Generation of Hypoid Gears on CNC Hypoid Generator

2011 ◽  
Vol 133 (12) ◽  
Author(s):  
Vilmos V. Simon
Keyword(s):  
Gear Tooth ◽  
Velocity Ratio ◽  
Transmission Error ◽  
Tooth Surface ◽  
Polynomial Functions ◽  
Gear Pair ◽  
Hypoid Gear ◽  
Kinematic Scheme ◽  
Hypoid Gears ◽  
Fifth Order

In this study, polynomial functions of orders up to five are applied to induce variations in the cradle radial setting and the velocity ratio in the kinematic scheme of the machine tool for the generation of the pinion tooth surfaces corresponding to reduced transmission error amplitudes of a hypoid gear pair. The new CNC hypoid generators have made it possible to perform this nonlinear correction motions for the cutting of the face-milled hypoid gears. An algorithm is developed for the execution of motions on the CNC hypoid generator for the generation of face-milled hypoid gear tooth surface, based on the machine tool setting variation on the cradle-type hypoid generator induced by the optimal polynomial functions up to fifth-order. By using the corresponding computer program, the motion graphs of the CNC hypoid generator are determined for the generation of hypoid gear tooth surface, based on the optimal variation in the velocity ratio in the kinematic scheme and on the variation in the cradle radial setting on a cradle-type generator. The results presented indicate that the variation of the velocity ratio in the kinematic scheme of the hypoid generator induced by a fifth-order polynomial function resulted in a 62% reduction of the maximum transmission error of the gear pair.

Optimal Tooth Modifications in Hypoid Gears

2004 ◽  
Vol 127 (4) ◽  
pp. 646-655 ◽  
Author(s):  
Vilmos Simon
Keyword(s):  
Load Distribution ◽  
Angular Position ◽  
Point Contact ◽  
Tooth Surface ◽  
Gear Pair ◽  
Hypoid Gear ◽  
Tooth Contact ◽  
Hypoid Gears ◽  
Transmission Errors ◽  
Tool Profile

A method for the determination of optimal tooth modifications in hypoid gears based on improved load distribution and reduced transmission errors is presented. The modifications are introduced into the pinion tooth surface by using a cutter with bicircular profile and optimal diameter. In the optimization of tool parameters the influence of shaft misalignments of the mating members is included. As the result of these modifications a point contact of the meshed teeth surfaces appears instead of line contact; the hypoid gear pair becomes mismatched. By using the method presented in (Simon, V., 2000, “Load Distribution in Hypoid Gears,” ASME J. Mech. Des., 122, pp. 529–535) the influence of tooth modifications introduced on tooth contact and transmission errors is investigated. Based on the results that was obtained the radii and position of circular tool profile arcs and the diameter of the cutter for pinion teeth generation were optimized. By applying the optimal tool parameters, the maximum tooth contact pressure is reduced by 16.22% and the angular position error of the driven gear by 178.72%, in regard to the hypoid gear pair with a pinion manufactured by a cutter of straight-sided profile and of diameter determined by the commonly used methods.

scholarly journals Meshing characteristics of a sphere–face gear pair with variable shaft angle

2019 ◽  
Vol 11 (6) ◽  
pp. 168781401985951 ◽  
Author(s):  
Lei Liu ◽  
Jinzhao Zhang
Keyword(s):  
Gear Tooth ◽  
Transmission Error ◽  
Tooth Surface ◽  
Gear Pair ◽  
Face Gear ◽  
Tooth Contact Analysis ◽  
Contact Points ◽  
Shaft Angle ◽  
Meshing Characteristics ◽  
Curvature Interference

This article presents a sphere–face gear pair by substituting the convex spherical gear for the pinion of a conventional face gear pair. The sphere–face gear pair not only maintains the advantages of the face gear pair with a longitudinally modified pinion but also allows variable shaft angles or large axial misalignments. Meshing characteristics of the proposed gear pair are studied in this article. The mathematical models of the sphere–face gear pair are derived based on machining principles. The tooth contact analysis (TCA) and curvature interference check are conducted for the sphere–face gear pair with variable shaft angles. The loaded TCA is also implemented utilizing the finite element method. The results of numerical examples show that proposed gear pair has the following features. Geometrical transmission error of constant shaft angle or varying shaft angle is zero; contact points of the sphere–face gear set with variable shaft angle are located near the centre region of face gear tooth surface; there is no curvature interference in meshing; and transmission continuity of the gear pair can be guaranteed in meshing.

Optimal Tooth Modifications in Hypoid Gears

2003 ◽  
Author(s):  
Vilmos V. Simon
Keyword(s):  
Angular Position ◽  
Point Contact ◽  
Tooth Surface ◽  
Gear Pair ◽  
Hypoid Gear ◽  
Tooth Contact ◽  
Hypoid Gears ◽  
Transmission Errors ◽  
Tool Profile

A method for the determination of optimal tooth modifications in hypoid gears based on improved load distribution and reduced transmission errors is presented. The modifications are introduced into the pinion tooth surface by using a cutter with bicircular profile and by changing the cutter diameter. In the optimization of tool parameters the influence of shaft misalignments of the mating members is included. As the result of these modifications a point contact of the meshed teeth surfaces appears instead of line contact; the hypoid gear pair becomes mismatched. By using the method presented in [1] the influence of tooth modifications introduced on tooth contact and transmission errors is investigated. Based on the results that was obtained the radii and position of circular tool profile arcs and the cutter diameter for pinion teeth generation were optimized. By applying the optimal tool parameters, the maximum tooth contact pressure is reduced by 16.22% and the angular position error of the driven gear by 178.72%, in regard to the hypoid gear pair with a pinion manufactured by a cutter of straight-sided profile and of diameter determined by the commonly used methods.

Effect of Tooth Contact and Gear Dimensions on Transmission Errors of Loaded Hypoid Gears

1991 ◽  
Vol 113 (2) ◽  
pp. 182-187 ◽  
Author(s):  
M. Sugimoto ◽  
N. Maruyama ◽  
A. Nakayama ◽  
N. Hitomi
Keyword(s):  
Gear Tooth ◽  
Transmission Error ◽  
Tooth Surface ◽  
Alignment Error ◽  
Tooth Contact ◽  
Hypoid Gears ◽  
Module Design ◽  
Transmission Errors ◽  
Loaded State ◽  
Final Drive

The effect of the tooth contact and alignment error of the hypoid gear assembly on transmission error was investigated with a new measuring apparatus which can measure the transmission errors of loaded hypoid gears assembled into a final drive unit. Measurements indicate that transmission error predictions made with the TCA and LTCA — analytical tools developed by Gleason Works for a no-load and loaded state, respectively — have sufficient accuracy when actual data on the gear tooth surface and alignment error of the gear assembly are used in the calculations. A systematic examination has also been made of the effects of tooth contact and gear assembly alignment error on transmission error on the basis of the LTCA calculations. It was found that the transmission errors relative to the applied load varied not only according to the tooth contact but also the no-load transmission error of the gears. This relationship was also examined by taking into account the effects of the gear dimensions. It was confirmed through calculation and experiment that a small module design was effective in reducing transmission error.

An Ease-Off Based Method for Loaded Tooth Contact Analysis of Hypoid Gears Having Local and Global Surface Deviations

2010 ◽  
Vol 132 (7) ◽  
Author(s):  
M. Kolivand ◽  
A. Kahraman
Keyword(s):  
Gear Tooth ◽  
Contact Analysis ◽  
Tooth Surface ◽  
Hypoid Gear ◽  
Tooth Contact Analysis ◽  
Tooth Contact ◽  
Hypoid Gears ◽  
Surface Deviations ◽  
Tooth Surfaces ◽  
Loaded Tooth Contact Analysis

Actual hypoid gear tooth surfaces do deviate from the theoretical ones either globally due to manufacturing errors or locally due to reasons such as tooth surface wear. A practical methodology based on ease-off topography is proposed here for loaded tooth contact analysis of hypoid gears having both local and global deviations. This methodology defines the theoretical pinion and gear tooth surfaces from the machine settings and cutter parameters, and constructs the surfaces of the theoretical ease-off and roll angle to compute for the unloaded contact analysis. This theoretical ease-off topography is modified based on tooth surface deviations and is used to perform a loaded tooth contact analysis according to a semi-analytical method proposed earlier. At the end, two examples, a face-milled hypoid gear set having local deviations and a face-hobbed one having global deviations, are analyzed to demonstrate the effectiveness of the proposed methodology in quantifying the effect of such deviations on the load distribution and the loaded motion transmission error.

How to Obtain the Formal Tooth Bearing Pattern Between Hypoid Gear and the Conjugate Pinion

2000 ◽  
Author(s):  
Norio Ito ◽  
Koichi Takahashi
Keyword(s):  
Conventional Method ◽  
Analytical Method ◽  
Second Order ◽  
Tooth Surface ◽  
Gear Pair ◽  
Hypoid Gear ◽  
Third Order ◽  
Hypoid Gears ◽  
Gear Cutting ◽  
Tooth Surfaces

Abstract In this paper, the relationships between the conjugate tooth surfaces of hypoid gears and the formal tooth bearing pattern are presented. First, we introduce the tooth surface elements necessary for the tooth bearing. Next, the tooth bearing pattern, which changes according to the generating condition of the pinion, is introduced. The hypoid gear pair is a formate gear and the pinion generated to run with such a gear. The conventional method for analyzing the tooth bearing pattern has been developed by the motion of generation between second-order tooth surfaces. In this paper, the tooth surface is expressed by the original third-order tooth surface, and the tooth bearing pattern is analyzed by the meshing motion of the tooth surface. The tooth bearing pattern obtained from such an analytical method becomes the formal tooth bearing. Therefore, the machine settings for accurate gear cutting become possible, and the desired tooth bearing pattern can be obtained beforehand without a trial cutting.

Investigation of Noise Features of Planetary Gear Trains Based on Human Aural Characteristic

2017 ◽  
Author(s):  
Masao Nakagawa ◽  
Dai Nishida ◽  
Deepak Sah ◽  
Toshiki Hirogaki ◽  
Eiichi Aoyama
Keyword(s):  
Gear Tooth ◽  
Structural Complexity ◽  
Planetary Gear ◽  
Transmission Error ◽  
Sound Level ◽  
Tooth Surface ◽  
Surface Error ◽  
Planetary Gear Trains ◽  
Tooth Stiffness ◽  
Gear Trains

Planetary gear trains (PGTs) are widely used in various machines owing to their many advantages. However, they suffer from problems of noise and vibration due to the structural complexity and giving rise to substantial noise, vibration, and harshness with respect to both structures and human users. In this report, the sound level from PGTs is measured in an anechoic chamber based on human aural characteristic, and basic features of sound are investigated. Gear noise is generated by the vibration force due to varying gear tooth stiffness and the vibration force due to tooth surface error, or transmission error (TE). Dynamic TE is considered to be increased because of internal and external meshing. The vibration force due to tooth surface error can be ignored owing to almost perfect tooth surface. A vibration force due to varying tooth stiffness could be a major factor.

Simulation and Experimental Measurement of the Transmission Error of Real Hypoid Gears Under Load

2000 ◽  
Vol 122 (1) ◽  
pp. 109-122 ◽  
Author(s):  
Claude Gosselin ◽  
Thierry Guertin ◽  
Didier Remond ◽  
Yves Jean
Keyword(s):  
Measurement Data ◽  
Simulation Models ◽  
Transmission Error ◽  
Contact Analysis ◽  
Hypoid Gear ◽  
Tooth Contact Analysis ◽  
Tooth Contact ◽  
Hypoid Gears ◽  
Loaded Tooth Contact Analysis ◽  
Analysis Models

The Transmission Error and Bearing Pattern of a gear set are fundamental aspects of its meshing behavior. To assess the validity of gear simulation models, the Transmission Error and Bearing Pattern of a Formate Hypoid gear set are measured under a variety of operating positions and applied loads. Measurement data are compared to simulation results of Tooth Contact Analysis and Loaded Tooth Contact Analysis models, and show excellent agreement for the considered test gear set. [S1050-0472(00)00901-6]

Tool Profile Modification of Hypoid Gear Machined by Duplex Helical Method

2021 ◽  
Author(s):  
Shunxing Wu ◽  
Hongzhi Yan ◽  
Zhiyong Wang ◽  
Rengui Bi ◽  
Jia Li
Keyword(s):  
Geometric Model ◽  
Tooth Surface ◽  
Gear Pair ◽  
Hypoid Gear ◽  
Tooth Contact Analysis ◽  
Edge Contact ◽  
Profile Modification ◽  
Tool Profile ◽  
Tooth Surfaces ◽  
Loaded Tooth Contact Analysis

Abstract For the hypoid gear pair of the heavy-duty vehicle drive axle machined by the duplex helical method, in order to avoid edge contact and stress concentration on the tooth surface, a four-segment tool profile is designed to modify the concave and convex surfaces simultaneously. First, the geometric model of the four-segment tool profile is established. Second, the mathematical model of the duplex helical method based on the four-segment tool profile is established, and the method of solving the tooth surface generated by the connecting points of the four-segment tool profile is given. Finally, the finite element method of loaded tooth contact analysis is used to analyze the meshing performance of the gear pair obtained by the four-segment tool profile modification, and the results are compared with the original gear pair. The results show that after the tooth surfaces are modified, the edge contact of the tooth surfaces are avoided, the stress distribution of the tooth surfaces are improved, the maximum contact stress of the tooth surfaces are reduced, and the fatigue and wear life of the tooth surface are improved.

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