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Understanding the contact behaviour of slewing-ring thrust ball bearings is essential for accurate predictions of load distribution and evaluations of static and dynamic load capacity. Applying Hertz's theory to non-standard slewing ring bearings presents unique challenges due to their complex geometries and difficulties in achieving uniform surface finishes, leading to significant deviations from actual stress. This study addresses these limitations by comparing experimental results, numerical results, and the Hertz theory. The analysis considers three Hertz contact configurations between the bearing ball and the raceway. The results reveal significant deviations from the experimental values. To determine the cause of these variations, the friction coefficient between the ball and the raceway is determined using the gravitational method by varying the number of balls. Uneven load distribution across balls in slewing ring bearings under mechanical loads is exposed by friction coefficient measurement. To further explore, load-deformation experiments are conducted on the LMMB by placing varying numbers of balls and their positions. Results expose variations in load-taking behaviour among the balls, emphasizing the critical influence of contact area load distribution. [ABSTRACT FROM AUTHOR]

Copyright of Journal of Dalian Polytechnic University is the property of Journal of Dalian Polytechnic University Editorial Department and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Hydraulic rolling reshaper is an advanced reshaping tool to solve the problem of casing deformation, which has been widely used in recent years. When it is used for well repair operation, the reshaping force provided by ground devices is generally determined by experience. However, too large reshaping force may destroy the deformed casing, and too small reshaping force may also prolong the construction period and affect the repairing effect. In this paper, based on Hertz contact theory and elastic-plastic theory, combined with the process parameters of shaping, and considering the structural characteristics of the deformed casing and reshaper, we propose a mathematical model for calculating the reshaping force required for repairing deformed casing by hydraulic rolling reshaper. Meanwhile, the finite element model and numerical method of hydraulic rolling reshaper repairing deformed casing are established by using the finite element method, and the reliability of the mathematical model is verified by several examples. On this basis, the control variable method is used to investigate the influence of each parameter on the reshaping force, and the influence degree of each parameter is explored by orthogonal simulation test and Pearson correlation analysis. The research results not only provide an important theoretical basis for the prediction of reshaping force in on-site construction, but also provide a reference for the subsequent improvement of the shaping process. [ABSTRACT FROM AUTHOR]

In order to more accurately reflect the real contact stress on the tooth surface of beveloid gear, this paper constructs the tooth surface contact coefficient of beveloid gear, and verifies its rationality. Based on fractal contact theory and Hertz contact theory, a contact model of beveloid gear is established, which comprehensively considers the parameters such as gear tooth surface roughness, elastic deformation of contact point and material characteristics. The effectiveness of this method is contact strength of beveloid gear, which is compared with the finite element calculation results by calculating. The relation between load and area during gear meshing is obtained through fractal theory, and four basic parameters are simulated to analyze the effect of fractal contact model. The results show that the accuracy of fractal contact model is verified by numerical simulation and analysis of the relation between actual contact area and load. This paper is based on the finite element theory, Hertz contact theory and fractal theory, the tooth surface contact strength of beveloid gear is compared and analyzed, the correctness of calculating the contact stress of beveloid gear by fractal contact model is verified. The establishment of this model provides a certain theoretical basis for the design and strength check of beveloid gear.

Wear mechanism is important since it leads to revisions in Total Hip Replacement (THR) surgeries. Contact pressure plays an important role in wear mechanisms and needs to be investigated in detail to obtain more accurate wear predictions to understand the wear performance of the implant in the design stage. This study proposes a methodology for verification of contact pressure and pressure distribution via numeric and analytic methods to be used in wear calculations. Based on Hertz’s contact theory, the contact pressure and the contact area are calculated in the analytical method. The results are compared to the numeric method’s results obtained from the finite element method. The linear and volumetric wear rates of bearing couples’ surfaces were estimated by Archard’s wear equation. The effect of design parameters on pressure such as head radius, cup thickness, material combination of bearing couples, coating film material, and film thickness are investigated in this study using the proposed methodology. The minimum error between the analytical and numerical results was 0.24% for 28 mm of head diameter, while the maximum error was 11.79 % for 48- mm of head diameter. The minimum contact pressure values were obtained from 48- mm of head radius at a half contact angle of 190 (degrees) in FEM and Hertz calculations, respectively. The maximum linear wear rate was calculated at 0.0026 mm/Mc at a 1- mm cup thickness, while minimum linear wear rate was 0.0022 mm/Mc at a 10- mm cup thickness in the numeric method. The maximum survival cycles of coating materials rate were 31847 cycles for the Stainless-steel coated cup with 500 µm of coating thickness, while the minimum cycles was 2359 cycles for the Ti64 coated cup surface with 100 µm of coating thickness. It is concluded that the most important design parameters are the cup thickness and the material combinations since they have a significant effect on the contact pressure and the contact area. This study provides a verification methodology for the parametric sensitivity analysis before experimental validations. The methodology utilized in this study could be utilized by designers while optimizing the design parameters to minimize the wear. [ABSTRACT FROM AUTHOR]

Geomembranes play an important role in the liner system of landfills, where the interfacial strength between rough geomembranes (GM) and nonwoven geotextiles (GT) is low and prone to landslides. There are highly uneven and randomly distributed asperities distributed on the surface of the rough geomembrane, and the mesomechanical properties of the asperity determine the interfacial strength of GMX/ GT. A modified large direct shear apparatus was used to conduct uniaxial compression tests on the GMX/ GT interface, and the contour height of the geomembrane surface before and after compression was measured using a profiler. By simplifying the contact model of GMX/ GT, the normal deformation law of a rough surface asperity with gradually increasing normal load was studied. By comparing the theoretical and experimental results, the deformation process of the asperity on the surface of the geomembrane is clarified, and the normal deformation mechanism of the rough geomembrane is revealed from a microscopic perspective. [ABSTRACT FROM AUTHOR]

The properties of the erodent, namely, size, shape, hardness, density, etc. have dominant effect on mass removal from the target material surface in slurry erosion. The area of contact of the erodent particle mainly depends on its size and shape. This further leads to variation in the stress development at the target surface due to particle impact. Therefore, it is necessary to investigate the effect of area of contact and stress concentration on the target surface due to different particles shapes and sizes. In view of this, in the present investigation AA6063 is selected as target material with three natural erodents, namely, quartz, SiC and alumina. The area of contact of impacting particle with target material surface is calculated by using Hertz contact stress theory and further determined by using ANSYS for similar conditions. The minimum area of contact of 256 µm size alumina particles with AA6063 target material has been observed around 0.82 x 10-4 mm2 and 0.98 x 10-4 mm2 using Hertz contact stress theory and ANSYS, respectively; which produces maximum stress concentration around 99 x 10-3, MPa using both the techniques. The stress concentration results by ANSYS software are compared with Hertz stress results and the maximum percentage error in stress concentration is observed around 4.19 %. The average mass loss per particle from target material surface is observed around 1.35, 1.94 and 2.11 (x 10-12 g) due to impact of quartz, SiC and alumina particles, respectively. The results obtained by Hertz theory and ANSYS software are observed in line with the mass loss per particle determined experimentally. SEM micrographs reveal the material removal mechanism from target material surface.

In order to improve the situation of discontinuity in the range of stresses caused by pin deformation, the mathematical theoretical model of peak contact stresses after pin node deformation in the test rig was established based on the Hertzian contact theory, and the pin node model was simulated and analysed using ANSYS software and compared with the theoretical model. The results show that the simulation results are in good agreement with the theoretical data. Combined with the actual engineering field application, five main indicators for reducing the peak stress in the contact area of the pin node hole wall were determined, namely: shaft hole gap, shaft casing thickness, node plate thickness, chamfer length, chamfer angle, and the use of Minitab software to establish the main effect cloud diagram for the three evaluation indicators: stress, tangential stress and strain; establish the affiliation function of the three evaluation indicators according to the fuzzy mathematical theory, and use the hierarchical Analysis of Hierarchy (AHP) was used to determine the weight vector of the evaluation indexes, and the optimal combination of parameters for the five main indexes was obtained by combining fuzzy comprehensive evaluation and the principle of maximum subordination, and the combination of parameters was simulated. The results show that the optimized pin node column peak stress reduction ratio is 58.77%, and the peak stress reduction ratio of the trunnion node is 12%. The optimal combination of solution parameters was applied in the field in the design and development of the 50 MN hydraulic support test stand, which verified the reasonableness of the optimised parameters and effectively improved the service life of the centre beam pin during the loading test of the hydraulic support test stand. It was further demonstrated that by adding slope chamfers to the pin nodes, setting reasonable initial clearances and plate thicknesses, the peak pin node loads could be reduced to a large extent and the length of the stress range improved, providing a reference for the practical engineering application of the design of plug-in and plug-out positioning pin assemblies for heavy equipment.

This study aims to address the current situation of the late start of mechanized harvesting technology for the pod pepper, the high damage rate of existing pod pepper harvesters, and the lack of theoretical support for key harvesting components. The Hertz theory is employed to investigate the damage mechanism of collisions between pod pepper and comb fingers. The study analyzes the maximum deformation of pod pepper and the critical speed at which damage occurs during the collision process. Furthermore, it explores the critical relative speed that leads to damage in pod pepper. Orthogonal tests are conducted to analyze the effects of rotational speed, hose thickness, and moisture content on the efficiency of pod pepper picking. The experimental results are then subjected to multifactorial ANOVA to identify the optimal test parameters. The structural and motion parameters of the picking device are optimized based on these conditions. It is determined that the critical relative velocity for damage to pod pepper during a collision with the comb finger is V0 = 11.487 m s−1. The collision velocities of pod pepper with different hose thicknesses are analyzed using the i-SPEED TR endoscopic high-speed dynamic analysis system to obtain the corresponding collision velocities for different hose thicknesses. The study finds that rotational speed, hose thickness, and the water content of pod pepper affect the damage rate and stem shedding rate. The optimal experimental parameters are determined to be a rotational speed of 705.04 rpm, hose thickness of 3 mm, and water content of the pepper of 71.27%. [ABSTRACT FROM AUTHOR]

Copyright of Journal of Mechanical Strength / Jixie Qiangdu is the property of Zhengzhou Research Institute of Mechanical Engineering and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Copyright of China Mechanical Engineering is the property of Editorial Board of China Mechanical Engineering and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Copyright of Coal Science & Technology (0253-2336) is the property of Coal Science & Technology and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Rockfall disasters have long restricted the further improvement of the safety level of steeply dipping coal seams (SDCSs). When a rockfall disaster occurs, it causes damage to the hydraulic support and other equipment at the working face. An effective way to carry out protection design is using the law of rockfall migration and energy evolution. Therefore, this study used the polyhedral rockfall migration and its impact process on the hydraulic support equipment of the working face as the research object and analyzed the influence of relevant parameters on the maximum contact deformation, maximum impact force, and energy absorption of the column during the collision and contact between the rockfall and the hydraulic support column. Firstly, with hexahedral rockfall as an example, the migration process of rockfall was simulated using PFC3D software. Secondly, according to the Hertz contact theory, the contact model of the shock process between the rockfall and the hydraulic support column was constructed, and the maximum deformation and maximum impact force of the collision contact between the rockfall and the column were obtained. Finally, the Hamilton principle and the Galerkin discrete method were used to construct the dynamic model of the collision between the rockfall and the column, and the energy evolution law of the shock process between the rockfall and the column was studied. The conclusions of this paper can provide a certain theoretical basis for the prediction of rockfall disasters and the design of rockfall protection devices. [ABSTRACT FROM AUTHOR]

The properties of the erodent, namely, size, shape, hardness, density, etc. have dominant effect on mass removal from the target material surface in slurry erosion. The area of contact of the erodent particle mainly depends on its size and shape. This further leads to variation in the stress development at the target surface due to particle impact. Therefore, it is necessary to investigate the effect of area of contact and stress concentration on the target surface due to different particles shapes and sizes. In view of this, in the present investigation AA6063 is selected as target material with three natural erodents, namely, quartz, SiC and alumina. The area of contact of impacting particle with target material surface is calculated by using Hertz contact stress theory and further determined by using ANSYS for similar conditions. The minimum area of contact of 256 µm size alumina particles with AA6063 target material has been observed around 0.82 x 10-4 mm2 and 0.98 x 10-4 mm2 using Hertz contact stress theory and ANSYS, respectively; which produces maximum stress concentration around 99 x 10-3, MPa using both the techniques. The stress concentration results by ANSYS software are compared with Hertz stress results and the maximum percentage error in stress concentration is observed around 4.19 %. The average mass loss per particle from target material surface is observed around 1.35, 1.94 and 2.11 (x 10-12 g) due to impact of quartz, SiC and alumina particles, respectively. The results obtained by Hertz theory and ANSYS software are observed in line with the mass loss per particle determined experimentally. SEM micrographs reveal the material removal mechanism from target material surface. [ABSTRACT FROM AUTHOR]

A 2D piston pump's mechanical efficiency is limited at high rotational speeds, in particular, its mechanical efficiency decreases as its load pressure rises. In this paper, the conventional 2D piston pump is redesigned by changing its suspension rotation into rail rotation to decrease mechanical loss. The mechanical efficiency of this new 2D piston pump is studied by building a mathematical model for analyzing the relationship between the load and the mechanical loss caused by the rolling of the cone rollers on the guiding rails. Hertz contact theory is used for the first time for such analysis. Test results prove that the mechanical efficiency of the 2D piston pump with rail rotation is better than that of a 2D piston pump with suspension rotation, with the former's mechanical efficiency increasing with the load. According to theoretical analysis and test results, the material used to manufacture the cone rollers and guiding rails is changed from 45 steel to GCr15 to improve the mechanical efficiency of the developed 2D piston pump further. [ABSTRACT FROM AUTHOR]

Eggshell strength is a critical quality factor for consumption eggs as it affects the probability of breakage in practice. In this study, a fast and low-cost methodology for the non-destructive determination of eggshell strength is presented. The method utilized a small steel ball to impact the egg and a microphone to analyse the impact characteristics. Hertz contact theory was applied to relate the measured impact characteristics to the local stiffness of the eggshell. Therefore, a total of 150 eggs were studied on which eight consecutive measurements per egg were taken around the equator at equidistant places. The results showed a strong correlation of 0.93 between the traditional static stiffness measured during quasi-static compression tests and the average stiffness obtained from the new methodology. This paves the way towards fast, low-cost and non-destructive in-line shell strength measurements to reduce the number of cracked eggs reaching the consumer. [ABSTRACT FROM AUTHOR]

In the egg industry, fast and highly reliable quality measurements are crucial. This study presents a novel method based on Hertz contact theory that allows for non-destructive determination of eggshell strength. The goal of the study was to evaluate the material strength (Young's Modulus) and structural strength (stiffness) of eggshells. To this end, an experimental setup was constructed to measure the collision of an eggshell with a small steel ball, which was recorded using a laser vibrometer. The study analyzed a sample of 120 eggs and found a correlation of 0.85 between the traditional static stiffness measured during quasi-static compression tests and the stiffness obtained from the Hertz contact theory. The results show that Hertz contact theory is valid for small steel spheres impacting eggshells, while a sensitivity analysis indicated that the most important factor in determining the strength of the eggshell is the contact duration between the egg and the impactor. These results open up the possibility of grading eggs based on their shell strength in a non-destructive manner. [ABSTRACT FROM AUTHOR]

In this study, based on ball–raceway Hertz point contact theory, mathematical models of the static and dynamic stiffnesses of angular contact ball bearings are established by introducing geometric dimension data and load distribution parameters. The nonlinear stiffnesses of the 60TAC120B angular contact ball bearing were calculated by the Newton–Raphson algorithm. For the static stiffness, the radial and axial stiffnesses for different external loads were obtained. The errors between the exact calculation method and the traditional empirical formula method were compared. For dynamic stiffness, the radial and axial stiffnesses for different rotational speeds were obtained under a defined external load. To verify the accuracy of the above theoretical calculation, the nonlinear contact finite-element method was used to accurately simulate the static and dynamic stiffnesses. Finally, an experimental study on the static and dynamic nonlinear stiffnesses was carried out using custom stiffness test equipment. In addition, the results of theoretical calculations, numerical simulations, and experiments were compared. The results showed that the stiffness model of the ball–raceway Hertz point contact theory was too ideal and deviated significantly from the experimental data curve. The finite-element numerical simulation method was not restricted by the channel control theory of the bearing rings, and the obtained results were closer to the measured values. This study provides the conditions for the analysis of the working accuracy of large, heavy-duty equipment affected by the joint stiffness, and it has important theoretical and practical significance. [ABSTRACT FROM AUTHOR]

The balls in the machine tool load-bearing system inevitably alternate with the movement of the worktable, resulting in the worktable's posture to change periodically during the ball circulation process. In the past, the dynamic behaviors of the machine tool load-bearing system have been analyzed by assuming that the worktable is in a specific position, and few models consider the effects of the ball circulation motion. To address this problem, this paper presents a five degree-of-freedom (DOF) nonlinear dynamic model for the machine tool load-bearing system, taking into account the ball arrangement and carriage flexibility, which is used to predict the dynamic behaviors under both constant and excitation loads. Firstly, the relation between the contact load and the carriage flexibility is determined, and the contact load in the working phase is derived by homogeneous coordinate transformation. Secondly, the elastic release is discussed for different cases and the contact load in the transition phase is derived. Then, a nonlinear dynamic model for the machine tool load-bearing system is established by deriving the restoring loads and moments, and the validity of the proposed model is verified experimentally. Finally, the variation law of the nonlinear dynamic response for the machine tool load-bearing system is discussed. [ABSTRACT FROM AUTHOR]

This study aims to address the current situation of the late start of mechanized harvesting technology for the pod pepper, the high damage rate of existing pod pepper harvesters, and the lack of theoretical support for key harvesting components. The Hertz theory is employed to investigate the damage mechanism of collisions between pod pepper and comb fingers. The study analyzes the maximum deformation of pod pepper and the critical speed at which damage occurs during the collision process. Furthermore, it explores the critical relative speed that leads to damage in pod pepper. Orthogonal tests are conducted to analyze the effects of rotational speed, hose thickness, and moisture content on the efficiency of pod pepper picking. The experimental results are then subjected to multifactorial ANOVA to identify the optimal test parameters. The structural and motion parameters of the picking device are optimized based on these conditions. It is determined that the critical relative velocity for damage to pod pepper during a collision with the comb finger is V0 = 11.487 m s−1. The collision velocities of pod pepper with different hose thicknesses are analyzed using the i-SPEED TR endoscopic high-speed dynamic analysis system to obtain the corresponding collision velocities for different hose thicknesses. The study finds that rotational speed, hose thickness, and the water content of pod pepper affect the damage rate and stem shedding rate. The optimal experimental parameters are determined to be a rotational speed of 705.04 rpm, hose thickness of 3 mm, and water content of the pepper of 71.27%.

In the process of mechanised sowing and harvesting, the damage and fragmentation of rapeseed are often caused by multiple contacts. The expansion of micro-defects and the accumulation of fusion damage in rapeseed can lead to fragmentation. To explore the law of mechanical damage of rapeseed, an elastoplastic model was established by Hertz contact mechanics. Combined with the continuous damage theory, the evolution equation of compression damage was established, and the accumulation method of compression damage was clarified. Three kinds of commercial seeds were taken as the experiment material. A single compression crushing test was carried out to verify the correctness of the elastoplastic model but multiple compression crushing tests were carried out to explore the damage accumulation process and method. The results show that the elastoplastic model can better fit the relationship between force and deformation during compression. The critical damage deformation δ d is equal to critical elastoplastic deformation δ s. When the deformation is more significant than 15 ± 2% of the diameter, the plastic deformation of rapeseed occurs. When the deformation is < δ d , the rapeseed will not be broken during the 30 cycles of equal displacement compression. When the deformation is > δ d , the damage leads to the decrease of the effective elastic modulus. With the increase of the compression deformation, the damage to the rapeseed intensified, resulting in the rapeseed being more easily broken. The research can provide a theoretical basis for designing structure and parameters in mechanised sowing and harvesting for rape. • An elastoplastic model for rapeseed was established by Hertz contact mechanics. • The evolution equation of compression damage for rapeseed was established. • The accumulation method of compression damage was clarified. • The damage leads to the decrease of the effective elastic modulus of rapeseed. [ABSTRACT FROM AUTHOR]

The blades of aero-engines and gas turbines are the power core components, and the polishing consistency of free-form surface directly affects the surface quality and the parts performance. Studying the material removal mechanism of free-form surfaces and building the material removal model are core issues in the robot-assisted abrasive cloth wheel polishing blade system. Therefore, based on the Hertz contact theory, the force in the macro-contact area of the abrasive cloth wheel and the blade is analyzed. The relationship between the normal polishing force in the contact area of the blade surface and the compression amount of the abrasive cloth wheel, and the distribution law of the pressure in the contact area are obtained. Combined with the microscopic force of the single abrasive grain on the surface of the blade and the mathematical model of the multiple abrasive grains distribution, then material removal volume at micro-elements on the blade surface was established, and the material removal depth model was derived, and the material removal model of the abrasive cloth wheel polishing blade was constructed. On this basis, the influence factors such as normal polishing force, linear speed, robot feed speed, and time were analyzed. The experimental verification results show that the maximum error between the experimental results and the theoretical model is 9.89%. The feasibility of the established material removal model for the abrasive cloth wheel polishing blades was verified. [ABSTRACT FROM AUTHOR]

The contact stress of flexible joint is an important factor affecting the safety of ultra-short-radius drilling tools. However, calculating the contact stress accurately is difficult, because the method for solving the multibody collision of the flexible joint is complex. A novel analytical method for the contact stress of ball cage flexible joint is presented in this study. The method was used to establish the relationship between the parameters and contact stress of the flexible joint during the drilling process. The contact stress analytical models of the ball head, ball key, and ball seat were established based on Hertz contact theory, and the finite element method was used to analyse the variations of contact stress under the weight of bit and torque. The influences of borehole curvature and deflection angle on contact stress were discussed for parameter optimization. Results demonstrate that the contact stress values on the ball key, inner raceway, and outer raceway are concentrative. The ball key is the most dangerous part of the flexible joint, and its safety can be improved by increasing its diameter. When the deflection angle between the flexible joint was increased from 0 ° to 18 °, the contact stress value also increased to 220 MPa. However, the contact position was random on the inside of deflection. The proposed method provides a good prospect to optimize the structure parameters of the flexible joint and ultra-short-radius drilling parameters. [ABSTRACT FROM AUTHOR]

• Developed a theoretical model for the conformal analysis of circular islands and substrates. • Predicts conformal behavior on surfaces of any curvature and modulus. • Proposed a generic strategy for conformal electronics in various applications. This paper introduces a set of design criteria that aim to integrate flexible electronics onto three-dimensional surfaces in a mechanically adaptive manner. Previous studies have been limited to conformal integration on specific shapes (Such as spherical surfaces and corrugated surfaces) of rigid surfaces or soft substrates, there is a lack of a universal design strategy that takes into account the complexity of substrate shapes and varying hardness. To address this gap, the paper outlines a mechanical model that utilizes Hertzian contact theory to describe the interaction between the thin film and the substrate, and the conformal surface morphology and stress state were derived from minimizing the total energy of the island-substrate structure. The proposed formulations are verified through finite element methods and experiments, analyzing the effects of Young's modulus, in-plane size, and thickness of the "island" on its conformability. Therefore, this paper proposes a generic on-demand conformal design strategy that takes into account the complexity and hardness of the substrate. This study's findings will contribute to the development of conformal electronics that can be used in various fields, such as epidermal electronics, flexible robots, robot electronic skin, and aircraft smart skin. [Display omitted] [ABSTRACT FROM AUTHOR]

In the egg industry, fast and highly reliable quality measurements are crucial. This study presents a novel method based on Hertz contact theory that allows for non-destructive determination of eggshell strength. The goal of the study was to evaluate the material strength (Young’s Modulus) and structural strength (stiffness) of eggshells. To this end, an experimental setup was constructed to measure the collision of an eggshell with a small steel ball, which was recorded using a laser vibrometer. The study analyzed a sample of 120 eggs and found a correlation of 0.85 between the traditional static stiffness measured during quasi-static compression tests and the stiffness obtained from the Hertz contact theory. The results show that Hertz contact theory is valid for small steel spheres impacting eggshells, while a sensitivity analysis indicated that the most important factor in determining the strength of the eggshell is the contact duration between the egg and the impactor. These results open up the possibility of grading eggs based on their shell strength in a non-destructive manner.

Eggshell strength is a critical quality factor for consumption eggs as it affects the probability of breakage in practice. In this study, a fast and low-cost methodology for the non-destructive determination of eggshell strength is presented. The method utilized a small steel ball to impact the egg and a microphone to analyse the impact characteristics. Hertz contact theory was applied to relate the measured impact characteristics to the local stiffness of the eggshell. Therefore, a total of 150 eggs were studied on which eight consecutive measurements per egg were taken around the equator at equidistant places. The results showed a strong correlation of 0.93 between the traditional static stiffness measured during quasi-static compression tests and the average stiffness obtained from the new methodology. This paves the way towards fast, low-cost and non-destructive in-line shell strength measurements to reduce the number of cracked eggs reaching the consumer.

To solve the deformations and stiffnesses changes of linear rolling guideway under different loads, and to provide reference for the structural design of the carriage, this paper presents an analytical model of three-degrees-of-freedom static stiffness for linear rolling guideway considering the structural deformations of the carriage. In this study, first, the contact loads and elastic deformations between balls and raceways caused by external loads and preload were obtained by Hertz contact theory. The elastic deformations between balls and raceways were described by the change of the curvature centers of the carriage raceways. Next, according to the constraints and loading conditions of the carriage, the elastic beam theory was introduced, and the structural deformations of the carriage under the contact loads were equivalent to the deformations of two cantilever beams. Then, the external loads and the displacements of the carriage were derived by the static equilibrium conditions of the carriage. At last, the proposed equivalent model of carriage structure deformations was validated by comparing the calculated deformations of the carriage with those from a commercial program under various loading conditions, and the accuracy of the static stiffness model proposed in this paper was further verified by the experimental results in the reference. The results show that the calculated structural deformations of carriage matched the deformations calculated by a commercial program well. Also, with relative errors of 4.4–17.5%, the calculated stiffnesses using the model proposed in this paper more closely matched the measured stiffnesses. Clearly, there is a better match between the calculated results of the proposed model and the measurements than with the conventional rigid model. [ABSTRACT FROM AUTHOR]

The Hertz contact law for two linear elastic spheres plays a very important role in the discrete element method (DEM). Within the classic Hertz contact theory, the contact strain energy distribution in the two contacting spheres is analytically derived, which states that the ratio between the strain energies stored in the two spheres is solely dependent on their material properties, regardless of their radii. This strain distribution law is generally valid for non-spherical and other contact cases, provided that the two surfaces in contact can be reasonably treated as two elastic half-spaces and that the deformation is small. The independence feature of the law from the contact geometry also greatly facilitates the computation of the contact strain energy stored at particle level. As a direct consequence of this law, the contact point between two particles in DEM could also be determined. The numerical simulations demonstrate good agreement between the theoretical prediction and the numerical results for the tested cases involving spheres and ellipsoids with varying sizes and material properties. [Display omitted] • Analytically derived a strain energy distribution law between two elastic spheres in contact. • Discussed the extension of the law to other non-spherical contact cases. • Proposed the determination of the contact point between two particles in DEM. • Used finite element simulations to validate the theoretical derivation. [ABSTRACT FROM AUTHOR]

This paper proposes a method that combines the finite element method with an improved energy wear model to establish a three-dimensional (3D) ball-plane contact structures fretting wear model. The correctness of the model was verified by Hertz contact theory and fretting wear experiments. Then, the fretting wear dynamic behaviors of 3D ball-plane contact structures were investigated in detail. The results show that when the contact structure is in the partial slip regime (PSR), the cross-sectional wear scar profile changes from the "W" shape to the "U" shape along the fretting direction. When the contact structure is in the gross slip regime (GSR), the cross-sectional wear scar profile always maintains a "U" shape along the fretting direction. In addition, it was also found in the study that when the contact structure is at GSR under a low normal load or PSR under a high normal load, it will help reduce wear. This study can provide significant theoretical guidance for reducing and protecting fretting wear in contact structures. • Improvements to the traditional energy wear model. • Proposing a new method for modeling fretting wear of ball-plane structure. • Theory, simulation and experiment are combined to verify the correctness of the model. • GSR under low normal loads or PSR under high normal loads can help reduce wear. [ABSTRACT FROM AUTHOR]

Copyright of Tobacco Science & Technology is the property of Tobacco Science & Technology and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Contact curvature plays a pivotal role in the Young's modulus determination and mechanical response of a particle. This paper presents the sensitivity analysis of a particle morphology to contact curvature and its influence on the Young's modulus determination during the elastic deformation of a particle. X-ray computed micro-tomography (μCT) was conducted to obtain the prototype of a single particle. The digital information of the scanned particle, including 2D slices and 3D rendering was processed and the variation of contact curvature of the particle was examined using the circular (spherical at 3D) and polynomial fitting methods. The fitting sections of the particle are taken into account. The effect of contact curvature on Young's modulus determination was investigated and it was found that Young's modulus changed substantially from global fitting to local fitting. Young's modulus is highly related to the surface roundness, which exerts a significant influence on the determination of Young's modulus. [ABSTRACT FROM AUTHOR]

Rail transport conveyor is a kind of rail transport equipment, which is widely used in railway, metallurgy, mining and other fields. However, the stability of its transmission structure is an urgent problem to be solved in production. In this study, the transmission structure of the lifting subsystem of rail transport conveyor has been taken as the research object. Based on the multi - body dynamics theory and Hertz contact theory, the meshing process of the worm gear and worm in the lifting transmission structure of rail transport conveyor are studied. Additionally, the influence of stiffness coefficient, motor driving speed and transmission distance on the stability of transmission are analyzed. Then, the variation law of contact force between the worm gear and the worm is explored, so as to find out the reasons of affecting the stability of lifting structure. Through the research on the change law of the contact force of the worm gear and worm transmission mechanism in the transmission structure, it is found that the instantaneous impact of contact and the periodic fluctuation of contact force are the main reasons for the instability of the transmission structure of the lifting subsystem. The research work in this paper provids a theoretical basis for both the study of the dynamic characteristics of the worm gear and worm transmission and the design of the new transmission structure of rail transport conveyor. [ABSTRACT FROM AUTHOR]

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The classical Greenwood and Williamson (GW) model assumes that the asperity is elastic, which does not take into account the changes of curvature radius of the asperity after wearing.On the basis of classical Hertz contact theory and GW model, the shear stiffness formula of the friction surface was derived when the asperity curvature is constant.According to the Mohr-Coulomb criterion, the yield point position of a single asperity under normal pressure and tangential friction force was discussed.And the critical pressure formula for a single asperity was derived, which showed that the pressure corresponds to the radius of curvature of asperity.A model considering the wear of asperities was proposed and the shear stiffness formula of the friction surface considering the changes of the curvature of the asperity was obtained by combining the shear stiffness formula with a constant curvature radius and the critical pressure formula for a single asperity.The calculation results of the model are in a good agreement with the test results.For the specific roughness of rock surface, with the increase of pressure, the rock surface gradually becomes smooth;for different roughness of rock surface, with the increase of roughness, the rock surface is easier to be smoothed.

Objective] This paper aimed to improve the hatching rate of walnut, the whole kernel rate and high dew kernel rate. [ Method] Based on Hertz contact theory, the curvature radius of the optimal contact surface was calculated to be - 33.64 mm, and then designed the three different kinds of contact surface which were a plane, concave spherical surface and the the sharp point, respectively. The three contact models were modeled and the static module was used for contact simulation in ANSYS workbench to analyze the stress, strain and deformation cloud map. [ Results ] When the contact surface was a concave sphere, the stress and deformation cloud map had the largest area distribution. Moisture content and compression stroke as well as the interface type chose as the three factors in the orthogonal experiment. Factors level : When the moisture content was 20 %, the extrusion stroke was 6 mm, the contact surface type was concave sphere with curvature radius of 33.64 mm, the shell cracking effect was the best, and the type of contact surface had the most significance influence on the cracking result. [ Conclusion] In the optimal conditions of test results, the comprehensive evaluation value was 2.82, and concave sphere with curvature radius of 33 . 64 mm could significantly improve walnut shell cracking effect. [ABSTRACT FROM AUTHOR]

The accurate calculation of gear contact stress is a significant parameter to judge the contact strength. It is the precondition for the investigation of gear's dynamic characteristics, fault diagnosis, and parameter optimization design. The calculation formula for the contact stress of double circular-arc helical gears is generalized from the finite element method and electrical testing, which neglects the influence of tooth surface morphology on the contact stress. In order to improve the calculation accuracy of the contact stress of the double-circular-arc helical gears, In this study, the 3D fractal contact stress of asperities on the joint surfaces was analyzed using 3D fractal theory to improve the calculation accuracy of the contact stress of the double circular-arc helical gears. Moreover, the influences of asperity deformation characteristics and sliding friction were considered. The fractal model of the normal contact stress for the double circulararc helical gears was established. Then, the model accuracy was verified by comparing the testing results, and the influences of the main parameters (fractal dimension, surface roughness amplitude, and friction coefficient) on the fractal contact model were acquired. Results show that a minimum value exists between the fractal dimension and normal contact stress. When the fractal dimension is smaller than the minimum value, the normal contact load increases with the fractal dimension. The normal contact stress increases with the surface roughness amplitude, whereas the normal contact stress reduces with the increase of the surface friction coefficient. The proposed model provides a theoretical basis for further research on the contact state of the double circular-arc helical gears and the vibration characteristics of the tooth surface. [ABSTRACT FROM AUTHOR]

The traditional Hertz contact theory has been widely used in solving contact problems. However, it is only applicable to the elastic contact, and cannot truly reflect the contact stress distribution and contact radius in the elasto-plastic contact. In this work, based on the Hertz contact theory, a fast solving method is proposed to calculate the contact stress distribution and contact radius in the elasto-plastic contact between two spheres. It is assumed that the elastic contact only occurs at the outer edge of contact patch and its contact stress distribution satisfies the Hertz contact theory, and the contact stress distribution at the inner edge of contact patch can be superimposed by a constant contact stress and several small ellipsoidal contact stress distributions. Moreover, based on the equivalent relation between the resultant force of contact stress and the normal external load, the contact radius in the elasto-plastic contact can be solved. Finally, an elasto-plastic contact example of two spheres is given based on the power-law hardening material model, and the influences of material parameters, contact radii and normal external loads on the accuracy of the proposed method are discussed by comparing the differences between the numerical results by finite element method and the predicted ones by the proposed method. It is shown that the proposed method can accurately calculate the maximum contact stress and contact radius in the elasto-plastic contact, and the relative errors of both maximum contact stress and contact radius are within ± 5 % . To sum up, the proposed fast solving method can be applied to perform the elasto-plastic contact analysis in engineering practice. [ABSTRACT FROM AUTHOR]

Rolling element bearing is a vital component in rotating machinery, such as a wind turbine (WT) system. By accurately monitoring its health condition, the faults can be detected at an early stage, providing sufficient lead time to perform maintenance and hence reducing accidents and economic losses. Bearing usually suffers from various wears and tears, which result in a gradual increase in clearance through its lifetime. Insufficient understanding of vibration characteristics under different clearances brings difficulties for bearing condition monitoring. Thus, this paper presents a nonlinear bearing vibration model with six degrees of freedom (DOF) to investigate the vibration characteristics under different radial clearances and load conditions. Then, a dedicated bearing test is established to verify the reasonability and effectiveness of the vibration model. Furthermore, a comprehensive simulation analysis is conducted to study the vibration characteristics over an extended range of the internal radial clearance and external load. Results show that the dynamic force on each ball presents an impulse whose magnitudes increases whereas the pulse width reduces with clearance increases. Ball pass frequency of outer race (BPFO) is the dominant modulation component and the frequency is in accordance with the number of dynamic force impulses. Two indicators, i.e., root mean square (RMS) value and spectral centroid, are proposed to indicate clearance changes. In general, they show an uptrend with the increase in clearance, which is in line with the dynamic force increasing with clearance, especially the spectral centroid of the low frequency band. However, it should be noted that the RMS value and spectral centroid exhibit a fluctuating behavior due to nonlinear vibration responses. For the first time, this study shows the details of vibration characteristics with clearance variations and provides a foundation for monitoring the bearing conditions before any obvious local defects on raceways. [ABSTRACT FROM AUTHOR]

Most studies on linear rolling guides usually assume the contact load between the ball and the raceway is uniform, which results in a deviation from the actual conditions. This study aims to establish a load distribution model based on the Hertz contact theory with ball combined interference which is converted from preload, raceway center-distance error, and installation error including ball geometry error. The reliability of the proposed model was verified by a numerical instance for the load distribution and deformation analysis. The result shows that the proposed approach agrees better with the experimental results compared only with the action of the preload. This work can provide an important starting point for studying friction and wear in machine tools. [ABSTRACT FROM AUTHOR]