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.

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.

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.

Advanced Developments in Computerized Design and Manufacturing of Spiral Bevel and Hypoid Gear Drives

2011 ◽  
Vol 86 ◽  
pp. 439-442 ◽  
Author(s):  
Qi Fan
Keyword(s):  
Error Correction ◽  
Surface Generation ◽  
Tooth Surface ◽  
Hypoid Gear ◽  
Form Error ◽  
Tooth Contact Analysis ◽  
Hypoid Gears ◽  
Design And Manufacturing ◽  
Spiral Bevel ◽  
Gear Drives

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.

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.

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

2009 ◽  
Author(s):  
M. Kolivand ◽  
A. Kahraman
Keyword(s):  
Gear Tooth ◽  
Contact Analysis ◽  
Tooth Surface ◽  
Surface Wear ◽  
Tooth Contact Analysis ◽  
Tooth Contact ◽  
Hypoid Gears ◽  
Manufacturing Errors ◽  
Spiral Bevel ◽  
Loaded Tooth Contact Analysis

Manufacturing errors typically cause real (measured) spiral bevel and hypoid gear surfaces to deviate from the theoretical ones globally. Tooth surface wear patterns accumulated through the life span of the gear set are typically local deviations that are aggravated especially in case of edge contact conditions. An accurate and practical methodology based on ease-off topography is proposed in this study to perform loaded tooth contact analysis of spiral bevel and hypoid gears having both types of local and global deviations. It starts with definition of the theoretical pinion and gear tooth surfaces from the machine settings and cutter parameters, and constructs the theoretical ease-off and roll angle surfaces to compute unloaded contact analysis. Manufacturing errors and localized surface wear deviations are considered to update the theoretical ease-off to form a new ease-off surface that is used to perform a loaded tooth contact analysis according to the semi-analytical method proposed earlier. At the end, a numerical example with locally deviated surfaces is analyzed to demonstrate the effectiveness of the proposed methodology as well as quantifying the effect of such deviations on load distribution and the loaded motion transmission error.

A novel operation approach to determine initial contact point for tooth contact analysis with errors of spiral bevel and hypoid gears

2017 ◽  
Vol 109 ◽  
pp. 155-170 ◽  
Author(s):  
Han Ding ◽  
Yuansheng Zhou ◽  
Jinyuan Tang ◽  
Jue Zhong ◽  
Zhenyu Zhou ◽  
...  
Keyword(s):  
Contact Point ◽  
Contact Analysis ◽  
Initial Contact ◽  
Tooth Contact Analysis ◽  
Tooth Contact ◽  
Hypoid Gears ◽  
Spiral Bevel

scholarly journals Theoretical and Experimental Study on Contact Characteristics of Spiral Bevel Gears under Quasi-Static and Large Loading Conditions

2020 ◽  
Vol 10 (15) ◽  
pp. 5109 ◽  
Author(s):  
Yimeng Fu ◽  
Yaobing Zhuo ◽  
Xiaojun Zhou ◽  
Bowen Wan ◽  
Haoliang Lv ◽  
...  
Keyword(s):  
Finite Element ◽  
Performance Test ◽  
Element Model ◽  
Transmission Error ◽  
Tooth Surface ◽  
Tooth Contact Analysis ◽  
Spiral Bevel Gears ◽  
Bevel Gears ◽  
Transition Surface ◽  
Spiral Bevel

The precise mathematical model for the tooth surface and transition surface of spiral bevel gears is derived. Taking a pair of spiral bevel gears of a heavy vehicle as an example of calculation and analysis, a finite element model of spiral bevel gears transmission system is established. Through the finite element tooth contact analysis under quasi-static loading and high loading condition, the influences of torque on the root stress distribution, contact stress, and transmission error are discussed, and the results are compared with the empirical formula results. Finally, a contact performance test bench of spiral bevel gear pair is developed, then the root bending stress, contact pattern, and transmission error tests are carried out. These experiment results are compared with analyzed ones, which showed a good agreement.

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