Optimal Machine-Tool Settings for the Manufacture of Face-Hobbed Spiral Bevel Gears

2014 ◽  
Vol 136 (8) ◽  
Author(s):  
Vilmos V. Simon
Keyword(s):  
Contact Pressure ◽  
Optimization Problem ◽  
Transmission Error ◽  
Search Method ◽  
Tooth Contact Analysis ◽  
Tooth Contact ◽  
Transmission Errors ◽  
Bevel Gears ◽  
Spiral Bevel ◽  
Loaded Tooth Contact Analysis

In this study, an optimization methodology is proposed to systematically define the optimal head-cutter geometry and machine-tool settings to simultaneously minimize the tooth contact pressure and angular displacement error of the driven gear (the transmission error), and to reduce the sensitivity of face-hobbed spiral bevel gears to the misalignments. The proposed optimization procedure relies heavily on the loaded tooth contact analysis for the prediction of tooth contact pressure distribution and transmission errors influenced by the misalignments inherent in the gear pair. The load distribution and transmission error calculation method employed in this study were developed by the author of this paper. The targeted optimization problem is a nonlinear constrained optimization problem, belonging to the framework of nonlinear programming. In addition, 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. For these reasons, a nonderivative method is selected to solve this particular optimization problem. That is the reason that the core algorithm of the proposed nonlinear programming procedure is based on a direct search method. The Hooke and Jeeves pattern search method is applied. The effectiveness of this optimization was demonstrated on a face-hobbed spiral bevel gear example. Drastic reductions in the maximum tooth contact pressure (62%) and in the transmission errors (70%) were obtained.

Optimal Machine Tool Settings for the Manufacture of Face-Hobbed Spiral Bevel Gears

2013 ◽  
Author(s):  
Vilmos V. Simon
Keyword(s):  
Machine Tool ◽  
Contact Pressure ◽  
Optimization Problem ◽  
Angular Displacement ◽  
Tooth Contact Analysis ◽  
Tooth Contact ◽  
Spiral Bevel Gears ◽  
Transmission Errors ◽  
Bevel Gears ◽  
Spiral Bevel

In this study, an optimization methodology is proposed to systematically define optimal head-cutter geometry and machine tool settings to simultaneously minimize tooth contact pressures and angular displacement error of the driven gear and to reduce the sensitivity of face-hobbed spiral bevel gears to misalignments, while concurrently confining the loaded contact pattern within the tooth boundaries and avoiding any edge- or corner-contact conditions. The proposed optimization procedure relies heavily on a loaded tooth contact analysis for the prediction of tooth contact pressure distribution and transmission errors influenced by the misalignments inherent in the gear pair. The targeted optimization problem is a nonlinear constrained optimization problem. The core algorithm of the proposed nonlinear programming procedure is based on a direct search method. Effectiveness of this optimization was demonstrated on a face-hobbed spiral bevel gear example. Drastic reductions in the maximum tooth contact pressure (62%) and in the transmission errors (70%) were obtained.

Loaded Tooth Contact Analysis and Stresses in Spiral Bevel Gears

2009 ◽  
Author(s):  
Vilmos V. Simon
Keyword(s):  
Contact Pressure ◽  
Angular Position ◽  
Contact Analysis ◽  
Tooth Contact Analysis ◽  
Tooth Contact ◽  
Spiral Bevel Gears ◽  
Bevel Gears ◽  
Exact Position ◽  
Spiral Bevel ◽  
Loaded Tooth Contact Analysis

The method for loaded tooth contact analysis is applied for the investigation of the influence of misalignments and tooth errors on load distribution, stresses and transmission errors in mismatched spiral bevel gears. By using the corresponding computer program the influence of pinion’s offset and axial adjustment error, angular position error of the pinion axis and tooth spacing error on tooth contact pressure, tooth root stresses and angular displacement of the driven gear member from the theoretically exact position based on the ratio of the numbers of teeth is investigated. The obtained results have shown that in general, the misalignments in spiral bevel gears worsen the conjugation of contacting tooth surfaces and in extreme cases cause edge contact with high tooth contact pressures. But, some mismatches, as are the axial movement of the pinion apex towards the gear teeth or the tip relief of pinion teeth (in this analysis it is represented by the tooth spacing error) reduce the maximum tooth contact pressure. Also it can be concluded that the misalignments and the tooth spacing errors significantly increase the angular position error of the driven gear from the theoretically exact position based on the numbers of teeth and make the motion graphs unbalanced.

Reduction of Sensitivity of Spiral Bevel Gears to Misalignments by the Use of Appropriate Machine Tool Settings

2007 ◽  
Author(s):  
Vilmos V. Simon
Keyword(s):  
Machine Tool ◽  
Contact Pressure ◽  
Angular Displacement ◽  
Angular Position ◽  
Tooth Contact Analysis ◽  
Tooth Contact ◽  
Spiral Bevel Gears ◽  
Transmission Errors ◽  
Bevel Gears ◽  
Spiral Bevel

The method for loaded tooth contact analysis is applied for the investigation of the combined influence of machine tool settings for pinion teeth finishing and misalignments of the mating members on load distribution and transmission errors in mismatched spiral bevel gears. By using the corresponding computer program the influence of pinion’s offset and axial adjustment error, angular position error of the pinion axis, tooth spacing error, and machine tool setting variation for pinion teeth finishing, on tooth contact pressure, tooth root stresses and angular displacement of the driven gear member from the theoretically exact position based on the ratio of the numbers of teeth is investigated. The obtained results show that by the use of appropriate machine tool settings the influence of misalignments and tooth errors on maximum tooth contact pressure and transmission errors can be significantly reduced.

Machine-Tool Settings to Reduce the Sensitivity of Spiral Bevel Gears to Tooth Errors and Misalignments

2008 ◽  
Vol 130 (8) ◽  
Author(s):  
Vilmos V. Simon
Keyword(s):  
Machine Tool ◽  
Contact Pressure ◽  
Angular Displacement ◽  
Angular Position ◽  
Slight Reduction ◽  
Tooth Contact ◽  
Spiral Bevel Gears ◽  
Transmission Errors ◽  
Bevel Gears ◽  
Spiral Bevel

The method for loaded tooth contact analysis is applied for the investigation of the combined influence of machine-tool settings for pinion teeth finishing and misalignments of the mating members on load distribution and transmission errors in mismatched spiral bevel gears. By using the corresponding computer program, the influence of pinion’s offset and axial adjustment error, angular position error of the pinion axis, tooth spacing error, and machine-tool setting correction for pinion teeth finishing, on tooth contact pressure, tooth root stresses, and angular displacement of the driven gear member from the theoretically exact position based on the ratio of the numbers of teeth is investigated. On the basis of the obtained results, the optimal combination of machine-tool settings is determined. By the use of this set of machine-tool settings, the maximum tooth contact pressure and transmission errors can be significantly reduced. However, in some cases, by the use of appropriate machine-tool settings for the reduction of tooth contact pressure, the angular displacement of the driven gear increases. Therefore, different optimized combinations of machine-tool settings for pinion tooth finishing for the reduction of the sensitivity of gears to misalignments in regard to maximum tooth contact pressure and transmission errors should be applied. By the use of the combination of machine-tool settings to reduce the sensitivity of gears to misalignments in regard to transmission errors, a slight reduction of maximal tooth contact pressure is achieved, too.

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.

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]

scholarly journals A Method for Thermal Analysis of Spiral Bevel Gears

1996 ◽  
Vol 118 (4) ◽  
pp. 580-585 ◽  
Author(s):  
R. F. Handschuh ◽  
T. P. Kicher
Keyword(s):  
Three Dimensional ◽  
Contact Analysis ◽  
Heat Transfer Analysis ◽  
Maximum Pressure ◽  
Tooth Contact Analysis ◽  
Tooth Contact ◽  
Finite Element Program ◽  
Spiral Bevel Gears ◽  
Bevel Gears ◽  
Spiral Bevel

A modelling method for analyzing the three-dimensional thermal behavior of spiral bevel gears has been developed. The model surfaces are generated through application of differential geometry to the manufacturing process for face-milled spiral bevel gears. Contact on the gear surface is found by combining tooth contact analysis with three-dimensional Hertzian theory. The tooth contact analysis provides the principle curvatures and orientations of the two surfaces. This information is then used directly in the Hertzian analysis to find the contact size and maximum pressure. Heat generation during meshing is determined as a function of the applied load, sliding velocity, and coefficient of friction. Each of these factors change as the point of contact changes during meshing. A nonlinear finite element program was used to conduct the heat transfer analysis. This program permitted the time- and position-varying boundary conditions, found in operation, to be applied to a one-tooth model. An example model and analytical results are presented.

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