The derivation of transformation matrix before and after thermal distortion for modification

2014 ◽  
Vol 229 (9) ◽  
pp. 1686-1692 ◽  
Author(s):  
Cheng Wang ◽  
Huan Yong Cui ◽  
Qing Ping Zhang
Keyword(s):  
Temperature Distribution ◽  
Contact Analysis ◽  
Transformation Matrix ◽  
Tooth Surface ◽  
Measured Temperature ◽  
Thermal Distortion ◽  
Tooth Contact Analysis ◽  
Tooth Contact ◽  
Contact Points ◽  
Before And After

The transformation matrix before and after thermal distortion is deduced for modification. Firstly, the thermal distortion equation of tooth profile is deduced based on noninvolute characteristic caused by the change of temperature. Secondly, the equation of temperature distribution along the direction of tooth surface width is deduced according to the measured temperature of instantaneous contact points. By combining it with the equation of temperature change along the radial direction, the temperature distribution of whole gear can be given. Finally, the thermal distortion equation of tooth surface and the transformation matrix before and after thermal distortion are deduced. Illustrated by an example of a high-speed helical gear, the surface equation of thermal distortion is obtained by the above methods. Compared with tooth surface before thermal distortion, the tooth surface after thermal distortion has significant change. In addition, compared with the theoretical values, the calculated values have little difference. The derivation of transformation matrix before and after thermal distortion provides the basis of theory for modification using the method of tooth contact analysis and loaded tooth contact analysis.

Stress Analysis of Spherical Gear Sets

2009 ◽  
Author(s):  
Li-Chi Chao ◽  
Chung-Biau Tsay
Keyword(s):  
Gear Tooth ◽  
Three Dimensional ◽  
Contact Analysis ◽  
Design Parameters ◽  
Tooth Contact Analysis ◽  
Tooth Contact ◽  
Contact Points ◽  
Tooth Surfaces ◽  
Loaded Tooth Contact Analysis ◽  
Spherical Gear

The spherical gear is a new type of gear proposed by Mitome et al. [1]. Different from that of the conventional spur or helical gear sets, the spherical gear set can allow variable shaft angles and large axial misalignments without gear interference during the gear drive meshing [1, 2]. Geometrically, the spherical gear has two types of gear tooth profiles, the concave tooth and convex tooth. In practical transmission applications, the contact situation of a spherical gear set is very complex. To obtain a more realistic simulation result, the loaded tooth contact analysis (LTCA) has been performed by employing the finite element method (FEM). According to the derived mathematical model of spherical gear tooth surfaces, an automatic meshes generation program for three-dimensional spherical gears has been developed. Beside, tooth contact analysis (TCA) of spherical gears has been performed to simulate the contact points of the spherical gear set. Furthermore, the contact stress contours of spherical gear tooth surfaces and bending stress of tooth roots have been investigated by giving the design parameters, material properties, loadings and boundary conditions of spherical gears.

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.

Optimal Tooth Surface Modifications in Face-Hobbed Hypoid Gears

2013 ◽  
Vol 572 ◽  
pp. 351-354
Author(s):  
Simon Vilmos
Keyword(s):  
Contact Pressure ◽  
Angular Displacement ◽  
Optimization Procedure ◽  
Contact Analysis ◽  
Tooth Surface ◽  
Tooth Contact Analysis ◽  
Tooth Contact ◽  
Hypoid Gears ◽  
Transmission Errors ◽  
Loaded Tooth Contact Analysis

In this study, an optimization methodology is proposed to systematically define head-cutter geometry and machine tool settings to introduce optimal tooth modifications in face-hobbed hypoid gears. The goal of the optimization is to simultaneously minimize tooth contact pressures and angular displacement error of the driven gear, while concurrently confining the loaded contact pattern within the tooth boundaries. The proposed optimization procedure relies heavily on a loaded tooth contact analysis for the prediction of tooth contact pressure distribution and transmission errors. 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. The core algorithm of the proposed nonlinear programming procedure is based on a direct search method. Effectiveness of this optimization was demonstrated by using a face-hobbed hypoid gear example. Considerable reductions in the maximum tooth contact pressure and in the transmission errors were obtained.

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.

scholarly journals The statistical analysis of the dynamic performance of a gear system considering random manufacturing errors under different levels of machining precision

2019 ◽  
Vol 234 (1) ◽  
pp. 3-18 ◽  
Author(s):  
Fang Guo ◽  
Zongde Fang
Keyword(s):  
Statistical Analysis ◽  
Dynamic Performance ◽  
Reference Value ◽  
Contact Analysis ◽  
Practical Significance ◽  
Tooth Surface ◽  
Machining Accuracy ◽  
Tooth Contact Analysis ◽  
Tooth Contact ◽  
Manufacturing Errors

Gear manufacturing error is one of the main sources of vibration and noise in gears; its influence on the dynamic transmission behaviour of gear systems is a research hotspot. In the current study on the effect of the manufacturing errors, the processing methods of the errors are mostly rough or hypothetical, so the analysis results cannot provide high reference value. This paper proposes a distinctive method to analyse the vibration response of helical gears in the presence of random manufacturing errors and modifications. The presented study performs tooth contact analysis (TCA) with the real tooth surface containing the random tooth profile error and the modification and performs loaded tooth contact analysis (LTCA) based on the superposition of the random pitch error and the initial gap between mating teeth obtained by TCA. Furthermore, the dynamic excitations, including time-varying mesh stiffness and meshing impact, are computed using the above-mentioned TCA and LTCA. The processing method for the manufacturing errors in this paper is reasonable and close to the actual situation of gear engagement. Using this proposed method, statistical analysis was carried out under machining accuracy grades 5, 6 and 7 to show the effect of the different distributions of random manufacturing errors on the gear vibration. The analysis results are of practical significance and provide references for the design and vibration control of gear drive systems.

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.

Offset Face Gear Drives: Tooth Geometry and Contact Analysis

1997 ◽  
Vol 119 (1) ◽  
pp. 114-119 ◽  
Author(s):  
Y. Zhang ◽  
Z. Wu
Keyword(s):  
Contact Analysis ◽  
Tooth Surface ◽  
Generation Process ◽  
Surface Geometry ◽  
Face Gear ◽  
Tooth Contact Analysis ◽  
Tooth Contact ◽  
Gear Design ◽  
Gear Drives ◽  
Meshing Process

This paper presents a detailed investigation on the manufacturing, tooth geometry and contact characteristics of face gear drives with offset axes. In the paper, the tooth geometry of offset face gears is analytically determined by simulating the conjugate motion between the gear and the cutting tool in the generation process. Design criteria are established for the optimal tooth element proportions of offset face gears that avoid tooth undercutting and pointing. The tooth surface geometry of the gear member of the drive is modified by using a shaper that resembles the pinion in profile but has a few more teeth than the pinion to localize the tooth contact. The contact characteristics of the offset face gears are analyzed by a tooth contact analysis (TCA) program that simulates the meshing process of the gear drive assembled under misalignment. An example of offset face gear design and contact analysis is included in the paper.

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.

Tooth Contact Analysis of Parabolic Gears with New Type of Profile

2013 ◽  
Vol 365-366 ◽  
pp. 294-298 ◽  
Author(s):  
Shu Yan Zhang ◽  
Hui Guo
Keyword(s):  
High Strength ◽  
Contact Analysis ◽  
Tooth Surface ◽  
Tooth Contact Analysis ◽  
Tooth Contact ◽  
Transmission Errors ◽  
Bearing Contact ◽  
New Type

The meshing principle of a new kind of parabolic gear is introduced, and the tooth surface equations of parabolic gear are obtained. A tooth contact analysis to simulate meshing and contact is applied. The paper investigates the influence of misalignment on transmission errors and shift of bearing contact. Examples to illustrate the developed approaches are proposed. The research provides the basis for design of new high strength parabolic gears.

Crowned Spur Gears: Methods for Generation and Tooth Contact Analysis—Part I: Basic Concepts, Generation of the Pinion Tooth Surface by a Plane

1988 ◽  
Vol 110 (3) ◽  
pp. 337-342 ◽  
Author(s):  
F. L. Litvin ◽  
J. Zhang ◽  
R. F. Handschuh
Keyword(s):  
Gear Tooth ◽  
Contact Analysis ◽  
Numerical Results ◽  
Degree Of Freedom ◽  
Tooth Surface ◽  
Spur Gears ◽  
Tooth Contact Analysis ◽  
Tooth Contact ◽  
Transmission Errors ◽  
Basic Concepts

A topology of crowned spur pinion tooth surface that reduces the level of transmission errors due to misalignment is proposed. The geometry of the deviated pinion tooth surface and regular gear tooth surface, along with tooth contact analysis is discussed. Generation of the deviated pinion tooth surface by a plane whose motion is controlled by a five-degree-of-freedom system is proposed. Numerical results are included and indicate that transmission errors remain low as the gears are misaligned.

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