Estimation of Gear Friction Coefficient using Directional Parameter of Tooth Surface

2021 ◽  
pp. 1-27
Author(s):  
Junichi Hongu ◽  
Ryohei Horita ◽  
Takao Koide
Keyword(s):  
Friction Coefficient ◽  
Contact Surface ◽  
Gear Tooth ◽  
Correction Term ◽  
Tooth Surface ◽  
Oil Film ◽  
Tooth Surfaces ◽  
Frictional Coefficients ◽  
Finishing Processes ◽  
The Relationship

Abstract This study proposes a modification of the Matsumoto equation using a directional parameter of tooth surfaces to adapt various gear finishing processes. The directional parameters of a contact surface, which affect oil film formations, have been discussed in the field of tribology; but this effect has been undetermined on the meshing gear tooth surfaces having directional machining marks. Thus, this paper investigates the relationship between the gear frictional coefficients and the directional parameters (based on ISO25178) of their tooth surfaces with the various finishing processes; and modifies the Matsumoto equation by introducing a new directional parameter to augment the various gear finishing processes. Our findings indicate that through optimizing the coefficient of the correction term the include the new directional parameter, the calculated friction values using the modified Matsumoto equation correlate more highly to the experimental friction values than that using the unmodified Matsumoto equation.

Optimal Design of Modified Cylindrical Gear Based on Minimum Flash Temperature of Tooth Surfaces

2013 ◽  
Vol 655-657 ◽  
pp. 573-577
Author(s):  
Jin Ke Jiang ◽  
Zong De Fang ◽  
Xian Long Peng
Keyword(s):  
Friction Coefficient ◽  
Film Thickness ◽  
Contact Line ◽  
Gear Tooth ◽  
Tooth Surface ◽  
Uniform Grid ◽  
Normal Vector ◽  
Flash Temperature ◽  
Oil Film ◽  
Tooth Surfaces

Considering the gap of the contact line of modified involute cylindrical gears influencing on loads, oil film thickness, the friction coefficient was determined on the basis theory of TCA、 LTCA and EHL. so oil film thickness and friction coefficient corresponded with loads on contact line were dispersed, which was used to computed discrete temperature according to the Blok flash temperature formula. and an approach of modified tooth surface optimum design based on the minimum flash temperature was proposed: the modified tooth surfaces was defined as a sum of theoretical tooth and cubic B-spline fit surface based on the uniform grid points created by double parabolas and a straight line and whose normal vector was deduced, besides, used genetic algorithm to optimize the parameter of curve, and get the best modified gear tooth surfaces. the results shows that oil film is thicker in engaging-out, coefficient of friction is contrary, which is responsible for lower flash temperature in engaging-in, besides the flash temperature has little changes in the single tooth meshing zone, and helical gear has a lower flash temperature than spur gear due to higher overlap ratio.

Tooth Undercutting of Beveloid Gears

2000 ◽  
Author(s):  
Chia-Chang Liu ◽  
Chung-Biau Tsay
Keyword(s):  
Gear Tooth ◽  
Singular Points ◽  
Tooth Surface ◽  
Involute Gear ◽  
Beveloid Gears ◽  
Tooth Surfaces

Abstract A beveloid gear can be viewed as an involute gear of which the profile-shifted coefficient linearly decreases from the heel to the toe. Therefore, tooth undercutting occurs and singular points appear on the tooth surfaces near the toe. When undercutting occurs, the gear tooth is comparatively weak. In this study, the conditions of tooth undercutting of beveloid gears were derived and specific phenomena were also investigated by numerical illustrated examples. In addition, according to the characteristics of tooth undercutting on the beveloid gear tooth surface, a novel type hob cutter with varying cutting depths was designed to avoid tooth undercutting of the beveloid gear.

A Contact Point Method for the Design of Form Cutters for Helical Gears

1994 ◽  
Vol 116 (3) ◽  
pp. 387-391 ◽  
Author(s):  
D. C. Xiao ◽  
C. Lee
Keyword(s):  
Minimum Distance ◽  
Gear Tooth ◽  
Contact Point ◽  
Point Method ◽  
Tooth Surface ◽  
Helical Gears ◽  
Contact Points ◽  
The Relationship ◽  
Gear Profile

This article introduces a method to calculate contours of form cutters for machining helical gears from given gear tooth profiles. It is essential to find a relationship between the cutter contour and the gear profile in order to carry out the calculation. The method introduced in this article uses contact points between the cutter rotary surface and the gear tooth surface to establish the relationship. A minimum distance principle is applied. Equations for the calculation are derived and an example is given.

The Undercutting of Circular-Cut Spiral Bevel Gears

1992 ◽  
Vol 114 (2) ◽  
pp. 317-325 ◽  
Author(s):  
Zhang-Hua Fong ◽  
Chung-Biau Tsay
Keyword(s):  
Gear Tooth ◽  
Sufficient Conditions ◽  
Bevel Gear ◽  
Tooth Surface ◽  
Spiral Bevel Gear ◽  
Spiral Bevel Gears ◽  
Bevel Gears ◽  
Tooth Surfaces ◽  
Sufficient And Necessary Conditions ◽  
Spiral Bevel

Undercutting is a serious problem in designing spiral bevel gears with small numbers of teeth. Conditions of undercutting for spiral bevel gears vary with the manufacturing methods. Based on the theory of gearing [1], the tooth geometry of the Gleason type circular-cut spiral bevel gear is mathematically modeled. The sufficient and necessary conditions for the existence and regularity of the generated gear tooth surfaces are investigated. The conditions of undercutting for a circular-cut spiral bevel gear are defined by the sufficient conditions of the regular gear tooth surface. The derived undercutting equations can be applicable for checking the undercutting conditions of spiral bevel gears manufactured by the Gleason Duplex Method, Helical Duplex Method, Fixed Setting Method, and Modified Roll Method. An example is included to illustrate the application of the proposed undercut checking equations.

Correlation of Tooth Surface Wear Prediction With Experimental Results of Spur and Helical Gears in Commercial Vehicle Transmissions

2013 ◽  
Author(s):  
Carlos H. Wink
Keyword(s):  
Commercial Vehicle ◽  
Gear Tooth ◽  
Numerical Procedure ◽  
Tooth Wear ◽  
Experimental Results ◽  
Analytical Models ◽  
Tooth Surface ◽  
Wear Prediction ◽  
Vehicle Transmissions ◽  
Tooth Surfaces

Gear pair dynamic loads can increase significantly with involute profile changes caused by wear resulting in vibration and noise issues. Tooth stresses such as root stress and contact stress can also increase reducing gear life. Wear prediction is important during the design phase to minimize the effects of worn tooth surfaces on product performance. Some analytical models have been proposed to predict gear tooth wear; however published correlations of predictions with experimental results are still limited, especially from the gear industry. But they are vital to build confidence in analytical tools. This paper presents a correlation of wear predictions with experimental results of spur and helical gear pairs that are used in commercial vehicle transmissions. Four different gear lubricants were considered, and also three tooth finishes, grinding, honing, and shaving. A modified Archard’s wear model was used for wear predictions. The model combines a gear contact model and an iterative numerical procedure to account for tooth surface changes. Wear coefficients were determined from experiments. The correlation between predictions and dynamometer testing data was established.

Revisiting Plane-Generated Gear Tooth Surfaces: A Novel Design Perspective

2015 ◽  
Author(s):  
Alessio Artoni ◽  
Massimo Guiggiani
Keyword(s):  
Gear Tooth ◽  
Transmission Function ◽  
Tooth Surface ◽  
Generation Process ◽  
Noise Emission ◽  
Helical Gears ◽  
Beveloid Gears ◽  
Tooth Surfaces ◽  
Involute Gears ◽  
The One

The teeth of ordinary spur and helical gears are generated by a (virtual) rack provided with planar generating surfaces. The resulting tooth surface shapes are a circle-involute cylinder in the case of spur gears, and a circle-involute helicoid for helical gears. Advantages associated with involute geometry are well known: in particular, the motion transmission function is insensitive to center distance variations, and contact lines (or points, when a corrective surface mismatch is applied) evolve along a fixed plane of action, thereby reducing vibrations and noise emission. As a result, involute gears are easier to manufacture and assemble than non-involute gears, and silent to operate. A peculiarity of their generation process is that the motion of the generating planar surface, seen from the fixed space, is a rectilinear translation (while the gear blank is rotated about a fixed axis): the component of such translation that is orthogonal to the generating plane is the one that ultimately dictates the shape of the generated, envelope surface. Starting from this basic fact, we set out to investigate this type of generation-by-envelope process and to profitably use it to explore new potential design layouts. In particular, with some similarity to the basic principles underlying conical involute (or Beveloid) gears, but within a broader scope, we propose a generalization of these concepts to the case of involute surfaces for motion transmission between skew axes (and intersecting axes as a special case). Analytical derivations demonstrate the theoretical possibility of involute profiles transmitting motion between skew axes through line contact and, perihaps more importantly, they lead to apparently novel geometric designs featuring insensitivity of transmission ratio to all misalignments within relatively large limits. The theoretical developments are confirmed by various numerical examples.

Simulation of Hypoid Gear Lapping

2008 ◽  
Vol 130 (11) ◽  
Author(s):  
Qimi Jiang ◽  
Claude Gosselin ◽  
Jack Masseth
Keyword(s):  
Gear Tooth ◽  
Tooth Surface ◽  
Wear Coefficient ◽  
Modeling Tools ◽  
Hypoid Gears ◽  
Coordinate Measurement ◽  
Sliding Motion ◽  
Light Load ◽  
Tooth Surfaces ◽  
Initial Results

In the lapping process of hypoid gears, a gear set is run at varying operating positions and under a light load in order to lap the complete tooth surface. Because of the rolling and sliding motion inherent to hypoid gears, the lapping compound acts as an abrasive and refines the tooth surface to achieve smoothness in rolling action and produce high quality gear sets. In this paper, the lapping process is reproduced using advanced modeling tools such as gear tooth vectorial simulation for the tooth surfaces and reverse engineering to analyze the tooth contact pattern of existing gear sets. Test gear sets are measured using a coordinate measurement machine prior to a special lapping cycle where the position of the gear sets on the lapper does not change, and then are remeasured after lapping in order to establish how much and where material was removed. A wear constant named “wear coefficient” specific to the lapping compound is then calculated. Based on the obtained wear coefficient value, an algorithm for simulating the lapping process is presented. Gear sets lapped on the production line at AAM are used for simulation case studies. Initial results show significant scattering of tooth distortion from tooth to tooth and from gear set to gear set, which makes the simulation process difficult. However, it is possible to predict a confidence range within which actual lapping should fall, thereby opening the door to the optimization of the lapping process.

Influence of Tooth Profile Deviations on Helical Gear Wear

2004 ◽  
Vol 127 (4) ◽  
pp. 656-663 ◽  
Author(s):  
A. Kahraman ◽  
P. Bajpai ◽  
N. E. Anderson
Keyword(s):  
Gear Tooth ◽  
Helical Gear ◽  
Tooth Profile ◽  
Tooth Surface ◽  
Surface Wear ◽  
Mechanics Model ◽  
Surface Slopes ◽  
Tooth Surfaces ◽  
Computation Algorithm ◽  
Gear Contact

In this study, a surface wear prediction model for helical gears pairs is employed to investigate the influence of tooth profile deviations in the form of intentional tooth profile modifications or manufacturing errors on gear tooth surface wear. The wear model combines a finite-element-based gear contact mechanics model that predicts contact pressures, a sliding distance computation algorithm, and Archard’s wear formulation to predict wear of the contacting tooth surfaces. Typical helical gear tooth modifications are parameterized by an involute crown, a lead crown, and an involute slope. The influence of these parameters on surface wear are studied within typical tolerance ranges achievable using hob/shave process. The results indicate that wear is related to the combined modification parameters of a gear pair rather than individual gear parameters. At the end, a design formula is proposed that relates the mismatch of contacting surface slopes to the maximum initial wear rate.

A Study on Hourglass-Worm Gearings Designed to Concentrate Surface Normals: Design for Worm Gearings With a Large Lead Angle

1992 ◽  
Author(s):  
Hiroshi Gunbara ◽  
Shigeyuki Shimachi ◽  
Tohru Kobayashi ◽  
Hiroshi Kawada
Keyword(s):  
Elastic Deformation ◽  
Deformation Theory ◽  
Gear Tooth ◽  
Design Concept ◽  
Tooth Surface ◽  
Edge Contact ◽  
Lead Angle ◽  
Tooth Surfaces ◽  
Worm Gearing

Abstract For moderating the edge contact of gear tooth surfaces on load, a new concept has been proposed on designing worm gearing. As a first step of research, restricting a field of application of the designing concept, a few methods for generating tooth surface of hourglass worm gearing having a small lead angle have been devised. This paper tries to apply this designing concept to wider general use — an hourglass worm gearings with a large lead angle. First, the worm axis displacement relative to the wheel axis is roughly calculated by means of elastic deformation theory. And, this idea is applied to the gear designs using two kinds of hourglass worm gearings. As a result, validity of this design concept is substantiated also in the case of large lead angle of worm gearing.

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