Kinematics of point-conjugate tooth surface couple and its application in mixed mismatched conical worm drive

2022 ◽  
Vol 167 ◽  
pp. 104528
Author(s):  
Qingxiang Meng ◽  
Yaping Zhao ◽  
Jian Cui ◽  
Shibo Mu ◽  
Gongfa Li ◽  
...  
Keyword(s):  
Tooth Surface ◽  
Conical Worm ◽  
Worm Drive ◽  
Point Conjugate

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.

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.

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 A generalized meshing analysis method and its application to toroidal surface enveloping conical worm drive

2021 ◽  
Vol 13 (11) ◽  
pp. 168781402110630
Author(s):  
Chongfei Huai ◽  
Chunlin Chen ◽  
Yaping Zhao
Keyword(s):  
Mathematical Model ◽  
Reference Point ◽  
Unit Vector ◽  
Normal Vector ◽  
Analysis Method ◽  
Profile Angle ◽  
Toroidal Surface ◽  
Conical Worm ◽  
Worm Drive ◽  
Application Scope

A generalized method for the meshing analysis of conical worm drive is proposed, whose mathematical model is more general and whose application scope is expanded. A universal mathematical model, which can be conveniently applied to left-handed and right-handed conical worm pairs and their tooth flanks on different sides, is established by introducing the helical spin coefficient and tooth side coefficient of the conical worm. The pressure angle at the reference point, which is a key parameter for calculating the curvature parameters and lubrication angle, is determined based on the unit normal vector of the worm helical surface and is no longer determined by the tooth profile angle in the worm shaft section. The above improvement breaks away from the limitation of the classic meshing analysis method based on the reference-point-based meshing theory and thus expands its application scope. The toroidal surface enveloping conical worm drive is taken as an instance to illustrate the proposed method and the numerical example studies are conducted. The approaches to determine the reference point, the normal unit vector, and the curvature parameters at the reference point are all demonstrated in detail. The numerical results all manifest that the method presented in the current work is correct and practicable.

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 Influence of grinding wheel parameters on the meshing performance of toroidal surface enveloping conical worm drive

2019 ◽  
Vol 10 (1) ◽  
pp. 199-211
Author(s):  
Chongfei Huai ◽  
Yaping Zhao
Keyword(s):  
Numerical Study ◽  
Tooth Surface ◽  
Grinding Wheel ◽  
Geometrical Parameters ◽  
Geometrical Shape ◽  
Numerical Result ◽  
Toroidal Surface ◽  
Conical Worm ◽  
Curvature Interference ◽  
Geometry Characteristic

Abstract. A new type of toroidal surface enveloping conical worm gearing is proposed in our recent work (Chongfei and Yaping, 2019b). According to its forming principle, the geometrical shape of the generating surface has an important influence on the geometry characteristic of the enveloping worm pair. To explore the reasonable principles for selecting the geometrical parameters of the grinding wheel, some numerical study examples are performed. In this process, the methods for the tooth crest width are developed. Simple strategies for estimating the risk of the worm tooth surface being located in the invalid area and the risk of the curvature interference on the tooth surface are proposed. The numerical result shows that increasing the radius of the toroidal-generating surface and the nominal pressure angle of the grinding wheel are beneficial to improve the engagement behavior of the conical worm pair, but the tooth crest sharpening of the conical worm may happen if they are too large. For the nominal radius of the grinding wheel, it has a negligible effect on the meshing characteristics of this worm set. In addition, the selection principle of the parameters is also suggested.

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