scholarly journals Simulation and Analysis on Tooth Meshing Ease-Off Surface of Gears Based on Polynomial Topology Modification

2020 ◽  
Vol 38 (4) ◽  
pp. 897-903
Author(s):  
Bingyang Wei ◽  
Xuemei Cao ◽  
Xiaozhong Deng
Keyword(s):  
Contact Line ◽  
Simulation Method ◽  
Transmission Error ◽  
Topological Optimization ◽  
Tooth Surface ◽  
Surface Mesh ◽  
Order Polynomial ◽  
Meshing Characteristics ◽  
Topological Construction ◽  
Topology Modification

Based on the principles of common-generating conjugation mapping of pinion-rank-gear meshing, the constructing of ease-off surface has been done by means of the topology modification of the 4-order polynomial surface. The simulation method of tooth surface mesh is purposed based on the ease-off surface. By analyzing topological structure characteristics of ease-off surface such as modification gradient curves, contact line-off and contact path-off, the meshing characteristics such as the contact area, the contact line and transmission error are determined. It is stated on the interaction relations of coefficients of the 4-order polynomial to the topological construction of surface. The methods for reconstruction and analysis of ease-off surface with considering axis misalignments are presented by the direct transformation of coordinate systems. Taking the topological construction of four kinds of surfaces as examples, characteristics parameters such as modification gradient of tooth surface, contact path and transmission errors are simulated. They are expounded on the corresponding parameters of controlling form and adjusting methods for tooth surface. These methods take goals of adjusting-modification and controlling-property for tooth surface mesh. It is improved and developed the meshing analysis method of ease-off surface of tooth. The presented method is liable to provide the basis data for the further loaded contact analysis of complicated tooth surface and the more direct technical for the 3-D topological optimization of tooth surface.

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.

Variable height modification of TA worm drive

2018 ◽  
Vol 233 (1) ◽  
pp. 227-243 ◽  
Author(s):  
Chongfei Huai ◽  
Yaping Zhao
Keyword(s):  
Theoretical Analysis ◽  
Contact Line ◽  
Gear Tooth ◽  
Computing Methods ◽  
Normal Operation ◽  
Tooth Surface ◽  
Modification Method ◽  
Worm Gearing ◽  
Meshing Characteristics ◽  
Worm Drive

The related research shows that a constant contact line, which is negative for the normal operation of the worm gearing, exists on the middle of the unmodified and the constant height modified TA worm wheel surface. To overcome this drawback, a variable height modification method is proposed for the TA worm drive. In line with this modification method, the height modification parameter is variable during the whole processing cycle. Accordingly, the obtained gearing can be named as the variable height modified TA worm drive. The mathematical model for the meshing analysis of this novel worm drive is established according to its generation mechanism and the mesh theory of gearing. The reason why the variable height modification can remove the constant contact line on the worm gear tooth surface is analyzed in detail. In addition, the classification criterion of the transmission type is also derived. The computing methods of the key points on the contact zone boundary and the instantaneous meshing line are elaborated. On the basis of the above theoretical analysis, the meshing characteristics of this novel worm gearing are well investigated. The results manifest that the above theoretical analysis is valid, and the obtained gearing has favorable meshing properties. Furthermore, it is pointed out that the linear variable height modification with larger quantity can be recommended as the ideal strategy in practice.

Effects of the Gear Tooth Modification on the Nonlinear Dynamics of Gear Transmission System

2010 ◽  
Vol 97-101 ◽  
pp. 2764-2769
Author(s):  
Si Yu Chen ◽  
Jin Yuan Tang ◽  
C.W. Luo
Keyword(s):  
Nonlinear Dynamics ◽  
Gear Tooth ◽  
Simulation Method ◽  
Transmission Error ◽  
Dynamic Responses ◽  
Meshing Stiffness ◽  
Gear Transmission System ◽  
Tooth Modification ◽  
Static Transmission Error ◽  
Misalignment Error

The effects of tooth modification on the nonlinear dynamic behaviors are studied in this paper. Firstly, the static transmission error under load combined with misalignment error and modification are deduced. These effects can be introduced directly in the meshing stiffness and static transmission error models. Then the effect of two different type of tooth modification combined with misalignment error on the dynamic responses are investigated by using numerical simulation method. The numerical results show that the misalignment error has a significant effect on the static transmission error. The tooth crowning modification is generally preferred for absorbing the misalignment error by comparing with the tip and root relief. The tip and root relief can not resolve the vibration problem induced by misalignment error but the crowning modification can reduce the vibration significantly.

Influence of the backlash generated by tooth accumulated wear on dynamic behavior of compound planetary gear set

2016 ◽  
Vol 231 (11) ◽  
pp. 2025-2041 ◽  
Author(s):  
Shijing Wu ◽  
Haibo Zhang ◽  
Xiaosun Wang ◽  
Zeming Peng ◽  
Kangkang Yang ◽  
...  
Keyword(s):  
Dynamic Response ◽  
Dynamic Model ◽  
Dynamic Behavior ◽  
Planetary Gear ◽  
Tooth Wear ◽  
Transmission Error ◽  
Gear Transmission ◽  
Tooth Surface ◽  
Contact Ratio ◽  
The Impact

Backlash is a key internal excitation on the dynamic response of planetary gear transmission. After the gear transmission running for a long time under load torque, due to tooth wear accumulation, the backlash between the tooth surface of two mating gears increases, which results in a larger and irregular backlash. However, the increasing backlash generated by tooth accumulated wear is generally neglected in lots of dynamics analysis for epicyclic gear trains. In order to investigate the impact of backlash generated by tooth accumulated wear on dynamic behavior of compound planetary gear set, in this work, first a static tooth surface wear prediction model is incorporated with a dynamic iteration methodology to get the increasing backlash generated by tooth accumulated wear for one pair of mating teeth under the condition that contact ratio equals to one. Then in order to introduce the tooth accumulated wear into dynamic model of compound planetary gear set, the backlash excitation generated by tooth accumulated wear for each meshing pair in compound planetary gear set is given under the condition that contact ratio equals to one and does not equal to one. Last, in order to investigate the impact of the increasing backlash generated by tooth accumulated wear on dynamic response of compound planetary gear set, a nonlinear lumped-parameter dynamic model of compound planetary gear set is employed to describe the dynamic relationships of gear transmission under the internal excitations generated by worn profile, meshing stiffness, transmission error, and backlash. The results indicate that the introduction of the increasing backlash generated by tooth accumulated wear makes a significant influence on the bifurcation and chaotic characteristics, dynamic response in time domain, and load sharing behavior of compound planetary gear set.

Investigation of Noise Features of Planetary Gear Trains Based on Human Aural Characteristic

2017 ◽  
Author(s):  
Masao Nakagawa ◽  
Dai Nishida ◽  
Deepak Sah ◽  
Toshiki Hirogaki ◽  
Eiichi Aoyama
Keyword(s):  
Gear Tooth ◽  
Structural Complexity ◽  
Planetary Gear ◽  
Transmission Error ◽  
Sound Level ◽  
Tooth Surface ◽  
Surface Error ◽  
Planetary Gear Trains ◽  
Tooth Stiffness ◽  
Gear Trains

Planetary gear trains (PGTs) are widely used in various machines owing to their many advantages. However, they suffer from problems of noise and vibration due to the structural complexity and giving rise to substantial noise, vibration, and harshness with respect to both structures and human users. In this report, the sound level from PGTs is measured in an anechoic chamber based on human aural characteristic, and basic features of sound are investigated. Gear noise is generated by the vibration force due to varying gear tooth stiffness and the vibration force due to tooth surface error, or transmission error (TE). Dynamic TE is considered to be increased because of internal and external meshing. The vibration force due to tooth surface error can be ignored owing to almost perfect tooth surface. A vibration force due to varying tooth stiffness could be a major factor.

Computation of Parameters of a Form Grinding Wheel for Grinding of Shaving Cutter for Plunge Shaving of Topologically Modified Involute Pinion

2005 ◽  
Vol 127 (4) ◽  
pp. 819-828 ◽  
Author(s):  
Stephen P. Radzevich
Keyword(s):  
Transmission Error ◽  
Low Noise ◽  
Tooth Surface ◽  
Grinding Wheel ◽  
Cnc Machine ◽  
Surface Machining ◽  
Form Grinding ◽  
Novel Approach ◽  
Light Trucks ◽  
Part Surface

The paper is targeting on the finishing of precision gears for low-noise/noiseless transmission for cars and light trucks. Transmission error is the predominant cause of gear noise. The application of a topologically modified pinion results in reduction of transmission error up to two times. The required modification of the pinion tooth surface is provided on a plunge shaving operation with application of a shaving cutter of an appropriate design. A novel approach for computation of parameters of a form grinding wheel for grinding of the shaving cutter for plunge shaving of a precision involute pinion with topologically modified tooth surface is reported in the paper. The developed approach for computation of parameters of the form grinding wheel is focused on application of the shaving cutter grinder with a lack of CNC articulation. The problem under consideration is solved using the DG/K-based approach of part surface machining earlier developed by the author. (The DG/K-approach is based on fundamental results obtained in differential geometry of surfaces, and in kinematics of multi-parametric motion of a rigid body in E3 space (See Radzevich, S.P., Sculptured Surface Machining on Multi-Axis CNC Machine. Monograph, 1991, Vishcha Shkola Publishers, Kiev (in Russian). See also Radzevich, S.P., 2001, Fundamentals of Surface Machining. Monograph, Rastan, Kiev (in Russian).) An analytical solution to the problem is discussed in the paper. The solution has been used for developing software for the Mitsubishi ZA30CNC shaving cutter grinder for the needs of the automotive industry. Computer simulation reveals high accuracy of the ground shaving cutter.

Manufacturing Process for Circular-Arc Curvilinear Cylindrical Gears with Predesigned Fourth Order Transmission Error

2010 ◽  
Vol 37-38 ◽  
pp. 623-627 ◽  
Author(s):  
Jin Zhan Su ◽  
Zong De Fang
Keyword(s):  
Fourth Order ◽  
Gear Tooth ◽  
Transmission Error ◽  
Circular Arc ◽  
Cylindrical Gears ◽  
Polynomial Curve ◽  
Order Polynomial ◽  
Tooth Surfaces ◽  
The Stability ◽  
Fourth Order Polynomial

A fourth order transmission error was employed to improve the stability and tooth strength of circular-arc curvilinear cylindrical gears. The coefficient of fourth order polynomial curve was determined, the imaginary rack cutter which formed by the rotation of a head cutter and the imaginary pinion were introduced to determine the pinion and gear tooth surfaces, respectively. The numerical simulation of meshing shows: 1) the fourth order transmission error can be achieved by the proposed method; 2) the stability transmission can be performed by increasing the angle of the transfer point of the cycle of meshing; 3) the tooth fillet strength can be enhanced.

Numerical and theoretical analyses of the dynamics of droplets driven by electrowetting on dielectric in a Hele-Shaw cell

2018 ◽  
Vol 839 ◽  
pp. 468-488 ◽  
Author(s):  
Yasufumi Yamamoto ◽  
Takahiro Ito ◽  
Tatsuro Wakimoto ◽  
Kenji Katoh
Keyword(s):  
Theoretical Model ◽  
Contact Line ◽  
Three Dimensional ◽  
Simulation Method ◽  
Movement Speed ◽  
Electrowetting On Dielectric ◽  
Moving Contact Line ◽  
Moving Contact ◽  
Droplet Movement ◽  
Hele Shaw Cell

Droplet movement by electrowetting on dielectric (EWOD) in a Hele-Shaw cell is analysed theoretically and numerically. We propose a simple theoretical model for the motion, which describes well the voltage dependency of droplet speed below the saturation voltage as measured experimentally. The simulation method for numerical analyses is constructed by using the Young–Lippmann equation to represent EWOD and the generalised Navier boundary condition to represent the moving contact line in the context of the front-tracking method. With an adjusted slip parameter, the present full three-dimensional numerical simulation reproduces well the shape evolution and movement speed of droplets as observed experimentally. We verify the proposed theoretical model in numerical experiments with various shapes and voltages. Furthermore, we analyse theoretically the behaviour of the contact line at the onset of droplet motion as observed in the simulation and experiment, and we are able to estimate very well the time scale on which the contact angle changes.

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.

scholarly journals Research on the Design and Modification of Asymmetric Spur Gear

2015 ◽  
Vol 2015 ◽  
pp. 1-13 ◽  
Author(s):  
Xiaohe Deng ◽  
Lin Hua ◽  
Xinghui Han
Keyword(s):  
Computer Aided Design ◽  
Design Method ◽  
Geometric Model ◽  
Simulation Method ◽  
Transmission Error ◽  
Spur Gear ◽  
Geometric Shape ◽  
Spur Gears ◽  
Gear Design ◽  
Aided Design

A design method for the geometric shape and modification of asymmetric spur gear was proposed, in which the geometric shape and modification of the gear can be obtained directly according to the rack-cutter profile. In the geometric design process of the gear, a rack-cutter with different pressure angles and fillet radius in the driving side and coast side was selected, and the generated asymmetric spur gear profiles also had different pressure angles and fillets accordingly. In the modification design of the gear, the pressure angle modification of rack-cutter was conducted firstly and then the corresponding modified involute gear profile was obtained. The geometric model of spur gears was developed using computer-aided design, and the meshing process was analyzed using finite element simulation method. Furthermore, the transmission error and load sharing ratio of unmodified and modified asymmetric spur gears were investigated. Research results showed that the proposed gear design method was feasible and desired spur gear can be obtained through one time rapid machining by the method. Asymmetric spur gear with better transmission characteristic can be obtained via involute modification.

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