Meshing theory and tooth profile geometry of toroidal surface enveloping conical worm drive

2019 ◽  
Vol 134 ◽  
pp. 476-498 ◽  
Author(s):  
Chongfei Huai ◽  
Yaping Zhao
Keyword(s):  
Tooth Profile ◽  
Toroidal Surface ◽  
Conical Worm ◽  
Worm Drive

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.

scholarly journals Meshing theory of axial arc tooth profile cylindrical worm drive

2021 ◽  
Vol 13 (4) ◽  
pp. 168781402110125
Author(s):  
Yuno Liu ◽  
Yaping Zhao ◽  
Xinyuan Chen ◽  
Gongfa Li
Keyword(s):  
Low Cost ◽  
Tooth Profile ◽  
Lubricating Oil ◽  
Grinding Wheel ◽  
Helical Surface ◽  
Simple Processing ◽  
Manufacturing Time ◽  
Orthogonal Frame ◽  
Worm Drive

In this paper, the axial arc tooth profile cylindrical worm drive is proposed, whose worm is cut by turning tool. Due to the simple processing equipment, short manufacturing time and low cost, this kind of worm can replace the cylindrical worm ground by grinding wheel under some conditions. The meshing theory of the worm drive is founded comprehensively. Moreover, a movable orthogonal frame is established on the non-orthogonal parametric curves net helical surface. Based on the founded meshing theory, the simulating study on the meshing quality of the worm drive is performed systematically. The numerical outcome shows that the meshing quality of this worm drive is quite favorable, and the condition of forming lubricating oil film is excellent. The working orthogonal clearance of the turning tool is decreased with the increase of the worm thread number, which must be a positive value in the process of worm cutting. This explains that the number of the worm thread is ≤4.

Comparative Study on Machining the Internal Stationary Toroidal Gear

2005 ◽  
Vol 291-292 ◽  
pp. 483-488 ◽  
Author(s):  
Li Gang Yao ◽  
Guo Wu Wei ◽  
Z.H. Lan ◽  
Jian Sheng Dai
Keyword(s):  
Comparative Study ◽  
Mathematical Modelling ◽  
Weight Ratio ◽  
Tooth Profile ◽  
Gear Train ◽  
Gear Drive ◽  
Toroidal Surface ◽  
Epicyclic Gear ◽  
Worm Gears ◽  
The Comparative Study

The toroidal drive offers the advantages such as a high horsepower-to-weight ratio, coaxial configurations, compactness and high operating efficiencies. It combines most of the positive attributes of a circular worm-gear drive and epicycle gear drive without their negative aspects due to the introduction of a set of rollers in meshing contact with rolling movement between a sun-worm and planet worm-gears, and between a stationary internal toroidal gear and planet worm-gears. However difficulties were encountered in machining the toroidal surface of the stationary internal toroidal tooth profile. This paper investigates the toroidal meshing surface and develops a mathematical modelling of the meshing surface and the conjugate surface using motion analysis of the epicyclic gear train. Then the enveloping and NC machining methods are proposed and based on these machining methods the stationary internal toroidal gear is manufactured. This results the comparative study of the tooth profile of manufactured toroidal gears by the proposed methods.

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

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.

scholarly journals Design and manufacture of the novel drum worm pair

2020 ◽  
Vol 103 (4) ◽  
pp. 003685042098122
Author(s):  
Jingzi Zhang ◽  
Jin’ge Wang ◽  
Kai Wang
Keyword(s):  
Contact Stresses ◽  
Primary Objective ◽  
Structure Design ◽  
Worm Gear ◽  
The Novel ◽  
Bending Stress ◽  
Manufacturing Method ◽  
Design And Manufacture ◽  
Maximum Contact ◽  
Worm Drive

Although a significant amount of research on robot joint reducer was conducted, there are few systematic investigations on a novel joint reducer adopting inner worm-gear plane enveloping drum worm drive. To satisfy the development of modular robot joint, the primary objective of this paper was to systematically investigate the drum worm drive adopted in the novel joint reducer with integrated structure of drive, transmission, and support in the following aspects: meshing theory, design, analysis, and manufacture. According to the gear meshing theory, mechanical design method, classical mechanics, finite element method, and machining principle of virtual center distance, the systematic investigations around the drum worm pair applied in the novel joint reducer were conducted including the macro and micro meshing theory, structure design, mechanical and contact properties analyses, and manufacturing method. The novel joint reducer’s integrated structure was designed, and the drum worm pair’s mechanical and contact properties analyses were conducted, which showed: (1) the worm’s bending stress and deflection, worm-gear teeth’s shear stress and bending stress as well as the maximum contact stresses were all below their corresponding allowable values; (2) the maximum contact stresses appeared at the engage-in position of the worm pair opposing to the engaging-out position where the largest contact areas appeared. Then the manufacturing of drum worm’s spiral tooth was conducted via the modified 4-axis linkage CNC grinder according to the conjugate motion. Finally the novel joint reducer’s industrial prototype was assembled. The novel joint reducer with integrated structure of drive, transmission and support was designed and manufactured for the first time. The flowchart of design and manufacture of the reducer’s drum worm pair in this process was formulated, which provides a new insight on the research of joint reducers as well as other fields.

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