Mathematical Description of Spatial Hob-Generating Motion for an Arbitrary Gear Tooth Profile

2004 ◽  
Vol 471-472 ◽  
pp. 409-413
Author(s):  
Xian Ying Feng ◽  
H. Li ◽  
Xing Ai
Keyword(s):  
Cutting Tool ◽  
Gear Tooth ◽  
Special Kind ◽  
Arbitrary Point ◽  
Economic Importance ◽  
Tooth Profile ◽  
Numerical Control ◽  
Special Shape ◽  
Great Economic Importance ◽  
Involute Gear

The purpose of this study is to develop a new kind of technology for the formation of an arbitrary gear tooth profile. In terms of spatial gear meshing theory, a universal transmission mathematical model for forming an arbitrary gear tooth profile has been constructed based on a standard involute gear hob. The coordinate relationship between an arbitrary point on hob cutting-edge curve and the generated point on workpiece has been deduced in detail. Hereby, an arbitrary gear tooth profile can be generated by means of computer flexible controlling each enveloped position on workpiece, and we do not need to spend so much money again to fabricate a special kind of gear cutting tool while cutting a special shape of gear tooth profile. So, this study has great economic importance, and has established the basis of generating an arbitrary gear tooth profile by means of an ordinary involute gear hob and a CNC (Computer Numerical Control) hobbing machine.

Research on S-gear design, manufacturing and measuring based on NC machining center

2020 ◽  
pp. 095440542098134
Author(s):  
Shao-ying Ren ◽  
Yan-zhong Wang ◽  
Yuan Li
Keyword(s):  
Convex Surface ◽  
Coordinate Measuring Machine ◽  
Nc Machining ◽  
Tooth Profile ◽  
Numerical Control ◽  
Machining Center ◽  
Involute Gear ◽  
Measuring Machine ◽  
Gear Contact ◽  
Nc Machining Center

This article presents a method of design, manufacturing, and measuring S-gear. S-gear is a kind of gear whose tooth profile is an S-shaped curve. The sine (cosine) gear, cycloid gear, polynomial gear, and circular arc gear are all S-gears in essence. In the S-gear transmission, the concave surface of one gear and the convex surface of the other gear contact each other. Therefore, the power transmitted by S-gear is much larger than that of the convex-convex-contact involute gear. Some scholars have studied the characteristics of S-gear, but few have explored its manufacturing. In this article, the Numerical Control (NC) machining technology of S-gear is studied in detail for its industrial application. The polynomial curve is used to construct the tooth profile of the S-gear based on the Gear Meshing Theory. The mathematical model of polynomial S-gear is established, by which involute gear can be represented as a special S-gear. The steps of generating NC codes are described. Then, the S-gear sample is processed with an NC machining center. Finally, the sample is measured with a Coordinate Measuring Machine (CMM), and the measurement results show that the accuracy of the S-gear processed by the NC machining center reaches ISO6. This research provides a feasible approach for the design, manufacturing, and measuring of S-gear.

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.

Optimization of Involute Gear Tooth Profile Modification for Tooth Scoring Reduction

1992 ◽  
Author(s):  
Prokop S'roda ◽  
Ronald L. Huston
Keyword(s):  
Bearing Capacity ◽  
Gear Tooth ◽  
Tooth Profile ◽  
Load Bearing Capacity ◽  
Load Bearing ◽  
Profile Modification ◽  
Design Charts ◽  
Tooth Profile Modification ◽  
Involute Gear

Abstract This paper presents a method for determining optimum involute tooth profile modifications to reduce scoring and to increase load bearing capacity. The method is based upon Bloks theory of lubrication and wear. The method leads to design charts incorporating common geometrical gearing parameters. An example is presented.

A novel engagement-pixel image edge tracking method for extracting gear tooth profile edge

2019 ◽  
Vol 234 (2) ◽  
pp. 405-416
Author(s):  
Jie Lu ◽  
Zhiqin Cai ◽  
Bin Yao ◽  
Binqiang Chen
Keyword(s):  
Cutting Tool ◽  
Gear Tooth ◽  
Contact Point ◽  
Tooth Profile ◽  
Complex Conjugate ◽  
Edge Tracking ◽  
Novel Method ◽  
Pixel Image ◽  
Image Edge ◽  
Gear Profile

Accurate gear profile plays an important role in determining the transmission performance of gear-drive equipment. In this paper, a novel method for extracting gear tooth profile edge is presented. The presented method is based on engagement-pixel image edge tracking (EPIET) technique, and does not rely on the traditional meshing theory. An algorithm for the proposed method is put forward. Firstly, instantaneous contact images between the envelope curves of the gear profile and the instantaneous locus of the cutting tool are acquired. Secondly, pixels on the boundary of the envelope curves are lighted and the instantaneous locus coordinates of the cutting tool are calibrated. Lastly, the pixel coordinates of instantaneous meshing points are extracted, based on the fact that there is exactly one contact point per instant, and major error sources of the presented method are discussed. To verify the effectiveness of the presented method, a case study is conducted on a face gear, which is a type of complex conjugate gear, to extract its tooth profile edge. In the study, the tooth profile error and the contact line error are investigated. The results demonstrate that the presented method, without knowing complicated meshing equations, can acquire feasible accuracy and stability, compared with traditional meshing equations. It is shown that the novel method can be extended to applications of digital design of complex conjugate curved surfaces, in a simple and fast manner.

Numerical Algorithm of Tooth Profile of Noncircular Gear Pair

2012 ◽  
Vol 201-202 ◽  
pp. 194-197
Author(s):  
Ming Hui Fang
Keyword(s):  
Numerical Algorithm ◽  
Cutting Tool ◽  
Gear Tooth ◽  
Tooth Profile ◽  
Gear Pair ◽  
Curve Part ◽  
Generating Method ◽  
Curve Change ◽  
Pitch Curve ◽  
Real Machine

According to the generating method theory, noncircular gear with all convex pitch curve can be processed by generating, author designed noncircular gear tooth profile, described a method of precisely calculating noncircular gear tooth profile. And proposed automatically optimizes the noncircular gear tooth profile meshing curve part separately by the identical rack cutting tool different side envelope. Through rack cutting tool along two gear center of rotation segment deviation pitch curve change modified quantity to avoid tooth undercut, realization nonzero modified. The driving gear and the driven gear tooth profile meshing curve part separately by the identical rack cutting tool different side envelope, guarantees when meshing zero clearance. The noncircular gear machined by this method has been used in real machine, which verifies the feasibility of the method.

Schwingungsüberlagertes Axialformen/Superimposed Oscillated Axial Forming

2020 ◽  
Vol 110 (11-12) ◽  
pp. 838-843
Author(s):  
Philipp Müller ◽  
Bernd-Arno Behrens ◽  
Sven Hübner ◽  
Hendrik Vogt ◽  
Daniel Rosenbusch ◽  
...  
Keyword(s):  
Surface Quality ◽  
Economic Importance ◽  
Combined Effect ◽  
Wird Eine ◽  
Forming Force ◽  
Forming Process ◽  
Forming Technology ◽  
Great Economic Importance ◽  
Gear Geometry

Techniken zur Steigerung der Formgebungsgrenzen in der Umformtechnik sind von hoher wirtschaftlicher Bedeutung. In dieser Arbeit wird eine Schwingungsüberlagerung im Krafthauptfluss eines Axialformprozesses zur Ausprägung einer Verzahnungsgeometrie untersucht. Die Auswirkungen der Schwingung auf die erzielbare Ausfüllung der Zahnkavitäten werden analysiert sowie die Parameter Schmierung und Oberflächengüte der Halbzeuge in ihrer kombinierten Wirkung untersucht. Es konnte eine Reduzierung der mittleren Umformkraft sowie eine Erhöhung der Formfüllung festgestellt werden. Techniques for extending the production limits in forming technology are of great economic importance. In this research, a superimposed oscillation in the main force flow of an axial forming process to form an axial gear geometry is investigated. The effects of the superimposed oscillation on the achievable form-filling of the tooth cavities are analyzed and the parameters lubrication and surface quality of the semi-finished products are investigated in their combined effect. A reduction of the averaged forming force as well as an increase of the form-filling could be achieved.

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.

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