Conjugation Curvature Theory of Higher Pairs

2017 ◽  
Author(s):  
Kwun-Lon Ting ◽  
Zhiyuan Yu
Keyword(s):  
Gear Tooth ◽  
Tooth Profile ◽  
Contact Pattern ◽  
Contact Strength ◽  
Conjugation System ◽  
Kinematic Synthesis ◽  
Curvature Theory ◽  
The Common ◽  
Three Body ◽  
Design Freedom

The paper pioneers the higher order conjugation theory that elevates the current Camus and Litvin based conjugation theory to a new level by offering the methodology to enable explicitly selecting conjugate pairs to meet the prescribed intrinsic contact characteristics or performance for contact strength. A conjugation theorem is proposed, in which a three-body conjugation system is characterized by the coinciding instant centers and from which the theory is established. Instantaneous invariants are introduced to characterize the instantaneous motion of a three-body conjugation system. The loci of points that generate conjugate pairs with the common relative curvature as well as first and second order stationary relative curvature are presented. These curvature properties determine the contact pattern and therefore the contact strength. An immediate and important application is on gear tooth profile synthesis. The proposed theory offers the design freedom that breaks the traditional constraint of using a specific curve, such as involute. It therefore fills a void in gear tooth profile synthesis and brings light to the question on seeking the strongest tooth profiles. On the other hand, this is the first kinematic synthesis theory that generate both elements of a higher pair simultaneously for a prescribed contact performance. It is a contrast to the conventional Burmester theory by using RR, PR, or RP dyads to form a linkage.

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.

The Research on Tooth Profile Total Deviation Measuring Method Based on Coordination Measuring Machine

2012 ◽  
Vol 184-185 ◽  
pp. 789-792
Author(s):  
Bing Li ◽  
Yu Lan Wei ◽  
Meng Dan Jin ◽  
Ying Ying Fan
Keyword(s):  
Mathematical Model ◽  
Data Processing ◽  
High Precision ◽  
Gear Tooth ◽  
Measuring Method ◽  
Tooth Profile ◽  
Cylindrical Gears ◽  
Total Deviation ◽  
Measuring Machine

Put forward a method that use scatter points which got in different places to measure the involution cylindrical gears, give a mathematical model that use the discrete points to sure the total deviation of gear tooth profile. The experience results show that this way is of high precision in measurement points, measurement an error data processing less intervention, etc.

Study on the Characteristics of Oval Gear

2014 ◽  
Vol 633-634 ◽  
pp. 1100-1103
Author(s):  
Yong Ping Liu ◽  
Peng Wang ◽  
Xi Long Xian ◽  
Shi Yi Zhang
Keyword(s):  
Gear Tooth ◽  
Three Dimensional ◽  
Tooth Profile ◽  
Transmission Characteristics ◽  
Conversion Method ◽  
Wire Cutting ◽  
Oval Gear

For the problem of generating oval gear tooth profile and driving characteristic, desgin the tooth profile of oval gear by the conversion method of tooth profile, and get its three-dimensional modal by Pro/E. The transmission characteristics of a pair of ovate gear are researched; it would help to further study wire cutting of the oval gear based on the involute profile ,which got by the conversion of method of tooth profile, and the driving characteristic help to study other characteristics of oval gear as well as the application in the machinery.

Into Mesh Lubrication of Spur Gears With Arbitrary Offset Oil Jet. Part 1: For Jet Velocity Less Than or Equal to Gear Velocity

1983 ◽  
Vol 105 (4) ◽  
pp. 713-718 ◽  
Author(s):  
L. S. Akin ◽  
D. P. Townsend
Keyword(s):  
Inclination Angle ◽  
Gear Tooth ◽  
Optimum Operating ◽  
Spur Gears ◽  
Optimum Operating Condition ◽  
Operating Condition ◽  
The Common ◽  
Jet Velocity ◽  
Oil Jet

An analysis was conducted for into mesh oil jet lubrication with an arbitrary offset and inclination angle from the pitch point for the case where the oil jet velocity is equal to or less than pitch line velocity. The analysis includes the case for the oil jet offset from the pitch point in the direction of the pinion and where the oil jet is inclined to intersect the common pitch point. Equations were developed for the minimum oil jet velocity required to impinge on the pinion or gear and the optimum oil jet velocity to obtain the maximum impingement depth. The optimum operating condition for best lubrication and cooling is provided when the oil jet velocity is equal to the gear pitch line velocity with both sides of the gear tooth cooled. When the jet velocity is reduced from pitch line velocity the drive side of the pinion and the unloaded side of the gear is cooled. When the jet velocity is much lower than the pitch line velocity the impingement depth is very small and may completely miss the pinion.

Errors in the gear-tooth profile in shaving

2013 ◽  
Vol 33 (5) ◽  
pp. 309-311 ◽  
Author(s):  
A. N. Golovko ◽  
I. V. Golovko
Keyword(s):  
Gear Tooth ◽  
Tooth Profile

Motion Simulation of Gears and Cams Using Working Model

1997 ◽  
Author(s):  
Shih-Liang Wang
Keyword(s):  
Complex Geometry ◽  
Gear Tooth ◽  
Tooth Profile ◽  
Line Contact ◽  
Motion Simulation ◽  
The Past ◽  
Working Model ◽  
Simulation Engine ◽  
Involute Gear ◽  
Involute Surface

Abstract Motion simulation of mechanism of line contact like gears and cams has been difficult in the past. With Working Model, NURBS based complex geometry can be modeled fairly easily, and its simulation engine can animate this type of mechanism accurately. In this paper several Working Model files are developed for visualization and analysis. An algorithm to generate involute gear tooth profile is introduced in this paper for the involute and a portion of non-involute surface.

Design of a special gear tooth profile in accordance with geometric criteria and fatigue strength

2017 ◽  
Vol 35 (2) ◽  
pp. 431-451
Author(s):  
Pedro Nel Martínez Henao ◽  
◽  
Nelson Arzola de la Peña ◽  
Keyword(s):  
Fatigue Strength ◽  
Gear Tooth ◽  
Tooth Profile

Multi-objective Optimization of Gear Tooth Profile Modifications

2013 ◽  
pp. 189-197 ◽  
Author(s):  
Ghribi Dhafer ◽  
Bruyère Jérôme ◽  
Velex Philippe ◽  
Octrue Michel ◽  
Haddar Mohamed
Keyword(s):  
Gear Tooth ◽  
Tooth Profile ◽  
Multi Objective Optimization ◽  
Multi Objective

Extended Camus Theory and Higher Order Conjugated Curves

2019 ◽  
Author(s):  
Cody Leeheng Chan ◽  
Kwun-Lon Ting
Keyword(s):  
Stationary Point ◽  
Higher Order ◽  
The Body ◽  
The Other ◽  
Body System ◽  
Straight Line ◽  
Pair Generation ◽  
Curvature Theory ◽  
Three Body ◽  
Two Bodies

Abstract According to Camus’ theorem, for a single DOF 3-body system with the three instant centers staying coincident, a point embedded on a body traces a pair of conjugated curves on the other two bodies. This paper discusses a fundamental issue not addressed in Camus’ theorem in the context of higher order curvature theory. Following the Aronhold-Kennedy theorem, in a single degree-of-freedom three-body system, the three instant centers must lie on a straight line. This paper proposes that if the line of the three instant centers is stationary (i.e. slide along itself), on the line of the instant centers a point embedded on a body traces a pair of conjugated curves on the other two bodies. Another case is that if the line of the three instant centers rotate about a stationary point, the stationary point embedded on the body also traces a pair of conjugated curves on the other two bodies. The paper demonstrates the use of instantaneous invariants to synthesize such a three-body system leading to a conjugate curve-pair generation. It is a supplement or extension of the Camus’ theorem. The Camus’ theorem may be regarded as a special singular case, in which all three instant centers are coincident.

A non-contact high precision measuring method for the radial runout of cylindrical gear tooth profile

2020 ◽  
Vol 138 ◽  
pp. 106543 ◽  
Author(s):  
Yong-Chen Pei ◽  
Hai-Liang Xie ◽  
Qing-Chang Tan
Keyword(s):  
High Precision ◽  
Gear Tooth ◽  
Measuring Method ◽  
Tooth Profile ◽  
Cylindrical Gear ◽  
Precision Measuring
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