scholarly journals Tribo-Dynamics of Differential Hypoid Gears

2013 ◽  
Author(s):  
Mahdi Mohammadpour ◽  
Stephanos Theodossiades ◽  
Homer Rahnejat
Keyword(s):  
Vibrational Energy ◽  
Point Contact ◽  
Elastohydrodynamic Lubrication ◽  
Operating Conditions ◽  
Hypoid Gear ◽  
Tooth Contact Analysis ◽  
Hypoid Gears ◽  
Dynamic Framework ◽  
Parametric Studies ◽  
Noise Vibration

Differential hypoid gears play an important role on the Noise, Vibration and Harshness (NVH) signature of vehicles. Additionally, friction developed between their teeth flanks under extreme loading conditions adds another source of power loss in the drivetrain which can mitigate vibrational energy. The paper considers the coupling between dynamics and analytical tribology to study dynamic response of hypoid gear pairs with lateral motion of support shafts also included in the analysis framework. Friction of teeth flank pairs is assumed to follow elastohydrodynamic lubrication under elliptical point contact geometry with lubricant film behavior conforming to Non-Newtonian thermal shear, also with surface asperity interactions. Tooth Contact Analysis (TCA) has been used to obtain the input data required for the investigation. The dynamic behavior and efficiency of a differential hypoid gear pair under realistic operating conditions is determined. The proposed tribo-dynamic framework provides a useful platform to conduct an extensive series of parametric studies.

scholarly journals Multiphysics Investigations on the Dynamics of Differential Hypoid Gears

2014 ◽  
Vol 136 (4) ◽  
Author(s):  
M. Mohammadpour ◽  
S. Theodossiades ◽  
H. Rahnejat
Keyword(s):  
Multiscale Analysis ◽  
Point Contact ◽  
Elastohydrodynamic Lubrication ◽  
Transmission Efficiency ◽  
Operating Conditions ◽  
Hypoid Gear ◽  
Tooth Contact Analysis ◽  
Hypoid Gears ◽  
Gear Teeth ◽  
Noise Vibration

Vehicular differential hypoid gears play an important role on the noise, vibration, and harshness (NVH) signature of the drivetrain system. Additionally, the generated friction between their mating teeth flanks under varying load-speed conditions is a source of power loss in a drivetrain while absorbing some of the vibration energy. This paper deals with the coupling between system dynamics and analytical tribology in multiphysics, multiscale analysis. Elastohydrodynamic lubrication (EHL) of elliptical point contact of partially conforming hypoid gear teeth pairs with non-Newtonian thermal shear of a thin lubricant film is considered, including boundary friction as the result of asperity interactions on the contiguous surfaces. Tooth contact analysis (TCA) has been used to obtain the input data required for such an analysis. The dynamic behavior and frictional losses of a differential hypoid gear pair under realistic operating conditions are therefore determined. The detailed analysis shows a strong link between NVH refinement and transmission efficiency, a finding not hitherto reported in literature.

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.

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.

The Isothermal Elastohydrodynamic Lubrication of Spheres

1981 ◽  
Vol 103 (4) ◽  
pp. 547-557 ◽  
Author(s):  
H. P. Evans ◽  
R. W. Snidle
Keyword(s):  
Iterative Method ◽  
Reynolds Equation ◽  
Point Contact ◽  
Numerical Procedure ◽  
Elastohydrodynamic Lubrication ◽  
Hydrodynamic Pressure ◽  
Operating Conditions ◽  
Analysis Of Results ◽  
Approximate Formulas ◽  
Pressure Analysis

The paper describes a numerical procedure for solving the point-contact elastohydrodynamic lubrication problem under isothermal conditions at moderate loads. Results are presented showing the shape of the film and variation of hydrodynamic pressure. Analysis of results for a range of operating conditions gives the following approximate formulas for minimum and central film thickness, repsectively: Hm = 1.9 M−0.17 L0.34 and Ho = 1.7 M−0.026 L0.40 where H, M, and L are the Moes and Bosma nondimensional groups. In common with earlier solutions based upon the forward-iterative method the solution breaks down under moderately heavily loaded conditions. Ways of extending the solution to heavier loads using the authors’ inverse solution of Reynolds’ equation under point-contact elastohydrodynamic conditions are discussed.

Mixed Elastohydrodynamic Lubrication With Three-Dimensional Machined Roughness in Spiral Bevel and Hypoid Gears

2015 ◽  
Vol 137 (4) ◽  
Author(s):  
Wei Pu ◽  
Jiaxu Wang ◽  
Rongsong Yang ◽  
Dong Zhu
Keyword(s):  
Three Dimensional ◽  
Elastohydrodynamic Lubrication ◽  
Operating Conditions ◽  
Strength Prediction ◽  
Flash Temperature ◽  
Hypoid Gears ◽  
Lubrication Performance ◽  
Lubrication Condition ◽  
Spiral Bevel ◽  
Film Lubrication

Spiral bevel and hypoid gears are key components widely used for transmitting significant power in various types of vehicles and engineering machineries. In reality, these gear surfaces are quite rough with three-dimensional (3D) topography that may significantly influence the lubrication formation and breakdown as well as components failures. Previous spiral bevel and hypoid gears lubrication studies, however, were limited mostly to cases under the full-film lubrication condition with smooth surfaces. In the present study, a comprehensive analysis for gearing geometry, kinematics, mixed lubrication performance, and friction and interfacial flash temperature in spiral bevel and hypoid gears is developed based on a recently developed mixed elastohydrodynamic lubrication (EHL) model that is capable of handling practical cases with 3D machined roughness under severe operating conditions and considering the effect of arbitrary entrainment angle. Obtained results from sample cases show that the simulation model developed can be used as an engineering tool for spiral bevel and hypoid gears design optimization and strength prediction.

Objektivierung der Tragbildprüfung/New Measurement Strategy for Quality Assurance of Lapped Hypoid Gear – Objectification of Contact Pattern Test

2021 ◽  
Vol 111 (06) ◽  
pp. 464-468
Author(s):  
Stefan Gerdhenrichs ◽  
Jimmy Chhor ◽  
Robert H. Schmitt
Keyword(s):  
Quality Assurance ◽  
Machine Vision ◽  
Expert Knowledge ◽  
Objective Evaluation ◽  
Operating Conditions ◽  
Contact Pattern ◽  
Hypoid Gear ◽  
Hypoid Gears ◽  
Measurement Strategy ◽  
Load Displacement

Die Fertigung und Prüfung geläppter Hypoidgetriebe basiert in der Praxis auf Erfahrungswissen und erschwert eine objektive Bewertung des Messverfahrens. Eine neu entwickelte Messstrategie nutzt simulierte Lastverschiebung und ein Bildverarbeitungssystem, um charakteristische Tragbildkennwerte aus erfassten Tragbildern in Mehrfachzahnkontakten zu extrahieren und erzielt unter Betriebsbedingungen erste vielversprechende Ergebnisse.   Current practices for manufacturing and testing of lapped hypoid gears exploit expert knowledge and impede an objective evaluation. A newly developed measurement strategy uses simulated load displacement and machine vision to extract characteristic contact pattern values in recordings of multiple tooth contacts. Early findings in operating conditions offer promising results and insights to this approach.

Flow Continuity of Isothermal Elastohydrodynamic Point-Contact Lubrication under Different Numerical Iteration Configurations

2021 ◽  
pp. 1-26
Author(s):  
Liangwei Qiu ◽  
Shuangbiao Liu ◽  
Zhijian Wang ◽  
Xiaoyang Chen
Keyword(s):  
Error Control ◽  
Multigrid Method ◽  
Point Contact ◽  
Elastohydrodynamic Lubrication ◽  
Operating Conditions ◽  
Point Contacts ◽  
Numerical Iteration ◽  
Mesh Method ◽  
Iteration Methods ◽  
Relaxation Factors

Abstract Elastohydrodynamic Lubrication (EHL) in point contacts can be numerically solved with various iteration methods, but so far the flow continuity of such solutions has not been explicitly verified. A series of closed regions with the same inlet side boundary is defined and two treatments to total all flows related to the other boundaries of the closed regions are defined to enable flow continuity verifications. The multigrid method and the traditional single mesh method with different relaxation configurations are utilized to solve different cases to evaluate computation efficiencies. For the multigrid method, the combination of a pointwise solver together with hybrid relaxation factors is identified to perform better than other combinations. The single mesh method has inferior degrees of flow continuity than the multigrid method and needs much smaller error control values of pressure to achieve a decent level of flow continuity. Because flow continuity has a physical meaning, its verifications should be routinely included in any self-validation process for any EHL results. Effects of control errors of pressure, mesh sizes, differential schemes and operating conditions on flow continuities are studied. Then, trends of film thickness with respect to speed are briefly discussed with meshes up to 4097 by 4097.

Flank Modification Methodology for Face-Hobbing Hypoid Gears Based on Ease-Off Topography

2006 ◽  
Vol 129 (12) ◽  
pp. 1294-1302 ◽  
Author(s):  
Yi-Pei Shih ◽  
Zhang-Hua Fong
Keyword(s):  
Design Parameters ◽  
Gear Pair ◽  
Hypoid Gear ◽  
Tooth Contact Analysis ◽  
General Technique ◽  
Local Synthesis ◽  
Hypoid Gears ◽  
Gear Drive ◽  
Polynomial Coefficients ◽  
Spiral Bevel

The fundamental design of spiral bevel and hypoid gears is usually based on a local synthesis and a tooth contact analysis of the gear drive. Recently, however, several flank modification methodologies have been developed to reduce running noise and avoid edge contact in gear making, including modulation of tooth surfaces under predesigned transmission errors. This paper proposes such a flank modification methodology for face-hobbing spiral bevel and hypoid gears based on the ease-off topography of the gear drive. First, the established mathematical model of a universal face-hobbing hypoid gear generator is applied to investigate the ease-off deviations of the design parameters—including cutter parameters, machine settings, and the polynomial coefficients of the auxiliary flank modification motion. Subsequently, linear regression is used to modify the tooth flanks of a gear pair to approximate the optimum ease-off topography suggested by experience. The proposed method is then illustrated using a numerical example of a face-hobbing hypoid gear pair from Oerlikon’s Spiroflex cutting system. This proposed flank modification methodology can be used as a basis for developing a general technique of flank modification for similar types of gears.

Mass Conserving Elastohydrodynamic Piston Lubrication Model With Incorporated Crown Lands

2007 ◽  
Author(s):  
Mustafa Duyar
Keyword(s):  
Elastohydrodynamic Lubrication ◽  
Cylinder Liner ◽  
Thermodynamic Cycle ◽  
Operating Conditions ◽  
Asperity Contact ◽  
Piston Skirt ◽  
Piston Crown ◽  
Parametric Studies ◽  
Volume Method ◽  
Crown Lands

This paper describes a comprehensive model of Elastohydrodynamic piston lubrication, incorporated the crown lands into solution domain to characterize the effect of crown-liner interactions on piston motion. Elastohydrodynamic Lubrication (EHL) analysis of a piston skirt-liner conjunction is in general a useful methodology for design analysis of pistons. The diameters of piston crown lands are much less than those of skirt and liner for typical piston designs. Therefore crown lands normally do not interact with liner under usual operating conditions and hence most of the researchers exclude crown lands from the EHL analysis and mainly focus on piston skirt. However, under some of the engine operating conditions piston crown lands play important role in the secondary dynamics and tribology aspects of pistons. During the thermodynamic cycle when piston is hot and cylinder liner is relatively colder, piston thermal expansion leads to crown-liner interaction, which necessitates EHL, asperity contact and wear considerations of piston crown along with piston skirt. The simulation methodology for piston EHL analysis uses a mass-conserving algorithm for the finite volume method solution of Reynolds equation, which is coupled to elasticity relations and Greenwood-Tripp asperity contact model. Elrod’s mass conserving algorithm enables to model and analyze partially lubricated piston-liner interface by the input of oil supply and moreover rigorously handles cavitated zones, and takes into account piston ring grooves, piston cut-outs and unlubricated areas due to piston geometry. Results are presented from parametric studies that show comparisons between the analyses of the models with piston skirt lubrication only and piston lubrication, which incorporates the crown lands to the EHL domain.

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