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

1987 ◽  
Vol 109 (2) ◽  
pp. 163-170 ◽  
Author(s):  
F. L. Litvin ◽  
Wei-Jiung Tsung ◽  
J. J. Coy ◽  
C. Heine

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.

Author(s):  
V. Simon

The design and advanced manufacture of face-hobbed spiral bevel gears on computer numerical control (CNC) hypoid generating machines is presented. The concept of face-hobbed bevel gear generation by an imaginary generating crown gear is established. In order to reduce the sensitivity of the gear pair to errors in tooth-surfaces and to the mutual position of the mating members, modifications are introduced into the teeth of both members. The lengthwise crowning of teeth is achieved by applying a slightly bigger lengthwise tooth flank curvature of the crown gear generating the concave side of pinion/gear tooth-surfaces, and/or by using tilt angle of the head-cutter in the manufacture of pinion/gear teeth. The tooth profile modification is introduced by the circular profile of the cutting edge of head-cutter blades. An algorithm is developed for the execution of motions on the CNC hypoid generating machine using the relations on the cradle-type machine. The algorithm is based on the condition that since the tool is a rotary surface and the pinion/gear blank is also related to a rotary surface, it is necessary to ensure the same relative position of the head cutter and the pinion on both machines.


1992 ◽  
Vol 114 (2) ◽  
pp. 317-325 ◽  
Author(s):  
Zhang-Hua Fong ◽  
Chung-Biau Tsay

Undercutting is a serious problem in designing spiral bevel gears with small numbers of teeth. Conditions of undercutting for spiral bevel gears vary with the manufacturing methods. Based on the theory of gearing [1], the tooth geometry of the Gleason type circular-cut spiral bevel gear is mathematically modeled. The sufficient and necessary conditions for the existence and regularity of the generated gear tooth surfaces are investigated. The conditions of undercutting for a circular-cut spiral bevel gear are defined by the sufficient conditions of the regular gear tooth surface. The derived undercutting equations can be applicable for checking the undercutting conditions of spiral bevel gears manufactured by the Gleason Duplex Method, Helical Duplex Method, Fixed Setting Method, and Modified Roll Method. An example is included to illustrate the application of the proposed undercut checking equations.


Author(s):  
Joe¨l Teixeira Alves ◽  
Miche`le Guingand ◽  
Jean-Pierre de Vaujany

The design of spiral bevel gears still remains complex since tooth geometry and the resulting kinematics performance stem directly from the manufacturing process. Spiral bevel gear manufacture owes most to the works of Gleason and Klingelnberg. However, recent advances in milling machine technology and CAM (Computer Aided Manufacturing) make it possible to manufacture good quality spiral bevel gears on a standard 5-axis milling machine. This paper describes the CAD definition and manufacturing of spiral bevel gear tooth surfaces. Process performance is assessed by comparing the resulting surfaces after machining with the pre-defined CAD surfaces. Using this manufacturing process allows to propose new type of geometry. This one is more theoretical and, in some respects, easier to design than the standard spiral bevel gear as it enables simpler mesh optimization. The latter can be achieved by using the model of meshing under load recalled in this paper.


Author(s):  
Vilmos V. Simon

In this study an attempt is made to predict displacements and stresses in face-hobbed spiral bevel gears by using the finite element method. A displacement type finite element method is applied with curved, 20-node isoparametric elements. A method is developed for the automatic finite element discretization of the pinion and the gear. The full theory of the generation of tooth surfaces of face-hobbed spiral bevel gears is applied to determine the nodal point coordinates on tooth surfaces. The boundary conditions for the pinion and the gear are set automatically as well. A computer program was developed to implement the formulation provided above. By using this program the influence of design parameters and load position on tooth deflections and fillet stresses is investigated. On the basis of the results, obtained by performing a big number of computer runs, by using regression analysis and interpolation functions, equations for the calculation of tooth deflections and fillet stresses are derived.


Author(s):  
Isamu Tsuji ◽  
Kazumasa Kawasaki

In this article, the assembly interference of spiral bevel gears in a Klingelnberg cyclo-palloid system is analyzed based upon tooth contact analysis and is investigated experimentally. Each backlash in increasing mounting distance of the pinion is calculated step by step, using developed tooth contact analysis. When the backlash increases, the assembly interference does not occur based upon the calculated results. When the backlash decreases and is less than zero, the assembly interference occurs. When the assembly interference occurs, the tooth surfaces should be modified in order to prevent the assembly interference. In this case, a method of the modification is proposed. The experimental results showed a good agreement with the analyzed ones. As a result, the validity of the analysis and avoidance of the assembly interference in this method was confirmed.


2013 ◽  
Vol 415 ◽  
pp. 636-641
Author(s):  
Xiao Zhong Deng ◽  
Geng Geng Li ◽  
Bing Yang Wei

In order to solve the small cutting strip width and poor surface quality problems when spiral bevel gears are CNC machined by ball-end mills£¬a machining method of face milling spiral bevel gears by using a disc cutter with a concave end is presented. Based on the researches of spiral bevel gears geometry structure, through a bigger diameter disc cutter with a concave end selected, the setting order of cutter orientation angles changed, and the functions of cutter tilt and yaw angle separated, tooth surfaces machined with big cutting strip width and no bottom land gouge can be expected. Finally, taking a spiral bevel gear pair as an example, through machining and measurement experiments, the method feasibility and correctness are verified


1981 ◽  
Vol 103 (1) ◽  
pp. 127-132 ◽  
Author(s):  
R. L. Huston ◽  
J. J. Coy

This paper discusses the fundamental geometrical characteristics of spiral bevel gear tooth surfaces. The parametric representation of an ideal spiral bevel tooth is developed. The development is based on the elements of involute geometry, differential geometry, and fundamental gearing kinematics. A foundation is provided for the study of nonideal gears and the effects of deviations from ideal geometry on the contact stresses, lubrication, wear, fatigue life, and gearing kinematics.


Author(s):  
Eric C. Ames ◽  
Raja V. Pulikollu

Spiral bevel gears are widely used in the tail rotor drive trains of most rotorcraft. The loads associated with the tail rotor drive train are generally much more variable than those in the main rotor drive train primarily resulting from maneuvers. Over the life of any particular military rotorcraft it is not uncommon for the aircraft’s operating gross weight to steadily increase, causing the aircraft to fly at higher mean power levels and thus increasing the operating load spectrum associated with the tail rotor drive train. Special missions and equipment such as pulling a mine sweeping sled or very high altitude high gross weight assaults can put severe load demands on the tail drive train. This paper details an effort conducted to evaluate the effects of short to moderate duration overloads on the spiral bevel gears of the UH-60 helicopter tail rotor drive train. The focus of the effort was on the Tail Take-off gear mesh (TTO). An initial analytical assessment of the effect of loads above the endurance limit was conducted using an American Gear Manufacturers Association (AGMA) based approach. To confirm the validity of this approach, overload testing of the TTO gear mesh was conducted by the U.S. Army’s Aviation Applied Technology Directorate at the Navy’s test facility in Paxtuent River MD. Following the testing, the gear tooth bending and surface fatigue lives were analyzed using a microstructure based probabilistic tool developed by Sentient Corporation. The tool, known as Digital Clone was able to run hundreds of virtual tests that closely simulated the actual testing thus providing a low cost method for increasing the confidence associated with the effects of short to moderate high transient loads.


2006 ◽  
Vol 129 (2) ◽  
pp. 201-209 ◽  
Author(s):  
Vilmos Simon

A new approach for the computerized simulation of load distribution in mismatched spiral bevel gears with point contact is presented. The loaded tooth contact is treated in a special way: it is assumed that the point contact under load spreads over a surface along the “potential” contact line (Simon, 2006, Mech. and Machine Theory, in press), which line is made up of the points of the mating tooth surfaces in which the separations of these surfaces are minimal, instead of assuming the usually applied elliptical contact area. The bending and shearing deflections of gear teeth, the local contact deformations of mating surfaces, gear body bending and torsion, the deflections of supporting shafts, and the manufacturing and alignment errors of mating members are included. The tooth deflections of the pinion and gear teeth are calculated by the finite element method. As the equations governing the load sharing among the engaged tooth pairs and load distribution along the tooth face are nonlinear, an approximate and iterative technique is used to solve this system of equations. The method is implemented by a computer program. By using this program the load and tooth contact pressure distributions, the angular displacements of the driven gear and the stresses in the pinion and gear teeth are calculated. The influence of design data and transmitted torque on load distribution parameters and fillet stresses is investigated and discussed.


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