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.

ZK-Type Dual-Lead Worm and Worm Gear Drives: Contact Teeth, Contact Ratios and Kinematic Errors

1998 ◽  
Vol 120 (3) ◽  
pp. 422-428 ◽  
Author(s):  
B.-W. Bair ◽  
C.-B. Tsay
Keyword(s):  
Design Parameter ◽  
Gear Tooth ◽  
Worm Gear ◽  
Contact Ratio ◽  
Tooth Contact Analysis ◽  
Design Factor ◽  
Gear Design ◽  
Dual Lead ◽  
Gear Drives ◽  
Kinematic Errors

Contact ratio is an important gear design parameter for gear bending and contact stresses. A higher contact ratio may reduce the stresses and kinematic errors of the gear set. In this study, we calculate the kinematic error of the ZK-type dual-lead worm gear set by applying the tooth contact analysis (TCA) method. Two kinds of contact ratios, the instantaneous contact teeth (ICT) and the average contact ratio (ACR), are investigated and calculated by applying TCA method. ICT is an important design parameter for a dual-lead worm gear set when the gear set is used in a machine subjected to large impact forces. ACR is also a useful design factor for assessing gear tooth strength and dynamic load. If gear surface elastic deformation 3μm is allowed for the worm gear set, the ICT may have 2, 3 or 4 teeth and the ACR reveals that the ZK-type dual-lead worm gear drive is a high-contact-ratio gear set. It is found that this type of worm gear set with a shorter center distance assembly can increase the value of ACR during the gear meshing. Illustrative examples presented herein demonstrate the effects of gear parameters on contact teeth, contact ratios, average contact ratios and kinematic errors under various conditions.

Contact Characteristics of Recess Action Worm Gear Drives With Double-Depth Teeth

2011 ◽  
Vol 133 (11) ◽  
Author(s):  
Wei-Liang Chen ◽  
Chung-Biau Tsay
Keyword(s):  
Worm Gear ◽  
Surface Topology ◽  
Design Parameters ◽  
Kinematic Error ◽  
Contact Ratio ◽  
Tooth Contact Analysis ◽  
Gear Drive ◽  
Contact Patterns ◽  
Bearing Contact ◽  
Gear Drives

Based on the previously developed mathematical model of a series of recess action (RA) worm gear drive (i.e., semi RA, full RA, and standard proportional tooth types) with double-depth teeth, the tooth contact analysis (TCA) technique is utilized to investigate the kinematic error (KE), contact ratio (CR), average contact ratio (ACR), instantaneous contact teeth (ICT) under different assembly conditions. Besides, the bearing contact and contact ellipse are studied by applying the surface topology method. Three numerical examples are presented to demonstrate the influence of the assembly errors and design parameters of the RA worm gear drive on the KE, CR, ACR, ICT, and contact patterns.

Finite element modelling and load share analysis for involute worm gears with localized tooth contact

2001 ◽  
Vol 215 (7) ◽  
pp. 805-816 ◽  
Author(s):  
F Yang ◽  
D Su ◽  
C. R. Gentle
Keyword(s):  
Finite Element ◽  
Load Capacity ◽  
Worm Gear ◽  
Tooth Contact Analysis ◽  
Fe Modelling ◽  
Tooth Contact ◽  
Transmission Errors ◽  
Meshing Stiffness ◽  
Worm Gears ◽  
Gear Drives

A new approach has been developed by the authors to estimate the load share of worm gear drives, and to calculate the instantaneous tooth meshing stiffness and loaded transmission errors. In the approach, the finite element (FE) modelling is based on the modified tooth geometry, which ensures that the worm gear teeth are in localized contact. The geometric modelling method for involute worm gears allows the tooth elastic deformation and tooth root stresses of worm gear drives under different load conditions to be investigated. On the basis of finite element analysis, the instantaneous meshing stiffness and loaded transmission errors are obtained and the load share is predicted. In comparison with existing methods, this approach applies loaded tooth contact analysis and provides more accurate load capacity rating of worm gear drives.

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]

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.

A Designing and Generating Method for Grinding Relief Surfaces of a Dual-Cone Double-Enveloping Hourglass Worm Gear Hob

2018 ◽  
Vol 140 (12) ◽  
Author(s):  
Chengjie Rui ◽  
Haitao Li ◽  
Jie Yang ◽  
Wenjun Wei ◽  
Xuezhu Dong
Keyword(s):  
Mathematical Model ◽  
Worm Gear ◽  
Double Cone ◽  
Grinding Wheel ◽  
Dual Cone ◽  
Generating Method ◽  
Motion Parameters ◽  
Grinding Machine ◽  
The Mathematical Model

Land widths and relief angles of a dual-cone double-enveloping hourglass worm gear hob are important factors that influence the life and the hobbing performance of the hob. Both of them are obtained by generating relief surfaces of the hob. Due to the reason that all teeth of this type of hob have different profiles with each other, all of the relief surfaces are difficult to generate for keeping all cutting teeth with uniformed relief angles and uniformed land widths. For the purpose that land widths and relief angles could be machined precisely, this paper puts forward a designing and generating method for grinding the relief surfaces. The relief surfaces are ground using the same double-cone grinding wheel as grinding the helical surfaces of the worm. Based on the theory of gearing, the mathematical model for grinding relief surfaces is built. Motion parameters when grinding the different points of the land edges on different teeth of the hob are solved. A generating simulation is built by putting those motion parameters into a four-axis hourglass worm-grinding machine. The results of the simulation show that the relief surfaces can be ground continuously and the land widths and the relief angles meet the requirements.

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.

Application and Investigation of Modified Helical Gears With Several Types of Geometry

2007 ◽  
Author(s):  
Ignacio Gonzalez-Perez ◽  
Alfonso Fuentes ◽  
Faydor L. Litvin ◽  
Kenichi Hayasaka ◽  
Kenji Yukishima
Keyword(s):  
Gear Tooth ◽  
Tooth Surface ◽  
Contact Ratio ◽  
Tooth Contact Analysis ◽  
Helical Gears ◽  
Transmission Errors ◽  
Advantages And Disadvantages ◽  
Bearing Contact ◽  
Tooth Surfaces ◽  
Gear Drives

Involute helical gears with modified geometry for transformation of rotation between parallel axes are considered. Three types of topology of geometry are considered: (1) crowning of pinion tooth surface is provided only partially by application of a grinding disk; (2) double crowning of pinion tooth surface is obtained applying a grinding disk; (3) concave-convex pinion and gear tooth surfaces are provided (similar to Novikov-Wildhaber gears). Localization of bearing contact is provided for all three types of topology. Computerized TCA (Tooth Contact Analysis) is performed for all three types of topology to obtain: (i) path of contact on pinion and gear tooth surfaces; (ii) negative function of transmission errors for misaligned gear drives (that allows the contact ratio to be increased). Stress analysis is performed for the whole cycle of meshing. Finite element models of pinion and gear with several pairs of teeth are applied. A relative motion is imposed to the pinion model that allows friction between contact surfaces to be considered. Numerical examples have confirmed the advantages and disadvantages of the applied approaches for generation and design.

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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