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Keywords = generalized Hertz contact theory

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12 pages, 3434 KiB  
Article
Experimental Study on the Dynamic Impact Characteristics of Iron Ore Under Free-Fall Conditions
by Zhongxin Wang, Bo Song, Yangyang Yi, Jianhua Hu, Hui Wang, Chang Liu and Xiangsen Li
Minerals 2025, 15(1), 29; https://doi.org/10.3390/min15010029 - 29 Dec 2024
Viewed by 909
Abstract
Ore processing equipment is constantly subjected to impacts from various types of ore. However, the impact force characteristics generated by ore particles of different masses have not been thoroughly studied, which has hindered the design and monitoring of such equipment. This paper presents [...] Read more.
Ore processing equipment is constantly subjected to impacts from various types of ore. However, the impact force characteristics generated by ore particles of different masses have not been thoroughly studied, which has hindered the design and monitoring of such equipment. This paper presents an experimental study on the dynamic impact characteristics of iron ore particles under free–fall conditions. The research focuses on understanding the mechanical behavior of ore particles of varying sizes and weights when colliding with metallic components, particularly crushers, which are critical in the ore processing industry. A modified Split Hopkinson Pressure Bar apparatus was utilized to measure the impact forces, durations, and deformation patterns during collisions. Two types of fired iron ore pellets were collected from industrial plants and sorted into different mass ranges for testing. The pellets were dropped from a height of 1 m to impact a steel rod, and the resulting impact forces were recorded using strain gauges. Additionally, finite element simulations were conducted to validate the experimental methodology. The results revealed significant variations in impact force, duration, and deformation patterns, influenced by particle mass and impact position. The maximum recorded impact force was approximately 7500 N, indicating the high energy involved in these collisions. Impact durations ranged from 0.05 to 0.11 milliseconds, emphasizing the rapid nature of the interactions. The deformation patterns were consistent across all particles, supporting the applicability of Hertz’s contact theory.This study offers valuable insights into the dynamic impact characteristics of iron ore particles, which are essential for optimizing the design and performance of mining machinery. Full article
(This article belongs to the Section Mineral Processing and Extractive Metallurgy)
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23 pages, 5711 KiB  
Article
Modeling and Dynamic Analysis of Double-Row Angular Contact Ball Bearing–Rotor–Disk System
by Haibiao Zhang, Zhen Li, Haijian Liu, Tao Liu and Qingshan Wang
Lubricants 2024, 12(12), 441; https://doi.org/10.3390/lubricants12120441 - 10 Dec 2024
Cited by 2 | Viewed by 1160
Abstract
This article presents a general numerical method to establish a mathematical model of a bearing–rotor–disk system. This mathematical model consists of two double-row angular contact ball bearings (DRACBBs), a rotor and a rigid disk. The mathematical model of the DRACBB is built on [...] Read more.
This article presents a general numerical method to establish a mathematical model of a bearing–rotor–disk system. This mathematical model consists of two double-row angular contact ball bearings (DRACBBs), a rotor and a rigid disk. The mathematical model of the DRACBB is built on the basis of elastic Hertz contact by adopting the Newton Raphson iteration method, and three different structure forms are taken into account. The rotor is modeled by employing a finite element method in conjunction with Timoshenko beam theory, and the rigid disk is modeled by applying the lumped parameter method. The mathematical model of the bearing–rotor–disk system is constructed by the coupling of the bearing, rotor and disk, and the dynamic response of the bearing–rotor–disk system can be solved by employing the Newmark-β method. The validation of the above mathematical model is demonstrated by comparing the proposed results with the results from the existing literature and finite element software. The dynamic characteristics of the DRACBBs and the dynamic response of the bearing–rotor–disk system are investigated by parametric study. A dynamic characteristic analysis of the DRACBB is conducted to ensure the optimal structure form of the DRACBB under complex external loads, and it can provide a reference for the selection of the structural forms of DRACBBs. Full article
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16 pages, 10203 KiB  
Article
Dynamic Analysis of Train–Bridge Coupling System for a Long-Span Railway Suspension Bridge Subjected to Strike–Slip Fault
by Sijie Chen, Wei Kang, Jian Yang, Shengyong Dai, Shixiong Zheng and Hongyu Jia
Appl. Sci. 2023, 13(18), 10422; https://doi.org/10.3390/app131810422 - 18 Sep 2023
Cited by 3 | Viewed by 2012
Abstract
Long-span railway bridges crossing active faults are more vulnerable owing to the joint combination of pulse ground motions and surface dislocation. To study the dynamic effects resulting from the coupling of long-span railway suspension bridges crossing strike–slip fault and trains, a nonlinear model [...] Read more.
Long-span railway bridges crossing active faults are more vulnerable owing to the joint combination of pulse ground motions and surface dislocation. To study the dynamic effects resulting from the coupling of long-span railway suspension bridges crossing strike–slip fault and trains, a nonlinear model in which wheel–rail contact was established based on Hertz’s nonlinear theory and Kalker creep theory. To generate the ground motions across strike–slip fault, an artificial synthetic method, which considers both the fling-step effect with a single pulse and the directivity effect with multiple pulses, is employed. The effects of fault-crossing angles (FCAs) and permanent ground rupture displacements (PGRDs) are systematically investigated based on wheel–rail dynamic (derailment coefficient, lateral wheel–rail force, and wheel–load reduction rate). Conclusions are drawn and can be applied in the practical seismic design and train running safety assessment of long-span railway suspension bridges crossing strike–slip fault. Full article
(This article belongs to the Section Civil Engineering)
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27 pages, 7851 KiB  
Article
Experimental and Numerical Study on Stress Distribution Characteristics of Traveling Wave Resonance of High-Speed Bevel Gear in Aero-Engine
by Xiaochi Luan, Yuhan Gao, Zhenpeng Zhang, Yundong Sha and Gongmin Liu
Appl. Sci. 2023, 13(3), 1814; https://doi.org/10.3390/app13031814 - 31 Jan 2023
Cited by 6 | Viewed by 2459
Abstract
Gear failure caused by traveling wave resonance (TWR) generally occurs quite suddenly and causes catastrophic results in aero-engines. In this study, the TWR characteristics and stress distribution characteristics of a high-speed bevel gear in an aero-engine are analyzed in detail by means of [...] Read more.
Gear failure caused by traveling wave resonance (TWR) generally occurs quite suddenly and causes catastrophic results in aero-engines. In this study, the TWR characteristics and stress distribution characteristics of a high-speed bevel gear in an aero-engine are analyzed in detail by means of experiments and simulations. Based on the acoustic waveguide system and dynamic stress test system, the TWR fatigue failure monitoring experiment of the central drive bevel gear in an aero-engine is carried out, and the TWR frequency, dangerous speed, dynamic stress and fatigue fracture characteristics of a driven bevel gear are obtained. Based on the transient dynamic analysis method and Hertz contact theory, the stress distribution characteristics of the driven bevel gear, which cannot be obtained in the test under the condition of TWR, are analyzed. The influence of the changes in the working temperature and the thickness of the spoke on the TWR characteristics and the stress distribution characteristics are discussed. The simulation and test results show that the gear has the problem of stress concentration at the root of the tooth and the back of the spoke plate under the 4th node-diameter (ND) TWR, and the stress distribution form is consistent with the fracture form of the test gear, covering 12 teeth. The relationship between the stress at the test monitoring point and the maximum stress at the tooth root is obtained, and the generality of the relationship is verified. Based on this relationship, the maximum stress of tooth root, which is difficult to monitor in the test, is predicted to be 1271.7 MPa. An accurate and convenient means to obtain the maximum stress at the tooth root of the central transmission bevel gear under TWR is obtained so as to provide a basis for failure cause analysis and central transmission bevel gear design and lay the foundation for future research focusing on the propagation of the gear under TWR conditions. Full article
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15 pages, 5015 KiB  
Article
Experimental Study on Pot Damage and Contact Stress Distribution Characteristics of Oil Sunflower Plug Seedlings
by Fandi Zeng, Xuying Li, Hongbin Bai, Ji Cui, Xuening Liu and Yongzhi Zhang
Appl. Sci. 2022, 12(21), 10889; https://doi.org/10.3390/app122110889 - 27 Oct 2022
Cited by 5 | Viewed by 1818
Abstract
To reveal the collision damage mechanisms of plug seedlings and improve the quality of seedlings, the kinetics equations of the plug seedlings were established based on the generalized Hertz-theory. The influence laws of different factors on pot damage were obtained through a drop [...] Read more.
To reveal the collision damage mechanisms of plug seedlings and improve the quality of seedlings, the kinetics equations of the plug seedlings were established based on the generalized Hertz-theory. The influence laws of different factors on pot damage were obtained through a drop impact test. The Tekscan pressure distribution measurement system measured the collision impact force, and the orthogonal tests were conducted. The test showed that the influence of the collision impact force was on the order of plug specification > drop height > contact material. The Tekscan pressure distribution measurement system measured the change law of contact stress distribution under significant influencing factors. The test results showed that the collision contact area between the plug seedlings and contact materials from large to small was soil, steel, and ABS plastic. The collision contact area between the plug seedlings and other plug specifications was 50 plug, 72 plug, and 105 plug from the largest to the smallest. When the plug seedlings collided with contact materials, the average contact stress between the seedlings and the steel plate ranged from 19.4 kPa to 22.8 kPa. When the plug seedlings of various sizes collided with steel plates, the average contact stress was ordered as 105 plug, 72 plug and 50 plug in descending order. A linear regression model between collision impact force and matrix loss rate under different factors was established based on the pressure data collected by the Tekscan pressure distribution measurement system. This study provides a basis for exploring the impact damage mechanisms of plug seedlings and improving the seedling quality. Full article
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23 pages, 7140 KiB  
Article
The Mechanical Structure Contact Mechanism Analysis Considering Modified Tangential Stiffness with Friction’s Effect
by Zhiyang Niu, Bing Chen, Hongwei Chen, Jiawei Hao, Junde Qi and Mingwei Wang
Appl. Sci. 2022, 12(9), 4658; https://doi.org/10.3390/app12094658 - 6 May 2022
Cited by 3 | Viewed by 2883
Abstract
This paper proposes a modified tangential contact stiffness model considering friction’s effect, which is the first key step to establish the dynamic model of the fixture-workpiece system, and this is the foundation of vibration suppression for the manufacturing process of aerospace blades. According [...] Read more.
This paper proposes a modified tangential contact stiffness model considering friction’s effect, which is the first key step to establish the dynamic model of the fixture-workpiece system, and this is the foundation of vibration suppression for the manufacturing process of aerospace blades. According to Love’s elastic deformation, the model’s derivation process starts with the potential function in each coordinate axis’s direction respectively. The generalized Hertz contact theory is employed to calculate the contact forces in this model. The symmetrical characteristic of the contact area has simplified the derivation process to obtain the eventual tangential contact stiffness model. A validation experiment focusing on a tangential stiffness measuring is achieved by putting two spherical objects in contact together to get the tangential contact stiffness. Based on the data collected in this experiment, a comparison with a most similar existed model is carried out, and the result shows that the relative error of this modified model are all less than 10%, while the original model’s (the most similar model) relative error exceeding 50% captures more than 3/4 of the 30 data sets randomly selected in each experiment group, and that means the modification of this paper brings great improvement to the contact stiffness model. Full article
(This article belongs to the Section Mechanical Engineering)
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18 pages, 4930 KiB  
Article
Study on Permeability Characteristics of Rocks with Filling Fractures Under Coupled Stress and Seepage Fields
by Zhende Zhu, Zihao Niu, Xiangcheng Que, Cheng Liu, Yanxin He and Xinghua Xie
Water 2020, 12(10), 2782; https://doi.org/10.3390/w12102782 - 6 Oct 2020
Cited by 14 | Viewed by 3780
Abstract
Infilling fractured rock masses are widely distributed in the deeply buried oil reservoirs and surrounding rocks of mine caves. The internal filling material has a great influence on the mechanical properties and seepage characteristics of fractured rock mass. In this paper, through theories [...] Read more.
Infilling fractured rock masses are widely distributed in the deeply buried oil reservoirs and surrounding rocks of mine caves. The internal filling material has a great influence on the mechanical properties and seepage characteristics of fractured rock mass. In this paper, through theories and experiments, the mechanism of permeability changes of infilling fractured rock under a coupling condition is studied. In terms of theory, the fracture compaction effect coefficient δ is added to the classical matchstick model, and the volume strain principle is used to propose a permeability model for fractured rock. Furthermore, based on the Hertz contact theory, mineral particles are generalized into rigid spheres, and the mechanism of crack development between mineral particles under seepage pressure is analyzed. In terms of experiment, a true triaxial seepage test was carried out on rock-like specimens to obtain the change law of the permeability characteristics of fractured rock. The test results are largely consistent with the theoretical calculation results of the theoretical model, which verifies the applicability of the model proposed in this paper. After the loading failure of the specimen, the internal filling material was taken out and analyzed, and by observing the distribution of cracks on the surface, it is verified that the seepage pressure promotes the development of cracks in the filling fracture. Full article
(This article belongs to the Section Hydrology)
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25 pages, 4881 KiB  
Article
Thermal Characteristic Analysis and Experimental Study of a Spindle-Bearing System
by Li Wu and Qingchang Tan
Entropy 2016, 18(7), 271; https://doi.org/10.3390/e18070271 - 22 Jul 2016
Cited by 25 | Viewed by 10062
Abstract
In this paper, a thermo-mechanical coupling analysis model of the spindle-bearing system based on Hertz’s contact theory and a point contact non-Newtonian thermal elastohydrodynamic lubrication (EHL) theory are developed. In this model, the effect of preload, centrifugal force, the gyroscopic moment, and the [...] Read more.
In this paper, a thermo-mechanical coupling analysis model of the spindle-bearing system based on Hertz’s contact theory and a point contact non-Newtonian thermal elastohydrodynamic lubrication (EHL) theory are developed. In this model, the effect of preload, centrifugal force, the gyroscopic moment, and the lubrication state of the spindle-bearing system are considered. According to the heat transfer theory, the mathematical model for the temperature field of the spindle system is developed and the effect of the spindle cooling system on the spindle temperature distribution is analyzed. The theoretical simulations and the experimental results indicate that the bearing preload has great effect on the frictional heat generation; the cooling fluid has great effect on the heat balance of the spindle system. If a steady-state heat balance between the friction heat generation and the cooling system cannot be reached, thermally-induced preload will lead to a further increase of the frictional heat generation and then cause the thermal failure of the spindle. Full article
(This article belongs to the Special Issue Entropy Application in Tribology)
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