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.

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 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.

Concave modifications of tooth surfaces of beveloid gears with crossed axes

2018 ◽  
Vol 233 (4) ◽  
pp. 1411-1425 ◽  
Author(s):  
Siyuan Liu ◽  
Chaosheng Song ◽  
Caichao Zhu ◽  
Qi Fan
Keyword(s):  
Film Thickness ◽  
Contact Ratio ◽  
Tooth Contact Analysis ◽  
Transmission Errors ◽  
Maximum Value ◽  
Contact Patterns ◽  
Beveloid Gears ◽  
Minimum Film Thickness ◽  
Tooth Surfaces ◽  
Crossed Axes

The mathematical models of the beveloid gear surfaces with different scenarios of combinations of profile concave modification and lead crowning are derived. Four schemes of modifications were proposed for beveloid gears with crossed axes. Tooth contact analysis is developed to study the influences of different schemes of concave modifications on the mesh behaviors including film thickness, transmission errors, contact ratio, root stresses, and contact patterns. Comparison of the contact characteristics of a beveloid gear drive with and without concave modifications is conducted. The results show that all the concave modification schemes can increase the area of contact patterns and decrease the maximum value of contact stresses, while the minimum film thickness can be increased. For the scheme i.e. the pinion with profile crowning modification and gear with profile concave modification, the contact ratio increases firstly then decreases to a relative lower value. Also, the root stresses are increased obviously. For the scheme for pinion without modification and gear with lead concave modification and the scheme for both pinion and gear with lead concave modification, the transmission errors are decreased slightly. The scheme for the pinion with combined crowning modification and gear with combined concave modification shows the largest improvement for the mesh behaviors in terms of the transmission errors and contact patterns where an almost contact condition can be found for the crossed beveloid gear pair.

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.

Application of Finite Element Analysis for Determination of Load Share, Real Contact Ratio, Precision of Motion, and Stress Analysis

1996 ◽  
Vol 118 (4) ◽  
pp. 561-567 ◽  
Author(s):  
F. L. Litvin ◽  
J.-S. Chen ◽  
J. Lu ◽  
R. F. Handschuh
Keyword(s):  
Finite Element ◽  
Stress Analysis ◽  
Point Contact ◽  
Principal Curvatures ◽  
Contact Ratio ◽  
Element Analysis ◽  
Transmission Errors ◽  
Real Contact ◽  
Tooth Surfaces

A loaded gear drive with point contact between tooth surfaces is considered. The principal curvatures and directions at a current point of tangency, the contact paths on tooth surfaces, and the transmission errors caused by misalignment we consider as known. In this paper the following topics are covered: (1) Determination of the contact force and its distribution over the contact ellipse; (2) Determination of the tooth deflection, the load share, and the real contact ratio; and (3) Stress analysis by application of the finite element method. The discussed approach is illustrated with a numerical example.

scholarly journals Geometric Design-based Dimensional Synthesis of a Novel Metamorphic Multi-fingered Hand with Maximal Workspace

2021 ◽  
Vol 34 (1) ◽  
Author(s):  
Wei An ◽  
Jun Wei ◽  
Xiaoyu Lu ◽  
Jian S. Dai ◽  
Yanzeng Li
Keyword(s):  
Geometric Design ◽  
Practical Significance ◽  
Design Parameters ◽  
Control Algorithms ◽  
Discretization Method ◽  
Dimensional Synthesis ◽  
Symmetrical Structure ◽  
Design And Optimization ◽  
Total Length

AbstractCurrent research on robotic dexterous hands mainly focuses on designing new finger and palm structures, as well as developing smarter control algorithms. Although the dimensional synthesis of dexterous hands with traditional rigid palms has been carried out, research on the dimensional synthesis of dexterous hands with metamorphic palms remains insufficient. This study investigated the dimensional synthesis of a palm of a novel metamorphic multi-fingered hand, and explored the geometric design for maximizing the precision manipulation workspace. Different indexes were used to value the workspace of the metamorphic hand, and the best proportions between the five links of the palm to obtain the optimal workspace of the metamorphic hand were explored. Based on the fixed total length of the palm member, four nondimensional design parameters that determine the size of the palm were introduced; through the discretization method, the influence of the four design parameters on the workspace of the metamorphic hand with full-actuated fingers and under-actuated fingers was analyzed. Based on the analysis of the metamorphic multi-fingered hand, the symmetrical structure of the palm was designed, resulting in the largest workspace of the multi-fingered hand, and proved that the metamorphic palm has a massive upgrade for the workspace of underactuated fingers. This research contributed to the dimensional synthesis of metamorphic dexterous hands, with practical significance for the design and optimization of novel metamorphic hands.

scholarly journals Computerized Design and Generation of Low-Noise Helical Gears with Modified Surface Topology

1995 ◽  
Vol 117 (2A) ◽  
pp. 254-261 ◽  
Author(s):  
F. L. Litvin ◽  
N. X. Chen ◽  
J. Lu ◽  
R. F. Handschuh
Keyword(s):  
Gear Tooth ◽  
Error Function ◽  
Transmission Error ◽  
Low Noise ◽  
Surface Topology ◽  
Helical Gears ◽  
Transmission Errors ◽  
Bearing Contact ◽  
Pinion Gear ◽  
Tooth Surfaces

An approach for the design and generation of low-noise helical gears with localized bearing contact is proposed. The approach is applied to double circular arc helical gears and modified involute helical gears. The reduction of noise and vibration is achieved by application of a predesigned parabolic function of transmission errors that is able to absorb a discontinuous linear function of transmission errors caused by misalignment. The localization of the bearing contact is achieved by the mismatch of pinion-gear tooth surfaces. Computerized simulation of meshing and contact of the designed gears demonstrated that the proposed approach will produce a pair of gears that has a parabolic transmission error function even when misalignment is present. Numerical examples for illustration of the developed approach are given.

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.

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