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.

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 Meshing characteristics of a sphere–face gear pair with variable shaft angle

2019 ◽  
Vol 11 (6) ◽  
pp. 168781401985951 ◽  
Author(s):  
Lei Liu ◽  
Jinzhao Zhang
Keyword(s):  
Gear Tooth ◽  
Transmission Error ◽  
Tooth Surface ◽  
Gear Pair ◽  
Face Gear ◽  
Tooth Contact Analysis ◽  
Contact Points ◽  
Shaft Angle ◽  
Meshing Characteristics ◽  
Curvature Interference

This article presents a sphere–face gear pair by substituting the convex spherical gear for the pinion of a conventional face gear pair. The sphere–face gear pair not only maintains the advantages of the face gear pair with a longitudinally modified pinion but also allows variable shaft angles or large axial misalignments. Meshing characteristics of the proposed gear pair are studied in this article. The mathematical models of the sphere–face gear pair are derived based on machining principles. The tooth contact analysis (TCA) and curvature interference check are conducted for the sphere–face gear pair with variable shaft angles. The loaded TCA is also implemented utilizing the finite element method. The results of numerical examples show that proposed gear pair has the following features. Geometrical transmission error of constant shaft angle or varying shaft angle is zero; contact points of the sphere–face gear set with variable shaft angle are located near the centre region of face gear tooth surface; there is no curvature interference in meshing; and transmission continuity of the gear pair can be guaranteed in meshing.

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.

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.

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.

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.

The Grinding of the Worm for Worm Gear Set

2018 ◽  
Vol 775 ◽  
pp. 473-479
Author(s):  
Chi Hsiang Chen ◽  
Duy Hoang Nguyen ◽  
Shinn Liang Chang ◽  
Truong Giang Nguyen
Keyword(s):  
Gear Ratio ◽  
Tooth Profile ◽  
Worm Gear ◽  
Tooth Surface ◽  
Grinding Wheel ◽  
Essential Requirement ◽  
Straight Line ◽  
Worm Gears ◽  
Crossed Axes ◽  
Grinding Machine

Worm gear set is composed by the worm and worm wheel. It is an important transmission device for crossed axes transmission with high gear ratio. Worm gears can be produced in several ways, depending on the size of the transmission, the number of threads, the type of the worm and the purpose of application, etc. The contact is highly related to the precision of tooth profile. The best way to control the characteristic of contact is done by the modified worm profile. This paper deals with the manufacture of ZI-Worm whose theoretical tooth surface is generated by a screw motion of a straight line. In order to manufacture the worm with modified high precision tooth profile, the most important consideration is how to develop the profile of the grinding wheel in the worm grinding process. It is the essential requirement for the development of grinding machine for the worm. This article therefore deals with the problems of how to generate the profile of the grinding wheel. By the development of the grinding machine, we can complete the worm surface and tools for the production.

scholarly journals Fundamental Research on the Gear Lubrication : 2nd Report, Lubrication Performance on Gear-Tooth Surface

1962 ◽  
Vol 5 (19) ◽  
pp. 561-570 ◽  
Author(s):  
Tokio SASAKI ◽  
Kenjiro OKAMURA ◽  
Tadataka KONISHI ◽  
Yoshinobu NISHIZAWA
Keyword(s):  
Gear Tooth ◽  
Tooth Surface ◽  
Lubrication Performance ◽  
Fundamental Research

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.

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