scholarly journals Design of Pinion Machine Tool-settings for Spiral Bevel Gears by Controlling Contact Path and Transmission Errors

2008 ◽  
Vol 21 (2) ◽  
pp. 179-186 ◽  
Author(s):  
Cao Xuemei ◽  
Fang Zongde ◽  
Xu Hao ◽  
Su Jinzhan
Keyword(s):  
Machine Tool ◽  
Spiral Bevel Gears ◽  
Transmission Errors ◽  
Bevel Gears ◽  
Spiral Bevel

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.

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.

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.

Design and Manufacture of Spiral Bevel Gears With Reduced Transmission Errors

2008 ◽  
Author(s):  
V. Simon
Keyword(s):  
Contact Point ◽  
Tooth Surface ◽  
Initial Contact ◽  
Generation Process ◽  
Polynomial Functions ◽  
Spiral Bevel Gears ◽  
Transmission Errors ◽  
Bevel Gears ◽  
Spiral Bevel ◽  
Two Sides

A method for the determination of the optimal polynomial functions for the conduction of machine-tool setting variations in pinion teeth finishing in order to reduce the transmission errors in spiral bevel gears is presented. Polynomial functions of order up to five are applied to conduct the variation of the cradle radial setting and of the cutting ratio in the process for pinion teeth generation. Two cases were investigated: in the first case the coefficients of the polynomial functions are constant throughout the whole generation process of one pinion tooth-surface, in the second case the coefficients are different for the generation of the pinion tooth-surface on the two sides of the initial contact point. The obtained results have shown that by the use of two different fifth-order polynomial functions for the variation of the cradle radial setting for the generation of the pinion tooth-surface on the two sides of the initial contact point, the maximum transmission error can be reduced by 81%. By the use of the optimal modified roll, this reduction is 61%. The obtained results have also shown that by the optimal variation of the cradle radial setting, the influence of misalignments inherent in the spiral bevel gear pair and of the transmitted torque on the increase of transmission errors can be considerably reduced.

Design and Manufacture of Spiral Bevel Gears With Reduced Transmission Errors

2009 ◽  
Vol 131 (4) ◽  
Author(s):  
Vilmos V. Simon
Keyword(s):  
Contact Point ◽  
Tooth Surface ◽  
Initial Contact ◽  
Generation Process ◽  
Polynomial Functions ◽  
Spiral Bevel Gears ◽  
Transmission Errors ◽  
Bevel Gears ◽  
Spiral Bevel ◽  
Two Sides

A method for the determination of the optimal polynomial functions for the conduction of machine-tool setting variations in pinion teeth finishing in order to reduce the transmission errors in spiral bevel gears is presented. Polynomial functions of order up to 5 are applied to conduct the variation in the cradle radial setting and in the cutting ratio in the process for pinion teeth generation. Two cases were investigated: In the first case, the coefficients of the polynomial functions are constant throughout the whole generation process of one pinion tooth-surface; in the second case, the coefficients are different for the generation of the pinion tooth-surface on the two sides of the initial contact point. The obtained results have shown that by the use of two different fifth-order polynomial functions for the variation in the cradle radial setting for the generation of the pinion tooth-surface on the two sides of the initial contact point, the maximum transmission error can be reduced by 81%. By the use of the optimal modified roll, this reduction is 61%. The obtained results have also shown that by the optimal variation in the cradle radial setting, the influence of misalignments inherent in the spiral bevel gear pair and of the transmitted torque on the increase in transmission errors can be considerably reduced.

Analytical Determination of Basic Machine-Tool Settings for Generation of Spiral Bevel Gears From Blank Data

2010 ◽  
Vol 132 (10) ◽  
Author(s):  
Ignacio Gonzalez-Perez ◽  
Alfonso Fuentes ◽  
Kenichi Hayasaka
Keyword(s):  
Machine Tool ◽  
Analytical Determination ◽  
Local Synthesis ◽  
Spiral Bevel Gears ◽  
Bevel Gears ◽  
Face Width ◽  
The Face ◽  
Shaft Angle ◽  
Spiral Bevel

An approach for analytical determination of basic machine-tool settings for generation of spiral bevel gears from blank data is proposed. Generation by face-milling is considered. The analytical procedure is based on the similitudes between the conditions of generation between the gear member and its head-cutter and the conditions of imaginary meshing between the gear member and its crown gear. The blank data considered are the number of teeth of the pinion and the gear, the module, the spiral and pressure angles, the face width, the shaft angle, the depth factor, the clearance factor, and the mean addendum factor. These starting data can be established following the directions of the Standard ANSI/AGMA 2005-D03. Once the gear machine-tool settings are determined, an existing approach of local synthesis is applied to determine the pinion machine-tool settings that provide the desired conditions of meshing and contact of the gear drive. The developed theory is illustrated with a numerical example.

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