scholarly journals The method for synthesis of the contact ratio of noncircular bevel gears

2021 ◽  
Vol 12 (1) ◽  
pp. 165-172
Author(s):  
Kan Shi ◽  
Shuai Lin ◽  
Yan'an Yao
Keyword(s):  
Transmission Ratio ◽  
Polar Coordinate System ◽  
Contact Ratio ◽  
Bevel Gears ◽  
Innovative Methods ◽  
Ratio Curve ◽  
Pure Rolling ◽  
Variable Transmission ◽  
Polar Coordinate ◽  
Pitch Curve

Abstract. As a type of spatial transmission mechanism, noncircular bevel gears can be used to transfer the power and motion with a variable transmission ratio between intersecting axes. In this paper, utilizing the spherical triangle theorem and meshing principle, the parametric equations of the contact ratio are established in the space polar coordinate system. Two innovative methods are proposed to analyze the contact ratio by using the rotation angle of the driving (driven) gears and the arc length of pitch curve as pure rolling. In the case of modified gear and X-zero gear, whether the noncircular bevel gear is continuously driven is deduced. The simulation transmission ratio curve and theoretical transmission ratio curve are compared to verify the rationality of the design.

Synthesis of N-Lobed Involute Modified Noncircular Bevel Gears

2014 ◽  
Author(s):  
Kan Shi ◽  
Jiqiang Xia ◽  
Chunjie Wang ◽  
Chunming Geng ◽  
Rui Wang
Keyword(s):  
3D Models ◽  
Tooth Profile ◽  
Transmission Ratio ◽  
Bevel Gears ◽  
Pure Rolling ◽  
Modification Method ◽  
Variable Transmission ◽  
Pitch Curve ◽  
Relationship Of ◽  
The Relationship

Noncircular bevel gears (NBG) can achieve variable transmission between intersecting axes. The transmission ratio function is obtained when giving the involute NBG’ pitch curve equations during their pure rolling. The relationship of least number of teeth avoiding undercutting and the pitch curve curvature of NBG is analyzed. Being directed against N-lobed involute NBG drive, a kind of varying-coefficient-profile-shift-modification method has been presented. The equations of the modified addendum and dedendum curves are implemented. The algorithm for generating tooth profile of NBG by shaper cutter under UG platform is proposed and significant examples are included. The 3D models of a pair of conjugate N-lobed involute modified NBG are demonstrated to verify the correctness of this modification method.

Design of noncircular bevel gear with concave pitch curve

2012 ◽  
Vol 227 (3) ◽  
pp. 542-553 ◽  
Author(s):  
Kan Shi ◽  
Jiqiang Xia ◽  
Chunjie Wang
Keyword(s):  
Design Method ◽  
Three Dimensional ◽  
Bevel Gear ◽  
Polar Coordinate System ◽  
Dimensional Model ◽  
Three Dimensional Model ◽  
Profile Equation ◽  
Variable Transmission ◽  
Polar Coordinate ◽  
Pitch Curve

Noncircular bevel gear can achieve variable transmission between intersecting axes. This article proposes the design method of high-order noncircular bevel gear with concave pitch curve. The parametric equations for driving and driven gear, addendum and dedendum surface under given transmission ratio and axis angle are established in a spherical polar coordinate system. The tooth profile equation of noncircular bevel gear is derived according to the generation method by using bevel gear cutter. The three-dimensional model for noncircular bevel gear is developed to verify the correctness of the design method.

Design Method for a Pair of Oval Bevel Gears

2011 ◽  
Vol 299-300 ◽  
pp. 887-890 ◽  
Author(s):  
Kan Shi ◽  
Ji Qiang Xia ◽  
Chun Jie Wang
Keyword(s):  
Design Method ◽  
Three Dimensional ◽  
Bevel Gear ◽  
Dimensional Model ◽  
Three Dimensional Model ◽  
Bevel Gears ◽  
Planar Curve ◽  
Variable Transmission ◽  
Polar Coordinate ◽  
Pitch Curve

Oval bevel gear is a kind of noncircular bevel gear which can achieve variable transmission between intersecting axes. We design the pitch curve by spherics cosine theorem in spatial polar coordinate because the pitch curve of oval bevel gear is not the planar curve. The bevel gear cutter is introduced, and we get the Three-dimensional model of oval bevel gear through extended development of UG. This method can make the calculation accurately, easily and get a wide variation of transmission ratio.

scholarly journals Synthesis of the base curves for <i>n</i>-lobed noncircular bevel gears

2020 ◽  
Vol 11 (2) ◽  
pp. 251-256
Author(s):  
Kan Shi ◽  
Yan'an Yao ◽  
Shuai Lin
Keyword(s):  
Coordinate System ◽  
Bevel Gear ◽  
Transmission Mechanism ◽  
Spherical Triangle ◽  
Polar Coordinate System ◽  
Arc Length ◽  
Bevel Gears ◽  
Variable Transmission ◽  
Polar Coordinate ◽  
Spatial Transmission

Abstract. As a type of spatial transmission mechanism, noncircular bevel gears can transfer power and motion between two intersecting axes with variable transmission. In this paper, the relation of arc length is expressed by Angle in spatial polar coordinate system, utilizing the spherical triangle theorem, the parametric equations of base curves are established by applying arc length relation. Further, an example is given to verify whether pitch curves is concave on osculating circle of noncircular bevel gear section cone. Similarly, this example illustrates the cause of the mutation for the base curves.

scholarly journals Design Method for N-Lobed Noncircular Bevel Gears

2020 ◽  
Vol 12 (2) ◽  
pp. 168781401989749
Author(s):  
Kan Shi ◽  
Yan-An Yao ◽  
Shuai Lin
Keyword(s):  
Design Method ◽  
Three Dimensional ◽  
Transmission Mechanism ◽  
Polar Coordinate System ◽  
Analytic Method ◽  
Bevel Gears ◽  
Variable Transmission ◽  
Polar Coordinate ◽  
Three Dimensional Models ◽  
Spatial Transmission

As a type of spatial transmission mechanism, noncircular bevel gears (NBGs) can transfer power and motion between two intersecting axes with variable transmission following a suitable program of motion. Utilizing the spherical triangle theorem and meshing principle, parametric equations are established in the spherical polar coordinate system for the driving and driven gears, for the pitch curves, and for the addendum and dedendum curves of a NBG for a given transmission ratio and axis angle. A formulation of the tooth profile of a NBG is deduced using an analytic method. Three-dimensional models of the 3- and 4-lobed NBGs are derived in verifying this method.

Algorithms for Involute and Octoidal Bevel-Gear Generation

2004 ◽  
Author(s):  
Giorgio Figliolini ◽  
Jorge Angeles
Keyword(s):  
Great Circle ◽  
Tooth Profile ◽  
Bevel Gear ◽  
Rolling Motion ◽  
Bevel Gears ◽  
Pure Rolling ◽  
Pitch Curve ◽  
Tooth Flank ◽  
Flank Surface

A suitable formulation and the implementing algorithms for involute and octoidal bevel-gear generation are proposed in this paper. In particular, the exact spherical involute tooth profile of bevel gears and their crown-rack is obtained through the pure-rolling motion of a great circle of the fundamental sphere on the base cone. Moreover, the tooth flank surface of octoidal bevel gears is obtained as the envelope of the tooth flat flank of the octoidal crown-rack during the pure-rolling motion of its flat pitch curve on the pitch cone. The proposed algorithms have been implemented in Matlab; several examples are included to illustrate their applicability.

Design of a non circular gear Mechanism with Twice Unequal Amplitude Transmission Ratio

2022 ◽  
pp. 1-13
Author(s):  
Jiangang Liu ◽  
Zhipeng Tong ◽  
Yu Gao-hong ◽  
Xiong Zhao ◽  
Haili Zhou
Keyword(s):  
High Speed ◽  
Planetary Gear ◽  
Tooth Profile ◽  
Gear Transmission ◽  
Gear Train ◽  
Transmission Ratio ◽  
High Speed Camera ◽  
Contact Ratio ◽  
Ratio Curve ◽  
Amplitude Transmission

Abstract This study proposes a new non–circular gear transmission mechanism with an involute–cycloid composite tooth profile to realize the twice unequal amplitude transmission (In a complete rotation cycle of gear transmission, instantaneous transmission ratio has twice fluctuations obvious with unequal amplitude) of non–circular gears. The twice unequal amplitude transmission ratio curve was designed based on Fourier and polynomial functions, the change law of the Fourier coefficient on the instantaneous transmission ratio(In non-circular gear transmission, the transmission ratio changes with time, and the transmission ratio of non-circular gear should be instantaneous transmission ratio) was analyzed, and the pressure angle and contact ratio of the involute–cycloid composite tooth profile was calculated. The involute–cycloid composite tooth profile non–circular gear was machined by WEDM technology, while its meshing experiment was performed using high-speed camera technology. The results demonstrate that the instantaneous transmission ratio curve value obtained via the high-speed camera experiment was consistent with the simulation value of virtual software. Furthermore, the involute–cycloid composite tooth profile was applied in the seedling pickup mechanism of non–circular gear planetary gear train. The possibility of the application of the involute–cycloid composite tooth profile in the seedling pickup mechanism was verified by comparing the consistency of the theoretical and simulated seedling picking trajectory.

scholarly journals Design of Linear Functional Noncircular Gear with High Contact Ratio Used in Continuously Variable Transmission

2020 ◽  
Author(s):  
Ya-Nan Hu ◽  
Chao Lin ◽  
Chun-Jiang He ◽  
Yong-Quan Yu ◽  
Zhi-Qin Cai
Keyword(s):  
Bearing Capacity ◽  
Linear Functional ◽  
Continuously Variable Transmission ◽  
Tooth Profile ◽  
Gear Transmission ◽  
Gear Pair ◽  
Contact Ratio ◽  
Variable Transmission ◽  
Pitch Curve ◽  
Working Section

Abstract Continuously variable transmission (CVT) of noncircular gears has the technical advantages of large bearing capacity and high transmission efficiency. This paper focuses on the linear functional noncircular gear pair to realize continuously variable transmission. According to the required working section transmission ratio of noncircular gear pair, the transmission ratio function in the non-working section, was constructed by using polynomial, and then the influence of pitch curve parameters in working section on which in non-working section was also analyzed. Furthermore, the pitch curve of the linear functional noncircular gear pair, which are suitable for transmission, were obtained. In order to improve the stability and bearing capacity of gear transmission, the noncircular gear pair transmission with high contact ratio was designed, and an indirect method to verify the contact ratio by detecting the contact length error of tooth profile was proposed. The error was calculated by comparing the actual contact tooth profile length obtained from the rolling experiment with the accurate value of contact tooth profile length based on the principle of gear and the property of involute profile, and the noncircular gear transmission with high contact ratio was verified.

Performance enhancement of normal contact ratio gearing system through correction factor

2019 ◽  
Vol 13 (3) ◽  
pp. 5242-5258
Author(s):  
R. Ravivarman ◽  
K. Palaniradja ◽  
R. Prabhu Sekar
Keyword(s):  
Finite Element Analysis ◽  
Finite Element ◽  
Correction Factor ◽  
Bending Strength ◽  
Performance Enhancement ◽  
Transmission Ratio ◽  
Contact Ratio ◽  
Element Analysis ◽  
Normal Contact ◽  
Root Region

As lined, higher transmission ratio drives system will have uneven stresses in the root region of the pinion and wheel. To enrich this agility of uneven stresses in normal-contact ratio (NCR) gearing system, an enhanced system is desirable to be industrialized. To attain this objective, it is proposed to put on the idea of modifying the correction factor in such a manner that the bending strength of the gearing system is improved. In this work, the correction factor is modified in such a way that the stress in the root region is equalized between the pinion and wheel. This equalization of stresses is carried out by providing a correction factor in three circumstances: in pinion; wheel and both the pinion and the wheel. Henceforth performances of this S+, S0 and S- drives are evaluated in finite element analysis (FEA) and compared for balanced root stresses in parallel shaft spur gearing systems. It is seen that the outcomes gained from the modified drive have enhanced performance than the standard drive.

scholarly journals Design and Experiment of a Teaching Tool for Oval Gears with Variable Transmission Ratio

2021 ◽  
Vol 1802 (2) ◽  
pp. 022085
Author(s):  
Zhidong Huang ◽  
Shan Zhi ◽  
Chunyang Shi
Keyword(s):  
Transmission Ratio ◽  
Teaching Tool ◽  
Variable Transmission
Sign in / Sign up

Export Citation Format

Share Document