There is a strong demand to insure traceability for the quality of gears. We propose a novel multiball artifact (MBA) for evaluation of pitch measuring accuracy of gear measuring instruments (GMIs). The aim of the MBA is to transfer minimum uncertainty from a calibrated value at a national institute to GMIs of a shop floor. The MBA is composed of equally spaced balls around an axis. The balls can be manufactured with profile accuracy of several tens of nanometers. Commercial GMIs can measure the pitch deviation of the MBA without special software because the virtual gear dimension for the MBA is built. We calibrated the MBA at the National Metrology Institute of Japan (NMIJ) and we evaluated the pitch measuring accuracy of a GMI using the calibrated MBA. The MBA was useful calibration artifact that can be transferred the small uncertainty from the NMIJ to the GMI.

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Reduction of vibration and noise is one of the serious problems about gear. The characteristics of vibration and noise of the gear are affected by the micro form on tooth flank and therefore precise measurement of tooth flank is demanded. However, artifact which inspects and calibrates the sensitivity performance of gear measuring instrument to the frequencies of micro forms on tooth flank does not exist. In this report, we propose inspection and calibration method of gear measuring instrument using V-groove artifact, which accommodates a plane surface with precise V-grooves. The theoretical measurement result of the V-groove artifact is mathematically calculated and it is verified that the form of the V-grooves can be observed in the measurement result.

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The influence of gear eccentricity is normally considered that it is not so important for gear transmissions. However gear eccentricity causes large delay motion, and tooth meshing noise is subjected to two kinds of modulations; frequency modulation and amplitude modulation. That is one of sources of beat noise and sideband noise of mesh frequency. The purpose of this research is to clarify the influence of gear eccentricity on the characteristics of noise spectrum using transmission error analysis. In this paper, relations between amplitude modulation and sidebands of mesh frequency were investigated. By assuming that the mesh wave is purely sinusoidal, the modulated spectrum was calculated theoretically. Sideband spectrum consists of two components, whose amplitudes were calculated by modulation indices. To identify the concrete modulation indices, the amount of amplitude modulation was detected directly by transmission error measurement under load. From measured data, modulation indices can be calculated using amplitude of mesh frequency components and amount of amplitude modulation.

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Sideband components of mesh harmonic frequencies are dynamically characterized by using a single-degree-of-freedom nonlinear model of a cylindrical gear pair. Time-varying mesh stiffness and tooth surface form are formulated in the model. In addition to mesh harmonic components, the first order of gear rotation is incorporated into each of the time-varying mesh stiffness and the tooth surface form as the effect of run out error. This model presents that the product of mesh harmonics and low order component of gear rotation frequency produces sidebands on either side of the mesh frequency. Then, the equation of motion was numerically integrated. The calculated results prove the existence of asymmetrical property of sidebands of mesh frequency. Finally, these sideband characteristics are verified by the experiment using a single-stage helical gearing.

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Tooth surface form inspection is generally performed for quality check of gears. But inspection of single gear can't estimate gear pair's characteristic, effect of alignment error, elastic deformation of shafts and gearbox. Therefore, inspection method not for single gear but for gear unit is desirable. Authors had proposed the method that estimate frequency response function(FRF) of a gear system with vibration measurement. It enables to obtain mesh excitation force and to estimate surface form characteristics. In the proposed study, vibration signal is measured on gear body. But mounting vibration transducers on rotating gear costs expensive for practical use on quality check, diagnosis, etc. In this study, we discuss about FRF estimation with vibration measurement on pedestal.

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The current paper presents a method to feed back loaded tooth contact analysis results to the ease-off topography design of spiral bevel gears in order to reduce running noise. Loaded tooth contact analysis is herein implemented using a FEM solver, with additional consideration of the effects of housing deformations, bearing displacements and shaft deflections. The resulting deformations at the tooth contact are processed with the aim of pre-compensating their effect on motion transmission. The result is the noise-optimized ease-off topography design, a type of crowning special in shape and extent. Such design leads to minimum loaded transmission error, so that the gear pair will exert minimum excitation on the transmission chain. Actual tooth geometries near this optimum can be realized by higher-order modifications of CNC gear generators. The method was tested on a full scale test bench of a truck rear axle drive, and proved to be efficient in reducing gear noise. A sound pressure level decrease from 115 to 85dB was achieved at the target speed (70-80km/h truck speed), as compared to the original gear design. The essence of the proposed method lies in the ease-off topography design. All other gear parameters and drive components may remain the same. Thus it can be considered a quick-to-implement and universal method for noise reduction. As a favorable side-effect of optimization, tooth root stresses and contact pressures also reduce in general. However, it is necessary to investigate extreme operating conditions too, where the effect may be opposite.

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It is known that assembly errors, often referred as misalignments, have significant influence on gear dynamics and ultimately noise generation. However the study of effects of assembly errors on the dynamic response for non-parallel axis gears, primarily hypoid or spiral bevel gears has been limited because of their complicated geometry, and time and spatial-varying mesh characteristics. In this study, four types of assembly errors, that are errors of shaft angle, pinion offset, pinion axial position and gear axial position, are examined in the tooth contact analysis of a typical spiral bevel gear pair. The load distribution results are synthesized to obtain the mesh parameters which are then applied to the dynamic simulation to investigate the sensitivity of the dynamic response subject to the assembly errors. This study yields a better understanding of the specific errors controlling the severity of vibratory response in a spiral bevel geared rotor system. The analytical results of this study can be applied to guide the gearbox transmission design improvements.

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It is widely accepted that transmission error fluctuations correlate well with the dynamic behavior of gears and most models in the literature are, to a lesser or greater extent, based on this concept. The objective of this paper is to present some recent advances in the modeling of tooth mesh excitations and dynamic tooth loads in relation with transmission errors. Based on a multi-degree of freedom finite element model of single stage gear system, the excitation functions are derived from the contact conditions between the teeth and the equations of motion are presented in terms of quasi-static transmission errors under load and no-load transmission errors. The range of application of the transmission error-based formulations is then analyzed and the link between transmission errors and dynamic tooth loads is examined. It is demonstrated that, as long as the linear behavior of helical gears is considered, a perturbation technique leads to an approximate formula which makes it possible to compute effectively dynamic tooth loads. Comparisons with the results obtained by a time-step integration method are favorable with considerable gains in computational time when multi-degree of freedom models are employed. From the same theoretical foundation, it is finally demonstrated that, in certain conditions, a linear relationship can be found between dynamic transmission error variations and dynamic tooth loads, thus confirming some recent experimental evidence obtained on a spur gear test rig.

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During the last decade, many new technical solutions dedicated to the comfort of automotive vehicle's drivers have raised, like Electrical Power Steering (EPS). To fulfill the more and more demanding requirements in terms of vibration and acoustics, the dynamic behavior of the whole steering is studied. The system is divided into dedicated finite elements describing the whole steering. The stress was first put on the gears models (worm gear and rack-and-pinion) and their anti-backlash systems as they have been identified as potential vibration sources. Mechanical non-linearities (clearances, non-linear stiffness) of the mechanical system are taken into account in these models. Then, this model allows simulating the transient response of the system to an input excitation. Each developed element is validated using a fitted experimental bench test. Then, the general model is correlated the same way. Hence models can be used to study the dynamic behavior of EPS systems or sub-systems.

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There are some NVH problems caused, or be thought to be caused, with drive line. However, drive line is a passive system in many cases. An engine or interaction in a powertrain is suspected as the cause of those problems. Gear rattle is common in manual transmissions and become uncomfortable noise when engine pulsation amplitude is larger than the threshold, depending on gear pair backlash and others, of the transmission. Torsional vibration of drive shafts is common in every vehicle. When the amplitude is larger enough, the driver or passengers complain longitudinal vibration caused by drive shafts. Possible triggers of the torsional vibration are engine toque rapid change (tip in & tip out), clutch engagement and nonlinear driving force transfer with torque converter immediate after starting from stand still. Mathematical models are derived for excitation source and transfer path to describe those NVH problems. NVH problem is alleviated when input force is shaped properly to avoid uncomfortable vibration or noise considering combined frequency property of excitation and transfer path in a power train system. Effectiveness of measures to reduce NVH problem is studied considering controllable range constraints of actual power plant.

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Due to the change in the number of contact tooth pairs, mesh stiffness is periodically time-varying, which leads to additional time-variant coefficients in the corresponding governing equations of geared dynamic system. Natural frequency of such system differs distinctly from that of the time-invariant system. However, it has not gained enough attentions in geared dynamic analysis, and the natural frequency of geared system is usually assumed to be the average frequency, obtained using the time-average mesh stiffness. Whether it is reasonable for us to obtain the natural frequency of geared system like this should be analyzed seriously. Thus, the natural frequency of parametric vibration for spur-gear-pair system will be researched using Floquet theory in this paper. Influences of the periodically time-varying mesh stiffness parameters (including: mesh frequency and contact ratio) on natural frequency will be discussed respectively in detail. Contrasts between natural frequency and average frequency for the system in stable and unstable regions will be processed and the scope of application for taking the average frequency as a substitution for the natural frequency of geared system will then be presented in the paper.

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In this study, we consider the automotive gear rattle noise resulting from vibro-impacts that can occur between the unloaded gears under excessive speed fluctuations imposed by the shaft-fixed gears. The main parameters governing such kind of vibrations, are the excitation source related to the engine torque fluctuation which can be modelled by an imposed periodic displacement, the inertia of the free gear, the drag torque acting during the free flight motion and the impact laws. In the case of rattling, it is reasonable to assume that duration of impacts between teeth is very short compared to the free flight duration. Then, impacts can be modelled by a restitution coefficient law. There exists several models for the restitution coefficient, the simplest being a constant one. In fact, it can depend on impact velocity. In this context, this study presents some effects of the restitution coefficient law on the dynamic response of the idle gear.

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A coupled flexible multibody dynamic model of planetary gear is presented to investigate the dynamic performance of the planetary gear and its supporting bearings. The bearing's and gear's kinematical deformation are first defined, the bearing has two degrees of freedom with respect to each axis of the coordinates, that is, the translation in the axis and rotation around the axis; the gear within the planetary gear has degrees of freedom of translations and rotation around its center. Because the carrier and shaft are assumed to have no bending deformation, the deformation freedom of bearing and gear are coupled together by algebraic equations. According to the bearing's and gear's constraints in the system, the corresponding constraints are set. After calculating the kinetic energy, potential energy as well as virtual work of external force, the system's governing equations are obtained by applying Lagrange function. Using the governing equation, the system's deformation modes are analyzed, planetary gear's dynamic performance is simulated during a carrier cycle and finally the bearing's dynamic behaviors are illustrated.

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This paper proposes a relatively simple method for estimating the planetary gear noise by predicting vibration of an automatic transmission (AT) with good accuracy. In the proposed method, the exciting force is calculated based on transmission error analysis, the vibration transfer characteristics from the excitation points to the observation points on the AT case is analyzed with FE model, and then AT case vibration characteristics are defined as the product of these two values. A comparison of the vibration levels predicted with this method and the experimental results measured for an actual AT case confirmed that the proposed method can predict AT case vibration characteristics simply and accurately. The useful insights gained from a case study are also discussed.

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The features of the support structures of the sun, carrier and ring gear that are the components of a planetary gear sets result in large alignment error in the form of eccentricity or inclination. Such error causes the relative tooth surface shape to vary periodically at each pinion position. The side band phenomena modulated by the rotation of the rotating elements appears around the mesh order components of transmission error. With the conventional method of calculating transmission error, it is not possible to evaluate the side band phenomena because of the inability to treat the periodical variation in the relative tooth surface shape. Therefore, we have developed a new method of simulating the transmission error of planetary gear sets taking into account such periodical variation of the eccentricity and inclination amount of each element. The predicted values are then input into the calculation, making it possible to evaluate the side band phenomena as well. Periodical variation in the relative tooth surface shape due to alignment error returns to the original state when the relative rotation between the rotating elements has completed one revolution. Accordingly, by repeating the calculation until the relative rotation between the sun gear and the carrier or between the carrier and the ring gear has completed one revolution, the new method makes it possible to analyze transmission error taking into account the periodical characteristic of the shape of the tooth surface error due to alignment error. This new calculation method was applied to analyze the transmission error of an actual transmission, and the results showed that the side band phenomena was also evaluated with relatively good accuracy.

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This paper investigates the modal characteristics of planetary gear systems using a finite element (FE) package of general purposes. Using the proposed continuous geometric model, effects of Young's modulus and supporting bearings of components in the gearings may be more effectively analyzed. Firstly, directly using tooth profile equations generated by a rack cutter, high quality elements of gears are parametrically and automatically created. Thus, dynamic models of gear systems are constructed. After assigning adequate analyzing boundary conditions and gear contact, structural natural frequencies and modal shapes are obtained using LS-DYNA. Besides, dimensionless slope is defined to evaluating the changing rates of natural frequencies to stiffnesses. Then, influences of individual or systematical supporting bearing stiffnesses on gearing modal characteristics are investigated. Besides, essential of carrier material stiffness is discussed. Several conclusions relating the modal characteristics to material and bearing stiffnesses are resulted. The proposal approach in this study may benefit the dynamic analyses of wide types of planetary gearings.

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Super-carburizing is a new surface hardening method, by which a surface contains more carbon than eutectoid-carburizing. The surface hardened by super-carburizing has a high hardness, a strong abrasion resistance, a high temper softening resistance and an excellent pitting resistance. The super-carburizing is attempted to apply to various machine elements. In this study, we investigated the bending strength and the surface durability of super-carburized steel gears and eutectoid carburized steel gears. Furthermore, we applied a shot peening to the carburized gears, and carried out the bending fatigue test and the contact fatigue test for the shot-peened carburized gears. We also discussed the effect of shot peening on the strength of the carburized gears.

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This paper describes a study on the load bearing capacity of newly developed high density sintered metal gears with surface-densification. High density sintered metal gears were hobbed, and then surface-rolled. These gears were case-carburized after surface-rolling. The effect of surface-rolling on the surface property was examined by measuring porosities and hardness near surfaces of rolled gears. Running tests for these gears were performed. A failure mode and load bearing capacity of high density sintered metal gears and the effects of surface-rolling on the load bearing capacity of sintered metal gears were determined, and the results were compared with those of carburized wrought steel gears and conventional sintered metal gears. The experimental results show that the load bearing capacity of a newly developed high density sintered metal gear with surface-densification is higher than that of a carburized wrought steel gear.

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A new cavitation peening processing unit was made to obtain greater peening effect. The purpose of this study is to investigate the improvement in fatigue strength of the steel gear cavitation-peened using this processing unit. The case-hardened steel rollers and gears were cavitation -peened under a processing time of 1 minute, and were fatigue-tested using a roller testing machine and a gear testing machine. The hardness and the compressive residual stress of the test specimens were increased by the cavitation peening. While, the surface roughness of the cavitation-peened test specimens was almost the same to that of the non-peened ones. In the fatigue tests, the fatigue life of the cavitation-peened test specimens was longer than that of the non-peened ones. Moreover, the fatigue strength of the test specimens was increased by the cavitation peening. This study revealed that the fatigue strength of steel gear was improved by the cavitation peening under a processing time of 1 minute.

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The gear-lapping process with a MC-nylon gear and abrasives for carburized gears was developed by the authors. In order to decrease the tooth flank roughness and improve the surface durability of carburized gears with fine particle shot-peening, the lapping process was applied. The surface durability of carburized gears was studied to clarify effects of the lapping process. The results show that the roughness of the tooth flanks decreased from about 4 μmRz by the shot-peening to about 1 μnRz during the lapping. The thin surface layer was removed during the lapping, but the hardness and compressive residual stress at tooth flank obtained by the shot-peening were kept, respectively. The surface durability of shot-peened gears finished with the lapping was improved. Its endurance limit was the maximum Hertzian pressure 2200MPa and was 10% higher than that of shot-peened gears.

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In the previous study, we have developed involute-cycloid composite tooth profile spur gear, and proved that this gear has greater bending strength, surface durability, and power transmission efficiency than the involute gear. However, it is unknown that how the design parameters influence on the tooth strength. To investigate this, we calculated the tooth root stress and the tooth contact stress of involute-cycloid composite tooth profile spur gears with changing some design parameters such as the rolling circle radius, the pressure angle, and the tooth depth of the gears, which define the tooth profile. Then, we investigated the influences of the design parameters on the strength and the driving performance of the involute-cycloid composite tooth profile spur gears from the calculation results. Furthermore, we calculated the tooth root stress and the tooth contact stress with the error of center distance, and examined the influence of the center distance on the driving performance of the involute-cycloid composite tooth profile spur gears from experiment.

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According to the state of the art, case hardened gears have residual compressive stresses in the surface layer. In the tooth root fillet area these stresses are generated mostly by heat treatment and eventually by additional mechanical cleaning or shot peening processes. Residual stresses together with load induced stresses and material resistance influence the tooth bending strength of a gear. Within a research project the influence of different residual stress conditions on tooth root strength was investigated. A factor "YRS" was defined on the basis of experimental results to take into consideration the influence of residual stresses on tooth root fatigue strength for the simplified calculation method according to the standards DIN 3990 / ISO 6336. After further theoretical studies on stress state and fracture mechanics a local concept model was developed for evaluate damage behaviour and showed a good consistency with the experimental results.

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Hardness measurements and observations of micro-structure of hardened layer of various case-carburized helical gears were carried out, and then the hardness distribution and the effective case depth were obtained. Bending fatigue tests of helical gear pairs of different case depths, carburized parts and helix angles meshed at the worst loading position were carried out, and then S-N curves were obtained. Effects of the carburized part, the case depth and the helix angle on the bending fatigue strength and the bending fatigue crack path of case-carburized helical gears were determined.

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The accumulation of fatigue damage near the tooth fillet may be used as an index for reliable prediction of gears. Fatigue life assessment method, which is based on the internal state variables i.e., damage variables, in material, known as damage mechanics has been proposed. The main advantage of the method is its ability to predict fatigue crack initiation and propagation in the structure using one failure criterion. In order to determine the damage variables during fatigue life, it needs to estimate the Young's modulus and Poisson's ratio in accuracy. On the other hand, we have been developed a strain measurement method based on the image processing for the accurate measurement of strain in a gear tooth. Purposes of this research are to evaluate fatigue damage and to predict residual life of carburized gears under cyclic load.

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Recently, power transmission gears have been running under the conditions of heavier load and higher lubricating oil temperature. In this study, the influences of surface texture and lubricating oil temperature on the surface failure of the rolling-sliding contact in the case of case-carburized alloy steels were investigated. The test rollers were made of low-alloyed steel, and they were carburized, hardened and tempered. After heat treatment, test rollers having three kinds of surface textures were finished by grinding and hand finishing. Roller tests were conducted under the rolling-sliding contact, high-load condition and various lubricating oil temperatures. In the case of test rollers with smoother initial surface roughness and lower lubricating oil temperature, the following results are obtained: The surface temperature does not rise under the high-load condition. The number of pits, the amount of wear and generating noise decrease. Therefore, it is found that the case-carburized gears with the higher surface durability can be developed by finishing the smooth tooth surface and controlling the lubricating oil temperature.

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The paper presents a model of the pitting damage in case hardened spur gears that aims at the assessment of the contact fatigue (pitting) limit. The calculation method is based on the local comparison of an equivalent stress level, computed by the use of a multiaxial fatigue criterion, and an allowable stress for heat treated gear materials. The complex surface and subsurface stress field generated by the contact loads is calculated including the influence of friction and the stresses induced by thermal effects. The effects of surface roughness on the contact load distribution and, therefore, on the contact stress field is also discussed. The influence of gear heat treatment processes on the material strength is taken into account assuming a variation of the material strength over depth and the presence of a residual stress field. The material strength is assessed by the Liu-Zenner multiaxial fatigue criterion taking into account the non-proportional stress path which undergoes the gear material during meshing. The proposed model is compared with results obtained using the ISO calculation method.

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Although the gearing of crossed helical gears theoretically takes place at a point, the contact point extends over a small ellipse due to elastic deformation under loading. Hence the contact stress between the tooth surfaces is comparatively high. Furthermore, the sliding velocity on the tooth surfaces is higher than for other gears. For above mentioned reasons, crossed helical gears are able to carry only very small loads. To make the most of its good features, it is important to improve the load carrying capacity of crossed helical gears. Two factors, that is, high sliding velocity and high contact stress seem to be important, but here we limit the discussion to the contact stress state. It is worthwhile to examine the subject more closely. Also, it is important to understand the meshing geometry of crossed helical gears, since it forms the theoretical basis of the meshing geometry of other types of gearing. The purpose of this report is exactly to investigate the contact stress states on the tooth surface of crossed helical gears.

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This paper presents the contact force and torsional rigidity analysis of a cycloid drive considering finite bearing and Hertz contact stiffness. Contacts between the disk and pin-rollers are simplified as linear spring elements, and the bearing is modeled as a rigid ring that has frictional contact to the disk and an elastic support. FE analysis for contact force and Hertz theory calculation for contact stiffness are performed iteratively until the contact stiffness converges less than 1%. Contact force and pressure distributions under different contact and bearing stiffness are analyzed. In addition, effects of the cycloid disk rotation are discussed. Finally, the torsional rigidity of the cycloid drive is analyzed. The results show that the bearing and nonlinear Hertz contact stiffness should be considered in analysis and design of the cycloid drive.

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A failure mode called 'flank breakage' is increasingly observed in different applications of cylindrical and bevel gears. These breakages typically start from the active flank at mid tooth height and propagate to the tooth root of the unloaded flank side. Crack initiation can be localized below the surface in the region between case and core of surface hardened gears. Mostly several parallel cracks can be recognized with one main fragment and several smaller pieces breaking out of the flank. This failure cannot be explained by the known mechanism of tooth root breakage. Therefore the German Forschungsvereinigung Antriebstechnik e.V. (FVA) initiated the research project No. 240/II to investigate the described failure mode in bevel gears and to develop a calculation method to predict the risk of flank breakage of such gears. The project was carried out at FZG (Gear Research Centre) at the Technical University of Munich (TUM), Germany. In the following the fundamental results of this research work are presented.

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The paper presents the developed discrete-analytical models of load state and load-capacity evaluation for heavy-loaded low-speed spiroid gearboxes. The pointed models were created by approximation of results of numeric simulation of mode of deformation for spiroid gears with different combinations of geometrical parameters by finite-element method. The developed approach was applied for creation of a number of spiroid gearboxes for pipeline valve drives.

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To explain the causes of pitting at contact end of gear teeth and rolling bearing race, the changing in shape and lubricating condition at contact end of rolling contact surfaces due to plastic deformation by local high contact pressure are investigated. By the in-situ observation used the EHL optical interference tester, the move of position where contact pressure shows maximum value was observed from the contact end to inside. And new contact end is produced. In order to confirm the position that rolling fatigue pit (pitting) occurs, 4-discs rolling contact machine was used under the contact condition in presence of plastic deformation at initial contact end. As results of rolling fatigue tests, fatigue pits arise at inside of contact. The pitting position is influenced considerably by the contact pressure, oil film thickness and number of revolutions under shake-downed surface profile due to plastic deformation. So to make the prevention measure at rolling contact end, it is necessary to predict the relation profile change and the pitting position.

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The surface temperature and friction coefficient for sliding-rolling contact, which has a large influence on gear pitting strength, are evaluated by numerical analysis compared with experimental measurements of a two-roller contact apparatus. As the results, surface temperature and friction coefficient evaluated by numerical analysis are in qualitative agreement with those of experimental measurements; the surface temperature increases with sliding velocity, and friction coefficient decreases with sliding velocity. The numerical analysis differ from experimental measurements on condition that contact pressure is low or that sliding velocity is low, however, the numerical analysis is in good agreement with experimental measurements on other condition. The remaining problem of numerical analysis is the contributing rate of sliding in the lubricant shearing force is estimated. Another remaining problem is heat transfer model of rollers. INTRODUCTION The estimation of contact surface temperature and friction coefficient are important for automotive parts design intending improvements of fuel milage and reliability. They are also important for developments of lubricants and material for automotive parts. Friction loss generated by contact surface of automotive parts, bearings, gears, and so on, has a large influence on fuel milage. The temperature rise caused by friction loss has a large

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A series of bench top experiments was conducted to determine the effects of metallic debris being dragged through meshing gear teeth. A test rig that is typically used to conduct contact fatigue experiments was used for these tests. Several sizes of drill material, shim stock, and pieces of gear teeth were introduced and then driven through the meshing region. The level of torque required to drive the "chip" through the gear mesh was measured. From the data gathered, chip size sufficient to jam the mechanism can be determined.

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The development of fatigue in a machine element can be divided into the fatigue crack initiation stage and the crack growth stage. The effects of the surface conditions, such as roughness and surface qualities, on the fatigue strength are considered to be restricted to the fatigue crack initiation stage. Thus, these effects can be evaluated exactly by the investigation on the fatigue crack initiation life. In this research a practical method is presented for detecting fatigue crack initiation during fatigue tests using an ion-sputtered film. Ion-sputtered films were formed on acrylic and steel test pieces having a specially designed round notch. Three-point bending fatigue tests were performed and the instants of fatigue crack initiation on the notched surface of both acrylic and steel test pieces during the tests were identified clearly; thus the fatigue crack initiation life can also be determined experimentally using the presented method. In addition, since the system used to measure the electric resistance of the film that indicates the crack initiation is extremely simple, that consists of a variable resistor, a DC power source and a data recorder, this method is considered very practical for monitoring crack initiation.

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A method for analyzing spur gear meshing is presented and applied. Analyzing the results of an example, it is shown that the path of contact and, in particular, the lowest (LPSTC) and the highest (HPSTC) single tooth contact points highly depend on profile modification amount and applied load. Furthermore, the root stress of a gear with profile modification reaches higher values than a gear with an involute profile. This increment is mainly due to an increase of the extension of the actual single tooth pair contact region of a modified gear with respect to the perfect involute gear.

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This paper deals with an experimental evaluation of bending fatigue strength for austempered ductile iron (ADI) spur gears. The module is 2.5 and the number of teeth is 26 in the test gears. The material of test gears is corresponding to JIS FCAD1100-15. Two types of fine particle bombarding (FPB) are processed for some gears. The surface roughness becomes worse slightly by FPB process. The obtained strengths are 623 MPa as austempered, and 1011 to 1085 MPa with FPBs. The strength is expressed by the fillet stress level, which is calculated by FEM. The strength of same-dimension gear, which is made by an alloy steel SCr420H and carburized is 1205 MPa. The strength of ADI gear is approximately half strength of carburized steel gear. The effect of FPB process is significant in ADI gears, and the strength is improved to 62-74%.

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Austempered Ductile Iron (ADI), which has much the same strength and toughness as usual steels, has been developed. ADI has many advantages in mechanical properties and manufacturing, for example, weight reduction due to smaller density than that of steel, good properties of vibration and noise, low cost in machining and heat treatment of blanks due to near-net-shape casting. It has been reported that ADI can be sufficiently applied as a medium hardness gear material. Recently, it is reported that S-N curve for the bending fatigue strength of ADI is different from another material such as steel. Then the fatigue phenomenon in long life region over 10,000,000 cycles is discussed. However, the surface durability in long life region has not been clarified until now. In this paper, surface durability of ADI rollers in long life region is investigated using a disk machine which simulates the rolling and sliding action of gears. Furthermore, fatigue limit for surface durability of ADI is estimated by observations of crack initiation and propagation.

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Since more than 20 years, CETIM has developed test on back to back test rigs and pulsators in order to quantify the load capacity of material for gears (steel and cast iron) with associated heat treatment. In this paper the authors present the complete data base obtained on a large variety of steel with the details of the method of analysis and a correlation with the ISO 6336-5 standard prediction. The main heat treatments covered are case carburizing; the results are given for contact pressure reference stress numbers.

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This paper investigates the fatigue strength and durability of injection molded nylon and poly-acetal spur gears by fatigue test. Accuracy variations and operational characteristics on fatigue life, wear and tooth surface temperature of nylon and poly-acetal gears are compared and represented. The fatigue strength and durability of the two types of gears is also obtained and represented by a function of unit load as well as by a function of K-factor.

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To data, a fatigue life of plastic gears under unlubricated conditions has been examined. As the results, it was confirmed that a material strength with a tooth surface temperature has effects on the fatigue life. These tests were conducted under the conditions of the tooth surface made clean entirely and dry enough, but in real machinery the gears may not be demanded such cleanliness. The effect of the oil coating on the fatigue life for plastic gears is investigated. It is shown that the fatigue life is extended considerably by the oil coating, because reduction in the tooth surface temperature depends on extensions of the fatigue life. Considering to the temperature, it is found that the cases can be arranged as same as unlubricated conditions, then there are no effects of the oil coating and water soaking on the fatigue life.

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Load carrying capacity of the crossed helical gears is considered to be low since the theoretical meshing is of a point contact. However, there is a possibility that a comparatively strong power can be transmitted because the contact area is widened by the elastic deformation and wear of gear tooth. In this study, the load carrying characteristics of the plastic (polyacetal co-polymer) crossed helical gears were investigated. The endurance experiment for the plastic crossed helical gears of helix angle of 20 degrees were performed with the angle between shafts of 40 degrees and a rotation speed of 500rpm (about lm/s in tangential speed). The meshing tooth and the atmosphere temperatures were measured during operation and the fatigue life of gear tooth was determined. As a result, the relation between the life of gears and the temperature of meshing tooth was clarified. And the relation between the temperature rise of meshing tooth from atmosphere temperature and the loading torque was clarified.

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The authors developed the new type hourglass worm gear of plastics involutes helical gear wheel. The theory, the calculation of the tooth contacts analysis for the prediction of the performance of the gear and the production method of the steel worm and the plastics wheel are reported. A set of the hourglass worm gears was manufactured. And the accuracy of the transmission was measured by the measuring machine for the angular transmission error (abbreviated to ATE) of the reducer invented by A. Horiuchi and others. The efficiency was tested by the power absorption type worm gear testing machine, designed and made by the authors. The efficiency of the hourglass worm gear was compared with the cylindrical worm gear of steel worm and plastics wormwheel whose dimensions was the same of the hourglass worm gear proposed in this report.

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The heat generation due to friction between tooth flanks and hysteresis of plastic material greatly affects the load capacity of plastic gear pair, especially in operation without lubricants. And, the bending strength is not proportional for module size and facewidth, because the plastic gear generation of heat. In addition, when the gear speed quickens, the possibility of generation of heat increases and the tooth temperature rise. However, as for the faster speed, the generation heat potential decreases and the tooth temperature falls. Therefore, The bending strength formula of plastic gear must consider for the generation heat by the module size, facewidth and gear speed. Then, the temperature should be the critical section of the tooth profile. It was analyzed by special heat software of the gear that developed by us. In the present paper, an effect with module and gear speed to the radiation was analyzed for the gear by various modules.

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Effects of swelling of nylon gear due to moisture absorption on noise and vibration are investigated. Gear swelling causes large negative pressure angle errors on the tooth profiles of nylon gear. Swelling of nylon gear influences the noise generation, however the effects appear limitative. Namely swelling of nylon gear has no very effect on the noise except the case operated under low load condition. In spite of existence of large pressure angle errors on tooth profiles, the body of swelled nylon gear does not vibrate so hard compared with that of non-swelled nylon gear. It is considered that swelling of nylon gear due to moisture absorption increases in the tooth compliance and increases in the acts on relaxation the dynamic mesh force.

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It is currently assumed that churning losses can be described by using only two physical parameters representative of the lubricant properties, i.e., density and viscosity. To verify this hypothesis, a specific gear test rig was used and a number of transient measurements were made with various oil temperatures. It appears that, for high temperatures and/or high rotational speeds, the drag torque may suddenly increase with an increasing Reynolds number. In order to explain this behavior, on-line lubricant aeration measurements were taken which show that this observation can be related to churning losses, as the drag torque becomes larger when the fraction of air in the lubricant increases. It is concluded that lubricant density and viscosity are not sufficient in themselves to estimate churning losses and that additional properties related to the lubricant aeration should be considered.

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A windage and churning losses are main factors of the power loss in a high-speed gearbox. To reduce these losses, shrouding the gear is effective. For the shroud design the shroud shape, oil drain hole location, hole size and hole shape are important. Currently, to design the optimum shroud shape, many times of rig test has been done by trial and error. This trial and error is time consuming and costly. And it is difficult to design the optimum shroud by this method. Because the oil/air flow in the gearbox can not be evaluated. In order to understand the oil/air flow around the gear, CFD simulation method is developed. In this study the optimum shroud shape for a spiral bevel gear is investigated parametrically by the CFD simulation. Then based on the CFD simulation, some types of shrouds that is expected to reduce the losses effectively are selected and verified by the rig test. A base line shape of the shroud is that enclosing a whole of bevel gear as much as possible and restricting the pumping action by the gear teeth. Investigation parameters are (1) shroud shape at the heel side of the bevel gear (2) circular location, size and shape of the oil drain hole. The most effective shroud was determined by the rig test. This shroud reduced the loss by 36% compared to the unshrouded gear. The CFD simulation results agreed quantitatively with the rig test results. This CFD simulation technique can be also applied to the optimization of the oil scavenging and housing shape. It is anticipated that further power loss reduction can be achieved.

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