Geometric Design of Pure Rolling Rack and Pinion Mechanisms

2019 ◽  
Author(s):  
Zhen Chen ◽  
Ming Zeng ◽  
Alfonso Fuentes-Aznar
Keyword(s):  
Design Criterion ◽  
Design Parameters ◽  
Basic Design ◽  
Contact Ratio ◽  
Pure Rolling ◽  
Different Types ◽  
Geometric Size ◽  
Tooth Surfaces ◽  
Active Design ◽  
Kinematic Performance

Abstract The study of different types of pure rolling rack and pinion mechanisms is presented. They are designed based on the active design of the meshing line to provide pure rolling for the whole cycle of meshing. Parametric equations for contact curves on the rack and pinion are determined by coordinate transformation of the meshing line equations. Moreover, parametric equations for the tooth surfaces of the rack and pinion of three types of meshing, including the convex-to-concave meshing, convex-to-plane meshing, and convex-to-convex meshing are derived according to the motion of generatrices along the calculated contact curves. Then, the basic design parameters are analyzed and formulas for calculation of the geometric size are given. The contact ratio of rack and pinion mechanisms can be designed to be higher than one, which satisfies the condition for the continuous transmission of gears. At last, a numerical simulation is conducted to validate the kinematic performance. This paper lays the foundation for further research of pure rolling rack and pinion mechanisms, their manufacture technology and strength design criterion.

Design of pure rolling line gear mechanisms for arbitrary intersecting shafts

2019 ◽  
Vol 233 (15) ◽  
pp. 5515-5531 ◽  
Author(s):  
Zhen Chen ◽  
Ming Zeng
Keyword(s):  
Mathematical Models ◽  
Design Method ◽  
Structural Parameters ◽  
Design Parameters ◽  
Arbitrary Angle ◽  
Geometry Design ◽  
Pure Rolling ◽  
Rolling Line ◽  
Tooth Surfaces ◽  
Active Design

Design of pure rolling line gear mechanisms for an arbitrary angle intersecting shafts was presented in this article. Based on the active design method of meshing line function for orthogonal shafts, three meshing types of conjugated tooth surfaces for an arbitrary angle intersecting shafts were discussed, including the parametric equations of different generatrix circles, the mathematical models of tooth surfaces, and central curves to be constructed, respectively. The validity of the active designed meshing line function was verified according to meshing equations, and the theoretical sliding rations were analyzed to prove pure rolling meshing. Then basic design parameters of pure rolling line gear mechanisms for the geometry design were determined, and the main structural parameters were obtained therefrom. Lastly, three groups of numerical examples were proposed according to mathematical models. Resin samples of line gears were processed by rapid prototyping technology and the kinematic performance of the pure rolling line gear mechanisms were validated. This paper laid the foundation of geometry and parameter design for pure rolling line gear mechanisms for an arbitrary angle intersecting shafts.

Geometric design, meshing simulation, and stress analysis of pure rolling cylindrical helical gear drives

2020 ◽  
Vol 234 (15) ◽  
pp. 3102-3115 ◽  
Author(s):  
Zhen Chen ◽  
Ming Zeng ◽  
Alfonso Fuentes-Aznar
Keyword(s):  
Mechanical Behavior ◽  
Stress Analysis ◽  
Helical Gear ◽  
Design Parameters ◽  
Basic Design ◽  
Helical Gears ◽  
Contact Patterns ◽  
Pure Rolling ◽  
Tooth Surfaces ◽  
Gear Drives

The geometric design, meshing performance, and mechanical behavior of pure rolling helical gear drives are presented. Parametric equations for contact curves on the pinion and gear are determined by coordinate transformation of the active designed pure rolling meshing line for the whole cycle of meshing. Moreover, parametric equations for the tooth surfaces of helical gears with convex-to-convex meshing type are derived according to the motion of generatrices in the transverse section along the calculated contact curves. Then, the basic design parameters are analyzed and formulas for calculation of the geometric size are given. The meshing performance and mechanical behavior, including contact patterns, loaded function of transmission errors, and variation of stresses for two pitch angles of meshing are compared with those of a reference design of micro-geometry modified involute helical gears. Besides, the influence of basic design parameters on tooth contact analysis and stress analysis is studied. The analysis of the results shows that the proposed pure rolling helical gears have the advantage of reducing the relative sliding between tooth surfaces and the possibility of designing pure rolling helical gears with a small number of teeth, though the contact strength of the surfaces is impaired. However, if the appropriate design parameters and Hermite curve parameters for the fillets are properly evaluated as proposed here, the mechanical behavior of the proposed pure rolling helical gear drive, in terms of contact patterns and variation of bending stresses can be superior to that of the micro-geometry modified involute helical gear drives.

Geometric Design, Meshing Simulation, and Stress Analysis of Pure Rolling Rack and Pinion Mechanisms

2019 ◽  
Vol 142 (3) ◽  
Author(s):  
Zhen Chen ◽  
Ming Zeng ◽  
Alfonso Fuentes-Aznar
Keyword(s):  
Mechanical Behavior ◽  
Stress Analysis ◽  
Geometric Design ◽  
Design Parameters ◽  
Transmission Errors ◽  
Contact Patterns ◽  
Pure Rolling ◽  
Standard Geometry ◽  
Geometric Size ◽  
Tooth Surfaces

Abstract The geometric design, meshing simulation, and stress analysis of pure rolling rack and pinion mechanisms are presented. Both the pinion and the rack are based on the active design of the meshing line to provide pure rolling for the whole cycle of meshing. The parametric equations of the contact curves on the rack and pinion tooth surfaces are determined by coordinate transformation of the meshing line equations. Three types of meshing are derived according to the motion of the generatrices along the calculated contact curves: convex-to-concave meshing, convex-to-plane meshing, and convex-to-convex meshing. Then, the basic design parameters are analyzed and formulas for calculation of the geometric size are given. Four different cases of design are considered to compare the meshing performance and mechanical behavior of the proposed gear mechanisms. The results include contact patterns, the unloaded function of transmission errors, and the evaluation of stresses along two cycles of meshing. The analysis of the results shows that the proposed method of design of pure rolling meshing reduces the relative sliding between tooth surfaces, whereas it decreases the contact strength of the tooth surfaces. However, if the design parameters are properly evaluated as a result of simulation and applied as proposed here, the mechanical behavior of the proposed rack and pinion mechanisms can be more favorable than that of the standard geometry of involute rack and pinion sets.

Deformations and Stresses in Face-Hobbed Spiral Bevel Gears

2011 ◽  
Author(s):  
Vilmos V. Simon
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Nodal Point ◽  
Design Parameters ◽  
Element Discretization ◽  
Spiral Bevel Gears ◽  
Bevel Gears ◽  
Tooth Surfaces ◽  
Spiral Bevel ◽  
Element Method

In this study an attempt is made to predict displacements and stresses in face-hobbed spiral bevel gears by using the finite element method. A displacement type finite element method is applied with curved, 20-node isoparametric elements. A method is developed for the automatic finite element discretization of the pinion and the gear. The full theory of the generation of tooth surfaces of face-hobbed spiral bevel gears is applied to determine the nodal point coordinates on tooth surfaces. The boundary conditions for the pinion and the gear are set automatically as well. A computer program was developed to implement the formulation provided above. By using this program the influence of design parameters and load position on tooth deflections and fillet stresses is investigated. On the basis of the results, obtained by performing a big number of computer runs, by using regression analysis and interpolation functions, equations for the calculation of tooth deflections and fillet stresses are derived.

Analytical Model of the Efficiency of Spur Gears: Study of the Influence of the Design Parameters

2011 ◽  
Author(s):  
Miguel Pleguezuelos ◽  
Jose´ I. Pedrero ◽  
Miryam B. Sa´nchez
Keyword(s):  
Load Distribution ◽  
Gear Ratio ◽  
Design Parameters ◽  
Spur Gears ◽  
Transmitted Power ◽  
Power Losses ◽  
Contact Ratio ◽  
Complete Study ◽  
Uniform Model ◽  
Analytical Expressions

An analytic model to compute the efficiency of spur gears has been developed. It is based on the application of a non-uniform model of load distribution obtained from the minimum elastic potential criterion and a simplified non-uniform model of the friction coefficient along the path of contact. Both conventional and high transverse contact ratio spur gears have been considered. Analytical expressions for the power losses due to friction, for the transmitted power and for the efficiency are presented. From this model, a complete study of the influence of some design parameters (as the number of teeth, the gear ratio, the pressure angle, the addendum modification coefficient, etc.) on the efficiency is presented.

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.

Effect of basic design parameters on IC debonding of CFRP-strengthened shallow RC beams

2015 ◽  
Vol 34 (18) ◽  
pp. 1526-1539 ◽  
Author(s):  
Mohammed A Al-Saawani ◽  
Ahmed K El-Sayed ◽  
Abdulaziz I Al-Negheimish
Keyword(s):  
Design Parameters ◽  
Basic Design ◽  
Rc Beams

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.

Quasi-Periodicity, Chaos and Coexistence in the Time Delay Controlled Two-Cell DC–DC Buck Converter

2014 ◽  
Vol 24 (10) ◽  
pp. 1450124 ◽  
Author(s):  
Karama Koubaâ ◽  
Moez Feki
Keyword(s):  
Numerical Simulation ◽  
Time Delay ◽  
Chaotic Attractor ◽  
Chaotic Behavior ◽  
Buck Converter ◽  
Design Parameters ◽  
Bifurcation And Chaos ◽  
Different Types ◽  
2D Torus ◽  
Discrete Map

In addition to border collision bifurcation, the time delay controlled two-cell DC/DC buck converter is shown to exhibit a chaotic behavior as well. The time delay controller adds new design parameters to the system and therefore the variation of a parameter may lead to different types of bifurcation. In this work, we present a thorough analysis of different scenarios leading to bifurcation and chaos. We show that the time delay controlled two-cell DC/DC buck converter may also exhibit a Neimark–Sacker bifurcation which for some parameter set may lead to a 2D torus that may then break yielding a chaotic behavior. Besides, the saturation of the controller can also lead to the coexistence of a stable focus and a chaotic attractor. The results are presented using numerical simulation of a discrete map of the two-cell DC/DC buck converter obtained by expressing successive crossings of Poincaré section in terms of each other.

Sign in / Sign up

Export Citation Format

Share Document