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 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.

A parameterized numerical method for generating discrete helical gear tooth surface allowing non-standard geometry

2008 ◽  
Vol 222 (6) ◽  
pp. 1033-1038 ◽  
Author(s):  
J Hedlund ◽  
A Lehtovaara
Keyword(s):  
Gear Tooth ◽  
Numerical Approach ◽  
Helical Gear ◽  
Tooth Surface ◽  
Tool Profile ◽  
Standard Geometry ◽  
Gear Manufacturing ◽  
Involute Gears ◽  
Gear Geometry ◽  
Tooth Flank

Gear analysis is typically performed using calculation based on gear standards. Standards provide a good basis in gear geometry calculation for involute gears, but these are unsatisfactory for handling geometry deviations such as tooth flank modifications. The efficient utilization of finite-element calculation also requires the geometry generation to be parameterized. A parameterized numerical approach was developed to create discrete helical gear geometry and contact line by simulating the gear manufacturing, i.e. the hobbing process. This method is based on coordinate transformations and a wide set of numerical calculation points and their synchronization, which permits deviations from common involute geometry. As an example, the model is applied to protuberance tool profile and grinding with tip relief. A fairly low number of calculation points are needed to create tooth flank profiles where error is <1 μm.

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.

Mathematical Model and Surface Deviation of Helipoid Gears Cut by Shaper Cutters

2003 ◽  
Vol 125 (2) ◽  
pp. 351-355 ◽  
Author(s):  
Jun-Long Wu ◽  
Chia-Chang Liu ◽  
Chung-Biau Tsay ◽  
Shigeyoshi Nagata
Keyword(s):  
Mathematical Model ◽  
Power Transmission ◽  
Tooth Surface ◽  
Cutting Mechanism ◽  
Hypoid Gears ◽  
Helical Gears ◽  
Number Of Teeth ◽  
Surface Deviations ◽  
Surface Deviation

Crossed-axis helical gears and hypoid gears are two conventional crossed-axis power transmission devices. Helipoid gears, a novel gear proposed herein, possess the merits of the crossed-axis helical and hypoid gears. A mathematical model of the proposed helipoid gear cut by shapers is also derived according to the cutting mechanism and the theory of gearing. The investigation shows that the tooth surface varies with the number of teeth of the shaper. Computer graphs of the helipoid gear are presented according to the developed gear mathematical model, and the tooth surface deviations due to the number of teeth of the shaper are also investigated.

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.

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.

Investigation on the Backlash of Roller Enveloping Hourglass Worm Gear: Theoretical Analysis and Experiment

2019 ◽  
Vol 141 (5) ◽  
Author(s):  
Xingqiao Deng ◽  
Jie Wang ◽  
Shike Wang ◽  
Shisong Wang ◽  
Jinge Wang ◽  
...  
Keyword(s):  
Mathematical Model ◽  
Model Comparison ◽  
Gear Tooth ◽  
Worm Gear ◽  
Gear System ◽  
Design Parameters ◽  
Comparison Results ◽  
Worm Gears ◽  
Base Circle ◽  
Roller Radius

This paper proposes a single-roller enveloping hourglass worm gear design and verifies its advantages compared to the existing double-roller worm gear system and the conventional worm gear set. Our hypothesis is that the single-roller worm gear with appropriate configurations and parametric values can eliminate the backlash in mating gear transmission while maintaining advantages of the double-roller worm gears. Also, the self-rotation of the rollers when they are in the worm tooth space (TS) will help the gear system to avoid jamming and gear tooth scuffing/seizing problems caused by zero backlash and thermal expansion. In order to test that hypothesis, a mathematical model for the single-roller enveloping hourglass worm gear is developed, which includes a gear engagement equation and a tooth profile equation. Using that model, a parametric study is conducted to inspect the influences of center distance, roller radius, transmission ratio, and the radius of base circle on the worm gear meshing characteristics. It is found that the most effective way in eliminating the backlash is to adjust the roller radius and the radius of base circle. Finally, a single-roller enveloping hourglass worm gear set is manufactured and scanned to generate a 3D computer model. That model is compared with a theoretical model calculated from the developed mathematical model. Comparison results show that both models match very well, which verifies the accuracy of the developed mathematical model and our initial hypothesis that it is possible to achieve transmissions with zero backlash by adjusting the design parameters.

Mathematical Model and Surface Deviation of Cylindrical Gears With Curvilinear Shaped Teeth Cut by a Hob Cutter

Volume 3 ◽  
2004 ◽  
Author(s):  
Jui-Tang Tseng ◽  
Chung-Biau Tsay
Keyword(s):  
Mathematical Model ◽  
Tooth Surface ◽  
Design Parameters ◽  
Cutting Mechanism ◽  
Cylindrical Gear ◽  
Tooth Gear ◽  
Surface Deviations ◽  
Tool Setting ◽  
Surface Deviation ◽  
Cutter Design

The generating motion of a cylindrical gear with curvilinear shaped teeth cut by a CNC hobbing machine is proposed. Based on the cutting mechanism and the gear theory, the surface equation of this kind of gear is developed as a function of hob cutter design parameters. Computer graphs of the curvilinear-tooth gear are presented based on the developed gear mathematical model, and the tooth surface deviations due to machine-tool setting with nominal radius of circular tooth trace are also investigated.

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