Generation Of Spiral Bevel Gears Research Articles

A Novel Asymmetric Face Gear Cut by Duplex Face-Milling With Multiple Auxiliary Flank Modification Motions

Abstract Face gear sets, comprising a face gear and a cylindrical pinion, are used in the crossed axes transmission with the advantages of easy assembly and a large gear ratio. Based on the geometry of a pinion tooth flank, the tooth surface of the face gear is derived and manufactured by gear hobbing or shaping processes. However, the hobbing and shaping processes to make a face gear require special machine attachments to achieve the spatial relationship between the gear cutter and the workpiece of the face gear. These special machine attachments are not always available in a typical gear-machining factory, so this study develops a manufacturing process that uses a standard spiral bevel gear generator and standard face-milling cutting tools to produce a face gear. The productivity and the gear quality of a face gear that is made using the proposed cutting method are similar to that for a spiral bevel gear that is produced by indexed duplex cutting. The machine settings for the spiral bevel gear generator are derived using the tooth surface of a face gear, which is conjugated to the tooth surface of specific pinion. This study uses a duplex face-milling method with multiple auxiliary flank modification motions to minimize the flank normal deviation between the conjugate and the generated face gear. A numerical example and a cutting experiment are performed to verify the feasibility of the proposed methodology.

Analytical determination of basic machine-tool settings for generation of spiral bevel gears and compensation of errors of alignment in the cyclo-palloid system

A model for computerized generation of spiral bevel gears in the cyclo-palloid system is proposed. Kinematic conditions of cutting are investigated for tooth thickness and backlash control. Basic machine-tool settings are analytically determined from basic transmission data with the aim of getting favorable conditions of meshing and contact when the gear drive is transmitting a nominal or design load and shaft deflections occur. Errors of alignment of the gear drive due to shaft deflections are considered as input data in the analytical procedure. The proposed procedure is tested through tooth contact and backlash analyses of the gear drive. Several numerical examples are presented.

Study on the generation of spiral bevel gears with spherical involute tooth profile by the tracing line

In this article, a new gear generating method for the spiral bevel gear with spherical involutes tooth curves was proposed. It was analysed that the tooth flank with cone-spiral involute surface could be formed by the space trajectory of a straight line. The straight line was named as a tracing line. In the method, three motions were demanded; those were the rotary motion of the workpiece, the rectilinear motion of the end of the tracing line along the dedendum, and the rotary motion of the tracing line in the plane. The motion equations were derived. The plate milling cutter with face cutting edges could be used to machine the spiral bevel gears and the chord line of the face circle worked as the tracing line. By the method, the spiral bevel gears without principle errors whose tooth flanks are exact spherical involute curves that could be achieved.

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.

Alternative formulation of the theory of gearing

In this paper the theory of gearing is presented by means of a new approach that does not need reference systems. All equations are written in terms of vectors and therefore are valid regardless of the reference system actually employed. The overall formulation becomes more compact and clearer. As an example, the proposed approach is applied to the generation of spiral bevel gears. To actually perform all calculations, only one reference system is required, thus avoiding the chain of reference systems typical of the traditional approach.

Mathematical model for generation of spiral bevel gears

The mathematical modelling of the tooth surface geometry of spiral bevel gears has been done applying the principles of differential geometry and the theory of conjugate surfaces. A comparison has been made with involute spiraloid surface, which is the corresponding theoretical surface. The surface coordinates that can be obtained using CMM inspection of generated surface are computed, to compare with actual surface. This approach can be used in the areas of CAD-CAM, Finite Element Analysis, Tooth Contact Analysis, CNC machining and inspection.

Kinematical Optimization of Spiral Bevel Gears

Kinematical optimization and sensitivity analysis of circular-cut spiral bevel gears are investigated in this paper. Based on the Gleason spiral bevel gear generator and EPG test machine, a mathematical model is proposed to simulate the tooth contact conditions of the spiral bevel gear set. All the machine settings and assembly data are simulated by simplified parameters. The tooth contact patterns and kinematic errors are obtained by the proposed mathematical model and the tooth contact analysis techniques. Loaded tooth contact patterns are obtained by the differential geometry and the Hertz contact formulas. Tooth surface sensitivity due to the variation of machine settings is studied. The corrective machine settings can be calculated by the sensitive matrix and the linear regression method. An optimization algorithm is also developed to minimize the kinematic errors and the discontinuity of tooth meshing. According to the proposed studies, an improved procedure for development of spiral bevel gears is suggested. The results of this paper can be applied to determine the sensitivity and precision requirements in manufacturing, and improve the running quality of the spiral bevel gears. Two examples are presented to demonstrate the applications of the optimization model.

Method for Generation of Spiral Bevel Gears With Conjugate Gear Tooth Surfaces

The authors proposed a method for generation of spiral bevel gears that provides conjugate gear tooth surfaces. This method is based on a new principle for the performance of parallel motion of a straight line that slides along two mating ellispses with related dimensions and parameters of orientation. The parallel motion of the straight line, that is the contact normal, is performed parallel to the line which passes through the foci of symmetry of the related ellipses. The manufacturing of gears can be performed with the existing Gleason’s equipment.

Study on Cutting Method of Novikov-Type Spiral Bevel Gears

Many papers on Novikov gear cutting have been published, but they have dealt with onle cylindrical gears. This paper describes the cutting method of Novikov-type spiral bevel gears. The results obtained are as follows : (1) By using a rotary cutter with elliptical cutting edges, they can be cut on Gleason's spiral bevel gear generator of ordinary type.(2) Composite test on them indicates smooth running, so they can be expected to be put into practical service.

Study on the Generating Method of Hypoid Gears : with the Spiral Bevel Gear Generator in Kyushu Univ. by the Gleason's No. 0 Cutter only

Hypoid gears have asymmetric tooth profile. In order to cut a hypoid pair, cutters with asymmetric blades must be used, otherwise the cutter shaft must be tilted as much as the amount of asymmetricity. For the small quantity production it is desirable and convenient to use the Gleason's No. 0 cutter. In the previous report the author theoretically showed that the hypoid gear could be cut by the No. 0 cutter without tilting its shaft. In this paper he carries out the experimental check of the theory using the spiral bevel gear generator installed in Kyushu University. The experimental results show that accurate pairs with good tooth bearing can be cut and ground without any trial work.

Spread Blade Cutting Method for Parallel Depth Spiral Bevel Gears

The spread blade method is the productive cutting method on Gleason's spiral bevel gear generator, but the conventional method is very difficult. If the Parallel depth bevel gears are cut on the same generator, many troubles are eliminated fairly well and we can get good spiral bevels productively.

Cutting the Parallel Depth Bevel Gears on Gleason's Spiral Bevel Gear Generator : 2nd Report, Tooth Bearing Adjustment

It was stated in full on my 1st Report that if the parallel depth bevel gears were cut on Gleason's spiral bevel gear generator, the machine setting and cutter used were very simple and we could get easily the good spiral bevels with high accuracy. Then, the bad tooth bearings appear in very few cases caused by the unexpected factors. Those bad tooth bearings, however, may be easily corrected, for the numerical relations between the setting errors and the tooth bearing position are researched and stated in this paper. These relations can be applied to the tooth bearing control of assembling too. Then the tooth bearing adjustment of parallel depth bevel gears can be performed accurately and rapidly, outdoing the conventional trial method.

Cutting the Parallel Depth Bevel Gears on Gleason's Spiral Bevel Gear Generator : 1st Report, Cutting Theory and Result of Experiments

Γo cut the spiral bevel gear the Gleason's Spiral Bevel Gear Generator is generally used. By the conventional cutting method, however, the machine setting and the cutter used are very complex in spite of the approximate cutting. So it is very difficult to get the accurate spiral bevels. If the Parallel Depth Bevel Gears are cut on the same Generator, many troubles above mentioned are quite swept away, and the cutting mechanism becomes theoretically correct too. So the cutting is performed very securely and we can get easily the good spiral bevels with high accuracy. In this paper the cutting theory of this method and the results of experiments are stated in full.