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.

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.

scholarly journals EHL Analysis of Spiral Bevel Gear Pairs considering the Contact Point Migration due to Deformation under Load

2020 ◽  
Vol 2020 ◽  
pp. 1-19
Author(s):  
Xiaoyu Sun ◽  
Yanping Liu ◽  
Yongqiang Zhao ◽  
Ming Liu
Keyword(s):  
Contact Point ◽  
Bevel Gear ◽  
Tooth Surface ◽  
Spiral Bevel Gear ◽  
Gear Pair ◽  
Spiral Bevel Gears ◽  
Actual Contact ◽  
Bevel Gears ◽  
Contact Points ◽  
Spiral Bevel

The actual contact point of a spiral bevel gear pair deviates from the theoretical contact point due to the gear deformation caused by the load. However, changes in meshing characteristics due to the migration of contact points are often ignored in previous studies on the elastohydrodynamic lubrication (EHL) analysis of spiral bevel gears. The purpose of this article is to analyze the impact of contact point migration on the results of EHL analysis. Loaded tooth contact analysis (LTCA) based on the finite element method is applied to determine the loaded contact point of the meshing tooth pair. Then, the osculating paraboloids at this point are extracted from the gear tooth surface geometry. The geometric and kinematic parameters for EHL simulation are determined according to the differential geometry theory. Numerical solutions to the Newtonian isothermal EHL of a spiral bevel gear pair at the migrated and theoretical contact points are compared to quantify the error involved in neglecting the contact point adjustment. The results show that under heavy-loaded conditions, the actual contact point of the deformed gear pair at a given pinion (gear) roll angle is different from the theoretical contact point considerably, and so do the meshing parameters. EHL analysis of spiral bevel gears under significant load using theoretical meshing parameters will result in obvious errors, especially in the prediction of film thickness.

Realization of Expected Direction Angle of SGM Spiral Bevel Gears Based on Local Synthesis

2010 ◽  
Vol 37-38 ◽  
pp. 927-933 ◽  
Author(s):  
Guang Lei Liu ◽  
Yue Jun Tian ◽  
Ping Jiang
Keyword(s):  
Objective Function ◽  
Contact Point ◽  
Optimization Method ◽  
Function Optimization ◽  
Tooth Surface ◽  
Tooth Contact Analysis ◽  
Local Synthesis ◽  
Spiral Bevel Gears ◽  
Bevel Gears ◽  
Spiral Bevel

The authors propose an optimization method based on local synthesis to fulfill the expected contact path (ECP) at mean contact point (M) of spiral bevel gears. The method is a combination of local synthesis, tooth contact analysis (TCA) and application of optimization. Machine-tool settings based on local synthesis are found and contact path (CP) on tooth surface is formed. TCA extracts the information from CP and transforms it to a projected CP (PCP) by rotation in a plane across gear axis. An objective function is established by contrasting ECP to PCP. A program in Matlab language is developed for the simulation of objective function optimization. A spiral bevel gear drive in aviation accessory gear box is used to prove the feasibility of the proposed method. It shows that the method is effective and does not affect transmission errors very much for the realization of ECP.

Geometry of Tooth Profile and Fillet of Face-Hobbed Spiral Bevel Gears

2007 ◽  
Author(s):  
Yi Zhang ◽  
Zhi Wu
Keyword(s):  
Gear Tooth ◽  
Mathematical Formulation ◽  
Tooth Profile ◽  
Tooth Surface ◽  
Generation Process ◽  
Tooth Contact Analysis ◽  
Spiral Bevel Gears ◽  
Bevel Gears ◽  
Spiral Bevel

The determination of the geometry for the whole tooth profile, including the meshing profile and the tooth fillet, is important for tooth contact analysis and the mesh generation for FEM analysis of gear pairs. This paper presents a systematic approach for the determination of the complete tooth geometry of face-hobbed hypoid and spiral bevel gears. The detailed mathematical formulation for the generation of gear tooth surface and the equations for the tooth surface coordinates are provided in the paper. The surface coordinates and normal vectors are calculated at grid points selected based on the gear blank dimension. Using the machine tool settings as input, the computer model simulating the gear generation process precisely calculates the tooth geometry parameters on the selected grid. A numerical example is included in the paper to illustrate the presented approach.

scholarly journals Lubrication characteristics of gear after shot peening base on 25-pellet model

2018 ◽  
Vol 10 (7) ◽  
pp. 168781401879065 ◽  
Author(s):  
Shuai Mo ◽  
Shengping Zhu ◽  
Guoguang Jin ◽  
Jiabei Gong ◽  
Zhanyong Feng ◽  
...  
Keyword(s):  
Shot Peening ◽  
High Speed ◽  
Target Material ◽  
Bevel Gear ◽  
Tooth Surface ◽  
Spiral Bevel Gear ◽  
Spiral Bevel Gears ◽  
Bevel Gears ◽  
Spiral Bevel ◽  
Lubrication Characteristics

High-speed heavy-load spiral bevel gears put forward high requirement for flexural strength; shot peening is a technique that greatly improves the bending fatigue strength of gears. During shot peening, a large number of fine pellets bombard the surface of the metal target material at very high speeds and let the target material undergo plastic deformation, at the same time strengthening layer is produced. Spiral bevel gear as the object of being bombarded inevitably brought the tooth surface micro-morphology changes. In this article, we aim to reveal the effect of microtopography of tooth shot peening on gear lubrication in spiral bevel gear, try to establish a reasonable description of the microscopic morphology for tooth surface by shot peening, to reveal the lubrication characteristics of spiral bevel gears after shot peening treatment based on the lubrication theory, and do comparative research on the surface lubrication characteristics of a variety of microstructures.

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.

Mathematical Modeling and Simulation of the External and Internal Double Circular-Arc Spiral Bevel Gears for the Nutation Drive

2010 ◽  
Vol 132 (2) ◽  
Author(s):  
Ligang Yao ◽  
Bing Gu ◽  
Shujuan Haung ◽  
Guowu Wei ◽  
Jian S. Dai
Keyword(s):  
Mathematical Modeling ◽  
Numerical Control ◽  
Tooth Surface ◽  
Circular Arc ◽  
Spiral Bevel Gears ◽  
Bevel Gears ◽  
Nc Simulation ◽  
Helical Angle ◽  
Nc Milling ◽  
Spiral Bevel

The purpose of this paper is to propose a pair of external and internal spiral bevel gears with double circular-arc in the nutation drive. Based on the movement of nutation, this paper develops equations of the tooth profiles for the gear set, leading to the mathematical modeling of the spiral bevel gear with a constant helical angle gear alignment curve, enabling the tooth surface to be generated, and permitting the theoretical contacting lines to be produced in light of the meshing function. Simulation and verification are carried out to prove the mathematical equations. Numerical control (NC) simulation of machining the external and internal double circular-arc spiral bevel gears is developed, and the spiral gears were manufactured on a NC milling machine. The prototype of the nutation drive is illustrated in the case study at the end of this paper.

Theoretical and experimental analyses of spiral bevel gears with two contact paths

2017 ◽  
Vol 232 (4) ◽  
pp. 665-676 ◽  
Author(s):  
Rulong Tan ◽  
Bingkui Chen ◽  
Dong Liang ◽  
Changyan Peng
Keyword(s):  
Differential Geometry ◽  
Contact Stress ◽  
Logarithmic Spiral ◽  
Transmission Efficiency ◽  
Tooth Surface ◽  
Spiral Bevel Gears ◽  
Bevel Gears ◽  
Generating Method ◽  
Spiral Bevel ◽  
Maximum Contact

This paper investigates the geometrical design principal of the spiral bevel gears with two contact paths from spatial conjugate curve theory. Differential geometry and gearing kinematics are introduced to derive this model. In this process, the calculation method of contact paths and tooth surface generating method are presented. According to the arguments in this paper, a process of designing the tooth surface of logarithmic spiral bevel gears with two contact paths is investigated. Then, through this process, the design of a pair of logarithmic spiral bevel gears with two contact paths is completed. Besides, the prototype is manufactured and the performance experiment is completed. Results show the maximum contact stress of spiral bevel gears with two contact paths is reduced compared to those with one contact path. Besides, the transmission efficiency of the spiral bevel gears with two contact paths can reach 98.2%.

The Undercutting of Circular-Cut Spiral Bevel Gears

1992 ◽  
Vol 114 (2) ◽  
pp. 317-325 ◽  
Author(s):  
Zhang-Hua Fong ◽  
Chung-Biau Tsay
Keyword(s):  
Gear Tooth ◽  
Sufficient Conditions ◽  
Bevel Gear ◽  
Tooth Surface ◽  
Spiral Bevel Gear ◽  
Spiral Bevel Gears ◽  
Bevel Gears ◽  
Tooth Surfaces ◽  
Sufficient And Necessary Conditions ◽  
Spiral Bevel

Undercutting is a serious problem in designing spiral bevel gears with small numbers of teeth. Conditions of undercutting for spiral bevel gears vary with the manufacturing methods. Based on the theory of gearing [1], the tooth geometry of the Gleason type circular-cut spiral bevel gear is mathematically modeled. The sufficient and necessary conditions for the existence and regularity of the generated gear tooth surfaces are investigated. The conditions of undercutting for a circular-cut spiral bevel gear are defined by the sufficient conditions of the regular gear tooth surface. The derived undercutting equations can be applicable for checking the undercutting conditions of spiral bevel gears manufactured by the Gleason Duplex Method, Helical Duplex Method, Fixed Setting Method, and Modified Roll Method. An example is included to illustrate the application of the proposed undercut checking equations.

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