This paper presents the definitions and calculation methods for predicting torsional mesh stiffness equations for spur gears in mesh. The torsional mesh stiffness formula for meshing gears were developed from a series of finite element models including the effects of parameter variation of gear module, gear ratio, number of teeth and shaft diameter. The comparison between the formula results and FEA results shows that the formula accuracy is within the expected accuracy normally achieved with FEA models. The stiffness equations are also in a form readily useable for practical application in areas such as the investigation of static transmission error of gears and the simulation of gear system vibration.

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A test rig for the measurement of transmission error under load on cylindrical gearsets was built. The specific design features allowed to measure the Dynamic Transmission Error (DTE) bypassing traslational vibrations. Tests on spur gears in several torque and speed conditions were conducted and the behavior was evaluated. Before each test the topography of the gear pair was measured by an 8^*8 grid sampling on 4 teeth on both pinion and gear. Employing an analytical calculation tool that accounts from microgeometric topography variations, the Static Transmission Error (STE) was calculated for any possible combination of pinion and gear teeth : calculations show that a wide variation of STE between these results may exist : some combinations of profiles are providing STE amplitudes five times higher the results of other combinations. A further comparison with DTE measurements showed that in low speed tests, near to a quasi-static condition, the difference between calculations and experimental results is slight ; as expected, for higher speeds, the calculation results are generally higher than the measurements.

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The local steady state solutions of a non-linear geared system with backlash are investigated in this paper. The time-variable mesh stiffness, the excitation caused by the static transmission errors (referred to be as errors excitation here) and the static external forces are included in the analyzing dynamic model. Two kinds of methods are applied here to obtain the approximate analytical solutions at different working situation of a gear pair. The method of multiple scales is used in the case that no impact of the meshing gears occurs, and the average method is used in the case that impact occurs. In addition, the stabilities of the steady state responses are also studied in this work. The validities of the method proposed here are verified by the numerical results.

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This paper investigates resonance frequency behavior of three-dimensional, thin-rimmed spur gears (3DTRG) by experimental and theoretical methods. Resonance frequencies of the 3DTRG are measured by using "Power-circulating Form" gear test rig at the speed range from 500rpm to 3000rpm. "Strain Phrase Method" is presented to measure mode shapes of the 3DTRG. Effect of tooth rigidity of the mating gears on resonance frequency behavior of the 3DTRG is also investigated experimentally. Experimental results show that vibration of the 3DTRG is structural vibration of the thin rim and web structures rather than tooth bending vibration like the solid gears. There are many resonance frequencies existing at the same time when the 3DTRG vibrates. Natural frequency and mode shapes of the 3DTRG are also analyzed by 3D-finite element method (FEM). Calculated natural frequencies and mode shapes are agreement with the measured ones very well. Effect of module on the natural frequencies of the 3DTRG is investigated by the FEM analysis. Finally, close and duplicated frequency phenomena of the 3DTRG structural vibration that have never occurred in the case of solid gear vibration are discussed.

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Noise reduction is increasingly important in gear design, which highlights new problems in robust design of gears. The performance of gears is influenced by perturbation factors beyond the control of the designer. These perturbation factors (which often are of random character) may be divided into three categories : variation in the use of the product, i. e. torque, unit-to-unit variation, i. e. manufacturing errors, and deterioration, i. e. wear. Gears are considered robust if their qualities are not unacceptably affected by the random perturbation factors. The entry of noise as an objective in the gear design process forces the designer to consider wear of the flank along with the traditional objectives (strength, efficiency etc.). During service life, wear changes the tooth profile. The profile change, although it is small, may drastically change the transmission error (TE), which is assumed to be the major source of noise. Hence, wear might significantly change the noise characteristics of the gear. A robustness analysis of a gear is performed where the aim is to determine how design parameters influence the transmission error (noise), while the gear is exposed to perturbations. The perturbations considered in the analysis are variation in torque value, variation in flank geometry due to manufacturing and due to wear. In general, it can be stated that a gear with robust noise characteristics with respect to varying torque, manufacturing errors and wear should have some profile- and lead crowning and a large helix angle. The transverse contact ratio is a trade-off factor in the sense that both low peak-to-peak TE (PPTE) and low dispersion in PPTE can not simultaneously be achieved. Therefore, for minimization of gear noise by increasing the total contact ratio, it is better to increase the face contact ratio rather than the transverse contact ratio since high transverse contact ratio deteriorates the robustness of the gear.

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A three-dimensional lumped-mass vibration model of spiral bevel gears (with 11 degrees of freedom) was derived. The model forms the basis of a method for calculating the response to a transmission error. The method shows that, at highest natural frequency, tooth deflection dominates other displacements. However, the resonance of this highest natural frequency with tooth contact frequency occurs at fairly low speed. At higher speeds, the transmission error due to cumulative pitch deviation resonated with lower orders of natural frequencies and increased the dynamic tooth load. A closed-power-circuit gear test machine was used to experimentally measure Klingeluberg-profile spiral bevel gears. The measured dynamic tooth root stress was found to agree well with the dynamic load predicted by the above-mentioned method. It is thus concluded that, in the design stage, the dynamic factor should be calculated by ISO 10300 method C rather than method B.

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In this study, the influence of gear dimensions, tooth flank modifications and loads on transmission error, that has been considered as the major exciter of gear whine, are comprehensively analyzed. Transmission error is composed of tooth flank modifications, misalignments and tooth deflections that are computed by FEM for the bending deflection and the Hertzian equation for the approach deflection. The applied conditions spread widely across the expected actual situation of vehicles are as follows. The range of geometrical contact ratio is from 2.56 to 4.75, the range of applied loads is from 0 to 300Nm, and the amount of tooth flank modifications is from 5 to 35μm as crowning. As the result, the interacting influence of gear dimensions, tooth flank modifications and loads is clarified.

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In helical gears by shaving processing and hypoid gears by lapping processing, it is known that dispersions exist in tooth profile in one gear and pitch deviations. These dispersions must not be ignored in analysis of gears, but transmission error analysis that considered dispersions in one gear is hardly reported. In addition, dispersions in one gear should be considered when tooth profile is designed. The following investigation and suggestion were done for hypoid gears in this study. Analysis technique of transmission error that could consider dispersions in one gear of tooth profiles and pitch deviations was developed. The influence that dispersions in one gear of tooth profiles and pitch deviations gave to transmission error was made clear. On the basis of these relations, design technique of tooth profile that considered dispersions in one gear was suggested.

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Gear dynamic models rely on several commonly accepted concepts like transmission errors and mesh stiffness for instance. This paper presents a review of some modelling problems as well as an examination of some of the many, simplifying assumptions that have been made either explicitly or implicitly by prior investigators. From a 3D model using instantaneous contact conditions between mating teeth, the questions of the normal contact formulation, tooth elastic models suited to dynamic calculations and mesh excitations are tackled. It is concluded that the definition of some familiar notions can be confusing and that the links between mesh excitations and transmission errors is not always direct.

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The present paper deals with the computation of mesh stiffness between two meshing gears. One of the requirements of the procedure is that it should be applicable even if the tooth profile is non- standard. The procedure invokes the simultaneous use of finite elements, as well as numerical iterations and analytical solutions. Through the use of this method, the F. E. does not require contact simulation and it needs a non-refined mesh to achieve reliable results. One of the objectives of this technique is to combine mesh stiffness evaluation with global dynamic analysis of a gear train.

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The popular kinds of tooth surface deviations of helical gears, i. e. Profile slope deviations, Lead slope deviations, Bias, Lead crowning, Profile crowning, Tip relief and so on, do not always have a good correlation with gear noise by themselves. So, even if all inspected factors of tooth surface are within the allowable tolerance, gear noise could be often bad, and even if all inspected factors of tooth surface are without the allowable tolerance, gear noise could be often good. In this paper, the most important factor of tooth surface that has a good correlation with gear noise is discussed. At first, many kinds of tooth surface deviations are investigated. It is found that gear noise is very sensitive to the slope along the path of contact and the convex curvature along the path of contact has a good correlation with gear noise. Next, the design method of tooth modifications is proposed. When the slope deviation along the path of contact could be large as the limit of the tolerance, the level of gear noise is in the worst condition. In this condition, a gear pair with some large convex curvature along the path of contact is quieter than with small convex curvature. Therefor, the convex curvature along the path of contact should be determined by the allowable tolerance of tooth surface slope.

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Noise measurement on a population of gearbox manufactured in large number often reveals high variability due to tolerances on each gear design parameter (manufacturing errors). Gearbox noise results mainly from housing vibration induced by the gear meshing process. High acoustic levels correspond to excitation in a resonant manner of some critical modes. All gearbox modes and especially these critical modes depend on tolerances related to gear design parameters through the meshing stiffness. Tolerances are considered on shaft misalignment errors, teeth profile errors and teeth longitudinal errors. We introduce these tolerances as geometric random gaussian parameters. The critical modes are extracted using an efficient procedure. The retained "statistical" method to treat tolerances is the Taguchi's method. We illustrate this methodology considering two different gearbox dynamic models fitted out with a single spur gear. Obtained dispersion results are validated by comparison with Monte-Carlo simulations.

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In the article a non-linear electromechanical system consisting of DC motor and mechanical gearbox with gearing clearance is solved. The existence of clearance and hence possible development of transient phenomena postulate an improved accuracy of linear models used so far. This is why an elastic coupling torque is introduced in the article as a non-linear function. Harmonic linearization is applied to achieve approximate solutions, supposing a sinusoidal dependence of maximum deviation in gears vs. frequency of excitation.

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In this paper, a simplified model is studied to predict analytically the radiated noise from the helical gear system due to an axial excitation of helical gear. The simplified model describes gear, shaft, bearing, and housing. To obtain the axial force of helical gear, mesh stiffness is calculated in the load deflection relation. The influence function of the bending deflection is calculated from the results of FEA and the influence function of contact deformation is specially calculated to use them in the load deflection relation. The axial force is obtained from the solution of the equation of motion, using the mesh stiffness. It is used as a longitudinal excitation of the shaft, which in turn drives the gear housing through the bearing. In this study, the shaft is modeled as a rod, while the bearing is modeled as a parallel spring and damper only supporting longitudinal forces. The gear housing is modeled as a clamped circular plate with viscous damping. For the modeling of this system, transfer function from the shaft to the clamped plate are used, using a spectral method with four pole parameters. Out-of-plane displacement for the thin circular plate with viscous damping is derived and sound pressure radiated from the plate is also derived. Using the model, parameter studies are carried out.

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Sometimes, peculiar vibration of a helical gear pair that appears at non-integer order of the mesh frequency becomes predominant component even on a ground gear. It is because of the irregularity of tooth surface form having different cycles of transmission error from tooth mesh cycle and is called as 'ghost noise' [2]. But, it is difficult to detect ghost noise with a measured tooth profile because there are few cycles of the undulation on a measured tooth trace. In this research, we measured two-dimensional surface forms of all teeth of a helical gear. With this detailed tooth surface measurement result, we discuss about how to detect surface undulation which generate ghost noise. Because the frequency resolution of Fourier analysis become worse when measured tooth number is a few, we discuss about the effectivity of applying Maximum Entropy Method comparing with Fourier analysis.

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Important advancements in preventive maintenance of rotor-craft gear transmission systems are currently being sought for the development of an accurate machine health diagnostic system. Such a diagnostic system would use vibration or acoustic signals from the gear transmission system for (1) rapid on-line evaluation of gear wear or damage status, and (2) prediction of remaining gear life. Such health diagnostic capabilities would be essential for effective machine event/life management and advance warning before critical component failures. This paper demonstrates the use of vibration signature analysis procedures for health monitoring and diagnostics of a gear transmission system. The procedures used in this paper include (i) the numerical simulation of the dynamics of a gear transmission system with single and multiple tooth damage, (ii) the application of the Wigner-Ville Distribution (WVD) and the Wavelet transform in damage identification and quantification of damaged tooth based on the numerically generated vibration signal, and (iii) the application of both WVD and the Wavelet transform on experimental data at various stage of gear failure obtained from an accelerated gear damage test rig. This paper demonstrates that the developed signature analysis procedure can successfully detect faulty gears in both numerically simulated and experimental tested transmission system. General conclusions on identification and quantification of gear tooth damage are drawn based on the results of this study.

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Research into gear pair dynamic behaviour together with gear whine has been reported in detail by many authors. The understanding and control of these phenomena is of paramount importance to the automotive engineer. As the power of predictive modelling software has increased, it has enabled the automotive engineer to control levels of transmission error and gear pair dynamic behaviour thus reducing tonal gear whine, resulting in substantial improvements in transmission refinement. With the development of more powerful analytical tools the need for an advanced experimental means of validation has become apparent. This paper reviews the literature and recent advances made since a series of reviews by Powell [1,2], Munro [3], Ozguven et al [4] and Houser [5] published circa 1990. The principal conclusion of this review points to the need for a dedicated research tool that permits the investigation of gear pair behaviour under real-time automotive conditions. The University of Leeds in conjunction with Ricardo MTC Ltd. have developed a research tool that meets the requirements identified by the review. This paper discloses information on the new gear pair test rig that will be based at Leeds University and the areas of research that the new automotive transmissions research group will undertake.

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The study on dynamic modeling and coupled vibration for gearbox is carried out in detail by theoretic analysis combined with experimental method. The finite element dynamic model of whole gearbox with 51099 elements and 76219 nodes is set up in which the joint equivalent parameters between gear transmission and gearbox housing are identified by experimental modal analysis method. The numerical results of vibration response are in agreement with the experimental results in a broad manner.

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In this paper a full model to study dynamic behaviour of gear trains is presented. The model takes into account all the twelve dofs of the gears during meshing of mating gears. The complete expression of the potential energy of the spring connection between the mating gears used for stiffness evaluation is given. Multi-meshing can be faced by generated code that allows the solution while considering different approximated modelling approaches. Among these facilities, the one, that allows the modal analysis with part of structures considered as a rigid body (through the use of QR algorithm), can be employed to concentrate attention to the behaviour of single part of the gear train. A test case is given studying a gear train made of 4 shafts and 3 gear stages, where different levels of simplified analyses are compared, together with an insight of effects of rotating speed on modal behaviour because of gyroscopic effects.

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A new method - utilizing gear-vibration analysis and finite-element-method (FEM) analysis - for calculating the three-dimensional-vibration behavior of a multi-stage helical gear system including a gearbox has been developed. First, to predict three-dimensional multi-stage helical gear vibration, each gear was modeled with six-DOF (degrees of freedom) ; three translational motions, and three swing motions. Stiffness matrices for each gear shaft and for each tooth meshing were made and overlapped into a stiffness matrix for the total system. Next, an FEM model of the gear system, which included separate models for the gearbox, gear shafts, gear meshings, bearings, and legs of the gearbox, was made. The results of a three-dimensional gear-vibration analysis were input into the model, to obtain the vibration responses of the gearbox. The calculated eigen frequencies and vibration responses of the gearbox agreed well with measured values.

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Through the improvement of gear parameter design and manufacturing processes directed at reducing transmission error, the gear noise level has been continually reduced in recent years. Demands for reducing gear noise are continually becoming more stringent, but the improvement of transmission error of gear pairs for gear noise reduction is nearing its limit. It has become increasingly difficult to estimate gear noise on the basis of transmission error, especially in high-frequency bands. In addition to these usual methods, there is a greater need to recognize the gear train itself as a transmitter of vibration and adopt approaches in which improvements are made to the gear train for the purpose of reducing gear noise. In this paper we present a new method of analyzing the vibration of a helical gear system, which makes it possible to predict the influence of the entire gear train (consisting of the gear blanks, shafts, bearings and the gears themselves) on gear noise. To reproduce as closely as possible the real operating condition of a helical gear system, we have developed a model with twelve degrees of freedom. It is represented by two equivalent masses coupled with the tooth mesh stiffness. In this method, the equivalent masses and the equivalent stiffness of gear trains were estimated with simplified finite element models. It was verified that the gear vibrations simulated with this method correlated well with measured gear noise. In this vibration analysis, it was found that the influence of the gear train as a whole on gear noise was as great as that of the gears themselves and that gear vibration was more sensitive to tooth surface modifications than transmission error. One of the tooth surface modifications that was effective in reducing gear vibration is described. In addition, a simplified prediction of the high-frequency gear noise level made with this method is presented.

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Recently, going with interior noise reduction in a vehicle, gear noise which is of pure frequency has been becoming a great influence on the comfortable driving. For the purpose of reducing the gear noise, (1) the source of gear noise (the transmission error of gears) and (2) the dynamic characteristics of gear-shaft-bearing system (the transfer of vibration) must be clarified and those influences should be taken into the account in design process. In this paper, the procedure which coped with the gear noise peak coming up during the development period of automatic transmission is introduced. The procedure could clarify the influence of the transfer characteristics analytically and experimentally as well. The vibration analysis with the gear-shaft-bearing system model was carried out to estimate the resonance of the gear noise peak which was remarkable in the vehicle. In order to confirm the analytical preciseness the torsional excitation experiments with the actual automatic transmission were carried out. At the first, for the sake of simplicity of the experiments and analysis, the automatic transmission remaining the dominant parts for the gear meshing and transferring its vibration to the case was prepared. Necessary accelerometers were set up in the gear-shaft-bearing system. The input-shaft was excited in torsional direction by electric exciter while applying the static torque to the drive train, then the vibration characteristics of gear-shaft-bearing system were obtained. As a result, it was found by the simulation and experiments that some gear noise peaks were recognized as resonances, and could be reduced by modifying bearing stiffness and its damping characteristics.

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The efforts of gear noise reduction has traditionally focused on minimizing transmission error, improving tooth machining capability and manufacturing control. On the other hand, gears and gearbox resonance characteristics are also known to influence the gear noise level strongly. To reduce gear noise, therefore, the entire gear resonance system is clarified by experimental analysis and a dominant mechanism is specified. With the thin and large helical gears, the analysis has shown that mesh force, consisting of gear resonance characteristics, is the most significant parameter. To reduce the mesh force, an innovative gear structure has been devised. The structure aggressively controls gear resonance characteristics like a dynamic vibration reducer. With the FEM simulation, gears are re-designed by controlling resonance characteristics, which has successfully reduced gear noise. These analyses and reduction methods of gear noise can be applied to general gear noise problem in order to conduct parameter study or optimization.

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A model for analysing the quasi-static and dynamic behaviour of double helical gears is presented. It accounts for time-varying non-linear mesh stiffnesses, gear and pinion distortions, shape modifications and floating parts. The equations of motion are solved step-by-step in time and normal contact conditions are included in the numerical process. The interest of a floating pinion for equalizing quasi-static and dynamic tooth loads on the two halves is pointed out. It is also shown that tooth stagger between the two helices can significantly reduce the variations of quasi-static transmission error under load. Results at higher speeds reveal that dynamic amplifications are lower but, in the same time, critical tooth frequencies are shifted. It is therefore concluded that, depending on the operating speeds, staggering of the teeth is not necessarily beneficial.

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For lower vibration gear design, demand for multi degree-of-freedom (hereafter, DOF) vibration analysis is increasing. But damping parameters for a geared machinery is difficult to measure directly because its excitation force with gear meshing cannot be measured. This paper introduces an experimental identification method of damping coefficients of 2-DOF vibration model for a power transmitting gear system as a basis of multi DOF vibration analysis. In the proposed method, modal analysis was performed with measured vibration response and we have obtained 2-DOF damping coefficients, rotational and transverse vibration, without any trial and error process. For this purpose tubular shaft was used so that the damping coefficient can be changed by putting additional center core rod coaxially to give frictional losse. And the analyzed damping coefficients are verified experimentally with a gear test rig in which the damping effect can be intensionally changed.

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Several gear materials, gear processes and gear lubricants were evaluated for surface fatigue life in the NASA spur gear fatigue test rig during the last several years. Some of these materials include VIM-VAR AISI 9310, EX-53, CBS-1000M, CBS-600, VASCO-X2, M5O-Nil, VASCO Matrix II, VASCO Max 350, and Nitralloy N. Some of the various processes include shot peening at different intensities. Several aircraft gear lubricants with different viscosity's and additives were evaluated for their effect on surface fatigue of standard spur gears. These materials and lubricants were evaluated for possible use in advanced aircraft gear applications. The fatigue life of the gear materials and lubricants were compared with the life of the standard AISI 9310 gear material and the base lubricant. Surface fatigue tests were conducted at a lubricant inlet temperature of 49℃, a lubricant outlet temperature of 77℃, a maximum Hertz stress of 1.71 GPa and a speed of 10000rpm.

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There is a constant need for weight reduction and miniaturisation of automatic transmissions for passenger cars. The main reason is for fuel efficiency improvement however there is also a trend toward higher engine output for passenger cars. The control performance of Automatic transmission fluid is increasing, however, it also has characteristics which are not desirable for the lubrication of the gears. Tooth surface failures of carburised gears such as pitting fatigue have begun to increase for this reason. In this study, pitting fatigue tests were conducted using carburised gears with two methods of tooth surface strengthening. These were shot peening and manganese phosphate film treatment after shot peening. Three kinds of automatic transmission fluids were used Development of pitting of gears as influenced by differences in lubricating oil and the relation to gear wear was investigated by the experiments.

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During the last decades synthetic oils have become more and more common for worm gear lubrication. Because of their lower wear rate in comparison to mineral oils the pitting resistance becomes increasingly important. During the last years a large number of worm gear tests were carried out at the FZG-worm gear test rigs to investigate the pitting phenomena of worm gears. These tests showed, that even with pitting areas up to 60 % the end of the life of a worm gear drive is not reached. Furtheron a continuous pitting growth during the total life time of a worm gear drive was not confirmed. The life time of a worm gear drive can be devided into three characteristic stages : 1. Stage of no pittings and low wear rates 2. Stage of pitting growth 3. Stage of decreasing pitting areas and comparably high wear The first stage is characterized by very low wear rates and no visible pittings. At the beginning of the second stage first pittings usually occur in the outlet area. Then the pitting area is steadily rising to a maximum. In the third stage the pitting area is decreasing because of increased wear rates. The third stage can last even multiple times of the first two stages. The end of the life time is reached, if consequential damages like transmission error because of wear or tooth breakage occur. Based on these tests a new calculation procedure was developed. In comparison to existing methods the new method allows the calculation of the pitting growth and the life time for all three stages along with the total life time of the gear drive.

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The endurance test of the gears designed for very high loading capacity showed some types of failures, that are very characteristic to such gears : Big influence of edge contact at tooth side and tip on the failure was observed. It is because relatively small amount of crowning and tip relief was given to lead form and profile form of those gears respectively in comparison with that of usual gears to make the load distribution over whole tooth Hank flat. Material condition and pitting cracks observed on the surface near side boundary of contacting area of tooth flank suggested that a cause of such failure is the repeated go and back contact-slipping between tooth side edge and mating tooth flank surface. The trochoidal interference appeared near tooth root of the test helical gears and plastic flow and white layer were found there. Chipping was observed at edges of tooth of smaller-face-width gear and micro cracks initiated from the chipping. Fatigue fracture proceeded from those cracks into the subsurface of gear tooth and led to tooth breakage. Most of those failures are not well recognized by gear designers until now and there is not yet any method to predict load carrying capacity of gears concerning such failure modes.

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Face gear were designed and manufactured as a replacement of conventional spiral bevel gear using in the 1st stage of a helicopter main transimission. Design input speed was 6,000rpm and input torque was 482 N・m. They were made of AISI9310 steel, carburized and ground. Face gear teeth were ground by intermittent generating method with CBN wheel. Tooth form was inspected by 3D measuring machine. The quality of them was equivalent with AGMA class 12. The endurance test was conducted in Kawasaki Heavy Industries, LTD. (KHI) bench test rig. The effect of tooth flank modification was checked by the measurements of root stress. Scuffing was occured at the first run of the endurance test. Lublication oil temperature and input speed were decreased and continued the test. Finally the endurance test was performed at 140% torque and it was successfully finished at 3x10^7 pinion cycles. The result shows that the durability of face gear is equivalent to spiral bevel gear or more. The tests were performed in support of the Society of Japanese Aerospace Campanies inc. (SJAC) Advanced Aircraft Parts and Material Research Program.

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Operating conditions in typical automotive planetary gearsets lead to harsh tribological conditions. Relatively low operating speeds and low viscosity lubricants limit the formation of protective oil films. As power density demands increase, these conditions become more severe and pitting fatigue resistance becomes more important. In this study, typical gear contacts are characterized with two and three dimensional surface finish methods. The results are compared to film thickness predictions made with traditional EHD methods adapted to helical gear geometry and also with 3D contact analysis programs to establish the operating regimes. SEM and digital micro-graphs are used to illustrate the condition of the surfaces at several stages of testing.

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For Austempered Ductile Iron (ADI) gears, a shot-peening may be utilized to improve the bending fatigue strength. However, under some shot-peening conditions, the increase of surface roughness by shot-peening may decrease the surface durability of ADI gears. The authors investigated the influence of shot-peening on the surface durability of ADI rollers using a disk machine which simulates the rolling and sliding action of gears. Two types of shot-peenings were adopted, that is, the conventional shot-peening and the fine particle shot-peening. The results are summarized as follows : (1) The increase of surface roughness by the conventional shot-peening causes the decrease of surface durability. This is confirmed by testing rollers polished after the conventional shot-peening. (2) The surface roughness after the fine particle shot-peening is smaller than that after the conventional one. The surface durability of ADI rollers after the fine particle shot-peening is superior to that after the conventional one. (3) Consequently, if shot-peening is applied to improve the bending fatigue strength of ADI gears, the fine particle shot-peening is useful to prevent the decrease of the surface durability.

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In this paper, the load-carrying capacity, in particular, the surface durability of gear pairs with a combination of Austempered Ductile Iron (ADI) gear and hardened steel one is investigated using a power-circulating type gear testing machine. It is practical that a hardened steel such as case-carburized one is used for pinions to increase its bending strength and surface durability, and ADI is used for large gears to use its advantages such as near-net-shape casting. In this case, a shot-peening must be conducted on the tooth of ADI gears to increase its bending strength. But the surface durability of conventional shot-peened ADI gears decreases because the surface roughness increases by the conventional shot-peening with shots diameter of 0.3mm. The authors applied two types of fine particle shot-peening with shots diameter of about 40〜45μm in order not to make the gear tooth surface rough. As the result of experiments, the surface durability of fine particle shot-peened ADI gear is improved compared with conventional shot-peened one because the tooth surface roughness does not increase. In addition, the surface integrity, i. e. surface roughness, hardness and residual stress, is investigated in relation to the surface durability.

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The machine elements made of sintered powder metals are generally cheaper than those made of conventional steels, while they have a disadvantage in the fatigue strength. Therefore, the purpose of this study is to investigate the influence of shot peening on the surface durability of sintered powder metal rollers under a slidingrolling contact condition, for improving the strength. The compressive residual stress, the hardness and the surface roughness of all shot-peened rollers increased and the pores were deformed by shot peening. Only the surface durabilities of mild shotpeened rollers were higher than that of unpeened roller in this study. The failure mode of the rollers was mainly spalling. The spalling cracks propagated from the sharp notches of the pores deformed by shot peening. Therefore, the result of this study clearly shows that the mild shot peening which dose not cause the sharp deformed pore and too large surface roughness should be selected in order to improve the surface durability of sintered rollers.

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The tooth surface fatigue strength of the conical involute gear is evaluated in this paper. Test gears are straight intersecting-axis conical gears. The material of the test gear is normalized steel. The power circulating testing machine is used in this experiment. The circulating torque is kept constant and the number of times of contact is 10^7. The tooth surface life is evaluated by the pitting area rate. The critical value of the circulating torque is found between 147 (N・m) and 157 (N・m). For critical torque, the pitting area rate does not progress over 4 %. The Hertzian contact stress of the test gear is calculated at the circulating torque. The contact stress should be evaluated in consideration of the wearing effects. The tooth surface profile of the test gear is measured after the life test. The calculated Hertzian stress is modified by measured tooth surface profile. This value can be used the fundamental data for evaluation of the tooth surface strength.

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In order to analyze gear tooth face pitting, the previous research presented the influence of pitting factors and the life estimation formulas that were accomplished using carburized roller tests under various test conditions. This paper presents the evaluations of the tooth pitting life estimation method based on roller pitting analysis as compared with conventional calculation methods of the tooth face strength and the results of gear pitting tests. The coefficient values of the pitting factors in the roller formula for life estimation are within the limit of those values given in the conventional calculation methods ; ISO, AGMA and so on. The roller formula includes some important pitting factors that are not significantly considered in the conventional methods. Therefore, the tooth pitting life estimation based on the roller formula gives a more definite value than the conventional methods for carburized gears. The comparison of pitting life between the estimation of the roller formula and the actual gear tests was carried out. The result shows that the pitting lives estimated by the roller formula are shorter than that of actual gear tests. This is caused by the surface wear of the carburized gear's tooth face. The surface wear induces a decrease in the contact stress that strongly influences the pitting life. It also induces the fact that the oxidized-nonmartensitic layer wears out and the stronger case hardened surface appears.

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In order to assess the sliding-rolling contact fatigue lives of surface-hardened sintered rollers from the view point of linear fracture mechanics, the crack propagation behavior was investigated under a sliding-rolling contact condition. The surface-hardened rollers which have three kinds of artificial defects were fatigue tested, and the crack propagation rate was measured. The stress intensity factor was calculated using the finite element method. The crack propagated from the hole was almost parallel to the roller surface. Therefore, it could be said that the crack propagation under a sliding-rolling contact condition was in the mode II. The parameters m and C in Paris's law were obtained from this experiment. Using those parameters, the fatigue lives of the surface hardened sintered roller were estimated. The estimated fatigue lives were almost the same as the experimental ones. The fatigue lives of the sintered rollers depend mainly on the pore distribution and the hardness. It could be considered that the cracks of the sintered rollers occurred from many mean pores and propagated from one pore to another pore.

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The R-S-N (Reliability-Stress-Life) curves of a specific material are the important information if reliability-based design method is to be applied on mechanical components. As the bilinear equations of conventional S-N curves cannot express the S-N relation properly for long fatigue life, the study employed nonlinear and irrational functions to construct the R-S-N curves covering all range of fatigue lives. Using three non-linear models (i. e. Weibull, Bastenaire and Serensen), the R-S-N curves for the surface fatigue strength of JIS SCM 415H are constructed based on the resulting data of a fatigue test. Finally, comparisons of these R-S-N curves and discussion of the differences among these models have been made.

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As compared with external gearings, the proof of the fatigue strength in internal toothings of planetary gearings is becoming more and more complex. This is due to the additional stress proportions in the gear rim. A method based on analytical solutions for a simplified internal gear model and on approximate solutions from numerical calculations of variants allows the determination of local tooth root stresses and their rating. The draft of the VDI-Richtlinie 2737 (guideline 2737 by the Verein Deutscher Ingenieure) "Calculation of the Load Capacity of the Tooth Root in Internal Toothings with Influence of the Gear Rim" uses the systematics and the relationships of DIN 3990, extending or specifying them. The fixing of the internal gear has a considerable effect on the gear rim stiffness. For an approximate calculation of the load capacity there can be estimated the influence of the mounting of the internal gear without numerical simulations.

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The high load capacity of carburized gears mainly originates from the hardened layer and induced residual stress. On the other hand, the decarburization at the surface, which causes a nonmartensitic layer, and the inclusions such as oxides and segregation act as a latent defect and the defect considerably reduces the fatigue strength. In this connection, the authors have proposed a formula of strength evaluation by separately quantifying the influence of the defect. However, the principal defect which limits the strength of gears with several kinds of defects remains unclarified. This paper presents a method of inferential identification of principal defect based on the test results of carburized gears made of SCM420 clean steel, gears with both an artificial notch and nonmartensitic layer at the tooth fillet, and so forth. It makes clear the practical use of presented method, and the strength of carburized gears can be evaluated focussing on the principal defect size.

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Surface durability of gear teeth can be increased by increasing the hardness of the gears. However, when the hardness is increased beyond a certain limit (about 500 Vickers Hardness), the bending fatigue strength of teeth decreases with an increase in the hardness in the case of through hardened gears. It is generally believed that the reduction in the bending fatigue strength of teeth can be prevented by introducing case-hardening. In the present investigation, the test gears were casehardened by three different methods. As for the gear materials, plain carbon and alloy steels including high tension steel were used. The gears were hardened by carburizing, plasma nitriding and induction hardening. Specifications of test gears are module m=3, number of teeth Z=26 and face width b=10 mm. In contrary to general expectation, the impact bending fatigue lives of the induction hardened gears were longer than those of carburized or nitrided gears, in almost all cases. In some cases, plasma nitrided gears were stronger than carburized gears. The effective utilization of the induction hardened gears were discussed using measured bending fatigue lives and the hardness of the teeth of the hardened gears.

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This study deals with the characteristic of refrigerant for heat-treatment deformation control of SM45C steel. The control of heat-treatment deformation must need the progress of production parts for a landing gear. Most of the deformation is occurred on inconsistent cooling. The inconsistent cooling is occurred by a property of quenching refrigeration. When a heated metal is deposited in the refrigeration, the cooling speed is so slow in early period of cooling because of occurring a steam-curtain. After more cooling, the steam-curtain is destroyed. In this progress, the cooling speed is very fast. The object of this study is to control the deformation of heat-treatment for landing gear by improving the conditions of quenching. The cooling curves and cooling rates of water, oil and polymer solution are obtained and illustrated. From the characteristics of the quenching refrigerant, the effects of heat-treatments on thermal deformation and fatigue strength are also investigated.

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