Tooth Bending Fatigue Research Articles

Effect of Initial Crack Position on Crack Propagation Behaviors of Heavy-Duty Transmission Gear.

The tooth bending fatigue fracture is caused by the alternating loads for the heavy-duty transmission gears. The crack initiation and propagation are the two major parts in the failure process. The crack propagation behavior is mainly affected by initial crack position except for the load and material properties. In this paper, the crack propagation model of a gear is established under the considering of crack initiation location by using extended finite element method (XFEM). The model accuracy is verified by testing results of strain and fractography by conducting the single-tooth bending fatigue experiment. The influence of crack initiation locations on subsequent crack propagation behavior is analyzed. The crack length in the tooth width direction and depth direction is faster when the initial crack is located in the middle of root surface. The crack growth rate is lower for the initial crack located in the surface close to the end surface of the gear.

Research on transformation method of bending fatigue test for single tooth bending fatigue and running gear based on minimum order statistics

Research on transformation method of bending fatigue test for single tooth bending fatigue and running gear based on minimum order statistics

Residual stress relaxation by bending fatigue in induction-hardened gear studied by neutron Bragg edge transmission imaging and X-ray diffraction

The compressive residual stress on the gear tooth’s surface, a vital parameter to control mechanical properties, such as strength, has a beneficial effect on the component’s fatigue life. A novel procedure, double induction quenching (DIQ), effective for improving the fatigue strength of gear products, has been used for producing gears with steep gradients of compressive residual stress generated in the tooth surface. We performed a Bragg edge imaging experiment at a pulsed neutron source to determine the spatial distribution of the {110} lattice spacing (d110) and the broadening of the {110} Bragg edge (w110) on the DIQ gear product after tooth-bending fatigue tests to which different loading cycles were applied. No significant difference occurred in the d110 and the w110 at Hofer’s critical section (tensile side) of the teeth with different loading conditions within the accuracy of data analysis. However, we detected a decrease in the w110 and changes in the residual lattice strain distribution in the axial direction (through the thickness) along the tooth root directions at the opposite side of Hofer’s critical section for both teeth after 3 × 105 and 8 × 105 cycles, relieving the compressive residual stresses during the fatigue process. The residual stress close to the gear tooth surface determined by X-ray diffraction using sequential polishing showed a slight relaxation and redistribution from the tensile side in the hoop direction, complementary to the neutron Bragg edge imaging information in the axial direction.

Exploiting a numerical method to translate single tooth bending fatigue results into meshing gears design data: the influence of material properties

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Computational model for bending fatigue prediction of surface hardened spur gears based on the multilayer method

A computational model for predicting both the location and the required number of cycles for bending fatigue failure in surface hardened spur gears is proposed. Linear elastic stresses and strains in a single tooth bending fatigue test are corrected for elastic–plastic material behavior. The tooth root region of spur gear is divided into layers. Fatigue properties are assigned to each layer via the hardness method. Based on the multiaxial fatigue criteria, fatigue failure location and corresponding fatigue lives are estimated. Predicted fatigue lives, failure locations, and transition from surface to subsurface fatigue failure show good agreement with the experimental results.

Effect of layer orientation on the single tooth bending fatigue strength of polymer gears manufactured by selective laser sintering

This study investigates the influence of tooth layer orientation on the bending fatigue behaviour of Nylon 12 spur gears manufactured by a selective laser sintering process in an ‘on-edge’ configuration. The test gears were submitted to single tooth bending fatigue tests, and the thermal response of gears was recorded using Infrared thermography. The surface morphology of failed teeth was examined using microscopy. The effect of tooth layer orientation on the fatigue strength of selective laser sintering gears was evaluated by testing each tooth configuration. The tooth configurations with the highest and lowest strength were 40° and 160°, respectively. The performance of selective laser sintering gears was compared with that of injection moulded Nylon 66 gears. The injection moulded, selective laser sintering 40°, and selective laser sintering 160° gear teeth were tested at multiple loads to investigate the high cycle fatigue and low cycle fatigue behaviour. The bending fatigue life was highest for the injection moulded gears in both low cycle fatigue and high cycle fatigue regimes. The surface temperature was higher in selective laser sintering gears, with 160° configuration exhibiting the highest temperature. The difference between the temperatures of selective laser sintering 40° configuration and injection moulded gear magnified as the applied load increased. Consequently, the strength of the selective laser sintering 40° configuration with respect to injection moulded gear deteriorated in the low cycle fatigue region. Fractography indicated that crack propagation in selective laser sintering 40° and selective laser sintering 160° configurations were cross-laminar and inter-laminar, respectively. In the cross-laminar mode of propagation, the crack propagation was impeded by the layer structure. However, the crack propagation was expedited in the inter-laminar mode, as the crack path was along the interlayer region, which presents a path of least resistance.

Расчет цилиндрической прямозубой передачи на компьютере

Spur gear is used in machines to transmit rotary motion. Due to its simple design, reliability and compactness, it is widely used in technical devices — clocks, conveyors, cars. Two wheels of such a transmission have a constant gear ratio and high efficiency. The first performance criterion is the contact stress fatigue strength of the teeth. The second one is the tooth bending fatigue strength. Manual calculation of a spur gear is a difficult task due to the large number of formulas and conditions. The design area is limited to a small number of options that are not always optimal. It was proposed to expand the design boundaries to hundreds or thousands of options using a computer. Combinations of parameters (modulus, wheel width, number of teeth, material, etc.) form a variety of spur gears with different characteristics: dimensions, strength, weight, etc. The statistical analysis found hidden dependencies between characteristics and initial parameters. On the basis of regression metamodels, the relative importance of parameters for individual characteristics was established. When searching for optimal gears, the Desirability function D was applied with meta-models as arguments. On the basis of the existing standards, a system for computer-aided design of transmissions and statistical analysis of their performance has been developed. As a result of the study, the area of efficient spur gears with optimal characteristics was determined.

Comparison of the bending fatigue performances of selective laser sintered and injection moulded nylon spur gears

This study compares the bending fatigue performance of a selective laser sintered Nylon 12 spur gear with an injection moulded Nylon 66 gear. Test gears were subjected to load-controlled, single tooth bending fatigue tests in a custom-built test setup. Cyclic pulsating loads were applied on the test gear using a steel driver gear. The bending fatigue life of selective laser sintered gears was superior compared to the injection moulded gears. In the high cycle fatigue region, the difference between the fatigue life of selective laser sintered and injection moulded gears was higher, whereas it was lower in the low cycle fatigue region. The variation in the fatigue strength of the selective laser sintered gears was due to the different thermal behaviour at low cycle fatigue and high cycle fatigue regimes. The lower surface temperature caused the higher fatigue strength of the selective laser sintered gears in the high cycle fatigue regime. On the contrary, the selective laser sintered gears’ surface temperature was higher than injection moulded gear in the low cycle fatigue regime, which reduced fatigue strength. The crack path was tortuous in selective laser sintered gears and smoother in injection moulded gears. In selective laser sintered gears, the layered structure of the part aided in impeding the propagation of crack.

A comparison of gear tooth bending fatigue lives from single tooth bending and rotating gear tests

A comparison of gear tooth bending fatigue lives from single tooth bending and rotating gear tests

An analysis of the effect of pressure angle change on bending fatigue performance in asymmetrical spur gears

In this study, the fatigue performances of symmetrical and asymmetrical spur gears were analyzed by performing single tooth bending fatigue tests. The gears tested were determined to be symmetrical spur gears with a 20°/20° pressure angle, asymmetrical spur gears with a 20°/22° pressure angle, and asymmetrical spur gears with a 20°/25° pressure angle. These gears were made of AISI 4140 material. Single tooth bending fatigue tests were performed under variable loads. Considering the tests performed at the same torque values in asymmetrical spur gears with a 20°/22° pressure angle compared to symmetrical spur gears with a 20°/20° pressure angle, a statistically significant increase in performance was achieved at close to 90%. While gears with 20°/20° and 20°/22° pressure angles break at the tooth root, tooth flank fracture was observed in relatively high numbers of cycles in asymmetric spur gears with a 20°/25° pressure angle. It was observed that the formation of tooth flank damage negatively affected the fatigue performance.

Investigation on the high-cycle tooth bending fatigue and thermo-mechanical behavior of polymer gears with a progressive curved path of contact

A systematic combination of experimental and numerical methods was employed in a comprehensive study on the high-cycle tooth bending fatigue of polymer gears with a progressive curved path of contact (S-gears). A polymer/polymer combination was tested where the drive gear was made of POM and the driven one from PA 66. Gears were tested at three different torque levels, i.e. 0.6 Nm, 0.8 Nm, and 1.0 Nm, with no additional lubrication and until gear failure. S-gear pairs showed increased durability over the involute gear pairs. A 100% pronounced lifespan increase was observed at the tested load 0.6 Nm.

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.

Implementation of the Average-Log-Ratio ALR gear-damage detection algorithm on gear-fatigue-test recordings

The Average-Log-Ratio, ALR, gear-damage detection algorithm is exercised on accelerometer recordings made during earlier-performed accelerated gear testing. Results of ALR computations from tooth bending-fatigue failure and pitting failure are displayed and discussed. The periodic behavior of the rotational-harmonic frequency spectra of tooth working-surface damage is verified and utilized in ALR detection of both tooth bending-fatigue and pitting damage. Rotational-harmonic frequency spectra out to the tenth tooth-meshing harmonic of damaged gears are utilized. ALR computations of gears failing in tooth-bending fatigue are shown to provide strong periodic contributions out to (and beyond) the tenth tooth-meshing harmonic, whereas tooth pitting damage is shown to generate rotational harmonic spectra with strongest contributions determined by the fractional size of the pitting damage on tooth working surfaces. This differing character of ALR rotational harmonic spectra between bending-fatigue and pitting damage allows remote detection of damage that can distinguish between these two classifications of gear damage.

An Experimental Evaluation of High-Cycle Gear Tooth Bending Fatigue Lives Under Fully Reversed and Fully Released Loading Conditions With Application to Planetary Gear Sets

Abstract High-cycle gear tooth bending fatigue lives of spur gears under fully reversed and fully released loading conditions are compared in this experimental study. The experimental methodology described in an earlier publication, (Hong et al. 2020, “A Rotating Gear Test Methodology for Evaluation of High-Cycle Tooth Bending Fatigue Lives Under Fully Reversed and Fully Released Loading Conditions,” Int. J. Fatigue, 133, p. 105432. 10.1016/j.ijfatigue.2019.105432), is employed to perform two sets of rotating, gear tooth bending fatigue tests. Statistical analyses are performed to regress stress versus life (S–N) curves under both loading conditions. These curves indicate that a gear under fully reversed loads has a shorter bending life at the same maximum tooth root stress as a gear under fully released loads. Various planetary gear set kinematic conditions with different stationary members are considered to determine the equivalent number of tooth loading cycles per revolution of the sun gear. They are combined with established S–N curves under both loading conditions to determine the ratios of allowable maximum tooth root stresses amongst the gear components of a P-planet gear set such that each gear in the set has the same bending fatigue life. A “stress-balanced” gear set designed to these stress ratios is expected to have the same bending fatigue life for its sun, ring, and planet gears, ensuring that the planetary gear set life is the longest.

A rotating gear test methodology for evaluation of high-cycle tooth bending fatigue lives under fully reversed and fully released loading conditions

Gear bending fatigue life is a primary consideration in gear design. Each gear tooth is subjected to cyclic root stresses that may cause fatigue fracture. A gear in a transmission is subjected to either fully released or fully reversed loading conditions, with different fatigue lives. This study develops an experimental methodology for evaluation of high-cycle tooth bending fatigue lives of gears under both loading conditions. Unique specimens for tooth bending fatigue and an adaptive diagnostics method for test termination are designed while root strains under high-speed conditions are quantified. Example fatigue tests are presented to demonstrate the effectiveness of the proposed methodology.

Effect of friction on nominal stress results in a single tooth bending fatigue test

One of the main reasons for gear failure is bending fatigue, which occurs due to cyclic stresses at the tooth root region. Bending fatigue can cause crack initiation which, in turn, may propagate and result in catastrophic tooth breakage. Single tooth bending fatigue tests are frequently employed to generate statistically significant fatigue data at relatively low price. Hence, they are often employed as screening tests for bending fatigue behaviour of actual running gear pair. Since relatively small alteration of nominal tooth root stress values can produce significant change in bending fatigue lives, it is important to adequately consider the effect of friction and test fixture deformation when conducting single tooth bending fatigue tests. In this paper, numerical investigation of tooth flank friction effect on spur gear load capacity during single tooth bending fatigue test is carried out. Two different test fixtures are considered. Linear elastic finite element analysis is carried out to obtain nominal tooth root stresses. The results show that friction at gear tooth flank as well as fixture deformation can affect nominal tooth root stress results.

Study on the gear fatigue behavior considering the effect of residual stress based on the continuum damage approach

The fatigue failures of gears have great influence on lifetime and reliabilities of mechanical transmissions. Initial residual stress (IRS) induced in the manufacturing process, together with the applied loading stress, contributes to gear fatigue behavior. Gear fatigue behavior represents a continuous damaging process during a high-cycle period. In the present work, a damage-coupled numerical model considering the effect of IRS is developed to investigate the gear fatigue performance. The deterioration of gear material, the detailed evolution of damage and the stress response during the cyclic loading process are calculated and recorded based on the continuum damage mechanics (CDM) using a user material subroutine (UMAT) in ABAQUS. Both the tooth surface contact fatigue and tooth root bending fatigue of the gear are evaluated, and the influence of IRS on stress response and damage evolution is analyzed. Results show that the risk of surface contact fatigue failure of this gear is much greater than that of the tooth bending fatigue. The initial compressive residual stress has positive effect on contact fatigue performance while the initial tensile residual stress with amplitude of 380 MPa would reduce the gear contact fatigue life by 20%.

CHARACTERISTICS OF A NEW TEST RIG AND METHODOLOGY FOR CYCLIC TESTING OF GEAR TOOTH BENDING FATIGUE STRENGTH

Tooth fracture is the most dangerous form of gear wear that excludes the gear from further use. In order to counteract the occurrence of this type of damage, it is very important to properly design the toothed gear. To calculate the gear tooth bending strength, a strength parameter called the nominal stress number σFlim is necessary. ISO 6336-5:2003(E) and available material databases provide σFlim values for the most popular engineering materials used for gears, including those for case-hardened steels. There is, however, no data for a new generation of nanostructured engineering materials, which are the subject of research conducted at the Tribology Department of ITeE – PIB. The σFlim parameter is most often determined in cyclic fatigue tests on toothed gears with specially selected tooth geometry. In order to determine the above strength parameter, a pulsator (symbol T-32) was developed and manufactured at ITeE-PIB in Radom. The article presents a new device, research methodology, and the results of verification tests for case-hardened steel 18CrNiMo7-6, confirming the correctness of the adopted design assumptions and the developed research methodology. The results of tooth bending fatigue tests are the basis for the selection of a new engineering material dedicated to gears, which later undergoes tribological testing.

Bending fatigue behaviour of 17-4 PH gears produced via selective laser melting

The possibility of producing parts via the addition of material, instead of its removing, given by Additive Manufacturing (AM) processes is changing the way in which parts are designed. However, the design of some mechanical components like gears, for instance, requires specific resistance data that, up to now, are not presented in literature. This paper presents a research project aimed at investigating the bending fatigue properties of 17-4 PH steel applied to gears produced via selective laser melting. Single Tooth bending Fatigue (STF) tests were conducted in order to investigate the S-N curve. Results are presented in terms of tooth root stress calculated according to the ISO standard in order to compare them with data of other materials. In addition, Scanning Electron Microscopy (SEM) of the fractured surfaces has been performed on the failed teeth to investigate failure origin and therefore to find causes of tooth breakage.

Effect of friction in a single-tooth fatigue test

The primary objective of the single tooth fatigue test is to generate gear-tooth bending fatigue data at a comparatively low price. Assuming a negligible influence on fatigue data, the effect of friction is not evaluated. The aim of this study is to evaluate the effect of tooth friction on tooth bending fatigue life and on the location of the crack initiation site in a single-tooth fatigue test of case carburized steel spur gear. By using Neuber’s rule, tooth root stresses predicted by means of two-dimensional elastic finite element analysis are translated into estimates of elastic-plastic stress and strain behaviour. The fatigue life and location of crack initiation site are predicted on the basis of the strain-life approach with consideration of mean stress, surface finish and residual stress effects. Two load models are considered. In the first load model, which represents the operating principle commonly used in practice, the test tooth is loaded through the actuating arm. In the second one, which is proposed in this study, the test tooth supports the reaction through the fixed anvil. In both load models, the test tooth is contacted at the highest point of single tooth contact, while the other one is contacted at a lower position along the tooth profile. The computational model is validated against experimental crack initiation lives from literature. The study revealed that friction has a more significant impact on tooth bending fatigue life and location of the crack initiation for the first load model as opposed to the second one.