and processing big data, which has been widely used in various fields. After a brief review of early fault diagnosis methods, this paper focuses on the method models that are widely used in deep learning: deep belief networks (DBN), autoencoders (AE), convolutional neural networks (CNN), recurrent neural networks (RNN), generative adversarial networks (GAN), and transfer learning methods are summarized from the two aspects of principle and application in the field of fault diagnosis of rotating machinery. Then, the commonly used evaluation indicators used to evaluate the performance of rotating machinery fault diagnosis methods are summarized. Finally, according to the current research status in the field of rotating machinery fault diagnosis, the current problems and possible future development and research trends are discussed.

The efficient separation of coal and gangue in the mining process is of great significance for improving coal mining efficiency and reducing environmental pollution. Automatic detection of coal and gangue is the key and foundation for the separation of coal and gangue. In this paper, we proposed a hierarchical framework for coal and gangue detection based on deep learning models. In this framework, the Gaussian pyramid principle is first used to construct multi-level training data, leading to the sets of coal and gangue image features with multiple scales. Then, the coal and gangue regional proposal networks (CG-RPN) are designed to determine the candidate regions of the target objects in the image. Next, convolution neural networks (CNNs) are constructed to recognize coal and gangue objects on the basis of extracted candidate regions. We performed our method on three different datasets. Experimental results showed that the proposed method improves the detection accuracy of coal and gangue objects by 0.8% compared with the previous methods, reaching up to 98.33%. In addition, our proposed method enables the detection of multiple coal and gangue objects in an individual image and solves the problem of queuing requirements in traditional methods.

Identification of bearings’ stiffness and damping coefficients, which strongly affects the dynamic characteristics of rotors, is another inverse problem of Rotor Dynamics. In this paper, aiming at multi-disc and multi-span rotors, two novel algorithms are proposed for identifying each bearing’s coefficients based on the continuous rotor dynamic analysis method. A linear functional relationship between the main complex coefficients and the cross-coupled complex coefficients is obtained, which eliminates the coupling between the coefficients and the rotor unbalance in the forward problem. Then, Algorithm I is proposed. However, it is only suitable for rolling-bearing. To solve the problem, changing the rotating speed slightly is proposed to solve the difficulty that another set of equations cannot be developed because the slope of the proposed linear function is constant when the rotating speed is maintained at a fixed speed. Then, Algorithm II, which can be applied to both rolling-bearing and oil-journal bearing, is provided. Numerical investigations are conducted to study the two methods. It is indicated that there should be a measuring point, called an adjustment point, near each bearing, whose coefficients should be identified, to obtain high identification accuracy. Moreover, the identification accuracy of the two algorithms is strongly related to sensor resolution. When the measuring errors of all the required unbalance responses are zero or the same, the identification errors are almost equal to zero. In conclusion, the proposed algorithms provide a method for monitoring the stiffness and damping coefficients of all bearings in a multi-disc and multi-span rotor under operation conditions to predict rotor dynamic behavior for the safe and steady running of rotating machines.

Continuous rotor dynamics remains stagnant. In this paper, aim at multi-span and multi-disc rotor-bearing system, the continuous rotor dynamic analysis method (CRDAM) is proposed. The force acting on the shaft by the rotating eccentric disc is simulated as a point force. The counterforce of bearing is also considered as a point force. The shaft is considered free-ended. A continuous rotor dynamic model is obtained and an analytical solution is proposed to express the unbalance response as function of the position, unbalance, support stiffness and damping. The proposed method is validated by numerical experiments in which unbalance responses obtained by it are compared with that obtained by the two classical methods the finite element method (FEM) and Ricatti method. The results indicate that the proposed method is applicable to calculating unbalance response of multi-disc and multi-span rotor. Moreover, it is closer to FEM than Ricatti and can be applied to actual high speed rotors. Among the three methods, the calculating speed of Ricatti is the fastest, CRDAM is the second fastest and FEM is the slowest. The proposed method, which solves the forward problems of the continuous rotor dynamics for the multi-disc and multi-span rotors, can provide theoretical basis for further studies on inverse problems such as identification of rotor unbalance and bearing stiffness and damping coefficients without test runs and external excitations.

Rotor unbalance identification plays a critical role in balancing rotors. In this paper, concerned with multi-disc and multi-span rotor-bearing systems, two novel algorithms called the Single Direction Algorithm (SDA) and the Two Orthogonal Direction Algorithm (TODA) are proposed for identifying rotor unbalance from unbalance responses. A matrix method is proposed to solve the problem of the equations being non-linear transcendental, there being too many unknown variables in the equations, and rotor unbalances and bearing coefficients being coupled together. The unbalance responses at all the eccentric discs are necessary for identifying their unbalances. Numerical simulations are conducted to validate the proposed methods. Moreover, an adjustment point is found, and a proper sensor resolution is suggested to achieve high identification accuracy by means of numerical studies. In addition, the identification accuracy of SDA is better than TODA, and SDA is more practical and suitable for medium-speed and high-speed rotors. The proposed algorithms have the flexibility to incorporate any number of bearings and discs and provide a technique for monitoring rotor unbalance without test runs or external exciters.

In the coal mining process, various types of tramp materials will be mixed into the raw coal, which will affect the quality of the coal and endanger the normal operation of the equipment. Automatic detection of tramp materials objects is an important process and basis for efficient coal sorting. However, previous research has focused on the detection of gangue, ignoring the detection of other types of tramp materials, especially small targets. Because the initial Single Shot MultiBox Detector (SSD) lacks the efficient use of feature maps, it is difficult to obtain stable results when detecting tramp materials objects. In this article, an object detection algorithm based on feature fusion and dense convolutional network is proposed, which is called tramp materials in raw coal single-shot detector (TMRC-SSD), to detect five types of tramp materials such as gangue, bolt, stick, iron sheet, and iron chain. In this algorithm, a modified DenseNet is first designed and a four-stage feature extractor is used to down-sample the feature map stably. After that, we use the dilation convolution and multi-branch structure to enrich the receptive field. Finally, in the feature fusion module, we designed cross-layer feature fusion and attention fusion modules to realize the semantic interaction of feature maps. The experiments show that the module we designed is effective. This method is better than the existing model. When the input image is 300 × 300 pixels, it can reach 96.12% MAP and 24FPS. Especially in the detection of small objects, the detection accuracy has increased by 4.1 to 95.57%. The experimental results show that this method can be applied to the actual detection of tramp materials objects in raw coal.

In this paper, to identify the roof unconfined compressive strength (UCS) in the process of coal mine roadway support in real-time and optimize the real-time drilling speed while drilling, this paper proposes and establishes a drilling test method for assessing the uniaxial compressive strength (UCS) of a roof. This method can be used to optimize the speed of drilling. Moreover, a mathematical model of the power output is developed for a roof-strata identification system with a drilling test system. The results were as follows: (1) the system was able to identify the uniaxial compressive strength of roof rock; (2) the pressure of the drill leg of the pneumatic bolt did not match the output power of the pneumatic motor, the pneumatic motor could not reach the maximum power point, and the insufficient thrust of the pneumatic leg led to failure of the maximum output power of the pneumatic motor; (3) to increase the output power of the air motor and thus improve the drilling speed, we applied a booster valve for the system. The experimental results show that the power of the air motor has a linear relationship with drilling speed. In this way, the speed of the drill can be increased by increasing the motor power.

Fault diagnosis plays a very important role in ensuring the safe and reliable operations of machines. Currently, the deep learning-based fault diagnosis is attracting increasing attention. However, fault diagnosis under variable working conditions has been a significant challenge due to the domain discrepancy problem. This problem is also unavoidable in deep learning-based fault diagnosis methods. This paper contributes to the ongoing investigation by proposing a new approach for the fault diagnosis under variable working conditions based on STFT and transfer deep residual network (TDRN). The STFT was employed to convert vibration signal to time-frequency image as the input of the TDRN. To address the domain discrepancy problem, the TDRN was developed in this paper. Unlike traditional deep convolutional neural network (DCNN) methods, by combining with transfer learning, the TDRN can make a bridge between two different working conditions, thereby using the knowledge learned from a working condition to achieve a high classification accuracy in another working condition. Moreover, since the residual learning is introducing, the TDRN can overcome the problems of training difficulty and performance degradation existing in traditional DCNN methods, thus further improving the classification accuracy. Experiments are conducted on the popular CWRU bearing dataset to validate the effectiveness and superiority of the proposed approach. The results show that the developed TDRN outperforms those methods without transfer learning and/or residual learning in terms of the accuracy and feature learning ability for the fault diagnosis under variable working conditions.

Phase change flows between seal faces play an important role in the performance of mechanical seals. Cavitation and boiling phenomena are observed to occur between mechanical seal faces. Most studies on phase change flows in mechanical seals focus on only one phenomenon. However, in different mechanical seal structures, for example, sector-groove seals, cavitation and boiling may appear simultaneously when the temperature and speed are changed. This study contributes to ongoing investigations in the field by proposing a phase change flow model considering both cavitation and boiling in mechanical seals. First, the governing equations and main features of the proposed model are discussed based on the mass conservation law, which is particularly useful in cases where both cavitation and boiling occur. Then, numerical schemes were constructed by employing the liquid volume fraction and analyzed by considering two different forms of fluid flux equations. Case studies of two models, namely, the wavy face seal and hydrostatic seal, were conducted and separately analyzed, and the numerical results demonstrated the feasibility of the proposed model. Then, numerical simulation and experiment of a sector-groove seal were conducted to demonstrate the advantage of the proposed model. The proposed model is especially effective for analyzing the two-phase flow field bounded by complex solid surfaces.

A mine bolter is a fast, safe and economical support equipment, in which the manipulator is the key component for its parallel operation. In this study, the kinematics of mine bolter manipulator is selected as the research object. Aiming at the problem of the dynamic system response estimation of positive solution matrix with uncertain parameters, an interval estimation analysis method based on Chebyshev polynomial is proposed. The response envelope interval of the forward kinematics solution matrix of the manipulator with uncertain parameters is investigated using three types of surrogate models: scanning method, tensor product and collocation method. The feasibility and efficiency of the proposed algorithm are proved by a prototype test. The study of response interval with uncertain parameters has become a new method for predicting the spatial trajectory tracking and location of the manipulator to ensure that its prediction error is minimal.

A novel mobile serial–parallel mechanism with legs for in-pipe use is proposed. The mobile robotic mechanism is composed of two identical three-universal joint–prismatic joint–universal joint parallel mechanisms connected in series and two gripping modules. The proposed parallel mechanism has two rotational freedoms and one translational freedom. In addition, the parallel mechanism can achieve continuous and equivalent rotation. The singularities of the parallel mechanism are analyzed. The overall serial–parallel mechanism has six degrees of freedom, and each gripping module has four degrees of freedom. Each parallel mechanism in the waist module is driven by three servo-electric cylinders and each leg mechanism in the gripping modules is controlled by a linear actuator. The robotic mechanism can perform peristaltic movement and turning in space. The robotic mechanism possesses a simple structure and high flexibility, along with the merits of serial–parallel mechanism. In this article, analytic models for the kinematics and dynamics of the robotic mechanism are derived. Additionally, numerical examples are given, and their solutions are validated based on results obtained by SimMechanics and Adams.

Spring failure is one of the critical causes of the structural damage and low screening efficiency of mining vibrating screens. Therefore, spring failure diagnosis is necessary to prompt maintenance for the safety and reliability of mining vibrating screens. In this paper, a spring failure diagnosis approach is developed. A finite element model of mining vibrating screens is established. Simulations are carried out and the spring failure influence rules of spring failure on the dynamic characteristics of mining vibrating screens are obtained. These influence rules indicate that the amplitude variation coefficients (AVCs) of the four spring seats in the x, y, and z directions can reveal two kinds of single spring failure and four kinds of double spring failure, which are useful for diagnosing spring failure. Furthermore, experiments are conducted. Comparison analyses of the experimental results and simulation results indicate that the proposed approach is capable of revealing various kinds of spring failure. Therefore, this approach provides useful information for diagnosing spring failure and guiding technical staff to routinely maintain mining vibrating screens.

Springs are critical components in mining vibrating screen elastic supports. However, long-term alternating loads are likely to lead to spring failures, likely resulting in structural damages to the vibrating screen and resulting in a lower separation efficiency. Proper dynamic models provide a basis for spring failure diagnosis. In this paper, a six-degree-of-freedom theoretical rigid body model of a mining vibrating screen is proposed, and a dynamic equation is established in order to explore the dynamic characteristics. Numerical simulations, based on the Newmark-β algorithm, are carried out, and the results indicate that the model proposed is suitable for revealing the dynamic characteristics of the mining vibrating screen. Meanwhile, the mining vibrating screen amplitudes change with the spring failures. Therefore, six types of spring failure are selected for simulations, and the results indicate that the spring failures lead to an amplitude change for the four elastic support points in the x, y, and z directions, where the changes depend on certain spring failures. Hence, the key to spring failure diagnosis lies in obtaining the amplitude change rules, which can reveal particular spring failures. The conclusions provide a theoretical basis for further study and experiments in spring failure diagnosis for a mining vibrating screen.

This paper presents a method for calculating the health degree (HD) of a braking system of a mine hoist combined with three-level fuzzy comprehensive assessment (TLFCA) and a back-propagation neural network (BPNN). Firstly, the monitored values of a sensor are fused by multi-time fusion and the fuzzy comprehensive assessment values (FCAVs) of the health condition (HC) of the sensor are obtained. Secondly, the FCAVs of all sensors in a subsystem are fused by multi-sensor fusion, and FCAVs of the subsystem are obtained. Then the FCAVs of all subsystems are fused by multi-subsystem fusion and FCAVs of the system are obtained. All the FCAVs are fed into a pre-trained neural network, and the corresponding HD of the sensor, subsystem and system is obtained. Finally, the practicability, reliability and sensitivity of the proposed method are verified by the monitored values of the test rig. This paper presents a method to provide technical support for intelligent maintenance, and also provides necessary data for further prognostics health management (PHM) of the braking system. The method presented in this paper can also be used as a reference for the HD calculation of the whole hoist and other complicated equipment.

The central groove is a key component of armored face conveyor. Failure of welded joints in the central groove often occurs in engineering. In this article, the welding procedure parameters were analyzed to the improve strength and toughness of the dissimilar steel weld joint in the central groove. First, four types of super-high wear-resistant steel and two types of high-strength welding wire were chosen as the welding materials. Carbon equivalent method, cold crack sensitivity index method, and maximum hardness of heat-affected zone test were applied to analyze their welding properties. Second, to improve their weldability, the proper preheating temperature was determined using Y-groove cracking test and mechanical property tests. Finally, a semi-automatic CO 2 welding method was adopted, and a second mechanical property test was conducted to determine the proper welding wire. Results show that the chosen steels have poor weldability and cold cracking sensitivity. Preheating must be used to prevent cold cracking. When the preheating temperature is higher than 80°C, the cold crack rate can be controlled to under 20%, which can satisfy application requirements. Welding wire YMGR76 is appropriate. Using YMGR76, the preheating temperature drops to 120°C, and the strength and toughness of the weld joint are improved to 813 MPa and 112 KV 2 /J, respectively. This study provides a welding procedure to improve the reliability of the central groove.

As a basic mechanical component, the sealing ring is widely used in industrial, aerospatial, and other fields. In this study, an elastic metal C-shaped sealing ring with a wave structure was taken as an example, and its performance was analyzed theoretically and measured experimentally. First, an experimental study was performed on the C-ring seal. The proposed method for experimental measurement of the contact stress of the C-ring seal involved innovative use of a universal electronic testing machine and pressure sensitive paper, in conjunction with the hue⁻saturation⁻brightness (HSB) method. Based on the discoloration of the pressure sensitive paper after contact stress, computer software was used for analysis, the discoloration was digitized, and the contact stress was established. Second, a theoretical calculation model of the C-ring seal was established using ANSYS software, and a finite element theoretical calculation of the mechanical properties of the sealing ring was established. Finally, the contact stress results were compared with the model calculation results of the C-ring seal. The error between the two was small (4.8%), which proved the validity of the calculation model and the scientificity of the experimental method.

Rolling bearings are important components of rotating machines. For their preventive maintenance, it is not enough to know whether there is any fault or the fault type. For an effective maintenance, a fault severity monitoring needs to be conducted. Currently, the bearing fault diagnosis method based on time–frequency image (TFI) recognition is attracting increasing attention. This paper contributes to the ongoing investigation by proposing a new approach for the fault severity monitoring of rolling bearings based on the texture feature extraction of sparse TFIs. The first and main step is to obtain accurate TFIs from the vibration signals of rolling bearings. Traditional time–frequency analysis methods have disadvantages such as low resolution and cross-term interference. Therefore, the TFIs obtained cannot satisfactorily express the time–frequency characteristics of bearing vibration signals. To solve this problem, a sparse time–frequency analysis method based on the first-order primal-dual algorithm (STFA-PD) was developed in this paper. Unlike traditional time–frequency analysis methods, the time–frequency analysis model of the STFA-PD method is based on the theory of sparse representation, and is solved using the first-order primal-dual algorithm. For employing the sparse constraint in the frequency domain, the STFA-PD obtains a higher time–frequency resolution and is free from cross-term interference, as the model is based on a linear time–frequency analysis method. The gray level co-occurrence matrix is then employed to extract texture features from the sparse TFIs as input features for classifiers. Vibration signals of rolling bearings with different fault severity degrees are used to validate the proposed approach. The experimental results show that the developed STFA-PD outperforms traditional time–frequency analysis methods in terms of the accuracy and effectiveness for the fault severity monitoring of rolling bearings.