Computer-Aided Machine Setting for Lapping Optimization

2009 ◽  
Vol 131 (3) ◽  
Author(s):  
Qimi Jiang ◽  
Claude Gosselin ◽  
Jack Masseth
Keyword(s):  
Contact Region ◽  
Tooth Surface ◽  
Wear Coefficient ◽  
Hypoid Gears ◽  
Wear Process ◽  
Light Load ◽  
Computer Aided ◽  
Tooth Surfaces ◽  
Machine Setting ◽  
Point To Point

During hypoid gears lapping process, a gear set is running at varying operating positions and under a light load in order to lap the complete tooth surface. The pinions and gears are lapped in pairs. Hence, their tooth surfaces are not only cutters but also workpieces. In the contact region, the contact pressure and sliding speed are different from point to point. This makes lapping to be a very complicated abrasive wear process. So far, knowledge about the relationship between the removed materials and the lapping time as well as how to optimize the lapping process is quite limited. An algorithm was presented (Jiang et al., 2008, “Simulation of Hypoid Gear Lapping,” ASME J. Mech. Des., 130(11), p. 112601) to determine the wear coefficient k for the lapping process of hypoid gears. With the obtained wear coefficient k, a methodology for simulating the lapping process was proposed. Based on the wear coefficient obtained, this work presents a computer-aided machine setting procedure to optimize the lapping cycle in order to improve the lapping quality and efficiency.

Simulation of Hypoid Gear Lapping

2008 ◽  
Vol 130 (11) ◽  
Author(s):  
Qimi Jiang ◽  
Claude Gosselin ◽  
Jack Masseth
Keyword(s):  
Gear Tooth ◽  
Tooth Surface ◽  
Wear Coefficient ◽  
Modeling Tools ◽  
Hypoid Gears ◽  
Coordinate Measurement ◽  
Sliding Motion ◽  
Light Load ◽  
Tooth Surfaces ◽  
Initial Results

In the lapping process of hypoid gears, a gear set is run at varying operating positions and under a light load in order to lap the complete tooth surface. Because of the rolling and sliding motion inherent to hypoid gears, the lapping compound acts as an abrasive and refines the tooth surface to achieve smoothness in rolling action and produce high quality gear sets. In this paper, the lapping process is reproduced using advanced modeling tools such as gear tooth vectorial simulation for the tooth surfaces and reverse engineering to analyze the tooth contact pattern of existing gear sets. Test gear sets are measured using a coordinate measurement machine prior to a special lapping cycle where the position of the gear sets on the lapper does not change, and then are remeasured after lapping in order to establish how much and where material was removed. A wear constant named “wear coefficient” specific to the lapping compound is then calculated. Based on the obtained wear coefficient value, an algorithm for simulating the lapping process is presented. Gear sets lapped on the production line at AAM are used for simulation case studies. Initial results show significant scattering of tooth distortion from tooth to tooth and from gear set to gear set, which makes the simulation process difficult. However, it is possible to predict a confidence range within which actual lapping should fall, thereby opening the door to the optimization of the lapping process.

Mathematical Model of Klingelnberg Cyclo-Palloid Hypoid Gear

2013 ◽  
Vol 341-342 ◽  
pp. 572-576 ◽  
Author(s):  
Jin Fu Du ◽  
Zong De Fang ◽  
Min Xu ◽  
Xing Long Zhao ◽  
Yu Min Feng
Keyword(s):  
Mathematical Model ◽  
Contact Analysis ◽  
Tooth Surface ◽  
Hypoid Gear ◽  
Tooth Contact Analysis ◽  
Tooth Contact ◽  
Hypoid Gears ◽  
Tooth Surfaces ◽  
Normal Vectors

The geometry of the tooth surface is important for tooth contact analysis, load tooth contact analysis and the ease-off of gear pairs. This paper presents a mathematical model for the determination of the tooth geometry of Klingelnberg face-hobbed hypoid gears. The formulation for the generation of gear and pinion tooth surfaces and the equations for the tooth surface coordinates are provided in the paper. The surface coordinates and normal vectors are calculated and tooth surfaces and 3D tooth geometries of gear and pinion are obtained. This method may also applied to other face-hobbing gears.

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.

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.

Adaptive data-driven modular control approach to computer aided process planning for manufacturing spiral bevel and hypoid gears

2020 ◽  
pp. 095440542095676
Author(s):  
Kaibin Rong ◽  
Han Ding ◽  
Jinyuan Tang
Keyword(s):  
Process Planning ◽  
High Order ◽  
Data Driven ◽  
Computer Aided Process Planning ◽  
Hypoid Gears ◽  
Modular Control ◽  
Computer Aided ◽  
Gear Manufacturing ◽  
Machine Setting ◽  
Spiral Bevel

Machine setting modification has been an increasingly important access to the accurate flank manufacturing geometric accuracy control for spiral bevel and hypoid gears. More recently, machine setting driven integration of the theoretical design and the actual gear manufacturing is gaining more and more attention. In this paper, the traditional machine setting modification is extended to the case when higher-order component of the prescribed ease-off flank topography is investigated in form of high-order polynomial expression. Moreover, the actual gear manufacturing and general measurement are integrated into an adaptive data-driven high-order machine setting modification. In particular, this modification method is used to perform adaptive modular control for computer aided process planning (CAPP). Here, a data-driven operation and optimization is developed for adaptive high-order modification. It mainly includes: (i) Polynomial fitting and its optimization by using overall interpolation based on energy method, (ii) Data-driven ease-off flank parametrization based on the fastest descent Newton iteration method, (iii) adaptive control strategy by considering the sensitivity analysis, and (iv) Levenberg-Marquardt (L-M) based approximation for high-order machine setting modification. Given numerical test can verify the proposed method.

How to Obtain the Formal Tooth Bearing Pattern Between Hypoid Gear and the Conjugate Pinion

2000 ◽  
Author(s):  
Norio Ito ◽  
Koichi Takahashi
Keyword(s):  
Conventional Method ◽  
Analytical Method ◽  
Second Order ◽  
Tooth Surface ◽  
Gear Pair ◽  
Hypoid Gear ◽  
Third Order ◽  
Hypoid Gears ◽  
Gear Cutting ◽  
Tooth Surfaces

Abstract In this paper, the relationships between the conjugate tooth surfaces of hypoid gears and the formal tooth bearing pattern are presented. First, we introduce the tooth surface elements necessary for the tooth bearing. Next, the tooth bearing pattern, which changes according to the generating condition of the pinion, is introduced. The hypoid gear pair is a formate gear and the pinion generated to run with such a gear. The conventional method for analyzing the tooth bearing pattern has been developed by the motion of generation between second-order tooth surfaces. In this paper, the tooth surface is expressed by the original third-order tooth surface, and the tooth bearing pattern is analyzed by the meshing motion of the tooth surface. The tooth bearing pattern obtained from such an analytical method becomes the formal tooth bearing. Therefore, the machine settings for accurate gear cutting become possible, and the desired tooth bearing pattern can be obtained beforehand without a trial cutting.

Tooth Contact Analysis and Manufacture on Multitasking Machine of Large-Sized Straight Bevel Gears With Equi-Depth Teeth

2013 ◽  
Vol 135 (3) ◽  
Author(s):  
Isamu Tsuji ◽  
Kazumasa Kawasaki ◽  
Hiroshi Gunbara ◽  
Haruo Houjoh ◽  
Shigeki Matsumura
Keyword(s):  
Contact Analysis ◽  
Tooth Surface ◽  
Contact Pattern ◽  
Tooth Contact Analysis ◽  
Tooth Contact ◽  
Form Errors ◽  
Bevel Gears ◽  
Computer Aided ◽  
Tooth Surfaces ◽  
Tooth Flank

Straight bevel gears are widely used in the plant of large-sized power generation when the gears have large size. The purpose of this study is to manufacture the large-sized straight bevel gears with equi-depth teeth on a multitasking machine. The manufacturing method has the advantages of arbitrary modification of the tooth surface and machining of the part without the tooth surface. For this study, first, the mathematical model of straight bevel gears by complementary crown gears considering manufacture on multitasking machine is proposed, and the tooth contact pattern and transmission errors of these straight bevel gears with modified tooth surfaces are analyzed in order to clarify the meshing and contact of these gears. Next, the numerical coordinates on the tooth surfaces of the bevel gears are calculated and the tooth profiles are modeled using a 3D-Computer-Aided Design (CAD) system. Five-axis control machines were utilized. The gear-work was machined by a swarf cutting using a coated carbide end mill. After rough cutting, the gear-work was heat-treated, and it was finished based on a Computer-Aided Manufacturing (CAM) process through the calculated numerical coordinates. The pinion was also machined similarly. The real tooth surfaces were measured using a coordinate measuring machine and the tooth flank form errors were detected using the measured coordinates. As a result, the obtained tooth flank form errors were small. In addition, the tooth contact pattern of the manufactured large-sized straight bevel gears was compared with those of tooth contact analysis. The data showed good agreement.

Error-sensitivity analysis for hypoid gears using a real tooth surface contact model

2016 ◽  
Vol 231 (3) ◽  
pp. 507-521 ◽  
Author(s):  
Gang Li ◽  
Zhonghou Wang ◽  
Aizoh Kubo
Keyword(s):  
Sensitivity Analysis ◽  
Discrete Data ◽  
Tooth Surface ◽  
Analysis Model ◽  
Tooth Contact Analysis ◽  
Hypoid Gears ◽  
Error Sensitivity ◽  
Tooth Surfaces ◽  
Data Points ◽  
Error Sensitivity Analysis

Accurately and rapidly evaluated error sensitivity of actual tooth surfaces of hypoid gears can be a significant foundation for a variety of dynamic preference analysis and machine tool setting readjustments. Due to the complexity of local geometric features as well as the limitations of the data measurement on tooth surfaces of hypoid gears, automated error-sensitivity analysis for actual tooth surfaces still presents many substantial challenges. This paper presents a novel methodology for the error-sensitivity analysis of real tooth surfaces of hypoid gears. The methodology combines an error-sensitivity analysis model with a numerical analytical real tooth contact analysis (RTCA) model. The real tooth surfaces, describing local micro-geometry features on actual tooth surfaces, have been produced by 3D discrete data points reconstruction. In this method, the discrete data points on actual tooth surfaces are measured by using a coordinate measure machine (CMM). The location, size, and shape of contact patterns are determined from the predicted interference areas distribution by numerical analysis. In addition, the error-sensitivity analysis model is established for evaluation of the sensitivity of hypoid gears with real tooth surfaces that corresponds to misalignments. The results of experiment show that the proposed method can obtain actual contact properties that significantly improve the basic design performances significantly.

Function-Oriented Design and Verification of Point-Contact Tooth Surfaces of Spiral Bevel and Hypoid Gears with the Generated Gear

2010 ◽  
Vol 118-120 ◽  
pp. 675-680
Author(s):  
Xun Cheng Wu ◽  
Cong Li
Keyword(s):  
Mathematical Model ◽  
Point Contact ◽  
Bevel Gear ◽  
Tooth Surface ◽  
Hypoid Gears ◽  
Contact Points ◽  
Tooth Surfaces ◽  
Spiral Bevel ◽  
The Mathematical Model ◽  
Gear Machine

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.

Methods of Synthesis and Analysis for Hypoid Gear-Drives of “Formate” and “Helixform”—Part 1. Calculations For Machine Settings For Member Gear Manufacture of the Formate and Helixform Hypoid Gears

1981 ◽  
Vol 103 (1) ◽  
pp. 83-88 ◽  
Author(s):  
F. L. Litvin ◽  
Y. Gutman
Keyword(s):  
Tooth Surface ◽  
Hypoid Gear ◽  
Local Synthesis ◽  
Hypoid Gears ◽  
Methods Of Synthesis ◽  
Machine Setting ◽  
Gear Drives ◽  
Gear Manufacture

Methods for synthesis and analysis Hypoid gears generated by Helixform and Formabe methods are suggested. The article is a three-part one divided according to the considered stages of synthesis and analysis: (a) the determination of machine settings for the member-gear manufacture (after that tooth surface of the member-gear can be obtained); (b) machine setting calculations for the pinion on the base of the local synthesis for gears with approximate meshing; (c) methods for analysis (in the whole area of meshing) and optional synthesis for the mismatch gearing and its application for Hypoid gears.

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