Fundamental Research on the Gear Lubrication : 2nd Report, Lubrication Performance on Gear-Tooth Surface

Abstract The toroidal enveloping cylindrical worm drive, also called the ZC1 worm drive, is grinded by the toroidal grinding wheel. In this paper, the meshing theory for this worm drive is systematically established. According to this meshing theory, the meshing function, the meshing limit function, the equations of the worm helicoid and the worm gear tooth surface are obtained. A method for computing the normal vector of the instantaneous line of the ZC1 worm pair is proposed. Due to this method, the curvature interference limit function and the meshing quality parameters can be more simply and clearly obtained. Based on above results, the methods of the numerical calculation of the instantaneous lines and the conjugate zone are proposed. The initial values of the nonlinear equation systems, computed the conjugate zone and the contact lines, are detected and solved by the method based on the elimination method and geometric construction. The results of numerical example clearly reflect that the conjugate zone can almost cover the whole tooth surface of the worm gear and the effective working length of the worm cannot nearly exceed the half of its thread length. The values of the induced principle curvature and the sliding angle show that the lubrication performance is poor and the stress level is higher, near the meshing limit line and at the dedendum of the worm gear.

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

Proceedings of the Institution of Mechanical Engineers Part C Journal of Mechanical Engineering Science ◽

10.1177/0954406220978265 ◽

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.

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Investigation of Noise Features of Planetary Gear Trains Based on Human Aural Characteristic

Volume 8: 29th Conference on Mechanical Vibration and Noise ◽

10.1115/detc2017-67626 ◽

2017 ◽

Author(s):

Masao Nakagawa ◽

Dai Nishida ◽

Deepak Sah ◽

Toshiki Hirogaki ◽

Eiichi Aoyama

Keyword(s):

Gear Tooth ◽

Structural Complexity ◽

Planetary Gear ◽

Transmission Error ◽

Sound Level ◽

Tooth Surface ◽

Surface Error ◽

Planetary Gear Trains ◽

Tooth Stiffness ◽

Gear Trains

Planetary gear trains (PGTs) are widely used in various machines owing to their many advantages. However, they suffer from problems of noise and vibration due to the structural complexity and giving rise to substantial noise, vibration, and harshness with respect to both structures and human users. In this report, the sound level from PGTs is measured in an anechoic chamber based on human aural characteristic, and basic features of sound are investigated. Gear noise is generated by the vibration force due to varying gear tooth stiffness and the vibration force due to tooth surface error, or transmission error (TE). Dynamic TE is considered to be increased because of internal and external meshing. The vibration force due to tooth surface error can be ignored owing to almost perfect tooth surface. A vibration force due to varying tooth stiffness could be a major factor.

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New Geometry of Generating Spiral Bevel Gear

Volume 7: 10th International Power Transmission and Gearing Conference ◽

10.1115/detc2007-34485 ◽

2007 ◽

Author(s):

Kaihong Zhou ◽

Jinyuan Tang ◽

Tao Zeng

Keyword(s):

Gear Tooth ◽

Previous Method ◽

Bevel Gear ◽

Tooth Surface ◽

Spiral Bevel Gear ◽

Surface Geometry ◽

Numerical Examples ◽

Cone Surface ◽

Spiral Bevel ◽

Involute Curve

New geometry of generating spiral bevel gear is proposed. The key idea of the new proposed geometry is that the gear tooth surface geometry can be investigated in a developed curved surface based on the planar engagement principle. It is proved that the profile curve on the back of generating cone surface is a conical involute curve. The equations of generated gear tooth surface are achieved by the conical involute curve sweeping along the tooth trace of gear. The obtained equations are explicit and independent of the machine-tool settings. This differs from previous studies. The developed theory is illustrated with numerical examples to compare with the previous method, the comparison approves that the method is possible in this way. The new method indicates that there are new solutions to the design the production of spiral bevel gear.

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Establishing gear tooth surface geometry and normal deviation

Mechanism and Machine Theory ◽

10.1016/s0094-114x(97)00075-x ◽

1998 ◽

Vol 33 (5) ◽

pp. 517-524 ◽

Cited By ~ 10

Author(s):

M.S. Shunmugam ◽

S.V.R. Surya Narayana ◽

V. Jayaprakash

Keyword(s):

Gear Tooth ◽

Tooth Surface ◽

Surface Geometry

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Estimation of Gear Friction Coefficient using Directional Parameter of Tooth Surface

Journal of Tribology ◽

10.1115/1.4052558 ◽

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.

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On Satisfaction of the Fifth Necessary Condition of Proper Part Surface Generation in Design of Plunge Shaving Cutter for Finishing of Precision Involute Gears

Journal of Mechanical Design ◽

10.1115/1.2748452 ◽

2006 ◽

Vol 129 (9) ◽

pp. 969-980 ◽

Cited By ~ 7

Author(s):

Stephen P. Radzevich

Keyword(s):

Gear Tooth ◽

Numerical Control ◽

Proper Part ◽

Surface Generation ◽

Tooth Surface ◽

Necessary Condition ◽

Analytical Mechanics ◽

Part Surface ◽

Involute Gears ◽

Novel Design

In this paper, a novel modified scheme and effective computer representation for design of a plunge shaving cutter is presented. The paper aims to develop a novel design of shaving cutter for plunge shaving of precision involute gears. The study is carried out on the premise of satisfaction of the fifth necessary condition of proper part surface generation (PSG) when designing the plunge shaving cutter. In the current study, the author’s earlier developed DG/K method of surface generation is used together with the principal elements of analytical mechanics of gears. (The DG/K method is based on fundamental results obtained in differential geometry of surfaces, and on kinematics of multi-parametric motion of a rigid body in the E3 space. The interested reader may wish to go for details to the monograph: Radzevich, S.P., Fundamentals of Surface Generation, Monograph, Kiev, Rastan, 2001, 592 pp., and to: Radzevich, S.P., Sculptured Surface Machining on Multi-Axis NC Machine, Monograph, Kiev, Vishcha Schola, 1991, 192 pp.) In the particular case under consideration, the method employs (a) an analytical description of the gear tooth surface to be machined, (b) configuration of the plunge shaving cutter relative to the involute gear, (c) analytical representation of the coordinate systems transformations, and (d) the fifth condition of proper PSG that is adapted to finishing of precision involute gears. The fifth condition of proper PSG is investigated in the paper. On the premise of the obtained results of the investigation, a novel design of plunge shaving cutter for finishing of precision involute gears is proposed. The developed novel design of plunge shaving cutter can be used on shaving machines available on the market, e.g. on Gleason’s new Genesis™ 130SV computer numerical control (CNC) shaving machine.

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A parameterized numerical method for generating discrete helical gear tooth surface allowing non-standard geometry

Proceedings of the Institution of Mechanical Engineers Part C Journal of Mechanical Engineering Science ◽

10.1243/09544062jmes799 ◽

2008 ◽

Vol 222 (6) ◽

pp. 1033-1038 ◽

Cited By ~ 4

Author(s):

J Hedlund ◽

A Lehtovaara

Keyword(s):

Gear Tooth ◽

Numerical Approach ◽

Helical Gear ◽

Tooth Surface ◽

Tool Profile ◽

Standard Geometry ◽

Gear Manufacturing ◽

Involute Gears ◽

Gear Geometry ◽

Tooth Flank

Gear analysis is typically performed using calculation based on gear standards. Standards provide a good basis in gear geometry calculation for involute gears, but these are unsatisfactory for handling geometry deviations such as tooth flank modifications. The efficient utilization of finite-element calculation also requires the geometry generation to be parameterized. A parameterized numerical approach was developed to create discrete helical gear geometry and contact line by simulating the gear manufacturing, i.e. the hobbing process. This method is based on coordinate transformations and a wide set of numerical calculation points and their synchronization, which permits deviations from common involute geometry. As an example, the model is applied to protuberance tool profile and grinding with tip relief. A fairly low number of calculation points are needed to create tooth flank profiles where error is <1 μm.

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The Derivation and Simulation of Curved Tooth Face Gear Tooth Theoretical Contract-Point Trace Line Equations

Advanced Materials Research ◽

10.4028/www.scientific.net/amr.819.100 ◽

2013 ◽

Vol 819 ◽

pp. 100-104

Author(s):

Xue Yu Peng ◽

Qing Li ◽

Tai Yong Wang

Keyword(s):

Gear Tooth ◽

Theoretical Equation ◽

Tooth Surface ◽

Face Gear ◽

Machining Errors ◽

The Face ◽

Trace Line ◽

Contact Situation ◽

Meshing Process ◽

The Ideal

The face gear tooth surface theoretical equation, based on the mesh of curved tooth face gear and involute worm, was deduced by means of differential geometry, meshing theory and so on. According to the conditions of the gear meshing, studying the ideal contract-point trace line theoretical equation under the conditions of no machining errors, installation errors and so on. By solving the equations and simulating in SOLIDWORKS, finally the tooth contact situation of face gear and cylindrical worm in the meshing process was got.

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