Fillet Stresses Research Articles

An analytical approach for predicting the fillet and contact stresses in symmetric and asymmetric spur gears under frictional mesh assumptions

A precise estimation of the bending and contact stresses, as well as the true friction value during the gear mesh, are critical aspects of a cost-effective and safe gear design. Previous studies have usually neglected friction by assuming a frictionless contact. Additionally, the impact of friction on the bending stress of spur gears has rarely been addressed. Moreover, to the authors' best knowledge, the impact of friction on the weakest section, stress concentration factor, and Lewis form factor remain unexplored for both symmetric and asymmetric gears. This study presents an analytical model incorporating friction at different contact locations to calculate the variables related to the tooth's weakest section. This model facilitates the evaluation of the stress concentration factor, Lewis form factor, and maximum tensile stress for symmetric and asymmetric gears. The proposed model is especially beneficial for assessing the load-carrying capacity of spur gears operating in challenging conditions. The results showed that the asymmetric spur gear is superior to its equivalent symmetric counterpart in terms of tooth form factor; however, this superiority decreases as the coefficient of friction increases. In addition, friction has been found to have a greater effect on fillet stress than contact stress. For μ = 0.2, at the HPSTC, the contact load and tooth form factor decreased by 7 % and 12 %, respectively, and the fillet stress worsened by 13 % compared to the frictionless assumption. Meanwhile, at the LPSTC, the stress concentration factor and contact stress increased by 9 % and 3 %, respectively.

Simulation and experiment on residual stress and deflection of cruciform welded joints

Numerous engineering components and structures require welding, including ships, automobiles, and many other manufactured products. Distortions and residual stresses created in welded joints can lead to adverse and destructive effects on structural integrity, service life, and visual appearance, and can produce significant dimensional inaccuracies. The ability to predict these effects accurately is, therefore, crucial for ensuring weld functionality and long service life. This study aims to examine the characteristics of welding deformation and residual stress in cruciform fillet welded joints using the FE software Simufact Welding. In the work, experimental measurements of temperature, deflection, and residual stress were used to verify the simulation models. The effect of plate thickness and welding sequence on welding deformation was examined through numerical simulations and experimental work. Additionally, the cause of angular distortion was explained using an FE model. An X-ray diffraction technique was adopted to record residual stress levels for the cruciform fillet welded joints. Reasonable agreement was found between the experimental measurements and the results obtained from the simulations.

Experimental stress analysis of enhanced sliding contact spur gears using transmission photoelasticity and a numerical approach

Free-Form-Gear (FFG) is a recently published title for a gear that has a curved path of contact and offers contact between a convex addendum and a concave dedendum during the meshing cycle. Based on this method of designing a gear pair, the path of contact can be altered to improve the way the gears mesh and slide against each other by only adjusting the maximum pressure angle and the involute curve parameter. The analytical investigations into this gear pair indicated that, when compared to the standard involute gear pair, the sliding velocity, meshing efficiency, contact, and fillet strengths are improved while the contact ratio is decreased. In this study, experimental stress analysis is conducted on various configurations of the tooth profile and tooth fillet shape for the proposed FFG and the standard involute gear to validate the analytical results. Since it is difficult to measure the contact stress for the gear specimens, the contact stresses at critical points are estimated using an effective computational technique based on photoelastic data and a numerical approach utilizing the nonlinear least squares method. At the fillet zone, isochromatic fringe patterns are used to directly measure the maximum fillet stress. Using addendum modification coefficients, the reduction in contact ratio for the proposed FFG is eliminated, and the results are then verified experimentally. Based on the experimental estimations, the finite element analyses are conducted using ABAQUS to simulate the examined gear specimens. Under the same loading conditions, the experimental, analytical, and numerical results have all been in good agreement.

Optimization and S-N life cycle analysis of helical gear with nickel alloy MP35N

Gears are most critical components in mechanical power transmission systems. Helical gear is used to transmit power or torque at high speed, heavy loads with smooth and silent operation. It involves many variables including specific materials with consideration of force/stress analysis and its mechanical properties. The optimal design and its lead curve is the primary objective of the present work. The bending and surface strength of the gear tooth is considered to be the main contributors to gear failure. Thus, stress analysis on gear is vital to reduce the failures for optimal design. Analytical design for helical gear has been done with five different sets of parameters and then 3D modelling and FEM carried out with 30 cases and optimization was carried out to derive the best selection so that the fillet stress can be reduced and the life can be improved. The optimum lead curve is determined by the design of the experiment, transmission error calculation and response surface method. The results obtained in analytical design and FEM have been validated and it has been observed that by means of life it’s clear that Nickel alloy MP35N is more valuable and better material for manufacturing helical gear.

Analysis of fracture characteristics of thin and thick rim asymmetric spur gear based on strain energy release rate

Gears are one of the most important components in most mechanical machines, automobiles, and other wind mills. The gears are subjected to repeated fillet stress, which causes them to develop root fracture leading to the failure of the power transmission system. Hence, the gear should be resistant to fracture. Furthermore, reduced weight and size of the gear is necessary to reduce the overall weight of the transmission system. The effect of backup ratio on the fatigue crack behaviour of symmetric and asymmetric spur gear under mix mode fracture is investigated in this study. The strain energy release rate (SERR), T-stress, and stress intensity factors (SIFs) of thick and thin rim asymmetric spur gear under mixed-mode condition are determined. Additionally, the effective SIF and the shape factor are evaluated for all spur gears. It is noticed that the fracture resistance of asymmetric spur gear (ANCR) increases with an increase in rim thickness. Further, an increase in backup ratio increases the stability of the crack and hence retards the crack growth. In addition, the influence of backup ratio on fracture resistance decreases with an increase in drive side pressure angle. Hence, an increase in pressure angle at drive side increases the crack stability, and the resistance towards fracture. The inference of this study gives valuable guidelines for designing asymmetric spur gears to reduce the weight without compromising the service life.

A novel design for enhancing the surface durability of the spur gear systems

In this study, a general mathematical model for defining the gear tooth profile and its geometrical aspects that meet a desirable sliding contact during the meshing cycle is built. This model is based on the path of contact shape predefinition. In the contact path, a straight-line segment through the pitch point and a universal transition curve for the other segments are combined to create a free-form tooth profile with desired radius of curvature in the designed gear. The maximum pressure angle during the meshing cycle and the involute curve length parameter are only introduced to characterize this model. The designed gear in this study is given the title “free-form-gear” since it provided a universal manner of establishing the path of contact that provides desirable sliding conditions during the meshing cycle. The proposed tooth form, interference condition, contact ratio, contact stress, sliding coefficient, and meshing efficiency are derived and investigated in this study. The fillet stress and torsional mesh stiffness of the proposed gear pair are obtained using the finite element method (FEM). The performance of the new gear is compared to that of the standard involute and non-involute gear types. The results indicated that the method proposed in this study can be utilized to construct a gear pair with higher surface durability and strength than typical involute gear of the same size.

Effect of jet flow on cooling performance and thermal stress of a radial turbine back disc

In view of the development status of high-reliability and low-cost cooling technology for radial turbine of micro-gas turbine or vehicle turbocharger, the impingement cooling technology of the radial turbine back disc was proposed, and the improvement of the cooling efficiency and thermal stress of the turbine back disc was numerically simulated. The results show that the impingement cooling technology can greatly improve the cooling efficiency of the turbine back disc and reduce the stress level. When the relative cooling flow is 1.0%–3.0%, the average cooling efficiency of the lower part of the turbine back disc is increased by 258%–486% compared with no cooling, which can reduce the thermal stress at the fillet of the back disc by 140–216 MPa. Both the average cooling efficiency and the fillet stress of the back disc increase slightly as the relative position of the jet hole moves outward. When the relative cooling flow is controlled within 2.0%, the effect of this cooling technology on the performance of the turbine can be ignored.

Dynamic contact behavior of asymmetric spur gear

Abstract There is a growing demand for superior performing gear drives which can bear huge loads and has better endurance at high speed. Also, these gear pair should cost less and have a longer life of operation. There are some applications like automobile drive train, Aero-Engine, wind turbines where the loading on the gear drive is uni-directional. This gives the designers to freely look into non-standard gear design, where the drive side of the the gear needs not be symmetric when compared with the coast side. This led to developing of Asymmetric gear teeth. This work assesses in depth the dynamic contact behaviors of an involute asymmetric gear pair. The effect of the pressure angle change on the drive side is analyzed. Matlab was used to generate the gear teeth. This research gave an insight for evaluating the dynamic gear contact and predicting the dynamic loads occurring on gear tooth, which helps to optimize gear parameter design and to understand the complex gear meshing effect phenomenon. Dynamic analysis of spur gear pairs was solved numerically using LS-DYNA. The spur gear pair's dynamic fillet stress was correlated with an experimental result. The simulation results indicate that the stress distribution of the gear surface is governed by alteration of the tooth pressure angle. The current solution by the finite element application is intended to be implemented in gear dynamics for better understanding of the transient behavior and its harmonics.

Effect of easement geometry on rail end fillet stress at bolted rail joints for transit track

Continuously welded rail (CWR) has become more popular than bolted joints because of the advantages of continuous geometry and stiffness and the resulting maintenance savings. Due to a variety of reasons, a considerable number of bolted joints are still in service in rail transit systems. With the high frequency of impact loads, rail at bolted joints are vulnerable to defects, such as cracking and head-web separation that could lead to more drastic failures and consequences (i.e. derailments, etc.). To prolong the service life of joint bars and rails, rail-end easements in the center of the bar were proposed and became standard in some freight rail companies. However, the effectiveness of a joint bar easement largely depends on the geometry of the easement. Therefore, the easement designed for freight track may not be effective for rail transit infrastructure. Further, the effect of easement geometry has not been thoroughly investigated and documented. Therefore, this study investigates the stress distribution at the rail end bolt-hole and upper fillet areas for joint bars with different easement geometries through a parametric analysis performed with Finite Element (FE) modeling. The FE model used in this study was developed specifically to study rail joints and was validated through full-scale laboratory testing. Results from this study show that a deeper easement yields lower contact stresses, while a longer easement does not necessarily reduce the contact stresses with the studied combination of rails and bolted joints for transit track. An easement may reduce the service life of the joint if the geometry of the easement is not properly engineered.

RESEARCH OF THE STRESS-STRAIN STATE OF THE MAIN CYLINDER OF THE HYDRAULIC PRESS

In the article the stress-strain state of the main cylinder of the hydraulic press for the manufacturing of large-sized plastic products has been investigated using software of finite-element analysis. It is established that the stress-strain state is characterized by a general and local uneven distribution of stresses and displacements. The nature of the distribution of stresses, deformations, displacements, safety factors along the length of the cylinder allowed conditionally divide the cylinder into three characteristic zones: flange zone, Lame zone, bottom zone. In each of the zones we found the areas in which the maximum stresses and strains are observed. It was found that the maximum equivalent stresses calculated according to the Huber-Mises energy theory of strength are observed on the inner surface of the cylinder, and in their fillets in the zones of the bottom and flange. A comparative analysis of the stresses and displacements determined by the Lame formulas and the finite element method showed that in the Lame zone their values do not change significantly. Studies on the influence of the radius, which varied over a wide range, and the fillet angle, made it possible to establish the region of maximum principal and equivalent stresses and reduce their magnitude. The calculations revealed the fillet region in which the axial tensile stresses act and determine the fillet angle at which the axial stresses are equal in magnitude and sign The study allowed to change the geometry of the cylinder, reduce the stress in the cylinder fillet and its weight. The results of the study can be applied to improve the existing and design of new hydraulic presses of the chemical industry, as well as the basis for further research.

Characteristics of Bending Stress with Whirling at the Rear End of a Crankshaft in an Inline 4-Cylinder High Speed Diesel Engine

<div class="section abstract"><div class="htmlview paragraph">As engines become lighter and achieve higher output to meet carbon dioxide emissions targets, it becomes more challenging to design a crankshaft that is both lighter and capable of handling higher loads. Therefore, it is necessary to understand the characteristics of forces imposed on the crankshaft, and the mechanisms by which stresses are created in the crankshaft. This paper describes the characteristics of bending stresses measured on the rearmost crank pin fillet of a crankshaft. Two basic crankshaft resonant modes are described. Forward crankshaft whirl then has the effect of increasing the system natural frequencies by the stiffening effect, while reverse whirl reduces the system natural frequencies by the softening effect. The effect of whirl grows with increasing engine speed. This results in what appears to be four crankshaft natural frequencies rather than two. The four resonances appear at all non-zero engine speeds. The influence of flywheel mass on the stresses and natural frequencies is also described. It is shown that the bending stress in the crank fillet is proportional to the radial force acting on the crank pin. It is also shown that the direction of whirl affects the amplitude of stress imposed by the radial crank pin force, and that the effect of whirl becomes larger as the flywheel inertia is increased. Because increasing engine speed causes more whirl force and moment, engine speed has an influence on bending stress amplitude. Finally, the paper explains why the ratio of crank stress amplitude to radial force varies as a function of the rotational direction of whirl.</div></div>

Influence of Addendum Modification Factor on Root Stresses in Normal Contact Ratio Asymmetric Spur Gears

Tooth root crack is considered as one of the crucial causes of failure in the gearing system and it occurs at the tooth root due to an excessive bending stress developed in the root region. The modern power transmission gear drives demand high bending load capacity, increased contact load capacity, low weight, reduced noise and longer life. These subsequent conditions are satisfied by the aid of precisely designed asymmetric tooth profile which turns out to be a suitable alternate for symmetric spur gears in applications like aerospace, automotive, gear pump and wind turbine industries. In all step up and step down gear drives (gear ratio > 1), the pinion (smaller in size) is treated as a vulnerable one than gear (larger in size) which is primarily due to the development of maximum root stress in the pinion tooth. This paper presents an idea to improve the bending load capacity of asymmetric spur gear drive system by achieving the same stresses between the asymmetric pinion and gear fillet regions which can be accomplished by providing an appropriate addendum modification. For this modified addendum the pinion and gear teeth proportion equations have been derived. In addition, the addendum modification factors required for a balanced maximum fillet stress condition has been determined through FEM for different parameters like drive side pressure angle, number of teeth and gear ratio. The bending load capacity of the simulated addendum modified asymmetric spur gear drives were observed to be prevalent (very nearly 7%) to that of uncorrected asymmetric gear drives.

The mathematical model and a case study of the cosine face gear drive that has a predesigned fourth order function of transmission errors and a localized bearing contact

Traditionally, a face gear drive uses an involute pinion. If the number of teeth of pinion is smaller than the minimum number of teeth without undercutting, the pinion will be undercut. To avoid undercutting, it is necessary to quit using involute pinion. This paper proposes a new face gear drive called cosine face gear drive. The cosine face gear drive has a predesigned fourth order function of transmission errors and a localized bearing contact. Therefore, it has a smoother motion curve and no edge contact problem. According to coordinate transformation theory, the theory of gearing, and differential geometry, the mathematical model of the cosine face gear drive is created, including position vectors, unit normal vectors, principal curvatures, principal directions, the condition of contact, and the condition for producing the predesigned fourth order function of transmission errors. A numerical case is studied to verify the mathematical model. The geometric solid model of the case is created. The actual form of the function of transmission error is analyzed. Contact paths and contact ellipses are analyzed. The effects of assembly errors on contact paths and on the function of transmission errors are analyzed. Contact and fillet stresses are analyzed using finite element analysis.

Fast tooth root load capacity optimization based on improved design of hob geometry

The competitiveness of gearboxes is significantly influenced by their performance ability. Increasing the tooth root load capacity has always been in focus of current research because in case of a failure of the gearwheel due to a tooth root fracture, the complete gearbox fails. This paper presents a new calculation method that enables the optimization of hob geometries within a few minutes so that they lead to reduced stresses in the tooth root fillet of spur gears. This results in reductions of the maximum tooth root stress of 10% and more for most gearwheels. The manufacturing costs for the optimized hob are only influenced slightly. In order to increase the computational speed compared to purely FE-based optimization methods, the present paper shows a method in which the decisive part of the optimization process is based on an analytical equation which are derived by a small number of FE-calculations.

Improving strength for automotive plastic gears through directional fibre reinforcement

In this paper, a new topology of reinforcing plastic gears with carbon fibres is introduced. The reinforcement is placed tangentially to the critical cross section at the tooth fillet to improve bending strength. The mechanical modelling of the fibrous reinforcement is performed using an anisotropic material stiffness matrix derived from the analysis of a representative volume element using commercial stress analysis software. Benchmarking against conventional plastic gears illustrates that the maximum fillet stress, which is responsible for tooth failure in overloading conditions is greatly reduced, therefore rendering these gears suitable for considering their use in high load applications such as in the automotive industry. Also, the effect of the thickness of the reinforcement on the maximum developed tensile stress at the root is examined. The results show significant decrease of the bending stress at the root fillet rendering this design an alternative way in reinforcing plastic gears.

Improving strength for automotive plastic gears through directional fibre reinforcement

In this paper, a new topology of reinforcing plastic gears with carbon fibres is introduced. The reinforcement is placed tangentially to the critical cross section at the tooth fillet to improve bending strength. The mechanical modelling of the fibrous reinforcement is performed using an anisotropic material stiffness matrix derived from the analysis of a representative volume element using commercial stress analysis software. Benchmarking against conventional plastic gears illustrates that the maximum fillet stress, which is responsible for tooth failure in overloading conditions is greatly reduced, therefore rendering these gears suitable for considering their use in high load applications such as in the automotive industry. Also, the effect of the thickness of the reinforcement on the maximum developed tensile stress at the root is examined. The results show significant decrease of the bending stress at the root fillet rendering this design an alternative way in reinforcing plastic gears.

Comparison of meshing characteristics of helical gears with spalling fault using analytical and finite-element methods

Abstract This paper investigates the effect of a gear tooth spalling in a helical gear. An analytical model was developed to study the effect of the damage to the time-varying mesh stiffness, contact stress and tooth root fillet stress. In order to validate the efficiency and the accuracy of the proposed method, a finite element method is presented for simulation, such to compare the mesh stiffness and stresses obtained from the analytical method under different spalling variables, including the spalling lengths, widths, axial positions (in the direction of face width) and tooth orientation positions (from dedendum to addendum). The results show that the proposed analytical method has higher computation efficiency than the finite element method, and the mesh stiffness obtained from two methods shows a good agreement. However, some errors exist between the time-varying mesh stiffness and stresses obtained by the two methods, but change laws of the tooth root stress and contact stress obtained from the two methods are similar. This is because the effects of flank-tip contact and spalling edge contact are considered in the finite element method, which makes the results more accurate than the results obtained by the proposed analytical method.

Stress Concentration factor Analysis of Helical Gear Drives with Asymmetric Teeth Profiles

This study investigates the influence of asymmetric involute teeth profiles for helical gears on the bending stress. Theoretically, bending stress has been estimated in spur involute gears which have symmetric teeth profile by based on the Lewis, 1892 equation. Later, this equation is developed by, Abdullah, 2012. to determine the effect of an asymmetric tooth profile for the spur gear on the bending stress. And then these equations are applied with stress concentration factor once for symmetric and once other for asymmetric teeth profile. In this paper, the bending stresses for various types of helical gear with various types of asymmetric teeth profile are calculated numerically for defined the stress concentration factor. The numerical solution based on the finite element method technique which that done by using the software simulation SolidWorks 2016. The results of this study indicate that the helical gear drive with asymmetric teeth profile having 'loaded side pressure angle' of ( ) and 'unloaded side pressure angle' of ( ) is better than a helical gear with standard teeth profile having pressure angle of ( ) from the regarding of tooth bending strength. Also, notes that the great enhancement in the results of maximum tooth bending stress for modified involute of tooth profile compared with the standard teeth profile. In addition to, predict the equation of stress concentration factor which is a function of both unloaded side pressure angle and helix angle and then it used with Abdullah equation for to determine the nominal stresses in the root fillet.

Aspects of stress in optimal shaft shoulder fillet

Shafts are among the most common machine elements. The typical shape used to reduce stress concentrations is circular arches due to the simplicity. A shaft is typically loaded by axial, bending, and torsional loads in different combinations. The stress concentration factors are found in tables and charts. The circular design is not optimal from a strength point of view, and the strength can be increased using shape optimization. It is in this article shown how the maximum stress from the combined loads can be minimized, when the shape is parameterized using the simple super ellipse. This makes the resulting optimized designs easily transferable to practical design. The stress evaluation is numerically performed using the finite element method using harmonic elements that facilitates an axisymmetric model although the loading is unsymmetric. The stresses are reduced by up to a factor of [Formula: see text].

Influence of gear ratio on wear depth of nonstandard HCR spur gear drive with balanced fillet stress

In this paper, the wear depth of a nonstandard High Contact Ratio (HCR) spur gear drive is investigated using contact analysis considering the load share between the tooth in contact, fillet stress and contact stress for number of mesh cycles in steel gears. The fillet stresses obtained using finite element method is balanced by varying the tooth thickness along the reference line. This method of changing the tooth thickness is referred as nonstandard HCR spur gear drive. Using this method, an improved nonstandard HCR spur gear drive is obtained in terms of bending strength. In this enhanced nonstandard HCR spur gear drive the wear depth is estimated analytically for balanced fillet stress. Also, this paper explores the influence of gear ratio over wear depth of nonstandard HCR spur gear drive and finally the results are discussed.