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.

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.

An Investigation on the Design of Formate and Generate Face Milled Hypoid Gears

2020 ◽  
Author(s):  
Tufan Gürkan Yılmaz ◽  
Onur Can Kalay ◽  
Fatih Karpat ◽  
Mert Doğanlı ◽  
Elif Altıntaş
Keyword(s):  
Power Transmission ◽  
Face Milling ◽  
Tool Geometry ◽  
Hypoid Gear ◽  
Mathematical Equation ◽  
Spiral Bevel Gears ◽  
Hypoid Gears ◽  
Bevel Gears ◽  
Milling Method ◽  
Spiral Bevel

Abstract Hypoid gears are transmission elements that transfer power and moment between shafts whose axes do not intersect. They are similar in structure to spiral bevel gears. However, there are many advantages compared to spiral bevel gears in terms of load carrying capacity and rigidity. Hypoid gear pairs are mostly used as powertrain on the rear axles of cars and trucks. Hypoid gears are manufactured by two essential methods called face-milling and face-hobbing, and there are mainly two relative kinematic movements (Formate® and Generate). In this study, the gears produced with the Face-milling method are discussed. Face milled hypoid gears can be manufactured with both Formate® and Generate, while pinions can only be manufactured with the Generate method. The most crucial factor that determines the performance of hypoid gears is the geometry of hypoid gears. The gear and pinion geometry is directly dependent on the tool geometry, machine parameters, and relative motion between the cradle and the workpiece. The gear geometry determines the contact shape and pressure during power transmission. In this study, the mathematical equation of the cutting tool is set. After that, using differential geometry, coordinate transformation, and the gearing theory, the mathematical equation of hypoid gear is obtained.

Mathematical Model for a Universal Face Hobbing Hypoid Gear Generator

2006 ◽  
Vol 129 (1) ◽  
pp. 38-47 ◽  
Author(s):  
Yi-Pei Shih ◽  
Zhang-Hua Fong ◽  
Grandle C. Y. Lin
Keyword(s):  
Mathematical Model ◽  
Object Oriented ◽  
Face Milling ◽  
Object Oriented Programming ◽  
Hypoid Gear ◽  
Hypoid Gears ◽  
Proposed Model ◽  
Spiral Bevel ◽  
Cutter Head ◽  
Cutting System

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.

Fourth-Order Kinematic Synthesis for Face-Milling Spiral Bevel Gears With Modified Radial Motion (MRM) Correction

2005 ◽  
Vol 128 (2) ◽  
pp. 457-467 ◽  
Author(s):  
Pei-Yu Wang ◽  
Zhang-Hua Fong
Keyword(s):  
Fourth Order ◽  
Face Milling ◽  
Bevel Gear ◽  
Radial Motion ◽  
Numerical Control ◽  
Tooth Surface ◽  
Kinematic Synthesis ◽  
Bevel Gears ◽  
Tooth Surfaces ◽  
Spiral Bevel

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.

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.

Flank Correction for Spiral Bevel and Hypoid Gears on a Six-Axis CNC Hypoid Generator

2008 ◽  
Vol 130 (6) ◽  
Author(s):  
Yi-Pei Shih ◽  
Zhang-Hua Fong
Keyword(s):  
Correction Method ◽  
Numerical Control ◽  
Cnc Machine ◽  
Hypoid Gears ◽  
Nc Code ◽  
Machine Errors ◽  
Contact Patterns ◽  
Spiral Bevel ◽  
Tooth Flank ◽  
Cutter Head

Because the contact patterns of spiral bevel and hypoid gears are highly sensitive to tooth flank geometry, it is desirable to reduce the flank deviations caused by machine errors and heat treatment deformation. Several methods already proposed for flank correction are based on the cutter parameters, machine settings, and kinematical flank motion parameters of a cradle-type universal generator, which are modulated according to the measured flank topographic deviations. However, because of the recently developed six-axis Cartesian-type computer numerical control (CNC) hypoid generator, both face-milling and face-hobbing cutting methods can be implemented on the same machine using a corresponding cutter head and NC code. Nevertheless, the machine settings and flank corrections of most commercial Cartesian-type machines are still translated from the virtual cradle-type universal hypoid generator. In contrast, this paper proposes a flank-correction methodology derived directly from the six-axis Cartesian-type CNC hypoid generator in which high-order correction is easily achieved through direct control of the CNC axis motion. The validity of this flank-correction method is demonstrated using a numerical example of Oerlikon Spirac face-hobbing hypoid gears made by the proposed Cartesian-type CNC machine.

Mathematical Model of Universal Hypoid Generator With Supplemental Kinematic Flank Correction Motions

2000 ◽  
Vol 122 (1) ◽  
pp. 136-142 ◽  
Author(s):  
Zhang-Hua Fong
Keyword(s):  
Mathematical Model ◽  
Computer Program ◽  
Computer Programming ◽  
Object Oriented ◽  
Face Milling ◽  
Helical Motion ◽  
Hypoid Gear ◽  
Hypoid Gears ◽  
The Face ◽  
Spiral Bevel

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]

Generation of Noncircular Spiral Bevel Gears by Face-Milling Method

2016 ◽  
Vol 138 (8) ◽  
Author(s):  
Fangyan Zheng ◽  
Lin Hua ◽  
Dingfang Chen ◽  
Xinghui Han
Keyword(s):  
Face Milling ◽  
Cnc Machining ◽  
Tooth Surface ◽  
Free Form ◽  
Spiral Bevel Gears ◽  
Bevel Gears ◽  
Tooth Surfaces ◽  
Milling Method ◽  
Spiral Bevel ◽  
Crown Gear

Noncircular bevel gears are applied in variable-speed transmissions with intersecting axes. Since dedicated machines for manufacturing noncircular bevel gears are not available, noncircular bevel gears are normally manufactured using universal computer numerically controlled (CNC) machining centers, resulting in poor productivity. This paper describes a face-milling method for generation of noncircular spiral bevel gears, which is analogous to the generation of spiral bevel and hypoid gears using CNC hypoid gear generators, such as Gleason free-form hypoid generators. As a result, the productivity is significantly improved. Based on the theory of gearing, this paper first describes the basic concept of generation of conjugate noncircular spiral bevel gears. Generation of the tooth surfaces using crown-gear generation concept is analytically discussed with association to the face-milling process of generation of the proposed noncircular spiral bevel gears. The tooth surface geometries are represented by the position vectors and normals. The kinematical model of free-form machines is developed. The machine motion parameters are determined based on the theoretically defined tooth surfaces using the crown-gear generation concept. The developed method is verified by manufacturing a real pair of noncircular spiral bevel gears with satisfactory contact patterns which agree well with those modeled using a commercial cae software program.

Cutter Interchangeability for Spiral-Bevel and Hypoid Gear Manufacturing

2003 ◽  
Author(s):  
Claude Gosselin ◽  
Jack Masseth ◽  
Wei Liang
Keyword(s):  
Test Case ◽  
Hypoid Gear ◽  
Hypoid Gears ◽  
Manufacturing Operations ◽  
Before And After ◽  
Gear Manufacturing ◽  
Spiral Bevel ◽  
Tooth Flank ◽  
Tooth Flank Surface Topography ◽  
Flank Surface

In the manufacturing of spiral-bevel and hypoid gears, circular cutter dimensions are usually based on the desired performance of a gear set. In large manufacturing operations, where several hundred gear geometries may have been cut over the years, the necessary cutter inventory may become quite large since the cutter diameters will differ from one geometry to another, which results in used storage space and associated costs in purchasing and maintaining the cutter parts. Interchangeability of cutters is therefore of significant interest to reduce cost while maintaining approved tooth geometries. An algorithm is presented which allows the use of a different cutter, either in diameter and/or pressure angle, to obtain the same tooth flank surface topography. A test case is presented to illustrate the usefulness of the method: the OB cutter diameter of an hypoid pinion is changed from 8.9500" to 9.1000". CMM results and the comparison of the bearing patterns before and after change show excellent correlation, and indicate that the new pinion can be used in place of the original pinion without performance or quality problems. Significant cost reductions may be obtained with the application of the method.

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