Tooth Load Sharing in High-Contact Ratio Spur Gears

1985 ◽  
Vol 107 (1) ◽  
pp. 11-16 ◽  
Author(s):  
A. H. Elkholy
Keyword(s):  
Contact Stress ◽  
Applied Load ◽  
Normal Load ◽  
Closed Form Solution ◽  
Load Sharing ◽  
Form Solution ◽  
Spur Gears ◽  
Contact Ratio ◽  
Profile Modification ◽  
The Individual

A closed-form solution is presented for calculating the load sharing among meshing teeth in high contact ratio gearing (HCRG). The procedure is based upon the assumption that the sum of the tooth deflection, profile modification and spacing error at each of two or three pairs of contacts are all equal. It is also assumed that the sum of the normal loads contributed by each of two or three pairs of contacts is equal to the maximum normal load. Once the individual loads are determined, the tooth fillet stress, contact stress may be determined from the applied load and tooth geometry. An experimental example appears to verify the method.

scholarly journals Compliance and Stress Sensitivity of Spur Gear Teeth

1981 ◽  
Vol 103 (2) ◽  
pp. 447-459 ◽  
Author(s):  
R. W. Cornell
Keyword(s):  
Closed Form Solution ◽  
Time History ◽  
Peak Stress ◽  
Spur Gear ◽  
Stress Sensitivity ◽  
Form Solution ◽  
Sensitivity Analyses ◽  
Spur Gears ◽  
Contact Ratio ◽  
Gear Teeth

The magnitude and variation of tooth pair compliance with load position affects the dynamics and loading significantly, and the tooth root stressing per load varies significantly with load position. Therefore, the recently developed time history, interactive, closed form solution for the dynamic tooth loads for both low and high contact ratio spur gears [1] was expanded to include improved and simplified methods for calculating the compliance and stress sensitivity for three involute tooth forms as a function of load position. The compliance analysis is based on Weber [2] and O’Donnell [3] but with an improved fillet/foundation compliance analysis. The stress sensitivity analysis is a modified version of the Heywood method [4] but with an improvement in the magnitude and location of the peak stress in the fillet. These improved compliance and stress sensitivity analyses are presented along with their evaluation using test, finite element, and analytic transformation results, which showed good agreement.

Influence of Linear Profile Modification and Loading Conditions on The Dynamic Tooth Load and Stress of High-Contact-Ratio Spur Gears

1991 ◽  
Vol 113 (4) ◽  
pp. 473-480 ◽  
Author(s):  
Chinwai Lee ◽  
Hsiang Hsi Lin ◽  
Fred B. Oswald ◽  
Dennis P. Townsend
Keyword(s):  
Computer Simulation ◽  
Contact Stress ◽  
Dynamic Load ◽  
Applied Load ◽  
Gear Tooth ◽  
Load Force ◽  
Loading Conditions ◽  
Contact Ratio ◽  
Profile Modification ◽  
Root Stress

This paper presents a computer simulation for the dynamic response of high-contact-ratio spur gear transmissions. High contact ratio gears have the potential to produce lower dynamic tooth loads and minimum root stress but they can be sensitive to tooth profile errors. The analysis presented in this paper examines various profile modifications under realistic loading conditions. The effect of these modifications on the dynamic load (force) between mating gear teeth and the dynamic root stress is presented. Since the contact stress is dependent on the dynamic load, minimizing dynamic loads will also minimize contact stresses. This paper shows that the combination of profile modification and the applied load (torque) carried by a gear system has a significant influence on gear dynamics. The ideal modification at one value of applied load will not be the best solution for a different load. High-contact-ratio gears were found to require less modification than standard low-contact-ratio gears. High-contact-ratio gears are more adversely affected by excess modification than by under modification. In addition, the optimal profile modification required to minimize the dynamic load (hence the contact stress) on a gear tooth differs from the optimal modification required to minimize the dynamic root (bending) stress. Computer simulation can help find the design tradeoffs to determine the best profile modification to satisfy the conflicting constraints of minimizing both the load and root stress in gears which must operate over a range of applied loads.

scholarly journals Study of the tooth contact for high contact ratio spur gears with long tip relief

2019 ◽  
Vol 287 ◽  
pp. 01004
Author(s):  
José I. Pedrero ◽  
Miguel Pleguezuelos ◽  
Miryam B. Sánchez
Keyword(s):  
Load Sharing ◽  
Transmission Error ◽  
Spur Gears ◽  
Contact Ratio ◽  
Tooth Contact ◽  
Gear Teeth ◽  
Profile Modification ◽  
Static Transmission Error ◽  
Tooth Pair

Profile modifications are commonly used to avoid shocks between meshing gear teeth produced by the delay of the driven gear, and the subsequent sooner start of contact, due to the teeth deflections. A suitable tip relief at the driven tooth shifts the start of contact to the proper location at the theoretical inner point of contact. The shape of the relief governs the loading curve of the tooth pair, while the length of relief determines the intervals in which this actual loading curve differs from the theoretical one of unmodified teeth. As at least one tooth pair should be in contact at the unmodified involute profile interval, the length of modification should be smaller than the length of the intervals of two pair tooth contact; otherwise, a shock at the end of contact of the previous pair is unavoidable. However this problem does not occur for high contact ratio spur gears, in which at least two couples of teeth are in contact at any moment. In this work, a study on the load sharing and the quasi-static transmission error for high contact ratio spur gears with long profile modification has been performed, and a model for the tooth contact has been developed.

Dynamic Modeling and Analysis of Tooth Profile Modification for Multimesh Gear Vibration

2008 ◽  
Vol 130 (12) ◽  
Author(s):  
Gang Liu ◽  
Robert G. Parker
Keyword(s):  
Finite Element ◽  
Closed Form Solution ◽  
Form Solution ◽  
Tooth Profile ◽  
Modeling And Analysis ◽  
Profile Modification ◽  
Tooth Profile Modification ◽  
Proposed Model ◽  
Nonlinear Analytical Model ◽  
The Individual

This work studies the effects of tooth profile modification on multimesh gearset vibration. The nonlinear analytical model considers the dynamic load distribution between the individual gear teeth and the influence of variable mesh stiffnesses, profile modifications, and contact loss. The proposed model yields better agreement than two existing models when compared against nonlinear gear dynamics from a finite element/contact mechanics benchmark. These comparisons are made for different loads, profile modifications, and bearing stiffness conditions. This model captures the total and partial contact losses demonstrated by finite element. Perturbation analysis based on the proposed model finds approximate frequency response solutions for the case of no total contact loss due to the optimized system parameters. The closed-form solution is compared with numerical integration and provides guidance for optimizing mesh phasing, contact ratios, and profile modification magnitude and length.

scholarly journals Analytical Expressions of the Efficiency of Standard and High Contact Ratio Involute Spur Gears

2013 ◽  
Vol 2013 ◽  
pp. 1-14 ◽  
Author(s):  
Miguel Pleguezuelos ◽  
José I. Pedrero ◽  
Miryam B. Sánchez
Keyword(s):  
Friction Coefficient ◽  
Contact Point ◽  
Load Sharing ◽  
Gear Ratio ◽  
Spur Gears ◽  
Contact Ratio ◽  
Transmission Parameters ◽  
Constant Friction ◽  
Analytical Expressions ◽  
Approximate Expressions

Simple, traditional methods for computation of the efficiency of spur gears are based on the hypotheses of constant friction coefficient and uniform load sharing along the path of contact. However, none of them is accurate. The friction coefficient is variable along the path of contact, though average values can be often considered for preliminary calculations. Nevertheless, the nonuniform load sharing produced by the changing rigidity of the pair of teeth has significant influence on the friction losses, due to the different relative sliding at any contact point. In previous works, the authors obtained a nonuniform model of load distribution based on the minimum elastic potential criterion, which was applied to compute the efficiency of standard gears. In this work, this model of load sharing is applied to study the efficiency of both standard and high contact ratio involute spur gears (with contact ratio between 1 and 2 and greater than 2, resp.). Approximate expressions for the friction power losses and for the efficiency are presented assuming the friction coefficient to be constant along the path of contact. A study of the influence of some transmission parameters (as the gear ratio, pressure angle, etc.) on the efficiency is also presented.

Effect of profile modification on the performance of spur gears in isothermal mixed-EHL regime using load-sharing concept

2018 ◽  
Vol 233 (6) ◽  
pp. 936-948 ◽  
Author(s):  
Masoud Kimiaei ◽  
Saleh Akbarzadeh
Keyword(s):  
Wear Rate ◽  
Power Transmission ◽  
Elastohydrodynamic Lubrication ◽  
Load Sharing ◽  
Spur Gears ◽  
Gear Teeth ◽  
Profile Modification ◽  
Model Based ◽  
Mechanical Element ◽  
The Cost

Spur gears are one of the most important tools for power transmission in the industry and thus can be considered a key mechanical element. As a result of power transmission, gears might fail or experience wear and fatigue. So the improvement in the design and modification of tooth profile of gears can significantly reduce friction loss and wear of the gear teeth and therefore it increases the useful life, improves the quality, and reduces the cost. The purpose of this study is to show the influence of addendum modification on the tribological performance of spur gears which are operating in the mixed elastohydrodynamic lubrication. In this paper, a model based on the load-sharing concept is employed to study the effect of changing addendum modification on the performance of spur gears, the amount of wear rate, and the lubricant film thickness. To this end, a model based on the load-sharing concept is employed which takes the geometry and lubricant properties as input and predicts the friction coefficient, load carried by fluid film and asperities, efficiency, and wear rate as output.

Sign in / Sign up

Export Citation Format

Share Document