Masana Kato

Effects of Gear Dimensions and Tooth Surface Modifications on the Loaded Transmission Error of a Helical Gear Pair

Analysis of the loaded transmission error proved that the actual contact ratio and the effective contact ratios are the valid indices. In order to calculate the loaded transmission error, deformations of a pair of teeth are estimated using Hertzian formulas for the approach deformation and approximate formulas based on the FEM for the bending deflection. The actual contact ratio E, is defined using the rotational angle during which a tooth pair is actually in contact with each other. E, increases with the increase of applied loads. The effective contact ratio, e n , is determined geometrically by gear dimensions and modified tooth surfaces based on the path of contact. Adopting these ratios, the following characteristics are derived. 1) The loaded transmission error correlates to e r when it is smaller than e n and correlates to e n when e r exceeds e n . 2) Loaded transmission errors have their minimums and maximums at the same values of e r . 3) No load transmission error is the largest among the maximums. 4) Gear pairs with higher values of e n show lower loaded transmission error.

Effect of Surface Treatments on the Strength of Carburized Gears

This paper deals with effects of surface treatment on the bending fatigue strength of SCM415 carburized spur gears. The test gears are treated by the combination of shot peening, chemical polishing and electropolishing after carburization. The fatigue tests demonstrate that the strength is sensitive to the surface condition of tooth fillet and the removal of the nonmartensitic layer caused by decarburization is considerably effective in enhancing the strength. In the first part of this paper, the influence of surface treatments such as shot peening, chemical polishing and electropolishing on the strength enbancement for carburized gears are summarized and discussed. In the second part, the crack lengths are calculated from the fatigue test results for the carburized and surface-treated gears, and the effect of surface treatments is discussed from the view point of fracture mechanics.

Crack growth resistance due to shot peening in carburized gears

This article deals with the effect of shot peening on crack growth in carburized gears. Since residual stress plays an important role in this analysis, an evaluation of the residual stress induced in a carburized gear tooth due to shot peening is presented first. It has been proposed on the basis of the assumption that the residual stress is caused by the difference of volume expansion between the case and the core, and the influence of both the reduction of retained austenite and the strain caused by shot peening are considered. The shot peening is fairly effective to the reduction of fatigue crack growth rate. The resistance to crack growth is demonstrated by the simulation of crack propagation in both the carburized gear and the shot-peened gear.

Estimation of Fatigue Strength Enhancement for Carburized and Shot-Peened Gears

An experimental formula has been proposed to estimate the bending fatigue strength of carburized gears from the hardness and the residual stress. The derivation of the formula is briefly reviewed, and the effectiveness of the formula is demonstrated in this article. The comparison with many test results for carburized and shot-peened gears verifies that the formula is effective for the approximate estimation of the fatigue strength. The formula quantitatively shows a way of enhancing fatigue strength, i.e., the increase of hardness and residual stress at the fillet. The strength is enhanced about 300 MPa by an appropriate shot peening, and it can be improved still more by the surface removal by electropolishing. 25 refs.

Initial Temperature Evaluation for Flash Temperature Index of Gear Tooth

In the AGMA standard for the scoring resistance evaluation of gears, flash temperature is used as an index indicating the risk of scoring. The flash temperature is expressed as the sum of flash rise of temperature and initial temperature. In this research, the initial temperatures are measured for various gear sets in running by thermocouples which are mounted just beneath the working surface of pinion. The effects of gear dimensions, rotating speed, and lubrication conditions on the initial temperature are clarified. An experimental formula is proposed for estimating the initial temperature, which depends on the temperature of oil inlet, the frictional power loss, and the running conditions such a rotating speed, contact position, and the oil supply rate. The estimated initial temperature are in good agreement with the measured values. The proposed method is available for the scoring resistance evaluation of the vehicle transmissions

Surface Temperature Calculation and its Application to Surface Fatigue Strength Evaluation

In recent years, power transmission gears for vehicles run at higher speeds and loads and are accompanied by very high surface temperatures. Under such a high surface temperature condition, the surface strength cannot be evaluated correctly only by the use of Hertzian stress. This research attempts to introduce a new surface strength evaluation method considering the surface temperature rise. First, the surface temperatures of rollers under different rolling and sliding conditions are measured using a thermocouple. The effects of load P, mean tangential velocity V m and sliding velocity V s on surface temperature are investigated and analyzed. Then, an experimental equation is presented which shows the linear relationship between surface temperature and G R P 0.86 V 1.31 s V -0.83 m value. Based on the comparisons between calculated and measured tooth surface temperatures, this equation is confirmed applicable to gear tooth surface temperature evaluation as well. A surface temperature index is proposed for surface strength evaluation. The relationship between the surface temperature index and the number of load cycles of the rollers is investigated. The results indicate the possibility to evaluate the surface strength based on the surface temperature.

Size Effect in Bending Strength of Carburized Gear Teeth

This paper deals with the bending strength and the size effect of carburized fine module gears. The fine module test gears (m = 1–1.5) are made of a low-carbon alloy steel, and they are carburized to have various effective case depths. The bending fatigue tests are performed using these gears. From the test results, the AGMA recommendation of the effective case depth is confirmed to be valid in view of the bending strength. The SN curves are obtained and they are expressed by the experimental formulas. The fatigue strength of fine module gears are compared with the strength of gear of m = 5, and the size factor is evaluated. In order to make clear the size effect, the fracture mechanics is applied to the fatigue test results. The fatigue life is assumed to be the crack propagation process, and the maximum initial length of crack is evaluated. This crack length is proportional to the thickness of nonmartensitic layer at the fillet. The size effect is discussed on the basis of stress intensity factor and the thickness of nonmartensitic layer.

Evaluation of Bending Strength of Carburized Gears Based on a Quantification of Defect Size in the Surface Layer

Generally, fatigue strength of steel correlates with hardness up to a certain point. However, the relationship of hardness and fatigue strength is more complicated for high strength materials, mainly because strength is sensitive to material defects. This paper presents a determination of defect size in carburized gear teeth and a strength evaluation method based on that size. A micro notch is artificially processed at the fillet of carburized gear tooth by means of a Focused Ion Beam, and a bending fatigue test is performed. Threshold notch depth a n th , the limit beyond which fatigue strength declines, is obtained by the test. Threshold notch depth is used as a measure to determine latent defect size in the surface layer. The a n th of gears from which a nonmartensitic layer is removed by electro-polishing is shorter than the a n th of gears with a nonmartensitic layer. The surface layer is observed by scanning electron microscope and electron probe micro analyzer to clarify latent defect characteristics. Many micro cracks, in addition to long cracks in the nonmartensitic layer, Cr oxides and Mn oxides near the surface, and Si segregated in grain boundary are observed. This demonstrates that they trigger fatigue crack initiation; and therefore defect size limits strength. Consequently, strength is expressed by an experimental formula of Vickers hardness and the square root of projected area of the defect obtained above.

Effect of CBN Grinding on the Bending Strength of Carburized Gears

The surface condition of a carburized gear is improved by CBN grinding, in addition to the generation of a compressive residual stress at the ground surface. To clarify the effect of these merits on the strength enhancement, a bending fatigue test is performed for the carburized and the CBN-ground gears. The fillet as well as involute tooth surface is ground by an electroplated threaded CBN wheel. The low axial feed rate and the spark-out treatment are effective in improving the surface finish and increasing the compressive residual stress, and the strengths of CBN-ground gears are increased from 100 MPa to 160 MPa in comparison with the carburized gears. Moreover, the test results are discussed on the basis of the fracture mechanics-based strength evaluation which has been proposed by the authors. This analysis demonstrates that the influence of CBN grinding on strength is smaller than the effects of surface-treatments such as shot peening and chemical polishing.

A Study on Sealing for Silver Oxide Battery Electrolyte. (1st Report). Estimation of Clearance between Anode Can and Gasket.

Experimental estimation is carried out on the clearance between anode can and gasket of silver oxide battery. Although the qualitative evaluation of electrolyte leakage of silver oxide batteries is given by IEC standard, it presents no quantity of leaked electrolyte but outside appearance. In this paper, flame analysis is carried out the typical samples of each grades of IEC standard for watch batteries, and the relationship between each grade of IEC standard and quantity of leaked electrolyte is given. Leak speed of electrolyte is estimated by the experimental data on alkaline creeping for the copper electrode. On account of these data, cross section area of leak path in the boundary zone between anode can and gasket is estimated. The clearance varies as time elapses, so its behavior is investigated in the valuation of leakage for silver oxide batteries under high temperature and high humidity surroundings. In conclusion, variation of clearance or of leak speed of electrolyte is an important parameter for better sealing.