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.

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.

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.

The Influence of Gear Hobbing on Worm Gear Characteristics

2005 ◽  
Author(s):  
V. Simon
Keyword(s):  
Computer Program ◽  
Machine Tool ◽  
Finite Number ◽  
Gear Tooth ◽  
Worm Gear ◽  
Tooth Surface ◽  
Design Parameters ◽  
Tooth Contact ◽  
Gear Hobbing

A method is presented for the determination of the influence of gear hobbing on the precision and loaded tooth contact of worm gears. In order to get a worm gear set with fully conjugated teeth surfaces the gear teeth should be processed by a hob whose generator surface is identical to the worm surface. This requirement can be achieved by the use of a hob whose diameter is equal to the worm diameter and with infinite number of cutting edges. But because of the teeth in the hob are relieved, the diameter of the new hob should be slightly larger than the worm diameter to provide tool life. On the other hand, because of the finite number of hob teeth, the gear tooth surface, manufactured by such a hob, is not a smooth surface; it consists of a relatively big number of small parts of helical surfaces formed by the cutting edges of the hob. In this paper a method is presented for the determination of differences between the gear tooth surface processed by an oversized hob of finite number of teeth or by a flying tool, and the theoretically required gear tooth surface. Also the influence of hob oversize and machine tool settings on tooth contact pressure and transmission errors is determined. The full geometry and kinematics of gear tooth processing by an oversized hob or by flying tool is included. The theoretical background is implemented by a computer program. By using this program, the influence of relevant design parameters of worm gear set and hob and of machine tool settings on processed gear tooth errors and on loaded tooth contact of the worm gear pair is investigated and discussed. By another computer program the influence of cutter diameter and machine tool settings for pinion teeth processing on tooth contact pattern in spiral bevel gears is investigated and presented.

The Influence of Gear Hobbing on Worm Gear Characteristics

2007 ◽  
Vol 129 (5) ◽  
pp. 919-925 ◽  
Author(s):  
Vilmos Simon
Keyword(s):  
Machine Tool ◽  
Gear Tooth ◽  
Theoretical Background ◽  
Worm Gear ◽  
Tooth Surface ◽  
Design Parameters ◽  
Tooth Contact ◽  
Transmission Errors ◽  
Gear Hobbing

In this paper, a method is presented for the determination of the differences between the worm gear tooth surface processed by an oversized hob of finite number of teeth or by a flying tool, and the theoretically required gear tooth surface. The influence of hob oversize and machine tool settings on tooth contact pressure and transmission errors is determined. The full geometry and kinematics of gear tooth processing by an oversized hob or by a flying tool is included. The theoretical background is implemented by a computer program. By using this program, the influence of relevant design parameters of the worm gear set and the hob and of machine tool settings on processed gear tooth errors and on loaded tooth contact of the worm gear pair is investigated and discussed.

Meshing Theory of ZC1 Worm Drive

2019 ◽  
Author(s):  
Yaping Zhao
Keyword(s):  
Gear Tooth ◽  
Worm Gear ◽  
Tooth Surface ◽  
Grinding Wheel ◽  
Normal Vector ◽  
Limit Function ◽  
Lubrication Performance ◽  
Working Length ◽  
Curvature Interference ◽  
Worm Drive

Abstract The toroidal enveloping cylindrical worm drive, also called the ZC1 worm drive, is grinded by the toroidal grinding wheel. In this paper, the meshing theory for this worm drive is systematically established. According to this meshing theory, the meshing function, the meshing limit function, the equations of the worm helicoid and the worm gear tooth surface are obtained. A method for computing the normal vector of the instantaneous line of the ZC1 worm pair is proposed. Due to this method, the curvature interference limit function and the meshing quality parameters can be more simply and clearly obtained. Based on above results, the methods of the numerical calculation of the instantaneous lines and the conjugate zone are proposed. The initial values of the nonlinear equation systems, computed the conjugate zone and the contact lines, are detected and solved by the method based on the elimination method and geometric construction. The results of numerical example clearly reflect that the conjugate zone can almost cover the whole tooth surface of the worm gear and the effective working length of the worm cannot nearly exceed the half of its thread length. The values of the induced principle curvature and the sliding angle show that the lubrication performance is poor and the stress level is higher, near the meshing limit line and at the dedendum of the worm gear.

scholarly journals Mathematical description of tooth flank surface of globoidal worm gear with straight axial tooth profile

2017 ◽  
Vol 7 (1) ◽  
pp. 407-415 ◽  
Author(s):  
Piotr Połowniak ◽  
Mariusz Sobolak
Keyword(s):  
Mathematical Description ◽  
Worm Gear ◽  
Tooth Surface ◽  
Contact Pattern ◽  
Contact Lines ◽  
Kinematic System ◽  
Worm Wheel ◽  
Axial Profile ◽  
Tooth Flank ◽  
Flank Surface

AbstractIn this article, a mathematical description of tooth flank surface of the globoidal worm and worm wheel generated by the hourglass worm hob with straight tooth axial profile is presented. The kinematic system of globoidal worm gear is shown. The equation of globoid helix and tooth axial profile of worm is derived to determine worm tooth surface. Based on the equation of meshing the contact lines are obtained. The mathematical description of globoidal worm wheel tooth flank is performed on the basis of contact lines and generating the tooth side by the extreme cutting edge of worm hob. The presented mathematical model of tooth flank of TA worm and worm wheel can be used e.g. to analyse the contact pattern of the gear.

Characteristics of a Modified Double Enveloping Worm Gear Drive

1992 ◽  
Author(s):  
Vilmos Simon
Keyword(s):  
Gear Tooth ◽  
Worm Gear ◽  
Performance Characteristics ◽  
Tooth Surface ◽  
Gear Teeth ◽  
Gear Drive ◽  
Load Distributions ◽  
Worm Gearing ◽  
Axial Profile ◽  
New Type

Abstract A modified new type of double enveloping worm gearing is developed. The gear tooth surface is generated by a flying tool whose cutting edge has the modified profile of the entering edge of the worm, and the worm surface has a straight-lined axial profile and circular lead changed to the established rule. The same rule governs the motion of the flying tool in processing the gear teeth. To compare the performance characteristics of the classical and the modified new type of double enveloping worm gearings, the load distributions are calculated and the elastohydrodynamic analysis of lubrication is carried out for both types of worm gearings. The obtained results show the advantages of the new type of double enveloping worm gear drive.

Kinematic Study of the Face Gear

1990 ◽  
Author(s):  
Yih-Jen Dennis Chen
Keyword(s):  
Computer Program ◽  
Mathematical Description ◽  
Design Automation ◽  
Gear Tooth ◽  
Tooth Surface ◽  
Face Gear ◽  
Gear Drive ◽  
Face Width ◽  
Kinematic Study ◽  
The Face

Abstract This paper presents the kinematic study of the face gear drive system. The study includes three different configurations which are: (1) the on-center orthogonal face gear drive, (2) the on-center non-orthogonal face gear drive, and (3) the offset orthogonal face gear drive. The mathematical description for the gear meshing and the resulting face gear tooth surface is developed. This paper also presents the criteria for detecting the limitation of the effective face width due to tooth pointing and undercutting. The technique presented is applied to develop a computer program. This design automation tool allows visualizing the gear meshing and tooth geometry of the face gear drive.

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