Kenichi Hayasaka

Topology of modified surfaces of involute helical gears with line contact developed for improvement of bearing contact, reduction of transmission errors, and stress analysis

The main defects of misaligned helical gear drives with parallel axes are: edge contact, noise, and not favorable conditions of bearing contact. One of the greatest concern of manufacturing of helical gear drives (with parallel axes) is the edge contact of tooth surfaces that is caused by misalignment. At present, attempts to avoid edge contact are based on providing chamfers of the tooth surfaces of the gears that may be obtained by modification of the profile of the cutting hobs. The zones of tooth surfaces with chamfers and zones with conventional screw involute surfaces are not connected smoothly, in many cases the magnitude of required chamfers is not determined analytically, and the edge contact is not avoided. The finishing process of helical gears with chamfers is a complicated one. The existing design has to be complemented with TCA (tooth contact analysis). These are the reasons why a new topology of modified helical gear tooth surfaces with involute and crowned zones is proposed. An involute zone is provided in the central area of gear tooth surfaces that will allow line contact if misalignment does not occur. Zones at the top, bottom, front, and back sides of tooth surfaces are crowned and allows localization of the bearing contact when misalignments occur. Crowned zones with smooth connections to the involute zone are obtained as the result of profile and longitudinal crowning. The function of transmission errors is provided at each cycle of meshing as the sum of three branches. Two branches of a parabolic function at the extremes of the cycle of meshing are in tangency with the middle branch of zero transmission errors. The generation of gear tooth surfaces is accomplished by a grinding worm. This has required the solution of two problems,(i)determination of the worm thread surface that is conjugated to the theoretical pinion tooth surface, and (ii)generation by the grinding worm of a crowned pinion tooth surface. Simulation of meshing of misaligned gear drives is accomplished by application of TCA program developed by the authors. The formation of the bearing contact is analyzed considering more than one cycle of meshing. Existence of areas of severe contact stresses is avoided. The developed approach is illustrated with numerical examples.

Geometry and Investigation of Klingelnberg-Type Worm Gear Drive

The computerized design, generation, and tooth contact analysis of a Klingelnberg-type cylindrical worm gear drive is considered wherein localization of contact is obtained by application of an oversized hob and mismatch geometries of hob and worm of the drive. A computerized approach for the determination of contacting surfaces and the investigation of their meshing and contact by tooth contact analysis is presented. The developed theory results in an improvement of bearing contact and reduction of sensitivity to misalignment. The theory is illustrated with numerical examples and may be applied for other types of cylindrical worm gear drives.

Analytical Determination of Basic Machine-Tool Settings for Generation of Spiral Bevel Gears From Blank Data

An approach for analytical determination of basic machine-tool settings for generation of spiral bevel gears from blank data is proposed. Generation by face-milling is considered. The analytical procedure is based on the similitudes between the conditions of generation between the gear member and its head-cutter and the conditions of imaginary meshing between the gear member and its crown gear. The blank data considered are the number of teeth of the pinion and the gear, the module, the spiral and pressure angles, the face width, the shaft angle, the depth factor, the clearance factor, and the mean addendum factor. These starting data can be established following the directions of the Standard ANSI/AGMA 2005-D03. Once the gear machine-tool settings are determined, an existing approach of local synthesis is applied to determine the pinion machine-tool settings that provide the desired conditions of meshing and contact of the gear drive. The developed theory is illustrated with a numerical example.

Computerized Design and Tooth Contact Analysis of Spiral Bevel Gears Generated by the Duplex Helical Method

The duplex helical method, among the different generation methods of spiral bevel gears, has shorter times of manufacturing since both sides of the gear tooth are generated simultaneously. The duplex helical method is based on the application of a helical motion of the cradle respect to the gear blank during the infeed of the sliding base on which the work spindle is mounted. Computerized design and generation of spiral bevel gears by the duplex helical method is a complex problem since the machine-tool settings are specific for each hypoid generator and optimization of the contact pattern and the function of transmission errors is not straightforward. The proposed goals in this research paper are as follows: (i) conversion of the specific machine-tool settings of a given hypoid generator to the so-called neutral machine-tool settings that can be applied at any hypoid generator, (ii) computerized generation of the generated spiral bevel gears by the duplex helical method considering the neutral-machine tool settings, (iii) illustration of results of tooth contact analysis of a spiral bevel gear drive where the pinion has been generated by the duplex helical method for investigation of the contact pattern and the function of transmission errors, and (iv) adjustment of the contact pattern by considering parabolic profiles on the blades of the head-cutter. A numerical example is represented considering a spiral bevel gear drive generated at the Hypoid Generator 106 of Gleason.Copyright

On the Behaviour of Asymmetric Cylindrical Gears in Gear Transmissions

Asymmetric gears have been proposed more than twenty years ago as the ultimate solution to increase the load capacity of gear drives while reducing their weight and dimensions. However, there are apparently contradictive statements in the literature regarding whether the higher pressure angle should be applied to the driving or coast side of the gear tooth surfaces. In this work, modern technologies of design and analysis of enhanced gear drives will be applied in order to validate the advantages of application of asymmetric gears and to determine what the right configuration of the asymmetric gear drive should be in terms of application of the higher pressure angle to the driving or coast side of the gear teeth. The evolution of contact and bending stresses as well as contact pressure for the whole cycle of meshing is investigated and compared for symmetric and asymmetric gears. Two configurations of asymmetric gears will be considered, taking into account both, the higher and the lower pressure angle for the driving side. In this way, the advantages of application of asymmetric cylindrical gears as well as the right configuration to get them are established.

Application and Investigation of Modified Helical Gears With Several Types of Geometry

Involute helical gears with modified geometry for transformation of rotation between parallel axes are considered. Three types of topology of geometry are considered: (1) crowning of pinion tooth surface is provided only partially by application of a grinding disk; (2) double crowning of pinion tooth surface is obtained applying a grinding disk; (3) concave-convex pinion and gear tooth surfaces are provided (similar to Novikov-Wildhaber gears). Localization of bearing contact is provided for all three types of topology. Computerized TCA (Tooth Contact Analysis) is performed for all three types of topology to obtain: (i) path of contact on pinion and gear tooth surfaces; (ii) negative function of transmission errors for misaligned gear drives (that allows the contact ratio to be increased). Stress analysis is performed for the whole cycle of meshing. Finite element models of pinion and gear with several pairs of teeth are applied. A relative motion is imposed to the pinion model that allows friction between contact surfaces to be considered. Numerical examples have confirmed the advantages and disadvantages of the applied approaches for generation and design.Copyright

Design, Manufacture, and Evaluation of Prototypes of Low-Noise High-Endurance Spiral Bevel Gear Drives

An enhanced approach for the design of low-noise high-endurance spiral bevel gear drives is presented. The contents of the paper cover the design, manufacture, stress analysis, and evaluation of prototypes of spiral bevel gear drives. The proposed approach is based on the simultaneous application of both methods the local synthesis and tooth contact analysis (TCA) for design of gear drives, application of stress analysis for investigation of formation of the bearing contact and validation of optimal design, and application of blades of different pro les (straight, parabolic, or top-rem) to avoid areas of severe contact stresses. The main goals are the improvement of the bearing contact, the achievement of a favorable shape of the function of transmission errors, reduction of the magnitude of transmission errors as the precondition of reduction of noise and vibration, and avoidance of areas of severe contact stresses for the increase of the endurance of the gear drive. The proposed ideas have been tested by the manufacturing of prototypes of spiral bevel gear drives. An example of design and optimization of a spiral bevel gear drive is represented.Copyright

Modified Surface Topology of Involute Helical Gears Developed for Improvement of Bearing Contact and Reduction of Transmission Errors

A modified surface topology of involute helical gears is proposed. The proposed new topology provides an involute zone in the central area of gear tooth surface smoothly connected to crowned zones at the top, bottom, front, and back sides. The involute zone allows line contact in case of aligned gear drives while the crowned zones provide a localized bearing contact and low levels of transmission errors in case of misaligned gear drives. In many cases, non-standard cutting hobs are required to provide chamfers to gear tooth surfaces for avoiding of edge contact when misalignments are presented, but the chamfers are not connected smoothly, the magnitude of required chamfers is not determined analytically, and consequently, severe contact and linear functions of transmission errors may appear. The new topology is based on generation of gear tooth surfaces by an involute grinding worm, Modified roll is applied to the involved motions of generation in order to provide profile and longitudinal crowned zones with smooth connections to the involute zone. Tooth contact analysis and stress analysis by the finite element method has allowed the advantages of the proposed topology to be verified. Finite element models with three pairs of contacting teeth are considered. A function of transmission errors with a low level is obtained as a precondition of reduction of noise and vibration. An uniform transition of load is guaranteed between the adjacent pairs of teeth avoiding areas of severe contact stresses.© 2005 ASME

An Enhanced Finite Element Model for Determination of Load Capacity in Planetary Gear Trains

Planetary gear trains are being intensively applied in automobile drivelines during recent years due to its high load capacity, compact size, high gear ratio, and axial direction of power path. Determination of the load capacity in the design stage requires the calculation of contact pressures and bending stresses at the ring, sun, and planet gears. The knowledge of the load sharing between the planet gears and how it is affected by any assembly error or by the deflection of supporting shafts and carrier is needed for the determination of tolerances before manufacturing and assembly stages are accomplished. An enhanced finite element model is presented in this paper for the purpose of determination of the load capacity in planetary gear trains and investigation of the load sharing between the planet gears. A numerical example is presented.

Gear Whine Noise Spectra Caused by Transmission Errors

The modern theory of gearing is based on the design of gear drives according to the size and location of the contact pattern as well as the maximum level and type of the obtained function of transmission errors. These factors may reduce the life and the endurance of the gear drive for power transmission or even cause its failure. However, there is a factor that affects the quality perception of the performance of the gear drive and deserves to be taken into account in the design stage of the gear drive. It is called gear whine noise and it depends, among other factors, on the type and maximum level of the function of transmission errors. In this paper, an approach for the determination of the amplitude spectrum of different types and levels of functions of transmission errors is proposed in order to predict one of the sources of the radiated gear whine noise. The evaluation of the amplitude spectrum of the function of transmission errors will be made in terms of Fourier series, using the discrete Fourier transform. Therefore, the influence of the type and level of the function of transmission errors on the amplitude spectrum of their Fourier transforms will be investigated in order to find the suitable type of the function of transmission errors for reduction of the radiated gear whine noise and therefore for designing quiet gears.© 2011 ASME