Gear Generation Research Articles

The Grinding Head Design in Non-Circular Gear Grinding Teeth Based on the Planar Regions Interference Inspection

In the noncircular gear grinding methods using gear generator with form-grinding process, grinding headstock and workpiece may appear interference collision. The form-grinding radius selection problem based on the shaper has been discussed. Based on the designed grinding head, an effective form-grinding radius choose method and the head stock interference detection system has been established. This detection system is directly used in the grinder machining process; the solutions to the problems of both grinding head interference inspection and form-grinding radius selection in the grinding machine design process are introduced. In this paper, we briefly introduced the process for the design of inspection system and the relative algorithm of the method. Finally, The Program flow chart of the program design and implementation process was given and actual example of an outside triangle gear machining results is given, which validates the reliability of the system.

20804 歯車まわりの流体の流れに関する研究(一般講演 熱流体)

Nowadays, plastic gears are used in many scene of our life such as domestic electrical products, AV equipments, vehicle parts and any others. And plastic gears are planned low cost, compactable, of high quality. Therefore, it will be used in more various products. But it is known as reaches the damage by the heat that assumed abrasion a cause. Moreover, the detailed mechanism on damage is not solved. The gear's generation of heat, atmosphere temperature, etc. by engagement is considered to have affected the damage mechanism. Therefore, I researched the relationship between heat and gears by the CFD2000 simulation software use the rack model.

Tooth Surface Error Correction for Face-Hobbed Hypoid Gears

Face-hobbing is a continuous generating process employed in manufacturing spiral bevel and hypoid gears. Due to machining dynamics and tolerances of machine tools, the exact tooth surface geometry may not be obtained from the machining process using theoretical machine tool settings. Repeatable tooth surface geometric errors may be observed. The tooth surface errors will cause unfavorable displacement of tooth contact and increased transmission errors, resulting in noisy operation and premature failure due to edge contact and highly concentrated stresses. In order to eliminate the tooth surface errors and ensure precision products, a corrective machine setting technique is employed to modify the theoretical machine tool settings, compensating for the surface errors. This paper describes a method of correcting tooth surface errors for spiral bevel and hypoid gears generated by the face-hobbing process using computer numerically controlled hypoid gear generators. Polynomial representation of the universal motions of machine tool settings is considered. The corrective universal motion coefficients are determined through an optimization process with the target of minimization of the tooth surface errors. The sensitivity of the changes of the tooth surface geometry to the changes of universal motion coefficients is investigated. A numerical example of a face-hobbed hypoid pinion is presented.

Computerized Tooth Profile Generation and Undercut Analysis of Gears Manufactured With Pre-Shaving Hobs

This paper investigated the feature of pre-shaving hob contour and the generated gear tooth profile. By tooth generation method, a complete geometry of the gear tooth can be mathematically derived in terms of the design parameters of the pre-shaving hob cutter. The mathematical model consisted of equations describing the generated fillet and involute profiles. The degree of undercutting and the radii of curvatures of a fillet were investigated by considering the model. Finally, a computer program for generating the profile of the gear teeth was developed by simulating the cutting methods. The methods proposed in this study were expected to be a valuable guidance for pre-shaving hob designers and manufacturers.

Development of steel grades for heat treated power train components: a review

The development of new carburising steel grades by Daido Steel for heat treated transmission parts is reviewed. These developments are driven by the need for cost reduction, weight saving, fuel economy and higher mechanical performance in new car models under development in response to environmental and economic demands. The next generation of gears will be peened, then vacuum carburised to improve fatigue and impact strength in lighter components designed with smaller tooth cross-sections, and new steels giving improved performance have been developed. Case studies of new steels for pulleys (allowing shorter carburising times) and constant velocity joints are also described.

GDN-04 METHOD FOR DESIGNING SILENT RUNNING SPIRAL BEVEL GEARS USING LOADED TOOTH CONTACT ANALYSIS(DYNAMICS AND NOISE PROBLEMS OF GEARS AND GEAR BOXES)

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.

Relation between CNC Bevel Gear Generator Spatial Errors and Machine Setting Errors

In order to obtain the error terms causing great machine setting errors, the physics meaning of spiral bevel generator spatial errors are analyzed, and the geometrical model of machine spatial errors are built.Based on transformation matrices the geometric relations of machine settings and machine spatial errors are obtained.It's found that the straightness error of axis x and perpendicularity error between axis x and axis y can bring great error to machine tool position settings, and the straightness errors of axis z and axis B, position error of axis A can bring great setting error to workpiece position settings.It provides theoretical foundation for optimization of machine settings and error compensation of spiral bevel gears.

Simulation of generation and tooth contact analysis of helical gears with crowned flanks

The present paper describes a method for the determination of equations representing modified flanks using an assumed technology of gear generation. Modification of flanks is introduced by a suitable change of the trajectory of tool motion. The developed equations allow for the creation of precise geometric models of mating teeth by considering the shapes of modified flanks obtained after gear generation. After simulation of gear generation, proper finite element analysis of tooth contact of mating teeth is done, which is necessary for checking and optimization purposes.

Tooth profile generation and analysis of oval gears with circular-arc teeth

Abstract An oval gear drive, which is used in an oil pump with larger pumping volume, is generated by using a rack cutter with circular-arc teeth. The generated oval gears have convex–concave tooth profile contact. The mathematical models of oval gears with circular-arc teeth are derived based on the theory of gearing and gear generation mechanism. Owing to its complex geometry, the pitch curves and tooth profiles of oval gears may exhibit convex–concave centrodes and tooth undercutting, respectively. A rack cutter with circular-arc teeth cannot be used to generate oval gears with convex–concave centrodes. Therefore, curvature analysis is utilized to design oval centrodes with convex curves. The equation of singular point is utilized to analyze tooth undercutting. In addition, a computer simulation program is developed to generate the tooth profiles of oval gears with circular-arc teeth having convex centrodes and without tooth undercutting. Various numerical examples illustrate the computerized design process.

Higher-Order Tooth Flank Form Error Correction for Face-Milled Spiral Bevel and Hypoid Gears

The increasing demand for low noise and high strength leads to higher quality requirements in manufacturing spiral bevel and hypoid gears. Due to heat treatment distortions, machine tolerances, variation of cutting forces, and other unpredictable factors, the real tooth flank form geometry may deviate from the theoretical or master target geometry. This will cause unfavorable displacement of tooth contact and increased transmission errors, resulting in noisy operation and premature failure due to edge contact and highly concentrated stresses. In the hypoid gear development process, a corrective machine setting technique is usually employed to modify the machine settings, compensating for the tooth flank form errors. Existing published works described the corrective machine setting technique based on the use of mechanical hypoid gear generators, and the second-order approximation of error surfaces. Today, computer numerically controlled (CNC) hypoid gear generators have been widely employed by the gear industry. The universal motion concept has been implemented on most CNC hypoid generators, providing additional freedoms for the corrections of tooth flank form errors. Higher-order components of the error surfaces may be corrected by using the higher-order universal motions. This paper describes a new method of tooth flank form error correction utilizing the universal motions for spiral bevel and hypoid gears produced by the face-milling process. The sensitivity of the changes of tooth flank form geometry to the changes of universal motion coefficients is investigated. The corrective universal motion coefficients are determined through an optimization process with the target of minimization of the tooth flank form errors. A numerical example of a face-mill completing process is presented. The developed new approach has been implemented with computer software. The new approach can also be applied to the face-hobbing process.

A twist exponential approach to gear generation with general spatial motions

This paper presents a novel formulation of gear generation with general spatial motions obtained by parameterizing the computer numerically controlled (CNC) machine employed for cutting via the product-of-exponentials (POE) formula. By exploiting its interpretation as a serial kinematic chain, a systematic methodology is presented for efficiently computing the forward kinematics of the generating tool relative to the gear blank, which is essential, e.g., in the derivation of the envelope (tooth) surface. A key feature of the proposed method is that elementary motions allowed by the machine joints are parameterized directly via twist exponentials, with the twofold advantage of: (1) avoiding the introduction of a long chain of reference frames; (2) obtaining the rigid-body velocity (twist) of the enveloping motion directly from the parametrization. A layout typical of the face-milling process for hypoid gears is chosen as a paradigm in the unfolding of the theory, although the approach can be adapted to any process and arrangement. As examples of application, explicit expressions pertinent to gear generation between two fixed axes, and for a set-up typical of a 9-axis Gleason CNC universal motion concept (UMC) machine are presented.

A reconfigurated rack-tool for the generation of gears

The cutting processes with tools that generate “through-winding straight-involute teeth-gears”, tools associated with couples of centrodes-in-rolling (such as the rack-tool), are characterized by a fairly complicated cutting scheme, due to the specific shape of the tools and, at the same time, due to the rolling process of the axodes associated with the tool and the blank. The present solutions are not accorded well enough to the process and lead to significant variations in the detached chip area value regarding the machined wheel teeth number. It is accepted that the main cutting force size depends on the size of the area of the cutting layer (the geometrical area of the once detached chip by the assembly of operative edges of this kind of tools). The geometrical modeling of the generation process proves this and it could be considered a criterion for the reconfiguration of the cutting tool. In this work, there is defined a criterion so as to describe the cutting scheme, and based on this criterion we can compare the variation laws for the chip area size when generating the modeling of the cylindrical straight teethed gears. We propose a modeling of the cutting schemes in order to get new constructive forms of the cutting tools that will lead to cutting schemes adaptable to the number of teeth of the processed gear with the purpose of diminishing the teething cutting force. Also, there is presented a constructive solution for a rack-tool with reconfigurable structure with the purpose of according the teething process with the processed gear number of teeth.

Kinematics transformation for tilt generated method and simulation

The kinematics transform model between two machines about tilt generated method is built.Motions of axes when using tilt method are approximately represented with a group of 4th-order Maclaurin formula.To feed the need of real-time for generated simulation,the simplified representations of n-th transform matrix derivatives are achieved through the clear derivat ion of equations. The assessment of time consumption between the simplified equations and the unhandled ones is made with an example.Based on the reduced equations,a virtual software which can simulating the gear generation process is designed.A set of practical gear parameters is presented as an example.A virtual gear,which is made by the simulation software with the given parameters,is compared to the real gear.Errors of the approximate formula are presented with the several figures.Based on the correct building of virtual software,precise gear solid model can be got for the tooth contact analysis (TCA),virtual machining experiment,and other deep researches.The reduced matrix derivative equations and its methodology could be spread to the whole spatial kinematics.

A comparative analysis of the geometrical surface texture of a real and virtual model of a tooth flank of a cylindrical gear

The paper presents the methodology of modelling tooth flanks of cylindrical gears in the CAD environment. The modelling consists in a computer simulation of gear generation. A model of tooth flanks is an envelope surface of a family of envelopes that originates from the rolling motion of a solid tool model in relation to a solid model of the cylindrical gear. The surface stereometry and topography of the tooth flanks, hobbed and chiselled by Fellows method, are compared to their numerical models. Metrological measurements of the real gears were carried out using a coordinated measuring machine and a two-dimensional profilometer. A computer simulation of the gear generation was performed in the Mechanical Desktop environment.

Generation of planar and helical elliptical gears by application of rack-cutter, hob, and shaper

The developed approaches are directed at obtaining of: (a) the generated surfaces of elliptical gears by enveloping process, and (b) computerization of the process of generation by application of existing equipment and tools. A matrix approach is proposed and developed for generation of equation of meshing. The developed theory is illustrated with examples of generation of planar and helical elliptical gears.

Modelling the tooth flanks of hobbed gears in the CAD environment

The paper presents the computer simulation methodology of modelling tooth flanks of cylindrical gears. The modelling consists of a computer simulation of a gear generation. A model of tooth flanks is an envelope curve of a family of envelopes that originate from the rolling motion of a solid tool model in relation to a solid model of the cylindrical gear. The surface stereometry and topography of the tooth flanks, hobbed, are compared to their numerical models. A computer simulation of the gear generation was performed in a mechanical desktop environment.

A FEM Study of the Bending Strength of Circular Fillet Gear Teeth Compared to Trochoidal Fillets Produced with Enlarged Cutter Tip Radius#

Circular fillet (CF) gears have been proven to possess a higher bending strength than their standard trochoidal fillet (TF) counterparts. However, stronger nonstandard variants of the TF are already possible to produce by increasing the tip radius of the cutters used for gear generation (racks, hobs, pinion cutters), affording competitive results. In this paper a comparison of the bending strength is made between the CF and the nonstandard large tip radius TF designs spanning the entire usable tooth number range using FEA. The results suggest a systematic advantage of the CF over the stronger variants of the TF for numbers less than 17 teeth, which is the undercut limit for the 20° involute gear system.

Flank Modification Methodology for Face-Hobbing Hypoid Gears Based on Ease-Off Topography

The fundamental design of spiral bevel and hypoid gears is usually based on a local synthesis and a tooth contact analysis of the gear drive. Recently, however, several flank modification methodologies have been developed to reduce running noise and avoid edge contact in gear making, including modulation of tooth surfaces under predesigned transmission errors. This paper proposes such a flank modification methodology for face-hobbing spiral bevel and hypoid gears based on the ease-off topography of the gear drive. First, the established mathematical model of a universal face-hobbing hypoid gear generator is applied to investigate the ease-off deviations of the design parameters—including cutter parameters, machine settings, and the polynomial coefficients of the auxiliary flank modification motion. Subsequently, linear regression is used to modify the tooth flanks of a gear pair to approximate the optimum ease-off topography suggested by experience. The proposed method is then illustrated using a numerical example of a face-hobbing hypoid gear pair from Oerlikon’s Spiroflex cutting system. This proposed flank modification methodology can be used as a basis for developing a general technique of flank modification for similar types of gears.

Synthesis of Spiral Bevel Gear Transmissions With a Small Shaft Angle

An algorithm for synthesis of spiral bevel gear transmissions with a small shaft angle is presented. The algorithm of synthesis provides machine-tool settings with account of design limits for majority of gear generating machines. The proposed algorithm makes it possible to decrease the dimensions of machines that are used for gear and pinion tooth generation. The computer program of synthesis is developed that is based on described algorithm. Recommendations on selection of proper synthesis parameters are presented. An example of synthesis and analysis of a transmission is considered.

Can non-standard involute gears of different modules mesh?

Under the current standardized involute gear systems, meshing of gears of different modules is a practical impossibility. However, by performing a fresh reinterpretation of the well-established fundamental meshing principles, a more insightful form for the compatibility equations that govern involute gear tooth generation and meshing can be obtained. This article reports some first non-standard designs based on this analysis that allows gears of different modules to mesh. By the same token, standard gears can be manufactured with non-standard hobs and vice versa. Initial investigation suggests that practical benefits such as increasing the root bending strength without affecting the pitting resistance and the sliding velocity can be achieved that may justify such deviation from standard designs.