218 Analysis of Tooth Contact and Transmission Error of Large-Sized Spiral Bevel Gears in Cyclo-Palloid System

2007 ◽  
Vol 2007 (0) ◽  
pp. 174-176
Author(s):  
Isamu TSUJI ◽  
Kazumasa KAWASAKI
Keyword(s):  
Transmission Error ◽  
Tooth Contact ◽  
Spiral Bevel Gears ◽  
Bevel Gears ◽  
Spiral Bevel

An Extremum Principle for Computation of the Zone of Tooth Contact and Generalized Transmission Error of Spiral Bevel Gears

1988 ◽  
Vol 110 (2) ◽  
pp. 211-220 ◽  
Author(s):  
W. D. Mark
Keyword(s):  
Computational Procedure ◽  
Transmission Error ◽  
Error Component ◽  
Tooth Contact ◽  
Spiral Bevel Gears ◽  
Bevel Gears ◽  
Spiral Bevel ◽  
True Values ◽  
Method Of Steepest Descent ◽  
Three Components

For a given set of forces transmitted by the gears, each of the three components of the generalized transmission error of spiral bevel gears is shown to be stationary with respect to small independent variations in the positions of the endpoints of the lines of tooth contact about their true values. The tangential generalized transmission error component is shown to take on a minimum value at the true endpoint positions. A computational procedure based on the method of steepest descent is described for computing the true line of contact endpoint positions and the three components of the generalized transmission error. A method for computing the Fourier series coefficients of the tooth meshing harmonics of the three generalized transmission error components also is provided.

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.

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.

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.

Kinematical Optimization of Spiral Bevel Gears

1992 ◽  
Author(s):  
Zhang-Hua Fong ◽  
Chung-Biau Tsay
Keyword(s):  
Mathematical Model ◽  
Bevel Gear ◽  
Tooth Surface ◽  
Spiral Bevel Gear ◽  
Tooth Contact ◽  
Spiral Bevel Gears ◽  
Bevel Gears ◽  
Contact Patterns ◽  
Spiral Bevel ◽  
Kinematic Errors

Abstract Kinematical optimization and sensitivity analysis of circular-cut spiral bevel gears are investigated in this paper. Based on the Gleason spiral bevel gear generator and EPG test machine, a mathematical model is proposed to simulate the tooth contact conditions of the spiral bevel gear set. All the machine settings and assembly data are simulated by simplified parameters. The tooth contact patterns and kinematic errors are obtained by the proposed mathematical model and the tooth contact analysis techniques. Loaded tooth contact patterns are obtained by the differential geometry and the Hertz contact formulas. Tooth surface sensitivity due to the variation of machine settings is studied. The corrective machine settings can be calculated by the sensitive matrix and the linear regression method. An optimization algorithm is also developed to minimize the kinematic errors and the discontinuity of tooth meshing. According to the proposed studies, an improved procedure for development of spiral bevel gears is suggested. The results of this paper can be applied to determine the sensitivity and precision requirements in manufacturing, and improve the running quality of the spiral bevel gears. Two examples are presented to demonstrate the applications of the optimization model.

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.

Design and analysis of high contact ratio spiral bevel gears by modified curvature motion method

2017 ◽  
Vol 232 (19) ◽  
pp. 3396-3409 ◽  
Author(s):  
Yanming Mu ◽  
Zongde Fang
Keyword(s):  
Transmission Error ◽  
Bevel Gear ◽  
Spiral Bevel Gear ◽  
Contact Ratio ◽  
Spiral Bevel Gears ◽  
Bevel Gears ◽  
Curvature Motion ◽  
Seventh Order ◽  
Spiral Bevel ◽  
Motion Method

This paper presents a new method to design a seventh-order transmission error for high contact ratio spiral bevel gears by the modified curvature motion method to reach the purpose of reducing or eliminating gear vibration and noise. In this paper, firstly, based on the predesigned seventh-order transmission error, the polynomial coefficients of transmission error curve can be obtained. Secondly, a method named modified curvature motion method is used to generate the spiral bevel gear with the predesigned transmission error. Lastly, based on TCA and LTCA, we verify the feasibility of the modified curvature motion method to generate spiral bevel gear with seventh-order transmission error, and the meshing impact of gear set with the seventh-order and second-order function of transmission error is analyzed and compared. The results of a numerical example show that the seventh-order transmission error acquired by the modified curvature motion method can effectively reduce the meshing impact of spiral bevel gears. The tooth modification method and meshing impact analysis method can serve as a basis for developing a general technique of flank modification for spiral bevel gears.

Computerized Design and FE Simulation of Meshing of Involute Spiral Bevel Gears with Alignment Errors

2011 ◽  
Vol 199-200 ◽  
pp. 386-391 ◽  
Author(s):  
Ben Wang ◽  
Lin Hua
Keyword(s):  
Fe Simulation ◽  
Transmission Error ◽  
Load Carrying Capacity ◽  
Spiral Bevel Gears ◽  
Bevel Gears ◽  
Load Carrying ◽  
Contact Models ◽  
Stress Transmission ◽  
Spiral Bevel ◽  
Alignment Errors

Influence of alignment errors on the meshing of involute spiral bevel gears using FEM is investigated in this paper. 3D geometrical models of involute spiral bevel gear drive are computationally designed and the reliable non-linear finite element contact models are also developed. Furthermore, based on the valid 3D FE models, simulations of meshing of loaded spiral bevel gears with four types of alignment errors are performed. The influence of four types of alignment errors on contact stress, transmission error and shift of path of contact has been discussed in detail. The results demonstrate that the alignment errors have different degrees of adverse effects on the load-carrying capacity and the smoothness of transmission. Therefore, the study provides useful reference for the modification design and the assembling of spiral bevel gears in practice.

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