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Journal articles on the topic 'Hypoid Bevel gears'

Author: Grafiati

Published: 4 June 2021

Last updated: 1 February 2022

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1

Wu, Xun Cheng, Jing Tao Han, and Jia Fu Wang. "A Mathematical Model for the Generated Gear Tooth Surfaces of Spiral Bevel and Hypoid Gears." Advanced Materials Research 314-316 (August 2011): 384–88. http://dx.doi.org/10.4028/www.scientific.net/amr.314-316.384.

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It is an important and fundamental work to establish a general mathematical model for the gear tooth surfaces of spiral bevel and hypoid gears. Based on the three-axis CNC bevel gear machine, a mathematical model with the equations of the radial position vector, the normal unit vector and the second order parameters for the generated gear tooth surfaces of spiral bevel and hypoid gears is established. The mathematical model can be used for the gear tooth surfaces generated in different types on both the three-axis CNC bevel gear machine and the cradle bevel gear machine. As an application example of the mathematical model, the generating motions of the cradle bevel gear machine are determined.

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2

Wang, Li Mei. "Study on the Processing and Simulation of End-Gear Based on CNC Theory." Applied Mechanics and Materials 608-609 (October 2014): 77–80. http://dx.doi.org/10.4028/www.scientific.net/amm.608-609.77.

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Based on NC machining principle of hypoid gears and NC machining with high efficiency quality, This paper discusses the feasibility of the hypoid gear processing, establishes the mathematical model of face gear wheel hypoid milling machining adjustment, that will be take the basic data into vertical machining center machine tool. Through analyze the principle of the oscillating tooth face gear transmission, and compared the structure differences between face gear and bevel gear, and the realization processing method of face gear is discussed by improving the bevel gear shaper.

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3

Osakue, Edward, Lucky Anetor, and Kendall Harris. "Contact stress in helical bevel gears." FME Transactions 49, no. 3 (2021): 519–33. http://dx.doi.org/10.5937/fme2103519o.

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Helical bevel gears have inclined or twisted teeth on a conical surface and the common types are skew, spiral, zerol, and hypoid bevel gears. However, this study does not include hypoid bevel gears. Due to the geometric complexities of bevel gears, commonly used methods in their design are based on the concept of equivalent or virtual spur gear. The approach in this paper is based on the following assumptions, a) the helix angle of helical bevel gears is equal to mean spiral angle, b) the pitch diameter at the backend is defined as that of a helical gear, and c) the Tredgold's approximation is applied to the helical gear. Upon these premises, the contact stress capacity of helical bevel gears is formulated in explicit design parameters. The new contact stress capacity model is used to estimate the contact stress in three gear systems for three application examples and compared with previous solutions. Differences between the new estimated results and the previous solutions vary from -3% and -11%, with the new estimates being consistently but marginally or slightly lower than the previous solution values. Though the differences appear to be small, they are significant because the durability of gears is strongly influenced by the contact stress. For example, a 5% reduction in contact stress may result in almost 50% increase in durability in some steel materials. The equations developed do not apply to bevel crown gears.

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4

Fan, Qi. "Advanced Developments in Computerized Design and Manufacturing of Spiral Bevel and Hypoid Gear Drives." Applied Mechanics and Materials 86 (August 2011): 439–42. http://dx.doi.org/10.4028/www.scientific.net/amm.86.439.

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Design and manufacturing of spiral bevel and hypoid gears is highly complicated and has to be based on the employment of computerized tools. This paper comprehensively describes the latest developments in computerized modeling of tooth surface generation, flank form error correction, ease-off calculation, and tooth contact analysis for spiral bevel and hypoid gears. Accordingly, advanced software programs for computerized design and manufacturing of hypoid gears are developed.

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5

Wu, Xun Cheng, and Cong Li. "Function-Oriented Design and Verification of Point-Contact Tooth Surfaces of Spiral Bevel and Hypoid Gears with the Generated Gear." Advanced Materials Research 118-120 (June 2010): 675–80. http://dx.doi.org/10.4028/www.scientific.net/amr.118-120.675.

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Establishing a general technical platform for the function-oriented design of point-contact tooth surfaces of spiral bevel and hypoid gears is an important and fundamental work. Based on the three-axis CNC bevel gear machine, a general mathematical model for the generated gear tooth surfaces of spiral bevel and hypoid gears is established. According to the principle and the method for the function-oriented design of point-contact tooth surfaces, the locus of spatial tooth contact points on the tooth surface is described on the axial plane of the gear, and then the formulae for the design with the generated gear are derived from the mathematical model. The mathematical model and the formulae can be used in the function-oriented design of point-contact tooth surfaces with the gear generated in different types on both the three-axis CNC bevel gear machine and the conventional cradle one. A theoretical method for the verification of point-contact tooth surfaces is proposed and the formulae for the verification are presented. And lastly an example is given to demonstrate the function-oriented design of point-contact tooth surfaces of the hypoid gear drive with the generated gear.

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6

Shih, Yi-Pei, and Zhang-Hua Fong. "Flank Modification Methodology for Face-Hobbing Hypoid Gears Based on Ease-Off Topography." Journal of Mechanical Design 129, no. 12 (December 30, 2006): 1294–302. http://dx.doi.org/10.1115/1.2779889.

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The fundamental design of spiral bevel and hypoid gears is usually based on a local synthesis and a tooth contact analysis of the gear drive. Recently, however, several flank modification methodologies have been developed to reduce running noise and avoid edge contact in gear making, including modulation of tooth surfaces under predesigned transmission errors. This paper proposes such a flank modification methodology for face-hobbing spiral bevel and hypoid gears based on the ease-off topography of the gear drive. First, the established mathematical model of a universal face-hobbing hypoid gear generator is applied to investigate the ease-off deviations of the design parameters—including cutter parameters, machine settings, and the polynomial coefficients of the auxiliary flank modification motion. Subsequently, linear regression is used to modify the tooth flanks of a gear pair to approximate the optimum ease-off topography suggested by experience. The proposed method is then illustrated using a numerical example of a face-hobbing hypoid gear pair from Oerlikon’s Spiroflex cutting system. This proposed flank modification methodology can be used as a basis for developing a general technique of flank modification for similar types of gears.

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7

Fong, Zhang-Hua. "Mathematical Model of Universal Hypoid Generator With Supplemental Kinematic Flank Correction Motions." Journal of Mechanical Design 122, no. 1 (January 1, 2000): 136–42. http://dx.doi.org/10.1115/1.533552.

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A mathematical model of universal hypoid generator is proposed to simulate virtually all primary spiral bevel and hypoid cutting methods. The proposed mathematical model simulates the face-milling, face-hobbing, plunge cutting, and bevel-worm-shaped hobbing processes with either generating or nongenerating cutting for the spiral bevel and hypoid gears. The supplemental kinematic flank correction motions, such as modified generating roll ratio, helical motion, and cutter tilt are included in the proposed mathematical model. The proposed mathematical model has more flexibility in writing computer program and appropriate for developing the object oriented computer programming. The developed computer object can be repeatedly used by various hypoid gear researchers to reduce the effort of computer coding. [S1050-0472(00)01201-0]

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8

Shih, Yi-Pei, Zhang-Hua Fong, and Grandle C. Y. Lin. "Mathematical Model for a Universal Face Hobbing Hypoid Gear Generator." Journal of Mechanical Design 129, no. 1 (May 17, 2006): 38–47. http://dx.doi.org/10.1115/1.2359471.

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Based on the theory of gearing and differential geometry, a universal hypoid generator mathematical model for face hobbing spiral bevel and hypoid gears has been developed. This model can be used to simulate existing face hobbing processes, such as Oerlikon’s Spiroflex© and Spirac© methods, Klingelnberg’s Cyclo-Palloid© cutting system, and Gleason’s face hobbing nongenerated and generated cutting systems. The proposed model is divided into three modules: the cutter head, the imaginary generating gear, and the relative motion between the imaginary generating gear and the work gear. With such a modular arrangement, the model is suitable for development of object-oriented programming (OOP) code. In addition, it can be easily simplified to simulate face milling cutting and includes most existing flank modification features. A numerical example for simulation of the Klingelnberg Cyclo-Palloid© hypoid is presented to validate the proposed model, which can be used as a basis for developing a universal cutting simulation OOP engine for both face milling and face hobbing spiral bevel and hypoid gears.

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9

Skawiński, Piotr. "An application of neural network in recognizing of the tooth contact of spiral and hypoid bevel gears." Advanced Technologies in Mechanics 2, no. 4(5) (December 29, 2016): 2. http://dx.doi.org/10.17814/atim.2015.4(5).28.

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The special computer system KONTEPS for calculation of spiral and hypoid bevel gears generally supports technology for the conventional and CNC machines (milling machines). In this system environment, the special computer application generates solid or surface models of gears by cutting simulation. Other computer application, based on Matlab functions and methods of artificial intelligence, supports the tooth contact development. The special classifiers which allow to recognize the tooth contact, select the first, second and third order of changes and support the technologist in manufacturing process. This paper describes computerized integration of design and manufacturing of the spiral and hypoid bevel gear supported by the artificial intelligence.

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10

Pellkofer, J., I. Boiadjiev, D. Kadach, M. Klein, and K. Stahl. "New calculation method for the scuffing load-carrying capacity of bevel and hypoid gears." Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science 233, no. 21-22 (April 26, 2019): 7328–37. http://dx.doi.org/10.1177/0954406219843954.

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Future trends indicate that the demands on bevel and hypoid gears for higher power transmission and lower weight are continuously increasing. Beside typical fatigue failures such as pitting, tooth root breakage, and tooth flank fracture, spontaneous failures such as scuffing are often observed if the load-carrying capacity of the tribological system consisting of gears and lubricant is exceeded. This paper gives an overview of the newest findings on scuffing specifically on bevel and hypoid gears and discusses the hypoid-specific decisive influence parameters. Furthermore, the newly developed calculation method as well as its verification with test results and results from field application are presented.

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11

Fan, Qi. "Enhanced Algorithms of Contact Simulation for Hypoid Gear Drives Produced by Face-Milling and Face-Hobbing Processes." Journal of Mechanical Design 129, no. 1 (April 6, 2006): 31–37. http://dx.doi.org/10.1115/1.2359475.

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Modeling of tooth surface generation and simulation of contact is an important part of computerized design and manufacturing of spiral bevel and hypoid gears. This paper presents new developments in this subject. Specifically, the paper covers: (i) development of a generic model of tooth surface generation for spiral bevel and hypoid gears produced by face-milling and face-hobbing processes conducted on free-form computer numerical control (CNC) hypoid gear generators which are incorporated with the Universal Motions Concept (UMC); (ii) a modified algorithm of tooth contact simulation with reduced number of equations of the nonlinear iterations and stabilized iteration convergence; and (iii) an algorithm of numerical determination of contact lines that form the contact patterns. The enhanced approach of contact simulation can be generally applied to other forms of gearings. Two examples, a face-hobbing design and a face-milling design, are illustrated to verify the implementation of the developed algorithms.

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12

Vogel, O., A. Griewank, and G. Bär. "Direct gear tooth contact analysis for hypoid bevel gears." Computer Methods in Applied Mechanics and Engineering 191, no. 36 (August 2002): 3965–82. http://dx.doi.org/10.1016/s0045-7825(02)00351-1.

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13

Sabo, Ivan, Milan Kljain, Mirko Karakašić, and Željko Ivandić. "Design and calculation of planetary transmission with bevel gears." Tehnički glasnik 13, no. 2 (June 17, 2019): 154–61. http://dx.doi.org/10.31803/tg-20190503183526.

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In this paper, the design and calculation of planetary transmission with bevel gears for road vehicles is presented. It must transfer power to the wheels with the possibility that wheels can rotate at different speeds. The basic calculation of transmission is performed for the drive machine, where an internal combustion engine is chosen, and for the driven machine, which is a car, all forces of resistance are calculated so that the transmission needs to be overcome to move the car. Based on the standard ISO 23509:2016 norm, the calculation of geometry is performed for the input gear pair and it is defined as a hypoid gear pair. For the planetary transmission, a calculation of gear module for bevel gears is first performed, and after that, the geometry is calculated. The calculation of the stress for root stress and Hertz contact pressure is performed for all bevel gears in transmission.

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14

Dooner, D. B. "On the Invariance of Gear Tooth Curvature." Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science 220, no. 7 (July 1, 2006): 1083–96. http://dx.doi.org/10.1243/09544062jmes208.

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A method is presented for the determination of the principal curvatures along with their principal directions of two gear teeth in direct contact. The procedure used to determine these extreme curvatures and directions is based on the nominal position of contact. Moreover, these extreme curvatures and directions are invariant with tooth type (viz. involute and cycloidal) and manufacturing process. Such curvatures and directions depend on the instantaneous pressure angle, spiral or helix angle, and position of contact. This generalized method is applicable to cylindrical gears (spur and helical), conical gears (straight and spiral), as well as hyperboloidal gears (hypoid and worm). Three examples are included to illustrate the determination of principal curvatures and directions. The first example is a helical gear pair, the second is a spiral bevel gear pair, and the third example is a hypoid gear pair.

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15

Stadtfeld, Hermann J., and Uwe Gaiser. "The Ultimate Motion Graph." Journal of Mechanical Design 122, no. 3 (August 1, 1999): 317–22. http://dx.doi.org/10.1115/1.1286124.

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The innovation was to develop a gear geometry that reduces or eliminates gear noise and increases the strength of gears. Gear noise is a common problem in all bevel and hypoid gear drives. A variety of expensive gear geometry optimizations are applied daily in all hypoid gear manufacturing plants, to reduce gear noise. In many cases those efforts have little success. Additional expensive finishing operations (lapping after the grinding) are applied to achieve the goal of quiet and stong gear sets. The ultimate motion graph is a concept for modulating the tooth surfaces that uses a physical effect to cancel out the dynamic disturbances that are naturally generated by all up-to-date known kind of gears. The ultimate motion graph also eliminates the sensitivity of gears against deflection under load or displacements because of manufacturing tolerances. Lower dynamic disturbances will also increase the dynamic strength. [S1050-0472(00)00203-8]

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16

Yu, Jian Wu, Yi Jian Deng, Wen Yi Zou, and Gong Fa Zhang. "A New Automatic Backlash Adjustment Method for Lapping of Spiral Bevel Gear." Advanced Materials Research 565 (September 2012): 307–11. http://dx.doi.org/10.4028/www.scientific.net/amr.565.307.

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Based on the lapping principle of spiral bevel gears and hypoid gears, this paper focuses on a new automatic backlash adjustment method for lapping process, which includes on-line detection and measurement of backlash, automatic backlash control and software etc. The experimental results shows that this on-line automatic backlash control method is efficiency and stable in lapping process, and it can improve gear surface finishing and reduce transmission noise apparently.

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17

Rong, Kaibin, Han Ding, Biyun Song, Jinhao Gao, and Jinyuan Tang. "Data-driven process control for manufacturing spiral bevel and hypoid gears by using design for six sigma (DFSS) considering numerical loaded tooth contact analysis (NLTCA)." Proceedings of the Institution of Mechanical Engineers, Part B: Journal of Engineering Manufacture 235, no. 12 (June 4, 2021): 1875–91. http://dx.doi.org/10.1177/09544054211023625.

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Data-driven process control considering both geometric and loaded contact performance evaluations has been an increasingly important stage in field of spiral bevel and hypoid gears. A new data-driven manufacturing process control strategy is proposed for a high performance spiral bevel and hypoid gears. Here, to distinguish with the conventional simulated loaded tooth contact analysis (SLTCA) using economical finite element software package, the numerical loaded tooth contact analysis (NLTCA) is of more flexibility and practicality. In light of the advantages of the improved design for six sigma (DFSS), it is integrated with NLTCA for establishing a novel data-driven process control of gear manufacturing. Firstly, in improved DFSS framework, quality function deployment (QFD) is used to determine four sub-objective high-performance evaluation items. Then, their data-driven relationships between machine settings are respectively determined by using NLTCA. In particular, the manufacturing process control is further converted into multi-objective optimization (MOO) modification of the hypoid generator settings. Finally, an interactive preference point approach is applied for data-driven control of its iterative step and it can obtain a robust solution from Pareto optimal front. A case study is provided to verify the proposed methodology.

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18

Litvin, F. L., C. Kuan, J. Kieffer, R. Bossler, and R. F. Handschuh. "Straddle Design of Spiral Bevel and Hypoid Pinions and Gears." Journal of Mechanical Design 113, no. 4 (December 1, 1991): 422–26. http://dx.doi.org/10.1115/1.2912799.

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The design of spiral bevel and hypoid gears that have a shaft extended from both sides of the cone apex (straddle design) is considered. A main difficulty of such a design is determining the length and diameter of the shaft that might be undercut by the head cutter during gear tooth generation. A method that determines the free space available for the gear shaft is proposed. The approach avoids collision between the shaft being designed and the head cutter during tooth generation. The approach is illustrated with a numerical example.

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19

Höhn, Bernd Robert, Karsten Stahl, and Christian Wirth. "New Calculation Method for the Load Capacity of Bevel And Hypoid Gears Based on Loaded Tooth Contact Analysis." Applied Mechanics and Materials 86 (August 2011): 237–42. http://dx.doi.org/10.4028/www.scientific.net/amm.86.237.

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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.

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20

Li, J.-G., S.-M. Mao, J.-L. He, and X.-T. Wu. "Optimization of Pinion Roughing of Spiral Bevel and Hypoid Gear." Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science 220, no. 4 (April 1, 2006): 483–88. http://dx.doi.org/10.1243/09544062c04105.

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Roughing plays a very important role in spiral bevel and hypoid gear manufacturing. The roughing machine settings and cutter blade profile are optimized in this article on the basis of three considerations: the transition between the roughing root and the finishing fillet is smoothened, which causes the gear to obtain minimum possible bending stress and maximum bending strength; the finishing stock is distributed evenly to improve the residual stress, which causes the distortion of pinion during the process of heat treatment; and the working load of finishing cutter tip is minimized, and the maximum cutter life is obtained. The complex shape method is successfully used to optimize the roughing machine settings and cutter blade profile. The advantages and benefits of the newly developed roughing process are verified in the manufacture of hypoid gears for a heavy truck axle in a Chinese vehicle company.

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21

Kuryjański, Ryszard. "Hypoid spiral bevel gears – development, design limits and possibility to manufacturing on spiral bevel gears machine." Mechanik, no. 12 (December 2016): 1764–68. http://dx.doi.org/10.17814/mechanik.2016.12.561.

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22

Fan, Qi. "Computerized Modeling and Simulation of Spiral Bevel and Hypoid Gears Manufactured by Gleason Face Hobbing Process." Journal of Mechanical Design 128, no. 6 (December 24, 2005): 1315–27. http://dx.doi.org/10.1115/1.2337316.

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The Gleason face hobbing process has been widely applied by the gear industry. But so far, few papers have been found regarding exact modeling and simulation of the tooth surface generations and tooth contact analysis (TCA) of face hobbed spiral bevel and hypoid gear sets. This paper presents the generalized theory of the face hobbing generation method, mathematic models of tooth surface generations, and the simulation of meshing of face hobbed spiral bevel and hypoid gears. The face hobbing indexing motion is described and visualized. A generalized description of the cutting blades is introduced by considering four sections of the blade edge geometry. A kinematical model is developed and analyzed by breaking down the machine tool settings and the relative motions of the machine elemental units and applying coordinate transformations of the elemental motions. The developed face hobbing generation model is directly related to a physical bevel gear generator. A generalized and enhanced TCA algorithm is proposed. The face hobbing process has two categories, non-generated (Formate®) and generated methods, applied to the tooth surface generation of the gear. In both categories, the pinion is always finished with the generated method. The developed tooth surface generation model covers both categories with left-hand and right-hand members. Based upon the developed theory, an advanced tooth surface generation and TCA program is developed and integrated into Gleason CAGE™for Windows Software. Two numerical examples are provided to illustrate the implementation of the developed mathematic models.

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23

Wu, Xun Cheng, Cong Li, Ruo Ping Zhang, and Hai Bo Zhang. "Function-Oriented Designing and Generating Technology for the Point-Contact Tooth Surfaces of Spiral Bevel and Hypoid Gears." Advanced Materials Research 44-46 (June 2008): 495–502. http://dx.doi.org/10.4028/www.scientific.net/amr.44-46.495.

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A function-oriented designing and generating technology for the point-contact tooth surfaces of spiral bevel and hypoid gears is introduced. The tooth surface parameters are determined directly with the designing variables of the instantaneous transmission function, the locus of tooth contact points and the tooth contact ellipse dimension to design the point-contact tooth surfaces with the expected performances. The formulae for designing are provided. The designed tooth surfaces are generated with the free-form bevel gear machine, and the basic equations and formulae for the four-axis generating of the tooth surfaces are presented. The generating motions are expressed as the functions of the work gear rotary angle, which is taken as a motion parameter. The methods to determine the motion functions and the other machine setting parameters are explained through an example.

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24

Wang, Jun, and Teik C. Lim. "On the Boundary between Nonlinear Jump Phenomenon and Linear Response of Hypoid Gear Dynamics." Advances in Acoustics and Vibration 2011 (May 26, 2011): 1–13. http://dx.doi.org/10.1155/2011/583678.

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A nonlinear time-varying (NLTV) dynamic model of a hypoid gear pair system with time-dependent mesh point, line-of-action vector, mesh stiffness, mesh damping, and backlash nonlinearity is formulated to analyze the transitional phase between nonlinear jump phenomenon and linear response. It is found that the classical jump discontinuity will occur if the dynamic mesh force exceeds the mean value of tooth mesh force. On the other hand, the propensity for the gear response to jump disappears when the dynamic mesh force is lower than the mean mesh force. Furthermore, the dynamic analysis is able to distinguish the specific tooth impact types from analyzing the behaviors of the dynamic mesh force. The proposed theory is general and also applicable to high-speed spur, helical and spiral bevel gears even though those types of gears are not the primary focus of this paper.

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25

Zhu, De-Rong, Jian-Jun Yang, Xiao-Zhong Deng, Chuang Jiang, and Ju-Bo Li. "Influence of gear parameters on dynamic characteristics of an ultrasonic vibration system." Transactions of the Canadian Society for Mechanical Engineering 42, no. 3 (September 1, 2018): 252–67. http://dx.doi.org/10.1139/tcsme-2017-0036.

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A spiral bevel gear is subject to a special load in ultrasonic lapping, which is not only a processing object but also a processing tool, it is necessary to study dynamic characteristics of an ultrasonic vibration system. First, the spiral bevel gear is reasonably simplified to a frustum, which is then combined with a horn to form a new type of composite horn. Based on the theory of plane longitudinal wave propagation, the resonance mathematical model of the gear’s ultrasonic vibration system is established, and the frequency equation of the vibration system with gear characteristic parameters is obtained. Second, the frequency and displacement characteristics of an ultrasonic vibration system are analyzed by means of design examples, and the influence of the law of gear characteristic parameters on dynamic characteristics of the vibration system is studied. Finally, ultrasonic lapping and vibration measurement experiments are carried out using two pairs of different hypoid gears. The results show that the change in dynamic characteristics of an ultrasonic vibration system has a large influence on the finished machining quality of the gear. Therefore, it is necessary to consider the gear characteristic parameters when ultrasonic vibration system is designed. The research results provide an accurate theoretical basis for the detailed design of an ultrasonic lapping vibration system.

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26

Litvin, F. L., Y. Zhang, M. Lundy, and C. Heine. "Determination of Settings of a Tilted Head Cutter for Generation of Hypoid and Spiral Bevel Gears." Journal of Mechanisms, Transmissions, and Automation in Design 110, no. 4 (December 1, 1988): 495–500. http://dx.doi.org/10.1115/1.3258950.

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Kinematics of mechanisms of hypoid and spiral bevel cutting machines is considered. These mechanisms are designated to install the position and tilt of the head cutter. The tilt of the head cutter with standard blades provides the required pressure angle. The authors have developed the matrix presentation of kinematics of these mechanisms and basic equations for the required settings. An example is presented based on the developed computation procedure.

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27

Wang, Huiliang, Jubo Li, Yang Gao, and Jianjun Yang. "Closed-Loop Feedback Flank Errors Correction of Topographic Modification of Helical Gears Based on Form Grinding." Mathematical Problems in Engineering 2015 (2015): 1–11. http://dx.doi.org/10.1155/2015/635156.

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To increase quality, reduce heavy-duty gear noise, and avoid edge contact in manufacturing helical gears, a closed-loop feedback correction method in topographic modification tooth flank is proposed based on the gear form grinding. Equations of grinding wheel profile and grinding wheel additional radial motion are derived according to tooth segmented profile modification and longitudinal modification. Combined with gear form grinding kinematics principles, the equations of motion for each axis of five-axis computer numerical control forming grinding machine are established. Such topographical modification is achieved in gear form grinding with on-machine measurement. Based on a sensitivity analysis of polynomial coefficients of axis motion and the topographic flank errors by on-machine measuring, the corrections are determined through an optimization process that targets minimization of the tooth flank errors. A numerical example of gear grinding, including on-machine measurement and closed-loop feedback correction completing process, is presented. The validity of this flank correction method is demonstrated for tooth flank errors that are reduced. The approach is useful to precision manufacturing of spiral bevel and hypoid gears, too.

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28

Lin, Chung-Yunn, Chung-Biau Tsay, and Zhang-Hua Fong. "Computer-aided manufacturing of spiral bevel and hypoid gears with minimum surface-deviation." Mechanism and Machine Theory 33, no. 6 (August 1998): 785–803. http://dx.doi.org/10.1016/s0094-114x(97)00101-8.

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29

Lin, Chung-Yunn, Chung-Biau Tsay, and Zhang-Hua Fong. "Computer-aided manufacturing of spiral bevel and hypoid gears by applying optimization techniques." Journal of Materials Processing Technology 114, no. 1 (July 2001): 22–35. http://dx.doi.org/10.1016/s0924-0136(01)00734-8.

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30

Shih, Yi-Pei. "A novel ease-off flank modification methodology for spiral bevel and hypoid gears." Mechanism and Machine Theory 45, no. 8 (August 2010): 1108–24. http://dx.doi.org/10.1016/j.mechmachtheory.2010.03.010.

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31

Yang, J. J., Z. H. Shi, H. Zhang, T. X. Li, S. W. Nie, and B. Y. Wei. "Dynamic analysis of spiral bevel and hypoid gears with high-order transmission errors." Journal of Sound and Vibration 417 (March 2018): 149–64. http://dx.doi.org/10.1016/j.jsv.2017.12.022.

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32

Xie, Shuangxi. "A genuine face milling cutter geometric model for spiral bevel and hypoid gears." International Journal of Advanced Manufacturing Technology 67, no. 9-12 (January 24, 2013): 2619–26. http://dx.doi.org/10.1007/s00170-012-4678-y.

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33

MUELLER, Hartmuth, and Heinz EDER. "GM-16 CLOSED LOOP TECHNOLOGY FOR DRY CUTTING OF SPIRAL BEVEL AND HYPOID GEARS(GEAR MANUFACTURING)." Proceedings of the JSME international conference on motion and power transmissions I.01.202 (2001): 393–97. http://dx.doi.org/10.1299/jsmeimpt.i.01.202.393.

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Jia, Pan, Huaiju Liu, Caichao Zhu, Wei Wu, and Guocheng Lu. "Contact fatigue life prediction of a bevel gear under spectrum loading." Frontiers of Mechanical Engineering 15, no. 1 (December 7, 2019): 123–32. http://dx.doi.org/10.1007/s11465-019-0556-8.

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AbstractRolling contact fatigue (RCF) issues, such as pitting, might occur on bevel gears because load fluctuation induces considerable subsurface stress amplitudes. Such issues can dramatically affect the service life of associated machines. An accurate geometry model of a hypoid gear utilized in the main reducer of a heavy-duty vehicle is developed in this study with the commercial gear design software MASTA. Multiaxial stress—strain states are simulated with the finite element method, and the RCF life is predicted using the Brown–Miller–Morrow fatigue criterion. The patterns of fatigue life on the tooth surface are simulated under various loading levels, and the RCF S–N curve is numerically generated. Moreover, a typical torque—time history on the driven axle is described, followed by the construction of program load spectrum with the rain flow method and the Goodman mean stress equation. The effects of various fatigue damage accumulation rules on fatigue life are compared and discussed in detail. Predicted results reveal that the Miner linear rule provides the most optimistic result among the three selected rules, and the Manson bilinear rule produces the most conservative result.

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Lin, Chung-Yunn, Chung-Biau Tsay, and Zhang-Hua Fong. "Mathematical model of spiral bevel and hypoid gears manufactured by the modified roll method." Mechanism and Machine Theory 32, no. 2 (February 1997): 121–36. http://dx.doi.org/10.1016/s0094-114x(96)00043-2.

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Zhou, Zhen-yu, Jin-yuan Tang, and Han Ding. "Accurate modification methodology of universal machine tool settings for spiral bevel and hypoid gears." Proceedings of the Institution of Mechanical Engineers, Part B: Journal of Engineering Manufacture 232, no. 2 (April 4, 2016): 339–49. http://dx.doi.org/10.1177/0954405416640173.

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Universal machine tool settings with higher-order motion coefficients are developed to make accurate modification considering the actual machine geometric error compensation for spiral bevel and hypoid gears. First, the universal machine tool settings are exploited for the identification of the real tooth flank form error. Furthermore, the error sensitivity analysis method and an improved Levenberg–Marquardt algorithm with a trust-region strategy are utilized to obtain the solution of modification amount. Finally, a higher-order modification methodology for the universal machine tool settings is proposed which mainly covers three vital parts: (a) optimized selection of the modification settings, (b) modification of universal machine tool settings, and (c) machine geometric error compensation. Especially, a higher-accuracy fitting method for the form error tooth flank is investigated. Some numerical examples verify that the tooth flank form error after higher-order modification can reach less than 0.5 µm or even a smaller one, and the position error after compensating process spindle can be reduced from 0.0044861° to 0.0009232°. In addition, given experimental result can validate the feasibility of the proposed methodology.

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KUBO, Aizoh, Ichiro TARUTANI, Claude GOSSELIN, Tetsuya NONAKA, Noboru AOYAMA, and Zhonghou WANG. "A Computer Based Approach for Evaluation of Operating Performances of Bevel and Hypoid Gears." JSME International Journal Series C 40, no. 4 (1997): 749–58. http://dx.doi.org/10.1299/jsmec.40.749.

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38

Pellkofer, J., M. Hein, T. Reimann, M. Hombauer, and K. Stahl. "New calculation method of the micropitting load carrying capacity of bevel and hypoid gears." Forschung im Ingenieurwesen 83, no. 3 (August 21, 2019): 603–9. http://dx.doi.org/10.1007/s10010-019-00344-7.

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Yang, Yu, Shimin Mao, Wenchao Guo, and Yuhua Kuang. "Pinion development of face-milled spiral bevel and hypoid gears based on contact attributes." International Journal of Advanced Manufacturing Technology 84, no. 9-12 (October 1, 2015): 2347–56. http://dx.doi.org/10.1007/s00170-015-7886-4.

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Wang, Pei-Yu, and Zhang-Hua Fong. "Fourth-Order Kinematic Synthesis for Face-Milling Spiral Bevel Gears With Modified Radial Motion (MRM) Correction." Journal of Mechanical Design 128, no. 2 (March 3, 2005): 457–67. http://dx.doi.org/10.1115/1.2168466.

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The use of a fourth-order motion curve is proposed by Stadtfeld and Gaiser to reduce the running noise of a bevel gear set recently. However, the methodology of synthesizing the tooth surfaces was not clearly shown in the literature. In this work, we proposed a methodology to synthesize the mating tooth surfaces of a face-milling spiral bevel gear set transmitting rotations with a predetermined fourth-order motion curve and contact path. A modified radial motion (MRM) correction in the machine plane of a computer numerical control (CNC) hypoid generator is introduced to modify the pinion tooth surface. With MRM correction, an arbitrary predetermined contact path on the pinion tooth surface with predetermined fourth-order motion curve can be achieved. Parameters of MRM correction are calculated according to the predetermined contact path and motion curve. As shown by the numerical examples, the contact path and the motion curve were obtained as expected by applying the MRM correction. The results of this work can be applied to the pinion, which is generated side-by-side (for example, fixed setting method, formate method, and Helixform method) and can be used as a basis for further study on the motion curve optimizations.

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Wu, Xuncheng. "ACTIVE CONTROL MANUFACTURING TECHNOLOGY FOR THE POINT-CONTACT TOOTH SURFACES OF SPIRAL BEVEL AND HYPOID GEARS." Chinese Journal of Mechanical Engineering 41, no. 10 (2005): 97. http://dx.doi.org/10.3901/jme.2005.10.097.

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ZHANG, Yu. "Cutting Principle and Tooth Contact Analysis of Spiral Bevel and Hypoid Gears Generated by Duplex Helical Method." Journal of Mechanical Engineering 51, no. 21 (2015): 15. http://dx.doi.org/10.3901/jme.2015.21.015.

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Ding, Han, Jinyuan Tang, and Jue Zhong. "An accurate model of high-performance manufacturing spiral bevel and hypoid gears based on machine setting modification." Journal of Manufacturing Systems 41 (October 2016): 111–19. http://dx.doi.org/10.1016/j.jmsy.2016.08.004.

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Wang, Qi, Chi Zhou, Liangjin Gui, and Zijie Fan. "Optimization of the loaded contact pattern of spiral bevel and hypoid gears based on a kriging model." Mechanism and Machine Theory 122 (April 2018): 432–49. http://dx.doi.org/10.1016/j.mechmachtheory.2018.01.008.

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Zhang, Yu, and Hongzhi Yan. "New methodology for determining basic machine settings of spiral bevel and hypoid gears manufactured by duplex helical method." Mechanism and Machine Theory 100 (June 2016): 283–95. http://dx.doi.org/10.1016/j.mechmachtheory.2016.02.015.

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He, Di, Han Ding, and Jinyuan Tang. "A new analytical identification approach to the tooth contact points considering misalignments for spiral bevel or hypoid gears." Mechanism and Machine Theory 121 (March 2018): 785–803. http://dx.doi.org/10.1016/j.mechmachtheory.2017.12.003.

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Shao, Wen, Han Ding, and Jinyuan Tang. "Data-driven operation and compensation approaches to tooth flank form error measurement for spiral bevel and hypoid gears." Measurement 122 (July 2018): 347–57. http://dx.doi.org/10.1016/j.measurement.2018.03.004.

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Zhou, Yuansheng, Zezhong C. Chen, Jinyuan Tang, and Shengjun Liu. "An innovative approach to NC programming for accurate five-axis flank milling of spiral bevel or hypoid gears." Computer-Aided Design 84 (March 2017): 15–24. http://dx.doi.org/10.1016/j.cad.2016.11.003.

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Ding, Han, Jinyuan Tang, Jue Zhong, and Zhenyu Zhou. "A hybrid modification approach of machine-tool setting considering high tooth contact performance in spiral bevel and hypoid gears." Journal of Manufacturing Systems 41 (October 2016): 228–38. http://dx.doi.org/10.1016/j.jmsy.2016.09.003.

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Artoni, Alessio, Marco Gabiccini, and Mohsen Kolivand. "Ease-off based compensation of tooth surface deviations for spiral bevel and hypoid gears: Only the pinion needs corrections." Mechanism and Machine Theory 61 (March 2013): 84–101. http://dx.doi.org/10.1016/j.mechmachtheory.2012.10.005.

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