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.

Algorithms for Involute and Octoidal Bevel-Gear Generation

2004 ◽  
Vol 127 (4) ◽  
pp. 664-672 ◽  
Author(s):  
Giorgio Figliolini ◽  
Jorge Angeles
Keyword(s):  
Great Circle ◽  
Tooth Profile ◽  
Bevel Gear ◽  
Rolling Motion ◽  
Bevel Gears ◽  
Pure Rolling ◽  
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 (surface) on the pitch cone. The proposed algorithms have been implemented in MATLAB; several examples are included to illustrate their applicability.

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.

The Design and Experiment of Oval Bevel Gear

2011 ◽  
Vol 86 ◽  
pp. 297-300 ◽  
Author(s):  
Chao Lin ◽  
Yu Jie Hou ◽  
Qing Long Zeng ◽  
Hai Gong ◽  
Ling Nie ◽  
...  
Keyword(s):  
Tooth Profile ◽  
Bevel Gear ◽  
Gear Transmission ◽  
Experimental Result ◽  
Engagement Theory ◽  
Generating Method ◽  
Solid Models ◽  
Complex Design ◽  
Pure Rolling ◽  
Pitch Curve

Aiming at the complex design and analysis methods of noncircular bevel gear, combining the gear space engagement theory and the generating method of tooth profile, the profile generating process was seen as the pure rolling between the pitch line of virtual processing tool and pitch curve of oval bevel gear based on the virtual generating method. The blank parameters and relation equation between tool parameters and procedure parameters of generating method were deduced. General parametric solid models of oval bevel gear were founded. Based on experimental result of oval bevel gear transmission, the design profile of oval bevel gear which was obtained according to generating method was verified.

Research on Mathematical Modeling and Kinematic Simulation of Elliptic Family Gears

2013 ◽  
Vol 579-580 ◽  
pp. 300-304 ◽  
Author(s):  
Lian Xia ◽  
Da Zhu Li ◽  
Jiang Han
Keyword(s):  
Performance Analysis ◽  
Tooth Profile ◽  
High Order ◽  
Numerical Control ◽  
Gear Pair ◽  
Cylindrical Gear ◽  
Kinematic Simulation ◽  
Cad Modeling ◽  
Pure Rolling ◽  
Pitch Curve

Elliptic family gears are commonly used in non-circular gears, which include elliptic gear, high-order gear, elliptic deformed gear and high-order deformed gear, thereinto high-order deformed gear can include the elliptic family gears through adjust its order and deformed coefficient. Because non-circular gear has different tooth profile in different position of pitch curve and there is difference in the left and right tooth profile of the same gear tooth, thus the CAD modeling of non-circular gear is difficult for these characteristics; but the precise model of non-circular gear has important significance to the realization of numerical control machining, kinematic simulation and relevant mechanical analysis. This paper deduce the corresponding pure rolling mathematical model based on the pure rolling contact theory that cylindrical gear and non-circular gear mesh in the end face, and realize the CAD modeling of non-circular straight and helical gears by letting the cylindrical gear and non-circular gear make solid geometry operation, which is suitable for pitch curve with convex and concave. The non-circular gear shaping methods with equal polar and equal arc length are simulated by setting different discrete polar angles, and the transmission ratio curve and the angular acceleration curve of driven gear are get through the kinematic simulation of gear pair, which realize the transmission performance analysis of elliptic family gear pair. The above research results can be applied to the modeling and kinematic performance analysis of other non-circular gears.

Generation of Noncircular Bevel Gears With Free-Form Tooth Profile and Curvilinear Tooth Lengthwise

2016 ◽  
Vol 138 (6) ◽  
Author(s):  
Fangyan Zheng ◽  
Lin Hua ◽  
Xinghui Han ◽  
Dingfang Chen
Keyword(s):  
Screw Theory ◽  
Mapping Method ◽  
Tooth Profile ◽  
Bevel Gear ◽  
Free Form ◽  
Arc Length ◽  
Screw Axis ◽  
Bevel Gears ◽  
Generating Method ◽  
Instant Screw Axis

Noncircular bevel gear is applied to intersecting axes, realizing given function of transmission ratio. Currently, researches are focused mainly on gear with involute tooth profile and straight tooth lengthwise, while that with free-form tooth profile and curvilinear tooth lengthwise are seldom touched upon. Based on screw theory and equal arc-length mapping method, this paper proposes a generally applicable generating method for noncircular bevel gear with free-form tooth profile and curvilinear tooth lengthwise, covering instant screw axis, conjugate pitch surface, as well as the generator with free-form tooth profile and curvilinear tooth lengthwise. Further, the correctness of the proposed method is verified through illustrations of computerized design.

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.

Research on NC Technologies of Loxodromic Normal-Arc Bevel Gear

2014 ◽  
Vol 621 ◽  
pp. 570-575
Author(s):  
Su Zhen Wu ◽  
Jing Wang ◽  
Xue Liang Sui
Keyword(s):  
Planning Process ◽  
Tooth Profile ◽  
Bevel Gear ◽  
Spiral Bevel Gear ◽  
Circular Arc ◽  
Primary Condition ◽  
Bevel Gears ◽  
New Type ◽  
Machining Planning ◽  
Relationship Of

Normal circular-arc spiral bevel gear is a new type gear based on Bertrand conjugation principle. Normal circular-arc bevel gear selects directrix on the basis of paying attention to machining planning process. When the directrix serves as loxodrome, the formed tooth profile surface not only has fine transmissibility like general arc bevel gear, but also is convenient to machining. Starting with differential geometry, the geometry nature and inner relationship of Bertrand conjugation surface are studied. Then the normal circular-arc surface id put forward which is a typical Bertrand surface; the conjugation theory of loxodrome normal circular-arc bevel gears is studied. The characters of loxodrome line are analyzed. The tooth profile of loxodrome normal circular-arc bevel gears, the primary condition the directrix line must be satisfied, the relative curvature of the conjugating surfaces, the relations between non-interventional condition and curvature axle of the directrix line is provided; the NC machining theory of normal circular-arc bevel gears is studied, including the designing and manufacture of the tool, the movement of the machine, the adjustment of the tool under the condition of tangency and non-interventional condition and so on.

Synthesis of the Pitch Cones of N-Lobed Elliptical Bevel Gears

2004 ◽  
Author(s):  
Giorgio Figliolini ◽  
Paolo Migliozzi
Keyword(s):  
Rolling Motion ◽  
Computer Animations ◽  
Bevel Gears ◽  
Matlab Program ◽  
Pure Rolling

A general formulation for the synthesis of the pitch cones of N-lobed elliptical bevel gears and the pitch surface of their conjugate crown-rack is proposed. In particular, both pitch cones and the pitch surface of their crown-rack can be obtained for any number and combination of lobes and in any configuration during their pure-rolling motion. This formulation has been implemented in a suitable Matlab program and several significant examples are shown, where circular bevel gears become a particular case. Computer animations are also available at URL: http://webuser.unicas.it/weblarm/larmindex.htm.

scholarly journals Angular velocity and contact force simulation of the spiral bevel gear meshing based on the hertz contact theory

2019 ◽  
Vol 39 (2) ◽  
pp. 148-156
Author(s):  
Lizhi Gu ◽  
Tieming Xiang ◽  
Can Zhao ◽  
Shuailiang Guo
Keyword(s):  
Angular Velocity ◽  
Contact Force ◽  
Tangential Component ◽  
Bevel Gear ◽  
Contact Theory ◽  
Spiral Bevel Gear ◽  
Hertz Contact ◽  
Bevel Gears ◽  
Spiral Bevel ◽  
Tooth Flank

To obtain the change tendency of the wheel’s angular velocity and tangential component of contact force with time of the pinion under the step input during spiral bevel gear meshing, the tooth flank equation of spiral bevel gear was constructed based on the Non-Uniform Rational B-splines curve. The three-dimensional model of the pinion and the wheel were built based on the tooth flank equation. The calculation equation and relative parameters set for the contact force of spiral bevel gear meshing were done based on the Hertz contact theory. A mating of spiral bevel gears was taken as an example for dynamics simulation and the simulation results show that the relative error rate of the angular velocity between simulation and theoretical calculation is 0.054%, and that the relative error rate of tangential component of the contact force between simulation and theoretical calculation is 4.82%. These findings provide the theoretical basis for dynamic characteristics optimization of the spiral bevel gears.

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.

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