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D. P. Vakharia - One of the best experts on this subject based on the ideXlab platform.
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Extending Hertz Equation for an elastic contact between a layered cylindrical hollow roller and flat plate through an experimental technique
Industrial Lubrication and Tribology, 2017Co-Authors: Mitul Thakorbhai Solanki, D. P. VakhariaAbstract:Purpose The purpose of this paper is to extend the Hertz Equation for the contact interaction between a layered cylindrical hollow roller and a flat plate through an experimental technique. Design/methodology/approach In this work, an experimental investigation is carried out for an elastic contact between layered cylindrical hollow rollers of different hollowness, ranging from 30 to 75 per cent hollowness and a flat plate. The footprint method was used for the evaluation of the contact width corresponding to the applied load. Findings The contact width for the layered cylindrical hollow roller was evaluated and the Hertz Equation was extended on the basis of the experimental results. Originality/value The value of this research work is the development of an extended Hertz Equation for a cylinder-on-plate configuration for a new kind of cylindrical roller.
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Evaluation of contact width for elastic hollow cylinder and flat contact through experimental technique and extending the capabilities of Hertz Equation
International Journal of Surface Science and Engineering, 2013Co-Authors: P. H. Darji, D. P. VakhariaAbstract:The phenomenon of two surfaces in contact is important in the field of tribology and has been studied by many researchers. The tribological problem arises from the points of contact between two surfaces. This paper presents a numerical and experimental analysis of the contact interaction between two elastic bodies ‘cylinder and flat’. In the numerical analysis Hertz theory is used to determine contact width of elastic contacts. Experimental investigation has been performed using aluminium foil, ink of carbon paper and by footprint method which is used to analyse a real contact area between two bodies for applied load conditions. A comparison of contact width between experimentally evaluated and numerically calculated is carried to validate the experimental procedure. The test results of footprint method are almost equal and very close with the numerical data. The experimental analysis suggested in this paper is useful to determine contact width and distribution of the load and stress in cylindrical roller bearing. Using this experimental method elastic contact between hollow cylinder of 67% hollowness and flat body has been studied. Finally in the present work extended Hertz Equation was developed for the calculation of half contact width for hollow cylinder and cylinder/flat body contact.
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Extending the Capabilities of Hertz Equation Through Theoretical and Experimental Method
Volume 4: Design and Manufacturing, 2009Co-Authors: P. H. Darji, D. P. VakhariaAbstract:Contact analyses have been conducted over more than one century starting with Hertz who analyzed normal frictionless elastic contact between half-spaces with small deformation. The phenomenon of two surfaces in contact is important in the field of tribology and has been studied my many researchers. Hollow roller bearings find wide applications owing to their lower inertia, better radial stiffness and cooler running. The preloading of the rollers ensures many superior operating characteristics such as higher radial stiffness, rotational accuracy and higher speed capability. For hollow roller method is available for the calculation of contact width and contact stresses and all other important terminologies which are available for the solid roller. This paper presents a numerical and experimental analysis of the contact interaction between two elastic bodies “Cylinder and Flat”. In the numerical analysis Hertz theory is used to determine contact width for elastic contact. Experimental investigation has been performed by footprint method which is used to analyze a real contact area between two bodies for applied loading conditions. A comparison with the numerical data is given to validate the experimental procedure. The test results are almost similar and very close with the numerical data. Using this experimental method elastic contact between hollow cylinder and flat has been studied. Finally in the present work modified Hertz Equation was developed for the calculation of half contact width for hollow cylinder and cylinder/flat body contact.
Babatunde Abdulkarim Eweina - One of the best experts on this subject based on the ideXlab platform.
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Predicting cashew nut cracking using Hertz theory of contact stress
Journal of the Saudi Society of Agricultural Sciences, 2019Co-Authors: Joshua Sunday Ojolo, Babatunde Abdulkarim EweinaAbstract:Abstract The cracking force is an important parameter in the design of cracking machines. A mathematical model for predicting the exact cracking force of cashew nut was presented based on the existing Hertz’s theory of contact stress of two bodies under uniaxial compressive load. Hertz Equation was adapted to loading of cashew nuts to cracking at three different loading orientations (X, Y, and Z) and two strain rates of 5 mm/min and 10 mm/min. The average moisture content of the dried cashew nuts was determined at 5% (db.). The physical properties of cashew nut varieties such as Length, Width, Thickness, mass, Geometric Mean diameter, Sphericity index, Surface area and Aspect ratio were 34.31 mm, 24.86 mm, 16.55 mm, 6.13 g, 24.13 mm, 0.70, 1834.65 mm 2 and 0.73 respectively. Some mechanical parameters such as cracking force, deformation and stiffness modulus at loading orientations (X, Y, and Z) (355,288 and 289 N), (1.396, 1.5002 and 1.815 mm) and (313, 195 and 160 N/mm) at 5 mm/min, and (458, 276 and 480 N), (2.28, 1.767 and 3.7197 mm) and (202, 162 and 146 N/mm) at 10 mm/min were also obtained from the force-deformation curve respectively. These physical and mechanical parameters were required in the derived model. The aspect ratio was introduced as a correcting factor to the stiffness modulus to improve the prediction of the Hertz model. The highest value of mean cracking force (355 N) was determined at the X (Width) orientation at 5 mm/min while the highest value of mean cracking force (480 N) at 10 mm/min strain rate was found at the Z (Thickness) orientation. A two-sample t -test comparism of experimental cracking force values and that of the Hertz model were acceptable at 5% probability level which gave good prediction of cracking force during compression. The force required for the design of suitable cashew nut shell cracking machine should be considered at the range of 400–500 N at X (width) and Z (thickness) loading orientations, therefore the magnitude of applied force with the loading orientation could determine the extent of mechanical damage and kernel recovery during cracking and separation processes.
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Predicting cashew nut cracking using Hertz theory of contact stress
Elsevier, 2019Co-Authors: Joshua Sunday Ojolo, Babatunde Abdulkarim EweinaAbstract:The cracking force is an important parameter in the design of cracking machines. A mathematical model for predicting the exact cracking force of cashew nut was presented based on the existing Hertz’s theory of contact stress of two bodies under uniaxial compressive load. Hertz Equation was adapted to loading of cashew nuts to cracking at three different loading orientations (X, Y, and Z) and two strain rates of 5 mm/min and 10 mm/min. The average moisture content of the dried cashew nuts was determined at 5% (db.). The physical properties of cashew nut varieties such as Length, Width, Thickness, mass, Geometric Mean diameter, Sphericity index, Surface area and Aspect ratio were 34.31 mm, 24.86 mm, 16.55 mm, 6.13 g, 24.13 mm, 0.70, 1834.65 mm2 and 0.73 respectively. Some mechanical parameters such as cracking force, deformation and stiffness modulus at loading orientations (X, Y, and Z) (355,288 and 289 N), (1.396, 1.5002 and 1.815 mm) and (313, 195 and 160 N/mm) at 5 mm/min, and (458, 276 and 480 N), (2.28, 1.767 and 3.7197 mm) and (202, 162 and 146 N/mm) at 10 mm/min were also obtained from the force-deformation curve respectively. These physical and mechanical parameters were required in the derived model. The aspect ratio was introduced as a correcting factor to the stiffness modulus to improve the prediction of the Hertz model. The highest value of mean cracking force (355 N) was determined at the X (Width) orientation at 5 mm/min while the highest value of mean cracking force (480 N) at 10 mm/min strain rate was found at the Z (Thickness) orientation. A two-sample t-test comparism of experimental cracking force values and that of the Hertz model were acceptable at 5% probability level which gave good prediction of cracking force during compression. The force required for the design of suitable cashew nut shell cracking machine should be considered at the range of 400–500 N at X (width) and Z (thickness) loading orientations, therefore the magnitude of applied force with the loading orientation could determine the extent of mechanical damage and kernel recovery during cracking and separation processes. Keywords: Cashew nuts, Hertz theory, Strain rates, Cracking force, Physical propertie
Miguel Pleguezuelos - One of the best experts on this subject based on the ideXlab platform.
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contact stress calculation of high transverse contact ratio spur and helical gear teeth
Mechanism and Machine Theory, 2013Co-Authors: Miryam B. Sánchez, Jose I Pedrero, Miguel PleguezuelosAbstract:Abstract For contact stress calculations of spur and helical gears, the Hertz Equation can be used in combination with a model of load distribution along the line of contact. This load distribution is not uniform due to the changing rigidity of the pair of teeth along the path of contact and has decisive influence on the location and the value of the critical contact stress to consider for calculations. Moreover, the load distribution can be highly influenced for non-standard gearing conditions as the presence of undercut, enlarged tooth addendum or reduced center distance, often present in high transverse contact ratio gears. In this paper, a new calculation method of the contact stress of spur and helical gears with transverse contact ratio greater than 2 is developed. It is based on the Hertz Equation and an enhanced model of load distribution, obtained from the minimum elastic potential criterion, suitable for non-standard gearing conditions. A complete study on the critical load conditions and the value of the critical contact stress has been carried out. As a result, a recommendation for pitting load capacity calculations is proposed.
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critical stress and load conditions for pitting calculations of involute spur and helical gear teeth
Mechanism and Machine Theory, 2011Co-Authors: Jose I Pedrero, Miguel Pleguezuelos, Marta MunozAbstract:Abstract Calculation methods of spur and helical gear drives for preliminary designs or standardization purposes available in technical literature, use the Hertz Equation to evaluate the contact stress, assuming the load to be uniformly distributed along the line of contact. However, this model presents some discrepancies with experimental results because the changing rigidity of the pair of teeth along the path of contact produces a non-uniform load distribution, which implies that some load distribution factors are required to compute the contact stress. In this paper, a non-uniform model of load distribution along the line of contact, recently developed, obtained from the minimum elastic potential criterion, has been used. This model combined with the Hertz Equation yields more accurate values of the contact stress. As the load per unit of length at any point of the line of contact and any position of the meshing cycle has been described by a very simple analytic Equation, a complete study of the location and value of the critical contact stress has been carried out. From this study, a recommendation for the calculation of the pitting load capacity of spur and helical gears is proposed.
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Contact stress calculation of undercut spur and helical gear teeth
Mechanism and Machine Theory, 2011Co-Authors: Jose I Pedrero, Miguel Pleguezuelos, Marta MunozAbstract:Abstract The presence of undercut at the pinion root may affect the load sharing among couples of spur gear teeth in simultaneous contact, as well as the load distribution along the line of contact of helical gears. This occurs if the outside points of the wheel profile do not find, due to undercut, mating profile to mesh with, which is called vacuum gearing. Under these conditions, the effective contact ratio is reduced, and the critical contact points may be shifted from their locations at non-undercut profiles. In this paper, a non-uniform model of load distribution along the line of contact, obtained from the minimum elastic potential criterion, has been used combined with the Hertz Equation for the calculation of the contact stress. A complete study on the critical load conditions and the value of the critical contact stress has been carried out, considering a wide range of the values of the geometrical parameters. As a result, a recommendation for pitting load capacity calculations of vacuum-gearing spur and helical gears is proposed.
Tomasz Panczyk - One of the best experts on this subject based on the ideXlab platform.
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Studies of the collision frequency of ideal gas particles with the surfaces of the objects created using the ballistic deposition technique
Applied Surface Science, 2008Co-Authors: Tomasz Panczyk, T. P. Warzocha, Wladyslaw RudzinskiAbstract:Abstract This paper is a continuation of our studies of the collision frequency of ideal gas particles with the rough/fractal surfaces. Here, we applied a more realistic surface growth model, i.e. ballistic deposition for creation of fractal objects. We found that the collision frequency with irregular surfaces is the linear function of pressure and this frequency per unit pressure is quite a complicated function of the surface fractal dimension as well as the diameter of colliding particle. The collision frequency with rough surfaces cannot be exactly described by the analytical formula called the Langmuir–Hertz Equation. However, we have stated that the deviations of the true collision frequency from the Langmuir–Hertz prediction are not huge and in typical catalytic studies the error introduced by replacing the true frequency by the Langmuir–Hertz prediction can be safely neglected. We have also studied the probability of finding on the surface an atom which has been hit a certain number of times by a gas particle. This probability reveals an interesting behaviour for small gas particles, i.e. it perfectly correlates with the number of directions from which the surface atom is accessible from the gas phase. We have also estimated the evolution of the adsorption energy distribution with the increasing fractal dimension of the surface in the ballistic deposition.
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Collisions of ideal gas molecules with a rough/fractal surface. A computational study.
Journal of Computational Chemistry, 2006Co-Authors: Tomasz PanczykAbstract:The frequency of collisions of ideal gas molecules (argon) with a rough surface has been studied. The rough/fractal surface was created using random deposition technique. By applying various depositions, the roughness of the surface was controlled and, as a measure of the irregularity, the fractal dimensions of the surfaces were determined. The surfaces were next immersed in argon (under pressures 2 × 103 to 2 × 105 Pa) and the numbers of collisions with these surfaces were counted. The calculations were carried out using a simplified molecular dynamics simulation technique (only hard core repulsions were assumed). As a result, it was stated that the frequency of collisions is a linear function of pressure for all fractal dimensions studied (D = 2, …, 2.5). The frequency per unit pressure is quite complex function of the fractal dimension; however, the changes of that frequency with the fractal dimension are not strong. It was found that the frequency of collisions is controlled by the number of weakly folded sites on the surfaces and there is some mapping between the shape of adsorption energy distribution functions and this number of weakly folded sites. The results for the rough/fractal surfaces were compared with the prediction given by the Langmuir-Hertz Equation (valid for smooth surface), generally the departure from the Langmuir-Hertz Equation is not higher than 48% for the studied systems (i.e. for the surfaces created using the random deposition technique). © 2006 Wiley Periodicals, Inc. J Comput Chem 28: 681–688, 2007
Jose I Pedrero - One of the best experts on this subject based on the ideXlab platform.
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contact stress calculation of high transverse contact ratio spur and helical gear teeth
Mechanism and Machine Theory, 2013Co-Authors: Miryam B. Sánchez, Jose I Pedrero, Miguel PleguezuelosAbstract:Abstract For contact stress calculations of spur and helical gears, the Hertz Equation can be used in combination with a model of load distribution along the line of contact. This load distribution is not uniform due to the changing rigidity of the pair of teeth along the path of contact and has decisive influence on the location and the value of the critical contact stress to consider for calculations. Moreover, the load distribution can be highly influenced for non-standard gearing conditions as the presence of undercut, enlarged tooth addendum or reduced center distance, often present in high transverse contact ratio gears. In this paper, a new calculation method of the contact stress of spur and helical gears with transverse contact ratio greater than 2 is developed. It is based on the Hertz Equation and an enhanced model of load distribution, obtained from the minimum elastic potential criterion, suitable for non-standard gearing conditions. A complete study on the critical load conditions and the value of the critical contact stress has been carried out. As a result, a recommendation for pitting load capacity calculations is proposed.
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critical stress and load conditions for pitting calculations of involute spur and helical gear teeth
Mechanism and Machine Theory, 2011Co-Authors: Jose I Pedrero, Miguel Pleguezuelos, Marta MunozAbstract:Abstract Calculation methods of spur and helical gear drives for preliminary designs or standardization purposes available in technical literature, use the Hertz Equation to evaluate the contact stress, assuming the load to be uniformly distributed along the line of contact. However, this model presents some discrepancies with experimental results because the changing rigidity of the pair of teeth along the path of contact produces a non-uniform load distribution, which implies that some load distribution factors are required to compute the contact stress. In this paper, a non-uniform model of load distribution along the line of contact, recently developed, obtained from the minimum elastic potential criterion, has been used. This model combined with the Hertz Equation yields more accurate values of the contact stress. As the load per unit of length at any point of the line of contact and any position of the meshing cycle has been described by a very simple analytic Equation, a complete study of the location and value of the critical contact stress has been carried out. From this study, a recommendation for the calculation of the pitting load capacity of spur and helical gears is proposed.
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Contact stress calculation of undercut spur and helical gear teeth
Mechanism and Machine Theory, 2011Co-Authors: Jose I Pedrero, Miguel Pleguezuelos, Marta MunozAbstract:Abstract The presence of undercut at the pinion root may affect the load sharing among couples of spur gear teeth in simultaneous contact, as well as the load distribution along the line of contact of helical gears. This occurs if the outside points of the wheel profile do not find, due to undercut, mating profile to mesh with, which is called vacuum gearing. Under these conditions, the effective contact ratio is reduced, and the critical contact points may be shifted from their locations at non-undercut profiles. In this paper, a non-uniform model of load distribution along the line of contact, obtained from the minimum elastic potential criterion, has been used combined with the Hertz Equation for the calculation of the contact stress. A complete study on the critical load conditions and the value of the critical contact stress has been carried out, considering a wide range of the values of the geometrical parameters. As a result, a recommendation for pitting load capacity calculations of vacuum-gearing spur and helical gears is proposed.