A General Method for Computing Worm Gear Conjugate Mesh Property: Part 2—The Mathematic Model of Worm Gear Manufacturing and Working Processes

1989 ◽  
Vol 111 (1) ◽  
pp. 148-152 ◽  
Author(s):  
Changqi Zheng ◽  
Jirong Lei
Keyword(s):  
Contact Line ◽  
Relative Velocity ◽  
Velocity Vector ◽  
Gear Tooth ◽  
Mathematic Model ◽  
Worm Gear ◽  
Tooth Surface ◽  
Gear Manufacturing ◽  
General Method ◽  
Working Processes

Part 2 of this article is devoted to building a generalized mathematic model of worm gear manufacturing and working processes which can be used for calculating the contact line, the profile, the normal curvature, the conjugate boundary and the angle between the directions of contact line and relative velocity vector for any kind of worm gear tooth surface.

A General Method for Computing Worm Gear Conjugate Mesh Property: Part 1—The Generating Surface

1989 ◽  
Vol 111 (1) ◽  
pp. 143-147 ◽  
Author(s):  
Changqi Zheng ◽  
Jirong Lei ◽  
Michael Savage
Keyword(s):  
Mathematical Description ◽  
Gear Tooth ◽  
Mathematic Model ◽  
Worm Gear ◽  
Tooth Surface ◽  
Initial Curve ◽  
Parametric Description ◽  
General Method

This article is a two-part one: (1) the generating surface; (2) the mathematic model of the worm gear tooth surface. In this paper, a general method is presented for the description of generating surface enveloping any kind of worm tooth surface. This method is laid on the parametric description of the dresser curve as an initial curve. The initial curves of four common dressers are presented. By using these descriptions, the mathematical description and properties of any kind of worm gear tooth surface can also be obtained.

Mesh analysis for toroidal drive with roller teeth

2008 ◽  
Vol 222 (3) ◽  
pp. 473-481
Author(s):  
L Xu ◽  
Z Huang
Keyword(s):  
Contact Line ◽  
Relative Velocity ◽  
Velocity Vector ◽  
Current Paper ◽  
Normal Curvature ◽  
Tooth Surface ◽  
Contact Lines ◽  
Mesh Analysis ◽  
Meshing Equation ◽  
Design And Manufacture

In the current paper, for the toroidal drive with roller teeth, its meshing equation, equations of the contact lines, the limit curves, the induced normal curvature, and the angle of the relative velocity vector to the contact line are determined. Using the equations, contact lines, meshing zones, limit curves, induced normal curvatures, and angles of the relative velocity vector to the contact line are calculated for two kinds of the toroidal drives with roller teeth, respectively. The results are compared with those for the toroidal drive with ball teeth. For the roller tooth surface of the drive, the distribution of the mesh parameters has given. The changes of the mesh parameters along with drive parameters have been investigated. The results are compared with those for the toroidal drive with ball teeth. The results are useful for design and manufacture of the toroidal drive.

A parameterized numerical method for generating discrete helical gear tooth surface allowing non-standard geometry

2008 ◽  
Vol 222 (6) ◽  
pp. 1033-1038 ◽  
Author(s):  
J Hedlund ◽  
A Lehtovaara
Keyword(s):  
Gear Tooth ◽  
Numerical Approach ◽  
Helical Gear ◽  
Tooth Surface ◽  
Tool Profile ◽  
Standard Geometry ◽  
Gear Manufacturing ◽  
Involute Gears ◽  
Gear Geometry ◽  
Tooth Flank

Gear analysis is typically performed using calculation based on gear standards. Standards provide a good basis in gear geometry calculation for involute gears, but these are unsatisfactory for handling geometry deviations such as tooth flank modifications. The efficient utilization of finite-element calculation also requires the geometry generation to be parameterized. A parameterized numerical approach was developed to create discrete helical gear geometry and contact line by simulating the gear manufacturing, i.e. the hobbing process. This method is based on coordinate transformations and a wide set of numerical calculation points and their synchronization, which permits deviations from common involute geometry. As an example, the model is applied to protuberance tool profile and grinding with tip relief. A fairly low number of calculation points are needed to create tooth flank profiles where error is <1 μm.

Quality Control Method Based on Gear Tooth Contact Evaluation Using Near-Infrared Ray Imagery

2010 ◽  
Vol 447-448 ◽  
pp. 569-573
Author(s):  
Masaki Nagata ◽  
Toshiki Hirogaki ◽  
Eiichi Aoyama ◽  
Takahiro Iida ◽  
Yasuhiro Uenishi ◽  
...  
Keyword(s):  
Contact Area ◽  
Near Infrared ◽  
Control Method ◽  
Gear Tooth ◽  
Scattered Light ◽  
Infrared Image ◽  
Tooth Surface ◽  
Image Method ◽  
Tooth Contact ◽  
Gear Manufacturing

Conventionally, tooth contact evaluation has been performed visually by machine operators in gear manufacturing fields when finishing a gear or during assembly. With automation, the contact area’s boundary is unclear due to scattered light when visible light is used to obtain an image for tooth contact evaluation. We therefore focused on using near-infrared to prevent scattered light. First, we confirmed that the tooth contact image obtained by image binarization is hardly affected by the image threshold. Second, we propose a new method to extract the boundary part of the tooth contact by differential calculation of the fine near-infrared image. These methods allow automatic division of near-infrared images into the contact area, the boundary, and the non-contact area. Finally, the obtained result is compared with the tooth contact calculated from the measured tooth surface. We demonstrated that the near-infrared image method is effective for automatic tooth contact evaluation.

Optimal Design of Modified Cylindrical Gear Based on Minimum Flash Temperature of Tooth Surfaces

2013 ◽  
Vol 655-657 ◽  
pp. 573-577
Author(s):  
Jin Ke Jiang ◽  
Zong De Fang ◽  
Xian Long Peng
Keyword(s):  
Friction Coefficient ◽  
Film Thickness ◽  
Contact Line ◽  
Gear Tooth ◽  
Tooth Surface ◽  
Uniform Grid ◽  
Normal Vector ◽  
Flash Temperature ◽  
Oil Film ◽  
Tooth Surfaces

Considering the gap of the contact line of modified involute cylindrical gears influencing on loads, oil film thickness, the friction coefficient was determined on the basis theory of TCA、 LTCA and EHL. so oil film thickness and friction coefficient corresponded with loads on contact line were dispersed, which was used to computed discrete temperature according to the Blok flash temperature formula. and an approach of modified tooth surface optimum design based on the minimum flash temperature was proposed: the modified tooth surfaces was defined as a sum of theoretical tooth and cubic B-spline fit surface based on the uniform grid points created by double parabolas and a straight line and whose normal vector was deduced, besides, used genetic algorithm to optimize the parameter of curve, and get the best modified gear tooth surfaces. the results shows that oil film is thicker in engaging-out, coefficient of friction is contrary, which is responsible for lower flash temperature in engaging-in, besides the flash temperature has little changes in the single tooth meshing zone, and helical gear has a lower flash temperature than spur gear due to higher overlap ratio.

Sensitivity Analysis and Surface-Deviation Minimization of ZK-Type Dual-Lead Worm Gear Drives

1999 ◽  
Vol 121 (3) ◽  
pp. 409-415 ◽  
Author(s):  
Biing-Wen Bair ◽  
Chung-Biau Tsay
Keyword(s):  
Mathematical Model ◽  
Sensitivity Analysis ◽  
Machine Tool ◽  
Gear Tooth ◽  
Data File ◽  
Worm Gear ◽  
Tooth Surface ◽  
Tool Profile ◽  
Surface Deviation ◽  
Dual Lead

This work uses the mathematical model of ZK-type dual-lead worm gear drive proposed in our recent work (1998). Based on the proposed mathematical model, coordinates and unit normals of the worm gear surface grid points can be determined and a data file subsequently formed. The data file is considered as the theoretical tooth surface data and then input into the computer of a three-dimensional coordinate measurement machine (3-D CMM) to numerically calculate the surface deviations of a real-cut worm gear. In addition, a computerized tooth surface measurement model compatible with the 3-D CMM is developed. Sensitivity analysis is also performed on machine-tool settings and tool-profile errors to the generated gear tooth surface variations. Minimization on gear tooth surface variations can be determined by applying the proposed measurement and calculation methods. In addition, optimum machine tool settings and tool-profile modifications are obtained by applying the developed computer simulation softwares. Moreover, the singular value decomposition (SVD) and sequential quadratic programming (SQP) methods are compared to establish the optimum machine-tool settings and resolve the minimum surface deviation problems.

Meshing Characteristic of Arc-Toothed Cylindrical Worm Pair and Cutting Geometric Condition of Its Worm

2020 ◽  
Vol 143 (6) ◽  
Author(s):  
Qingxiang Meng ◽  
Yaping Zhao ◽  
Jian Cui ◽  
Tonghao Dou
Keyword(s):  
Gear Tooth ◽  
Numerical Results ◽  
Worm Gear ◽  
Lubricating Oil ◽  
Tooth Surface ◽  
Geometric Condition ◽  
Normal Vector ◽  
Helical Surface ◽  
Double Line ◽  
Working Length

Abstract The arc-toothed cylindrical worm has an arc tooth profile in a section, which may be the axial section, the normal section, or an offsetting plane of the worm helical surface. The meshing principle for a gearing containing such a worm is established. The normal vector of instantaneous contact line is determined in the natural frame and the meshing performance parameters are obtained without the help of the curvature parameters of the worm helical surface to ensure the established meshing principle is concise and practical. The numerical results show that the worm working length can be beyond half of the thread length and the meshing zone of the worm pair can cover most of the worm gear tooth surface. The instantaneous contact lines are uniformly distributed and the worm pair forms double-line contact. The numerical outcomes of the induced principal curvature show that the contact stress level between the teeth is higher in the middle of the worm gear tooth surface and near its dedendum. The forming condition of the lubricating oil film is poorer in the middle of the worm gear tooth surface and from addendum to dedendum as demonstrated by the numerical results of the sliding angle. The normal arc-toothed worm lathed by an offsetting cutter is recommended to apply in industry after various researches and analyses. The cutting geometric condition of the worm is investigated quantitatively. It is discovered that the rule of the cutter working relief angle changes along the cutting edge during lathing the worm.

scholarly journals Analysis of the mathematical correlation between post-sharped hob and worm gear tooth surface

2021 ◽  
Vol 11 (4) ◽  
pp. 278-286
Author(s):  
József Ábel
Keyword(s):  
Gear Tooth ◽  
Research Work ◽  
Worm Gear ◽  
Tooth Surface ◽  
Axial Section ◽  
Surface Error ◽  
Mathematical Correlation ◽  
General Mathematical Model ◽  
Manufacturing Knowledge ◽  
Gear Drives

The production geometry development of the worm gear drives with circle arched profile in axial section requires the combined management of complex mathematical, geometric and manufacturing knowledge. In this paper has been presented an analysis of the relation between the post-sharpening of the cylindrical hob with circle arched profile in axial section and gear tooth surface error according to the functions determined by previous research work, that fits to the Dudás type ProMAT general mathematical model, which is suitable for the analysis of technological processes in manufacturing. During the research the extension of this method to any type of worm gear drives has been aspired.

Variable height modification of TA worm drive

2018 ◽  
Vol 233 (1) ◽  
pp. 227-243 ◽  
Author(s):  
Chongfei Huai ◽  
Yaping Zhao
Keyword(s):  
Theoretical Analysis ◽  
Contact Line ◽  
Gear Tooth ◽  
Computing Methods ◽  
Normal Operation ◽  
Tooth Surface ◽  
Modification Method ◽  
Worm Gearing ◽  
Meshing Characteristics ◽  
Worm Drive

The related research shows that a constant contact line, which is negative for the normal operation of the worm gearing, exists on the middle of the unmodified and the constant height modified TA worm wheel surface. To overcome this drawback, a variable height modification method is proposed for the TA worm drive. In line with this modification method, the height modification parameter is variable during the whole processing cycle. Accordingly, the obtained gearing can be named as the variable height modified TA worm drive. The mathematical model for the meshing analysis of this novel worm drive is established according to its generation mechanism and the mesh theory of gearing. The reason why the variable height modification can remove the constant contact line on the worm gear tooth surface is analyzed in detail. In addition, the classification criterion of the transmission type is also derived. The computing methods of the key points on the contact zone boundary and the instantaneous meshing line are elaborated. On the basis of the above theoretical analysis, the meshing characteristics of this novel worm gearing are well investigated. The results manifest that the above theoretical analysis is valid, and the obtained gearing has favorable meshing properties. Furthermore, it is pointed out that the linear variable height modification with larger quantity can be recommended as the ideal strategy in practice.

Sign in / Sign up

Export Citation Format

Share Document