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.

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.

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.

Crowned Spur Gears: Methods for Generation and Tooth Contact Analysis—Part I: Basic Concepts, Generation of the Pinion Tooth Surface by a Plane

1988 ◽  
Vol 110 (3) ◽  
pp. 337-342 ◽  
Author(s):  
F. L. Litvin ◽  
J. Zhang ◽  
R. F. Handschuh
Keyword(s):  
Gear Tooth ◽  
Contact Analysis ◽  
Numerical Results ◽  
Degree Of Freedom ◽  
Tooth Surface ◽  
Spur Gears ◽  
Tooth Contact Analysis ◽  
Tooth Contact ◽  
Transmission Errors ◽  
Basic Concepts

A topology of crowned spur pinion tooth surface that reduces the level of transmission errors due to misalignment is proposed. The geometry of the deviated pinion tooth surface and regular gear tooth surface, along with tooth contact analysis is discussed. Generation of the deviated pinion tooth surface by a plane whose motion is controlled by a five-degree-of-freedom system is proposed. Numerical results are included and indicate that transmission errors remain low as the gears are misaligned.

scholarly journals Study on Wear Characteristics Evolution of Helical Gear With Linear Initial Defect

2021 ◽  
Author(s):  
Yuqi Zhu ◽  
Wei Yuan ◽  
Qianjian Guo ◽  
Liguo Zhang ◽  
Wenhua Wang ◽  
...  
Keyword(s):  
Oil Pollution ◽  
Gear Tooth ◽  
Lubricating Oil ◽  
Tooth Surface ◽  
Wear Characteristics ◽  
Wear Process ◽  
Initial Defect ◽  
Hard Particles ◽  
Wear Life ◽  
Tooth Width

Abstract The initial defects have greatly affected the gear transmission under harsh working conditions in the fields of wind power and ships. The influence of linear initial defects on the evolution of wear characteristics of helical gears was studied. The laser marking device was used to process the linear initial defect along the tooth width direction, and the gear without initial defect was used for comparison. It can be concluded that the linear initial defect changed the meshing state of the gear tooth, and greatly shortened the normal wear life of the gear, the normal wear life of the gear is shortened by about 45%, and the wear rate in the stable wear stage is increased by about 56%, a great deal of pitting corrosion and plastic flow on the tooth surface occurred in the pitch circle position of the defective gear. In addition, the lubrication condition deteriorated in the later period caused by lubricating oil pollution and the hard particles falling off the gearbox bearings entered the meshing surface and the emerged crack, which further accelerated the wear process of gear.

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 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.

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