Tooth Bending Strength Research Articles

Effect of Abnormal Surface Layer on Tooth Surface Strength of Gas Carburized Gears.

The effect of abnormal surface layer produced by gas carburizing on the bending strength of gear tooth has already been reported, although the effect on the tooth surface strength has not been clarified. The authors carried out experiments to study the effect of abnormal surface layer on the tooth surface strength. The test gears with various conditions of abnormal surface layer used in this experiments were prepared by changing the machining process and the material of gears. As a result of experiments, the tooth surface strength of gas carburized gears is affected by the existence of abnormal surface layer. With in the limits of this experiments, it showed that the tooth surface strength of gears with abnormal surface layer is higher than that of gears without abnormal surface layer. Furthermore, it was observed that the quantitative effect of abnormal surface layer on the tooth surface strength is different from the coilditions of abnormal surface layer, i. e. the uniformity and the hardness of slack quenching layer, and the production shape of intergranular oxidation. We concluded from the experiments that the suitable conditions of abnormal surface layer improve thye tooth surface strength of gas carburized gears.

A Study on Polyacetal Gears Filled with Glass Fibers.

When glass fiber filled plastic is injection molded into gears through a conventional metal mold, there is a possibility that the end of the filled fiber will face and damage the tooth surface of the mating gear. In order to prevent the above damage and to increase the bending strength of teeth by arranging filled fibers uniformly in the direction of tooth form, we devised a metal mold in which as many fibers as possible can be arranged uniformly in the direction of tooth form at the time of injection molding. In this research, both kinds of composite plastic gears, containing 25% or 40% glass fibers respectively in polyacetal, were injection molded through this metal mold. Together with examining the bending fatigue strength and running characteristics of the teeth of the above gears by experiments, we performed the same experiments for composite plastic gears which were injection molded through a conventional metal mold. Comparing these results, we studied the profitability of the devised metal mold.

Centrifugal Lubrication of Spur Gears. (1st Report, Behavior and Flow Rate of Oil Jet).

Increasing demands of high speed, heavy duty, and small size for a gear device promote the bulk temperature rise in gear teeth. The temperature rise affects both bending strength and surface durability of the gear teeth as well as the scoring resistance and causes a decrease in accuracy of the gear device due to thermal expansion. To establish an effective lubrication method for ultrahigh-speed gears, this study aims at determining an optimum centrifugal lubrication method to cool spur gear teeth. In this paper, on the basis of the observation of oil jet behavior, we proposed a new centrifugal lubrication method in which oil is injected through a hole drilled on the tooth crest. Oil jetted out from a gear splashes after striking against both addendum and dedendum flanks of a mating gear. A multiple regression equation for estimating the flow rate of oil jetted out through a hole was obtained by dimensional analysis and experiments.

Bending strength of upper canine tooth in domestic dogs

The bending strength of the upper canine tooth is analyzed on 51 domestic dogs of various breeds. Data show that canine tooth length is greater among small domestic dogs when compared to small wild dogs, and large wild dogs when compared among large domestic dogs. Tooth strength is also greater among small domestic dogs and large wild dogs. The greater tooth strength of the small domestic dogs may be attributed to the idea that small domestic dogs are closer in ancestry to the grey wolf (Canis lupus) than are small wild canids. Skull foreshortening and tooth strength appear to be correlated in the canidae.

破壊力学に基づく浸炭歯車の強度評価に関する研究 : 第2報, 浸炭層を想定した材料の疲労き裂進展特性

An experimental formula of fatigue crack growth rate (FCGR) in the carburized layer is presented for the purpose of the evaluation of bending strength of carburized gear teeth. The FCGR is assumed to depend only on the hardness at the crack tip in this study. In order to obtain the FCGR at a certain depth in the case layer, bend specimens are made of carbon steels, which contain equal amounts of carbon at the depth, and are heat treated to have the hardness equivalent to the case hardness. Many experimental data in the literature as well as the bend test results are arranged and an experimental formula is obtained. The formula is represented as a function of threshold, fracture toughness and two other parameters, and covers all the regions of the crack propagation.

The bending strength of carburized fine module gear teeth. 1st Report. Carburizing conditions and their effects on the fatigue strength.

The bending strength of carburized fine module gear teeth. 1st Report. Carburizing conditions and their effects on the fatigue strength.

潤滑下における動力伝達用ポリアセタール歯車の強度 Ｉ 鋼歯車とかみ合わせた場合

A polyacetal gear of module 2 is engaged with a steel gear coated by gear oil or grease only initial stage, and different loads are applied to the set. Bending strengths and wears of polyacetal gear teeth under lubricated conditions are compared with those obtained under unlubricated conditions. Experiments are also carried out under the conditions of forced lubrication, and similar comparative studies are made on the results. Obtained test results are summarized as follows : (1) Reduction of bending strength of gear teeth caused by temperature increase is suppressed by lubricating gears. Furthermore, it is found that the extent of reduction of bending strength of gear teeth varied according to the lubrication methods applied even under the same load. The smallest is in the case of forced oil lubrication in which large amount of oil is used, followed by the case of grease coating, and the largest is in the case of oil coating. (2) Marked improvement of allowable loads, in which wears of gear teeth are taken into consideration, are recognized under the lubricated conditions compared to those obtained under unlubricated conditions.

The effect of shot peening on the bending strength of carburized gear teeth.

The quantitative effects of hardness and residual stress produced by shot peening on the bending strength of carburized spur gears of m=5 are investigated. The residual stress of every test tooth is measured by an X-ray diffraction method. The intensity of shot peening has little effect on the fatigue strength. The mean strength is about 1200 MPa, which is about 1.3 times that of carburized gears without shot peening. When a tooth surface is electropolished and a higher compressive residual stress is applied to the fillet, the fatigue strength is still 250 MPa higher than that of the shot-peened gears. In this study, the improvement of fatigue strength is assumed to be caused by an increase of both hardness and residual stress, and an experimental formula is proposed to estimate the fatigue strength.

Bending strength of spur gear teeth made of austempered ductile iron.

The use of gears for power transmission is conditioned by the strength as well as the accuracy. The employment of austempered ductile iron is examined from this view point. The test gears are made of ductile irons FCD45 and FCD60. They are austenized at 900°C then austempered at 300 to 400°C. In the austempering process, the bainitic transformation causes size expansion and a considerable tooth profile error of the gears. The profile error can be reduced by austempering at 400°C or employing the ferrite-bainite dual phase ductile iron. The bending fatigue tests are performed by using electro hydraulic servo controlled pulsators, and SN curves are obtained. The higher the austempering temperature, the higher the fatigue strength. The fatigue strength of gears austempered at 400°C is about 520MPa and it is higher than the strength of normalized S45C gears.

The effect of shot peening on the bending strength of carburized spur gear teeth.

The quantitative effects of hardness and residual stress produced by shot peening on the bending strength of carburized spur gears of m=5 are investigated. The residual stress of every test tooth is measured by an X-ray diffraction method. The intensity of shot peening has little effect on the fatigue strength. The mean strength is about 1200 MPa which is about 1.3 times that of carburized gears without shot peening. When a tooth surface is electropolished and a higher compressive residual stress is applied to the fillet, the fatigue strength is still 250 MPa higher than that of the shot peening gears. In this study, the improvement of fatigue strength is assumed to be caused by an increase of both hardness and residual stress, and an experimental formula is proposed to estimate the fatigue strength.

Canine tooth strength and killing behaviour in large carnivores

Bending strength of upper canine teeth is examined among living canids, felids, hyaenids and several extinct species including sabretooth cats, borophagine dogs and the dire wolf, Canis dirus. The tooth is modelled as a cantilever with an elliptical cross‐section. Using beam theory, the bending strength of the upper canine is calculated given a constant force applied to the canine tip. Results indicate that felids and hyaenids have relatively stronger canines than canids, particularly in bending about the anteroposterior (AP) rather than the mediolateral axis. It is suggested that canine shape reflects the forces produced during killing and feeding. As shown by an analysis of jaw muscle moment arms, felids and hyaenids have relatively stronger bites than canids. Moreover, the canines of hyaenids and felids are perhaps more likely to contact bone during feeding and killing and consequently may be subjected to larger and more frequent bending moments about the AP axis. The canines of sabretooth cats are shown to be more similar in shape and strength characteristics to those of living canids than felids, whereas those of the borophagine dogs and the dire wolf are closer to modern hyaenas.

Effects of Rim and Web Thicknesses on Bending Fatigue Strength of Internal Gear

This paper presents a study on the effects of rim and web thicknesses on bending fatigue strength of internal gears. A stress analysis by means of the 3-dimensional finite element method (FEM) and a static loading test for internal gears of different rim and web thicknesses were carried out and the effects of rim and web thicknesses on the root, rim and web stresses of internal gears were clarified. A bending fatigue test for thin-rimmed internal gears with a thin web was carried out and the effects of rim and web thicknesses on the bending fatigue strength were investigated. Furthermore the validity of the calculating formula of tooth bending strength of internal gear proposed by ISO was examined.

Effects of Rim Thickness on Root Stress and Bending Fatigue Strength of Internal Gear Tooth

This paper presents a study on the effects of rim thickness on root stress and bending fatigue strength of internal gear tooth. A root stress analysis by the 2-dimensional finite element method (FEM), a static loading test and a bending fatigue test for internal gears of different rim thicknesses were carried out. The root stresses increase with a decrease in rim thickness on both the tensile and compressive sides. The bending fatigue-limit-load of the thin-rimmed internal gears decreases with a decrease in rim thickness for lw<3m and remains almost constant for lw≥3m. The validity of the calculating formula of tooth bending strength of internal gear proposed by ISO was examined on the basis of the results of the static loading and the bending fatigue tests.

A new look at the bending strength of gear teeth

This paper reports on an extensive two-dimensional photoelastic study of the basic deformation behavior of gear teeth under load. Limitations of existing bending-strength design procedures are used to formulate a test program which considers the magnitude of the critical root-fillet stresses, the effects of varying the load position on the flank, the effects of friction forces at contact and the relationship between bending and shearing deformations. Particular interest is devoted to a study of the observed movement of the maximum-stress position around the fillet as load moves up the tooth flank and to the associated variation in stress-concentration factors (around the fillets) due to radial, bending and shear loads. Note is also made of the problems associated with observed ‘proximity effects’ and of the procedures carried out in an attempt to qualify the nature of the effect.

Bending Strength Design of Gears

In this paper is presented a new design formula for the bending strength of a gear tooth based on the true stress on the root fillet of the gear tooth, which differs from conventional design for mulas based on the tooth-form factor. The bending fatigue limit values for gears of various kinds of materials and heat-treatments, obtained after years of experiments, which have been carried out by the authors, are shown in a table. Moreover the values of driving condition factor (alternative load factor) and life factor (load repetition factor) involved in the design for mula are also given in this paper in a table or by a formula. Thus the defects of the conventional design formulas of a gear tooth are expected to be removed.

On the Bending Stress of a Spur Gear : 3rd Report, On the Calculation Results of Bending Stress of a Gear Tooth

For the purpose of calculating the bending strength of the gear tooth in general use, the authors studied theoretically the position of the weakest section of a gear tooth and the point of the worst loading, and consequently defined the calculating method of nominal stress. Then by using the calculating equation of bending stress and stress concentration factor of gear teeth of various shapes in general use at present, they studied these relations.

On the Bending Stress of a Spur Gear : 1 st Report, Stress at the Fillet Curve and Inner Stress at the Root of Gear Tooth

The present study was carried out for the purpose of calculating the bending stress of a gear tooth theoretically and finding the bending strength of a spur gear. Using the two-dimensional elastic theory and the transform function, the authors introduced equations for the calculation of the stress at the fillet curve of a gear tooth. Investigating the stress calculated by these equations in various loading conditions, the authors reached the conclusion that it was reasonable to take the shearing force into consideration for the calculation of the bending stress of a gear tooth. Then they introduced equations for the calculation of the inner stress, and obtained the following result : the inner stress shows a smaller value than the stress at the fillet curve, so it is reasonable to determine the bending strength of a gear tooth by calculating the maximum stress at the fillet curve.

On the Bending Stress of Spur Gear : (3rd Report, On the Calculation Results of Bending Stress of Gear Tooth)

For the purpose of calculating the bending strength of the gear tooth in general use, the authors studied theoretically the position of the weakest section of gear tooth and the point of the worst loading, and consequently definited the calculating method of nominal stress. Then by using the calculating equation of bending stress reduced above, authors calculated bending stress and stress concentration factor of gear teeth of various shapes in general use at present, and studied these relations.

On the Bending Stress of Spur Gear : (1st Report, Stress at the Fillet Curve and Inner Stress at the Root of Gear Tooth)

For the purpose of calculating the bending stress of gear tooth theoretically and finding the bending strength of spur gear the present study was carried out. Using the two-dimensional elastic theory and the transform function, the authors introduced equations for the calculation of the stress at the fillet curve of gear tooth. Investigating the stress calculated by these equations in various loading conditions, the authors reached a conclusion that it was reasonable to take the shearing force into consideration for the calculation of bending stress of gear tooth. Then the authors introduced equations for the calculation of the inner stress, and obtained the following result : the inner stress shows smaller value than the stress at the fillet curve, so it is resonable to determine the bending strength of gear tooth by calculating the maximum stress at the fillet curve.

Bending Strength of Gear Teeth by Cantilever-Plate Theory

This paper presents a study of the bending strength of gear teeth based on a cantilever-plate approach. A semiempirical solution is given for the finite cantilever plate under transverse loads at any location on its surface. The solution which is based on the principle of superposition and a proposed moment-image method showed good agreement with results from strain-gage investigations on cantilever plates simulating the gear tooth. The effects of the position of the line load and the variation of load intensity on the stress distribution at the root are discussed.