Contact Ratio of Spatial Helix Gearing Mechanism

2012 ◽  
Author(s):  
Y.-Z. Chen ◽  
Z. Chen ◽  
Y. Zhang
Keyword(s):  
Gear Ratio ◽  
Design Methods ◽  
Contact Ratio ◽  
Compact Structure ◽  
Numerical Examples ◽  
Design Formula ◽  
Impacting Factors ◽  
Tooth Number ◽  
Driving Wheel

The contact ratio of spatial helix gear is deduced, and impacting factors of the contact ratio are analyzed. Then different design methods of contact ratio are discussed. The contact ratio could be designed flexibly. The theoretical gear ratio could be expanded to 36 with compact structure. The least tooth number of the driving wheel should be only 1. Numerical examples illustrate the design formula of contact ratio and the kinematics performance of the spatial helix gearing mechanism.

A CONTACT RATIO AND INTERFERENCE-PROOF CONDITIONS FOR A SKEW LINE GEAR MECHANISM

2015 ◽  
Vol 39 (3) ◽  
pp. 647-656 ◽  
Author(s):  
Yueling Lv ◽  
Yangzhi Chen ◽  
Xiuyan Cui
Keyword(s):  
Geometric Parameter ◽  
Mechanical Systems ◽  
Contact Ratio ◽  
Design Formula ◽  
Force And Motion ◽  
Tooth Number ◽  
Gear Mechanism ◽  
Influencing Parameters

Line Gear (LG) is an innovative gear which is mainly applicable to micro mechanical systems proposed by Yangzhi Chen. A Skew Line Gear Mechanism (SLGM) is one pair of LGs transmitting force and motion between two skewed axes. In this study, a design formula of a contact ratio for a SLGM is deduced, and eight influencing parameters are found. The influences of six parameters on a contact ratio for a SLGM with non-vertical skewed axes are studied by using of two coordinate parameters given definitely. The principal influencing parameters on a contact ratio for a SLGM are obtained. Moreover, two types of interferences between the driving and the driven line teeth are discussed, then these geometric parameter formulas for the interference-proof conditions are deduced, and design formulas of a maximum line tooth number for the driving line gear are derived for different interference-proof conditions.

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.

Polyhedral Space Curve Meshing Reducer With Multiple Output Shafts

2012 ◽  
Author(s):  
Yangzhi Chen ◽  
Jiang Ding ◽  
Chuanghai Yao ◽  
Yueling Lv
Keyword(s):  
Design Method ◽  
Low Cost ◽  
Space Curve ◽  
Compact Structure ◽  
Input Shaft ◽  
Space Curves ◽  
Rotation Axes ◽  
Polyhedral Space ◽  
Driving Wheel ◽  
Single Input

In recent years, a gear named Space Curve Meshing Wheel (SCMW) has been invented based on the meshing theory of space curves instead of classic space surfaces. Well improved in many aspects after its invention, it has been applied within the Space Curve Meshing Reducer (SCMR). The design method of an invention named polyhedral SCMR is presented in this paper. With single input shaft and multiple output shafts, this SCMR has advantages like compact structure, flexible design and low cost. It is characterized by the application of the SCMW group containing one driving wheel and several driven wheels, whose rotation axes are concurrent at a point and radiate in polyhedral directions. A SCMW group can form a single-stage SCMR, while SCMW groups connected can form a multiple-stage SCMR. In this paper, geometric parameters of the polyhedral SCMR are defined, design formulas are derived, and an example is provided to illustrate the design process.

scholarly journals Optimal Tooth Numbers for Compact Standard Spur Gear Sets

1982 ◽  
Vol 104 (4) ◽  
pp. 749-757 ◽  
Author(s):  
M. Savage ◽  
J. J. Coy ◽  
D. P. Townsend
Keyword(s):  
Optimal Design ◽  
Objective Function ◽  
Design Space ◽  
Spur Gear ◽  
Gear Ratio ◽  
Contact Ratio ◽  
Bending Fatigue ◽  
Gear Mesh ◽  
Compact Design ◽  
Center Distance

The design of a standard gear mesh is treated with the objective of minimizing the gear size for a given ratio, pinion torque, and allowable tooth strength. Scoring, pitting fatigue, bending fatigue, and the kinematic limits of contact ratio and interference are considered. A design space is defined in terms of the number of teeth on the pinion and the diametral pitch. This space is then combined with the objective function of minimum center distance to obtain an optimal design region. This region defines the number of pinion teeth for the most compact design. The number is a function of the gear ratio only. A design example illustrating this procedure is also given.

scholarly journals Analytical Expressions of the Efficiency of Standard and High Contact Ratio Involute Spur Gears

2013 ◽  
Vol 2013 ◽  
pp. 1-14 ◽  
Author(s):  
Miguel Pleguezuelos ◽  
José I. Pedrero ◽  
Miryam B. Sánchez
Keyword(s):  
Friction Coefficient ◽  
Contact Point ◽  
Load Sharing ◽  
Gear Ratio ◽  
Spur Gears ◽  
Contact Ratio ◽  
Transmission Parameters ◽  
Constant Friction ◽  
Analytical Expressions ◽  
Approximate Expressions

Simple, traditional methods for computation of the efficiency of spur gears are based on the hypotheses of constant friction coefficient and uniform load sharing along the path of contact. However, none of them is accurate. The friction coefficient is variable along the path of contact, though average values can be often considered for preliminary calculations. Nevertheless, the nonuniform load sharing produced by the changing rigidity of the pair of teeth has significant influence on the friction losses, due to the different relative sliding at any contact point. In previous works, the authors obtained a nonuniform model of load distribution based on the minimum elastic potential criterion, which was applied to compute the efficiency of standard gears. In this work, this model of load sharing is applied to study the efficiency of both standard and high contact ratio involute spur gears (with contact ratio between 1 and 2 and greater than 2, resp.). Approximate expressions for the friction power losses and for the efficiency are presented assuming the friction coefficient to be constant along the path of contact. A study of the influence of some transmission parameters (as the gear ratio, pressure angle, etc.) on the efficiency is also presented.

Computerized Simulation of Generation of Internal Involute Gears and Their Assembly

1992 ◽  
Author(s):  
F. L. Litvin ◽  
C.-L. Hsiao ◽  
J.-C. Wang ◽  
X. Zhou
Keyword(s):  
Computer Graphics ◽  
Computer Programs ◽  
Numerical Examples ◽  
Design Charts ◽  
Paper Cover ◽  
Involute Gears ◽  
Tooth Number ◽  
Computerized Simulation ◽  
Internal Gear

Abstract The contents of the paper cover the determination of conditions : (i) of nonundercutting by axial and axial-radial generation of internal gears by shapers, and (ii) avoidance of interference by axial and axial-radial assembly. The authors have developed computer programs for simulation of undercutting and interference, design charts and a table that allow to determine the limiting number of teeth of the cutter and pinion considering the tooth number of internal gear as known. The details of developed algorithms are given in Appendices. The paper is illustrated with computer graphics and numerical examples.

Determination of Addendum Modification Coefficients for Spur Gears Operating at Non-Standard Center Distances

2003 ◽  
Author(s):  
M. A. Sahir Arikan
Keyword(s):  
Gear Tooth ◽  
Gear Ratio ◽  
Spur Gears ◽  
Contact Ratio ◽  
Performance Variables ◽  
Practical Design ◽  
Gear Drives ◽  
Maximum Contact ◽  
Center Distance

Although it is possible to find some recommended conventional values both for the sum of the addendum modification coefficients and for the allocation of the sum of the addendum modification coefficients (e.g. ISO/TR 4467), a detailed analysis is necessary to determine the addendum modification coefficient values for the desired optimization criteria and the performance since the main objective of the above mentioned sources is to facilitate practical design of non-standard gear drives which will not have problems while operating. They give practical average values within a safe range. In this study, by considering the required gear ratio, center distance and the desired backlash, alternative gear pairs are determined and corresponding gear performance variables are calculated in order to allocate the addendum modification coefficients for the pinion and the gear by using criteria such as: not having undercut or pointed (or excessively-thinned-tip) tooth, having desired proportions for the lengths of the dedendum and addendum portions of the line of action, having maximum contact ratio, having sufficient bottom clearance, having minimum contact stresses, having balanced pinion and gear tooth root stresses, having equal pinion and gear lives, etc.

External High-Order Multistage Modified Elliptical Helical Gears and Design Procedure of Its Gear Pair

2014 ◽  
Author(s):  
Jiang Han ◽  
Youyu Liu ◽  
Dazhu Li ◽  
Lian Xia
Keyword(s):  
Design Procedure ◽  
Mathematical Expression ◽  
Gear Ratio ◽  
Helical Gear ◽  
High Order ◽  
Curvature Radius ◽  
Gear Pair ◽  
Contact Ratio ◽  
Helical Gears ◽  
Helical Gear Pair

In view of the limited number of the modified segments for high-order and two-stage modified elliptical helical gears, and poor adjustment capacity for gear ratio, the formation mechanism of a high-order multistage modified ellipse was studied, and a unified mathematical expression of the family of ellipses was obtained. Thus, a design procedure for the helical gear pair of the high-order multistage modified ellipse was suggested, and its transmission characteristics were discussed exhaustively. Moreover, some checking methods such as the curvature radius of the pitch curve, convexity, pressure angle, root cutting, and contact ratio were offered. Finally, two design cases, including two-order and three-stage modified elliptical helical gear pair and two-order and four-stage one, were implemented. The cases indicate that a high-order multistage modified elliptical helical gear can be utilized in practice.

Computerized Simulation of Generation of Internal Involute Gears and Their Assembly

1994 ◽  
Vol 116 (3) ◽  
pp. 683-689 ◽  
Author(s):  
F. L. Litvin ◽  
C.-L. Hsiao ◽  
J.-C. Wang ◽  
X. Zhou
Keyword(s):  
Computer Graphics ◽  
Computer Programs ◽  
Numerical Examples ◽  
Design Charts ◽  
Paper Cover ◽  
Involute Gears ◽  
Tooth Number ◽  
Computerized Simulation ◽  
Internal Gear

The contents of the paper cover the determination of conditions: (i) of nonundercutting by axial and axial-radial generation of internal gears by shapers, and (ii) avoidance of interference by axial and axial-radial assembly. The authors have developed computer programs for simulation of undercutting and interference, design charts and a table that allow to determine the limiting number of teeth of the cutter and pinion considering the tooth number of internal gear as known. The details of developed algorithms are given in the Appendices. The paper is illustrated with computer graphics and numerical examples.

scholarly journals Performance-Based Seismic Design of Steel Frames Utilizing Colliding Bodies Algorithm

2014 ◽  
Vol 2014 ◽  
pp. 1-6 ◽  
Author(s):  
H. Veladi
Keyword(s):  
Seismic Design ◽  
Optimization Algorithm ◽  
Pushover Analysis ◽  
Steel Frames ◽  
Design Methods ◽  
Frame Structures ◽  
Analysis Method ◽  
Numerical Examples ◽  
Colliding Bodies Optimization ◽  
Performance Based Seismic Design

A pushover analysis method based on semirigid connection concept is developed and the colliding bodies optimization algorithm is employed to find optimum seismic design of frame structures. Two numerical examples from the literature are studied. The results of the new algorithm are compared to the conventional design methods to show the power or weakness of the algorithm.

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