scholarly journals Tooth Surface Modification for Helical Gear Pairs considering Mesh Misalignment Tolerance

2021 ◽  
Vol 2021 ◽  
pp. 1-13
Author(s):  
Guosheng Han ◽  
Bing Yuan ◽  
Guan Qiao
Keyword(s):  
Surface Modification ◽  
Gear Tooth ◽  
Transmission Error ◽  
Helical Gear ◽  
Tooth Surface ◽  
Tooth Contact Analysis ◽  
Nsga Ii ◽  
Design Variables ◽  
Tooth Flank ◽  
Tooth Surface Modification

Mesh misalignment in mating the gear tooth surface is common and difficult to be determined accurately because of system deformation and bearing clearances, as well as manufacturing and assembly errors. It is not appropriate to consider the mesh misalignment as a constant value or even completely ignore it in the tooth surface modification design. Aiming to minimize the expectation and variance of static transmission error (STE) fluctuations in consideration of mesh misalignment tolerance, a multiobjective optimization model of tooth surface modification parameters is proposed through coupling the NSGA-II algorithm and an efficient loaded tooth contact analysis (LTCA) model. The modified tooth flank of helical gear pairs is defined using 6 design variables which are related to profile modification, lead modification, and bias modification. The influences of mesh misalignment on time-dependent meshing stiffness (TDMS) and STE of unmodified and modified helical gear pairs are investigated. Then, the dynamic transmission error (DTE) of modified helical gears in consideration of mesh misalignment is discussed. The results indicate that the designed modified tooth surface shows good robustness to mesh misalignment.

Tooth Contact Analysis of Longitudinal Cycloidal-Crowned Helical Gears With Circular Arc Teeth

2010 ◽  
Vol 132 (3) ◽  
Author(s):  
Wei-Shiang Wang ◽  
Zhang-Hua Fong
Keyword(s):  
Gear Tooth ◽  
Longitudinal Direction ◽  
Transmission Error ◽  
Helical Gear ◽  
Contact Analysis ◽  
Tooth Contact Analysis ◽  
Tooth Contact ◽  
Circular Arc ◽  
Tooth Flank ◽  
Assembly Error

This paper proposes a new type of double-crowned helical gear that can be continuously cut on a modern Cartesian-type hypoid generator with two face-hobbing head cutters and circular-arc cutter blades. The gear tooth flank is double crowned with a cycloidal curve in the longitudinal direction and a circular arc in the profile direction. To gauge the sensitivity of the transmission errors and contact patterns resulting from various assembly errors, this paper applies a tooth contact analysis technique and presents several numerical examples that show the benefit of the proposed double-crowned helical gear set. In contrast to a conventional helical involute gear, the tooth bearing and transmission error of the proposed gear set are both controllable and insensitive to gear-set assembly error.

A novel tooth surface modification methodology for wide-faced double-helical gear pairs

2021 ◽  
Vol 160 ◽  
pp. 104299
Author(s):  
Bing Yuan ◽  
Geng Liu ◽  
Yanjiong Yue ◽  
Lan Liu ◽  
Yunbo Shen
Keyword(s):  
Surface Modification ◽  
Helical Gear ◽  
Tooth Surface ◽  
Tooth Surface Modification

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.

scholarly journals Meshing characteristics of a sphere–face gear pair with variable shaft angle

2019 ◽  
Vol 11 (6) ◽  
pp. 168781401985951 ◽  
Author(s):  
Lei Liu ◽  
Jinzhao Zhang
Keyword(s):  
Gear Tooth ◽  
Transmission Error ◽  
Tooth Surface ◽  
Gear Pair ◽  
Face Gear ◽  
Tooth Contact Analysis ◽  
Contact Points ◽  
Shaft Angle ◽  
Meshing Characteristics ◽  
Curvature Interference

This article presents a sphere–face gear pair by substituting the convex spherical gear for the pinion of a conventional face gear pair. The sphere–face gear pair not only maintains the advantages of the face gear pair with a longitudinally modified pinion but also allows variable shaft angles or large axial misalignments. Meshing characteristics of the proposed gear pair are studied in this article. The mathematical models of the sphere–face gear pair are derived based on machining principles. The tooth contact analysis (TCA) and curvature interference check are conducted for the sphere–face gear pair with variable shaft angles. The loaded TCA is also implemented utilizing the finite element method. The results of numerical examples show that proposed gear pair has the following features. Geometrical transmission error of constant shaft angle or varying shaft angle is zero; contact points of the sphere–face gear set with variable shaft angle are located near the centre region of face gear tooth surface; there is no curvature interference in meshing; and transmission continuity of the gear pair can be guaranteed in meshing.

Robust Optimization of Cylindrical Gear Tooth Surface Modifications Within Ranges of Torque and Misalignments

2013 ◽  
Author(s):  
Alessio Artoni ◽  
Massimo Guiggiani ◽  
Ahmet Kahraman ◽  
Jonny Harianto
Keyword(s):  
Performance Metrics ◽  
Gear Tooth ◽  
Surface Modifications ◽  
Transmission Error ◽  
Robust Design Optimization ◽  
Tooth Surface ◽  
Global Optimality ◽  
Cylindrical Gear ◽  
Geometry Design ◽  
Design Variables

Tooth surface modifications are small, micron-level intentional deviations from perfect involute geometries of spur and helical gears. Such modifications are aimed at improving contact pressure distribution, while minimizing the motion transmission error to reduce noise excitations. In actual practice, optimal modification requirements vary with the operating torque level, misalignments, and manufacturing variance. However, most gear literature has been concerned with determining optimal flank form modifications at a single design point, represented by fixed, single load and misalignment values. A new approach to the design of tooth surface modifications is proposed to handle such conditions. The problem is formulated as a robust design optimization problem, and it is solved, in conjunction with an efficient gear contact solver (LDP), by a direct search, global optimization algorithm aimed at guaranteeing global optimality of the obtained micro-geometry solutions. Several tooth surface modifications can be used as micro-geometry design variables, including profile, lead, and bias modifications. Depending on the contact solver capabilities, multiple performance metrics can be considered. The proposed method includes the capability of simultaneously and robustly handling several conflicting design objectives. In the present paper, peak contact stress and loaded transmission error amplitude are used as objective functions (to be minimized). At the end, two example optimizations are presented to demonstrate the effectiveness of the proposed method.

Robust Optimization of Cylindrical Gear Tooth Surface Modifications Within Ranges of Torque and Misalignments

2013 ◽  
Vol 135 (12) ◽  
Author(s):  
Alessio Artoni ◽  
Massimo Guiggiani ◽  
Ahmet Kahraman ◽  
Jonny Harianto
Keyword(s):  
Performance Metrics ◽  
Gear Tooth ◽  
Surface Modifications ◽  
Transmission Error ◽  
Robust Design Optimization ◽  
Tooth Surface ◽  
Global Optimality ◽  
Cylindrical Gear ◽  
Design Variables ◽  
Gear Contact

Tooth surface modifications are small, micron-level intentional deviations from perfect involute geometries of spur and helical gears. Such modifications are aimed at improving contact pressure distribution, while minimizing the motion transmission error to reduce noise excitations. In actual practice, optimal modification requirements vary with the operating torque level, misalignments, and manufacturing variance. However, most gear literature has been concerned with determining optimal flank form modifications at a single design point, represented by fixed, single load and misalignment values. A new approach to the design of tooth surface modifications is proposed to handle such conditions. The problem is formulated as a robust design optimization problem, and it is solved, in conjunction with an efficient gear contact solver (Load Distribution Program (LDP)), by a direct search, global optimization algorithm aimed at guaranteeing global optimality of the obtained microgeometry solutions. Several tooth surface modifications can be used as microgeometry design variables, including profile, lead, and bias modifications. Depending on the contact solver capabilities, multiple performance metrics can be considered. The proposed method includes the capability of simultaneously and robustly handling several conflicting design objectives. In the present paper, peak contact stress and loaded transmission error amplitude are used as objective functions (to be minimized). At the end, two example optimizations are presented to demonstrate the effectiveness of the proposed method.

Effect of Tooth Surface Modification on the Load Sharing and Strength of Offset Face Gear Drive with Spur Involute Pinion

2011 ◽  
Vol 86 ◽  
pp. 327-332
Author(s):  
Jin Hua Wang ◽  
Yun Bo Shen ◽  
Ze Yong Yin ◽  
Jie Gao ◽  
Yan Ying Jiang
Keyword(s):  
Surface Modification ◽  
Load Sharing ◽  
Contact Analysis ◽  
Tooth Surface ◽  
Contact Ratio ◽  
Face Gear ◽  
Tooth Contact Analysis ◽  
Tooth Contact ◽  
Gear Drive ◽  
Tooth Surface Modification

Load sharing is one of the main factors that determine gear strength. In this paper, Tooth Contact Analysis (TCA) and Loaded Tooth Contact Analysis (LTCA) have been performed to investigate the effect of tooth surface modification on the contact ratio, load sharing and strength of an orthogonal offset face gear drive with spur involute pinion. The results indicate that the contact ratio of 2.0 or higher could be achieved. The maximum load carried by single tooth and bending stress are significantly reduced when appropriate tooth surface modification is applied to the orthogonal offset face gear drive.

scholarly journals Experimental and Theoretical Study of Gear Dynamical Transmission Characteristic Considering Measured Manufacturing Errors

2018 ◽  
Vol 2018 ◽  
pp. 1-20 ◽  
Author(s):  
Fang Guo ◽  
Zongde Fang
Keyword(s):  
Transmission Error ◽  
Helical Gear ◽  
Tooth Surface ◽  
Time Varying ◽  
Mesh Stiffness ◽  
Tooth Contact Analysis ◽  
Gear Mesh ◽  
Manufacturing Errors ◽  
Tooth Modification ◽  
Helical Gear Pair

In the research of gear transmission, the vibration and noise problem has received many concerns all the times. Scholars use tooth modification technique to improve the meshing state of gearings in order to reduce the vibration and noise. However, few of researchers consider the influence of measured manufacturing errors when they do the study of tooth modification. In order to investigate the efficiency of the tooth modification in the actual project, this paper proposes a dynamic model of a helical gear pair including tooth modification and measured manufacturing errors to do a deterministic analysis on the dynamical transmission performance. In this analysis, based on the measured tooth deviation, a real tooth surface (including modification and measured tooth profile error) is fitted by a bicubic B-spline. With the tooth contact analysis (TCA) and loaded tooth contact analysis (LTCA) on the real tooth surface, the loaded transmission error, tooth surface elastic deformation, and load distribution can be determined. Based on the results, the time-varying mesh stiffness and gear mesh impact are computed. Taking the loaded transmission error, measured cumulative pitch error, eccentricity error, time-varying mesh stiffness, and gear mesh impact as the internal excitations, this paper establishes a 12-degree-of-freedom (DOF) dynamic model of a helical gear pair and uses the Fourier series method to solve it. In two situations of low speed and high speed, the gear system dynamic response is analyzed in the time and frequency domains. In addition, an experiment is performed to validate the simulation results. The study shows that the proposed technique is useful and reliable for predicting the dynamic response of a gear system.

scholarly journals Dynamic Analysis of High-Speed Helical Gear Transmission in Pure Electric Vehicle Gearbox

2020 ◽  
Vol 2020 ◽  
pp. 1-19
Author(s):  
Yanchao Zhang ◽  
Jinfu Du ◽  
Jin Mao ◽  
Min Xu
Keyword(s):  
Surface Modification ◽  
Electric Vehicle ◽  
High Speed ◽  
Helical Gear ◽  
Gear Transmission ◽  
Tooth Surface ◽  
Gear Pair ◽  
Two Stage ◽  
Rotating Speed ◽  
Tooth Surface Modification

This study is to systematically analyze the influences of time-varying meshing stiffness (TVMS) and meshing impact on the dynamic characteristics of high-speed gear transmission in the two-stage pure electric vehicle (PEV) gearbox, as well as the effect of tooth surface modification on the vibration control. First, the dynamic model was established, and the TVMS and meshing impact were calculated. Then, the vibration characteristics of single-stage and two-stage helical gear transmission were analyzed under three different excitation conditions, excitation of TVMS, excitation of meshing impact, and excitation of both. The results show that the effect of rotating speed on the system vibration is not significant outside the resonant region under the excitation of TVMS, while the effect of meshing impact becomes the main exciting component with the increasing rotating speed. The vibrations of the two gear pairs interact with each other; the vibration frequency of one gear pair contains both its meshing frequency and the coupling frequency of the other gear pair. Tooth surface modification in the input-stage gear pair can reduce the vibration of both the input- and the output-stage obviously; that is, more attention should be paid to the input-stage gear pair in the modification design of PEV gearbox.

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