An Intelligent System for Spur Gear Design and Analysis

2001 ◽  
Author(s):  
El-Sayed Aziz ◽  
C. Chassapis
Keyword(s):  
Finite Element ◽  
Closed Form ◽  
Intelligent System ◽  
Tooth Profile ◽  
Hertzian Contact ◽  
Design Parameters ◽  
Analysis Model ◽  
Closed Form Solutions ◽  
Gear Teeth ◽  
Gear Design

Abstract A methodology for the analysis of load distribution and contact stress on gear teeth, which utilizes a combination of closed form solutions and two-dimensional finite element methods, within a constraint-based knowledge-based environment, is presented. Once the design parameters are specified, the complete process of generating the analysis model, starting from the determination of the coordinates of the tooth profile, the creation of a sector of the mating gear teeth, automatic mesh generation, boundary conditions and loading, is totally automated and transparent to the designer. The effects of non-standard geometry, load sharing on the contact zone, friction and root stresses are easily included in the model. The Finite Element Method (FEM) based results compare favorably with those obtained from closed form solutions (AGMA equations and classical Hertzian contact solution). The advantage of the approach rests in the ability to modify any of the gear design parameters such as diametral pitch, tooth profile modification etc., in an automated manner along with obtaining a better estimation of the risks of failure of the gear design on hand. The procedure may be easily extended to other types of gearing systems.

Validation of Nitinol SMA Characteristics Using Finite Element Analysis and Closed Form Solutions

2013 ◽  
Vol 856 ◽  
pp. 147-152
Author(s):  
S.H. Adarsh ◽  
U.S. Mallikarjun
Keyword(s):  
Experimental Data ◽  
Finite Element Analysis ◽  
Finite Element ◽  
Closed Form ◽  
Closed Form Solution ◽  
Form Solution ◽  
Fe Analysis ◽  
Element Analysis ◽  
Complex Behaviour ◽  
Closed Form Solutions

Shape Memory Alloys (SMA) are promising materials for actuation in space applications, because of the relatively large deformations and forces that they offer. However, their complex behaviour and interaction of several physical domains (electrical, thermal and mechanical), the study of SMA behaviour is a challenging field. Present work aims at correlating the Finite Element (FE) analysis of SMA with closed form solutions and experimental data. Though sufficient literature is available on closed form solution of SMA, not much detail is available on the Finite element Analysis. In the present work an attempt is made for characterization of SMA through solving the governing equations by established closed form solution, and finally correlating FE results with these data. Extensive experiments were conducted on 0.3mm diameter NiTinol SMA wire at various temperatures and stress conditions and these results were compared with FE analysis conducted using MSC.Marc. A comparison of results from finite element analysis with the experimental data exhibits fairly good agreement.

scholarly journals IKBT: Solving Symbolic Inverse Kinematics with Behavior Tree (Extended Abstract)

2020 ◽  
Author(s):  
Dianmu Zhang ◽  
Blake Hannaford
Keyword(s):  
Closed Form ◽  
Inverse Kinematics ◽  
Intelligent System ◽  
Logical Reasoning ◽  
Robot Arm ◽  
Kinematics Analysis ◽  
Closed Form Solutions ◽  
Behavior Tree ◽  
Behavior Trees ◽  
High Level

Inverse kinematics solves the problem of how to control robot arm joints to achieve desired end effector positions, which is critical to any robot arm design and implementations of control algorithms. It is a common misunderstanding that closed-form inverse kinematics analysis is solved. Popular software and algorithms, such as gradient descent or any multi-variant equations solving algorithm, claims solving inverse kinematics but only on the numerical level. While the numerical inverse kinematics solutions are relatively straightforward to obtain, these methods often fail, even when the inverse kinematics solutions exist. Therefore, closed-form inverse kinematics analysis is superior, but there is no generalized automated algorithm. Up till now, the high-level logical reasoning involved in solving closed-form inverse kinematics made it hard to automate, so it's handled by human experts. We developed IKBT, a knowledge-based intelligent system that can mimic human experts' behaviors in solving closed-from inverse kinematics using Behavior Tree. Knowledge and rules used by engineers when solving closed-from inverse kinematics are encoded as actions in Behavior Tree. The order of applying these rules is governed by higher level composite nodes, which resembles the logical reasoning process of engineers. It is also the first time that the dependency of joint variables, an important issue in inverse kinematics analysis, is automatically tracked in graph form. Besides generating closed-form solutions, IKBT also explains its solving strategies in human (engineers) interpretable form. This is a proof-of-concept of using Behavior Trees to solve high-cognitive problems.

A Conical Beam Finite Element for Rotor Dynamics Analysis

1985 ◽  
Vol 107 (4) ◽  
pp. 421-430 ◽  
Author(s):  
L. M. Greenhill ◽  
W. B. Bickford ◽  
H. D. Nelson
Keyword(s):  
Finite Element ◽  
Closed Form ◽  
Cross Section ◽  
Rotor Dynamics ◽  
General Purpose ◽  
Closed Form Expression ◽  
Dynamics Analysis ◽  
Closed Form Solutions ◽  
Analysis Computer ◽  
Rotor Dynamic

The development of finite element formulations for use in rotor dynamics analysis has been the subject of many recent publications. These works have included the effects of rotatory inertia, gyroscopic moments, axial load, internal damping, and shear deformation. However, for most closed-form solutions, the element geometry has been limited to a cylindrical cross-section. This paper extends these previous works by developing a closed-form expression including all of the above effects in a linearly tapered conical cross-section element. Results are also given comparing the formulation to previously published examples, to stepped cylinder representations of conical geometry, and to a general purpose finite element elasticity solution. The elimination of numerical integration in the generation of the element matrices, and the ability of the element to represent both conical and cylindrical geometries, make this formulation particularly suited for use in rotor dynamic analysis computer programs.

Corner-Filleted Flexure Hinges

2000 ◽  
Vol 123 (3) ◽  
pp. 346-352 ◽  
Author(s):  
Nicolae Lobontiu ◽  
Jeffrey S. N. Paine ◽  
Ephrahim Garcia ◽  
Michael Goldfarb
Keyword(s):  
Finite Element ◽  
Closed Form ◽  
Finite Element Simulation ◽  
Analytical Approach ◽  
Flexure Hinge ◽  
Closed Form Solutions ◽  
Flexure Hinges ◽  
Element Simulation ◽  
Model Predictions ◽  
The Right

The paper presents an analytical approach to corner-filleted flexure hinges. Closed- form solutions are derived for the in-plane compliance factors. It is demonstrated that the corner-filleted flexure hinge spans a domain delimited by the simple beam and the right circular flexure hinge. A comparison that is made with the right circular flexure hinges indicates that the corner-filleted flexures are more bending-compliant and induce lower stresses but are less precise in rotation. The finite element simulation and experimental results confirmed the model predictions.

An Algorithm for Reducing the Size of Finite Element Closed-Form Source Code Files

2009 ◽  
Author(s):  
Sara McCaslin ◽  
Kent Lawrence
Keyword(s):  
Finite Element Analysis ◽  
Finite Element ◽  
Closed Form ◽  
Source Code ◽  
Simple Algorithm ◽  
Higher Order ◽  
Error Estimator ◽  
Element Analysis ◽  
Closed Form Solutions ◽  
Large Source

Closed-form solutions, as opposed to numerically integrated solutions, can now be obtained for many problems in engineering. In the area of finite element analysis, researchers have been able to demonstrate the efficiency of closed-form solutions when compared to numerical integration for elements such as straight-sided triangular [1] and tetrahedral elements [2, 3]. With higher order elements, however, the length of the resulting expressions is excessive. When these expressions are to be implemented in finite element applications as source code files, large source code files can be generated, resulting in line length/ line continuation limit issues with the compiler. This paper discusses a simple algorithm for the reduction of large source code files in which duplicate terms are replaced through the use of an adaptive dictionary. The importance of this algorithm lies in its ability to produce manageable source code files that can be used to improve efficiency in the element generation step of higher order finite element analysis. The algorithm is applied to Fortran files developed for the implementation of closed-form element stiffness and error estimator expressions for straight-sided tetrahedral finite elements through the fourth order. Reductions in individual source code file size by as much as 83% are demonstrated.

Thermal Stresses in Compliantly Joined Materials

1990 ◽  
Vol 112 (1) ◽  
pp. 24-29 ◽  
Author(s):  
J. C. Glaser
Keyword(s):  
Finite Element ◽  
Closed Form ◽  
Thermal Stresses ◽  
Material Interface ◽  
Element Mesh ◽  
Closed Form Solutions ◽  
First Order ◽  
The Past ◽  
Compliant Layer ◽  
Analytical Relations

In the past several years there have been a number of papers published which provide closed-form solutions for the stresses in bonded layers of materials. These closed-form solutions offer a rapid method to obtain first-order stresses for materials which are joined together and the compliant layer between them. However, before using them, it is desirable to have some feeling as to the accuracy of the results from these closed-form equations. Comparisons between these analytical relations and other approaches found in published works on bonding and to finite element solutions for several example problems are given. An attempt is made to qualify these closed-form equations in terms of their accuracy, as compared to other methods of analysis. The effects of finite element mesh refinement on the material interface stress results are also given.

Computerized Tooth Profile Generation and Undercut Analysis of Gears Manufactured With Pre-Shaving Hobs

2009 ◽  
Vol 16-19 ◽  
pp. 1278-1282
Author(s):  
Xiang Wei Kong ◽  
Jing Zhang ◽  
Meng Hua Niu
Keyword(s):  
Mathematical Model ◽  
Computer Program ◽  
Gear Tooth ◽  
Tooth Profile ◽  
Design Parameters ◽  
Gear Teeth ◽  
The Mathematical Model

This paper investigated the feature of pre-shaving hob contour and the generated gear tooth profile. By tooth generation method, a complete geometry of the gear tooth can be mathematically derived in terms of the design parameters of the pre-shaving hob cutter. The mathematical model consisted of equations describing the generated fillet and involute profiles. The degree of undercutting and the radii of curvatures of a fillet were investigated by considering the model. Finally, a computer program for generating the profile of the gear teeth was developed by simulating the cutting methods. The methods proposed in this study were expected to be a valuable guidance for pre-shaving hob designers and manufacturers.

Contact-Point Response for Modal Identification of Bridges by a Moving Test Vehicle

2018 ◽  
Vol 18 (05) ◽  
pp. 1850073 ◽  
Author(s):  
Y. B. Yang ◽  
Bin Zhang ◽  
Yao Qian ◽  
Yuntian Wu
Keyword(s):  
Finite Element ◽  
Closed Form ◽  
Frequency Response Function ◽  
Contact Point ◽  
Modal Identification ◽  
Mode Shapes ◽  
Test Vehicle ◽  
Closed Form Solutions ◽  
Road Surfaces ◽  
Vehicle Response

The response of the contact point of the vehicle with the bridge, rather than the vehicle itself, is proposed for modal identification of bridges by a moving test vehicle. To begin, approximate closed-form solutions were derived for the vehicle and contact-point responses, and they were verified by finite element solutions. The contact-point acceleration is born to be free of the vehicle frequency, an annoying effect that may overshadow the bridge frequencies in case of rough surface. From the frequency response function (FRF) of the vehicle with respect to the contact point, it was shown that the contact-point response generally outperforms the vehicle response in extracting the bridge frequencies because it could identify more frequencies. In the numerical simulations, the contact-point response was compared with the vehicle response for various scenarios. It is concluded that in each case, say, for varying vehicle speeds or frequencies, for smooth or rough road surfaces, with or without existing traffic, the contact-point response outperforms the vehicle response in extracting either the frequencies or mode shapes of the bridge.

Comparison of tooth profiles and oil formulation focusing lower power losses

2012 ◽  
Vol 226 (6) ◽  
pp. 529-540 ◽  
Author(s):  
Luís Magalhães ◽  
Ramiro Martins ◽  
Ivo Oliveira ◽  
Jorge Seabra
Keyword(s):  
Power Loss ◽  
Raw Materials ◽  
Helix Angle ◽  
Tooth Profile ◽  
Power Losses ◽  
Gear Teeth ◽  
Gear Design ◽  
Lubricant Formulation ◽  
Oil Formulation ◽  
Energetic Model

Environmental awareness, lower consumption of raw materials and longer life of equipment are main concerns nowadays and are leading to the research and development of lubricants and equipment to access those requirements. In this study, the power loss performance of three different tooth profile geometries, developed with the purpose of decreasing power losses while keeping the predicted life, were tested and evaluated in a FZG test rig. The path to reduce power losses was based on the decrease of the module, the increase of the helix angle and increase of the addendum modification coefficients in order to reduce the path of contact, i.e. the sliding velocity. The power loss behaviour of two different lubricants was also evaluated for each tooth profile geometry considered. The influence of the oil level in the gearbox was also evaluated. One of the lubricants has an ester base while the other has a polyalphaolefin base and both are fully formulated. An energetic model was developed for the FZG test gearbox and applied to these tests to improve the knowledge about the influence of tooth geometries as well as lubricant formulation in the power losses and coefficient of friction between gear teeth. The developed geometries showed that the path followed for the reduction of power losses produced the expected results and can be implemented with success on gear design.

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