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.

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.

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.

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.

Natural Frequencies and Mode Shapes of Elliptic Plates With Boundary Characteristic Orthogonal Polynomials As Assumed Shape Functions

1991 ◽  
Author(s):  
C. Rajalingham ◽  
R. B. Bhat ◽  
G. D. Xistris
Keyword(s):  
Coordinate System ◽  
Orthogonal Polynomials ◽  
Natural Frequencies ◽  
Ritz Method ◽  
Mode Shapes ◽  
Polar Coordinate System ◽  
Free Boundaries ◽  
Natural Modes ◽  
Polar Coordinate ◽  
Boundary Characteristic

Abstract The natural frequencies and natural modes of vibration of uniform elliptic plates with clamped, simply supported and free boundaries are investigated using Rayleigh-Ritz method. A modified polar coordinate system is used to investigate the problem. Energy expressions in Cartesian coordinate system are transformed into the modified polar coordinate system. Boundary characteristic orthogonal polynomials in the radial direction, and trigonometric functions in the angular direction are used to express the deflection of the plate. These deflection shapes are classified into four basic categories, depending on its symmetrical or antisymmetrical property about the major and minor axes of the ellipse. The first six natural modes in each of the above categories are presented in the form of contour plots.

Nonrelative sliding of spiral bevel gear mechanism based on active design of meshing line

2018 ◽  
Vol 233 (3) ◽  
pp. 1055-1067 ◽  
Author(s):  
Zhen Chen ◽  
Ming Zeng
Keyword(s):  
Design Method ◽  
Bevel Gear ◽  
Transmission Mechanism ◽  
Tooth Surface ◽  
Design Parameters ◽  
Spiral Bevel Gear ◽  
Bevel Gears ◽  
Gear Mechanism ◽  
Active Design ◽  
Spiral Bevel

In this paper, an active design method of meshing line for a spiral bevel gear mechanism with nonrelative sliding is presented. First, the general meshing line equations for a nonrelative sliding transmission mechanism between two orthogonal axes are proposed based on the active design parameters. Then, parametric equations for contact curves on the drive and driven spiral bevel gears are deduced by coordinate transformation of the meshing line equations. Further to this, parametric equations for the tooth surface of each bevel gear are derived according to the conical spiral motion of a generatrix circle along the calculated contact curves. Finally, a set of numerical examples is presented based on two types of motion equation of the meshing points. Material prototypes are fabricated and experimentally tested to validate the kinematic performance of the functionally designed spiral bevel gear set.

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