Tooth Bending Strength Research Articles

Assessment of the Uniform Wear Bending Strength of Large Modulus Rack and Pinion Pair: Theoretical vs. Experimental Results

Due to long-term operation under low-speed and heavy-load conditions, large module gears and racks are inevitably subject to tooth surface wear. To investigate the changes in gear tooth bending strength, the Three Gorges ship lift was taken as the research object and a simulation test bench was established. An analytical method, a finite element method, and an experimental method were utilized to analyze the bending stress of gears under normal and various uniform wear conditions. The obtained results revealed that with the increase in wear degree and load, the bending stress of single-tooth meshing was significantly higher than that of double-tooth meshing, and the single-tooth meshing time also increased, which indicates that gear wear accelerated the process of performance degradation. Furthermore, the relative errors obtained by the three calculation methods were all at a low level. This investigation aims to provide a solid theoretical and experimental basis for the dynamic analysis of large module gear and rack transmission.

Reverse engineering of geometric design parameters using shape information of non‐standard spur gear

AbstractIn this study, we conducted research on a method to reverse engineer geometric design parameters from the shape information of gears. The module and normal pressure angle were tracked using the bisection method, and the profile shift coefficient was extracted from the relationship between the working pitch circle diameter, center distance modification coefficient, and working pressure angle. It was confirmed that there are limitations to reverse engineering the shape using only a coordinate measuring machine or 3D scanner because various geometric information is additionally required to trace back the design requirements for gear strength. Finally, the gear tooth bending strength was calculated using finite element analysis and theoretical formula, and through this, the required level of gear strength design was inferred, and the verification of the gear reverse engineering method presented in this study was attempted.

FORCE CALCULATION OF THE ABENICS ACTIVE HINGE OF THE MANIPULATOR-MOTOR OF THE MULTI-PURPOSE ROBOTIC PLATFORM

It has been established that the prerequisite for multi-purpose robotic platform (MPRP), which determines the use of a manipulator-mover with an active Abenics joint, is, first of all, road conditions (locality), because in field conditions or as a result of missile and artillery damage, such extreme conditions occur when the movement on the main mover is impossible and there is a need to involve auxiliary (additional) mechanisms. The design features of the Abenics technology were analyzed and its advantages in providing three degrees of freedom at one point of contact were clarified. On the basis of the provisions of the theory of machine parts and the Solid Works software, the strength calculation of the Abenics hinge was carried out, namely: allowable contact fatigue stresses 412 MPa, allowable bending stresses 267 MPa; circular Ft 683 N and radial Fr 247,9 N forces in engagement. The transmission was checked for contact stress strength H 407,6 MPa and for the bending strength of the wheel teeth in 41,95 MPa; the torque around the Abenics active joint is determined in Mкрш 136 Nm. The distribution of stresses relative to the faces to which a force of 683 N was applied is graphically presented. The manipulators-movers in which the Abenics active hinge will be used, with the above results, will have a load capacity of 150-200 kg, which makes it possible to evacuate a wounded soldier with equipment or deliver corresponding load on the front edge (firing positions). Thus, the approach proposed by the author can be the basis for the creation of new promising MPRPs with increased operational properties such as passability and stability, because their manipulators will be able, if necessary, to perform the function of a stepping or wheel drive. It is proposed to first of all implement the capabilities of Abenics technology on MPRPs of rear, technical and medical support, which will not require additional stabilization of their hull in comparison with combat and special ground robotic complexes. In the future, the same technology can be applied in the field of mobile robotics, because it allows you to design the connection of links (kinematic pairs) of the manipulator on an active ball joint, that is, at one point, while increasing the efficiency of the operation of the manipulator by reducing the consumption of resources.

Analysis of the Effect of Shaft Misalignment on Tooth Bending Strength and Contact Stress of Helical Gear

Analysis of the Effect of Shaft Misalignment on Tooth Bending Strength and Contact Stress of Helical Gear

Fully ceramic versus steel gears: Potential, feasibility and challenges

The most common gear strength calculations performed in accordance with ISO/TC 60/SC 2 include surface durability and root bending strength. Typical geared power transmissions are characterized by high Hertzian contact stresses (surface durability) on the flanks – frequently in the order of 103 MPa – versus almost half an order magnitude lower first principal stresses on the tooth root (tooth bending strength). Therefore, the use of high strength special steel alloys is almost mandatory, especially in high-end applications, mainly to withstand the high contact stress values. Ceramic materials are typically characterized by high compressive strength versus very low flexural strength that at first glance makes them inefficient for gear transmissions since they are unlikely to withstand the tensile root stresses. Nevertheless, ceramic materials possess a number of advantages that makes them potential candidates for geared transmissions, such as their exceptional thermal properties, their low density (weight), their excellent wear characteristics and limited lubrication demands. The present work investigates the main challenges of using high-end ceramic gears and attempts to provide an insight on defining the design envelope of such gears to counter the main disadvantages. The increase of the normal pressure angle beyond the 25° limit set by ISO 6336 is primarily investigated, since in minimizes the tensile tooth root stresses, while also increasing the curvature of the contact surfaces without greatly increasing Hertzian stresses. Comparative assessment of the performance of fully ceramic gear designs versus their conventional steel counterparts is performed through quasi-static FEA simulations to set the basic design requirements for such gears and to promote further investigation of the feasibility of their usage in high power density applications.

Binder jetting in gears

Due to near netshape production, powder metallurgically manufactured (PM) gears have a high potential to increase cost and resource efficiency. Compared to conventionally machined gears, the advantages of PM gears are the different local density distribution in the component and the potential integration of secondary design elements. These advantages are accompanied by the reduction of weight and the possibility of optimizing the NVH-behavior of a gear. PM gears may be manufactured by both, die pressing and additive manufacturing (AM). The powder bed-based additive manufacturing processes for metals can be classified into binder-based (e.g. Binder Jetting, BJT) and beam-based thermal processes (e.g. Laser Powder Bed Fusion, LPBF). Due to the specific process technology, the manufacturing of PM gears by die pressing is only economical for large batch sizes in series production. For small batches, AM offers an approach to manufacture gears that meet the requirements in terms of quality, strength, acoustics and economic efficiency of the manufacturing process.This report describes the potential of BJT gears made of stainless steel 17-4PH (X5CrN-CuNb16-4) with a relative density of ρ0,rel ≈ 99% regarding the tooth bending strength. The reliability of the process and thus the tooth bending strength can be increased further by a specific adjustment of process parameters. Subsequently, the gears are tested with regard to the tooth bending strength on the pulsator test rig. The results are summarized in a SN-curve.

Comparison of Tooth Bending Strength of Speed-increasing and Speed-reducing Involute Spur Gears

Comparison of Tooth Bending Strength of Speed-increasing and Speed-reducing Involute Spur Gears

OPTIMAL DESIGN OF INVOLUTE SPUR GEARS WITH INCREASED CONTACT RATIO: OBJECTIVE FUNCTION, VARIABLES PLANNING AND CONSTRAINTS

Reducing the mass and dimensions of involute spur gears is an actual task of modern mechanical engineering. One of the perspective ways to solve it is the use of gearing with an increased working tooth depth and profile contact ratio εα ≥ 2. The study is devoted to the development of optimal design methods for such gears. Optimality criteria is formulated as follows: the contact stresses in the pitch point must take a minimum value when all constructive, geometric, kinematic, and technological constraints are met, first, when the profile contact ratio εα ≥ 2 is ensured. Variables planning are defined. These are addendum coefficients of the basic racks tooth for pinion and wheel , ; profile angle of the basic rack α; addendum modification coefficient of the pinion x1. Formed a system of constraints for the variables planning: the main functional constraint of the minimum value of the profile contact ratio: εα ≥ 2; constraint for the addendum coefficients of the basic racks tooth for pinion and wheel , ; constraint for profile angle of the basic rack α; constraint for addendum modification coefficients x1, x2; absence of the cutter interference for tooth dedendum; absence of the sharpening for tooth addendum; absence of the mesh interference; ensuring the bending strength of pinion and wheel teeth. A method for solving the problem of optimal design is chosen. The method of probing the space of design parameters was chosen from all the variety. The points of the LPτ-sequence are used as test points. The method allows you to operate with a significant number of parameters – up to 51, provides a sufficiently large number of evenly distributed test points – up to 220. In further studies, it is planned developing of methods and algorithms for solving the problem. Also carry out test and verification calculations to confirm and evaluate the theoretical results. Keywords: spur gear, profile contact ratio, contact stress, optimal design, objective function, variables planning, constraints of the variables planning.

COMPARATIVE SERVICE LIFE ANALYSIS FOR WORM GEARS ACCORDING TO DIFFERENT FAILURE CRITERIA

In this paper, a comparative analysis of the service life of worm gear wheels for various failure criteria is carried out. Based on this analysis, a method is proposed for selecting the worm gear wheel material, the values of the modulus, on which the bending strength of the teeth depends. Research has shown that increasing the bending strength of teeth is of great practical importance, both for one-sided and two-sided loads. This also makes it possible to significantly increase the lifetime of one-side loaded gear wheels by replacing their working flanks with non-working ones. it was proposed to replace the working surfaces of the teeth of worm wheels after a certain service life.

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.

Методика расчета на прочность глобоидной червячной передачи

Worm gears are widely used in mechanical engineering. Recently, worm gears with a globoid worm attract a considerable interest. To improve the quality characteristics of globoid gears, their geometric dimensions and parameters, as well as the production technologies are being improved. It is also important to have a methodology for calculating the strength, which is, however, currently unavailable, and the state standards cover the issue of determining and calculating only the transmission geometry. In this regard, the development of the technique for calculating the contact and bending strength of a globoid worm gear appears relevant. The basic areas of the research are gear enhancement, production technology improvement, the gearing pattern study, working surfaces mathematical simulation, 3-D modeling, and the transmission calculation. The contact strength calculation is based on the Hertz’s formula taking into account the geometric features of globoid worm gears. The authors developed the calculation of the bending strength of the worm gear teeth based on the helical gear calculation method. The paper presents data on the influence of the mechanical properties of the materials of a worm and a worm gear wheel on the gear contact strength, gives the computed coefficients estimated values. The authors note that the dynamic load factor can increase significantly with the wear of the gear working surfaces. The research findings can be used to develop the design calculation technique, as well as to improve it to take into account the effect of transmission wear and working temperature on the operation duration.

Experimental investigation on the coconut fiber reinforced hybrid gear composites

Increasingly important in the realm of engineering, composite materials are becoming increasingly popular. This work focused on natural fiber reinforced polymer composite gear components. The sheath extracted from the coconut tree (natural fiber) is used as reinforcement for the epoxy matrix in this study. These coconut coir sheaths have a number of additional advantages, including low cost, lightweight, and availability. Experimental Study the influence of coir fiber treatment on the mechanical characteristics of a coir fiber reinforced epoxy composite. When compared to untreated coir composites, the mechanical characteristics of treated coir hybrid composites improved. Moreover, 20%, 30%, and 40% volume of glass short fiber were added with coir fiber to increase the composites' stiffness. The bending strength and impact strength of hybrid composites were determined experimentally. Also, the bending strength of the coir gear tooth was analyzed by FEA analysis.

Influence of grinding zones on the tooth root bending strength of case carburized gears

Knowledge of the expected tooth root bending strength plays a decisive role in the design of gear sets. Due to dimensional and shape changes resulting from distortion due to the heat treatment, unintentional, partial grinding in the tooth root area may occur, particularly in the application range of large gears. The influences of an unintentional grinding zone on the tooth root bending strength have not yet been clarified with sufficient accuracy. As a result, grinding zones lead to uncertainties when evaluating the tooth root bending strength and thus to a loss of time and cost in the field of industrial practice.This paper presents experimental investigations on the influence of grinding zones on the tooth root bending strength of case carburized gears. For the experimental investigations, there are three unground reference variants with different blasting treatments: non-blasted, mechanical cleaned by shot blasting and shot peened. The unground reference variants are examined regarding their tooth root bending strength. For the other test gear variants, different grindings zones are applied resulting in light and strong material removal by grinding. The variants with the different grinding zones are examined analogously regarding their tooth root bending strength and are subsequently compared to the reference variants.The results of the experimental investigations show that grinding zones can have diverse influences on the tooth root bending strength of case carburized gears– Non-blasted gears do not show changes regarding the tooth root bending strength with regard to light or strong grinding zones applied within this investigation.– Shot blasted (mechanical cleaned) gears show no change in the tooth root bending strength for light grinding zones (grinding application does not significantly alter the original residual stress state in the tooth root area).– Shot blasted (mechanical cleaned) gears show a reduction of the tooth bending strength of up to 20 % with regard to strong grinding zones (grinding application does significantly alter the original residual stress state in the tooth root area).– Shot peened gears show a behavior similar to that of shot blasted gears with reductions of the tooth root bending strength of up to 30 %.– Shot peening the strong grinding zones as a repair measure can increase the reduced tooth root bending strength again. However, for the investigated test gears, the resulting tooth root bending strength was below the shot blasted reference variant.The results of this paper help to evaluate the influence of grinding zones on the tooth root bending strength of case carburized gears more precisely compared to the generalized reductions of current standards and classifications. The results can be incorporated in standards such as DIN 3390 as well as ISO 6336 and can be applied in the field of industrial practice. Eventually, the findings help to reduce the current loss of time and cost caused by uncertainties regarding grinding zones.

Tooth bending strength of gears with a progressive curved path of contact

Abstract The article presents a comprehensive study on the tooth bending strength of spur gears with a progressive curved path of contact, or so-called S-gears. Systematic gear meshing simulations were conducted to study the effects of S-gear geometry parameters on tooth bending strength. Different S-gear geometries were analysed in a systematically organized manner, and a comparison was made against a standard 20° pressure angle involute shape. Furthermore, different material combinations, e.g. polymer/polymer, steel/polymer, and steel/steel, of both drive and driven gear were analysed within a meaningful range of loads. The gear profile shape, material combination of the drive and the driven gear, and the transmitted load were found as the main parameters affecting gear tooth bending stress. Complex, non-linear relations between the recognized effects and the corresponding root stress were observed. Based on the numerical results, a shape factor, which considers the above-mentioned effects, was introduced, and a model for root strength control of S-gears was proposed and verified employing the finite element method (FEM).

Gear Root Bending Strength: A Comparison Between Single Tooth Bending Fatigue Tests and Meshing Gears

Abstract Gear tooth breakage due to bending fatigue is one of the most dangerous failure modes of gears. Therefore, the precise definition of tooth bending strength is of utmost importance in gear design. Single tooth bending fatigue (STBF) tests are usually used to study this failure mode since they allow to test gears, realized and finished with the actual industrial processes. Nevertheless, STBF tests do not reproduce exactly the loading conditions of meshing gears. The load is applied in a predetermined position, while in meshing gears, it moves along the active flank; all the teeth can be tested and have the same importance, while the actual strength of a meshing gear, practically, is strongly influenced by the strength of the weakest tooth of the gear. These differences have to be (and obviously are) taken into account when using the results of STBF tests to design gear sets. The aim of this article is to investigate in detail the first aspect, i.e. the role of the differences between two tooth root stress histories. In particular, this article presents a methodology based on high-cycle multi-axial fatigue criteria to translate STBF test data to the real working condition; residual stresses are also taken into account.

Indicator of bending strength of planetary gear satellite teeth, cut with non-standard tool of various types

A method is presented for determining the radii of curvature of the transition curves of the tooth profiles of satellites of planetary gears with internal gearing of wheels, cut by a tool with a modified initial contour and having increased bending strength. A comparative analysis of the radii of curvature of the profiles of the teeth of the satellites, cut with standard and non-standard tools of different types (gear shaping and rack) is carried out. Keywords: non-standard gear cutting tool, transition curve, radius of curvature. Alexandrsun4009@gmail.com

Fiber deformation behavior of discontinuous CFRTP in gear forging

The purpose of the study is to elucidate fiber deformation behavior during the forging of a spur gear by using a carbon fiber reinforced thermoplastic billet. The billet was composed of PA6/UD chips with a fiber length of 30 mm and fiber volume fraction of 50%. A gear forging mold was developed to deform the billet into a gear shape without cutting the fibers. Three types of billets were prepared: a horizontal billet with fibers orientated in the X and the Y directions, a vertical billet with fibers orientated in the Z and the X directions, and a random billet with fibers randomly orientated in the X–Y plane. The fibers along the tooth profile were formed using the horizontal and vertical billets. The adjacent teeth were connected by the fibers. A maximum tooth bending strength was 500 MPa. The delamination occurred under the tooth valley. The orientation of fibers in the teeth using the random billet was also random. The fracture occurred in the middle of the tooth. The results indicated that the fiber orientation in the billet is strongly correlated to the fiber orientation in the gear teeth and the tooth strength. The fiber orientation in the billet proposed in the study can form a tooth with fibers along its profile and with high strength.

Comparative Service Life Analysis for Gears According to Different Failure Criteria

In this paper, a comparative analysis of the service life of gears for various failure criteria is carried out. Based on this analysis, a method is proposed for selecting the gearwheel material, the values of the modulus and the wheel width factor, on which the bending strength of the teeth depends. Research has shown that increasing the bending strength of teeth is of great practical importance, both for one-sided and two-sided loads. This also makes it possible to significantly increase the lifetime of one-side loaded gearwheels by replacing their working flanks with non-working ones. In this regard, a method has been developed for changing the working flanks of gear teeth after a certain operating life.

Investigation of the Nominal Tooth Root Stress for External, Cylindrical Gears with Symmetric and Asymmetric Profile

The determination of tooth bending strength is a basic issue in gear design. This work presents the change of nominal tooth root stress of external toothed, cylindrical gears depending on the geometry used. The nominal tooth root stress is analyzed with using finite element simulations. The numerical calculations are executed in Abaqus. The imported geometries are produced by our own program in MATLAB. The boundary conditions to the models are defined accordance with the most significant analytical methods used in practice. This approach allows mapping direct correlation analysis by these calculations. The optimization of computational capacity used is also considered. In addition to the examination of the significant tooth stress value of symmetrical element pairs, the position of the critical cross-section is also analyzed. The effect of the asymmetric design of the tooth profile on the nominal tooth root stress is also presented in our investigations. The purpose of the numerical simulations carried out here is to determine the effect of the coast side angle on the magnitude of the significant tooth root stress and the position of the critical cross-section.

Driving Performance of Natural Fiber Gears Made Only from Bamboo Fibers Extracted with a Machining Center

Plastic gears are light and can be used without any lubricant, but they have low strength and an adverse effect on the environment. Therefore, a new gear that maintains these advantages while mitigating the disadvantages has been proposed. The development of sustainable and reproducible natural materials is desired to address these environmental problems. Therefore, in this study, a method was devised to extract high-quality and precise bamboo fibers using a machining center. Then, the hot press method was used to produce a novel spur gear made from only bamboo fibers, which is a green and organic machine element with a complicated shape. The present paper describes the characteristics of the proposed bamboo fiber gears, considering experimental results, including the hot press molding conditions, and the influence of fiber length on tooth bending strength, root strain, and vibration due to meshing teeth.