Analytical Reconstruction of the Running Surfaces of Gear Teeth Using Standard Profile and Lead Measurements

1983 ◽  
Vol 105 (4) ◽  
pp. 725-735 ◽  
Author(s):  
W. D. Mark
Keyword(s):  
Gear Tooth ◽  
Tooth Surface ◽  
Spur Gears ◽  
Gear Teeth ◽  
Tooth Width ◽  
Least Squares Fit ◽  
Geometric Deviations ◽  
Standard Profile ◽  
Involute Surface ◽  
Class Of Functions

A method is developed for analytically reconstructing the geometric deviations of the running surface of a gear tooth from a perfect involute surface. The method uses standard profile and lead deviation measurements and is applicable to both helical and spur gears. The reconstruction is carried out by using normalized Legendre polynomials. For this class of functions, it is shown that the optimum locations of the profile and lead deviation measurements are the locations of the zeros of the Legendre polynomial of degree equal to the number of profile or lead deviation measurements taken–after appropriate normalization of the tooth width or depth, as appropriate. A least squares fit procedure for establishing a common origin of ordinates for sets of profile and lead deviation measurements is formulated, and its solution is carried out in closed form. Account is taken of the noninsignificant errors that typically arise in profile and lead deviation measurements so that the final analytically reconstructed tooth surface is free of inconsistencies.

Investigation of Effects of Additive for ATF and Test Condition on Pitting Life of Gear Tooth in the FZG Pitting Test

2011 ◽  
Author(s):  
Toshihiko Ichihashi ◽  
Yutaka Takakura ◽  
Susumu Matsumoto
Keyword(s):  
Fuel Economy ◽  
Gear Tooth ◽  
Automatic Transmission ◽  
Tooth Surface ◽  
Severe Condition ◽  
Gear Teeth ◽  
Tooth Width ◽  
Sulfur Containing ◽  
Transmission Gear ◽  
Transmission Test

The reduction in viscosity of Automatic Transmission Fluids (ATFs) for improving fuel economy results in a reduction in transmission gear fatigue life due to occurring pitting. The aim of this study is to establish a suitable test condition for evaluating differentiation in the gear pitting life between ATFs by using a Forschungsstelle fur Zahnrader und Getriebebau (FZG). In this study FZG gear sets were modified so that gear teeth were misaligned and the contact tooth width was shortened by offset in the direction of the shaft. The fatigue pitting life in response to ATFs under this modified FZG test condition was of the same order as that obtained in the actual transmission test under a severely offset condition. A sulfur-containing additive could play a role on the gear tooth life under severe condition, which was most likely attributed to tribofilm for motion on the gear tooth surface.

scholarly journals Study of Lubricant Jet Flow Phenomena in Spur Gears

1975 ◽  
Vol 97 (2) ◽  
pp. 283-288 ◽  
Author(s):  
L. S. Akin ◽  
J. J. Mross ◽  
D. P. Townsend
Keyword(s):  
Motion Picture ◽  
High Speed ◽  
Drop Size ◽  
Gear Tooth ◽  
Jet Flow ◽  
Spur Gear ◽  
Spur Gears ◽  
Gear Teeth ◽  
Flow Phenomena ◽  
Oil Jet

Lubricant jet flow impingement and penetration depth into a gear tooth space were measured at 4920 and 2560 using a 8.89-cm- (3.5-in.) pitch dia 8 pitch spur gear at oil pressures from 7 × 104 to 41 × 104 N/m2 (10 psi to 60 psi). A high speed motion picture camera was used with xenon and high speed stroboscopic lights to slow down and stop the motion of the oil jet so that the impingement depth could be determined. An analytical model was developed for the vectorial impingement depth and for the impingement depth with tooth space windage effects included. The windage effects on the oil jet were small for oil drop size greater than 0.0076 cm (0.003 in.). The analytical impingement depth compared favorably with experimental results above an oil jet pressure of 7 × 104 N/m2 (10 psi). Some of this oil jet penetrates further into the tooth space after impingement. Much of this post impingement oil is thrown out of the tooth space without further contacting the gear teeth.

Determining the Lewis Factor for Plastic Spur Gears With Asymmetric Teeth

2009 ◽  
Author(s):  
J. L. Moya ◽  
A. S. Machado ◽  
A. M. Becerra ◽  
J. A. Vela´zquez ◽  
R. Goytisolo
Keyword(s):  
Theoretical Analysis ◽  
Direct Effect ◽  
Spur Gear ◽  
Spur Gears ◽  
Gear Teeth ◽  
Tooth Fracture ◽  
Tooth Width

The basic weakness of plastic spur gear teeth is tooth fracture brought on by the accumulation of stress at the root of the tooth and by the geometry of the tooth. Tooth width and height play a major role in failure, as does the Lewis factor, which has a direct effect on the expression to calculate tooth strength. This study describes a theoretical analysis of a procedure to determine the Lewis factor for asymmetric teeth.

Mixed Lubricated Line Contact Analysis for Spur Gears using a Deterministic Model

2012 ◽  
Vol 134 (2) ◽  
Author(s):  
Huaiju Liu ◽  
Ken Mao ◽  
Caichao Zhu ◽  
Xiangyang Xu
Keyword(s):  
Deterministic Model ◽  
Gear Tooth ◽  
Spur Gear ◽  
Tooth Surface ◽  
Spur Gears ◽  
Line Contact ◽  
Unified Approach ◽  
Asperity Contacts ◽  
Newtonian Behavior ◽  
Pressure Ripples

The unified approach based upon the Reduced Reynolds technique is applied to develop a deterministic transient mixed lubrication line contact model. This model is used in spur gear applications to comprehensively show effects of roughness, working conditions, i.e., rotational speeds and loads on pressure ripples and severity of asperity contacts. Results show effects of the speed, the load, as well as the RMS value are coupled which makes it difficult to evaluate lubrication states by only considering one variable. Considering the Ree-Eyring non-Newtonian behavior could alleviate pressure ripples significantly, compared with the Newtonian fluid assumption. Small RMS values of surfaces, which could be achieved by superfinish techniques, would be desirable when evaluating gear tooth surface contact performances.

On the Dynamic Gear Tooth Loading as Affected by Bearing Clearances in High Speed Machinery

1982 ◽  
Vol 104 (4) ◽  
pp. 724-730 ◽  
Author(s):  
B. M. Bahgat ◽  
M. O. M. Osman ◽  
T. S. Sankar
Keyword(s):  
High Speed ◽  
Design Method ◽  
Gear Tooth ◽  
Contact Point ◽  
Velocity Ratio ◽  
Spur Gears ◽  
Governing Equations ◽  
Contact Mode ◽  
Gear Teeth ◽  
Geometrical Constraints

The paper studies the effect of bearing clearances in the dynamic analysis of gear mechanisms in high speed machinery. For this purpose, an analytical model is developed based on the interdependence between kinematics and kinetic relationships that must be satisfied when contact is maintained between the journal and its bearing. The contact modes are formulated such that the bearing eccentricity vector must align itself with bearing normal force at the point of contact. The analysis mainly relies on determining the direction of the bearing eccentricity vector defined as the clearance angles βi at the bearing revolutes for each contact mode of the gear teeth. The governing equations of the clearance angles are developed using the geometrical constraints of the contact point location and the velocity ratio. The clearance angles and their derivatives are subsequently used to systematically evaluate kinematic and dynamic quantities of each gear as well as the dynamic tooth load. A pair of rigid tooth spur gears with two revolute clearances is analyzed to illustrate the procedure. The model presented in the paper provides a design method for investigating the effect of bearing tolerances and wear on the evaluation of dynamic tooth load in high speed gearing systems.

Analytical Reconstruction of the Running Surfaces of Gear Teeth. Part 2: Combining Tooth Spacing Measurements with Profile and Lead Measurements

1987 ◽  
Vol 109 (2) ◽  
pp. 268-274
Author(s):  
W. D. Mark
Keyword(s):  
Measurement Errors ◽  
Legendre Polynomials ◽  
Tooth Surface ◽  
Rectangular Array ◽  
Gear Teeth ◽  
Surface Deviations ◽  
Geometric Deviations ◽  
The Mean ◽  
Analytical Reconstruction ◽  
The Absolute

Methods are developed for analytically reconstructing the absolute geometric deviations of the running surfaces of all teeth on a gear or pinion from perfect equispaced involute surfaces. Two of the methods utilize a rectangular array of tooth spacing deviation point measurements optimally located at the zeros of Legendre polynomials in the axial and radial directions where profile and lead deviation measurements are assumed to have been made. Each of these two methods utilizes the multiple tooth spacing deviation measurements to determine the absolute spacing deviations of the mean planes of the deviations of the tooth running surfaces determined from profile and lead measurements. A convergent two-dimensional Legendre polynomial representation of tooth surface deviations that interpolates between point measurements of tooth surface deviations located in rectangular arrays at the aforementioned zeros of Legendre polynomials is described. A discussion of the general relationships between adjacent and accumulated tooth spacing deviations is provided. The noninsignificant measurement errors that typically arise in profile, lead, and tooth spacing deviation measurements are taken into account at each step in the work.

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.

scholarly journals An Analysis of the Surface Geometric Structure and Geometric Accuracy of Cylindrical Gear Teeth Manufactured with the Direct Metal Laser Sintering (DMLS) Method

2019 ◽  
Author(s):  
Jadwiga Małgorzata Pisula ◽  
Grzegorz Budzik ◽  
Łukasz Przeszłowski
Keyword(s):  
Surface Roughness ◽  
Geometric Structure ◽  
Gear Tooth ◽  
Spur Gear ◽  
Laser Sintering ◽  
Tooth Surface ◽  
Direct Metal Laser Sintering ◽  
Cylindrical Gear ◽  
Sand Blasting ◽  
Gear Teeth

This paper presents findings concerning the accuracy of the geometry of cylindrical spur gear teeth manufactured with the direct metal laser sintering (DMLS) method. In addition, the results of the evaluation of the tooth surface geometric structure are presented in the form of selected two-dimensional and three-dimensional surface roughness parameters. An analysis of the accuracy of the fabricated gear teeth was performed after gear sand-blasting and gear tooth milling processes. Surface roughness was measured before and after sand-blasting and gear tooth milling. The test gear wheel was manufactured from GP1 high-chromium stainless steel on an EOS M270 machine.

scholarly journals Study on Wear Characteristics Evolution of Helical Gear With Linear Initial Defect

2021 ◽  
Author(s):  
Yuqi Zhu ◽  
Wei Yuan ◽  
Qianjian Guo ◽  
Liguo Zhang ◽  
Wenhua Wang ◽  
...  
Keyword(s):  
Oil Pollution ◽  
Gear Tooth ◽  
Lubricating Oil ◽  
Tooth Surface ◽  
Wear Characteristics ◽  
Wear Process ◽  
Initial Defect ◽  
Hard Particles ◽  
Wear Life ◽  
Tooth Width

Abstract The initial defects have greatly affected the gear transmission under harsh working conditions in the fields of wind power and ships. The influence of linear initial defects on the evolution of wear characteristics of helical gears was studied. The laser marking device was used to process the linear initial defect along the tooth width direction, and the gear without initial defect was used for comparison. It can be concluded that the linear initial defect changed the meshing state of the gear tooth, and greatly shortened the normal wear life of the gear, the normal wear life of the gear is shortened by about 45%, and the wear rate in the stable wear stage is increased by about 56%, a great deal of pitting corrosion and plastic flow on the tooth surface occurred in the pitch circle position of the defective gear. In addition, the lubrication condition deteriorated in the later period caused by lubricating oil pollution and the hard particles falling off the gearbox bearings entered the meshing surface and the emerged crack, which further accelerated the wear process of gear.

Mesh Stiffness Calculation of Spur Gears With Tooth Surface Crack

2019 ◽  
Author(s):  
Luke Zhang ◽  
Yimin Shao
Keyword(s):  
Surface Crack ◽  
Theoretical Basis ◽  
Gear Tooth ◽  
Tooth Surface ◽  
Spur Gears ◽  
Mesh Stiffness ◽  
Early Failure ◽  
Proposed Model ◽  
Potential Energy Method ◽  
The Relationship

Abstract Tooth surface crack is an early fault before spalling, which has an important influence on mesh stiffness and vibration characteristics of the gear system. However, the researches on tooth surface crack are limited as scholars pay little attention to this early fault. In this study, an analytical model of spur gears with tooth surface crack is established. Using the potential energy method, the equations for mesh stiffness calculation of spur gears with tooth surface crack are derived. By adopting the proposed model, the influences of tooth surface crack fault on mesh stiffness of gear tooth are studied. The relationship between tooth surface crack and mesh stiffness of gear tooth under different lengths and depths can be further calculated. This study provides a theoretical basis for the diagnosis of early failure of spalling.

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