Traditional Japanese method for producing steel, or tamahagane, from iron sand by use of Tatara system is introduced which is still active only to make swords. Japanese swords are basically made of the tamagagane by sword master, for which scientific discussions from viewpoint of metallo-thermo-mechanics are stated. Computer simulation during quenching reveals to show how the distortion, or sori and blade pattern called hamon behaves.

This paper proposes a method of directly designing the surface of action of a hypoid gear. In the proposed method, the characteristics of the gear meshing are independent of the manufacturing process. The conjugate gear surfaces can then be accurately obtained by coordinate transformation. A plane was selected as the surface of action to achieve hypoid gears with a higher performance than face gears. The proposed hypoid gear may have the same features as cylindrical involute gears that also mesh in the plane of action and are unaffected by translational assembly error.
A design example is presented in this paper to verify that tooth surface meshing in the plane of action can be achieved for a high-reduction ratio hypoid gear. The influence of different types of assembly error on the tooth flank error was examined numerically.

Hypoid gears are used as the final reduction gear of vehicles to transmit and change direction torque. Plastic deformation of a hypoid gear tooth flank occurs when a load exceeding the yield stress acts on the tooth surface. This study analyzed the plastic deformation mechanism of hypoid gears. First, the relationship between plastic deformation and these stresses was identified by finite element analysis of approximated tooth contact. The results of this analysis found that local plastic deformation of the tooth flank is caused by Hertzian stress under the line of contact. Second, a plastic deformation index which was defined to simulate plastic deformation consists of three elements: 1) yield stress considering the hardness of a case-hardened gear, 2) Hertzian stress under the line of contact, and 3) a correction coefficient at the contact point. The correlation between the plastic deformation index and plastic deformation was confirmed by a deformation test.

Plastic deformation under high load is a phenomenon that affects the ring gear when heavy torque is applied to the hypoid gear. This study clarified the mechanism of plastic deformation under high load and identified its cause as an internal yield under the line of contact. It was also found that the line of contact near the heel has a large influence. Finally, a hypoid gear design method was formulated based on the contribution of each design variable to plastic deformation under high load.

The process of designing and analyzing the performance of spiral-bevel and hypoid gear sets requires a compact description of the gear set deflections under load. Three translational deflections E, P, G, and one angular deflection α are traditionally used to uniquely specify the relative orientation of a single spiral-bevel or hypoid pair.
The movement of the contact pattern correlates strongly with these deflections, but only if the deflections E, P, G, α represent local deformations in the vicinity of the contacting teeth, rather than global deflections.
It is possible to compute E, P, G, α that better represent the local deformations. This paper provides the mathematical basis for extracting the E, P, G and α numbers from a dispersed Finite Element nodal field.
The assumptions and mathematics of the regression process, and its limitations are presented. An examples of its application to a flexible hypoid gear pair is shown.

The kinematic/transmission error is one of the indices used for the performance evaluation of the cycloidal gear drive. It can be usually simulated by performing a tooth contact analysis when the design parameters are given. In the tooth contact analysis, equations of constraints from contact point and contact normal are derived. Usually, solving these equations of constraints requires nonlinear equation solver and hence assumes computing time. In this paper, a simplified method for calculating the kinematic error is proposed. The profile of the cycloidal gear as well as the output angle of the drive is discretized by certain number of precision points and positions. An algorithm is developed to check the interference status between the pin and discretized points and calculate the output angle. By using this algorithm, the computing time for calculating the kinematic error can be reduced about 16 percent with the loss of accuracy about 0.25 arcsec in the numerical example illustrated.

The purpose of this paper is to clarify the contact stress calculation methods taking into account the profile modification. In contrast to [5], where more general problem was considered, this work examines calculation of contact stresses in gears, the profile of the teeth which is a modification of type "C". The influence of gear teeth parameters and depth of profile relief on the level of contact stress determined from The formulas obtained in this paper can be used as a complement to the formulas for calculating contact stress with the "C" lead modification of the teeth, obtained in [11].

This paper presents a meshing analysis of face gears with a low gear ratio. A tooth contact analysis (TCA) method for face gears was developed that takes into account contact line changes associated with meshing, tooth accuracy and assembly misalignment. The results of a study of the motion curve pattern showed that the contact line length is shorter on the toe side and becomes longer toward the heel side and that the motion curve is likely to jump because of the influence of tooth accuracy and assembly misalignment. The results also showed that an appropriate pinion lead angle modification is effective in controlling motion curve jumping.
The results of fatigue durability tests are also presented. It was observed that the pinion gear broke not at the tooth root but at the tip near the border between single and double contact regions. A loaded tooth contact analysis (LTCA) method was developed to find the cause. It was found that the contact line where the single contact region begins is short and the distributed load on it is very large. It was verified that modifying the blank shape of a face gear so as to reduce the abrupt change in the total contact line length is effective in improving fatigue strength.

The tooth profile characteristics of the conical surface enveloping spiroid are taken into consideration. According to the formation mechanism, the equation of the helicoid of an enveloping spiroid is deduced. From this, the equation of the axial tooth profile is obtained. An approach is proposed to portray the axial tooth profile by means of the aforesaid equations. Two techniques are put forward to compute the tooth profile angle of the enveloping spiroid. One is based on the computation of the tangential vector of the tooth profile, and the other is based upon interpolation. The results attained from these two techniques are nearly accordant. Consequently, the theory and methodology are well verified and validated. A numerical example is provided and the effect law of the leading processing parameters on the axial tooth profile is pointed out.

Powder metal (PM) gears are becoming a more prospective solution for high performance gears, not only because of part price but also because the technology offers a wider design window. Since powder metal alloys have a lower Modulus of Elasticity and Poisson Ratio — the factors that amplify gear tooth deflections — the design window opens up further.
The contact ratio is a critical gear mesh parameter that greatly affects gear drive performance, including load capacity, noise, and vibration. Gear drive operating load produces bending and contact tooth deflections, which increase the actual effective contact ratio.
The article describes the analysis and gear macrogeometry optimization of powder metal gears with transitional nominal contact ratios ε_α = 1.7-1.85. Under the operating load, the effective contact ratio of these gears is increased to ε_αe ≥ 2.0 creating greater load sharing, as well as providing stress and transmission error reduction.

Powder metallurgy (PM) is an efficient, cost effective technology for making, for instance, gears for automotive transmissions. The technology allows for complex geometries to be produced with few process steps, and design features that are difficult and expensive to produce with traditional machining can easily be incorporated. As a step in demonstrating the possibilities with the powder technology a manual six speed transmission has been reengineered, prototyped and put into a demonstrator vehicle. The gearbox platform is called a M32 and found in for instance Opel Insignia or Saab 9-5. This paper describes the process of developing the demonstrator from the design phase to implementation in a car and summarizes the key findings from the project and technical benefits with PM gear technology.

Curve-face gear is a new type transmission device combining the common transmission characteristics of non-circular gears and face gears, which can transfer the motion and power between the intersecting shaft and staggered shaft. Given the complexity of the tooth generation of curve-face gear, 1) some machining methods, including three axis NC machining method , five-axis CNC machining method and the combined processing method of additive manufacturing and five-axis CNC machining, were introduced. 2) Based on space gear meshing theory and the machining principle, the machining models of curve-face gear were established.
In order to verify the accuracy of the obtained gear, tooth surface measurement was applied, a new accuracy evaluation method for pitch deviations and tooth profile deviation of curve-face gear was processed. The results show that the tooth surface accuracy of the curve-face gear is high. The design of the curve-face gear, and its processing methods have been verified.

When cutting gears e.g. by hobbing, more or less burrs will occur on the faces of those gears, which have to be removed. In addition, the wish of a defined chamfer on the faces along the tooth gap gains importance.
To solve this issue, there are many different solutions available, which are more or less suitable depending on the batch size, the requested chamfer form, the process chain and the part geometry.
In this paper, the chamfering principles Gratomat, press chamfering and especially ChamferCut [1] will be presented. The processes will be explained and typical application examples as well as the resulting chamfer form are presented.
For ChamferCut, there are also two variants where the chamfering tools are placed next to the hob on the same hob arbor or in a separate chamfering station inside the hobbing machine.
The advantages and disadvantages of each principle will be analyzed to give the user a decision guidance.

In order to improve load-carrying capacity and noise behavior, gears usually have profile and lead modifications. Furthermore, in gears where a specified tooth-flank load application direction (for drive and coast flanks) is a design enhancement, or even compulsory, the asymmetric tooth profile is a further solution.
Nowadays, many gears need to be hard finished. Continuous generating grinding offers a very high process efficiency, but is this process able to grind asymmetric gears? Yes, it is!
Besides the advantages of the asymmetric tooth profile, the paper will report about the main hard finishing methods for asymmetric gears, such as:
•skive hobbing,
•profile grinding with electroplated CBN disks
• and new, the continuous generating grinding.

The objective of industry is to produce components in the shortest possible time, to the lowest costs and in the required quality. It isn´t only demanded in the machine development, but also in the technology development and in the technology integration. Another requirement of industrial production is the order-based production of components. These objectives require very high standards in the development of new machine-concepts. They lead to the concentration of technological machining processes in a single machine. The actual development of special CAM software additionally extends the range of applications. Profound machining Know-how and technological knowledge in the different fields of action e.g. in kinematics, workpiece material, machining strategies etc., are essential.
This paper shows you, our work on the optimization of the gear manufacturing process chain on 5X multitasking machines.

Electro-discharge manufacturing, or EDM, is a common process used to create the punches required in the manufacturing of small size powder-metal (PM) bevel gears.
For small module straight, Coniflex, or spiral-bevel gears, 5Axis CNC manufacturing of EDM electrodes using End Mill and Ball Mill tools offers flexibility, reduced tool inventory, and especially the use of only one CNC machine as opposed to several dedicated gear-cutting machines.
This paper presents an approach to 5Axis CNC milling of straight-bevel, Coniflex and spiral-bevel gears with modules in the 1 to 1.5 mm range. The gears are made of copper and are used as electrodes in EDM to produce punches for PM manufacturing.
The basic mathematical approach to CNC gear manufacturing with End Mill or Ball Mill tools is presented, keeping in mind that EDM electrodes must be smaller than the final tooth in order to allow clearance in the EDM machine when creating the punch mold.
Examples illustrate the excellent results that are achieved and some difficulties linked to manufacturing gears of small tooth sizes.

In the frame of the activity of JSME RC-268 committee, new bevel gear i.e. Invo-Planar bevel gear is developed, the tooth flank of which wheel is plane or whose transverse tooth profile is straight line. The cutting/grinding time of this bevel wheel can be more than 10 times shorter than the working time for conventional bevel gear wheel, when it is cut with 5-axis machine, because it cuts or grind the tooth flank through one path of tool movement. The finished tooth flank is far smoother than the curved tooth flank manufactured by many paths of cutting blades of tool. The production rate of the mating pinion with 5-axis machine is same as that of conventional bevel pinion. Some experiences in the production, quality of the product gears and performance survey of this new bevel gear is introduced to promote the discussion.

Hobbing and form milling processes of gears with indexable inserts are investigated in the current work, by means of model-based process analysis. In the applied model, the approach of penetration calculation is extended for indexable inserts applications. Therefore, the tool profile is split to take into account the individual indexable inserts. With the extended model approach the chip geometry for each indexable insert and therefore local characteristic values of the machining process can be calculated. These values are locally calculated for each point at the cutting edge and for each single chip as well as for the complete process. To validate the model both, maximum chip thickness and chip volume, are compared to the real chip geometry. With a validated model, the model-based process analysis can be used to improve the design of hobbing and form milling processes with indexable inserts and to provide a better understanding of both processes.

The dry hobbing is a gear manufacturing method capable of reducing environmental pollutions and product costs. However, it causes high cutting temperature and shortening tool life. In order to solve these problems, we have proposed the new gear hobbing method - the vibration hobbing. The vibration hobbing gives axial micro vibration to the hob by external vibration generator during gear processing. Our study showed that the vibration hobbing method was effective for reducing the cutting heat under the dry environment.
The purpose of this study is to establish a model to understand the features of our vibration hob system, and decide the suitable cutting condition for the vibration hobbing. This paper explains the structure of our vibration hobbing machine. Next, we propose the model of vibration hob system, and show the frequency response curve calculated from our model is good agreement with our experimental result. Finally, we consider the suitable processing conditions experimentally.

We clarified the effect that the positional relationship of the workpiece and the tool have on gear accuracy, including the pitch error and the tooth run-out of the workpiece in the hobbing process, which is the first process realizing “hobbing ⇒ heat treatment ⇒ gear honing” in the manufacturing process for automotive gears.
In this report, we devised a hobbing simulation that can elucidate the relationship of the tool to the workpiece, and conducted verifications using hobbing experiments, and as a result we report that we were able to confirm the effectiveness of the hobbing simulation.

This paper presents the result of a systematic dry hobbing experiment to examine the influence of cutting speed on the tool life and machining performance for a TiN-coated HSS hob. The hobbing experiments were performed under different cutting speeds from 100 m/min to 300 m/min. Some important machining items related to the tool life, for example, the influence of instantaneous cutting temperature, the characteristics of hob wear, the chip deformation and the effect of chip crush behavior are discussed in detail. The importance of the cutting speed employed in a dry hobbing process is verified, i.e. an appropriate speed not only leads to the small deformation and better fluidity of the chips and thus reduces the occurrence of chip crushing action, but also effectively control the oxidation progress of coat material. Based on the experiment results, a suitable cutting speed range due to the tested hobbing conditions is confirmed.

The gear accuracy is deteriorated due to the heat treatment distortion. To remove this heat treatment distortion of the surface-hardened small gear is rehobbed with a carbide hob. However, the rehobbing makes a tool mark on the gear tooth surface. This tool mark may cause vibration/noise of the gear. Therefore, a tooth surface finishing method for small gears to remove this tool marks is required. However, a gear-shaped grinding tool for small gears is difficult to manufacture because the tooth of one is too small. This study proposes the gear-shaped tool which is manufactured using the alumina-fiber-reinforced plastic (ALFRP), and the removal experiments of tool marks of surface-hardened gear tooth are performed using the ALFRP gear-shaped tool and a new gear tooth surface finishing device with an oscillation/traversal system. It is shown that this proposed new finishing method can remove the tool marks on the gear tooth surface.

In this paper, the tooth contact pattern and transmission errors are analyzed using tooth contact analysis (TCA) in order to manufacture the worm gears with high precision. Before manufacturing worm gear set, profile errors of a worm hob cutter for tool are measured using a gear measuring machine and these measured results are fed back to TCA results in order to improve the accuracy of TCA. The setting of the hobbing machine for worm wheel manufacturing and the amounts of modification in profile and lead directions of worm grinding machine for worm are determined so that the expected meshing conditions can be obtained based on TCA results. The dual lead worm gears in ISO type I were designed and manufactured based on this method and the experimental tooth contact patterns and transmission errors were compared with analyzed ones. As a result, the validity of this method was confirmed.

In recent years, gear skiving, also known as power skiving, has been drawing increased attention as a productive and precise cutting method, especially for internal gears. However, the technical problems of gear skiving have prevented its installation in mass production lines. These problems include high frequency vibrations caused by cutting power fluctuations during the cutting process, which lead to form errors in cut gear profiles and leads, and chip packing under high-speed cutting conditions. Based on the results of newly developed kinematical analysis, these problems have been addressed by modifying cutting machine structures, providing advanced cutter designs, and adjusting cutting conditions. The present paper discusses these problems and their solutions to make gear skiving applicable to the mass production of ring gears for the automatic transmissions of middle-sized commercial vehicles. In addition, this paper discusses the prospects for gear skiving.

Gear skiving is a very old technique for cutting internal gears, and its high productivity causes many attentions to focus again on itself. However, for gear skiving processes, tool designers are required to have knowledges about mesh geometry of internal gear pairs with shaft angle. Then, the conjugate pinion exist only in the limited regions along the facewidth because of undercut, pointed tooth, and lack of tooth space. The limited regions would depend on parameters; e.g., a gear ratio, a shaft angle, and a helix angle. Knowing the regions, tool designers could make use of the information to decide starting points for examining cutter geometry. The present paper describes maps representing such existence regions of a conjugate pinion. The maps generally show horseshoe shapes on the pinion axis vs center distance diagrams. The maps could be useful for skiving cutter design.

In recent years, the automotive industry has been demanding high-efficiency and high-precision processing of internal gears used for planetary gear devices in terms of improvement of fuel efficiency and reduction of noise. To achieve these, manufacturers are developing a skiving cutting system. However, the conventional skiving cutting system using gear shaper cutter has not come into practical use because tool life is shortened and production costs are increased. Against such a background, Mitsubishi Heavy Industries Machine Tool Co., Ltd. (MAT) has established a new process technology, “Super Skiving System” with similar accuracy to the skiving cutting while exceeding it in efficiency and tool life. This paper presents the machining technology of internal gears comprising of 3 elements, namely the new super skiving cutter with long tool life, the specialized super skiving machine and the skiving cutting simulation software.

The internal gear grinding machine, ZI20A is the first of its kind that is applicable for mass production of internal gears. It is suitable for grinding planetary gears, heat-treated internal or external gears at high speeds with high accuracy. One of the features of this machine is its ability to grind stepped workpieces. In case of stepped workpieces, it is difficult to determine the axial stroke required to achieve proper grinding of the entire tooth surface without causing any interference of the stepped region with the machine parts or grinding wheel. During the grinding test of such workpieces, sometimes the tooth flank remains unground at the ends due to inadequate axial stroke. A new simulation tool has been developed to visualize and analyse the internal gear grinding process. Using this simulation tool, the axial stroke required for grinding can be estimated without performing actual grinding tests.

Estimating the tooth meshing conditions of a hypoid gear is difficult because of its complex shape and tooth contact conditions. Therefore, a non-contact method of analysis is proposed for determining tooth contact conditions. The proposed method uses high-speed and high-response photography to analyze the temperature distribution between the pinion and the gear. The high-speed photography is performed using thermography, and the temperature data is extracted from the resulting thermal images.
Additionally, a model is proposed to predict the tooth surface temperature distribution during tooth meshing. The proposed method is based on a thermal network model and uses a simple RC circuit to represent the thermal conductivity of an object. Using thermal images, the thermal properties of a given material are identified by comparing the temperature changes obtained with the calculated results. Additionally, the effects of various parameters are discussed. The comparison shows that infrared tooth surface imagery is effective in estimating hypoid gear tooth meshing conditions. Infrared images and thermal network models are successfully used to determine the heat conduction in a gear, which confirms that it is possible to predict temperature increase on tooth surfaces due to gear meshing. It is concluded that the proposed method is effective in estimating hypoid gear tooth meshing conditions using high-speed video thermography.

If no modification is made to the tooth flank of a face gear, a more time-consuming adjustment during spinning reel assembly will likely be required. Modification of the tooth flank with a transmission error (TE) controlled curve has proven to be robust against alignment errors. However, the TE controlled curve has proven weak against manufacturing errors on the face and the pinion gears, particularly involving the pressure angle error on the pinion gear. Conversely, the helix angle error on the pinion gear has been previously shown to have no effect on TE when a face gear has a TE controlled curve. This study focused on the relationship between the pressure and helix angles of a pinion gear with the objective of reducing TE and improving a spinning reel's rotational feel.

Gears are used in many machineries and it is important to make their accuracy higher and improve their performance. Gear vibration and noise is a severe problem for automobiles. It is influenced by micron-meter-order accuracy of tooth of gear and therefore inspection of gears is necessary using gear measuring instruments. Test of accuracy of gear measuring instruments is important for quality control. In most cases, a gear measuring instrument is calibrated by an artifact with higher accuracy than the calibrated instrument. However, conventional artifacts have a problem in accuracy because of its complicated form. In addition, various testing methods exist depending on measuring machine companies because there is no standard on testing method of gear measuring instrument. This paper introduces a new evaluation method of involute artifact, newly developed artifacts, a developed testing method of gear measuring instruments, and Japanese Industrial Standards concerning them.

The objective of this study is the development of a flexible Gear Measuring Machine (GMM) which can measure cylindrical gears including working flanks, tooth root and bottom profiles as well as tip edge profiles in various patterns by installing a 3D scanning probe. In this presentation, scanning measurement of a helical gear outline is proposed without detaching the stylus tip from the gear surface. The stylus offset due to the helix angle of a helical gear is analyzed. The strategy for scanning measurement in a cross section is proposed and actual measurement is conducted. Compensated stylus contact paths are analyzed and evaluated by comparing to the corresponding ideal paths. By using the pre-measured discrete points, the deviations of the stylus tip along axial direction are minimized and profile measurement in a single cross sectional plane is achieved.

In this study, a measurement method of surface texture of tooth flanks with CNC gear measuring instruments is validated. Especially, in order to inspect the effect of probe profiles of the measuring instruments on the evaluation of surface texture, this paper proposes a numerical calculation method simulating contacts between the probe of the CNC gear measuring instruments or the surface roughness instruments and tooth flanks of interest. The profile curves of the surface measured by the different probes are calculated with this method. In the simulation, scanned data of roughness standard test pieces are used as the height of tooth flanks, and ideal models of probe based on design drawings are used to calculate the probe motion. Finally, the statistical characteristic quantities of the simulated profile curves are evaluated to show the effect of the prove profile difference on the measurement results.

The purpose of this study is to understand the nature of one of the oldest gears used in traditional Japanese clock. Today's gear manufacturing technology in Japan came mostly from Europe and America, but we do not know exactly, when and how the gears were manufactured for the first time in Japan. It is interesting to search for this history. It is also exciting to study the tooth profile, precision and accuracy of the gears, and materials of the gears at that time. Fortunately we have a chance this time to investigate gears for Japanese watch drive that was made in 1688. In the old days, there was no study on conjugate tooth profile theory available, but mysteriously, tooth profile was nearly made in the form of cycloid. Tooth profile and pitch error were measured, and transmission error analysis was also performed. Moreover, the gear material investigation was very interesting. This research enabled us to discover how Japanese gear technology was born and developed.

The coupled lateral-torsional-axial dynamical model of the two-stage NGW spur planetary gear system is established using the shafting element method. The mode characteristics and the parameter sensitivity are studied, and the analysis indicates that the flexibility of ring-gear has a larger effect on natural frequency. Several distinct types of vibration mode are summarized, such as planet torsional mode, sun-gear shaft axial mode, ring-gear axial mode and so on. However, the translational mode which is one of the modes in the lumped mass coupled lateral-torsional dynamical model is not found in this study. The variation of radial bearing stiffness will also do effect on axial vibration mode, and the variation of bearing stiffness not only affects the vibration modes of adjacent stage of planetary gear train, but also affects the nonadjacent stage. The results demonstrate the coupling characteristics of the system under the free vibration condition.

Dynamic characteristics of gearings in giant wind turbines are demanded for reliability improvement since they need situating in harsh condition due to varying wind and grid safety. This work focuses on transient dynamic analyses of a planetary gear system (PGS) especially at start-up stage including gross motion and gravity effect. At first, a 3D discrete dynamic model of PGS is formulated. The time varying equivalent spring stiffness can be derived for meshing gear pairs but only the stiffness average is adopted in the work. Transient responses of a PGS are obtained under assigned initial and operation conditions. Then, the dynamics of contact pairs of gears and bearings are analyzed. The transient responses are solved under four types of initial and operation conditions. Dynamic forces of a PGS are verified by a published experimental result. Finally, dynamic characteristics under kinds of operation conditions simulating the speed and torque shifting process during start-up or stop of the PGS are resulted.

Recently, planetary gear trains have been widely used in hybrid vehicle power distribution systems and electric vehicle reduction systems. In this study, we considered a novel three-axis drive design for a planetary gear train that uses universal joints. The proposed gear train treats the planet gear axis (rotation component) and the carrier axis (revolution component) as a coaxial drive unit using universal joints. The ring gear serves as the drive shaft. The rotational speed of the planet gear based on the output rotational speed of the ring gear was lower than that of conventional 2K-H gear train systems. As such, the proposed planetary gear train may exhibit reduced mesh frequencies and vibration noise. In this study, a prototype of the planetary gear train was developed, and experimentation was performed to determine its application potential as a transmission mechanism.

Recently, planetary gear trains have been widely used in hybrid vehicle power distribution systems and electric vehicle reduction systems. In this study, we considered a novel three-axis drive design for a planetary gear train that uses universal joints. The proposed gear train treats the planet gear axis (rotation component) and the carrier axis (revolution component) as a coaxial drive unit using universal joints. The ring gear serves as the drive shaft. The rotational speed of the planet gear based on the output rotational speed of the ring gear was lower than that of conventional 2K-H gear train systems. As such, the proposed planetary gear train may exhibit reduced mesh frequencies and vibration noise. In this study, a prototype of the planetary gear train was developed, and experimentation was performed to determine its application potential as a transmission mechanism.

An enhanced time-varying load dependent hypoid gear mesh generation model that comprises of effective mesh point, mesh stiffness, line-of-action (LOA) and transmission error (TE) is proposed. The model accounts for the instantaneous torque variation within each shaft rotation cycle by employing a three-dimensional (3D) interpolation scheme to construct the mesh parameter surfaces. The proposed model yields variation of mesh parameters within one pinion shaft rotation cycle and may generate more accurate dynamic prediction of geared rotor system as compared to constant load mesh model especially under light load cases. A comparative study of external excitation orders reveals that high order excitations tend to have significant influence on dynamic responses under certain torque load conditions. The study introduced aims to provide an effective way of predicting hypoid gear mesh characteristics and dynamic responses in a more reasonable and accurate way when there exists complex external load conditions during practical application.

This paper is focused on the modelling and analysis of vibrations and dynamic loads in aeronautical multi-mesh gears comprising several spatial gear arrangements (idler gears, several pinions on one shaft. Optimum profile modifications are sought by applying a metaheuristic Genetic Algorithm to the local quasi-static transmission errors under load associated with each individual mesh. It is shown that the resulting linear symmetric profile modifications all lie in the vicinity of the so-called analytical Master Curves initially defined for a single pinion-gear pair. The theory is applied to a 6-mesh aeronautical transmission and it is found that the proposed profile modifications can effectively reduce dynamic overloads and improve the vibrational behaviour of complex multi-mesh gears with different power circulations. Finally, it is shown that for systems submitted to several load levels, short optimal reliefs seem preferable with regard to vibration levels.

Based on analytical developments, it is found that families of profile modifications can render transmission error nearly constant which can be represented by so-called dimensionless master curves. These analytical findings compare well with the quasi-static numerical optimal profile relief obtained by coupling a lumped parameter model and a genetic algorithm. Extensive dynamic simulations have been performed for spur and helical gears whose results prove that the analytical findings are sound and actually correspond to profile modifications leading to reduced dynamic mesh forces over broad ranges of speeds. The proposed theory appears therefore as sound and can readily be used to help define adapted reliefs in terms of transmission error and dynamic tooth loading with minimum effort.

The stationary dynamic response of a geared system with time-varying mesh stiffness subjected to stationary stochastic external excitation is examined in this paper. To this end, a spur gear pair model with periodical time-varying mesh stiffness is extended to include stochastic external force excitations. These random forces are introduced as second-order stationary and ergodic processes. In order to compute the stationary response, a very efficient method, called the iterative spectral method is used. This method is derived in the frequency domain and provides the explicit power spectral density of the response. The PSD response is expressed as a function of the bispectrum which is the bilinear Fourier transform of the bitemporal impulse response of the parametric system. As an application, we consider a single-degree-of-freedom spur gear running at constant speed. Effects of viscous damping and of the spectral content of the meshing stiffness, respect to the natural frequency, are analysed.

Failure of the gear drive provides a large adverse influence on the machine systems. Detection of early failure on the gear tooth is crucial to prevent the serious damage in the machine systems. In this study, we diagnosed the tooth surface of normal gears without a failure and spot damaged gears. Diagnosis was accomplished with the vibration acceleration on a bearing stand. A synchronous averaging processing for the measured vibration acceleration waveform in one rotation period of the gear was employed to exclude the noise of measured signal. Then, the synchronous averaged data was divided into each one pitch. Tooth surface damage was diagnosed with a nearest neighbor method for the pattern recognition. The nearest neighbor method identified the class through the distance of the feature vector between input factors and a prototype. We demonstrated that the presence of damage can be detected with the nearest neighbor method.

We proposed a new signal processing method to estimate angular position of gears without help of speed sensors. In the method, a neural oscillator, which was able to synchronize with meshing vibration measured by an accelerometer, was used, and the angular position of gears was estimated from the period of the synchronized oscillator. The design method of oscillator's parameters, such as time constants, coupling coefficients, etc., was shown to obtain desired amplitude and frequency. However, there was no way to determine the input gain of the oscillator. Generally, synchronization region on a frequency axis broadens with an increase in the input gains of oscillators, and length of time it takes to synchronize is saved with the increase. In other words, saving the length of convergence time by an increase in the input gain worsens the susceptibility to noise. Therefore, the input gain of neural oscillator should be determined with consideration for the design trade-off. The long-term objective of this study is to show the design method of the oscillator's input gain. As a very first step, this paper shows that the estimation error of angular position of gears is affected by the input gain change. Especially, we show the effect, that several different neural oscillators have, on the estimation errors with an increase in the input gains. The target neural oscillators have natural frequencies, which are set at the meshing frequency of a gear pair of interest or not. Acceleration responses were measured with a pickup set at the top of a housing of a driving-side gear shaft bearing during gear operation tests, and input to the neural oscillators. Then, synchronous generation and the estimation error of the proposed method had were investigated. As a result of this investigation, it was concluded that the estimation error in the case of the neural oscillators, whose natural frequencies were shifted from the meshing frequency, have the local minimal values with an increase in the input gains, useful information for determine the input gain of the neural oscillator was included.

This study proposes a rotary encoder less time synchronous average using a non-linear filter for vibration analysis of gears in operation. This non-linear filter has smaller phase lag than that of conventional linear filters and a property synchronized with the meshing vibration. Therefore, the proposed method is able to estimate accurate rotational phase of gears. The accurate estimation of rotational phase of gears enable us to average the vibration responses including meshing frequency without any speed sensors and eliminate noises incoherent with the revolution periods of the gears of interest. In this paper, we explicate the difference of frequency characteristic between the linear and non-linear filters, and show the availability of the new method by numerical simulations using a vibration model of meshing gear with noise. The numerical simulation result discloses the noise-reducing by the averaging method using the non-linear filter outperforming the conventional liner filter.

Gear power transmissions are responsible for upsetting vibroacoustic phenomena. The gear teeth compliance, the manufacturing errors and the tooth corrections lead to a periodic transmission error fluctuation and a parametric excitation associated to gear mesh stiffness fluctuation. Under operating conditions, these excitation sources generate dynamic mesh forces transmitted to the housing and responsible for the whining noise radiated from the gearbox.
This work is focused on the multiphysics coupling between the gear mesh internal excitation and the external excitation associated with the upstream engine and downstream receiver system. These excitations mix the high frequencies of internal meshing excitations and low frequencies of the external excitations of the rotating shafts. The coupling between excitations generates an enrichment of the vibratory frequency response.
The goal of this paper is to present the spectral iterative methodology used and the dynamic results induced by this coupling in the case of a root vacuum pump.

The drum shearer is one of the main equipment of the long-wall mining system that has been widely used in coal mining for decades. Influenced by large fluctuation and intensive impact of drum load, the drum driving system is a weak part of the drum shearer due to the large dynamic deformation on cutting unit housing and changes of gear meshing state. This study is concerned with hybrid finite element/lumped parameter dynamic modeling of the housing-transmission coupled system. The influence of housing topological optimization on the dynamic characteristics of gear is also analyzed through the hybrid dynamic model. In order to model the drum driving system, it is subdivided into two substructure: housing and transmission system, the housing is modeled by finite element method while the transmission system is modeled by lumped parameter method. Then the dynamic substructuring method (DSM) is used to develop a hybrid dynamic model, taking elastic coupling between the housing and transmission system into consideration. The housing topological optimization is conducted through the Optistruct solver in Hypermesh, aiming at increasing the natural frequency of housing. The effect of topological optimization on reducing the gears' equivalent mesh misalignment is validated through dynamic analysis under both random and step load.

Vibration and noise are the key concerns in doublehelical star gear transmission system. The vibration and noise can be reduced by planet phasing whose basis is a clearly classification of the vibration mode of doublehelical star gear transmission system.
This work uses an analytical model to investigate the natural frequencies and vibration modes. In this model, the double-helical gear are treat as two helical gears with opposite spiral angle connected by massless spring which has the bending, torsion and axial stiffness. Each of the helical gears and carrier have 4 degrees of freedom with coupled lateral-torsional-axial. The natural cyclic frequencies and vibration modes of the system are calculated. Vibration modes are classified into four categories and the multiplicities and values of the eigenvalue are theoretically analyzed. For each class of these modes, reduced-order eigenvalue problems are derived.

Planetary gear train (PGT) is one of the most important components of new hybrid and electric vehicles owing to its high torque-to-weight ratio and to its compact geometry. However, this system generates a large number of vibrations, which increase the noise, due to its complex geometry and to its various mesh-coupled motions. The aim of this study is to construct a novel torsional coupled vibration model based on the bond graph method and to understand the PGT motion and modal behavior. The novel simulation is based on the energy flow in the component including damping, not on complex coupled equation of motion. The result from the bond graph agrees well with the observation result. It is found that bond graph is appropriate in simulating the dynamic behavior of a PGT compared with the use of the traditional equation of motion.