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.

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.

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.

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.

scholarly journals Cutter Head Approximation Machining Method of Line Contact Spiral Bevel Gear Pairs Based On Controlling Topological Deviations

2021 ◽  
Author(s):  
Mingyang Wang ◽  
Yuehai Sun
Keyword(s):  
Simulation Analysis ◽  
Gear Tooth ◽  
Bevel Gear ◽  
Spiral Bevel Gear ◽  
Line Contact ◽  
Bevel Gears ◽  
Spiral Bevel ◽  
Tooth Flank ◽  
Cutter Head ◽  
The Mathematical Model

Abstract To improve the meshing performance and increase the bearing capacity and service life of spiral gear pairs, the cutter head approximation machining method based on controlling topological deviations was proposed to solve the problem where line contact spiral bevel gears with tapered teeth depth cannot be directly machined by cutter heads. First, the mathematical model of line contact conjugate flanks was established, and meshing equations and conjugate flank equations of bevel gear pairs were derived. Second, the gear tooth flank was set as the datum tooth flank for priority machining, and the pinion theoretical tooth flank which is fully conjugate with the gear tooth flank and the pinion machining tooth flank matching with the gear were solved. Then, the geometric topological deviations model of the comparison between the pinion machining tooth flank and its theoretical tooth flank can be established. Finally, with the pinion machining tooth flank approaching its theoretical tooth flank as the modification, the additional cutting motions and machining compensation parameters of cutter heads were obtained to control the pinion machining tooth flank deviations and reduce them to the allowable deviations of its theoretical tooth flank. The contact simulation analysis and rolling test verified the correctness of the line contact conjugate flank model and feasibility of the cutter head approximation machining method.

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.

Simulation of Accessory Drives Bevel Gears Dynamic Conditions

2014 ◽  
Author(s):  
Egor Kozharinov ◽  
Jury Temis
Keyword(s):  
Stress Concentration ◽  
Dynamic Load ◽  
Maximum Amplitude ◽  
Transmission Error ◽  
Tooth Profile ◽  
Bevel Gear ◽  
Principal Stresses ◽  
Disturbing Force ◽  
Profile Modification ◽  
Bevel Gears

Bevel gears of modern aviation motors operate at high rotation velocities and transmitted torques. High dynamic load in bevel mesh due to impact interaction of teeth in contact actuates gear rim oscillations. Coincidence of dynamic load frequency and bevel gear natural frequency of nodal diameter can cause oscillation amplitude grow and gear rim breakdown. By harmonic response analysis it is shown, that highest stresses in gear rim appears during gear oscillation by two or three nodal diameters. Gear root is a stress concentration in this case. In this paper methods of bevel gears dynamic behavior simulation are considered. A 3D solid dynamic model of bevel gear drive with transient contact interaction between pinion and gear by curvilinear teeth subject to tooth profile modification has been developed. An actuation was made by kinematic way by applying rotational velocity to driving pinion. A transmitted torque is applied to driven gear. An energy dissipation in gear material is considered in model. A transmission error of bevel gears depending on profile modification, transmitted torque and diaphragm stiffness is calculated. It is shown, that applying tooth profile modification helps to avoid stress concentration on teeth flank, decreases transmission error and derivatives of it’s function. As a result of calculation a function of disturbing force, actuating in gear mesh, dynamic transmission error and first principal stresses of gear crown face in time domain has been obtained. A spectral analysis of disturbing force and first principal stresses of gear rim is executed. As a result, it is shown, that gearing mesh is a source of poly-harmonic excitation of bevel gears. The maximum amplitude in contact force spectra is at frequency four times greater, than tooth frequency, and the maximum amplitude in first principal stresses of gear crown face spectra is at tooth frequency. Using a first principal stresses law of variation a new criterion of bevel gear rim strength is obtained.

Design of the Pitch Cones of Noncircular Bevel Gears

2012 ◽  
Author(s):  
Kan Shi ◽  
Jiqiang Xia ◽  
Chunjie Wang ◽  
Chunming Geng
Keyword(s):  
Design Method ◽  
Rolling Motion ◽  
Bevel Gears ◽  
Pure Rolling

A design method for the pitch cones of noncircular bevel gears is proposed. In particular, the accurate formulation of the pitch cones of the driving gear and the driven gear are obtained for any number and combination of lobes and in any configuration during their pure-rolling motion. This design method is implemented in Pro/E and several significant examples are included.

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

2011 ◽  
Vol 133 (3) ◽  
Author(s):  
Giorgio Figliolini ◽  
Jorge Angeles
Keyword(s):  
Rolling Motion ◽  
Bevel Gears ◽  
Pure Rolling

A general formulation of the synthesis of the pitch cones of a pair of N-lobed elliptical bevel gears and the pitch surface of its conjugate crown-rack is proposed. In particular, two pitch cones and the pitch surface of their crown-rack are obtained for any number and combination of lobes and in any configuration during their pure-rolling motion. This formulation is implemented in MATLAB; several significant examples are included, with circular bevel gears becoming a particular case thereof.

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