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 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.

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.

Manufacture of Optimized Face-Hobbed Spiral Bevel Gears on Computer Numerical Control Hypoid Generator

2014 ◽  
Vol 136 (3) ◽  
Author(s):  
Vilmos V. Simon
Keyword(s):  
Machine Tool ◽  
Angular Displacement ◽  
Transmission Error ◽  
Numerical Control ◽  
Tooth Surface ◽  
Surface Geometry ◽  
Tooth Contact ◽  
Spiral Bevel Gears ◽  
Bevel Gears ◽  
Spiral Bevel

In this study, a method is proposed for the advanced manufacture of face-hobbed spiral bevel gears on CNC hypoid generators with optimized tooth surface geometry. An optimization methodology is applied to systematically define optimal head-cutter geometry and machine tool settings to introduce optimal tooth modifications. The goal of the optimization is to simultaneously minimize tooth contact pressures and angular displacement error of the driven gear (the transmission error). The optimization is based on machine tool setting variation on the cradle-type generator conducted by optimal polynomial functions. An algorithm is developed for the execution of motions on the CNC hypoid generator using the relations on the cradle-type machine. Effectiveness of the method was demonstrated by using a face-hobbed spiral bevel gear example. Significant reductions in the maximum tooth contact pressure and in the transmission errors were obtained.

Computerized Design and Tooth Contact Analysis of Spiral Bevel Gears Generated by the Duplex Helical Method

2011 ◽  
Author(s):  
Ignacio Gonzalez-Perez ◽  
Alfonso Fuentes ◽  
Kenichi Hayasaka
Keyword(s):  
Machine Tool ◽  
Contact Analysis ◽  
Spiral Bevel Gear ◽  
Contact Pattern ◽  
Tooth Contact Analysis ◽  
Spiral Bevel Gears ◽  
Transmission Errors ◽  
Bevel Gears ◽  
Gear Drive ◽  
Spiral Bevel

The duplex helical method, among the different generation methods of spiral bevel gears, has shorter times of manufacturing since both sides of the gear tooth are generated simultaneously. The duplex helical method is based on the application of a helical motion of the cradle respect to the gear blank during the infeed of the sliding base on which the work spindle is mounted. Computerized design and generation of spiral bevel gears by the duplex helical method is a complex problem since the machine-tool settings are specific for each hypoid generator and optimization of the contact pattern and the function of transmission errors is not straightforward. The proposed goals in this research paper are as follows: (i) conversion of the specific machine-tool settings of a given hypoid generator to the so-called neutral machine-tool settings that can be applied at any hypoid generator, (ii) computerized generation of the generated spiral bevel gears by the duplex helical method considering the neutral-machine tool settings, (iii) illustration of results of tooth contact analysis of a spiral bevel gear drive where the pinion has been generated by the duplex helical method for investigation of the contact pattern and the function of transmission errors, and (iv) adjustment of the contact pattern by considering parabolic profiles on the blades of the head-cutter. A numerical example is represented considering a spiral bevel gear drive generated at the Hypoid Generator 106 of Gleason.

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.

Assembly interference and its avoidance of spiral bevel gears in cyclo-palloid system

2019 ◽  
Vol 234 (2) ◽  
pp. 704-717
Author(s):  
Isamu Tsuji ◽  
Kazumasa Kawasaki
Keyword(s):  
Contact Analysis ◽  
Experimental Results ◽  
Tooth Contact Analysis ◽  
Tooth Contact ◽  
Spiral Bevel Gears ◽  
Bevel Gears ◽  
Tooth Surfaces ◽  
Spiral Bevel ◽  
Good Agreement

In this article, the assembly interference of spiral bevel gears in a Klingelnberg cyclo-palloid system is analyzed based upon tooth contact analysis and is investigated experimentally. Each backlash in increasing mounting distance of the pinion is calculated step by step, using developed tooth contact analysis. When the backlash increases, the assembly interference does not occur based upon the calculated results. When the backlash decreases and is less than zero, the assembly interference occurs. When the assembly interference occurs, the tooth surfaces should be modified in order to prevent the assembly interference. In this case, a method of the modification is proposed. The experimental results showed a good agreement with the analyzed ones. As a result, the validity of the analysis and avoidance of the assembly interference in this method was confirmed.

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