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.

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.

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.

Simulation Analysis of Contact Pattern and Strength of WN Gears Having Tooth Surface Deviations

2012 ◽  
Vol 479-481 ◽  
pp. 944-948 ◽  
Author(s):  
Dian Hua Chen ◽  
Zhong Wei Zhang
Keyword(s):  
Simulation Analysis ◽  
Practical Method ◽  
Transmission Error ◽  
Tooth Surface ◽  
Contact Pattern ◽  
The Finite Element Method ◽  
Tooth Contact Analysis ◽  
Surface Deviations ◽  
Tooth Surfaces ◽  
Loaded Tooth Contact Analysis

A practical method based on normal gaps topography is proposed here for loaded tooth contact analysis of WN gear having tooth surface deviations. The simulation of meshing state and tooth strength of WN gear are provided with real tooth surfaces. In the study normal gaps distribution is adopted to calculate tooth surface contact elastic deformation and local deviations due to manufacturing errors and tooth surface wear. For WN gear, the loaded distribution on the contact zone in meshing tooth surface has not been investigated because of their complexity in the contact state. The finite element method is adopted to analyze the contact pattern and tooth strength. The study has concretely calculated the contact pressure and zone of meshing in different loaded and transmission error. At the end examples are analyzed to demonstrate the effectiveness of the proposed method in quantifying effect of such deviations on the loaded distribution and tooth stress distribution.

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.

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.

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.

Requirement for Limits of Action and Wildhaber’s Limit Normal

2003 ◽  
Author(s):  
Sho Honda
Keyword(s):  
Tooth Surface ◽  
Gear Pair ◽  
Hypoid Gear ◽  
Coordinate Systems ◽  
Design Point ◽  
Tooth Surfaces ◽  
Angular Velocities ◽  
The Common ◽  
The Given ◽  
Designing Method

One of the most important criteria to design a gear pair which has smooth tooth surfaces around a given design point is how far the design point is from the limits of action. However, in the present theories, the definition is obscure and the calculation methods are not clear except for cylindrical gears. In this paper, when a path of contact and its contact normals are given according to the unified designing method applicable to all kinds of gears having the same equations defined in the common coordinate systems which are determined by the disposition of the gear axes and the angular velocities, the infinitesimal surface of action along the path of contact and the corresponding tooth surfaces are determined and the requirement for limit of action for all kinds of gears is obtained. To design a smooth tooth surface around the design point, it is convenient to look for the limit path of contact with its contact normal whose limit of action coincides with the design point, from which a design path of contact must be inclined adequately. Finally, it is shown that Wildhaber’s limit normal is the contact normal of the limit path of contact solved under the condition that the given path of contact is an arc around the gear axis and is just one solution of the limits of action of a hypoid gear pair.

A calculation method of sliding friction coefficient on tooth surface for helical gear pair based on loaded tooth contact analysis and elastohydrodynamic lubrication theory

2020 ◽  
pp. 135065012096689
Author(s):  
Cheng Wang ◽  
Mao Ken
Keyword(s):  
Friction Coefficient ◽  
Sliding Friction ◽  
Elastohydrodynamic Lubrication ◽  
Helical Gear ◽  
Tooth Surface ◽  
Gear Pair ◽  
Tooth Contact Analysis ◽  
Sliding Friction Coefficient ◽  
Loaded Tooth Contact Analysis ◽  
Helical Gear Pair

The sliding friction coefficient on tooth surface is related to power loss, carry capacity and transmission performance of gear. Reasonable transmission analysis of gear pair is the premise of accurate calculation of sliding friction coefficient on tooth surface. However, for helical gear pair, the line contact without considering machining error/installation error/modification of gear is usually adopted to replace the major axis of ellipse caused by contact load. Therefore, in this paper, contact path on tooth surface, length of contact line, load distribution on tooth surface and loaded transmission errors are accurately calculated by loaded tooth contact analysis (LTCA). Combing with elastohydrodynamic lubrication (EHL) theory, a calculation method of sliding friction coefficient on tooth surface for helical gear pair is proposed.

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]

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