Correction of tooth surface deviations for aero spiral bevel and hypoid gears

2014 ◽  
Author(s):  
Yu Yang ◽  
Shimin Mao ◽  
Pengju Zhao ◽  
Wenchao Guo
Keyword(s):  
Tooth Surface ◽  
Hypoid Gears ◽  
Surface Deviations ◽  
Spiral Bevel

Mathematical Model and Surface Deviation of Helipoid Gears Cut by Shaper Cutters

2003 ◽  
Vol 125 (2) ◽  
pp. 351-355 ◽  
Author(s):  
Jun-Long Wu ◽  
Chia-Chang Liu ◽  
Chung-Biau Tsay ◽  
Shigeyoshi Nagata
Keyword(s):  
Mathematical Model ◽  
Power Transmission ◽  
Tooth Surface ◽  
Cutting Mechanism ◽  
Hypoid Gears ◽  
Helical Gears ◽  
Number Of Teeth ◽  
Surface Deviations ◽  
Surface Deviation

Crossed-axis helical gears and hypoid gears are two conventional crossed-axis power transmission devices. Helipoid gears, a novel gear proposed herein, possess the merits of the crossed-axis helical and hypoid gears. A mathematical model of the proposed helipoid gear cut by shapers is also derived according to the cutting mechanism and the theory of gearing. The investigation shows that the tooth surface varies with the number of teeth of the shaper. Computer graphs of the helipoid gear are presented according to the developed gear mathematical model, and the tooth surface deviations due to the number of teeth of the shaper are also investigated.

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.

Tooth Surface Error Correction for Face-Hobbed Hypoid Gears

2009 ◽  
Vol 132 (1) ◽  
Author(s):  
Qi Fan
Keyword(s):  
Machine Tool ◽  
Machining Process ◽  
Tooth Surface ◽  
Surface Geometry ◽  
Premature Failure ◽  
Hypoid Gears ◽  
Surface Errors ◽  
The Face ◽  
Spiral Bevel ◽  
Universal Motion

Face-hobbing is a continuous generating process employed in manufacturing spiral bevel and hypoid gears. Due to machining dynamics and tolerances of machine tools, the exact tooth surface geometry may not be obtained from the machining process using theoretical machine tool settings. Repeatable tooth surface geometric errors may be observed. The tooth surface errors will cause unfavorable displacement of tooth contact and increased transmission errors, resulting in noisy operation and premature failure due to edge contact and highly concentrated stresses. In order to eliminate the tooth surface errors and ensure precision products, a corrective machine setting technique is employed to modify the theoretical machine tool settings, compensating for the surface errors. This paper describes a method of correcting tooth surface errors for spiral bevel and hypoid gears generated by the face-hobbing process using computer numerically controlled hypoid gear generators. Polynomial representation of the universal motions of machine tool settings is considered. The corrective universal motion coefficients are determined through an optimization process with the target of minimization of the tooth surface errors. The sensitivity of the changes of the tooth surface geometry to the changes of universal motion coefficients is investigated. A numerical example of a face-hobbed hypoid pinion is presented.

Function-Oriented Designing and Generating Technology for the Point-Contact Tooth Surfaces of Spiral Bevel and Hypoid Gears

2008 ◽  
Vol 44-46 ◽  
pp. 495-502 ◽  
Author(s):  
Xun Cheng Wu ◽  
Cong Li ◽  
Ruo Ping Zhang ◽  
Hai Bo Zhang
Keyword(s):  
Point Contact ◽  
Transmission Function ◽  
Tooth Surface ◽  
Free Form ◽  
Tooth Contact ◽  
Hypoid Gears ◽  
Contact Points ◽  
Tooth Surfaces ◽  
Spiral Bevel ◽  
Basic Equations

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.

Computerized Modeling and Simulation of Spiral Bevel and Hypoid Gears Manufactured by Gleason Face Hobbing Process

2005 ◽  
Vol 128 (6) ◽  
pp. 1315-1327 ◽  
Author(s):  
Qi Fan
Keyword(s):  
Modeling And Simulation ◽  
Surface Generation ◽  
Tooth Surface ◽  
Generation Model ◽  
Tooth Contact Analysis ◽  
Hypoid Gears ◽  
Left Hand ◽  
The Face ◽  
Blade Edge ◽  
Spiral Bevel

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.

Enhanced Algorithms of Contact Simulation for Hypoid Gear Drives Produced by Face-Milling and Face-Hobbing Processes

2006 ◽  
Vol 129 (1) ◽  
pp. 31-37 ◽  
Author(s):  
Qi Fan
Keyword(s):  
Face Milling ◽  
Numerical Control ◽  
Surface Generation ◽  
Tooth Surface ◽  
Free Form ◽  
Generic Model ◽  
Hypoid Gear ◽  
Hypoid Gears ◽  
Contact Patterns ◽  
Spiral Bevel

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.

An Ease-Off Based Method for Loaded Tooth Contact Analysis of Hypoid Gears Having Local and Global Surface Deviations

2010 ◽  
Vol 132 (7) ◽  
Author(s):  
M. Kolivand ◽  
A. Kahraman
Keyword(s):  
Gear Tooth ◽  
Contact Analysis ◽  
Tooth Surface ◽  
Hypoid Gear ◽  
Tooth Contact Analysis ◽  
Tooth Contact ◽  
Hypoid Gears ◽  
Surface Deviations ◽  
Tooth Surfaces ◽  
Loaded Tooth Contact Analysis

Actual hypoid gear tooth surfaces do deviate from the theoretical ones either globally due to manufacturing errors or locally due to reasons such as tooth surface wear. A practical methodology based on ease-off topography is proposed here for loaded tooth contact analysis of hypoid gears having both local and global deviations. This methodology defines the theoretical pinion and gear tooth surfaces from the machine settings and cutter parameters, and constructs the surfaces of the theoretical ease-off and roll angle to compute for the unloaded contact analysis. This theoretical ease-off topography is modified based on tooth surface deviations and is used to perform a loaded tooth contact analysis according to a semi-analytical method proposed earlier. At the end, two examples, a face-milled hypoid gear set having local deviations and a face-hobbed one having global deviations, are analyzed to demonstrate the effectiveness of the proposed methodology in quantifying the effect of such deviations on the load distribution and the loaded motion transmission error.

Optimization of Face Cone Element for Spiral Bevel and Hypoid Gears

2011 ◽  
Vol 133 (9) ◽  
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 machines.

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