Allowable Contact Stress Research Articles

Tooth surface analysis method based on thermo-mechanical coupling and its application in prediction of gear dry-running bearing capacity

In gear transmission, the continuous meshing of the teeth will lead to an increase in their temperature, which will have a certain impact on the working performance of the tooth surface. In order to explore the failure-bearing capacity of gears under dry-running conditions, temperature effects were considered in existing methods for determining tooth surface failure, making it more suitable for high-temperature working conditions caused by a lack of lubrication. The failure situation of gears within 35 min after losing lubrication was analyzed. The results indicate that when the gear loses lubrication, the tooth surface temperature of the gear pair has exceeded the material melting point after working at an input power of 2000 kW for 12 min. But when the power drops to 1000 kW, the instantaneous temperatures of the driving and driven gear tooth surfaces at the end of 35 min reach 1090 and 995°C, respectively, which are lower than the scuffing temperature of the tooth surface. The cumulative wear depths of the driving and driven gear tooth surfaces at the end of 35 min were 239 and 86.6 um, respectively, which were lower than the failure wear depth of the tooth surface; The allowable contact stress of the gear pair within 35 min is greater than its contact stress, meeting the judgment condition of no pitting failure. This indicates that reducing power can appropriately extend the failure time of gear teeth, thereby improving the ultimate working capacity of gears under dry-running conditions. In addition, a gear dry-running experiment was carried out. By comparing the theoretical calculation results with the measured gear failure degree, it shows that the improved method for determining gear surface failure is effective.

Time-varying Reliability Analysis of Contact Fatigue Strength for Nutation Face Gear Transmission

Background: Nutation face gear transmission is a patent about a new type of transmission based on meshing between two face gears. It replaces spur gear with internal face gear to form a “faceface” meshing gear pair and actualizes its deceleration function by combining the nutation principle, which has the advantages of both face gear and nutation drive. Objective: The purpose of this paper is to establish the time-varying reliability calculation model of contact fatigue strength based on fractal contact theory, so as to improve the reliability, safe service and further optimization design of the nutation face gear transmission. Methods: The time-varying uncertainties of the contact stress and the allowable contact stress of the face gear teeth are analyzed respectively, and then the time-varying reliability model of the contact fatigue strength is established. Finally, the drift rate and fluctuation rate of each random variable are simulated using the Monte Carlo simulation method to obtain the time-varying reliability of the contact fatigue strength for the nutation face gear drive. Results: The results show that the general trend of geometric Brownian motion locus of each random variable is consistent with the actual situation. Conclusion: For the given example of the nutation face gear transmission device, the reliability of the contact fatigue strength of the planetary face gear meshing with the fixed face gear and the rotating face gear within one year is calculated to be 0.9912 and 0.9856 respectively, and the maximum vibration noise is about 68dB, which meets the expected value.

Failure analysis of spline coupling in an engine starting motor

A failure analysis of starting motor is performed using analytical method and finite element method. The influence of external load and material properties on the stress characteristics were discussed. For 45 steel internal spline, the maximum contact stress is greater than the allowable contact stress. This may cause internal splines failure. The bending stress and shear stress are less than the corresponding allowable stress. To be specific, when the maximum 130 N/m applied to the spline coupling in finite element analysis, the contact stress, bending stress, and shear stress are 260, 144, and 40 MPa, respectively. The corresponding allowable contact stress, allowable bending stress, and allowable shear stress are 197, 400, and 200 MPa, respectively. The stress value at the addendum and side of internal spline is maximum, which has good consistency with the failure position of experimental test. In fact, the calculation results obtained from analytical study may have the possibility of underestimating or overestimating the true stress state. This is mainly because analytical study has certain limitations. Therefore, it is necessary to use finite element method to analyze the stress state of the spline structure under design loads and determine whether its strength meets the design requirements.

Failure analysis of overdrive gear of passenger car gearbox fabricated from powder metallurgy

In this paper, investigations into the premature failure of gearbox overdrive gears were done in three passenger car models. The premature failure occurred when a replaced gear model was used instead of the original gear. A series of experiments were carried out on gears made by two manufacturers, including failed gear after an average operation of 100,000 km and gear with partial failure but usable with an average operation of 200,000 km. Numerical and experimental results showed that sharp hardness slope (reduction of 300 HV in 0.15 mm), high porosity, and Hertz stress distribution of about 90% of the allowable contact stress σHa are the factors affecting premature failure. In addition, replacement gear samples with low density compared to original gear have low yield and ultimate strength due to high porosity and interconnected structure of pores. Pores with sharp corners act as the initiation points of the cracks, resulting in final fracture.

Cost optimization of two-stage helical gearboxes with second stage double gear-sets

In practice, the cost of a gearbox plays a very important role in the trade. Therefore, reducing the cost of gearboxes is an important task not only when manufacturing the gearboxes but also when designing them. In order to reduce the cost of a gearbox, there are many solutions in which determining the optimal partial gear ratios of a gearbox is an effective measure. This is because it not only the size, the mass but also the cost of a gearbox depends greatly on the partial gear ratios. This work presents a method for calculating the cost function of two-stage helical gearboxes with second-stage double gear-sets based on the mass of the components that construct the gearbox. The cost objective function is minimized to achieve the optimal transmission ratios. Furthermore, screening experiments are carried out with nine important input parameters that have significant effects on the optimum transmission ratio of the second stage. These parameters are the total gearbox ratio, the coefficient of wheel face width of the first stage, coefficient of wheel face width of the second stage, the allowable contact stress of the first stage, the allowable contact stress of the second stage, the output torque, the cost of gearbox housing, the cost of gears, and the shaft cost. The experimental results of were analysed by using the Analysis of Variance (ANOVA) method with the help of Minitab 19 software. The results demonstrate that the effective weight of the input parameters and their interactions on the output response was investigated. Also, a regression model for computing the optimal transmission ratio of the second stage was proposed. This brings significance not only in the design process but also in manufacturing since the gearbox cost can decrease

A new incremental calculated approach to predict maximum contact stress of compressed packer in large deformation

Compressed packer rubber is large deformation material, which endures biaxial contact friction between oil-pipe and casing-pipe in sitting and sealing process. Large-deformation theory analysis of rubber brings huge difficulties to solve, this is due to the material, geometry and contact non-linearity should be considered. In this article, the deformation of compressed packer rubber tube (CPRT) is divided into free deformation, unidirectional and bidirectional constrained deformations. Based on the theory of thick-wall-cylinder and the linear constitutive of rubber material segment, the CPRT mathematical model in different deformation processes is established and the influences of axial load, axial height of CPRT and contact friction coefficient of casing inner wall etc are considered. Based on incremental calculated approach, the mathematical model is solved. By comparing the results of the theoretical model with the results of finite element method and experimental results, it is found that the theoretical maximum contact stress is more conservative than the FEM and experimental solutions, so the sealing reliability of packer effectively predicted under the premise of allowable contact stress and the theoretical results can provide a lower limit reference value for the contact stress of the packer in the actual seal process. Meanwhile, the deviation of contact stress in FEM and theoretical value at z150 height of CPRT is among 1.13%∼4.90%, which can predict the contact stress in the compressed area near the stress concentration upper end-face of CPRT under the low friction factor, the results provide a reference for the compressed packer design.

Failure Analysis of Worm Gear in Worm Transmission

The failure cause of the worm drive in the NMRV reducer of the grounding knife-switch mechanism of State Grid was analyzed in this paper. The macroscopic analysis, chemical composition inspection, microscopic metallographic observation, hardness test, SEM analysis were carried out to evaluate the worm gear failure mechanism. The stress distributions of the tooth flank using dynamic contact finite element simulation were obtained based on ANSYS Workbench software. The results showed that an initial crack at the root position of softer worm gear was caused by excessively high impact at the initial stage of meshing in the worm drive, whose value was 308MPa higher than the allowable contact stress of 220MPa. The main reason for the hardness of the worm gear decreasing was that the amount of (α+δ) eutectoids fell and distributed unevenly.

Determination of optimum gear ratios of a two-stage helical gearbox with second stage double gear sets

This paper introduces a study on the optimum calculation of the gear ratios of a two-stage helical gearbox with second stage double gear sets. In this study, for finding the optimum gear ratios of the gearbox, an optimization problem was conducted. In the optimization problem, the objective function was the acreage of the cross section of the gearbox. Besides, the effect of the input parameters including the total gearbox ratio, the wheel face width coefficient, the allowable contact stress and the output torque were considered. For investigation of the influence of these factors on the optimum gear ratios, an “experiment” was designed and a computer program was built for conducting the “experiment”. Also, models for determination of the optimum gear ratios of the gearbox were proposed. By using these models, the gear ratios can be calculated accurately and simply.

A study on determination of optimum gear ratios of a worm -helical gearbox

This paper introduces a new study on the optimum calculation of the gear ratios of a worm-helical gearbox. For finding the gear ratios, the cross section area of the gearbox was chosen as the objective function of the optimization problem. Moreover, the influence of the input parameters including the total gearbox ratio, the allowable contact stress and the wheel face width coefficient of the helical gear set, the output torque was investigated. For evaluation of the influence of these parameters on the optimum gear ratios, an “experiment” was designed and a computer program was built for performing the “experiment”. In addition, models for determining the optimum gear ratios of the gearbox were proposed. Based on those models, the gear ratios can achieve high accuracy with simplification.

Calculating optimum gear ratios of a two-stage helical reducer with first stage double gear sets

This paper presents a study on the determination of the optimum gear ratios of a two-stage helical reducer with first stage double gear sets. In the study, an optimization problem was built in order to find the optimum gear ratios of the reducer. In the optimization problem, the objective function was the reducer cross section area. Also, the influence of the input factors including the total reducer ratio, the wheel face width coefficient, the allowable contact stress and the output torque were evaluated. In order to investigate the effects of these factors on the optimum gear ratios, a simulation experiment was designed and conducted. In addition, equations for calculating the optimum gear ratios were introduced. By using these equations, the gear ratios can be determined accurately in a simple way.

Determination of optimum gear ratios of a three stage bevel helical gearbox

This paper presents a study on the determination of optimum gear ratios of a three stage bevel helical gearbox. In the study, for finding the optimum gear ratios, an optimization problem was conducted. In the optimization problem, the cross sectional area of the gearbox was chosen as the objective function. Also, the influence of input factors including the total gearbox ratio, the coefficient of the face width of the bevel and the helical gear sets, the allowable contact stress and the output torque were considered. evaluating the effect of these parameters on the optimum gear ratios, an “experiment” was designed and a computer program was constructed to perform the “experiment”. From the results of the study, the effect of the input factors on the optimum gear ratios were learned and several models for determination of the optimum gear ratios were proposed.

Maximum Torque of Combinations Threat for Spur Gear Based on AGMA Standard

This study is an approach to investigate the transformations curve of gearing safety. Two types of failure can occur on a gear namely the bending stress and the surface pitting failure. There are many standards for gearing in used worldwide such as AGMA, JGMA, ISO, DIN, etc. but the focus of this study will be on AGMA standard. The main data for this study is the torque value applied which can be distinguished into causing bending strength or surface pitting failure. The Autodesk Inventor spur gear component accelerator was used as a tool for data acquisition based on the AGMA standard of calculations. Two gear materials with high value of allowable contact stress compared to its allowable bending stress was chosen for the study as they are predicted to have a transformation curve from surface durability to bending strength when its torque values are plotted against number of teeth. This is then repeated on various gear modules for both materials to obtain a series of combination curves useful in determining the maximum torque that can be applied on the spur gear before failures occur either by bending stress or surface pitting depending on the curve.

Analysis of Affecting Factors on Allowable Contact Stress of Four-Point-Contact Slewing Rings with Single Row

In this paper, some experiments was implemented for analyzing the affecting factors on allowable contact stress of four-point-contact slewing rings with single row including the hardening depth, hardness and the osculation between the steel ball and the raceway. Firstly, the common material 42CrMo was chosen and heat-treated with some process of heat treatment for getting different hardening depth. And then, the indentation tests were conducted with the test-rig, followed by the data process. Finally, some conclusions can be obtained by comparing and analyzing the data. It concludes that when the hardening depth beyond 0.3 and the hardness is not lower than 57HRC, a better allowable contact stress can be got, besides, the better osculation 0.52 is better for the load capacity.

A fracture mechanics interpretation of rolling bearing fatigue

In fatigue assessment of structures and components, it is now commonplace to use a defect-tolerant approach to account for the inevitable presence of surface and internal flaws, both detectable and undetectable. This approach has been applied to rolling bearings in an attempt to present contact stress limits as a function of defect size below which fatigue failure would not be expected. In essence, it is an extension to the existing rating life methods developed by Ioannides and Harris that incorporate a fatigue limit stress in the estimation of bearing life, a concept similar to that of the endurance limit in structural fatigue. Such a fracture mechanics approach to sub-surface initiated fatigue in rolling bearing steels containing non-metallic inclusions, based upon the work of Murakami, has led to an allowable contact stress limit as a function of maximum inclusion size (as estimated by extreme value analysis). An alternative, less conservative fracture mechanics based stress limit is the prevention of propagation of cracks formed on inclusions (termed ‘butterflies’) by shear (Mode II) loading. The approach has been developed by examination of butterflies formed in service in rolling element bearings manufactured in bainitic steel with maximum inclusion sizes in excess of 100 µm. The observed lack of micro-crack formation on inclusions and non-propagation of butterflies support the concept of a fatigue endurance limit that is related to the cleanliness of the bearing steel.

Performance Test of Diamond-Like Carbon Films for Lubricating ITER Blanket Maintenance Equipment under GPa-Level High Contact Stress

Diamond-like carbon (DLC) coating was tested as a candidate solid lubricant for transmission gears of the maintenance equipment of the blanket of the ITER instead of an oil lubricant. The wear tests using the pin-on-disk method were performed on disks with SCM440 and SNCM420 as the base materials and coated with soft, layered, and hard DLCs. All cases satisfied the required allowable contact stress (2 GPa) and lifetime (104 cycles), and therefore the feasibility of the DLC coating was validated. Among the three types of DLCs, the soft DLC showed the best performance.

Pitting failure of truck spiral bevel gear

Spiral bevel gears are some of the most important elements used in truck differential. In this study, the fracture of spiral bevel gear for truck differential produced from case hardening steel is investigated. In order to study the causes of the failure, specimens prepared from the damaged spiral bevel gears were subjected to experiments, such as visual inspection, hardness, chemical analysis and metallurgical tests. Pitting occurrence on gear surfaces was observed. The effect of microstructure on the fracture was considered. Low surface hardness values were found. The calculated contact stress was higher than the allowable contact stress which is emphasized in literature.

コニカルギヤの歯面疲労におけるすべりの影響(S52-3 機素潤滑設計部門第10回卒業研究コンテスト(3),S52 機素潤滑設計部門第10回卒業研究コンテスト)

The contact between tooth surfaces of the conical involute gear is a point contact. Therefore, tooth surface strength of the conical involute gear is smaller than the cylindrical gear. In the design of the conical involute gear, the evaluation of tooth surface strength is more important than bending strength. Tooth surface strength is evaluated at the allowable contact stress of tooth surface. A fatigue test is performed in order to evaluate this allowable contact stress. But, tooth surface is worn out during this test. Therefore, it is difficult to calculate the contact stress. Wear of tooth surface is influenced slip. Slip is evaluated the spesific sliding. But, there is no theoretical formula of the conical involute gear's spesific sliding now, so this theoretical formula is asked on an approximation target in this research. The relation between wear of the test gear and the spesific sliding is considered.

高負荷用浸炭焼入れ歯車の加工と運転性能に関する基礎研究 : 各種処理網の熱履歴による硬さの変化と面圧強さとの関連(O.S.02-3 歯車の強度(3))

The manufacture and performance of case-carburized gears for the high load-carrying capacity were investigated. First, the various processing steels were finished after case-carburizing and quenching treatments. Secondly, the hardness distribution of various processing steels which were given the heat pattern by using a heated oil tank was examined. In addition, surface durability of various processing steels was studied by using a 2-roller-type contact fatigue tester. In the case of the subzero treated and tempered steel, the tempered and shot peened steel, and, the subzero treated, tempered and shot peened steel, the following results are obtained : (1) The surface hardness remarkably decreases when high temperature is received. (2) The allowable contact stress for the surface fatigue lowers in comparison with the tempered steel. (3) The relation between changed surface hardness and surface durability is clarified.

116 コニカルギヤの歯面疲労強度試験における歯面形状の測定

The conical involute gear is the involute gear that external form is a cone. The strength design of the conical involute gear has not been established yet. The contact between tooth surfaces is a point contact. Therefore, in the design of the conical involute gear, the evaluation of tooth surface strength is more important than bending strength. A fatigue test is performed in order to evaluate the allowable contact stress of tooth surface. Since the material of the test gear is normalized steel, and tooth surface is worn out during this test. By this research, tooth surface form under examination is measured and it considers how wear of tooth surface. The final aim of this research is establishment of strength design of the conical involute gear.

Design, Manufacture and Performance of Internal Gear Pumps : 1st Report, Non-Involute Type Pumps for Easy Manufacture

For easy manufacture of internal gear pumps, an internal gear with a convex tooth profile and an external gear, of which tooth-top edge contacts with the convex profile, are used for the gear pumps. Gearing theory of these gears and the theoretical delivery of the internal gear pumps with these gears are clarified. The prominent characteristic found in the gear pumps is that the theoretical torque caused by delivery pressure is zero for the external gear (idler). In practice, a small value of the resistance torque appears on the idler due to viscous friction, etc. It is shown that the resistance torque has no detrimental effects on the tooth surface up to a delivery pressure of about 2 MPa in the present experiments because the Hertzian contact pressure is less than the allowable contact stress of a low hardness steel when the tooth-top edge is rounded to a radius of about 0.5 mm. Six kinds of gear pumps were designed and made by the authors, and almost all characteristics of these gear pumps were clarified by experiments with the support of the theoretical results obtained in the present investigation.