Tooth Root Strength Research Articles

Design of a Cost-Effective and Statistically Validated Test Specification with Selected Machine Elements to Evaluate the Influence of the Manufacturing Process with a Focus on Additive Manufacturing

Due to their versatile advantages, the use of additively manufactured components is growing. In addition, new additive manufacturing processes are constantly being developed, so that a wide range of printing processes are now available for metal. Despite the same starting material, the microstructure and thus also the final mechanical properties differ greatly compared to conventional processes. In most cases, only direction-dependent characteristic values from the uniaxial tension are used to qualify a printing process before it is used. The literature, on the other hand, demonstrates that the results are not transferable to other loading conditions. In this work, several engineering tests were integrated into a single test specimen so that they can be determined on the same specimen. The test specimen can be used to test tooth root strength, bending strength, notched bar impact energy, and thread strength depending on the mounting direction, thus representing industrial loading cases. In this study, test specimens were fabricated by conventional manufacturing (machining), L-PBF (Laser Powder Bed Fusion), and WA-DED (Wire Arc Direct Energy Deposition), and the results were compared using statistical methods. Factors to capture manufacturing influence and buildup direction were statistically validated on 316L. The work shows a benchmark with a typical initial microstructure of rolled and milled material, L-PBF, and WA-DED parts on loads close to the application and thus simplifies an industry-oriented evaluation of a new manufacturing process.

Biomimetics Design of Tooth Root Zone at Cylindrical Gears Profile.

During the last few decades, the requirements for modern machine elements in terms of size reduction, increasing the energy efficiency, and a higher load capacity of standard and non-standard gears have been very prevalent issues. Within these demands, the main goals are the optimization of the gears' tooth profiles, as well as the investigation of new tooth profile designs. The presented design idea is based on the optimal solutions inspired by nature. Special attention is paid to the new design of the tooth root zones of spur gears in order to decrease the stress concentration values and increase the tooth root fatigue resistance. The finite element method is used for stress and strain state calculations, and the particular gear pair is modeled and optimized for these purposes. For tooth root strength analysis, the estimations are based on the theory of critical distances and the stress gradients obtained through finite element analysis. The obtained stress gradients have shown important improvements in the stress distribution in the transition zone optimized by biomimetics. An analysis of the material variation influence is also performed. Based on the investigations of a particular gear pair, a significant stress reduction of about 7% for steel gears and about 10.3% for cast iron gears is obtained for tooth roots optimized by bio-inspired design.

Study on the Influence of Tool Tip Radius on the Tooth Root Strength of Helical Cylindrical Gear

The bending fatigue strength of the tooth is an important index to measure the bearing capacity of the gear. The tooth root transition curve has a great influence on the bending strength of the gear. The profile of the tooth root transition curve depends on the shape of the tooltip. Therefore, the geometry of the tooltip must be considered in the simulation process of tooth profile generation. Contact analysis of helical gears with accurate geometric models is carried out in this paper. After generating tooth profiles machined by tools with different tip radii using MATLAB software, the three-dimensional model of involute helical cylindrical gears is established in CREO, and the stress distribution of gears under diverse load conditions is analyzed by FE software. In the end, it is concluded that the size of the tooltip fillet radius has a great influence on the maximum bending strength of the tooth root, and the strength of the tooth root decreases by increasing the tool tip radius.

Design and Manufacturing Strategy of a Back-to-Back Test Rig for Investigation of Ultra High Cycle Fatigue Strength Regarding Tooth Root Strength in Aerospace Applications

Geared turbofans increase the efficiency of aircraft engines. By decoupling the fan and low- ressure turbine, both components can be operated at their optimum speed. Due to the high number of flight hours and the high turbine speeds of n > 10,000 rpm, the number of load cycles at the gear teeth of the planetary gear unit is significantly higher than the conventional fatigue strength of gear teeth. The planetary gears under fully reversed bending load are particularly susceptible to tooth root fractures. Pulsator test rigs are not suitable for testing tooth root load capacity under fully reversed bending load. The concept of a modified 3-shaft backto-back test rig was set up to cope with this challenge. A back-to-back test rig consists of a test and reference gearbox, which are connected by shafts to form a closed power circuit. In order to perform the investigation efficiently, the test rig is operated at a speed of n > 12,000 rpm with a recirculating power of P > 5 MW. This performance class results in special requirements for the test rig design. The roller bearing arrangements normally used for back-to-back test rigs no longer offer sufficient load carrying capacity, so that a changeover to journal bearings is necessary. This leads to high power losses of the bearings of P ≈ 200 kW and oil quantities of Q ≈ 450 l/min on the cooling and bearing lubrication side. The journal bearings of the gearboxes have a decisive disadvantage. Starting under load is not possible. Therefore, a hydraulic load unit was designed which allows load application at operating speed. In the reference gearbox, this unit shifts two helical gears on a spline shaft, which are slanted in opposite directions, towards each other, so that a torsional load is generated in the test gearbox by means of a closed power circuit. The two displaceable helical gears represent the greatest challenge from a manufacturing point of view. In order to achieve an even load distribution on both gears, they must be manufactured very precisely to each other and to the spline profile. In the report, the focus is set on the double helical reference gearbox including the axial load unit. Besides the design of the components the requirements regarding manufacturing are analysed and possible manufacturing chains are discussed.

Optimum design of the tooth root profile for improving bending capacity

Gear transmission is a major form of power transmission, of which the reliability greatly affects the life of many mechanical devices. Gears have two main failure modes, namely tooth surface pitting and tooth root fracture. Tooth surface pitting is mainly due to excessive contact stress and tooth root fracture is mainly due to excessive bending stress. In this paper, we focus on increasing the tooth root strength of spur gears by optimizing the hob tip contour. A hobbing simulation model is developed to generate the tooth root profile from its corresponding hob tip contour. The hob tip contour is defined by introducing a Bezier curve of five points. An optimization process based on genetic algorithm and FEM analysis is designed to find the optimal tooth root profile with larger bending load capacity. The optimal tooth root profile and its corresponding hob tip contour can be obtained for engineering application. This work provides a theoretical basis for spur gear design with a high bending load capacity.

High-strength gears produced by powder metallurgical processes – KL500/93-2

Purpose The purpose of this study is to optimize high-strength gears produced by powder metallurgical process and to provide a material model to predict the tooth root bending fatigue strength. Powder metal (PM) technology offers great opportunities for the reduction of the carbon footprint and improvement of the cost efficiency of gear production. PM gears can achieve flank load-carrying capacities comparable to wrought steel gears if the loaded volume is fully densified. Still, the tooth root strength is of particular importance. Design/methodology/approach The tooth root stresses can be minimized by optimizing the tooth root geometry. This usually leads to a target conflict, as fully optimized tooth root geometries cannot be manufactured by generating processes such as hobbing, generating-grinding or rolling. To use the increase in tooth root load-carrying capacity of fully optimized root geometry on PM gears, a non-generating method for surface densifying is needed. The shot-peening process is used as an alternative densification process for PM gears. The properties of both shot peened and cold-rolled PM gears are analyzed and compared. To quantify the effect of both manufacturing processes, the tooth root bending fatigue strength will be evaluated and compared to wrought gears. Findings From the fatigue strength perspective, a material model is developed, which is able to predict local endurable stress amplitudes. The model is gained through regression varying carbon content, density and size effect on bending specimens. Originality/value It is transferable to PM gears of the same material using a load transfer coefficient.

A model approach for considering nonmetallic inclusions in the calculation of the local tooth root load-carrying capacity of high-strength gears made of high-quality steels

Demands for higher performance have caused a need for improved component characteristics, e.g. through surface strengthening of gears and increased cleanliness of gear steels. Unfortunately, a resultant drawback is that cracks in such high-strength gears are more often initiated in the material matrix at nonmetallic inclusions and not at the surface. In standardized calculation methods, the degree of cleanliness of steels is not yet directly correlated to the tooth root load-carrying capacity. This paper considers the effects of nonmetallic inclusions in the steel matrix on the tooth root strength based on the theoretical approach of Murakami.

Fatigue Fracture Behaviour of Asymmetric Spur Gear Tooth Under Cyclic Loading

When the research on the gears are investigated, it is seen that there are different studies on the design and analysis. In the majority of research studies, the tooth root curve is designed as a trochoid curve as a results of production method. According to literature, application of the circular fillet method instead of the trochoid curve in the tooth root would increase the strength of the tooth root.Fatigue life will also be positively affected with increase of tooth strength. Because the less stress will develop in the tooth root, the fatigue life of the gear tooth will increase. In this study, we have designed and manufactured involute profile asymmetric spur gears using the circular fillet method in tooth root region.Involute profile asymmetric gears tooth have lower contact stress and superior tooth root strength than symmetric gears tooth. In this work, fatigue damages on asymmetric gear tooth caused by cyclic loads and effects of material hardness on fatigue life of gear tooth were investigated.In the extent of the study, a new single-tooth bending fatigue test apparatus (STBFT) was developed to investigate the fatigue performance of the gears. Low-cycle and high-cycle tests were done to detect the fatigue performance of the asymmetric gears.

Bending Fatigue Analysis of PM Gears

The paper discusses the computational and experimental approach for determination of the PM gears service life concerning bending fatigue in a gear tooth root. A proposed computational model is based on the stress-life approach where the stress field in a gear tooth root is determined numerically using FEM. The experimental procedure was done on a custom made back-to-back gear testing rig. The comparison between computational and experimental results has shown that the proposed computational approach is appropriate calculation method for service life estimation of sintered gears regarding tooth root strength. Namely, it was shown that in the case of proper heat treatment of tested gears, the tooth breakage occurred inside the interval with 95 % probability of failure, which has been determined using proposed computational model.

Comparative analysis of tooth-root strength using stress–strength interference (SSI) theory with FEM-based verification

Gear geometry plays a significant role in deciding the tooth deflection, magnitude of stress induced and stress distribution. Accurate evaluation of the stress state and distribution of stresses at the tooth root requires application of experimental methods to determine, such as electric resistance wire strain gauges, or photoelastic gauges, etc. These experimental methods are especially complicated, expensive, and laborious. Therefore, they are applied mainly in special cases. In the recent years, the methods of probabilistic design have been commonly accepted in the design of mechanical components and systems to assist the designer in making decisions on the best balanced design with respect to several design criteria. In probabilistic design, it is common to use parametric statistical models to calculate the probability of failure obtained from the Stress–Strength Interference (SSI) theory, which more nearly models the true situation. This paper discusses the application of the SSI theory that has been used to support the detailed gear design as part of the “Design for Reliability” approach to evaluate the tooth-root strength with finite element method-based verification. The SSI theory is formulated to predict the effect of the root fillet generated by rack or hob tool with and without protuberance on the gear system reliability. The results indicate the high fillet root stresses and gear tooth deflection in gears with the lowest tip radius of the generating tool.

Gear tooth rooth stress and fillet radii dependence

Tooth root form and fillet radius have a great influence on gear tooth root strength that is one of the primary subjects of this paper. Special attention is given to analysis on impact of gear tooth fillet radius at the critical cross section on stress value and distribution. A first initial crack appears at the gear tooth and it is affected, the most, by root stress concentration. Hence, this paper's research topic is focused on finding the optimal fillet tooth root radius to minimize the tooth root stress intensity. This paper provides results achieved by application of numerical methods - finite element method (FEM) and real working conditions simulation. The results of this analysis are presented as figures and tables of Von Mises and normal stresses as well as charts against different values of tooth root fillet radius ρF in two case: with one tooth root fillet radius ρF and with two fillet radii ρF1 and ρF2 ('two level approach' in a root).

Strength Optimization Design of a Helical Hydraulic Rotary Actuator

A helical hydraulic rotary actuator for part-turn motion control is presented. Because of its compact structure and large output torque, strength study for the helical hydraulic rotary actuator becomes very necessary. Using AWE, influences of multi-start thread engagement length, thread start number, spline pressure angle and piston material on strength of the actuator’s key parts are studied in depth, so as to optimize the actuator’s strength and structure. The results show that the influences of nut width, thread start number and piston material on multi-start thread root strength of nut are notable, the influence of pressure angle on spline tooth root strength of output shaft is visible, and stress concentration on multi-start thread root and spline tooth root is very obvious.

S111032 遠心力の影響を考慮した傾斜ウェブを持つ三次元構造薄肉平歯車の歯面接触応力及び歯元応力の理論解析([S11103]伝動装置の基礎と応用(3))

Deformations of thin-rimmed spur gears with inclined webs are analyzed by finite element method (FEM) when the gears are loaded under centrifugal forces. Then loaded tooth contact analyses of the gears with centrifugal deformations are conducted by mathematical programming method and FEM when the gears contact with a solid mating gear. Tooth contact stress and root bending stress are analyzed by FEM at the same time. It is found that centrifugal load exerts greater effect on tooth root stress when gear speed is over 10000rpm. So, it is necessary to take the effect of centrifugal load into account in tooth root strength calculation when gear speed is over 10000rpm. It is also found that centrifugal deformations of the gears almost have no effect on tooth contact patterns of the gears having inclined webs, though it has been reported that centrifugal deformations of the gears with the straight web have great effect on tooth contact patterns. This is because shape of the inclined web after centrifugal deformation is completely different from the shape of the straight web after centrifugal deformation. This difference results in the difference of tooth attitudes and then the difference of the effects of tooth centrifugal deformations on tooth contact patterns. It can be concluded that the effect of centrifugal deformations of the inclined web gears on tooth contact pattern can be neglected even if the gears have very high speeds.

Probabilistic Simulation Approach to Evaluate the Tooth-Root Strength of Spur Gears with FEM-Based Verification

Dependency on deterministic design techniques without attention to inherent process variations and uncertainties in gear design and manufacturing processes can lead to unreliable results and affect the performance of a gearing system. A better understanding of the impact of uncertainty associated with the system input on the system output can be achieved by including reliability techniques to accomplish a reliable design methodology. This emerged the need to consider the probabilistic behavior of the stress distribution on the gear tooth during the design phase. The present effort reports on the application of the SSI theory within the context of a “Design for Reliability” approach in support a detailed gear design methodology for the evaluation the tooth-root strength with FEM-based verification. The SSI theory is formulated to predict the effect of the root fillet generated by a rack or hob tool with and without protuberance on the gear system reliability. The results obtained from the probabilistic analysis strongly agreed with the FEM’ results across a range of different gear tooth fillet profiles. A quantitative assessment of the investigated gear sets showed the highest tooth-root stress was associated with the lowest tip radius of the generating tool. This approach helps with making the decision by quantifying the impact of stress and strength variations during the gear design stage.

Tooth Root Strength of Spur and Helical Gears Manufactured With Gear-Shaper Cutters

At the beginning of gear transmission design, mainly simplified methods of gear strength analysis based on ISO or AGMA standards are used. However, they allow for calculation of approximate and sometimes biased stresses. Moreover, ISO standard is generally focused on using racks for gear manufacturing. A method proposed in this paper allows for computation of the parameters of critical section, strength coefficients YF, YS, and tooth root stress σF according to the procedure from ISO standard also in the case of machining gears with gear type tools. The proposed improvement of ISO standard leads to replacement of real gear tool with rack with substitute tip radius ρa0*. The developed method maintains basic assumptions and advantages of ISO standard, including its simplicity. Simultaneously, it allows for computing the maximum tooth root stresses σF: (i) very close to results of accurate geometric analysis and finite element analysis, and (ii) much closer, compared to conventional ISO procedure, to results obtained using AGMA standard.

Comparative Analysis of Tooth-Root Strength Using ISO and AGMA Standards in Spur and Helical Gears With FEM-based Verification

Current trends in engineering globalization require researchers to revisit various normalized standards that determine “best practices” in industries. This paper presents comparative analysis of tooth-root strength evaluation methods used within ISO and AGMA standards and verifying them with developed models and simulations using the finite element method (FEM). The presented analysis is conducted for (1) wide range of spur and helical gears manufactured using racks or gear tools; and for (2) various combinations of key geometrical (gear design), manufacturing (racks and gear tools), and performance (load location) parameters. FEM of tooth-root strength is performed for each modeled gear. FEM results are compared with stresses calculated based on the ISO and AGMA standards. The comparative analysis for various combinations of design, manufacturing, and performance parameters are illustrated graphically and discussed briefly. The results will allow for a better understanding of existing limitations in the current standards applied in engineering practice as well as provide a basis for future improvements and/or unifications of gear standards.

Tooth-root stress calculation of internal spur gears

This paper is focused on analysis of tooth-root strength of internal gears. Methods of calculation of the tooth-root stress of internal gears according to the ISO 6336-3:1996 and DIN 3990-3:1987 standards are briefly described. Reasons for potential errors in the strength calculations of internal gears performed in accordance with the ISO 6336-3:1996 and DIN 3990-3:1987 standards are discussed. Determination of the precise values of the parameters of the critical section and introducing them to use with the ISO 6336-3:1996 standard, proposed in the paper and called the modified ISO 6336-3:1996 method, is presented. Finite element analysis of various accurate models of internal gears is performed and location of critical section as well as its parameters are determined for all considered models of gears. On the grounds of results of precise finite element computations made for a large number of models of gears. On the grounds of results of precise finite element computations made for a large number of models of gears the influences of several main parameters of the machined gear and applied tool on the tooth-root strength of internal gears are investigated. General conclusions concerning the tooth-root strength of internal gears are formulated. They concentrate on the influences of several main parameters of the machined gear and tool on the tooth-root stresses of gear. They are useful for correct determination of the parameters of the critical section of the internal spur gear and for proper selection of the main parameters of the machined gear and applied tool.