Optimization of the Loaded Contact Pattern in Hypoid Gears by Automatic Topography Modification

2008 ◽  
Vol 131 (1) ◽  
Author(s):  
Alessio Artoni ◽  
Andrea Bracci ◽  
Marco Gabiccini ◽  
Massimo Guiggiani
Keyword(s):  
Optimization Problems ◽  
Mathematical Framework ◽  
Contact Pattern ◽  
Tooth Contact ◽  
Hypoid Gears ◽  
Computational Speed ◽  
Tool Setting ◽  
Unconstrained Nonlinear Optimization ◽  
Time Required ◽  
Time Frames

Systematic optimization of the tooth contact pattern under load is an open problem in the design of spiral bevel and hypoid gears. In order to enhance its shape and position, gear engineers have been assisted by numerical tools based on trial-and-error approaches, and/or they have been relying on the expertise of skilled operators. The present paper proposes a fully automatic procedure to optimize the loaded tooth contact pattern, with the advantage of eventually reducing design time and cost. The main problem was split into two identification subproblems: first, to identify the ease-off topography capable of optimizing the contact pattern; second, to identify the machine-tool setting variations required to obtain such ease-off modifications. Both of them were formulated and solved as unconstrained nonlinear optimization problems. In addition, an original strategy to quickly approximate the tooth contact pattern under load was conceived. The results obtained were very satisfactory in terms of accuracy, robustness, and computational speed. They also suggest that the time required to optimize the contact pattern can be significantly reduced compared with typical time frames. A sound mathematical framework ensures results independent of the practitioner’s subjective decision-making process. By defining a proper objective function, the proposed method can also be applied to affect other contact properties, such as to improve the motion graph or to decrease the sensitivity of the transmission to assembly errors. Furthermore, it can be easily adapted to any gear drive by virtue of its systematic and versatile nature.

Robust Optimization of the Loaded Contact Pattern in Hypoid Gears With Uncertain Misalignments

2009 ◽  
Author(s):  
M. Gabiccini ◽  
A. Bracci ◽  
M. Guiggiani
Keyword(s):  
Optimization Problems ◽  
Optimization Procedure ◽  
Target Area ◽  
Contact Pattern ◽  
Unified Framework ◽  
Hypoid Gears ◽  
Contact Patterns ◽  
Unconstrained Nonlinear Optimization ◽  
The One ◽  
Micro Topography

This paper presents an automatic procedure to optimize the loaded tooth contact pattern of face-milled hypoid gears with misalignments varying within prescribed ranges. A two-step approach is proposed to solve the problem: in the first step, the pinion tooth micro-topography is automatically modified to bring the perturbed contact patterns (as the assembly errors are varied within the tolerance limits) match a target area of the tooth, while keeping them off the edges; in the second step, a subset of the machine-tool settings is identified to obtain the required topography modifications. Both steps are formulated and solved as unconstrained nonlinear optimization problems. While the general methodology is similar to the one recently proposed by the same authors for the optimization at nominal conditions, here the robustness issues with respect to misalignment variations are considered and directly included in the optimization procedure: no a posteriori check for robustness is therefore required. Numerical tests show that nominally satisfactory and globally robust hypoid pairs can be designed by a direct process and within a unified framework, thus avoiding tiresome trial-and-error loops.

Robust Optimization of the Loaded Contact Pattern in Hypoid Gears With Uncertain Misalignments

2010 ◽  
Vol 132 (4) ◽  
Author(s):  
M. Gabiccini ◽  
A. Bracci ◽  
M. Guiggiani
Keyword(s):  
Optimization Problems ◽  
Optimization Procedure ◽  
Target Area ◽  
Contact Pattern ◽  
Trial And Error ◽  
Unified Framework ◽  
Hypoid Gears ◽  
Contact Patterns ◽  
Unconstrained Nonlinear Optimization ◽  
The One

This paper presents an automatic procedure to optimize the loaded tooth contact pattern of face-milled hypoid gears with misalignments varying within prescribed ranges. A two-step approach is proposed to solve the problem: in the first step, the pinion tooth microtopography is automatically modified to bring the perturbed contact patterns (as the assembly errors are varied within the tolerance limits) match a target area of the tooth while keeping them off the edges; in the second step, a subset of the machine-tool settings is identified to obtain the required topography modifications. Both steps are formulated and solved as unconstrained nonlinear optimization problems. While the general methodology is similar to the one recently proposed by the same authors for the optimization at nominal conditions, here, the robustness issues with respect to misalignment variations are considered and directly included in the optimization procedure: no a posteriori check for robustness is therefore required. Numerical tests show that nominally satisfactory and globally robust hypoid pairs can be designed by a direct process and within a unified framework, thus avoiding tiresome trial-and-error loops.

Loaded TCA of Measured Tooth Flanks for Lapped Hypoid Gears

2007 ◽  
Author(s):  
Kohei Saiki ◽  
Keiichiro Tobisawa ◽  
Masaki Kano ◽  
Yasuharu Ohnishi ◽  
Takashi Kusaka
Keyword(s):  
Coordinate Measuring Machine ◽  
Contact Pattern ◽  
Tooth Contact Analysis ◽  
Tooth Contact ◽  
Hypoid Gears ◽  
Practical Applications ◽  
Wheel Drive ◽  
Measuring Machine ◽  
Loaded Tooth Contact Analysis ◽  
Shape Data

Usually, the Loaded Tooth Contact Analysis (i.e. LTCA) of hypoid gears uses the nominal tooth flanks described by the machine setting and the cutter specifications. Only a few studies are performed on the LTCA directly using the measured tooth flanks such as carbonize-hardened and lapped hypoid gears. This paper presents an innovative LTCA method directly using the measured tooth flanks at each manufacturing step including not only the milling or hobbing process but also the troublesome heat-treatment, lapping or grinding processes. The proposed new LTCA method is extremely concise. Firstly, the 3-D shape data of the manufactured tooth flanks, which are the original x-y-z coordinates but not the differences against their nominal tooth flanks as before, are obtained on a coordinate-measuring machine. Another important factors the load deflections are measured on the assembled transmission by applying the static transmitting torque. Secondly, the pinion and gear are localized at the nominal mounting position, and the no load TCA can be obtained by calculating the gap between the original tooth flanks at each roll angle. Lastly, since the load deflections can be considered as the movement of mounting position, the Loaded TCA can be obtained by calculating the gap between the moved tooth flanks at new mounting position. As practical applications, the new LTCA method is used to improve the strength of high-torque hypoid gears for an All-Wheel-Drive transmission. As a result, the tooth contact pattern and pitting position observed in endurance test agreed well to the LTCA predictions and the demanding life is achieved by modifying the loaded contact pattern of lapped hypoid gears.

A method for the global optimization of the tooth contact pattern and transmission error of spiral bevel and hypoid gears

2017 ◽  
Vol 18 (5) ◽  
pp. 377-392 ◽  
Author(s):  
Yao-bin Zhuo ◽  
Xue-yan Xiang ◽  
Xiao-jun Zhou ◽  
Hao-liang Lv ◽  
Guo-yang Teng
Keyword(s):  
Global Optimization ◽  
Transmission Error ◽  
Contact Pattern ◽  
Tooth Contact ◽  
Hypoid Gears ◽  
Spiral Bevel

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]

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.

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