Load Distribution in Hypoid Gears

1998 ◽  
Vol 122 (4) ◽  
pp. 529-535 ◽  
Author(s):  
Vilmos Simon
Keyword(s):  
Load Distribution ◽  
Point Contact ◽  
Relaxation Method ◽  
Contact Pattern ◽  
Design Data ◽  
New Approach ◽  
Hypoid Gears ◽  
Gear Teeth ◽  
Tooth Surfaces ◽  
Elliptical Contact

A new approach for the computerized simulation of load distribution in mismatched hypoid gears with point contact is presented. The load distribution calculation is based on the bending and shearing deflections of gear teeth, on the local contact deformations of the mating surfaces, on gear body bending and torsion, on the deflections of the supporting shafts, and on the manufacturing and alignment errors of the mating members. The tooth deflections of the pinion and gear teeth are calculated by FEM, and the tooth contact is treated in a special way: it is assumed that the point contact under load spreads over a surface along the “potential” contact line, which line is made up of the points of the mating tooth surfaces in which the separations of these surfaces are minimal, instead of assuming an elliptical contact pattern. The system of governing equations is solved by approximations and by using the successive-over-relaxation method. The corresponding computer program is developed. The calculations, performed by this program, show that in the case of hypoid gears, the new approach gives a more realistic contact pattern and contact pressure than the usually assumed and applied elliptical contact approach, especially for the tooth pairs contacting on the toe and on the heel of teeth, and in the case of load distribution calculations made in misaligned gear pairs. By using this program the influence of design data on load distribution parameters is investigated and discussed. [S1050-0472(00)00504-3]

Load Distribution in Spiral Bevel Gears

2006 ◽  
Vol 129 (2) ◽  
pp. 201-209 ◽  
Author(s):  
Vilmos Simon
Keyword(s):  
Load Distribution ◽  
Point Contact ◽  
Design Data ◽  
Tooth Contact ◽  
Spiral Bevel Gears ◽  
Gear Teeth ◽  
Bevel Gears ◽  
Tooth Surfaces ◽  
Machine Theory ◽  
Spiral Bevel

A new approach for the computerized simulation of load distribution in mismatched spiral bevel gears with point contact is presented. The loaded tooth contact is treated in a special way: it is assumed that the point contact under load spreads over a surface along the “potential” contact line (Simon, 2006, Mech. and Machine Theory, in press), which line is made up of the points of the mating tooth surfaces in which the separations of these surfaces are minimal, instead of assuming the usually applied elliptical contact area. The bending and shearing deflections of gear teeth, the local contact deformations of mating surfaces, gear body bending and torsion, the deflections of supporting shafts, and the manufacturing and alignment errors of mating members are included. The tooth deflections of the pinion and gear teeth are calculated by the finite element method. As the equations governing the load sharing among the engaged tooth pairs and load distribution along the tooth face are nonlinear, an approximate and iterative technique is used to solve this system of equations. The method is implemented by a computer program. By using this program the load and tooth contact pressure distributions, the angular displacements of the driven gear and the stresses in the pinion and gear teeth are calculated. The influence of design data and transmitted torque on load distribution parameters and fillet stresses is investigated and discussed.

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 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.

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.

Influence of Misalignments on EHD Lubrication in Hypoid Gears

2007 ◽  
Author(s):  
Vilmos V. Simon
Keyword(s):  
Angular Position ◽  
Density Variation ◽  
Oil Viscosity ◽  
Hypoid Gears ◽  
Oil Film ◽  
Gear Teeth ◽  
Ehd Lubrication ◽  
Load Carrying ◽  
Tooth Surfaces ◽  
Oil Film Pressure

The thermal elastohydrodynamic analysis of lubrication is applied to investigate the influence of misalignments of the meshing members on EHD lubrication in hypoid gears. The calculation is based on the simultaneous solution of the Reynolds, elasticity, energy, and Laplace’s equations. The full thermal EHD lubrication analysis is applied, therefore, the oil viscosity variation with respect to pressure and temperature and the density variation with respect to pressure are included. The real shape of the gap existing between the contacting tooth surfaces is treated, based on gear teeth geometry defined by the gear processing method and including the misalignments of mating members. By using the corresponding computer program, the influence of pinion’s running offset and axial adjustment errors, and angular position error of pinion axis on maximum oil film pressure and temperature, EHD load carrying capacity, and on power losses in the oil film is investigated. The obtained results are presented and discussed.

Load Distribution in Cylindrical Worm Gears

2000 ◽  
Author(s):  
Vilmos V. Simon
Keyword(s):  
Load Distribution ◽  
Gear Tooth ◽  
Point Contact ◽  
Transmission Error ◽  
Worm Gear ◽  
Gear Teeth ◽  
Total Transmission ◽  
Transmission Errors ◽  
Gear Drive ◽  
Worm Gears

Abstract A method for the determination of load sharing between the instantaneously engaged worm threads and gear teeth, for the calculation of load distribution along the teeth and transmission errors in different types of cylindrical worm gears is presented. The method covers both cases — that of the theoretical line and point contact. The bending and shearing deflections of worm thread and gear tooth, the local contact deformations of the mating surfaces, the axial deformations of worm body, gear body bending and torsion, deflections of the supporting shafts, and the manufacturing and alignment errors of worm and gear are included. Based on the real load distribution the tooth contact pressure is calculated, in the case of point contact in two different ways, and the obtained results are compared. Also, the total transmission error, consisting of the kinematical transmission error due to the mismatch of the worm gear drive and of the transmission error caused by the deflections of worm thread and gear teeth, is calculated. The method is implemented by a computer program. By using this program the influence of the type of worm gear drive and of design and manufacturing parameters on load distribution and transmission errors is investigated and discussed.

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.

Influence of Tooth Modifications on Load Distribution in Face-Hobbed Spiral Bevel Gears

2011 ◽  
Author(s):  
Vilmos V. Simon
Keyword(s):  
Load Distribution ◽  
Point Contact ◽  
Surface Generation ◽  
Tooth Surface ◽  
Spiral Bevel Gears ◽  
Bevel Gears ◽  
Distribution Calculation ◽  
Potential Contact ◽  
Tooth Surfaces ◽  
Spiral Bevel

In this study a novel method for load distribution calculation is applied to investigate the influence of tooth modifications on loaded tooth contact in face-hobbed spiral bevel gears. As a result of these modifications introduced to the teeth of the pinion, the gear pair becomes mismatched, and a point contact replaces the theoretical line contact. In the applied load distribution calculation it is assumed that the point contact under load is spreading over a surface along the whole or part of the “potential” contact line, which line is made up of the points of the mating tooth surfaces in which the separations of these surfaces are minimal. The separations of contacting tooth surfaces are calculated by applying the full theory of tooth surface generation in face-hobbed spiral bevel gears. A computer program was developed to implement the formulation provided above. By using this program the influence of tooth modifications introduced by the variation in machine tool settings and in head cutter profile on load and pressure distributions, transmission errors, and fillet stresses is investigated and discussed.

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