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.

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.

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.

Optimal Tooth Surface Modifications in Face-Hobbed Hypoid Gears

2013 ◽  
Vol 572 ◽  
pp. 351-354
Author(s):  
Simon Vilmos
Keyword(s):  
Contact Pressure ◽  
Angular Displacement ◽  
Optimization Procedure ◽  
Contact Analysis ◽  
Tooth Surface ◽  
Tooth Contact Analysis ◽  
Tooth Contact ◽  
Hypoid Gears ◽  
Transmission Errors ◽  
Loaded Tooth Contact Analysis

In this study, an optimization methodology is proposed to systematically define head-cutter geometry and machine tool settings to introduce optimal tooth modifications in face-hobbed hypoid gears. The goal of the optimization is to simultaneously minimize tooth contact pressures and angular displacement error of the driven gear, while concurrently confining the loaded contact pattern within the tooth boundaries. The proposed optimization procedure relies heavily on a loaded tooth contact analysis for the prediction of tooth contact pressure distribution and transmission errors. The objective function and the constraints are not available analytically, but they are computable, i.e., they exist numerically through the loaded tooth contact analysis. The core algorithm of the proposed nonlinear programming procedure is based on a direct search method. Effectiveness of this optimization was demonstrated by using a face-hobbed hypoid gear example. Considerable reductions in the maximum tooth contact pressure and in the transmission errors were obtained.

Analysis of tooth contact and transmission errors of curve-face gear

2016 ◽  
Vol 231 (19) ◽  
pp. 3579-3589 ◽  
Author(s):  
Chao Lin ◽  
Chunjiang He
Keyword(s):  
Contact Line ◽  
Contact Point ◽  
Tooth Surface ◽  
Gear Pair ◽  
Face Gear ◽  
Tooth Contact ◽  
Transmission Errors ◽  
Generating Method ◽  
Mathematical Equations ◽  
Curve Face

The authors have established the mathematical equations for the tooth surface of non-circular gear and curve-face gear based on the external generating method with the same shaper cutter. The paper covers the derivation of contact line on both non-circular gear and curve-face gear, the derivation of contact point on curve-face gear, the transmission functions with errors of alignment, the analysis of transmission errors and the comparison between curve-face gear pair and normal face gear pair. The developed theory is verified by experiment.

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.

Function-Oriented Designing and Generating Technology for the Point-Contact Tooth Surfaces of Spiral Bevel and Hypoid Gears

2008 ◽  
Vol 44-46 ◽  
pp. 495-502 ◽  
Author(s):  
Xun Cheng Wu ◽  
Cong Li ◽  
Ruo Ping Zhang ◽  
Hai Bo Zhang
Keyword(s):  
Point Contact ◽  
Transmission Function ◽  
Tooth Surface ◽  
Free Form ◽  
Tooth Contact ◽  
Hypoid Gears ◽  
Contact Points ◽  
Tooth Surfaces ◽  
Spiral Bevel ◽  
Basic Equations

A function-oriented designing and generating technology for the point-contact tooth surfaces of spiral bevel and hypoid gears is introduced. The tooth surface parameters are determined directly with the designing variables of the instantaneous transmission function, the locus of tooth contact points and the tooth contact ellipse dimension to design the point-contact tooth surfaces with the expected performances. The formulae for designing are provided. The designed tooth surfaces are generated with the free-form bevel gear machine, and the basic equations and formulae for the four-axis generating of the tooth surfaces are presented. The generating motions are expressed as the functions of the work gear rotary angle, which is taken as a motion parameter. The methods to determine the motion functions and the other machine setting parameters are explained through an example.

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.

Optimal Machine Tool Setting for Hypoid Gears Improving Load Distribution

2000 ◽  
Author(s):  
Vilmos V. Simon
Keyword(s):  
Machine Tool ◽  
Load Distribution ◽  
Angular Position ◽  
Distribution Factor ◽  
Hypoid Gears ◽  
Gear Teeth ◽  
Transmission Errors ◽  
Tool Setting ◽  
Load Distribution Factor ◽  
Optimal Machine

Abstract A method for the determination of optimal machine tool setting for manufacturing modified (mismatched) hypoid gears based on improved load distribution and reduced transmission errors is presented. The applied load distribution calculation is based on the conditions that the total angular position errors of the gear teeth being instantaneously in contact under load must be the same, and along the contact line of every tooth pair instantaneously in contact, the composite displacements of tooth surface points — as the sums of tooth deformations, geometrical surface separations, gear body bending and torsion, deflections of the supporting shafts, misalignments, and composite tooth errors — should correspond to the angular position of the gear. The tooth defonnations consists of the bending and shearing deflections of gear teeth and of the local contact deformations of the mating surfaces. The tooth deflections are calculated by the finite element method. As the equations governing the load sharing and load distribution are nonlinear, an approximate and iterative technique is used to solve this system of equations. The method is implemented by a computer program. Using the program that was developed the influence of machine tool setting parameters for pinion manufacture on maximum tooth contact pressure, load distribution factor, and transmission errors is investigated. By successively choosing the optimal value for every machine tool setting parameter, and by applying the optimal set of these parameters, the maximum tooth contact pressure is reduced by 5.8%, the load distribution factor by 5.9%, and the angular position error of the driven gear by 65.4%, in regard to the hypoid gear pair manufactured by the machine tool setting determined by the commonly used method.

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