New Calculation Method for the Load Capacity of Bevel And Hypoid Gears Based on Loaded Tooth Contact Analysis

2011 ◽  
Vol 86 ◽  
pp. 237-242 ◽  
Author(s):  
Bernd Robert Höhn ◽  
Karsten Stahl ◽  
Christian Wirth
Keyword(s):  
Calculation Method ◽  
Load Capacity ◽  
Experimental Investigations ◽  
Tooth Root ◽  
Test Results ◽  
Tooth Contact Analysis ◽  
Hypoid Gears ◽  
Helical Gears ◽  
Bevel Gears ◽  
Loaded Tooth Contact Analysis

At the FZG (Gear Research Centre, Munich, Germany) a research project was carried out to analyze the influence of the hypoid offset on the load capacity of bevel gears by systematic theoretical and experimental investigations. For the experimental investigations two types of bevel gears were designed, one for the pitting tests and one for the tooth root tests. The results of the tooth root tests showed as expected an increasing load capacity with higher offsets. In contrast the pitting tests showed an increasing, but after reaching a maximum, a decreasing load capacity with higher offsets. Regarding the test results a new calculation method was developed that is based on a loaded tooth contact analysis (LTCA). The method is able to consider the local stresses on the flank and in the tooth root. The local strength values are derived out of the standard ISO 6336 for the calculation of helical gears. For bending the local geometry of the tooth root is considered to adopt the strength values of helical gears to bevel and hypoid gears. As a result the local safety factors might be calculated along the face width of pinion and wheel. For pitting the local sliding conditions are taken into account in order to appraise the local lubrication conditions as well as the risk of crack initiations due to shear stresses and higher contact temperatures. The recalculation of the test showed for both types of failure a good correlation between the test results and the calculated values.

Pitting Load Capacity of Helical Gears

2007 ◽  
Author(s):  
Bernd-Robert Ho¨hn ◽  
Peter Oster ◽  
Gregor Steinberger
Keyword(s):  
Calculation Method ◽  
Load Distribution ◽  
Load Capacity ◽  
Test Results ◽  
Calculation Methods ◽  
Helical Gears ◽  
Capacity Calculation ◽  
Overlap Ratio ◽  
Tooth Flank

In experimental analyzes the pitting load capacity of case carburized spur and helical gears is determined in back-to-back test rigs. The research program with one type of spur and 8 types of helical gears includes tests for the determination of influences of varying load distribution, overlap ratio and transmission ratio. The test results are presented and evaluated on the basis of the pitting load capacity calculation methods of ISO 6336-2/DIN 3990, part 2. A new DIN/ISO compatible calculation method for pitting load capacity is presented. This new calculation method comprehends helical gears more adequate than ISO 6336-2 / DIN 3990, part 2 and has the possibility to consider tooth flank modifications. The new calculation method is applied on test results and gears of a calculation study. It shows better accordance with the experimental test results than the present ISO 6336-2 / DIN 3990, part 2.

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 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.

Optimization of Face Cone Element for Spiral Bevel and Hypoid Gears

2011 ◽  
Author(s):  
Qi Fan
Keyword(s):  
Tip Clearance ◽  
Tooth Surface ◽  
Root Tip ◽  
Tooth Root ◽  
Contact Ratio ◽  
Tooth Contact Analysis ◽  
Hypoid Gears ◽  
Straight Line ◽  
The Face ◽  
Spiral Bevel

In the blank design of spiral bevel and hypoid gears, the face cone is defined as an imaginary cone tangent to the tops of the teeth. Traditionally, the face cone element or generatrix is a straight line. On the other hand, the tooth root lines which are traced by the blade tips are normally not straight lines. As a result, the tooth top geometry generally does not fit the mating member’s real root shape, providing an uneven tooth root-tip clearance; additionally, in some cases root-tip interference between the tooth tip and the root tooth surfaces of the mating gear members may be observed. To address this issue, this paper describes a method of determining an optimized face cone element for spiral bevel and hypoid gears. The method is based on the incorporation of calculation of tooth surface and root geometries, the conjugate relationship of the mating gear members, the ease-off topography, and the tooth contact analysis. The resulting face cone element may not be a straight line but generally an optimized curve that, in addition to avoidance of the interference, offers maximized contact ratio and even tooth root-tip clearance. Manufacturing of bevel gear blanks with a curved face cone element can be implemented by using computer numerically controlled (CNC) machines.

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.

Pitting Resistance and Bending Strength of Bevel and Hypoid Gear Teeth

1992 ◽  
Author(s):  
B.-R. Höhn ◽  
H. Winter ◽  
K. Michaelis ◽  
F. Vollhüter
Keyword(s):  
Bending Strength ◽  
Load Carrying Capacity ◽  
Test Results ◽  
Hypoid Gear ◽  
Hypoid Gears ◽  
Gear Teeth ◽  
Bevel Gears ◽  
Load Carrying ◽  
Calculation Results ◽  
Good Agreement

Abstract Bevel and hypoid gears are widely used for gears with crossed axis. The influence of a pinion offset on the load carrying capacity — pitting resistance and bending strength — is introduced in a different way in commonly used calculation methods. Load carrying and measurement investigations on the influence of pinion offset on pitting resistance and bending strength are reported. Tests show an increasing bending strength and decreasing maximum tooth root stresses with increasing pinion offset. Also a slight increase of pitting resistance and a slight decrease of the Hertzian pressure was evaluated. The load carrying calculation results for bevel gears without pinion offset, DIN 3991, is in good agreement with test results. The bending strength of hypoid gears calculated according to Niemann/Winter, is greater than that experimentally measured. For pitting resistance, however, the calculation is less than the measured results.

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.

Loaded TCA of Measured Tooth Flanks for Lapped Hypoid Gears

2007 ◽  
Author(s):  
Kohei Saiki ◽  
Keiichiro Tobisawa ◽  
Masaki Kano ◽  
Yasuharu Ohnishi ◽  
Takashi Kusaka
Keyword(s):  
Coordinate Measuring Machine ◽  
Contact Pattern ◽  
Tooth Contact Analysis ◽  
Tooth Contact ◽  
Hypoid Gears ◽  
Practical Applications ◽  
Wheel Drive ◽  
Measuring Machine ◽  
Loaded Tooth Contact Analysis ◽  
Shape Data

Usually, the Loaded Tooth Contact Analysis (i.e. LTCA) of hypoid gears uses the nominal tooth flanks described by the machine setting and the cutter specifications. Only a few studies are performed on the LTCA directly using the measured tooth flanks such as carbonize-hardened and lapped hypoid gears. This paper presents an innovative LTCA method directly using the measured tooth flanks at each manufacturing step including not only the milling or hobbing process but also the troublesome heat-treatment, lapping or grinding processes. The proposed new LTCA method is extremely concise. Firstly, the 3-D shape data of the manufactured tooth flanks, which are the original x-y-z coordinates but not the differences against their nominal tooth flanks as before, are obtained on a coordinate-measuring machine. Another important factors the load deflections are measured on the assembled transmission by applying the static transmitting torque. Secondly, the pinion and gear are localized at the nominal mounting position, and the no load TCA can be obtained by calculating the gap between the original tooth flanks at each roll angle. Lastly, since the load deflections can be considered as the movement of mounting position, the Loaded TCA can be obtained by calculating the gap between the moved tooth flanks at new mounting position. As practical applications, the new LTCA method is used to improve the strength of high-torque hypoid gears for an All-Wheel-Drive transmission. As a result, the tooth contact pattern and pitting position observed in endurance test agreed well to the LTCA predictions and the demanding life is achieved by modifying the loaded contact pattern of lapped hypoid gears.

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