The Combined Influence of Helix Angle and Total Contact Ratio on the p-FEM Calculated Tooth Root Stress in Cylindrical Gears

2000 ◽  
Author(s):  
Andrea Piazza ◽  
Maurizio Uberti
Keyword(s):  
Transverse Section ◽  
Helix Angle ◽  
Tooth Root ◽  
Finite Element Method Analysis ◽  
Contact Ratio ◽  
Profile Modification ◽  
Cylindrical Gears ◽  
Angle Correction ◽  
Method Analysis ◽  
Root Stress

Abstract Many parametrical studies about the effect of the helix angle on the maximum tooth root stress on cylindrical gears were conducted by means of a p-FEM (polynomial Finite Element Method) analysis, using models that comprehend all the contacting teeth and the adjacent ones. The studies were conducted in a way that the helix angle was varied from 0 to 35 degrees, keeping the transverse section constant (i.e. twisting the gears). Many non-HCR existing spur and helical gearsets, with different transverse contact ratio εα, transmission ratio, pressure angle, correction factor, and facewidth to module ratio were examined. Neither profile modification, nor crowning were considered. For each gearset the maximum p-FEM-calculated tooth root stress in both pinion and gear drops considerably when the total contact ratio εγ reaches the value of 2, with a minimum noticed around εγ = 2.1 ÷ 2.4; then the stress rises monotonically except for a non-remarkable drop when εγ reaches the value of 3. The p-FEM results were also compared with those based on ISO 6336-3 method B and AGMA 2001, showing noticeable differences.

Meshing Stiffness and Tooth Root Stress for Internal Cylindrical Gears With Thin Rim

2003 ◽  
Author(s):  
Jean-Pierre de Vaujany ◽  
Miche`le Guingand ◽  
Didier Remond
Keyword(s):  
3D Model ◽  
Statistical Design ◽  
Tension Stress ◽  
Tooth Root ◽  
Meshing Stiffness ◽  
Cylindrical Gears ◽  
Maximal Tension ◽  
Experiment Method ◽  
Internal Gear ◽  
Root Stress

The main objective of this study is to quantify the influence of the deformation of the rim of an internal gear on the meshing stiffness and the stress distribution in tooth fillets. The 3D model used is based on a method derived from the Finite Prism Method. Tooth bending effects and contact deformations are processed simultaneously. Scientific use of the software has resulted in formulating an equation to calculate the maximal tension stress in the tooth root. This formula has been obtained by using the statistical design of experiment method.

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.

Tooth-root stress calculation of high transverse contact ratio spur and helical gears

Meccanica ◽  
2013 ◽  
Vol 49 (2) ◽  
pp. 347-364 ◽  
Author(s):  
Miryam B. Sánchez ◽  
Miguel Pleguezuelos ◽  
José I. Pedrero
Keyword(s):  
Tooth Root ◽  
Contact Ratio ◽  
Helical Gears ◽  
Stress Calculation ◽  
Root Stress

scholarly journals Investigation of the Nominal Tooth Root Stress for External, Cylindrical Gears with Symmetric and Asymmetric Profile

2020 ◽  
Vol 15 ◽  
Keyword(s):  
Finite Element ◽  
Cross Section ◽  
Bending Strength ◽  
Critical Cross Section ◽  
Tooth Root ◽  
Gear Design ◽  
Cylindrical Gears ◽  
Basic Issue ◽  
Root Stress

The determination of tooth bending strength is a basic issue in gear design. This work presents the change of nominal tooth root stress of external toothed, cylindrical gears depending on the geometry used. The nominal tooth root stress is analyzed with using finite element simulations. The numerical calculations are executed in Abaqus. The imported geometries are produced by our own program in MATLAB. The boundary conditions to the models are defined accordance with the most significant analytical methods used in practice. This approach allows mapping direct correlation analysis by these calculations. The optimization of computational capacity used is also considered. In addition to the examination of the significant tooth stress value of symmetrical element pairs, the position of the critical cross-section is also analyzed. The effect of the asymmetric design of the tooth profile on the nominal tooth root stress is also presented in our investigations. The purpose of the numerical simulations carried out here is to determine the effect of the coast side angle on the magnitude of the significant tooth root stress and the position of the critical cross-section.

scholarly journals Computer-Aided Design of High-Contact-Ratio Gears for Minimum Dynamic Load and Stress

1993 ◽  
Vol 115 (1) ◽  
pp. 171-178 ◽  
Author(s):  
Hsiang Hsi Lin ◽  
Chinwai Lee ◽  
F. B. Oswald ◽  
D. P. Townsend
Keyword(s):  
Dynamic Load ◽  
Computer Aided Design ◽  
Numerical Procedure ◽  
Tooth Profile ◽  
Lower Sensitivity ◽  
Contact Ratio ◽  
Profile Modification ◽  
Parabolic Profile ◽  
Profile Design ◽  
Optimum Profile

This paper presents a numerical procedure for minimizing dynamic effects on high-contact-ratio gears by modification of the tooth profile. The paper examines and compares both linear and parabolic tooth profile modifications of high-contact-ratio gears under various loading conditions. The effects of the total amount of modification and the length of the modification zone were systematically studied at various loads and speeds to find the optimum profile design for minimizing the dynamic load and the tooth bending stress. Parabolic profile modification is preferred over linear profile modification for high-contact-ratio gears because of its lower sensitivity to manufacturing errors. For parabolic modification a greater amount of modification at the tooth tip and a longer modification zone are required. Design charts are presented for high-contact-ratio gears with various profile modifications operating under a range of loads. A procedure is illustrated for using the charts to find the optimum profile design.

Comparative study of stress analysis of gears with different helix angle using the ISO 6336 standard and tooth contact analysis methods

2016 ◽  
Vol 230 (7-8) ◽  
pp. 1350-1358 ◽  
Author(s):  
Layue Zhao ◽  
Robert C Frazer ◽  
Brian Shaw
Keyword(s):  
Stress Analysis ◽  
Contact Stress ◽  
Helix Angle ◽  
Contact Analysis ◽  
Bending Stress ◽  
Contact Ratio ◽  
Tooth Contact Analysis ◽  
Tooth Contact ◽  
Iso Standard ◽  
Analysis Methods

With increasing demand for high speed and high power density gear applications, the need to optimise gears for minimum stress, noise and vibration becomes increasingly important. ISO 6336 contact and bending stress analysis are used to determine the surface load capacity and tooth bending strength but dates back to 1956 and although it is constantly being updated, a review of its performance is sensible. Methods to optimise gear performance include the selection of helix angle and tooth depth to optimise overlap ratio and transverse contact ratio and thus the performance of ISO 6336 and tooth contact analysis methods requires confirmation. This paper reviews the contact and bending stress predicted with four involute gear geometries and proposes recommendations for stress calculations, including a modification to contact ratio factor Zɛ which is used to predict contact stress and revisions to form factor YF and helix angle factor Yβ which are cited to evaluate bending stress. The results suggest that there are some significant deviations in predicted bending and contact stress values between proposal methods and original ISO standard. However, before the ISO standard is changed, the paper recommends that allowable stress numbers published in ISO 6336-5 are reviewed because the mechanisms that initiate bending and contact fatigue have also changed and these require updating.

Multi-Objective Topology Optimization for Bevel Gear and Geometrical Reconstruction

2013 ◽  
Vol 278-280 ◽  
pp. 139-142
Author(s):  
Xiang Bian ◽  
Zong De Fang ◽  
Kun Qin ◽  
Lifei Lian ◽  
Bao Yu Zhang
Keyword(s):  
Topology Optimization ◽  
Optimization Method ◽  
Tooth Root ◽  
Multi Objective Optimization ◽  
Direct Optimization ◽  
Multi Objective ◽  
Gear Modification ◽  
Parametric Cad ◽  
Straight Lines ◽  
Root Stress

Usually the gear modification is a main measure to reduce the vibration and noise of the gears, but in view of the complexity of the gear modification, topology optimization method was used to optimize the structure of the gear. The minimum volume was set as the direct optimization goal. To achieve the target of reducing contact stress, tooth root bending stress and improving flexibility, the upper bound of the stress and lower bound of the flexibility were set appropriately, thus realizing multi-objective optimization indirectly. A method for converting topology result into parametric CAD model which can be modified was presented, by fitting the topology result with simple straight lines and arcs, the model can be smoothed automatically, after further regulating, the geometry reconstruction was finished. After topology optimization, the resulting structure and properties of the gear are consistent with cavity gear. While reducing the weight of the gear, the noise can be reduced and its life would be extended through increasing flexibility and reducing tooth root stress.

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