Application of the general mathematical model for CAD modelling of cylindrical and conical worm gear drives

2015 ◽  
Vol 6 (1) ◽  
pp. 71-75
Author(s):  
I. Dudás ◽  
S. Bodzás
Keyword(s):  
Mathematical Model ◽  
Geometric Analysis ◽  
Worm Gear ◽  
Tooth Surface ◽  
Cad Modelling ◽  
Cad Models ◽  
General Mathematical Model ◽  
Gear Drives ◽  
Conical Worm

Based on the general mathematical model of Dudás [3, 4] — which is appropriate for mathematical modelling of production technology methods and various toothed gear pairs — we have generated mathematical models which are appropriate for determination of tooth surface points of face gear and worm gear connection with conical and cylindrical worm by numerical way. After doing the necessary calculations, the CAD models of the worm gear drives could be generated. Based on these there is an opportunity for rapid prototyping (RP) technology for other connection and production geometric analysis. For the verification of our calculated results, we generate CAD models of one to one given geometric conical and cylindrical worm gear drives for other analysis.

scholarly journals Mathematical model to determination of resharpening territory of Conical Hob

2014 ◽  
Vol 8 (2) ◽  
pp. 45-50
Author(s):  
Illés Dudás ◽  
Sándor Bodzás
Keyword(s):  
Mathematical Model ◽  
Critical Angle ◽  
Worm Gear ◽  
Tooth Surface ◽  
Face Gear ◽  
Axial Section ◽  
Gear Drive ◽  
The Face ◽  
Conical Worm

Based on the general mathematical model of Illés Dudás which is appropriate for mathematical modelling of production technology methods we have worked out a model for resharpening analysis of conical hob. After the hob resharpening using numerical calculations the determination of the tooth surface of face gear by cutting edges is necessary for the analysis. Based on this methods we could calculate the permissible critical angle of the hob and the profiles of the hob and the face gear in axial section. The permissible critical angle of the hob is the critical angle the hob cutting edge of which manufactured face gear profile is situated in the permissible profile error tolerance. We have worked out a new geometric conical worm gear drive that is the conical worm gear drive having arched profile. Using this mathematical model we have done resharpening analysis for the hob having arched profile and determined the permissible critical angle.

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.

Research on a Generating Method of Spiral Flutes of Hourglass Worm Gear Hob

2017 ◽  
Author(s):  
Yang Jie ◽  
Li Haitao ◽  
Rui Chengjie ◽  
Wei Wenjun ◽  
Dong Xuezhu
Keyword(s):  
Mathematical Model ◽  
Manufacturing System ◽  
Worm Gear ◽  
Virtual Manufacturing ◽  
Transmission Ratio ◽  
Method Of Determination ◽  
Generating Method ◽  
Multiple Threads ◽  
Different Shapes

All of the cutting edges on an hourglass worm gear hob have different shapes and spiral angles. If the spiral angles are small, straight flutes are usually adopted. But for the hob with multiple threads, the absolute values of the negative rake angles at one side of the cutting teeth will greatly affect the cutting performance of the hob if straight flutes are still used. Therefore, spiral flutes are usually adopted to solve the problem. However, no method of determination of the spiral flute of the hourglass worm gear hob has been put forward till now. Based on the curved surface generating theory and the hourglass worm forming principle, a generating method for the spiral flute of the planar double enveloping worm gear hob is put forward in this paper. A mathematical model is built to generate the spiral flute. The rake angles of all cutting teeth of the hob are calculated. The laws of the rake angles of the cutting teeth of four hobs with different threads from one to four threads are analyzed when straight flutes and spiral flutes are adopted respectively. The laws between the value of the negative rake angles of the hob with four threads and the milling transmission ratio are studied. The most appropriate milling transmission ratio for generating the spiral flute is obtained. The machining of the spiral flutes is simulated by a virtual manufacturing system and the results verify the correctness of the method.

scholarly journals DETERMINING THE FORCES OF INTERACTION OF MAIN GEOKHODS SYSTEMS WITH GEO-ENVIRONMENT AND WITH EACH OTHER

2018 ◽  
pp. 23-30
Author(s):  
V. Yu. Beglyakov ◽  
V. V. Aksenov ◽  
I. K. Kostinets ◽  
A. A. Khoreshok
Keyword(s):  
Mathematical Modeling ◽  
Mathematical Model ◽  
Interaction Process ◽  
Generalized Model ◽  
Machine Elements ◽  
General Mathematical Model ◽  
Mine Workings ◽  
Modular Principles ◽  
Sufficient Strength

The processes occurring during the geodetic excavation of underground excavations are characterized by the interaction of the elements of the geokhod with each other and with the geo-environment. The interaction process can be investigated in mathematical modeling, solving the problems of justifying the parameters of the drives and interacting forces, ensuring sufficient strength of the machine elements and the bearing capacity of the contour array. The proposed block-modular principles of constructing a mathematical model allow solving particular problems of the system and its individual elements. From the solution of particular problems, it is now necessary to proceed to the solution of the generalized model, using equivalent loads and reduced total moments (forces). The construction of a generalized model requires a number of assumptions, but its solution will reveal the interaction between the elements of the geokhod and the geo-environment, which is very relevant.As an example, the solution of a particular problem is given-the determination of the value of the forces arising from the interaction of the blade of an external engine with the medium.A list of assumptions is formulated that allow us to describe a general mathematical model of the interaction between the geo-environment and the geokhod, as well as the processes occurring during geodetic excavation of mine workings.

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.

The Design, Generation, and Simulation of Meshing of Worm-Gear Drive With Longitudinally Localized Contacts

2000 ◽  
Vol 122 (2) ◽  
pp. 201-206 ◽  
Author(s):  
I. H. Seol
Keyword(s):  
Computer Program ◽  
Longitudinal Direction ◽  
Worm Gear ◽  
Contact Ratio ◽  
Transmission Errors ◽  
Gear Drive ◽  
Bearing Contact ◽  
Design Generation ◽  
Gear Drives

The design and simulation of meshing of a single enveloping worm-gear drive with a localized bearing contact is considered. The bearing contact has a longitudinal direction and two branches of contact path. The purpose of localization is to reduce the sensitivity of the worm-gear drive to misalignment. The author’s approach for localization of bearing contact is based on the proper mismatch of the surfaces of the hob and drive worm. The developed computer program allows the investigation of the influence of misalignment on the shift of the bearing contact and the determination of the transmission errors and the contact ratio. The developed approach has been applied for K type of single-enveloping worm-gear drives and the developed theory is illustrated with a numerical example. [S1050-0472(00)00502-X]

Designing and loaded tooth contact analysis of an Archimedean worm gear drive focusing for the connecting teeth of the worm wheel by loaded torques

2020 ◽  
Vol 21 (4) ◽  
pp. 405
Author(s):  
Sándor Bodzás
Keyword(s):  
Main Property ◽  
Worm Gear ◽  
Tooth Contact Analysis ◽  
Normal Deformation ◽  
Gear Drive ◽  
Contact Points ◽  
Worm Wheel ◽  
Loaded Tooth Contact Analysis ◽  
Gear Drives

The cylindrical worm gear drives are widely used in different mechanical construction such as in the vehicle industry, the robotics, the medical appliances etc. The main property of them is the perpendicular and space bypass axes arrangement. Quite high transmission ratio could be achieved because of the high number of teeth of the worm-wheel and a little number of threads of the worm. More teeth are connected on the worm-wheel at the same time that is why higher loads and power could be transferred. In this research an Archimedean type cylindrical worm gear drive was designed. After the determination of the geometric parameters the computer-aided models were created for the LTCA analysis. Knowing of the kinematic motions of the elements the contact points of the wrapping surfaces could be determined by mathematical way. The necessary coordinate system's arrangements and matrixes were also determined. Different torques were applied during the LTCA. The changing of the distribution of the normal stress and normal deformation into different directions was followed on each connecting tooth of the worm-wheel by the torques. Based on the results consequences were determined by the created diagrams which contain the torques and the analysed mechanical parameter for each tooth.

Optimum Tooth-Surface Modification for Axis-Displaced Worm-Gear Drive With Cylindrical ZA Worm

2007 ◽  
Author(s):  
Takashi Matsuda ◽  
Motohiro Sato ◽  
Satoshi Matsui
Keyword(s):  
Surface Modification ◽  
Relative Motion ◽  
Worm Gear ◽  
Tooth Surface ◽  
Design System ◽  
Gear Drive ◽  
Bearing Contact ◽  
Maximum Tolerance ◽  
Gear Drives ◽  
Tooth Surface Modification

Gear drives, which have larger misalignment than the maximum tolerance of misalignment for gear drives with parallel axes in the Standard of Japanese Gear Manufacture’s Association (JGMA Standard 114-02), are designated as axis-displaced gear drives in this study. So, axis-displacement is used in place of the misalignment. In this study, design system of optimum tooth-surface modification is developed for axis-displaced worm-gear drives with cylindrical ZA worm, which is sensitive to gear misalignments, to reduce the sensitivity to misalignment and to provide the high productivity and reliability. The system is composed by; (1) Axis-displaced wheel tooth-surface is defined as the envelope of worm tooth-surface family in their regular motion transmission (zero transmission error) under an axis-displacement. (2) Basic wheel tooth-surface is built by combining the axis-displaced tooth-surfaces under various axis-displacements. (3) Rack, whose pitch plane rolls on pitch cylinder of wheel, is introduced and then basic rack tooth-surface is obtained as the envelope of the basic wheel tooth-surface family in their regular relative motion. (4) It is illustrated how to get optimum rack tooth-surface from the basic rack tooth-surface. (5) Optimum wheel tooth-surface is generated as the envelope of the optimum rack tooth-surface family in their regular relative motion. (6) The performances of the axis-displaced worm-gear drive having the optimum wheel tooth-surface are analyzed by TCA (Tooth Contact Analysis) program which is developed for analysis of meshing and tooth bearing contact. The above-mentioned system is illustrated with its application for testing worm-gear drive. As a result, it is presented that the system can provide the testing worm-gear drive favorable tooth bearing contact and motion transmission, even in the maximum tolerance of misalignment in JGMA Standard 114-02.

ZK-Type Dual-Lead Worm and Worm Gear Drives: Geometry

1998 ◽  
Vol 120 (3) ◽  
pp. 414-421 ◽  
Author(s):  
B.-W. Bair ◽  
C.-B. Tsay
Keyword(s):  
Mathematical Model ◽  
Grid Point ◽  
Axial Direction ◽  
Worm Gear ◽  
Grinding Wheel ◽  
Contact Ratio ◽  
Tooth Contact Analysis ◽  
Cone Type ◽  
Dual Lead ◽  
Gear Drives

A dual-lead worm gear set is frequently used for machines to operate without backlash, which can be adjusted along the worm’s axial direction. The ZK-type dual-lead worm is generated by a cone-type straight-edged grinding wheel while an oversize worm-type hob cutter cuts the worm gear. The dual-lead worm gear set has two different axial modules and helix angles for the right- and left-side tooth surfaces. The mathematical model involving ZK-type dual-lead worm and worm gear surface geometries is developed based on the theory of gearing and gear cutting mechanism. According to the proposed mathematical model, computer graphs of the ZK-type dual-lead worm gear drives have been presented. Coordinates of the meshed grid-point on gear drive surfaces can thus be determined by applying the numerical method. Undercutting of the worm gear surface has been investigated based on the theory of gearing and the developed gear set mathematical model. The gear set mathematical model developed herein can facilitate gear set tooth contact analysis, contact teeth, contact ratio and other advanced investigations.

Computerized Design of Worm Gear Drives With Improved Conditions of Meshing and Bearing Contact

2006 ◽  
Author(s):  
Ignacio Gonzalez-Perez ◽  
Alfonso Fuentes ◽  
Faydor L. Litvin ◽  
Kenichi Hayasaka ◽  
Kenji Yukishima
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Worm Gear ◽  
Tooth Surface ◽  
Tooth Contact Analysis ◽  
Parabolic Profile ◽  
Gear Drive ◽  
Bearing Contact ◽  
Basic Ideas ◽  
Gear Drives

A new geometry of a cylindrical worm gear drive is proposed for: (i) reduction of sensitivity of the drive to errors of alignment, and (ii) observation of a favorable bearing contact. The basic ideas of new geometry are as follows: (i) the worm-gear is generated by a hob that is oversized in comparison with the worm of the drive and has a parabolic profile in normal section; (ii) the tooth surface of the worm of the drive is a conventional one. Due to deviation of the hob thread surface, the bearing contact of the worm and the worm-gear is localized. Reduction of sensitivity to misalignment and improved conditions of meshing are confirmed by application of TCA (Tooth Contact Analysis). Formation of bearing contact has been investigated by finite element method applied in 3D for more than one pair of contacting teeth. Developed ideas may be applied for various types of cylindrical worm gear drives.

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