Robert F. Handschuh

Modified involute helical gears: computerized design, simulation of meshing and stress analysis

The contents of the paper cover: (i) computerized design, (ii) methods for generation, (iii) simulation of meshing, and (iv) enhanced stress analysis of modified involute helical gears. The approaches proposed for modification of conventional involute helical gears are based on conjugation of double-crowned pinion with a conventional helical involute gear. Double-crowning of the pinion means deviation of cross-profile from an involute one and deviation in longitudinal direction from a helicoid surface. The pinion-gear tooth surfaces are in point contact, the bearing contact is localized and oriented longitudinally, edge contact is avoided, the influence of errors of alignment on the shift of bearing contact and vibration and noise are reduced substantially. The developed theory is illustrated with numerical examples that confirm the advantages of the gear drives of the modified geometry in comparison with conventional helical involute gears.

Computerized design, simulation of meshing, and contact and stress analysis of face-milled formate generated spiral bevel gears

A new approach for design, tooth contact analysis (TCA) and stress analysis of formate generated spiral bevel gears is proposed. The advantage of formate generation is the higher productivity. The purposes of the proposed approach are to overcome difficulties of surface conjugation caused by formate generation, develop a low noise and stabilized bearing contact, and perform stress analysis. The approach proposed is based on application of four procedures that enable in sequence to provide a predesigned parabolic function of transmission errors with limited magnitude of maximal transmission errors, a bearing contact with reduced shift of contact caused by misalignment, and perform stress analysis based on application of Finite Element Method. The advantage of the approach developed for finite element analysis (FEA) is the automatic generation of finite element models with multi-pairs of teeth. The stress analysis is accomplished by direct application of ABAQUS. Intermediate auxiliary CAD computer programs for development of solid models are not required. The theory developed is illustrated with an example of design and computation.

Face Gear Drive with Spur Involute Pinion: Geometry, Generation by a Worm, Stress Analysis

A face-gear drive with a spur involute pinion is considered. The generation of the face gear is based on application of a grinding or cutting worm whereas the conventional method of generation is based on application of an involute shaper. The authors have developed an analytical approach for determination of: (i) the worm thread surface, (ii) avoidance of singularities of the worm thread surface, (iii) dressing of the worm, and (iv) determination of stresses of the face-gear drive. A computer program is developed for simulation of meshing and contact of the pinion and face gear. Correction of machine-tool settings is proposed for reduction of the shift of the bearing contact caused by misalignment. An automatic development of the model of five contacting teeth has been proposed for stress analysis. Numerical examples for illustration of the developed theory are provided.

Computerized generation and simulation of meshing and contact of spiral bevel gears with improved geometry

The geometry, generation and simulation of meshing and contact of low-noise spiral bevel gears with a localized bearing contact have been developed. The influence of misalignment on the transmission errors and the shift of the bearing contact was investigated. An approach is proposed for detection and avoidance of an edge contact caused by interference of the working part of the surface of one of the gears with the fillet surface of the mating member. The theory that is developed is illustrated with numerical examples and experimental tests.

Application of Finite Element Analysis for Determination of Load Share, Real Contact Ratio, Precision of Motion, and Stress Analysis

A loaded gear drive with point contact between tooth surfaces is considered. The principal curvatures and directions at a current point of tangency, the contact paths on tooth surfaces, and the transmission errors caused by misalignment we consider as known. In this paper the following topics are covered: (1) Determination of the contact force and its distribution over the contact ellipse; (2) Determination of the tooth deflection, the load share, and the real contact ratio; and (3) Stress analysis by application of the finite element method. The discussed approach is illustrated with a numerical example.

Consideration of Moving Tooth Load in Gear Crack Propagation Predictions

Abstract : Robust gear designs consider not only crack initiation, but crack propagation trajectories for a fail-safe design. In actual gear operation, the magnitude as well as the position of the force changes as the gear rotates through the mesh. A study to determine the effect of moving gear tooth load on crack propagation predictions was performed. Two dimensional analysis of an involuted spur gear and three-dimensional analysis of a spiral-bevel pinion gear using the finite element method and boundary element method were studied and compared to experiments. A modified theory for predicting gear crack propagation paths based on the criteria of Erdogan and Sih was investigated. Crack simulation based on calculated stress intensity factors and mixed mode crack angle prediction techniques using a simple static analysis in which the tooth load was located at the highest point of single tooth contact was validated. For three-dimensional analysis, however, the analysis was valid only as long as the crack did not approach the contact region on the tooth.

Computerized Design of Low-noise Face-milled Spiral Bevel Gears

Abstract An advanced design methodology is proposed for the face-milled spiral level gears with modified tooth surface geometry that provides a reduced level of noise and has a stabilized bearing contact. The approach is based on the local synthesis of the gear drive that provides the “best” machine-tool settings. The theoretical aspects of the local synthesis approach are based on the application of a predesigned parabolic function for absorption of undesirable transmission errors caused by misalignment and the direct relations between principal curvatures and directions for mating surfaces. The meshing and contact of the gear drive is synthesized and analyzed by a computer program. The generation of gears with the proposed geometry design can be accomplished with existing equipment. A numerical example that ilustrates the proposed theory is presented.

Computerized generation and simulation of meshing of modified spur and helical gears manufactured by shaving

Abstract Modification of geometry of spur and helical gears with parallel axes and helical gears with crossed axes is proposed. The finishing process of gear generation is shaving. The purposes of modification of gear geometry are: (i) localization and stabilization of bearing contact, and (ii) reduction of noise and vibration. The goals mentioned above are achieved as follows: 1. The pinion shaver tooth surface, in comparison with a conventional screw involute surface, is profile crowned. 2. Plunging during the process of pinion shaving is provided by variation of shortest distance E between the shaver and pinion axes. Variation of E is executed by application of a parabolic function. 3. The pinion tooth surface becomes double-crowned, in profile and longitudinal directions, due to profile crowning of pinion shaver and variation of plunging. The gear tooth surface is generated as a conventional involute gear. Tooth contact analysis (TCA) computer program for simulation of meshing and contact of shaved pinion-gear tooth surfaces is developed. The developed theory is illustrated with TCA results obtained for spur and helical gears.

Computerized Design and Generation of Low-Noise Helical Gears with Modified Surface Topology

An approach for the design and generation of low-noise helical gears with localized bearing contact is proposed. The approach is applied to double circular arc helical gears and modified involute helical gears. The reduction of noise and vibration is achieved by application of a predesigned parabolic function of transmission errors that is able to absorb a discontinuous linear function of transmission errors caused by misalignment. The localization of the bearing contact is achieved by the mismatch of pinion-gear tooth surfaces. Computerized simulation of meshing and contact of the designed gears demonstrated that the proposed approach will produce a pair of gears that has a parabolic transmission error function even when misalignment is present. Numerical examples for illustration of the developed approach are given.

Integrated computer program for simulation of meshing and contact of gear drives

The authors propose an integrated Tooth Contact Analysis (TCA) computer program for simulation of meshing and contact of gear drives that enables to determine transmission errors and shift of bearing contact for misaligned gear drives. The developed computer program combines numerical solutions for the problems above and their graphical interpretation. The program is applicable for various gear drives but needs derivation of tooth surface equations specified for the considered gear drive. The computer program represents a set of integrated operations such as the development of required algorithms, storing in database, copying, deleting, printing, design correction from the database, etc. The proposed computer program is based on application of the Java programming language. Examples of application for a spiral bevel gear drive and a worm gear drive are provided.