Helical Gears With Involute Shaped Teeth: Geometry, Computer Simulation, Tooth Contact Analysis, and Stress Analysis

1988 ◽  
Vol 110 (4) ◽  
pp. 482-491 ◽  
Author(s):  
Chung-Biau Tsay
Keyword(s):  
Mathematical Model ◽  
Computer Simulation ◽  
Computer Program ◽  
Stress Analysis ◽  
Contact Analysis ◽  
Tooth Contact Analysis ◽  
Tooth Contact ◽  
Helical Gears ◽  
Bearing Contact ◽  
Kinematic Errors

The paper covers the solutions to the following problems: (1) Setting up a mathematical model for the involute helical gears; (2) Computer simulation of the conditions of meshing and bearing contact; (3) Investigation of the sensitivity of gears to the errors of manufacturing and assembly; and (4) Stress analysis of the gears. In this paper, the theory of gearing and the concept of differential geometry have been applied to deal with the relations of two mating helical gears and their bearing contact. Computer program for tooth contact analysis (T.C.A.) has been developed for the gears. The T.C.A. computer program makes it possible to simulate gear meshing and bearing contact, and to investigate the influence of gear misalignment on kinematic errors. A method of compensation for the dislocation of bearing contact and for kinematic errors induced by errors of manufacturing and assembly has been proposed. Four numerical examples have also been presented to illustrate the influence of the above-mentioned errors and the method of compensation for the dislocation of bearing contact. Based on the derived mathematical model, an automatic mesh generating computer program—AMG has been developed to define the geometry of the gears and to divide the gear tooth into elements as well as to generate nodal points automatically. The results of T.C.A. provide the locations and directions of the applied loadings for the finite element method (F.E.M.) stress analysis.

Comparative study of stress analysis of gears with different helix angle using the ISO 6336 standard and tooth contact analysis methods

2016 ◽  
Vol 230 (7-8) ◽  
pp. 1350-1358 ◽  
Author(s):  
Layue Zhao ◽  
Robert C Frazer ◽  
Brian Shaw
Keyword(s):  
Stress Analysis ◽  
Contact Stress ◽  
Helix Angle ◽  
Contact Analysis ◽  
Bending Stress ◽  
Contact Ratio ◽  
Tooth Contact Analysis ◽  
Tooth Contact ◽  
Iso Standard ◽  
Analysis Methods

With increasing demand for high speed and high power density gear applications, the need to optimise gears for minimum stress, noise and vibration becomes increasingly important. ISO 6336 contact and bending stress analysis are used to determine the surface load capacity and tooth bending strength but dates back to 1956 and although it is constantly being updated, a review of its performance is sensible. Methods to optimise gear performance include the selection of helix angle and tooth depth to optimise overlap ratio and transverse contact ratio and thus the performance of ISO 6336 and tooth contact analysis methods requires confirmation. This paper reviews the contact and bending stress predicted with four involute gear geometries and proposes recommendations for stress calculations, including a modification to contact ratio factor Zɛ which is used to predict contact stress and revisions to form factor YF and helix angle factor Yβ which are cited to evaluate bending stress. The results suggest that there are some significant deviations in predicted bending and contact stress values between proposal methods and original ISO standard. However, before the ISO standard is changed, the paper recommends that allowable stress numbers published in ISO 6336-5 are reviewed because the mechanisms that initiate bending and contact fatigue have also changed and these require updating.

Tooth contact analysis of a curvilinear gear set with modified pinion tooth geometry

2011 ◽  
Vol 225 (4) ◽  
pp. 975-986 ◽  
Author(s):  
Y-C Chen ◽  
M-L Gu
Keyword(s):  
Finite Element ◽  
Transmission Error ◽  
Contact Analysis ◽  
Design Parameters ◽  
Stress Distributions ◽  
Tooth Contact Analysis ◽  
Tooth Contact ◽  
Numerical Examples ◽  
Bearing Contact ◽  
Parallel Axis

This article investigated the contact behaviours of a modified curvilinear gear set for parallel-axis transmission, which exhibits a pre-designed parabolic transmission error (TE) and localized bearing contact. The proposed gear set is composed of a modified pinion with curvilinear teeth and an involute gear with curvilinear teeth. Tooth contact analysis enabled the authors to explore the influences of assembly errors and design parameters on TEs and contact ellipses of this gear set. It is observed that TEs were continuous and the contact ellipses were localized in the middle of the tooth flanks, even under assembly errors. Finite-element contact analysis was performed to study stress distributions under different design parameters. In addition, numerical examples are presented to demonstrate the contact characteristics of the modified curvilinear gear set.

Loaded Tooth Contact Analysis of Face Gear Drive with Modification

2010 ◽  
Vol 29-32 ◽  
pp. 1711-1716
Author(s):  
Shu Yan Zhang ◽  
Hui Guo
Keyword(s):  
Transmission Error ◽  
Contact Analysis ◽  
Tooth Surface ◽  
Face Gear ◽  
Tooth Contact Analysis ◽  
Tooth Contact ◽  
Gear Drive ◽  
Bearing Contact ◽  
Tooth Number ◽  
Loaded Tooth Contact Analysis

A double direction modification with a grinding worm is applied on tooth surface of face gear drive. The surface equations of the rack cutter, shaper and grinding worm are derived respectively. Loaded tooth contact analysis (LTCA) with finite element method (FEM) is performed to investigate the meshing performance of face gear drive before modification and after modification. The modification by a grinding worm can obviously reduce the sensitivity of face gear drive to misalignment; the bending stress and the contact stress are reduced with avoiding edge contact; the load transmission error is reduced. This method can obtain a more stable bearing contact in contrast to the method by increasing tooth number of shaper, and the modification magnitude can be controlled freely. The investigation is illustrated with numerical examples.

Tooth Contact Analysis of Parabolic Gears with New Type of Profile

2013 ◽  
Vol 365-366 ◽  
pp. 294-298 ◽  
Author(s):  
Shu Yan Zhang ◽  
Hui Guo
Keyword(s):  
High Strength ◽  
Contact Analysis ◽  
Tooth Surface ◽  
Tooth Contact Analysis ◽  
Tooth Contact ◽  
Transmission Errors ◽  
Bearing Contact ◽  
New Type

The meshing principle of a new kind of parabolic gear is introduced, and the tooth surface equations of parabolic gear are obtained. A tooth contact analysis to simulate meshing and contact is applied. The paper investigates the influence of misalignment on transmission errors and shift of bearing contact. Examples to illustrate the developed approaches are proposed. The research provides the basis for design of new high strength parabolic gears.

Mathematical Model of Klingelnberg Cyclo-Palloid Hypoid Gear

2013 ◽  
Vol 341-342 ◽  
pp. 572-576 ◽  
Author(s):  
Jin Fu Du ◽  
Zong De Fang ◽  
Min Xu ◽  
Xing Long Zhao ◽  
Yu Min Feng
Keyword(s):  
Mathematical Model ◽  
Contact Analysis ◽  
Tooth Surface ◽  
Hypoid Gear ◽  
Tooth Contact Analysis ◽  
Tooth Contact ◽  
Hypoid Gears ◽  
Tooth Surfaces ◽  
Normal Vectors

The geometry of the tooth surface is important for tooth contact analysis, load tooth contact analysis and the ease-off of gear pairs. This paper presents a mathematical model for the determination of the tooth geometry of Klingelnberg face-hobbed hypoid gears. The formulation for the generation of gear and pinion tooth surfaces and the equations for the tooth surface coordinates are provided in the paper. The surface coordinates and normal vectors are calculated and tooth surfaces and 3D tooth geometries of gear and pinion are obtained. This method may also applied to other face-hobbing gears.

Computer Simulation Analysis of Bending Stress for Face Gear with a New Type Fillet Tooth Surface

2011 ◽  
Vol 86 ◽  
pp. 411-414
Author(s):  
Yun Bo Shen ◽  
Jie Gao ◽  
Wen Qiang Ding
Keyword(s):  
Computer Simulation ◽  
Surface Structure ◽  
Spur Gear ◽  
Contact Analysis ◽  
Tooth Surface ◽  
Bending Stress ◽  
Face Gear ◽  
Tooth Contact Analysis ◽  
Tooth Contact ◽  
The Face

Bending stress is a principal factor that defines the fatigue life of face gear. A new tooth surface structure with circular arc of fillet surface for the face gear has been developed. A method of processing or cutting of fillet surfaces of helical face gear by application of a shaper with tooth rounded top has also been represented. The bending stress of the tooth of face gear with new surface structure has been performed by computer simulation. Two versions of finite element model of tooth surfaces of face gear are generated by application of numerical technology. One version is based on the cutting shaper with tooth top shaper corner and another version is with addendum rounded top. Tooth contact analysis (TCA) and loaded tooth contact analysis (LTCA) for the two versions of face gear drives with helical spur gear are also considered. The results of simulation show that the bending stress of tooth surface of the face gear with fillet surface generated by the rounded top of the shaper is 12% lower than the first version’s.

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