On the Invariance of Gear Tooth Curvature

2006 ◽  
Vol 220 (7) ◽  
pp. 1083-1096 ◽  
Author(s):  
D B Dooner
Keyword(s):  
Gear Tooth ◽  
Helix Angle ◽  
Gear Pair ◽  
Principal Curvatures ◽  
Gear Teeth ◽  
Conical Gears ◽  
Tooth Type ◽  
Instantaneous Pressure ◽  
Principal Directions

A method is presented for the determination of the principal curvatures along with their principal directions of two gear teeth in direct contact. The procedure used to determine these extreme curvatures and directions is based on the nominal position of contact. Moreover, these extreme curvatures and directions are invariant with tooth type (viz. involute and cycloidal) and manufacturing process. Such curvatures and directions depend on the instantaneous pressure angle, spiral or helix angle, and position of contact. This generalized method is applicable to cylindrical gears (spur and helical), conical gears (straight and spiral), as well as hyperboloidal gears (hypoid and worm). Three examples are included to illustrate the determination of principal curvatures and directions. The first example is a helical gear pair, the second is a spiral bevel gear pair, and the third example is a hypoid gear pair.

Characterization of 3D Surface Texture Directionality Using Multi-Scale Curvature Tensor Analysis

2017 ◽  
Author(s):  
Tomasz Bartkowiak
Keyword(s):  
Curvature Tensor ◽  
Surface Texture ◽  
Sampling Interval ◽  
Tensor Analysis ◽  
Principal Curvatures ◽  
Multi Scale ◽  
Principal Directions ◽  
2D And 3D ◽  
3D Surface Texture

Anisotropy of surface texture can in many practical cases significantly affect the interaction between the surface and phenomena that influence or are influenced by the topography. Tribological contacts in sheet forming, wetting behavior or dental wear are good examples. This article introduces and exemplifies a method for quantification and visualization of anisotropy using the newly developed 3D multi-scale curvature tensor analysis. Examples of a milled steel surface, which exhibited an evident anisotropy, and a ruby contact probe surface, which was the example of isotropic surface, were measured by the confocal microscope. They were presented in the paper to support the proposed approach. In the method, the curvature tensor T is calculated using three proximate unit vectors normal to the surface. The multi-scale effect is achieved by changing the size of the sampling interval for the estimation of the normals. Normals are estimated from regular meshes by applying a covariance matrix method. Estimation of curvature tensor allows determination of two directions around which surface bends the most and the least (principal directions) and the bending radii (principal curvatures). The direction of the normal plane, where the curvature took its maximum, could be plotted for each analyzed region and scale. In addition, 2D and 3D distribution graphs could be provided to visualize anisotropic or isotropic characteristics. This helps to determine the dominant texture direction or directions for each scale. In contrast to commonly used surface isotropy/anisotropy determination techniques such as Fourier transform or autocorrelation, the presented method provides the analysis in 3D and for every region at each scale. Thus, different aspects of the studied surfaces could clearly be seen at different scales.

Determination of Principal Curvatures and Contact Ellipse for Profile Crowned Helical Gears

1999 ◽  
Vol 121 (1) ◽  
pp. 107-111 ◽  
Author(s):  
P.-H. Feng ◽  
F. L Litvin ◽  
D. P. Townsend ◽  
R. F. Handschuh
Keyword(s):  
Gear Tooth ◽  
Principal Curvatures ◽  
Helical Gears ◽  
Bearing Contact ◽  
Pinion Gear ◽  
Straight Line ◽  
Tooth Surfaces ◽  
Simplified Solution ◽  
Contact Ellipse

Helical gears with localized bearing contact of tooth surfaces achieved by profile crowning of tooth surfaces are considered. Profile crowning is provided by application of two imaginary rack-cutters with mismatched surfaces. The goal is to determine the dimensions and orientation of the instantaneous contact ellipse that requires the determination of principle curvatures of pinion-gear tooth surfaces. A simplified solution to this problem is proposed based on the approach developed in [1, 2] for correlation of principal curvatures and directions of generating and generated tooth surfaces. The obtained equations are applied for profile crowning where the normal profiles of the rack-cutters are either a circular arc or a straight line.

Analysis of the Vibration Response of a Gearbox With Gear Tooth Faults

2004 ◽  
Author(s):  
Xinhao Tian ◽  
Ming J. Zuo ◽  
Ken R. Fyfe
Keyword(s):  
Gear Tooth ◽  
Spur Gear ◽  
Vibration Response ◽  
Gear Pair ◽  
Mesh Stiffness ◽  
Gear Teeth ◽  
Vibration Model ◽  
Vibration Signatures ◽  
Potential Energy Method ◽  
The Relationship

In this study, the steady-state vibration response of a gearbox with gear tooth faults is investigated. Based on the analytical expression of the position-dependent mesh stiffness of the gear with perfect gear teeth derived with the potential energy method and the characteristics of involute gear teeth, expressions of the mesh stiffness of a gear with tooth faults such as tooth chip, tooth crack, and tooth breakage are derived. Using a coupled lateral and torsional vibration model of a one-stage spur gear pair, we have numerically solved a set of nonlinear equations and obtained typical vibration response diagrams of the gear pair with perfect gears and gears with tooth faults. This study reveals the relationship between the waveforms of the vibration and the types of local faults of the gear. These results are useful for identification of vibration signatures when there are these types of tooth faults.

Innovative Design of a Thrust-Eccentric Gear Coupling for Submerged-Motor-Driven PC Pumping System

2001 ◽  
Author(s):  
Shijie Wang ◽  
Guang Hong
Keyword(s):  
Gear Tooth ◽  
Compressive Force ◽  
Oil Fields ◽  
Gear Pair ◽  
Axial Compressive Force ◽  
Innovative Design ◽  
Pumping System ◽  
System Verification ◽  
Eccentric Motion

Abstract The gear coupling, which transmits axial compressive force, torque and relative eccentric motion, is the key component of progressing cavity (PC) pumping systems. This paper reports an innovative design of such a gear coupling especially used for submerged-motor-driven PC pumping system applied in oil fields. The novelty of this design is the synergy of a zero-tooth-difference internal meshing gear pair and a spherical pair. The principle of transmission and the determination of the key parameters such as the tangential and radial modification factors are described in this paper. Considering the reduced thickness of the gear tooth and the harsh operating condition of the PC pumping system, verification for the contacting and bending fatigue strength of the zero-tooth-difference gear pair is recommended, and the corresponding method is discussed.

scholarly journals Possibility of Human Gender Recognition Using Raman Spectra of Teeth

Molecules ◽  
2021 ◽  
Vol 26 (13) ◽  
pp. 3983
Author(s):  
Ozren Gamulin ◽  
Marko Škrabić ◽  
Kristina Serec ◽  
Matej Par ◽  
Marija Baković ◽  
...  
Keyword(s):  
Raman Spectra ◽  
Principal Component ◽  
Support Vector ◽  
Gender Recognition ◽  
Proof Of Concept ◽  
Male And Female ◽  
Tooth Type ◽  
Tooth Apex ◽  
The Difference

Gender determination of the human remains can be very challenging, especially in the case of incomplete ones. Herein, we report a proof-of-concept experiment where the possibility of gender recognition using Raman spectroscopy of teeth is investigated. Raman spectra were recorded from male and female molars and premolars on two distinct sites, tooth apex and anatomical neck. Recorded spectra were sorted into suitable datasets and initially analyzed with principal component analysis, which showed a distinction between spectra of male and female teeth. Then, reduced datasets with scores of the first 20 principal components were formed and two classification algorithms, support vector machine and artificial neural networks, were applied to form classification models for gender recognition. The obtained results showed that gender recognition with Raman spectra of teeth is possible but strongly depends both on the tooth type and spectrum recording site. The difference in classification accuracy between different tooth types and recording sites are discussed in terms of the molecular structure difference caused by the influence of masticatory loading or gender-dependent life events.

Determination of gear tooth friction by disc machine

1991 ◽  
Vol 24 (5) ◽  
pp. 269-275 ◽  
Author(s):  
K.L. Johnson ◽  
D.I. Spence
Keyword(s):  
Gear Tooth

Effects of Moving Speeds of Dynamic Loads on the Deflections of Gear Teeth

1981 ◽  
Vol 103 (2) ◽  
pp. 357-363 ◽  
Author(s):  
K. Nagaya ◽  
S. Uematsu
Keyword(s):  
Dynamic Response ◽  
Timoshenko Beam ◽  
Gear Tooth ◽  
Bending Moment ◽  
Dynamic Loads ◽  
Gear Teeth ◽  
Moving Speed

For the dynamic response problems of gear teeth, the dynamic loads which act upon the gear teeth should be considered as a function of both the position and the moving speed. In previous studies, the effects of the moving speed have not been considered. In this paper the effects of the moving speed of dynamic loads on the deflection and the bending moment of the gear tooth are investigated. The results are obtained from the elastodynamic analysis of the tapered Timoshenko beam.

scholarly journals Gear Tooth Stress Measurements of Two Helicopter Planetary Stages

1992 ◽  
Author(s):  
Timothy L. Krantz
Keyword(s):  
Load Distribution ◽  
Gear Tooth ◽  
Nasa Lewis Research ◽  
Ring Gear ◽  
Gear Teeth ◽  
Load Variation ◽  
Planet Gear ◽  
Helicopter Main Rotor ◽  
Stress Variations ◽  
Root Location

Abstract Two versions of the planetary reduction stages from U.S. Army OH-58 helicopter main rotor transmissions were tested at the NASA Lewis Research Center. One sequential and one nonsequential planetary were tested. Sun gear and ring gear teeth strains were measured, and stresses were calculated from the strains. The alternating stress at the fillet of both the loaded and unloaded sides of the teeth and at the root of the sun gear teeth are reported. Typical stress variations as the gear tooth moves through the mesh are illustrated. At the tooth root location of the thin-rimmed sun gear, a significant stress was produced by a phenomenon other than the passing of a planet gear. The load variation among the planets was studied. Each planet produced its own distinctive load distribution on the ring and sun gears. The load variation was less for a three-planet, nonsequential design as compared to that of a four-planet, sequential design. The results reported enhance the data base for gear stress levels and provide data for the validation of analytical methods.

scholarly journals Strain in Shear, and Material Behaviour in Incremental Forming

2007 ◽  
Vol 344 ◽  
pp. 519-526 ◽  
Author(s):  
Wilko C. Emmens ◽  
A.H. van den Boogaard
Keyword(s):  
Experimental Data ◽  
Incremental Forming ◽  
Material Behaviour ◽  
Principal Directions ◽  
Circular Grid ◽  
Principal Strains

This paper discusses some consequences of forming by shear, a situation that is sometimes claimed to occur in incremental forming. The determination of the principal strains and principal directions is discussed in detail. Two methods are presented: using a circular grid (although simulated on the computer), and by deriving formulae from the theory; both yield identical results. The strains assuming forming by shear are found to be (much) higher than in situations of forming by stretch. This affects notably more fundamental studies on material behaviour in incremental forming. The effects are illustrated using experimental data obtained with pre-stressed material.

scholarly journals Mesh Phase Analysis of Encased Differential Gear Train for Coaxial Twin-Rotor Helicopter

2019 ◽  
Vol 2019 ◽  
pp. 1-9 ◽  
Author(s):  
Donglin Zhang ◽  
Rupeng Zhu ◽  
Bibo Fu ◽  
Wuzhong Tan
Keyword(s):  
Phase Difference ◽  
Gear Tooth ◽  
Phase Relations ◽  
Gear Train ◽  
Time Varying ◽  
Gear Pair ◽  
Meshing Stiffness ◽  
Differential Gear ◽  
Starting Point ◽  
Twin Rotor

Dynamic excitation caused by time-varying meshing stiffness is one of the most important excitation forms in gear meshing process. The mesh phase relations between each gear pair are an important factor affecting the meshing stiffness. In this paper, the mesh phase relations between gear pairs in an encased differential gear train widely used in coaxial twin-rotor helicopters are discussed. Taking the meshing starting point where the gear tooth enters contact as the reference point, the mesh phase difference between adjacent gear pairs is analyzed and calculated, the system reference gear pair is selected, and the mesh phase difference of each gear pair relative to the system reference gear pair is obtained. The derivation process takes into account the modification of the teeth, the processing, and assembly of the duplicate gears, which makes the calculation method and conclusion more versatile. This work lays a foundation for considering the time-varying meshing stiffness in the study of system dynamics, load distribution, and fault diagnosis of compound planetary gears.

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