Stress Analysis Of Gear Research Articles

ANSYS<sup>Ⓡ</sup>-Based Gear Stress Analysis of a Lightweight 3-DOF Wrist Mechanism for a Parallel Robot with Expanded Workspace

ANSYS<sup>Ⓡ</sup>-Based Gear Stress Analysis of a Lightweight 3-DOF Wrist Mechanism for a Parallel Robot with Expanded Workspace

Contact stress analysis of metallic and additive manufacturing material in transmission

Additive manufacturing is a skill hastily increasing on some of public and private sectors at national and international level. In the coming days, it is predicted that this 3D printing methodology can be utilized at mechanical, civil, agricultural and medical fields. In medical field, the parts made by this can be replaced in place of human organs. The purpose of the paper is to value the importance of additive manufacturing through contact stress analysis of Gear and Pinion in case by case. It is observed that contact stress is maximum in case 1 and minimum in case 4.

ISO Stress Analysis and Micro Geometry Corrections of Parallel Axis Gearbox Using Dontyne Systems Gear Production Suite

This paper shows the design procedure of a parallel axis gearbox for an electric power steering system using Dontyne Gear Production Suite (GPS) software. It will also investigate the effect of microgeometry correction on contact stress values. Initially, the quantitative design procedure of gears geometry is implemented through an iterative selection process. This includes a proper selection of several geometrical parameters to match the design requirements. Then, ISO 6336, which is the most common analytical gear stress analysis approach, is applied for calculating surface contact and root bending stresses in involute gears. Applying a good macro geometry technique is desirable in order to optimize gear design. However, the increasing demand for reliable and compact gear pair requires specifying proper micro geometry corrections in order to ensure minimum peak stress, low noise, and vibration. Thus, the tooth profile is modified by applying for tip relief from the start to the end of active profiles taken into consideration the value of the mean mesh deflection and the profile error. Similarly, tooth flank is crowned to compensate for equivalent misalignment and to achieve a uniform load distribution over the gear face width. The amount of crowning is determined by adding shaft deflection error to manufacturing error and torsional deflection. The results suggest that there is a significant improvement in contact stress value after applying tip relief and helix crowning.

Internal spur gear root bending stress: A comparison of ISO 6336:1996, ISO 6336:2006, VDI 2737:2005, AGMA, ANSYS finite element analysis and strain gauge techniques

The Association of German Engineers VDI 2737:2005 and the International Organisation for Standardisation ISO 6336:2006 are universally accepted analytical procedures for the analysis of internal gears. There is no official American Gear Manufacturers Association standard for internal gear stress analysis due to the validity of inscribing the Lewis parabola within internal concave profiles and the resulting errors associated with the location of maximum root bending stress. This research investigates the differences associated with using ISO 6336, VDI 2737 and an unofficial American Gear Manufacturers Association method, all of which are compared against a potentially more accurate numerical (ANSYS) method and strain gauge techniques.

Dimensional Optimization of Helical Gear Pair Through Finite Element Analysis Using Subproblem Approximation Method

Traditional helical gear stress analysis techniques such as AGMA and ISO standards provides very often over-dimensioned gear pairs with bulky design. Therefore, it is required to optimize the gear pair design using latest techniques like finite element analysis. Stress analysis technique chosen to investigate the feasibility of dimensional optimization of a gear was Finite Element Analysis platform ANSYS 12.1. ISO 6336 standards and Hertz contact theory neglect friction between contact teeth. This work reflects coefficient of friction between contact teeth using FEA predicts more accurate results for contact stress. In this work, case hardened steel helical gear is optimised for optimum tooth root stress level subsequently to reduce the face width of gears with other geometrical parameters unaffected. Efforts has been carried out to verify contact stress value using Lagrange multiplier algorithm of optimised helical gear pair. Subproblem approximation method was implemented for searching of optimal solution of design variable. Optimized gear pair was manufactured and experimentally investigated for actual stresses and strains, as per loading condition mention in the rules of TED. Percentage saving in the material for optimised gear pair also been included in this work.

Implementation of a Finite Element Model for Gear Stress Analysis Based on Tie-Surface Constraints and Its Validation Through the Hertz's Theory

A new finite element model for stress analysis of gear drives is proposed. Tie-surface constraints are applied at each tooth of the gear model to obtain meshes that can be independently defined: a finer mesh at contact surfaces and fillet and a coarser mesh in the remaining part of the tooth. Tie-surface constraints are also applied for the connection of several teeth in the model. The model is validated by application of the Hertz's theory in a spiral bevel gear drive with localized bearing contact and by observation of convergency of contact and bending stresses. Maximum contact pressure, maximum Mises stress, maximum Tresca stress, maximum major principal stress, and loaded transmission errors are evaluated along two cycles of meshing. The effects of the boundary conditions that models with three, five, seven, and all the teeth of the gear drive provide on the above-mentioned variables are discussed. Several numerical examples are presented.

Implementation of a finite element model for stress analysis of gear drives based on multi-point constraints

Gear researchers are always trying to find a trade-off solution between obtaining accurate results from gear stress analyses and low computational costs. Both factors, accuracy on the one hand, and a low computational cost on the other hand, usually go in opposite directions. In this paper, a finite element model for stress analysis of gear drives is proposed with the ultimate goal of obtaining accurate results regarding contact and bending stresses with lower computational cost than those finite element models where mesh refinement is not applied. The proposed finite element model allows the whole cycle of meshing to be analyzed and is based on the application of multi-point constraints for mesh refinement and the application of elements with a reduced number of integration points. Node coordinates are computationally and automatically determined by application of the gear theory. Several numerical examples are presented for a spur gear drive, although the same ideas can be applied in other types of gear drives. Accurate results of maximum contact pressure along the cycle of meshing with an important reduction of computational cost are achieved, mainly due to the reduction of the number of degrees of freedom that multi-point constrains provide, rather than by the use of reduced-integration elements.

External spur gear root bending stress: A comparison of ISO 6336:2006, AGMA 2101-D04, ANSYS finite element analysis and strain gauge techniques

The International Organisation for Standardisation ISO 6336:2006 and the American Gear Manufacturers Association AGMA 2101-D04 are the two most predominant empirically based analytical gear stress analysis methods for establishing contact and root bending stress in involute spur and helical gears. Although based on the same fundamental principles, they have evolved to such an extent that, for various reasons, they are not necessarily in agreement. The use of commercial universal numerical finite element software has become an increasingly popular alternative for gear stress analysis and this research compares the root bending stresses in external spur gears established using ISO 6336:2006, AGMA 2101-D04 and numerical finite element analysis (ANSYS) with experimental strain gauge validation.

Comparative study of stress analysis of gears with different helix angle using the ISO 6336 standard and tooth contact analysis methods

With increasing demand for high speed and high power density gear applications, the need to optimise gears for minimum stress, noise and vibration becomes increasingly important. ISO 6336 contact and bending stress analysis are used to determine the surface load capacity and tooth bending strength but dates back to 1956 and although it is constantly being updated, a review of its performance is sensible. Methods to optimise gear performance include the selection of helix angle and tooth depth to optimise overlap ratio and transverse contact ratio and thus the performance of ISO 6336 and tooth contact analysis methods requires confirmation. This paper reviews the contact and bending stress predicted with four involute gear geometries and proposes recommendations for stress calculations, including a modification to contact ratio factor Zɛ which is used to predict contact stress and revisions to form factor YF and helix angle factor Yβ which are cited to evaluate bending stress. The results suggest that there are some significant deviations in predicted bending and contact stress values between proposal methods and original ISO standard. However, before the ISO standard is changed, the paper recommends that allowable stress numbers published in ISO 6336-5 are reviewed because the mechanisms that initiate bending and contact fatigue have also changed and these require updating.

Mathematical model and algorithm for contact stress analysis of gears with multi-pair contact

The problem of contact pressure evaluation in gears with predesigned parabolic function of transmission errors and with localized contact is considered. It is proposed that several tooth pairs are in contact simultaneously. We construct an algorithm to define the torque transmitted by each pair in contact. Number of pairs in simultaneous contact depends on applied load and phase of meshing. This number is not known in advance. The feature of the algorithm is an automatic detection of the tooth pair number that is in contact in any phase of meshing under load. The algorithm allows you to define forces and torques that are transmitted on each of the pairs of teeth being in contact. Moreover, it allows determining the contact pressure and tooth-to-tooth accuracy of transmission. The proposed algorithm is universal and can be used to study the multi-pair contact in any gears.An application of the algorithm for a spiral bevel gear has been demonstrated. It is shown that tooth overlap factor, dimensions of instant contact patch, tooth bearing contact and tooth-to-tooth accuracy of gears increase with growth of load.

A CAE approach for the stress analysis of gear models by 3D digital photoelasticity

The use of numerical and experimental methods to determine the stress field of mechanical components is well known. In particular, 3D photoelasticity can be considered the only experimental technique for the complete stress state evaluation of 3D components. The advent of rapid prototyping techniques has allowed the manufacturing of complex models in a matter of hours by using birifrangent materials. The present paper is focused on the description of a Computer Aided Engineering (CAE) approach which combines Finite Element (FE) simulations and automatic photoelastic investigations for the stress analysis of face gear drives, made by stereolithography. Computer Aided Design (CAD) geometries, used to manufacture the stereolithographic models, are directly used to perform FE analyses, thus allowing the stress analysis process to become simpler and easier. The substantial agreement observed between experimental and numerical results proved the potentialities of the adopted approach and the usefulness of FE simulations to optimize photoelastic analyses through cost- and time-effective experiments even for complex 3D shapes.

Uncertainty Quantification in Gear Remaining Useful Life Prediction Through an Integrated Prognostics Method

Accurate health prognosis is critical for ensuring equipment reliability and reducing the overall life-cycle costs. The existing gear prognosis methods are primarily either model-based or data-driven. In this paper, an integrated prognostics method is developed for gear remaining life prediction, which utilizes both gear physical models and real-time condition monitoring data. The general prognosis framework for gears is proposed. The developed physical models include a gear finite element model for gear stress analysis, a gear dynamics model for dynamic load calculation, and a damage propagation model described using Paris' law. A gear mesh stiffness computation method is developed based on the gear system potential energy, which results in more realistic curved crack propagation paths. Material uncertainty and model uncertainty are considered to account for the differences among different specific units that affect the damage propagation path. A Bayesian method is used to fuse the collected condition monitoring data to update the distributions of the uncertainty factors for the current specific unit being monitored, and to achieve the updated remaining useful life prediction. An example is used to demonstrate the effectiveness of the proposed method.

Gear Stress Analysis and Discrete Optimization for Wheel-Legged Rover

The wheel-legged rover with a double-half-revolution mechanism uses two tandem planetary gear trains to drive. Its virtual prototype model was built in COSMOS Motion software, and the mechanical data of each gears of the wheel-legged rover were obtained by dynamic simulation under the typical working conditions. On this basis, the finite element analysis model of the wheel-leg planetary gear was established and its stress analysis was done. The discrete optimization mathematical model was built with the optimization target of minimizing the rover’s wheel-leg planetary gear volume and the constraint condition of keeping the Mises stress applied on the dedendum under the admissible Mises stress. Based on ANSYS Parametric Design Language (APDL), the optimization design was done for the above gear based on discrete optimization method. The result shows that the optimized gear not only meets the strength requirement, but also its weight is 58% lower than the original, which will provide a new effective method for optimizing the wheel-leg structure of the rover.

Computerized Developments in Design, Generation, Simulation of Meshing, and Stress Analysis of Gear Drives

The paper represents new computerized developments in design, generation, simulation of meshing, and stress analysis of gear drives. The main contents of the paper are: (i) application of a predesigned parabolic function of transmission errors for reduction of noise, (ii) computerized simulation of noise caused by transmission errors, (iii) modification of the basic algorithm of tooth contact analysis, and (iv) application of approaches developed for enhanced design and simulation of meshing of the following gear drives: (a) spiral bevel gear drives, (b) face-gear drives (including an approach for grinding), and (c) modified helical gear drives. The developed theory is illustrated with numerical examples.

Analysis of Stresses in Spur Gears by the Photoelastic Coating Method

Abstract This study uses a photoelastic coating method in spur gear stress analysis, and verifications of the results are made with two-dimensional boundary element analysis. The principal advantage of the photoelastic coating method comes from the fact that it is a full-field technique capable of showing the entire stress distribution over the surface of a part and thus highlighting the regions where the stresses are the largest. The general results of experimental work in which spur gears are analyzed, both in test fixtures and in loading conditions at the critical points, are presented in order to measure actual tooth root, tooth fillet, and blank stresses.

Gear Stress Analysis by the Hybrid Finite Element Method. Deviation Technique for the Global Local Finite Element Method.

A new numerical technique using the global local finite element method (GLFEM) has been proposed for analyzing a gear subjected to a single concentrated load. The GLFEM is a kind of deviational technique which combines the conventional finite element solutions and the analytical solution like Kelvin's one. One of the most interesting features of this method is considerable reduction in the data required in the modeling process in comparison to that based only on conventional finite elements. Clearly, the nature of the solution and the degree of approximation depend on the characteristics of the element equations. In this study, although there are many ways of formulation, the deviation technique and hybrid method combining the domain type and boundary type solutions are especially used for formulating the properties of elements. Then the GLFEM formulated in this study is applied to the gear tooth stress analysis to show the validity of this technique.

Global Local Finite Element Method in Gear Stress Analysis (Analytical Solution and Global Local Domain).

A Global Local Finite Element Method (GLFEM) has been applied to the analysis of the gear tooth stress field. The GLFEM is a numerical analysis technique in which finite element solutions and classical analytical ones (global function) are superposed in the global local domain on the basis of the energy principle. Hence, the reliability of the GLFEM greatly depends on which solution is used for the global function and/or which portion is selected for the global local domain. In the present paper, therefore, such effects on calculated stress field are discussed. Consequently, it is confirmed that Kelvin's solution is the most convenient one. Furthermore, the Lagrangian constraint is used for guaranteeing continuity of displacement on the boundary between the global local and local domains, but the constraint is not achieved sufficiently. Hence, sufficiently large area must be taken for the global local domain.

Finite element modelling and stress analysis of helical gear teeth

Because of the lower dynamic load, the noise level during operation and the demand for lighter and smaller automotive transmissions, helical gears have become the subject of attention. The three-dimensional way of calculating the root stresses of helical gears gives realistic results. This paper explains about the geometry of helical gears by simple mathematical equations, the load distribution for various positions of the contact line and the stress analysis of helical gears using the three-dimensional finite element method. A computer program has been developed for the stress analysis of the gears. Root stresses are evaluated for different positions of the contact line when it moves from the root to the tip. To check the validity of the present program, the changes in the trend of the maximum root stress values at various places of the tooth along the face width have been compared with the experimental results from other literature. A parametric study is made by varying the face width and the helix angle to study their effect on the root stresses of helical gears. Based on this investigation the effect of helix angle and face width on the root stresses of helical gears has been clarified for different positions of the contact line.

Gear tooth stress analysis by the complex potentials method

The complex potentials method of plane elasticity theory is applied to spur gear stress analysis. The concept is that the stress field in a gear tooth loaded by a point force can be obtained using the Boussinesq solution and a transformation function mapping a bell-shaped curve approximating the real tooth shape in the z-plane into the semi-infinite ζ-plane. The main features of an original computer code implementing this formulation are presented along with applications.

The mathematical model of Wildhaber-Novikov gears applicable to finite element stress analysis

The mathematical model and results of tooth contact analysis (TCA) of the Wildhaber-Novikov (W-N) gear are given in Ref. [1] [F.L. Livtin and C.-B. Tsay, Trans. ASME, J. mech. Trans. Auto. Des. 556-564 (December 1985)]. A finite element method (FEM), using the SAP IV package, is employed to the W-N gear stress analysis. An automatic nodal points and meshes generating (AMG) computer program has been developed. By utilizing the mathematical model of the W-N gear and the AMG computer program, nodal points and meshes for finite elements analysis can be obtained automatically. By applying the results of TCA, the location and direction of applied loading on gear teeth can be defined. Root bending stresses of pinion and gear with different loading positions have been analyzed. Effects on root stresses due to variations of fillet radius and normal pressure angle of pinion have also been investigated.