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.

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]

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.

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.

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.

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

2007 ◽  
Author(s):  
Yi-Pei Shih ◽  
Zhang-Hua Fong
Keyword(s):  
Correction Method ◽  
Numerical Control ◽  
Cnc Machine ◽  
Hypoid Gears ◽  
Nc Code ◽  
Machine Errors ◽  
Highly Sensitive ◽  
Spiral Bevel ◽  
Tooth Flank ◽  
Cutter Head

Because the contact bearings 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.

Multi-Toothed Milling Force Model and Simulation for Form Milling the Gear of the Hypoid Gears

2011 ◽  
Vol 328-330 ◽  
pp. 90-95 ◽  
Author(s):  
Xin Jie Jia ◽  
Xiao Zhong Deng ◽  
Xiao Zhong Ren
Keyword(s):  
Face Milling ◽  
Force Model ◽  
Geometrical Theory ◽  
Hypoid Gear ◽  
Milling Force ◽  
Hypoid Gears ◽  
Model And Simulation ◽  
Simulation Results ◽  
Milling Forces ◽  
Milling Force Model

Prediction of the forces in milling hypoid gear was often needed in order to establish automation and optimization of the tooth-milling processes. Based on the geometrical theory of the format face-milling, the multi-toothed milling forces theoretical model for form milling the gear of the hypoid gears is presented, the milling force factors were calibrated via single factor experiments and the simulation programs were prepared. Experiments were carried out to verify the availability of the multi-toothed dynamic milling force model, the experimental results is consistent with the simulation results.

Optimization of Pinion Roughing of Spiral Bevel and Hypoid Gear

2006 ◽  
Vol 220 (4) ◽  
pp. 483-488 ◽  
Author(s):  
J-G Li ◽  
S-M Mao ◽  
J-L He ◽  
X-T Wu
Keyword(s):  
Complex Shape ◽  
Bending Strength ◽  
Bending Stress ◽  
Hypoid Gear ◽  
Blade Profile ◽  
Hypoid Gears ◽  
Cutter Life ◽  
Gear Manufacturing ◽  
Heavy Truck ◽  
Spiral Bevel

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.

Determination of cutter-head geometry for the face-milling of hypoid gears

2016 ◽  
Vol 86 (9-12) ◽  
pp. 3081-3090 ◽  
Author(s):  
Muhammad Wasif ◽  
Zezhong Chevy Chen ◽  
Syed Mehmood Hasan
Keyword(s):  
Face Milling ◽  
Hypoid Gears ◽  
The Face ◽  
Cutter Head

scholarly journals A new Approach to Computer Analysis of Queuing Systems Without Programming

2015 ◽  
Vol 9 (1) ◽  
Author(s):  
Zoran Ž. Avramović ◽  
Radomir Z. Radojičić ◽  
Saša D. Mirković
Keyword(s):  
Mathematical Model ◽  
Object Oriented ◽  
Object Oriented Programming ◽  
Programming System ◽  
Queuing Systems ◽  
Queuing Network ◽  
New Approach ◽  
Computer Performance ◽  
Basic Characteristics ◽  
Significant Application

The paper presents original object oriented programming system ARS for modelling and simulation queuing systems. Programming system was developed in programming language C++. It establishes connection with intrinsic, but also with other Windows programming packages, in a simple way, through object oriented environment. Basic characteristics and possibilities of programming system, as well as comparative analysis of simulators: mathematical model (analytical solution) - GPSS/H - ARS, on the example of closed queuing network in the paper is given. The significant application for computer performance evaluation is reported.

Feature Based Numerical Bearing Pattern Development and Optimization for Spiral-Bevel and Hypoid Gears

2000 ◽  
Author(s):  
Claude Gosselin
Keyword(s):  
Automobile Industry ◽  
Control Parameters ◽  
Hypoid Gear ◽  
Hypoid Gears ◽  
Novel Approach ◽  
Tooth Surfaces ◽  
Feature Based ◽  
Pattern Development ◽  
The Mean ◽  
Spiral Bevel

Abstract A novel approach to the development of the bearing pattern for spiral-bevel and hypoid gears is presented. The numerical method uses the concept of “potential point of contact” to determine the shape of the separation between the meshing tooth surfaces in the vicinity of the Mean Point. Machine settings are used as control parameters in the numerical solution to modify the shape and location of the bearing pattern. The presented method, which has been used in the automobile industry for several years, allows substantial freedom in the development of spiral bevel and hypoid gear sets, even on conventional generators.

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