The Generating Space for Parabolic Motion Error Spiral Bevel Gears Cut by the Gleason Method

1993 ◽  
Vol 115 (3) ◽  
pp. 483-489 ◽  
Author(s):  
C. J. Gosselin ◽  
L. Cloutier
Keyword(s):  
Speed Ratio ◽  
Contact Deformation ◽  
Motion Error ◽  
Spiral Bevel Gears ◽  
Machine Center ◽  
Gear Teeth ◽  
Bevel Gears ◽  
Loaded State ◽  
Spiral Bevel ◽  
Tooth Flank

Because of their inherent pseudo-conjugate natures, spiral bevel gears cut by the Gleason method basically transmit motion in a nonuniform manner. This motion nonuniformity, or motion error, repeated at each tooth engagement and at high speeds and loads, can cause vibrations in transmissions and contact-entry impact loads on gear teeth which affect the life of a gearset. It is customary to make small changes to machine settings in order to produce gear pairs with vastly improved kinematics. Therefore, machine setting changes must be carefully chosen such as to produce appropriate unloaded kinematical motion error that will cancel tooth bending deflection and contact deformation at a given load, and thus reduce noise and vibrations due to motion nonuniformity. This paper presents a study on the effects of machine settings, such as cutter tilt, machine center to back and offset, on the unloaded kinematical motion error. Applying CAD Boolean operations on the results, it is found that, for a given speed ratio, an infinite number of cutter tilt, work offset and machine center to back combinations will produce gear sets with convex parabolic motion error curve of any desired amplitude. Moreover, the amplitude of motion error curves can be linked directly to contact bias on the tooth flank. Thus, gear sets with any parabolic motion error in the unloaded state can be produced, such as to cancel tooth bending deflection and contact deformation in the loaded state.

The Generating Space for Parabolic Motion Error Spiral Bevel Gears Cut by the Gleason Method

1992 ◽  
Author(s):  
Claude Gosselin ◽  
Louis Cloutier
Keyword(s):  
Speed Ratio ◽  
Contact Deformation ◽  
Motion Error ◽  
Spiral Bevel Gears ◽  
Machine Center ◽  
Bevel Gears ◽  
Loaded State ◽  
Spiral Bevel ◽  
Uniform Manner ◽  
Tooth Flank

Abstract Because of their inherent pseudo-conjugate natures, spiral bevel gears cut by the Gleason method basically transmit motion in a non uniform manner. This motion non uniformity, or motion error, repeated at each tooth engagement and at high speeds and loads, can cause vibrations in transmissions and contact-entry impact loads on gear teeth which affect the life of a gearset. It is customary to make small changes to machine settings in order to produce gear pairs with vastly improved kinematics. Therefore, machine setting changes must be carefully chosen such as to produce appropriate unloaded kinematical motion error that will cancel tooth bending deflection and contact deformation at a given load, and thus reduce noise and vibrations due to motion non-uniformity. This paper presents a study on the effects of machine settings, such as cutter tilt, machine center to back and offset, on the unloaded kinematical motion error. Applying CAD Boolean operations on the results, it is found that, for a given speed ratio, an infinite number of cutter tilt, work offset and machine center to back combinations will produce gear sets with convex parabolic motion error curve of any desired amplitude. Moreover, the amplitude of motion error curves can be linked directly to contact bias on the tooth flank. Thus, gear sets with any parabolic motion error in the unloaded state can be produced, such as to cancel tooth bending deflection and contact deformation in the loaded state.

Advanced Design and Manufacture of Face-Hobbed Spiral Bevel Gears

2009 ◽  
Author(s):  
V. Simon
Keyword(s):  
Gear Tooth ◽  
Numerical Control ◽  
Mutual Position ◽  
Spiral Bevel Gears ◽  
Bevel Gears ◽  
Pinion Gear ◽  
Tooth Surfaces ◽  
Spiral Bevel ◽  
Tooth Flank ◽  
Crown Gear

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.

Load Distribution in Spiral Bevel Gears

2006 ◽  
Vol 129 (2) ◽  
pp. 201-209 ◽  
Author(s):  
Vilmos Simon
Keyword(s):  
Load Distribution ◽  
Point Contact ◽  
Design Data ◽  
Tooth Contact ◽  
Spiral Bevel Gears ◽  
Gear Teeth ◽  
Bevel Gears ◽  
Tooth Surfaces ◽  
Machine Theory ◽  
Spiral Bevel

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.

Analytical and Experimental Tooth Contact Pattern of Large-Sized Spiral Bevel Gears in Cyclo-Palloid System

2009 ◽  
Author(s):  
Kazumasa Kawasaki ◽  
Isamu Tsuji
Keyword(s):  
Coordinate Measuring Machine ◽  
Tooth Surface ◽  
Contact Pattern ◽  
Tooth Contact ◽  
Spiral Bevel Gears ◽  
Form Errors ◽  
Bevel Gears ◽  
Measuring Machine ◽  
Spiral Bevel ◽  
Tooth Flank

The demand of large-sized spiral bevel gears has increased in recent years and hereafter the demand may increase more and more. The large-sized spiral bevel gears with equi-depth teeth are usually manufactured based on Klingelnberg cyclo-palloid system. In this paper, the tooth contact pattern of large-sized spiral bevel gears in this system are investigated analytically and experimentally. First, the tooth contact pattern and transmission errors of such gears are analyzed. The analysis method is based on simultaneous generations of tooth surface and simulations of meshing and contact. Next, the large-sized spiral bevel gears are manufactured and the tooth contact pattern of these gears is investigated experimentally. Moreover, the real tooth surfaces are measured using a coordinate measuring machine and the tooth flank form errors are detected using the measured coordinates. It is possible to analyze the tooth contact patterns of the spiral bevel gears with consideration of the tooth flank form errors expressing the errors as polynomial equations. Finally, the influence of alignment errors due to assembly on the tooth contact pattern is also investigated analytically and experimentally. These analyzed results were compared with experimental ones. As a result, two results showed a good agreement.

The Scuffing Resistance of WC/C Coated Spiral Bevel Gears

2014 ◽  
Vol 604 ◽  
pp. 36-40 ◽  
Author(s):  
Remigiusz Michalczewski ◽  
Marek Kalbarczyk ◽  
Waldemar Tuszynski ◽  
Marian Szczerek
Keyword(s):  
Bevel Gear ◽  
Spiral Bevel Gear ◽  
Test Rig ◽  
Low Friction ◽  
Spiral Bevel Gears ◽  
Gear Teeth ◽  
Bevel Gears ◽  
Trade Name ◽  
Gear Oil ◽  
Spiral Bevel

One of the main problems with the operation of spiral bevel gears is related to very severe conditions in the contact of the meshing teeth; therefore, lubrication is very difficult, which increases the risk of scuffing occurrence. One of the ways to achieve better scuffing resistance is by the deposition of a low-friction coating on the bevel gears teeth. Gear scuffing tests were performed using a bevel gear test rig designed and manufactured at ITeE-PIB. The authorial bevel gear scuffing test was performed. Specially designed, spiral bevel gears were used for testing. Two material combinations were tested: uncoated pinion - coated wheel and, for reference, both gears without coatings. The a-C:H:W (trade name WC/C) coating of DLC type was deposited on the wheel teeth. A mineral, automotive gear oil of API GL-5 performance level was used for lubrication. It is shown that the resistance to scuffing may be significantly improved when the a-C:H:W coating is deposited on the spiral bevel gear teeth.

scholarly journals Precision of Spiral-Bevel Gears

1983 ◽  
Vol 105 (3) ◽  
pp. 310-316 ◽  
Author(s):  
F. L. Litvin ◽  
R. N. Goldrich ◽  
J. J. Coy ◽  
E. V. Zaretsky
Keyword(s):  
Tooth Surface ◽  
Surface Geometry ◽  
Spiral Bevel Gears ◽  
Gear Teeth ◽  
Bevel Gears ◽  
Bearing Contact ◽  
Order Of Magnitude ◽  
Gear Trains ◽  
Spiral Bevel ◽  
Kinematic Errors

An analytical method was derived for determining the kinematic errors in spiral-bevel gear trains caused by the generation of nonconjugate surfaces, by axial displacements of the gear assembly, and by eccentricity of the assembled gears. Such errors are induced during manufacturing and assembly. Two mathematical models of spiral-bevel gears were included in the investigation. One model corresponded to the motion of the contact ellipse across the tooth surface (geometry I) and the other along the tooth surface (geometry II). The following results were obtained: 1) Kinematic errors induced by errors of manufacture may be minimized by applying special machine settings. The original error may be reduced by an order of magnitude. The procedure is most effective for geometry II gears. 2) When trying to adjust the bearing contact pattern between the gear teeth for geometry I gears, it is more desirable to shim the gear axially; for geometry II gears, shim the pinion axially. 3) The kinematic accuracy of spiral-bevel drives is most sensitive to eccentricities of the gear and less sensitive to eccentricities of the pinion. The pecision of mounting accuracy and manufacture is most crucial for the gear, and less so for the pinion.

scholarly journals On Dynamic Mesh Force Evaluation of Spiral Bevel Gears

2019 ◽  
Vol 2019 ◽  
pp. 1-26 ◽  
Author(s):  
Xiaoyu Sun ◽  
Yongqiang Zhao ◽  
Ming Liu ◽  
Yanping Liu
Keyword(s):  
Single Point ◽  
Transmission Error ◽  
Dynamic Mesh ◽  
Mesh Stiffness ◽  
Spiral Bevel Gears ◽  
Bevel Gears ◽  
Mesh Model ◽  
Spiral Bevel ◽  
Tooth Flank ◽  
Tooth Pair

The mesh model and mesh stiffness representation are the two main factors affecting the calculation method and the results of the dynamic mesh force. Comparative studies considering the two factors are performed to explore appropriate approaches to estimate the dynamic meshing load on each contacting tooth flank of spiral bevel gears. First, a tooth pair mesh model is proposed to better describe the mesh characteristics of individual tooth pairs in contact. The mesh parameters including the mesh vector, transmission error, and mesh stiffness are compared with those of the extensively applied single-point mesh model of a gear pair. Dynamic results from the proposed model indicate that it can reveal a more realistic and pronounced dynamic behavior of each engaged tooth pair. Second, dynamic mesh force calculations from three different approaches are compared to further investigate the effect of mesh stiffness representations. One method uses the mesh stiffness estimated by the commonly used average slope approach, the second method applies the mesh stiffness evaluated by the local slope approach, and the third approach utilizes a quasistatically defined interpolation function indexed by mesh deflection and mesh position.

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