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.

An integrated computerized approach for design and stress analysis of low-noise spiral bevel gear drives with adjusted bearing contact has been developed. The computational procedure is an iterative process requiring four separate steps that provide: (a) a parabolic function of transmission errors that is able to reduce the effect of errors of alignment, and (b) reduction of the shift of bearing contact caused by misalignment. Application of finite element analysis permits the contact and bending stresses to be determined and the formation of the bearing contact to be investigated. The design of finite element models and boundary conditions is automated and does not require intermediate CAD computer programs. A commercially available finite element analysis computer program with contact capability is used to conduct the stress analysis. The theory developed is illustrated with numerical examples.

An integrated computerized approach for design and stress analysis of low-noise Spiral bevel gear drives with adjusted bearing contact is proposed. The procedure of computations is an iterative process that requires four separate procedures and provide: (a) a parabolic function of transmission errors that is able to reduce the effect of errors of alignment on noise and vibration, and (b) reduction of the shift of bearing contact caused by misalignment. Application of finite element analysis enables us to determine the contact and bending stresses and investigate the formation of the bearing contact, The design of finite element models and boundary conditions is automated and does not require intermediate CAD computer programs for application of general purpose computer program for finite element analysis.

The authors propose an approach for the design of one-stage planetary gear train with reduced transmission errors, localized bearing contact and improved conditions of distribution of load between the planetary gears. The planetary gear train is considered as a multi-body mechanical system of rigid bodies. The proposed approach is based: (i) on modification of geometry of gear tooth surfaces, and (ii) minimization and equalization of the backlash between the contacting gear tooth surfaces. The modification of geometry is accomplished: (i) by double-crowning of planetary gears, and (ii) by application of screw involute surfaces of the same direction of screws for the sun and the ring gears. The proposed geometry enables: (i) predesign of parabolic function of transmission errors for reduction of noise and vibration, and (ii) a simple method of regulation and equalization of the backlash between the gear tooth.

A preliminary experimental investigation of the thermal behavior of high-speed helical gears will be presented. A full-scale torque regenerative test stand has been built to test a representative helical gear train as that used in tiltrotor aircraft. Power loss and temperature data from a wide range of operating conditions were measured. Loop power ranged up to 3730 kW (5000 hp). Drive system components representative of flight quality hardware were used in the test program. The results attained in this initial study indicated that windage losses due to the high rotational speeds that were tested were far more important than the losses due to the gear meshing losses.

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.

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.

A diagnostic tool for detecting damage to spiral bevel gears was developed. Two different monitoring technologies - oil debris analysis and vibration were integrated using data fusion into a health monitoring system for detecting surface fatigue pitting damage on gears. This integrated system showed improved detection and decision-making capabilities as compared to using individual monitoring technologies. This diagnostic tool was evaluated by collecting vibration and oil debris data from fatigue tests performed in the NASA Glenn Spiral Bevel Gear Fatigue Rigs. Data was collected during experiments performed in this test rig when pitting damage occurred. Results show that combining the vibration and oil debris measurement technologies improves the detection of pitting damage on spiral bevel gears.

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 involute 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 [18] 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.

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. (C) 2001 Elsevier Science B.V. All rights reserved.

Experimental durability tests were performed on carburized and ground AIS19310 steel face gears. The tests were in support of a Defense Advanced Research Projects Agency (DARPA) Technology Reinvestment Program (TRP) to enhance face-gear technology. The tests were conducted in the NASA Glenn spiral-bevel-gear/face-gear test facility. Tests were run at 2300 rpm face gear speed and at loads of 64, 76, 88, 100, and 112-percent of the design torque of 377 N-m (3340 in-lb). The carburized and ground face gears demonstrated the required durability when run for ten-million cycles at each of the applied loads. Proper installation was critical for the successful operation of the spur pinions and face gears. A large amount of backlash produced tooth contact patterns that approached the inner-diameter edge of the face-gear tooth. Low backlash produced tooth contact patterns that approached the outer-diameter edge of the face-gear tooth. Measured backlashes in the range of 0.178 to 0.254 mm (0.007 to 0.010 in) produced acceptable tooth contact patterns.

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.

An aerospace-quality spiral bevel gearset was analytically and experimentally rolled through mesh to investigate tooth bending stress. A nonlinear finite element model utilized multiple teeth from the pinion and gear to simulate three-dimensional multitooth contact. The results were compared to those obtained experimentally with strain gages. A total of five strain gages, mounted in the root/fillet region of three teeth, were used. Effects of changing speed and load were measured. Tests were conducted from static (slow roll) to 14,400 rpm at power levels up to 537 kW (720 hp).

Helical gears with localized bearing contact of tooth surfaces achieved by profile crowning of tooth surfaces are considered. Profile crowning is provided by application of two imaginary rack-cutters with mismatched surfaces. The goal is to determine the dimensions and orientation of the instantaneous contact ellipse that requires the determination of principle curvatures of pinion-gear tooth surfaces. A simplified solution to this problem is proposed based on the approach developed in [1, 2] for correlation of principal curvatures and directions of generating and generated tooth surfaces. The obtained equations are applied for profile crowning where the normal profiles of the rack-cutters are either a circular arc or a straight line.

The authors propose an approach for the design of low-noise, localized bearing contact gear drives.The approach applied to spiral bevel and hypoid gear drives is based on the proper mismatch of curvatures of generating surfaces. In case of cylindrical worm and spiroid worm gear drives, the approach is based on double-crowning of the worm with respect to the hob applied for worm-gear generation.Examples for illustration of the theory are provided.

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.

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.

Face-milled spiral bevel gears with uniform tooth height are considered. An approach is proposed for the design of low-noise and localized bearing contact of such gears. The approach is based on the mismatch of contacting surfaces and permits two types of bearing contact either directed longitudinally or across the surface to be obtained. Conditions to avoid undercutting were determined. A Tooth Contact Analysis (TCA) was developed. This analysis was used to determine the influence of misalignment on meshing and contact of the spiral bevel gears. A numerical example that illustrates the developed theory is provided.

A modelling method for analyzing the three-dimensional thermal behavior of spiral bevel gears has been developed. The model surfaces are generated through application of differential geometry to the manufacturing process for face-milled spiral bevel gears. Contact on the gear surface is found by combining tooth contact analysis with three-dimensional Hertzian theory. The tooth contact analysis provides the principle curvatures and orientations of the two surfaces. This information is then used directly in the Hertzian analysis to find the contact size and maximum pressure. Heat generation during meshing is determined as a function of the applied load, sliding velocity, and coefficient of friction. Each of these factors change as the point of contact changes during meshing. A nonlinear finite element program was used to conduct the heat transfer analysis. This program permitted the time- and position-varying boundary conditions, found in operation, to be applied to a one-tooth model. An example model and analytical results are presented.