Some Analytical Results on Transmission Errors in Narrow-Faced Spur and Helical Gears: Influence of Profile Modifications

2011 ◽  
Vol 133 (3) ◽  
Author(s):  
P. Velex ◽  
J. Bruyère ◽  
D. R. Houser
Keyword(s):  
Transmission Error ◽  
Direct Solution ◽  
Contact Ratio ◽  
Helical Gears ◽  
Transmission Errors ◽  
Versus Profile ◽  
Analytical Results ◽  
Gear Geometry ◽  
Theoretical Developments

Some theoretical developments are presented, which lead to approximate analytical results on quasi-static transmission errors valid for low and high contact ratio spur and helical gears. Based on a multidegree-of-freedom gear model, a unique scalar equation for transmission error is established. The role of profile relief is analyzed by using Fourier series and it is shown that transmission error fluctuations depend on a very limited number of parameters representative of gear geometry and profile relief definition. An original direct solution to the optimum relief minimizing transmission error fluctuations is presented, which is believed to be helpful for designers. The analytical results compare well with the numerical results provided by a variety of models and it is demonstrated that some general laws of evolution for transmission error fluctuations versus profile modifications can be established for spur and helical gears.

A Contribution to the Design of Robust Profile Modifications in Spur and Helical Gears by Combining Analytical Results and Numerical Simulations

2012 ◽  
Vol 134 (6) ◽  
Author(s):  
D. Ghribi ◽  
J. Bruyère ◽  
Ph. Velex ◽  
M. Octrue ◽  
M. Haddar
Keyword(s):  
Transmission Error ◽  
Computational Time ◽  
Design Parameters ◽  
Distribution Law ◽  
Helical Gears ◽  
Factorial Method ◽  
Transmission Errors ◽  
Analytical Results ◽  
Gradient Descent Algorithm ◽  
Definition Of

This paper addresses the definition of robust profile modifications in spur and helical gears. An original methodology is introduced which relies on closed-form analytical results on transmission errors combined with a gradient descent algorithm and a Gauss quadrature (GQ) based full factorial method. The results compare very well with those delivered by using classic Monte Carlo simulations with a considerable gain in computational time. The influence of the probability distribution law for the design parameters (depth and extent of modification) is analyzed along with the contribution of gear quality grade and load variation. Some optimum robust linear relief is presented which minimizes transmission error fluctuations over a broad range of loads even in the presence of significant geometrical tolerances.

scholarly journals Computerized Design and Generation of Low-Noise Helical Gears with Modified Surface Topology

1995 ◽  
Vol 117 (2A) ◽  
pp. 254-261 ◽  
Author(s):  
F. L. Litvin ◽  
N. X. Chen ◽  
J. Lu ◽  
R. F. Handschuh
Keyword(s):  
Gear Tooth ◽  
Error Function ◽  
Transmission Error ◽  
Low Noise ◽  
Surface Topology ◽  
Helical Gears ◽  
Transmission Errors ◽  
Bearing Contact ◽  
Pinion Gear ◽  
Tooth Surfaces

An approach for the design and generation of low-noise helical gears with localized bearing contact is proposed. The approach is applied to double circular arc helical gears and modified involute helical gears. The reduction of noise and vibration is achieved by application of a predesigned parabolic function of transmission errors that is able to absorb a discontinuous linear function of transmission errors caused by misalignment. The localization of the bearing contact is achieved by the mismatch of pinion-gear tooth surfaces. Computerized simulation of meshing and contact of the designed gears demonstrated that the proposed approach will produce a pair of gears that has a parabolic transmission error function even when misalignment is present. Numerical examples for illustration of the developed approach are given.

Derivation of Optimum Profile Modifications in Narrow-Faced Spur and Helical Gears Using a Perturbation Method

2013 ◽  
Vol 135 (7) ◽  
Author(s):  
J. Bruyère ◽  
P. Velex
Keyword(s):  
Perturbation Method ◽  
Closed Form ◽  
Contact Ratio ◽  
Helical Gears ◽  
Transmission Errors ◽  
Optimum Profile ◽  
Center Distance

A perturbation method is presented which makes it possible to obtain approximate closed-form expressions for profile relief that minimize the fluctuations of quasi-static transmission errors under load. A number of results are displayed which prove the theoretical effectiveness of the proposed solutions for low-contact ratio (LCR) and high-contact ratio (HCR) spur and helical gears. It is also shown that the corresponding relief performance is not significantly downgraded by center-distance (CD) variations. Finally, a number of practical considerations are brought up and commented.

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.

A Study on the Correlation Between Dynamic Transmission Error and Dynamic Tooth Loads in Spur and Helical Gears

2016 ◽  
Vol 139 (1) ◽  
Author(s):  
N. Sainte-Marie ◽  
P. Velex ◽  
G. Roulois ◽  
J. Caillet
Keyword(s):  
Experimental Evidence ◽  
Three Dimensional ◽  
Transmission Error ◽  
System Behavior ◽  
Helical Gears ◽  
Transmission Errors ◽  
Linear Dependency ◽  
Lumped Parameter ◽  
Excitation Model ◽  
The Relationship

A three-dimensional (3D) dynamic gear model is presented which combines classic shaft, lumped parameter, and specific two-node gear elements. The mesh excitation model is based on transmission errors (TEs), and its mathematical grounding is briefly described. The validity of the proposed methodology is assessed for both spur and helical gears by comparison with experimental evidence. The model is then employed to analyze the relationship between dynamic transmission errors (DTE) and dynamic tooth loads (DF) or root stresses. It is shown that a linear dependency can be found as long as the system behavior is dominated by shaft torsion but that this linear relationship tends to disappear when bending cannot be neglected.

Effects of Contact Ratio on Transmission Errors of Trochoidal Gears

2014 ◽  
Vol 136 (3) ◽  
Author(s):  
Hiroyuki Ohta ◽  
Masahumi Kurita ◽  
Kengo Kishi
Keyword(s):  
Rotational Speed ◽  
Type A ◽  
Transmission Error ◽  
Type B ◽  
Contact Ratio ◽  
Double Row ◽  
Single Row ◽  
Transmission Errors ◽  
Number Of Teeth ◽  
Type C

This article deals with the effects of the contact ratio ε on transmission errors of trochoidal gears (which consist of a roller gear anda cam gear). First, the experiments and multibody analysis (MBA) for the transmission errors of two types of single-row trochoidal gears (types A and B gears) were carried out. The type A gear is a commercial trochoidal gear with ε = 1.1 and the type B gear is a trochoidal gear with ε = 2.1 (by increasing the number of teeth). The experimental and MBA results showed that the peak-to-peak value TEP-P of the transmission errors of the type B gear (with ε = 2.1) was lower than the type A gear (with ε = 1.1). The TEP-P of types A and B gears increased as the rotational speed of the roller gear increased. However, the increasing rate of the measured TEP-P of the type B gear due to an increase of the rotational speed was less than that of the type A gear. Increasing the contact ratio due to an increase in the number of teeth in a single-row trochoidal gear (such as a type B gear) decreases the strength of the teeth and rollers. To overcome this problem, as a new transmission error reduction method, a double-row trochoidal gear (type C gear), having two times the contact ratio of the type A single-row trochoidal gear was presented and its transmission error was examined. The experimental and MBA results showed that the TEP-P of the transmission errors of the type C double-row trochoidal gear were lower than that of the type A single-row trochoidal gear. Therefore, it is clear that using a double-row trochoidal gear is effective for reducing the transmission errors of trochoidal gears.

Tooth flank modification to reduce transmission error and mesh-in impact force in consideration of contact ratio for helical gears

2020 ◽  
pp. 095440622097506
Author(s):  
Chao Jia ◽  
Zongde Fang ◽  
Ligang Yao ◽  
Jun Zhang
Keyword(s):  
Impact Force ◽  
Transmission Error ◽  
Contact Analysis ◽  
New Method ◽  
Contact Ratio ◽  
Tooth Contact Analysis ◽  
Helical Gears ◽  
Modification Method ◽  
Tooth Modification ◽  
Tooth Flank

In this paper, a new tooth modification method considering the contact ratio of gears and a new method for calculating the mesh-in impact force of modified helical gears are proposed. The new method for calculating the mesh-in impact force is based on tooth contact analysis and loaded tooth contact analysis. The mesh-in impact position can be calculated accurately via the new method. First, the procedures for creating the new tooth modification and the details of calculation method of the mesh-in impact force are exhibited. Second, the optimal modification of the tooth flank is achieved by solving the optimization problem. Third, a dynamic model of the gear system considering the loaded transmission error and the mesh-in impact force is used to study the dynamic characteristics. Ultimately, numerical examples are presented and the simulation results suggest that the amplitude of the loaded transmission error and the mesh-in impact force can be reduced more effectively based on the introduced new tooth modification method. And the mesh-in impact effects should not be neglected in gear dynamic analysis, regardless of whether the tooth modified or not, especially for high-speed gears.

The Role of the Discrete Fourier Transform in the Contribution to Gear Transmission Error Spectra from Tooth-Spacing Errors

1987 ◽  
Vol 201 (3) ◽  
pp. 227-229 ◽  
Author(s):  
W D Mark
Keyword(s):  
Fourier Transform ◽  
Fourier Series ◽  
Error Analysis ◽  
Discrete Fourier Transform ◽  
Transmission Error ◽  
Spur Gear ◽  
Contact Ratio ◽  
Elastic Deformations ◽  
Exact Agreement

An expression is derived for the Fourier series spectrum of the transmission error arising from tooth-spacing errors on a single spur gear meshing with a perfect involute mating gear for the case of a contact ratio of unity and no elastic deformations present. This expression is found to be in exact agreement with previously derived results. The expression illustrates the role of the discrete Fourier transform in transmission error analysis and interpretation.

The Effect of Tooth Wear on the Dynamic Transmission Error of Helical Gears with Smaller Number of Pinion Teeth

2014 ◽  
Vol 657 ◽  
pp. 649-653 ◽  
Author(s):  
Virgil Atanasiu ◽  
Cezar Oprişan ◽  
Dumitru Leohchi
Keyword(s):  
Dynamic Contact ◽  
Tooth Wear ◽  
Transmission Error ◽  
Analytical Investigation ◽  
Helical Gear ◽  
Wear Depth ◽  
Contact Ratio ◽  
Mesh Stiffness ◽  
Helical Gears ◽  
Dynamic Transmission Error

The paper presents an analytical investigation of the effect of the tooth wear on the dynamic transmission error of helical gear pairs with small number of pinion teeth. Firstly, the dynamic analysis is conducted to investigate only the effect of the time-varying mesh stiffness on the variation of dynamic transmission error along the line of action. Then, the tooth wear effect on the dynamics of helical gear with small number of pinion teeth is being researched. In the analysis, instantaneous dynamic contact analysis is used in wear depth calculations. A comparative study was performed to investigate the relation between total contact ratio, mesh stiffness and dynamic transmission error of helical gear pairs with small number of teeth.

Optimum Profile Modifications for the Minimization of Static Transmission Errors of Spur Gears

1986 ◽  
Vol 108 (1) ◽  
pp. 86-94 ◽  
Author(s):  
M. S. Tavakoli ◽  
D. R. Houser
Keyword(s):  
Transmission Error ◽  
Spur Gears ◽  
Contact Ratio ◽  
Transmission Errors ◽  
Gear Mesh ◽  
Starting Point ◽  
Frequency Components ◽  
Design Loads ◽  
Static Transmission Error ◽  
Optimum Profile

A procedure for computing static transmission errors and tooth load sharing was developed for low and high contact ratio internal and external spur gears. A suitable optimization algorithm was used to minimize any combination of the harmonics of gear mesh frequency components of the static transmission error. Different combinations of tip and root relief may be used to achieve optimization. These include varying the starting point of relief and varying the magnitude of relief, and selecting the gear and/or the pinion teeth to be tip and/or root-relieved. Also, there exists an option for using either linear or parabolic relief. In addition to the presentation of optimal profile modifications, the effects of off-design loads, nonoptimum modifications, and random spacing errors are presented.

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