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.

Research on the Discrete Algorithm of Tooth Surface for a Curve-Face Gear

2019 ◽  
Vol 142 (5) ◽  
Author(s):  
Zhiqin Cai ◽  
Chao Lin
Keyword(s):  
Gear Tooth ◽  
Theoretical Data ◽  
Surface Characteristics ◽  
Tooth Surface ◽  
Gear Pair ◽  
Face Gear ◽  
Distribution Law ◽  
Discrete Algorithm ◽  
Generating Method ◽  
Curve Face

Abstract The curve-face gear pair is a new type of face gear pair with a variable transmission ratio. Concerning the complexity of its tooth surface, based on the coordinate transformation principle and the spatial meshing theory, a discrete algorithm of this tooth surface was proposed. The determination rule of the limiting points on the tooth surface was analyzed by introducing the generating method and tooth surface characteristics of this gear tooth. Through the corresponding limiting angles and the distribution law of the contact line, the gear tooth surface was discretized, and the theoretical data points of the tooth surface were obtained. The variations in gear tooth surface in a meshing cycle and under different parameters were analyzed. By comparing the virtual tooth model and the corresponding rolling experiment, the correctness of the tooth surface discrete algorithm of the curve-face gear was verified.

Contact Analysis of Helical Face Gears

2000 ◽  
Author(s):  
Colin-Yann Jacquin ◽  
Michèle Guingand ◽  
Jean-Pierre de Vaujany ◽  
Daniel Play
Keyword(s):  
Analytical Method ◽  
Transmission Error ◽  
Contact Analysis ◽  
Computation Method ◽  
Contact Ratio ◽  
Face Gear ◽  
Contact Points ◽  
The Face ◽  
Shaft Angle ◽  
Crossed Axes

Abstract This paper presents an analytical method developed to design and study the tooth geometry and contact characteristics of helical face gears. The tooth geometry is first defined while simulating the meshing of the face gear with the shaper used to cut it. A second meshing simulation is then performed between the face gear and the meshing pinion to determine some characteristics of kinematics, i.e. exact location of contact points, theoretical contact ratio, kinematics transmission error. The computation method is very general and allows to study several types of face gears : crossed axes or offset, varying shaft angle, spur or helical pinion. Cutting and assembling errors are also included in the simulations. The study has shown the influence of the different errors on the kinematics characteristics. Relative sensibility of helical face gears under various misalignments has been also established.

Compound transmission principle analysis of eccentric curve-face gear pair with curvilinear-shaped teeth based on tooth contact analysis

2021 ◽  
pp. 095440622110470
Author(s):  
Chao Lin ◽  
Yu Wang ◽  
Yanan Hu ◽  
Yongquan Yu
Keyword(s):  
Axial Direction ◽  
Contact Analysis ◽  
Gear Pair ◽  
Face Gear ◽  
Tooth Contact Analysis ◽  
Tooth Contact ◽  
Contact Points ◽  
Tooth Surfaces ◽  
Set Up ◽  
Curve Face

A new type of compound transmission gear pair was put forward, called eccentric curve-face gear pair with curvilinear-shaped teeth. It could realize reciprocating motion of the gear shaft when the intersecting shafts achieve transferring motion and power through its unique tooth profile. The compound transmission principle of this gear pair was fully established based on the profile-closure process of axial direction and meshing process of the end face. The tooth surfaces of the eccentric curve-face gear and non-circular gear were generated. The contact paths of different teeth were obtained, and the compound transmission principle of eccentric curve-face gear pair with curvilinear-shaped teeth was verified by tooth contact analysis. By analyzing the mechanical characteristics of time-varying contact points, the changing rule of contact force was studied, and the compound transmission principle of the gear pair was further revealed from mechanics. Moreover, the experimental platform for transmission of eccentric curve-face gear pair with curvilinear-shaped teeth was set up to measure the motion law and contact area, and the correctness of the analysis results was verified.

Research on Meshing Characteristics for Face Gear with Arcuate Tooth

2011 ◽  
Vol 86 ◽  
pp. 39-42
Author(s):  
Xiang Wei Cai ◽  
Zong De Fang ◽  
Jin Zhan Su
Keyword(s):  
Contact Analysis ◽  
Tooth Surface ◽  
Face Gear ◽  
Tooth Contact Analysis ◽  
Surface Equation ◽  
Transmission Errors ◽  
Gear Drive ◽  
Parabolic Function ◽  
The Face ◽  
Meshing Characteristics

The generating of face gear with arcuate tooth has been proposed in this paper, and the meshing characteristics are investigated. Based on the concept of imaginary gear cutter, tooth surface equation has been derived, flank modification has also been considered. The transmission errors and bearing contacts of the face gear drive with arcuate tooth under different assembly conditions are investigated by applying the tooth contact analysis. The numerical results reveal that the bearing contacts are not sensitive to the errors of misalignments, and a more favorable type parabolic function of transmission errors with better symmetry and reduced amplitude may be obtained according to the modification of the face gear.

Research on Meshing of Face Gear Drive under Errors of Alignment and Machining

2010 ◽  
Vol 44-47 ◽  
pp. 1948-1951
Author(s):  
Ning Zhao ◽  
Hui Guo
Keyword(s):  
Helix Angle ◽  
Transmission Error ◽  
Contact Analysis ◽  
Tooth Surface ◽  
Face Gear ◽  
Tooth Contact Analysis ◽  
Tooth Contact ◽  
Gear Drive ◽  
Machining Errors ◽  
Alignment Errors

The coordinate systems for cutting face gears and for meshing of face gear drive with involute cylindrical pinion. The tooth surface equation of face gear with machining errors is deviated, such as change of shaft angle, change of shortest distance between face gear and cutter tool axes, helix angle of cutter tool. Tooth contact analysis applied in the paper considered with the alignment error of the driving system. The tooth contact path and the transmission error of the face gear drive were simulated through the tooth contact analysis for different alignment errors and machining errors. The simulation results indicate that all of the alignment errors and machining error don’t cause transmission error except helix angle error of the cutting tool. The errors will bring the shift of the contact path on gear teeth. The shift of bearing contact can be reduced by combination of different errors of alignment or machining.

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.

Coupled Tooth Contact Analysis of Intersected Beveloid Gears for Marine Transmissions

2013 ◽  
Author(s):  
Caichao Zhu ◽  
Haixia Wang ◽  
Mingyong Liu ◽  
Xuesong Du ◽  
Chaosheng Song
Keyword(s):  
Gear Tooth ◽  
Contact Analysis ◽  
Tooth Surface ◽  
Tooth Contact Analysis ◽  
Tooth Contact ◽  
Contact Patterns ◽  
Beveloid Gears ◽  
Shaft Angle ◽  
Loaded Tooth Contact Analysis ◽  
Mesh Condition

Beveloid gears are widely applied in fields like ships, automobiles and industrial precision transmissions. In this paper, the formulas of the beveloid gear tooth surface used in marine transmissions were derived and a mesh model for the intersected beveloid gear pair was setup. Then loaded tooth contact analysis was performed using the finite element method considering the coupling of the assembly errors and the elastic deformation of tooth surface. Through the analysis, the influences of assembly errors on contact patterns, mesh force and tooth surface deformations were investigated. In a further step, the tooth profile modifications were performed to alleviate the edge contact and a subsequent major improvement of the mesh condition was obtained. Finally, loaded tooth contact experiments for marine gearboxes with small shaft angle were conducted. The tested results showed good correlation with the computed results. This work may provide some value for the practical design aiming at improved contact characteristics of the beveloid gears with intersected axes.

scholarly journals The Mathematical Model of Curve-Face Gear and Time-Varying Meshing Characteristics of Compound Transmission

2021 ◽  
Vol 11 (18) ◽  
pp. 8706
Author(s):  
Yanan Hu ◽  
Chao Lin ◽  
Shuo Li ◽  
Yongquan Yu ◽  
Chunjiang He ◽  
...  
Keyword(s):  
Screw Theory ◽  
Point Contact ◽  
Transmission Ratio ◽  
Tooth Surface ◽  
Time Varying ◽  
Gear Pair ◽  
Surface Geometry ◽  
Face Gear ◽  
Meshing Characteristics ◽  
Curve Face

The curve-face gear pair is a new type of gear pair with variable transmission ratio for spatial finite helical motion. In this paper, mathematical models of a new developed curve-face gear were simplified and obtained directly by the standard shaper. The subsequent studies on the curve-face gear compound transmission characteristics were further analyzed by the combinations of the principle of space gearing and screw theory. Firstly, the conjugate tooth surface geometry as well the point contact traces of curve-face gears were derived. Secondly, the geometric relationships between gear pair and the corresponding meshing characteristics were evaluated by several basic geometric elements, including instantaneous screw, axodes, striction curve, and conjugate pitch surface. Based on that analysis, it was found that the tooth contact normal was reciprocal to the instantaneous twist, which demonstrated that the conjugate motion with the desired transmission ratio could be realized in current curve-face gear compound transmission. Moreover, the time-varying slip characteristics of the curve-face gear pair were also revealed, that is, rolling and sliding action coexist at all contact on the tooth surfaces. In brief, this work provided the theoretical basis for following researches on machining curve-face gear with standard shaper.

Reliability sensitivity analysis of tooth modification on dynamic transmission error of helical planetary gears

2020 ◽  
Vol 234 (19) ◽  
pp. 3903-3918
Author(s):  
Zhang Jun ◽  
Tang Wei-min ◽  
Chen Qin ◽  
Chen Tao
Keyword(s):  
Quantitative Relationship ◽  
Planetary Gear ◽  
Transmission Error ◽  
Gear Train ◽  
Gear Pair ◽  
Tooth Contact Analysis ◽  
Planetary Gear Train ◽  
Dynamic Transmission Error ◽  
Tooth Modification ◽  
Meshing Characteristics

As one of the most influential factors leading to gear vibrations, transmission errors of the engaging gears must be controlled to achieve a desirable dynamic performance for a power transmission system. It is well known that tooth modification is an effective way to reduce the fluctuations of the transmission error of a gear pair. The challenge is determining how to establish a quantitative relationship between the tooth modification parameters and the transmission error fluctuations of a gear pair. The present study aims to reveal the sensitivity of the tooth modification parameters on the transmission error fluctuations of a helical planetary gear train in a wind turbine gearbox. For this purpose, a sophisticated parametric three-dimensional contact model that included the micro-geometries of the tooth modification is developed in the ROMAX® environment. Based on this model, a loaded tooth contact analysis is carried out to compute the meshing characteristics, such as the contact pressure and transmission error of each gear pair in the planetary gear train. With the obtained meshing characteristics, the tooth modification amounts of the engaging gears were determined using empirical formulas. These modification amounts are designated as the mean values of the samples generated by the central composite method. After repeating the loaded tooth contact analysis process for each generated sample, a quadratic polynomial function is derived using the response surface method to describe the quantitative relationship between the tooth modification parameters and the dynamic transmission error fluctuations. A large number of random samples are generated using a Monte Carlo method, and the corresponding dynamic transmission error fluctuations are determined with the aforementioned quadratic polynomial function. Based on these samples, a reliability sensitivity analysis is carried out to demonstrate the effects of the tooth modification parameters on the dynamic transmission error fluctuations of the helical planetary gear train.

Surface design and tooth contact analysis of an innovative modified spur gear with crowned teeth

2005 ◽  
Vol 219 (2) ◽  
pp. 193-207 ◽  
Author(s):  
J-L Li ◽  
S-T Chiou
Keyword(s):  
Gear Tooth ◽  
Point Contact ◽  
Spur Gear ◽  
Contact Analysis ◽  
Tooth Surface ◽  
Tooth Contact Analysis ◽  
Tooth Contact ◽  
Surface Design ◽  
Tooth Surfaces ◽  
Meshing Characteristics

An innovative modified spur gear with crowned teeth and its generating mechanism are proposed in this study. The main purpose of tooth surface modification is to change line contact to point contact at the middle of gear tooth surfaces in order to avoid edge contact resulting from possible unavoidable axial misalignment. Moreover, the surface of one gear tooth can be generated with just one cutting process, thereby facilitating easy manufacturing. Based on gearing theory, the model for surface design is developed. A tooth contact analysis (TCA) model for the modified gear pair is also built to investigate meshing characteristics, so that transmission errors (TEs) under assembly errors can also be studied. Examples are included to verify the correctness of the models developed and to demonstrate gear characteristics.

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