Hertz Theory Research Articles

The Optimal Design of the Press Roller to Improve the Winding Molding Quality of Heat Insulation.

In the heat insulation winding molding process of solid rocket motors, the pressure applied by the press roller directly affects the quality of the winding molding. Insufficient pressure can result in poor bonding quality and may cause defects. This paper aims to provide an optimal design of the press roller to improve the winding molding quality of the heat insulation. The effect of the cylindrical press roller on the pressure distribution was analyzed using the elastic foundation model and a finite element (FE) model, which was assessed by Hertz theory. Subsequently, the press roller was optimized to an elliptical concave design. The effect of the radius of the elliptical concave press roller on the pressure distribution was analyzed. A comparison of the effect of the elliptical concave press roller and the cylindrical press roller on the pressure distribution was conducted using the FE model. The results show pressure uniformity is significantly improved when the elliptical concave press roller is employed on the mandrel with the smallest radius. Additionally, the elliptical concave press roller increases the pressure at the edge of the tape, which reduces the risk of lifted edges and, thereby, improves the winding molding quality of the heat insulation.

Mathematical framework for snake robot motion in a confined space

Snake robots have redundant kinematic structure which predetermines them for motion in rough and unstructured terrain with obstacles, narrow spaces or environments with different ground levels. Dynamic modeling of snake robots is an important element in the development of control strategies for them. This paper, deals with the dynamic model of a snake robot moving in a pipeline. The model is based on Newton's mechanics with consideration of the viscous as well as Coulomb friction model. The paper uses Hertz theory for modeling of contact between a snake robot and side walls of a pipeline. Based on optimization process results, the friction effects as well as analyses of snake robot propulsive force are investigated. The main contributions of the paper are the developed dynamic model for snake robot motion in a pipeline, open source code of the developed model in MATLAB, and analyses of individual parameters of snake robot motion.

Enhancement of the contact behavior of a quasi-isotropic carbon fiber/epoxy matrix laminate with an elastic body by modifying the fiber-matrix interphase using graphene nanoplatelets

This study analyzed the effect of incorporating graphene nanoplatelets in the fiber-matrix interphase on the behavior of a multiscale composite laminate based on carbon fibers and epoxy resin subjected to contact loads. The selected loading mode was the contact between an elastic surface and a cylinder. The multiscale composite material used was a quasi-isotropic laminate with graphene nanoplatelets (GnPs) added at the fiber-matrix interface. The specimens were prepared with 0.0%, 0.1%, and 0.25% by-weight GnPs. Laminate beams were used according to the ASTM D7264 standard, and contact was studied in two configurations, applying the load at the edge of the laminate and in the other, in the plane of the test pieces. The normal strains in the contact region were determined experimentally using the interferometric Moiré technique. These results were compared with estimations using the Hertz contact theory and the finite element method (FEM). The normal strains in the contact area of specimens with fibers modified with 0.1% GnPs were lower than those with 0.25% or fibers without surface modification. Excellent agreement between the experimental results along lines in the contact zone with those estimated with the FEM. The normal strains in a direction perpendicular to the applied load obtained by the Hertz theory for the maximum deformation were slightly higher than those obtained by FEM. Except for those calculated for the normal strain in εy for the load in the direction of the thickness, although the distribution was very similar to those obtained by FEM as well as the experimental one.

A Wear Prediction Framework for Ball-Screw of Electro-Mechanical Brake Unit on Railway Trains

The electro-mechanical brake is a new advancement in railway train braking. Ball-screws are important components of electro-mechanical braking units (EMBUs), and their wear can cause EMBUs to degrade in performance or even fail to function. In this paper, we present a framework for prediction of ball-screw wear with discrete operating conditions as inputs, taking into account the time-varying characteristics of EMBUs. The framework includes determining the contact type, analyzing relative motion, calculating contact deformations, and estimating wear. The contact type is determined based on the quasi-static approach of Hertz theory. A dynamics model using multiple coordinate systems is established to analyze how balls and raceways move in relation to each other. The contact deformations of the ball–raceway contact are determined using numerical calculation. Then, the wear depth increment is calculated using the Archard model. The results of the calculation and the endurance test indicate that the wear on the screw raceway is greater than that on the nut raceway. The effect of velocity is greater than the effect of axial force. The presented calculation framework is reasonable and can be used for predicting EMBU ball-screw wear.

Characteristics of Damage to Brown Rice Kernels under Single and Continuous Mechanical Compression Conditions.

During the rice milling process, single and continuous compression occurs between brown rice and the processing parts. When the external load exceeds the yield limit of brown rice, brown rice kernels are damaged; with an increase in compression deformation or the extent of compression, the amount of damage to the kernels expands and accumulates, ultimately leading to the fracture and breakage of kernels. In order to investigate the mechanical compression damage characteristics of brown rice kernels under real-world working conditions, this study constructs an elastic-plastic compression model and a continuous damage model of brown rice kernels based on Hertz theory and continuous damage theory; the accuracy of this model is verified through experiments, and the relevant processing critical parameters are calculated. In this study, three varieties of brown rice kernels are taken as the research object, and mechanical compression tests are carried out using a texture apparatus; finally, the test data are analysed and calculated by combining them with the theoretical model to obtain the relevant critical parameters of damage. The results of the single compression crushing test of brown rice kernels showed that the maximum destructive forces Fc in the single compression of Hunan Early indica 45, Hunan Glutinous 28, and Southern Japonica 518 kernels were 134.77 ± 11.20 N, 115.64 ± 4.35 N, and 115.84 ± 5.89 N, respectively; the maximum crushing deformations αc in the single compression crushing test were 0.51 ± 0.04 mm, 0.43 ± 0.01 mm, and 0.48 ± 0.17 mm, respectively; and the critical average deformations αs of elasticity-plasticity deformation were 0.224 mm, 0.267 mm, and 0.280 mm, respectively. The results of the continuous compression crushing test of brown rice kernels showed that the critical deformations αd of successive compression damage formation were 0.224 mm, 0.267 mm, and 0.280 mm, and the deformation ratios δ of compression damage were 12.24%, 14.35%, and 12.84%. From the test results, it can be seen that the continuous application of compression load does not result in the crushing of kernels if the compression deformation is less than αd during mechanical compression. The continuous application of compressive loads can lead to fragmentation of the kernels if the compressive deformation exceeds αd; the larger the compression variant, the less compression is required for crushing. If the compression deformation exceeds αc, then a single compressive load can directly fragment the kernels. Therefore, the load employed during rice milling should be based on the variety of brown rice used in order to prevent brown rice deformation, which should be less than αd, and the maximum load should not exceed Fc. The results of this study provide a theoretical reference for the structure and parameter optimisation of a rice milling machine.

A novel comprehensive framework for surface roughness prediction of integrated robotic belt grinding and burnishing of Inconel 718

Surface roughness serves as a critical metric for assessing surface integrity, directly influencing the service performance of components. Hardening burnishing is a regularly used post-grinding procedure for Inconel 718 that can simultaneously reduce surface roughness and improve surface mechanical characteristics. A novel comprehensive framework is proposed to predict the surface roughness of Inconel 718 processed by the integrated robotic belt grinding and burnishing system developed in this study. Accounting for abrasive grain conditions and material removal rate during grinding, the L-BFGS-B optimization algorithm and image processing are utilized to predict the ground surface roughness first. Building upon this foundation, theoretical models are applied to ascertain the critical burnishing force needed to enter the hardening burnishing stage. Following this, the Expansion Cavity Model and Hertz theory are used to predict the roughness of the hardening burnished surface, which is only applicable when the step-over value exceeds a critical value. The proposed framework not only enhances our comprehension of the mechanisms underlying material surface deformation but also offers a novel avenue for predicting surface roughness during integrated robotic belt grinding and burnishing with high accuracy.

An alternative model of process damping in milling based on Hertz theory

An alternative model of process damping in milling based on Hertz theory

Robert Hertz, Anthropophagic Practices and Traditional South Fore Mortuary Rites in Papua New Guinea.

In this paper we examine the traditional mortuary rites of the South Fore people of Papua New Guinea using Robert Hertz's theory of secondary burial and the three mechanisms of mourning identified by Daniel Lagache. The ethnographic data that we obtained on South Fore interpretations of their own mortuary rites showed that all forms of corpse handling achieved the same end results through the process of secondary burial. Furthermore, the three mechanisms of mourning applied equally to all forms of corpse disposal and we found no evidence to support psychosexual interpretations of mortuary anthropophagy which emphasise aggression. South Fore interpretations of mortuary anthropophagy show that the dead were eaten out of love, and to protect the mourners from the painful emotion of witnessing the decomposition of the corpse. These findings affirm the relevance of the concepts of Hertz and Lagache to the universal human experiences of death and mourning.

Adapting geometry-based polygonal contacts for simulating faulty rolling bearing dynamics

Rolling bearings are a leading cause of equipment breakdowns in electrical machines, underscoring the significance of predictive maintenance strategies. However, the given methods require high-quality big data, which is challenging to acquire, especially for faulty cases. Simulation models offer an alternative by generating large datasets to complement experimental data. However, bearings involve complex contact-related phenomena, such as slipping and clearance. Therefore, generating realistic data comparable to the real-world necessitates accuracy. Our study presents a multibody simulation system of a motor bearing, incorporating a geometry-based polygonal contact method (PCM), which accurately captures nonlinear bearing dynamics and allows for the simulation of various contact geometries. We introduce a systematic approach to adjust the PCM contact properties for rolling bearings, referencing the well-established Hertzian theory. Both healthy and faulty bearings with a local outer ring fault were simulated. The simulated output was a relative shaft displacement, experimentally validated using a capacitive sensor. Our model successfully demonstrates the potential to employ geometry-based contacts for generating realistic data on faulty bearings with the aim of predictive maintenance.

Modeling of contact mechanics and defects investigation in automated fiber placement

AbstractThe layup quality of prepreg fibers onto complex surfaces is the most concerned issue in automated fiber placement (AFP), which is intimately related to the contact stress in tractive rolling contact. An analytical model of tractive rolling contact is proposed in this paper to clarify the defects mechanism during the AFP process, which considers the mold curvatures, mechanical properties of contacted objects, and pose information to make it suitable for irregular surfaces and arbitrary conditions. Classical Hertz theory in this model is expanded to 3D contact area, and multi‐scale deformations are united in the accurate calculation of contact stress under geometric constraints. Based on the model, the phenomena of adhesion, microslip, and the transition between them in AFP are systematically analyzed. For engineering applications, a discrete processing strategy is proposed to quickly obtain the local curvatures of the mold. Additionally, an algorithm is designed to calculate the contact stress of any path. Experimental results on an aircraft component demonstrate the accuracy of the proposed model in restoring the contact stress distribution during AFP. In conjunction with specific layup information, this model exhibits utility in forecasting laying defects and parameter optimization.Highlights An analytical modeling approach based on Hertz theory is proposed to calculate the contact stress in automated fiber placement. A model‐based algorithm is designed and combined with the proposed discrete scheme to quickly restore the contact stress distribution. Contact states related to stress are systematically investigated and defects analysis based on computational mechanics results is illustrated.

Study on dynamic response of cushion layer-reinforced concrete slab under rockfall impact based on smoothed particle hydrodynamics and finite-element method coupling

Abstract In the rockfall prevention and control project, the reinforced concrete (RC) slab and sand (gravel soil) soil cushion layer are commonly used to form the protection structure, thereby resisting the rockfall impact. Considering that the oversized deformation of the cushion layer under impact load using the finite element simulation cannot converge, this article establishes a numerical calculation model using smoothed particle hydrodynamics–finite-element method coupling (SPH–FEM). First, the standard Lagrange finite-element mesh is established for the whole model using ABAQUS, and then the finite-element mesh of the soil cushion layer is converted to SPH particle at the initial moment of the calculation, and finally the calculation results are solved and outputted. The results indicate that, compared with the results of the outdoor rockfall impact test, the relative errors of the rockfall impact force and the displacement of the RC slab are within 10%, which proves the rationality of the coupling algorithm; moreover, in terms of the numerical simulation, the SPH–FEM coupling algorithm is more practical than the finite element for reproducing the mobility of the rockfall impacting the sand and soil particles. In addition, at an impact speed of less than 12 m·s−1, the cushion layer is able to absorb more than 85% of the impact energy, which effectively ensures that the RC slab is in an elastic working state under small impact energy and does not undergo destructive damage under large impact energy; the peak impact force of the rockfall is approximately linear with the velocity, and the simulated value of the peak impact force is basically the same as that of the theoretical value of Hertz theory; the numerical simulation is good for reproducing the damage process of the RC slab in accordance with the actual situation. The SPH–FEM coupling algorithm is more justified than the FEM in simulating the large deformation problem, and it can provide a new calculation method for the design and calculation of the rockfall protection structure.

Contribution of friction-induced vibration to the realistic failure analysis of spur gear cracked teeth

A cracked tooth is a common occurrence in gears. However, the dynamic behavior of gears with cracks and poor lubrication that leads to rubbing between the teeth is poorly understood, limiting the reliability and precision of gear transmission. This article proposes a comprehensive model for studying the dynamic behavior of a one-stage spur gearbox with cracked teeth under poor lubrication conditions. The inter-teeth rubbing generated by the sliding of one surface relative to another is caused by the variation in the curvature radii of both mating teeth when the contact point moves along the line of contact. In addition, under the load transmitted between the mating teeth, the common elastic deformed area, computed by Hertz's theory, also varies, generating noise with modulated and constant amplitudes. Adding this friction-induced noisy vibration to the impulsive periodic response was found to realistically mimic natural behavior experimentally measured on a test rig specially developed for this investigation. According to the time-domain statistical indicators, the study concluded that the combination of both components of friction-induced noise and the primary impacting response was found to accurately and realistically simulate the dynamic behavior of the gearbox.

Investigation of Collision Damage Mechanisms and Reduction Methods for Pod Pepper

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%.

Comparative analysis of angular contact bearing stiffness calculated by Hertz contact and thermo-elastohydrodynamic lubrication

Stiffness is the key dynamic parameter of the angular contact ball bearing. This work established a dynamic bearing model based on Hertz theory and thermo-elastohydrodynamic lubrication (TEHL) and compared the contact angle, inner race position, and stiffness. In most cases, the stiffness calculated via Hertz was higher than when using TEHL. The axial stiffness values determined via the two theories were close, while the radial stiffness calculated via the Hertz theory was smaller than that determined by TEHL under light load and high speed. Considering the elastic deformation of the races and the initial contact angle, the results obtained by TEHL displayed a lower error rate in the experiment than Hertz.

Deterministic Simulation of Surface Textures for the Piston Ring/Cylinder Liner System in a Free Piston Linear Engine

The use of synthesis gas (SYNGAS) from waste gasification has been pointed out as a key strategy to help the energy transition. However, SYNGAS’ low calorific power is considered a difficult obstacle to its technological use in internal combustion engines. To overcome this, a novel free-piston linear motor has been proposed to pave the way for the use of SYNGAS in the mobility sector. Surface texturing has vast potential to reduce friction losses in this system. This study utilizes a deterministic numerical model to investigate the mixed lubrication performance of a textured piston ring/cylinder liner conjunction in a free piston engine. The model considers the simultaneous solution of the lubrication and asperity contact problems at the roughness scale, including texturing features on the cylinder surface. The numerical model employs the Reynolds equation with mass-conserving cavitation to calculate the inter-asperity fluid pressure. The rough contact model utilizes the Hertz theory for elastic contact to calculate the contact pressure at each asperity between the piston liner surface and the admitted smooth and rigid ring surface. Surface texturing demonstrated remarkable effectiveness, particularly in the hydrodynamic lubrication regime, with a maximum friction reduction of 38.5% observed for an area coverage of 50%. This was accompanied by a notable shift in the transition from the boundary to the mixed lubrication regime. The textured surfaces exhibited consistent efficiency in reducing fluid pressure and shear stress as the coverage of the textured areas increased. The incorporation of dimples on these surfaces played a crucial role by augmenting the lubricant storage capacity while concurrently reducing the real shear and contact areas. This study offers valuable insights into the nuanced friction-reducing mechanisms of surface textures, illuminating their influence on the coefficient of friction and the formation of lubricant films across various lubrication regimes.

A method for estimating the contact area of a dual-mobility total hip prosthesis

The term “contact area” refers to the total surface area of two entities in direct physical touch. When discussing an artificial hip joint, “contact area” refers to the surface area of contact between the components of the artificial hip joint (ball and cup) positioned inside the patient. Several methods can be used to figure out the contact area of an artificial hip joint, such as finite element analysis and traditional experiments on contact mechanics with hip joint simulators. The contact area in an artificial hip joint ensures load distribution. For optimal and long-term performance, the prosthetic hip joint’s contact area must be well understood for design, fitting, and monitoring. This study presented a novel method to estimate the liner surface contact area due to interaction contact in the artificial hip joint using a computer-aided design (CAD) program. This study also contrasted numerical approaches utilizing computer-aided engineering software and theoretical predictions based on Hertz theory with three-dimensional processes using CAD software to determine the contact area in the inner liner. There were no significant discrepancies in the outcomes of the three approaches.

Prediction of Nanoscale Water Meniscus Shape between Deliquescent KDP Crystal Optics and AFM Probe for Water-Dissolution Repairing.

KDP (KH2PO4) crystal optics are the key elements for megajoule laser facilities. Nanoscale surface defects would cause laser-induced damage when the optics are irradiated by a high-fluence laser (over 10 J/cm2). Dip-pen nanolithography (DPN) could be used to repair the nanoscale surface defects in the KDP optics by the water meniscus. The high humidity required for high-efficiency and soft KDP surfaces penetrated by the AFM probe brings challenges for accurately predicting the water meniscus shape to evaluate the effectiveness of the DPN water-dissolution repairing. The multisolutions of the Young-Laplace and Kelvin equations also lead to the wrong water meniscus shape. A theoretical model that takes the high humidity and the penetration of the AFM probes into account is developed. The parametrization Young-Laplace equations are adopted for the zero contact angle of the water films, and the AFM probe is treated as the combination of the cone and sphere for the water meniscus whose size is larger than the AFM tip radius under high humidity. The penetration of the AFM probe is modeled by Hertz theory. Both the water films (3.3 nm thickness at 99% relative humidity) and indentations (1.46 nm depth at 300 nN contact force) are non-negligible for the nanoscale water meniscus between the KDP surface and the AFM probe. Moreover, the rough-fine two-step method is proposed to lock the correct solution of the Young-Laplace and Kelvin equations. The effectiveness of the proposed model is verified by comparison with reported ESEM images and pull-off forces. In addition, the overgrowth dots on the KDP surface are compared with the water meniscus. The linear growth of the water meniscus would cause the linear growth of the overgrowth dot, which proves the proposed model could be used to guide the DPN water-dissolution repairing for the nanoscale surface defects in the KDP optics.

Knowledge-wrapping method for prediction and evaluation of material removal behavior in robotic belt grinding

Reliable prediction and evaluation of material removal (MR) is a continuing pursuit in the grinding process. Mechanistic and empirical MR models always suffer from inaccuracies and restricted applicability, whereas data-driven approaches remain deficient in sample dependence, generalization, and physical interpretability. This motivates us to develop a knowledge-wrapping method (KWM) to predict and characterize the material removal behavior in robotic belt grinding. A physical material removal profile model (PHY) that suits the robotic belt grinding is first presented by appealing to the Archard law and Hertzian theory. Next, the knowledge-wrapping matrix is designed to wrap the physical constraints into a form of design matrix by transforming the mechanistic and empirical models into a linear system. The knowledge-wrapping matrix and the experimental data are then connected via a likelihood function with the consideration of measuring noise, yielding a hybrid-driven learning process that preserves interpretability from PHY. Comparative experiments and MR mechanism interpretations are finally presented to demonstrate the effectiveness and superiority of the proposed method.

Theoretical modeling of key parameters of wet film in roll coating process of coating panel

The purpose of this dissertation is to quantitatively regulate the wet film thickness of coating panels in metal packaging during roll coating, which has not been accomplished in previous studies. The aim of the research is to derive a formula model for the roll coating machine, which is a general-purpose equipment, to provide theoretical support for quantitatively regulating wet film thickness and calculating leveling time. Based on the coating leveling formula studied by Orchard [Appl. Sci. Res. 11, 451 (1963)], combined with the working conditions of the roll coating process, an innovative application of boundary slip theory and Hertzian theory is used to analyze the functional relationship of each parameter in the roll coating process, and to construct a model of wet film leveling time. The process data were obtained from factory equipment. The validation of the formula model refers to the method adopted by Wang and others, who processed experimental fixtures with different wavelengths and crest heights to experimentally validate the model. The average thickness of the wet film and the leveling time are the key to the roller coating process. The average wet film thickness is the key parameter affecting the quality of the product, and the leveling time determines when the wet film enters the dry film process. The wet film thickness mainly depends on the pressure of each roll in the roll coating process. The wet film leveling time model accurately constructs the functional relationship between process parameters, leveling time, and wet film thickness, which can be quantitatively calculated. The leveling time model is experimentally verified to be correct.

A Fractal Prediction Method for Contact Stiffness of Helical Gear Considering Asperity Lateral Contact and Interaction

The normal contact stiffness (NCS) on rough surfaces has a significant impact on the dynamic characteristics of helical gear. Aiming at the problem of inaccurate calculation of the NCS model under the traditional Hertz theory of smooth surfaces, a fractal prediction model of helical gear contact stiffness considering asperity lateral contact and interaction between asperities is proposed in this paper. The variation formula of asperity and the correction coefficient of a tooth contact surface under asperity lateral contact and interaction are derived, and the influence of micro-elements on normal load and NCS is qualitatively analyzed. The results show that the NCS of considering the interaction and lateral contact of asperity is closer to the experimental results; the contact surface correction coefficient increases with the increase of curvature radius and load. The NCS of a tooth surface increases with the increase in fractal dimension D or the decrease in roughness amplitude G. The influence of asperity lateral contact and interaction decreases with the increase in D and the decrease in G. The NCS of the helical gear decreases under the lateral contact and interaction of the asperity, which is critical for exact estimation of the NCS of contact surfaces in gear.