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.

Modeling of surface roughness in a novel magnetorheological gear profile finishing process

2020 ◽  
pp. 095440622097826
Author(s):  
Ravi Datt Yadav ◽  
Anant Kumar Singh ◽  
Kunal Arora
Keyword(s):  
Surface Roughness ◽  
Gear Tooth ◽  
Surface Characteristics ◽  
Spur Gear ◽  
Tooth Profile ◽  
Tooth Surface ◽  
Magnetic Flux Density ◽  
Element Analysis ◽  
Finishing Process ◽  
Gear Profile

Fine finishing of spur gears reduces the vibrations and noise and upsurges the service life of two mating gears. A new magnetorheological gear profile finishing (MRGPF) process is utilized for the fine finishing of spur gear teeth profile surfaces. In the present study, the development of a theoretical mathematical model for the prediction of change in surface roughness during the MRGPF process is done. The present MRGPF is a controllable process with the magnitude of the magnetic field, therefore, the effect of magnetic flux density (MFD) on the gear tooth profile has been analyzed using an analytical approach. Theoretically calculated MFD is validated experimentally and with the finite element analysis. To understand the finishing process mechanism, the different forces acting on the gear surface has been investigated. For the validation of the present roughness model, three sets of finishing cycle experimentations have been performed on the spur gear profile by the MRGPF process. The surface roughness of the spur gear tooth surface after experimentation was measured using Mitutoyo SJ-400 surftest and is equated with the values of theoretically calculated surface roughness. The results show the close agreement which ranges from −7.69% to 2.85% for the same number of finishing cycles. To study the surface characteristics of the finished spur gear tooth profile surface, scanning electron microscopy is used. The present developed theoretical model for surface roughness during the MRGPF process predicts the finishing performance with cycle time, improvement in the surface quality, and functional application of the gears.

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.

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.

Probe Position Planning for Measuring Cylindrical Gears on a Four-Axis CNC Machine

2012 ◽  
Vol 579 ◽  
pp. 297-311
Author(s):  
Yi Hui Lee ◽  
Shih Syun Lin ◽  
Yi Pei Shih
Keyword(s):  
Mathematical Models ◽  
Gear Tooth ◽  
Experimental Result ◽  
Tooth Surface ◽  
Measuring Process ◽  
Profile Grinding ◽  
Cylindrical Gears ◽  
Large Size ◽  
Grinding Machine ◽  
Gear Profile

During large-size gear manufacturing by form grinding, the actual tooth surfaces will differ from the theoretical tooth surface because of errors in the clamping fixture and machine axes and machining deflection. Therefore, to improve gear precision, the gear tooth deviations should be measured first and the flank correction implemented based on these deviations. To address the difficulty in large-size gear transit, we develop an on-machine scanning measurement for cylindrical gears on the five-axis CNC gear profile grinding machine that can measure the gear tooth deviations on the machine immediately after grinding, but only four axes are needed for the measurement. Our results can serve as a foundation for follow-up research on closed-loop flank correction technology. This measuring process, which is based on the AGMA standards, includes the (1) profile deviation, (2) helix deviation, (3) pitch deviation, and (4) flank topographic deviation. The mathematical models for measuring probe positioning are derived using the base circle method. We also calculate measuring positions that can serve as a basis for programming the NC codes of the measuring process. Finally, instead of the gear profile grinding machine, we used the six-axis CNC hypoid gear cutting machine for measuring experiments to verify the proposed mathematical models, and the experimental result was compared with Klingelnberg P40 gear measuring center.

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.

scholarly journals EHL Analysis of Spiral Bevel Gear Pairs considering the Contact Point Migration due to Deformation under Load

2020 ◽  
Vol 2020 ◽  
pp. 1-19
Author(s):  
Xiaoyu Sun ◽  
Yanping Liu ◽  
Yongqiang Zhao ◽  
Ming Liu
Keyword(s):  
Contact Point ◽  
Bevel Gear ◽  
Tooth Surface ◽  
Spiral Bevel Gear ◽  
Gear Pair ◽  
Spiral Bevel Gears ◽  
Actual Contact ◽  
Bevel Gears ◽  
Contact Points ◽  
Spiral Bevel

The actual contact point of a spiral bevel gear pair deviates from the theoretical contact point due to the gear deformation caused by the load. However, changes in meshing characteristics due to the migration of contact points are often ignored in previous studies on the elastohydrodynamic lubrication (EHL) analysis of spiral bevel gears. The purpose of this article is to analyze the impact of contact point migration on the results of EHL analysis. Loaded tooth contact analysis (LTCA) based on the finite element method is applied to determine the loaded contact point of the meshing tooth pair. Then, the osculating paraboloids at this point are extracted from the gear tooth surface geometry. The geometric and kinematic parameters for EHL simulation are determined according to the differential geometry theory. Numerical solutions to the Newtonian isothermal EHL of a spiral bevel gear pair at the migrated and theoretical contact points are compared to quantify the error involved in neglecting the contact point adjustment. The results show that under heavy-loaded conditions, the actual contact point of the deformed gear pair at a given pinion (gear) roll angle is different from the theoretical contact point considerably, and so do the meshing parameters. EHL analysis of spiral bevel gears under significant load using theoretical meshing parameters will result in obvious errors, especially in the prediction of film thickness.

Application and Investigation of Modified Helical Gears With Several Types of Geometry

2007 ◽  
Author(s):  
Ignacio Gonzalez-Perez ◽  
Alfonso Fuentes ◽  
Faydor L. Litvin ◽  
Kenichi Hayasaka ◽  
Kenji Yukishima
Keyword(s):  
Gear Tooth ◽  
Tooth Surface ◽  
Contact Ratio ◽  
Tooth Contact Analysis ◽  
Helical Gears ◽  
Transmission Errors ◽  
Advantages And Disadvantages ◽  
Bearing Contact ◽  
Tooth Surfaces ◽  
Gear Drives

Involute helical gears with modified geometry for transformation of rotation between parallel axes are considered. Three types of topology of geometry are considered: (1) crowning of pinion tooth surface is provided only partially by application of a grinding disk; (2) double crowning of pinion tooth surface is obtained applying a grinding disk; (3) concave-convex pinion and gear tooth surfaces are provided (similar to Novikov-Wildhaber gears). Localization of bearing contact is provided for all three types of topology. Computerized TCA (Tooth Contact Analysis) is performed for all three types of topology to obtain: (i) path of contact on pinion and gear tooth surfaces; (ii) negative function of transmission errors for misaligned gear drives (that allows the contact ratio to be increased). Stress analysis is performed for the whole cycle of meshing. Finite element models of pinion and gear with several pairs of teeth are applied. A relative motion is imposed to the pinion model that allows friction between contact surfaces to be considered. Numerical examples have confirmed the advantages and disadvantages of the applied approaches for generation and design.

Investigation of tooth contact deviations from the plane of action and their effects on gear transmission error

2005 ◽  
Vol 219 (5) ◽  
pp. 501-509 ◽  
Author(s):  
C H Wink ◽  
A L Serpa
Keyword(s):  
Gear Tooth ◽  
Transmission Error ◽  
Contact Analysis ◽  
Gear Transmission ◽  
Tooth Surface ◽  
Tooth Contact ◽  
Helical Gears ◽  
Influence Coefficients ◽  
Manufacturing Errors ◽  
Tooth Surfaces

In this paper tooth contact deviations from the plane of action and their effects on gear transmission error are investigated. Tooth contact deviations come from intentional modification of involute tooth surfaces such as tip and root profile relief; manufacturing errors such as adjacent pitch error, profile errors, misalignment and lead errors; and tooth elastic deflections under load, for example, bending and local contact deflections. Those deviations are usually neglected on gear tooth contact models. A procedure to calculate the static transmission error of spur and helical gears under loading is proposed. In the proposed procedure, contact analysis is carried out on the whole tooth surface, eliminating the usual assumption that tooth contact occurs only on the plane of action. Lead and profile modifications, manufacturing errors and tooth elastic deflections are considered in the calculation procedure. The method of influence coefficients is employed to calculate the tooth elastic deflections. Load distribution on gear meshing is determined using an iterative-incremental method. Results of some numerical examples of spur and helical gears are analysed and discussed. The results indicate that the tooth contact deviations from the plane of action can lead to imprecision on the gear transmission error calculation if they are not take into account. Therefore, the proposed procedure provides a more accurate calculation methodology of gear transmission error, since a global contact analysis is done.

A Study on Forging of Spiral Bevel Gear

2007 ◽  
Author(s):  
Masaki Watanabe ◽  
Minoru Maki ◽  
Sumio Hirokawa ◽  
Yasuhiro Kishimoto
Keyword(s):  
Gear Tooth ◽  
Conjugate Point ◽  
Point Contact ◽  
Bevel Gear ◽  
Tooth Surface ◽  
Spiral Bevel Gear ◽  
Tooth Contact ◽  
Contact Points ◽  
Tooth Surfaces ◽  
Spiral Bevel

This study reports the method of forging of spiral bevel gear. Two ideas for crowning of tooth surface to obtain point contact for forging gears are proposed. By one idea, tooth surface of pinion meshes with the gear tooth surface by conjugate point contact. And the trace of contact points on the gear tooth surface is perpendicular to the lengthwise direction of gear tooth, namely becomes the “square contact” so called in gear technology. The trace can be set arbitrarily on the gear tooth, by setting the pitch point arbitrarily. By another idea, the trace of contact points lies along the tooth trace of the gear tooth. Both ideas proposed in this report, the numerical dataset of teeth surface of pinion and gear are given by the contact lines with the cutter cone. The dataset of teeth surface of pinion and gear are calculated to cut a pair of electrodes of spiral bevel gear. Tooth contacts of proposed gearing are confirmed by the 3D drawing of tooth surfaces. The tooth contact of the master pinion and gear were made and tested by tooth contact testing apparatus. The contact marks coincide well with the theoretical contact pattern estimated by 3D/CAD expression. The good results of running test of the performance of the master gear has been given. The authors completed the forging of spiral bevel gear pairs by two methods proposed in this report.

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