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.

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.

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.

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.

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.

scholarly journals Digital Generating Method for Cylindrical Helical Gear based on Indexable Disk Milling Cutter

2021 ◽  
Author(s):  
Weiqing Zhang ◽  
Qing Zhou ◽  
Xiaodong Guo ◽  
Rulong Tan ◽  
Ruizhi Shu
Keyword(s):  
Tool Path ◽  
Tooth Profile ◽  
Free Form ◽  
Cutting Efficiency ◽  
Element Analysis ◽  
Milling Cutter ◽  
Generating Method ◽  
Analysis Experiment ◽  
Low Efficiency ◽  
Mill Cutter

Abstract To solve the problem of low efficiency in digital generating machining for producing small or medium batches of helical gears, a method to improve the machining efficiency with an indexable disc milling cutter is presented in this paper. First, the mathematical model of the tooth profile and the indexable disc milling cutter are established. Second, according to the spatial free-form envelope theory, the overall planning scheme of the tool path is given; the relative position and the relative transformation matrix of the tool and tooth profile during digital generating machining using the indexable disc milling cutter are solved, the simulation cutting and actual cutting experiments are conducted, and the cutting efficiency per unit time and cutting simulation time of the two tools under the same deformation conditions is obtained through a finite element analysis experiment. The results show that the cutting efficiency of the indexable disc milling tool was 2–3 times higher than that of the end mill cutter.

scholarly journals FORMATION OF GEARINGS FROMINVOLUTE-BEVEL GEARS

2020 ◽  
Vol 20 (1) ◽  
pp. 15-21
Author(s):  
B.A. Lopatin ◽  
◽  
S.V. Plotnikova ◽  
I.P. Deryabin ◽  
◽  
...  
Keyword(s):  
Load Capacity ◽  
Tooth Profile ◽  
Bevel Gear ◽  
Bevel Gears ◽  
Cylindrical Gears ◽  
Operational Load ◽  
Machine Drives ◽  
Modern Machine

When designing modern machine drives based on traditional gears, in some cases there are problems associated with the complexity of the rational layout of the drive, and its load capacity. These problems can be solved using gears with involute bevel wheels. The involute bevel gear (IBG) is the most common case of gearwheel with an involute tooth profile. In IBG, when teeth are formed, the tool displacement coefficient varies linearly along the width of the gear rim. The geometry of the IBG and the gears made up of them was developed at the Department of Technical Mechanics, a branch of SUSU in Zlatoust. The article presents the main dependencies necessary for determining the size of the IBG and possible schemes for the formation of gears with the IBG. Gearings on the base can be formed at any position of the axles of the gears in space. This paper presents schemes for the formation of spatial (on intersecting axes), bevel (on intersecting axes), cylindrical (on parallel axes) transmissions with IBG. The advantages of gears with IBG (layout, operational, load) in relation to gears from traditional cylindrical and bevel wheels are shown. Thus, transmissions from the IBG on intersecting axes make it possible to transmit rotation at arbitrarily small distancesbetween the axles of the wheels with the required contact localization, up to obtaining a linearcontact in gearing of the teeth. Bevel gears with IBG are less sensitive to errors and can be formed at small interaxial angles, which is problematic for traditional bevel gears. Cylindrical gears with IBG differ from traditional ones in increased load capacity and smooth operation. In addition, they can be used as backlashless and single-sided gears. Thus, gears with IBG due totheir versatility and advantages over traditional gears can be successfully used in modern drives(aviation, space, automobile, etc.) with any arrangement of gear axles in space.

The Synthesis of the Pitch Surfaces of Internal and External Skew-Gears and Their Racks

2005 ◽  
Vol 128 (4) ◽  
pp. 794-802 ◽  
Author(s):  
Giorgio Figliolini ◽  
Jorge Angeles
Keyword(s):  
Euclidean Space ◽  
Dual Space ◽  
Spatial Motion ◽  
Screw Axis ◽  
Dual Algebra ◽  
Screw Motion ◽  
Bevel Gears ◽  
The Subject ◽  
Instant Screw Axis ◽  
Spherical Motion

The synthesis of the pitch surfaces of any pair of external and internal skew gears, using dual algebra and the principle of transference, is the subject of this paper. The spatial motion of the Euclidean space is transferred to the dual space in order to obtain a simplified dual spherical motion, thus emulating the motion of bevel gears. The relative screw motion is hence analyzed by determining the position of the instant screw axis and the angular and sliding velocities. Moreover, the hyperboloid pitch surfaces of the driving and driven gears are synthesized, along with the helicoid pitch surface of their rack. Several numerical results are reported.

Sign in / Sign up

Export Citation Format

Share Document