Tooth Surface Modelling and Mesh Behaviors for Paralleled Beveloid Gears

2019 ◽  
Vol 142 (5) ◽  
Author(s):  
Ruihua Sun ◽  
Chaosheng Song ◽  
Caichao Zhu ◽  
Siyuan Liu ◽  
Changxu Wei
Keyword(s):  
Cone Angle ◽  
Transmission Error ◽  
Tooth Surface ◽  
Design Parameters ◽  
Tooth Contact Analysis ◽  
Geometry Design ◽  
Mesh Model ◽  
Helical Angle ◽  
Loaded Tooth Contact Analysis ◽  
Pressure Cone

Abstract This paper proposed a new tooth surface modeling method for beveloid gear based on the real cutter surface using two orthogonal variables. Then, the analytical mesh model with and without misalignments were derived and solved to study the influences of geometry design parameters on contact behaviors for paralleled beveloid gear pair. Loaded tooth contact analysis is used to validate the proposed mesh model by abaqus software, and the error is below 5%. Results suggest that the increase in pressure, cone, and helical angles enlarge the contact area for meshing without misalignments. The addendum coefficient has unsubstantial impacts on the contact behaviors. For meshing with axis error in the horizontal direction, the growth of pressure angle, cone angle, helical angle, and addendum coefficient improves the carrying capacity of single tooth. But the transmission error deteriorates with the increase in pressure, cone, and helical angles. All three types of misalignments have little influence on the size of the contact ellipse. The growth of axis errors in horizontal and vertical directions significantly increases the transmission error, but the center distance error has a little influence on the transmission precision.

Simulation Analysis of Contact Pattern and Strength of WN Gears Having Tooth Surface Deviations

2012 ◽  
Vol 479-481 ◽  
pp. 944-948 ◽  
Author(s):  
Dian Hua Chen ◽  
Zhong Wei Zhang
Keyword(s):  
Simulation Analysis ◽  
Practical Method ◽  
Transmission Error ◽  
Tooth Surface ◽  
Contact Pattern ◽  
The Finite Element Method ◽  
Tooth Contact Analysis ◽  
Surface Deviations ◽  
Tooth Surfaces ◽  
Loaded Tooth Contact Analysis

A practical method based on normal gaps topography is proposed here for loaded tooth contact analysis of WN gear having tooth surface deviations. The simulation of meshing state and tooth strength of WN gear are provided with real tooth surfaces. In the study normal gaps distribution is adopted to calculate tooth surface contact elastic deformation and local deviations due to manufacturing errors and tooth surface wear. For WN gear, the loaded distribution on the contact zone in meshing tooth surface has not been investigated because of their complexity in the contact state. The finite element method is adopted to analyze the contact pattern and tooth strength. The study has concretely calculated the contact pressure and zone of meshing in different loaded and transmission error. At the end examples are analyzed to demonstrate the effectiveness of the proposed method in quantifying effect of such deviations on the loaded distribution and tooth stress distribution.

Loaded Tooth Contact Analysis of Face Gear Drive with Modification

2010 ◽  
Vol 29-32 ◽  
pp. 1711-1716
Author(s):  
Shu Yan Zhang ◽  
Hui Guo
Keyword(s):  
Transmission Error ◽  
Contact Analysis ◽  
Tooth Surface ◽  
Face Gear ◽  
Tooth Contact Analysis ◽  
Tooth Contact ◽  
Gear Drive ◽  
Bearing Contact ◽  
Tooth Number ◽  
Loaded Tooth Contact Analysis

A double direction modification with a grinding worm is applied on tooth surface of face gear drive. The surface equations of the rack cutter, shaper and grinding worm are derived respectively. Loaded tooth contact analysis (LTCA) with finite element method (FEM) is performed to investigate the meshing performance of face gear drive before modification and after modification. The modification by a grinding worm can obviously reduce the sensitivity of face gear drive to misalignment; the bending stress and the contact stress are reduced with avoiding edge contact; the load transmission error is reduced. This method can obtain a more stable bearing contact in contrast to the method by increasing tooth number of shaper, and the modification magnitude can be controlled freely. The investigation is illustrated with numerical examples.

scholarly journals Effects of Geometry Design Parameters on the Static Strength and Dynamics for Spiral Bevel Gear

2017 ◽  
Vol 2017 ◽  
pp. 1-8 ◽  
Author(s):  
Zhiheng Feng ◽  
Chaosheng Song
Keyword(s):  
Dynamic Model ◽  
Bending Strength ◽  
Transmission Error ◽  
Design Parameters ◽  
Spiral Bevel Gear ◽  
Spiral Bevel Gears ◽  
Bevel Gears ◽  
Geometry Design ◽  
Mesh Model ◽  
Spiral Bevel

Considering the geometry design parameters, a quasi-static mesh model of spiral bevel gears was established and the mesh characteristics were computed. Considering the time-varying effects of mesh points, mesh force, line-of-action vector, mesh stiffness, transmission error, friction force direction, and friction coefficient, a nonlinear lumped parameter dynamic model was developed for the spiral bevel gear pair. Based on the mesh model and the nonlinear dynamic model, the effects of main geometry parameters on the contact and bending strength were analyzed. Also, the effects on the dynamic mesh force and dynamic transmission error were investigated. Results show that higher value for the pressure angle, root fillet radius, and the ratio of tooth thickness tend to improve the contact and bending strength and to reduce the risk of tooth fracture. Improved gears have a better vibration performance in the targeted frequency range. Finally, bench tests for both types of spiral bevel gears were performed. Results show that the main failure mode is the tooth fracture and the life was increased a lot for the spiral bevel gears with improved geometry parameters compared to the original design.

Simulation and Experimental Measurement of the Transmission Error of Real Hypoid Gears Under Load

2000 ◽  
Vol 122 (1) ◽  
pp. 109-122 ◽  
Author(s):  
Claude Gosselin ◽  
Thierry Guertin ◽  
Didier Remond ◽  
Yves Jean
Keyword(s):  
Measurement Data ◽  
Simulation Models ◽  
Transmission Error ◽  
Contact Analysis ◽  
Hypoid Gear ◽  
Tooth Contact Analysis ◽  
Tooth Contact ◽  
Hypoid Gears ◽  
Loaded Tooth Contact Analysis ◽  
Analysis Models

The Transmission Error and Bearing Pattern of a gear set are fundamental aspects of its meshing behavior. To assess the validity of gear simulation models, the Transmission Error and Bearing Pattern of a Formate Hypoid gear set are measured under a variety of operating positions and applied loads. Measurement data are compared to simulation results of Tooth Contact Analysis and Loaded Tooth Contact Analysis models, and show excellent agreement for the considered test gear set. [S1050-0472(00)00901-6]

Optimal Machine-Tool Settings for the Manufacture of Face-Hobbed Spiral Bevel Gears

2014 ◽  
Vol 136 (8) ◽  
Author(s):  
Vilmos V. Simon
Keyword(s):  
Contact Pressure ◽  
Optimization Problem ◽  
Transmission Error ◽  
Search Method ◽  
Tooth Contact Analysis ◽  
Tooth Contact ◽  
Transmission Errors ◽  
Bevel Gears ◽  
Spiral Bevel ◽  
Loaded Tooth Contact Analysis

In this study, an optimization methodology is proposed to systematically define the optimal head-cutter geometry and machine-tool settings to simultaneously minimize the tooth contact pressure and angular displacement error of the driven gear (the transmission error), and to reduce the sensitivity of face-hobbed spiral bevel gears to the misalignments. The proposed optimization procedure relies heavily on the loaded tooth contact analysis for the prediction of tooth contact pressure distribution and transmission errors influenced by the misalignments inherent in the gear pair. The load distribution and transmission error calculation method employed in this study were developed by the author of this paper. The targeted optimization problem is a nonlinear constrained optimization problem, belonging to the framework of nonlinear programming. In addition, the objective function and the constraints are not available analytically, but they are computable, i.e., they exist numerically through the loaded tooth contact analysis. For these reasons, a nonderivative method is selected to solve this particular optimization problem. That is the reason that the core algorithm of the proposed nonlinear programming procedure is based on a direct search method. The Hooke and Jeeves pattern search method is applied. The effectiveness of this optimization was demonstrated on a face-hobbed spiral bevel gear example. Drastic reductions in the maximum tooth contact pressure (62%) and in the transmission errors (70%) were obtained.

Tool Profile Modification of Hypoid Gear Machined by Duplex Helical Method

2021 ◽  
Author(s):  
Shunxing Wu ◽  
Hongzhi Yan ◽  
Zhiyong Wang ◽  
Rengui Bi ◽  
Jia Li
Keyword(s):  
Geometric Model ◽  
Tooth Surface ◽  
Gear Pair ◽  
Hypoid Gear ◽  
Tooth Contact Analysis ◽  
Edge Contact ◽  
Profile Modification ◽  
Tool Profile ◽  
Tooth Surfaces ◽  
Loaded Tooth Contact Analysis

Abstract For the hypoid gear pair of the heavy-duty vehicle drive axle machined by the duplex helical method, in order to avoid edge contact and stress concentration on the tooth surface, a four-segment tool profile is designed to modify the concave and convex surfaces simultaneously. First, the geometric model of the four-segment tool profile is established. Second, the mathematical model of the duplex helical method based on the four-segment tool profile is established, and the method of solving the tooth surface generated by the connecting points of the four-segment tool profile is given. Finally, the finite element method of loaded tooth contact analysis is used to analyze the meshing performance of the gear pair obtained by the four-segment tool profile modification, and the results are compared with the original gear pair. The results show that after the tooth surfaces are modified, the edge contact of the tooth surfaces are avoided, the stress distribution of the tooth surfaces are improved, the maximum contact stress of the tooth surfaces are reduced, and the fatigue and wear life of the tooth surface are improved.

scholarly journals Quasi-Static Characteristics and Vibration Responses Analysis of Helical Geared Rotor System with Random Cumulative Pitch Deviations

2020 ◽  
Vol 10 (12) ◽  
pp. 4403
Author(s):  
Bing Yuan ◽  
Geng Liu ◽  
Lan Liu
Keyword(s):  
Degrees Of Freedom ◽  
Transmission Error ◽  
Rotor System ◽  
Dynamic Responses ◽  
Contact Ratio ◽  
Tooth Contact Analysis ◽  
Long Period ◽  
Light Load ◽  
Vibration Responses ◽  
Loaded Tooth Contact Analysis

As one of the long period gear errors, the effects of random cumulative pitch deviations on mesh excitations and vibration responses of a helical geared rotor system (HGRS) are investigated. The long-period mesh stiffness (LPMS), static transmission error (STE), as well as composite mesh error (CMS), and load distributions of helical gears are calculated using an enhanced loaded tooth contact analysis (LTCA) model. A dynamic model with multi degrees of freedom (DOF) is employed to predict the vibration responses of HGRS. Mesh excitations and vibration responses analysis of unmodified HGRS are conducted in consideration of random cumulative pitch deviations. The results indicate that random cumulative pitch deviations have significant effects on mesh excitations and vibration responses of HGRS. The curve shapes of STE and CMS become irregular when the random characteristic of cumulative pitch deviations is considered, and the appearance of partial contact loss in some mesh cycles leads to decreased LPMS when load torque is relatively low. Vibration modulation phenomenon can be observed in dynamic responses of HGRS. In relatively light load conditions, the amplitudes of sideband frequencies become larger than that of mesh frequency and its harmonics (MFIHs) because of relatively high contact ratio. The influences of random cumulative pitch deviations on the vibration responses of modified HGRS are also discussed.

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.

Tooth contact analysis of a curvilinear gear set with modified pinion tooth geometry

2011 ◽  
Vol 225 (4) ◽  
pp. 975-986 ◽  
Author(s):  
Y-C Chen ◽  
M-L Gu
Keyword(s):  
Finite Element ◽  
Transmission Error ◽  
Contact Analysis ◽  
Design Parameters ◽  
Stress Distributions ◽  
Tooth Contact Analysis ◽  
Tooth Contact ◽  
Numerical Examples ◽  
Bearing Contact ◽  
Parallel Axis

This article investigated the contact behaviours of a modified curvilinear gear set for parallel-axis transmission, which exhibits a pre-designed parabolic transmission error (TE) and localized bearing contact. The proposed gear set is composed of a modified pinion with curvilinear teeth and an involute gear with curvilinear teeth. Tooth contact analysis enabled the authors to explore the influences of assembly errors and design parameters on TEs and contact ellipses of this gear set. It is observed that TEs were continuous and the contact ellipses were localized in the middle of the tooth flanks, even under assembly errors. Finite-element contact analysis was performed to study stress distributions under different design parameters. In addition, numerical examples are presented to demonstrate the contact characteristics of the modified curvilinear gear set.

Dynamics of Hypoid Gear Transmission With Nonlinear Time-Varying Mesh Characteristics

2003 ◽  
Vol 125 (2) ◽  
pp. 373-382 ◽  
Author(s):  
Yuping Cheng ◽  
Teik C. Lim
Keyword(s):  
Response Spectra ◽  
Transmission Error ◽  
Operating Conditions ◽  
Time Varying ◽  
Analysis Model ◽  
Tooth Contact Analysis ◽  
3 Dimensional ◽  
Resonant Modes ◽  
Loaded Tooth Contact Analysis ◽  
Backlash Nonlinearity

The coupled translation-rotation vibratory response of hypoid geared rotor system due to loaded transmission error excitation is studied by employing a generalized 3-dimensional dynamic model. The formulation includes the effects of backlash nonlinearity as well as time-dependent mesh position and line-of-action vectors. Its mesh coupling is derived from a quasi-static, 3-dimensional, loaded tooth contact analysis model that accounts for the precise gear geometry and profile modifications. The numerical simulations show significant tooth separation and occurrence of multi-jump phenomenon in the predicted response spectra under certain lightly loaded operating conditions. Also, resonant modes contributing to the response spectra are identified, and cases with super-harmonics are illustrated. The computational results are then analyzed to quantify the extent of non-linear and time-varying factors.

Sign in / Sign up

Export Citation Format

Share Document