Load Distribution in Double Enveloping Worm Gears

1993 ◽  
Vol 115 (3) ◽  
pp. 496-501 ◽  
Author(s):  
V. Simon
Keyword(s):  
Load Distribution ◽  
Gear Tooth ◽  
Design Parameters ◽  
Distribution Factor ◽  
Axial Deformation ◽  
Gear Teeth ◽  
Worm Gears ◽  
New Type ◽  
Alignment Errors ◽  
Gear Drives

A method for the determination of load sharing among the instantaneously engaged worm threads and gear teeth of double enveloping worm gears and for the calculation of load distribution along their instantaneous contact lines is presented. The bending and shearing deflection of worm thread and gear tooth, the contact deformation, the axial deformation of worm body, and the manufacturing and alignment errors of worm and gear are included. The obtained system of integral equations is solved by using approximations and an iterative technique. The corresponding computer program is developed. By using this program, the load distribution in the classical and in a new type of double enveloping worm gear drives is calculated. The influence of design parameters on load distribution factor and on maximum tooth pressure is investigated and discussed.

Load Distribution in Cylindrical Worm Gears

2000 ◽  
Author(s):  
Vilmos V. Simon
Keyword(s):  
Load Distribution ◽  
Gear Tooth ◽  
Point Contact ◽  
Transmission Error ◽  
Worm Gear ◽  
Gear Teeth ◽  
Total Transmission ◽  
Transmission Errors ◽  
Gear Drive ◽  
Worm Gears

Abstract A method for the determination of load sharing between the instantaneously engaged worm threads and gear teeth, for the calculation of load distribution along the teeth and transmission errors in different types of cylindrical worm gears is presented. The method covers both cases — that of the theoretical line and point contact. The bending and shearing deflections of worm thread and gear tooth, the local contact deformations of the mating surfaces, the axial deformations of worm body, gear body bending and torsion, deflections of the supporting shafts, and the manufacturing and alignment errors of worm and gear are included. Based on the real load distribution the tooth contact pressure is calculated, in the case of point contact in two different ways, and the obtained results are compared. Also, the total transmission error, consisting of the kinematical transmission error due to the mismatch of the worm gear drive and of the transmission error caused by the deflections of worm thread and gear teeth, is calculated. The method is implemented by a computer program. By using this program the influence of the type of worm gear drive and of design and manufacturing parameters on load distribution and transmission errors is investigated and discussed.

Load Distribution in Cylindrical Worm Gears

2003 ◽  
Vol 125 (2) ◽  
pp. 356-364 ◽  
Author(s):  
Vilmos Simon
Keyword(s):  
Load Distribution ◽  
Gear Tooth ◽  
Point Contact ◽  
Transmission Error ◽  
Worm Gear ◽  
Gear Teeth ◽  
Total Transmission ◽  
Transmission Errors ◽  
Gear Drive ◽  
Worm Gears

A method for the determination of load sharing between the instantaneously engaged worm threads and gear teeth, for the calculation of load distribution along the teeth and transmission errors in different types of cylindrical worm gears is presented. The method covers both cases—that of the theoretical line and point contact. The bending and shearing deflections of worm thread and gear tooth, the local contact deformations of the mating surfaces, the axial deformations of worm body, gear body bending and torsion, deflections of the supporting shafts, and the manufacturing and alignment errors of worm and gear are included. Based on the real load distribution the tooth contact pressure is calculated, in the case of point contact in two different ways, and the obtained results are compared. Also, the total transmission error, consisting of the kinematical transmission error due to the mismatch of the worm gear drive and of the transmission error caused by the deflections of worm thread and gear teeth, is calculated. The method is implemented by a computer program. By using this program the influence of the type of worm gear drive and of design and manufacturing parameters on load distribution and transmission errors is investigated and discussed.

scholarly journals Gear Tooth Stress Measurements of Two Helicopter Planetary Stages

1992 ◽  
Author(s):  
Timothy L. Krantz
Keyword(s):  
Load Distribution ◽  
Gear Tooth ◽  
Nasa Lewis Research ◽  
Ring Gear ◽  
Gear Teeth ◽  
Load Variation ◽  
Planet Gear ◽  
Helicopter Main Rotor ◽  
Stress Variations ◽  
Root Location

Abstract Two versions of the planetary reduction stages from U.S. Army OH-58 helicopter main rotor transmissions were tested at the NASA Lewis Research Center. One sequential and one nonsequential planetary were tested. Sun gear and ring gear teeth strains were measured, and stresses were calculated from the strains. The alternating stress at the fillet of both the loaded and unloaded sides of the teeth and at the root of the sun gear teeth are reported. Typical stress variations as the gear tooth moves through the mesh are illustrated. At the tooth root location of the thin-rimmed sun gear, a significant stress was produced by a phenomenon other than the passing of a planet gear. The load variation among the planets was studied. Each planet produced its own distinctive load distribution on the ring and sun gears. The load variation was less for a three-planet, nonsequential design as compared to that of a four-planet, sequential design. The results reported enhance the data base for gear stress levels and provide data for the validation of analytical methods.

Research on the method to calculate deformation of curve-face gear

2017 ◽  
Vol 232 (13) ◽  
pp. 2458-2468 ◽  
Author(s):  
Chao Lin ◽  
Zhiqin Cai
Keyword(s):  
Mathematical Model ◽  
Cross Section ◽  
Conventional Method ◽  
Load Distribution ◽  
Gear Tooth ◽  
Order Number ◽  
Face Gear ◽  
Actual Contact ◽  
New Type ◽  
Curve Face

As a new type of face gear, the tooth deformation of curve-face gear has always been one of the research focuses. The conventional method of calculating the tooth deformation of face gear is widely focused on the basis of Buckingham's opinion, without considering the actual contact status. Therefore, in order to resolve this problem, a new calculation of curve-face gear tooth deformation is proposed. Firstly, the tooth distribution regularity of curve-face gear was analyzed. Then, a model for predicting the tooth elastic deformation of curve-face gear, taking into account the equivalent teeth, cross-section property, actual contact status and load distribution, was presented. Finally, the deformation variations were analyzed by taking into account the specific parameters such as eccentricity e, order number n1 and n2, and the correctness of the proposed mathematical model was verified by the results of the related experiment.

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.

Computerized Tooth Profile Generation and Undercut Analysis of Gears Manufactured With Pre-Shaving Hobs

2009 ◽  
Vol 16-19 ◽  
pp. 1278-1282
Author(s):  
Xiang Wei Kong ◽  
Jing Zhang ◽  
Meng Hua Niu
Keyword(s):  
Mathematical Model ◽  
Computer Program ◽  
Gear Tooth ◽  
Tooth Profile ◽  
Design Parameters ◽  
Gear Teeth ◽  
The Mathematical Model

This paper investigated the feature of pre-shaving hob contour and the generated gear tooth profile. By tooth generation method, a complete geometry of the gear tooth can be mathematically derived in terms of the design parameters of the pre-shaving hob cutter. The mathematical model consisted of equations describing the generated fillet and involute profiles. The degree of undercutting and the radii of curvatures of a fillet were investigated by considering the model. Finally, a computer program for generating the profile of the gear teeth was developed by simulating the cutting methods. The methods proposed in this study were expected to be a valuable guidance for pre-shaving hob designers and manufacturers.

The ways to enhance durability and bearing capacity of the open gear drum mills

2021 ◽  
Vol 15 (3) ◽  
pp. 87-94
Author(s):  
Borys Vynohradov ◽  
Veronika Karpenko ◽  
Olena Lahoshna ◽  
Kostiantyn Bas ◽  
Iryna Slovska
Keyword(s):  
Bearing Capacity ◽  
Load Distribution ◽  
Functional Relation ◽  
Operational Conditions ◽  
Gear Teeth ◽  
Factors Influencing ◽  
Working Surface ◽  
World Class ◽  
Gear Drives ◽  
Practical Implications

Purpose is substantiating ways to enhance durability and bearing capacity of open gears of ore-pulverizing drum mills as well as efficiency of engineering solutions concerning the increase in their unit power at the expense of drive improvement. Methods. Results of continual experiments and theoretical studies have been generalized as for the abrasion of working surfaces of open gear teeth of drum mills and factors influencing load distribution in terms of a tooth rim width. Findings. Comparative analysis between domestic mills and the best world-class products has been carried out. Ways of solving problems to design large-capacity mills with a gearbox drive have been demonstrated. Influence of hardness of working teeth surfaces on their durability has been evaluated quantitatively. The factors, governing load distribution in terms of tooth rim width, have been analyzed. Use of self-adjusting gear drives for open gears has been evaluated. Originality. Functional relation between stress-strain properties of working surface of teeth; the number of running-in modes, determined by operational conditions; and durability of open gear has been identified. The factors, influencing load distribution in terms of tooth rim width, have been considered. Practical implications. It has been shown that use of such open gears, where hardness of working surface of gear teeth is (500-600) H1B1 and that of a tooth rim one is (260-300) H2B2, makes it possible to provide almost wear-free operation. Moreover, it is the required condition for the performance of a tooth rim with two drive gears.

Optimum Gear Tooth Geometry for Minimum Fillet Stress Using BEM and Experimental Verification With Photoelasticity

2005 ◽  
Vol 128 (5) ◽  
pp. 1159-1164 ◽  
Author(s):  
Vasilios A. Spitas ◽  
Theodore N. Costopoulos ◽  
Christos A. Spitas
Keyword(s):  
Gear Tooth ◽  
Optimization Procedure ◽  
Computational Time ◽  
Design Parameters ◽  
Gear Teeth ◽  
Design Variables ◽  
Maximum Root ◽  
Stress Minimization ◽  
Complex Algorithm ◽  
Root Stress

This paper introduces the concept of nondimensional gear teeth to be used in gear stress minimization problems. The proposed method of modeling reduces the computational time significantly when compared to other existing methods by essentially reducing the total number of design variables. Instead of modeling the loaded gear tooth and running BEA to calculate the maximum root stress at every iterative step of the optimization procedure, the stress is calculated by interpolation of tabulated values, which were calculated previously by applying the BEM on nondimensional models corresponding to different combinations of the design parameters. The complex algorithm is used for the optimization and the root stresses of the optimum gears are compared with the stresses of the standard gears for the same transmitted torque. Reduction in stress up to 36.5% can be achieved in this way. This reduction in stress has been confirmed experimentally with two-dimensional photoelasticity.

An Accurate Method for Calculating Load Distribution Factor Kβ of Involute Gears

2007 ◽  
Vol 339 ◽  
pp. 458-462
Author(s):  
D.C. Feng
Keyword(s):  
Axial Force ◽  
Load Distribution ◽  
Gear Tooth ◽  
Accurate Method ◽  
Distribution Factor ◽  
Linear Load ◽  
Tooth Width ◽  
Involute Gears ◽  
Load Distribution Factor ◽  
Gear Manufacture

A new method is given to determine the load distribution factor Kβ of involute gears. Compared with the old method, the new one gives up some improper assumptions such as linear load distribution along gear tooth width. While considering the effects of bearing deformations, gear manufacture and assembly errors, gear axial force and gear tooth run-in on Kβ, the paper calculates Kβ according to “Load- Deformation Coordination” of gear tooth. Practical examples show that this method is more accurate, more effective than old ones.

Characteristics of a New Type of Cylindrical Worm-Gear Drive

1998 ◽  
Vol 120 (1) ◽  
pp. 139-146 ◽  
Author(s):  
V. V. Simon
Keyword(s):  
Load Distribution ◽  
Elastohydrodynamic Lubrication ◽  
Worm Gear ◽  
Design Parameters ◽  
Grinding Wheel ◽  
Operating Characteristics ◽  
Tooth Contact Analysis ◽  
Gear Drive ◽  
Distribution Calculation ◽  
New Type

A new type of cylindrical worm-gear drive is presented. The worm is ground by a grinding wheel whose profile consists of two circular arcs, and the obtained worm profile is concave. The teeth of the gear are processed by a hob whose generator surface is identical to the worm surface. The aim of this paper is to introduce this new type of worm gearing and to compare the operating characteristics of the new type and of the commonly used worm-gear drives on the basis of tooth contact analysis, load distribution calculation, and thermal elastohydrodynamic lubrication analyses. The results obtained show the advantages of the new type of worm gear. The results of the load distribution calculation and EHD lubrication analysis are also used for the optimization of the design parameters of the new type of worm-gear drive.

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