Development of a multiblock procedure for automated generation of two-dimensional quadrilateral meshes of gear drives

This article describes a new multiblock procedure for automated generation of two-dimensional quadrilateral meshes of gear drives. The typical steps of the multiblock schemes have been investigated in depth to obtain a fast and simple way to mesh planar sections of gear teeth, allowing local mesh refinement and minimizing the appearance of distorted elements in the mesh. The proposed procedure is completed with two different mesh quality enhancement techniques. One of them is applied before the mesh is generated, and reduces the distortion of the mesh without increasing the computational time of the meshing process. The other one is applied once the mesh is generated, and reduces the distortion of the elements by means of a mesh smoothing method. The performance of the proposed procedure has been illustrated with several numerical examples, which demonstrate its ability to mesh different gear geometries under several meshing boundary conditions

A 2D finite element based approach to predict the temperature field in polymer spur gear transmissions

This article describes a new numerical approach to determine the temperature field of polymer spur gears during their operation. The approach is based on an uncoupled procedure in which a mechanical problem is solved to determine the amount of heat that is generated by friction during the meshing of the gears, and then this heat is considered as a thermal load to perform a thermal analysis of a finite element model of the transmission. The amount of heat generated by friction is determined from the results of a numerical loaded tooth contact analysis of the transmission, which is based on the finite element method. The generality of the finite element method enables this approach to be applied to any kind of spur gear transmission, regardless of the geometry and the material of the gears and lubrication conditions. The resulting approach is applied to determine the temperature field of a spur gear transmission where polymer and metallic gears are combined, under several different operating conditions. The results obtained from this approach are compared to those obtained from experimental analyses, showing a good degree of similarity between them

Contribution of the deflection of tapered roller bearings to the misalignment of the pinion in a pinion-rack transmission

The misalignment of the gears is one of the main causes of premature failure in gear transmissions. This misalignment can be caused by different phenomena where the deformation of the elastic elements of the transmission usually has a major importance. In this paper, a pinion and rack transmission is used to investigate the misalignment of the pinion produced by the deflection of both shaft and bearings, focusing in the contribution of the bearings to this misalignment. For this task, a design space with 261 different cases of pinion and rack transmission has been explored. For each case, a realistic 3D FEM model (including gears, shaft and roller bearings) has been created and the coupled structural and contact problem has been solved. From the results of the FEM models, the different parameters of misalignment of the pinion have been computed and analyzed through five studies. These studies revealed the high importance of the elasticity of the bearings in the misalignment of the pinion and, in general, the important error that can be assumed when the bearings are not included in the structural models of gear transmissions.The authors express their deep gratitude to the Spanish Ministry of Science and Innovation (MICINN) for the financial support of research project ref. DPI2013-47702-C2-2-P

Investigation of the effect of contact pattern design on the mechanical and thermal behaviors of plastic-steel helical gear drives

This article describes an investigation that has been conducted to assess the effects of the contact pattern design on the mechanical and thermal behaviors of plastic-steel helical gear drives. The maximum contact pressure, frictional power loss, transmission error function and operating temperature are determined for different designs of the pinion tooth surfaces. Several numerical examples based on loaded tooth contact analyses and steady-state heat transfer analyses are carried out considering different types of micro-geometry modifications of the involute tooth surfaces. The obtained results show that an appropriate design of the pinion tooth surfaces can help reducing the maximum contact pressure and the maximum operating temperature, increasing the durability of the transmission. The frictional power loss and the peak-to-peak transmission error can be diminished, improving the performance of the transmission and increasing its efficiency. Also, it has been shown that the design of the pinion tooth surfaces can provide some capability to the transmission to absorb angular misalignments.Funding for open access charge: CRUE-Universitat Jaume

An adaptive mesh refinement approach for solving nonHertzian elastic contact problems

Semi-analytical methods are a common way of solving non-hertzian contact problems when designing mechanical components. These methods require of the discretization of the domain into a set of pressure elements and their accuracy and computational cost are related to the number of elements in which the domain is discretized. But, while the accuracy increases as the pressure element mesh is refined, the computational cost increases quadratically with the number of pressure elements. So in the great majority of the cases, a commitment between accuracy and computational cost must be achieved. In this work, a new approach has been developed to improve the performance of semi-analytical methods for solving contact problems. This approach uses an adaptive mesh refinement strategy, based on the quadtree decomposition of the domain. As a result, the computational cost decreases, while the accuracy of the method remains constant

Adaptive Mesh Refinement Strategy for the Semi-Analytical Solution of Frictionless Elastic Contact Problems

Semi-analytical methods are commonly used to solve contact problems. These methods require the discretization of the domain into a mesh of pressure elements. In general, it can be said that their accuracy increases as the pressure element mesh is refined. However, the refinement of the pressure element mesh also implies an increase in their computational cost. So, in the great majority of the cases, a commitment between accuracy and computational cost must be achieved. In this work, a new approach is presented, whose main purpose is to improve the efficiency of the semi-analytical methods that are used to solve contact problems. To do so, an adaptive refinement of the pressure element mesh is implemented. This strategy allows for a reduction of the computational cost of the method, while its accuracy remains unaffected

A simple procedure for generating locally refined 2D quadrilateral finite element meshes of gears

This article describes a new procedure for automated generation of two-dimensional locally refined quadrilateral meshes of gear drives. In this new procedure, a base mesh is generated using a multiblock meshing procedure. Then, selected elements of the base mesh are subdivided to obtain a refined mesh in certain parts of the gear teeth. The proposed procedure is completed with a mesh quality enhancement technique, which is based on an optimization-based smoothing. It also includes strategies that allow to automatically identify and refine those areas of the gear that are typically subjected to elevated stress gradients. The performance of the proposed procedure is illustrated with numerical examples, and it is compared to other existing meshing procedures, both in terms of mesh distortion and accuracy of the results

Modified geometry of spur gear drives for compensation of shaft deflections

One of the main problems when standard spur gears are in mesh is the appearance of edge contact on the gear tooth surfaces caused by misalignments. Those misalignments are caused partially by deflections of gear supporting shafts. As a result of an edge contact, a non-favorable condition of the bearing contact occurs, yielding high level of contact stresses. An intensive research and many practical solutions have been directed to modify the gear tooth surfaces in order to avoid edge contact. An innovative procedure is proposed here for: (1) determination of errors of alignment caused by shaft deflections, (2) compensation of predicted shaft deflections during generation of spur gears, and (3), obtaining a favorable function of transmission errors for the design load. A finite element model of a spur gear drive that comprises pinion and gear supporting shafts is used for the determination of errors of alignment along a cycle of meshing. Compensation of misalignments caused by shaft deflections in gear generation is then accomplished by modification of pinion tooth surfaces whereas the gear tooth surfaces are kept unmodified. Additional modifications of pinion tooth surfaces may be required for obtaining a favorable function of transmission errors. The effect of several misalignment compensations in the reduction of contact stresses has been investigated. Postprocessing of load intensity functions and loaded transmission errors is included. The developed approach is illustrated with numerical examples.The authors express their deep gratitude to the Spanish Ministry of Economy and Competitiveness (MINECO) for the financial support of research projects Refs. DPI2010-20388-C02-01 (financed jointly by FEDER), DPI2013- 47702-C2-1, and DPI2013-47702-C2-2

Convective heat transfer modelling in dry-running polymer spur gears

Heat convection is an important phenomenon in the process of cooling polymer spur gears running in dry conditions, which ultimately affects the strength of the gears. In order to gain some insight into this phenomenon, a numerical heat convection model for polymer spur gears is proposed in this work, which is based on a detailed CFD simulation of the gears in operating conditions and it allows us to investigate the heat convection through their external surfaces. The performance of this numerical model is illustrated with several examples, in which a parametric study has been conducted to observe the variation of the heat transfer coefficients with the face width and the angular speed of the gears. The results obtained from this parametric study are compared to those obtained from a representative classical heat convection model, observing that the relative differences between them in terms of heat transfer coefficients can be as high as 125%. Finally, a new optimized heat convection model for polymer spur gears running in dry conditions is proposed, in which the convective heat transfer coefficients for the external surfaces of the gears are calculated from empirical equations based on the Newton’s law of cooling. This optimized model has lower computational cost than the numerical one, while it provides an important increase of the accuracy of the classical heat convection models, reducing the maximum relative differences to 10%.Funding for open access charge: CRUE-Universitat Jaume

Predicting Wrist Joint Angles from the Kinematics of the Arm: Application to the Control of Upper Limb Prostheses

Automation of wrist rotations in upper limb prostheses allows simplification of the human–machine interface, reducing the user’s mental load and avoiding compensatory movements. This study explored the possibility of predicting wrist rotations in pick-and-place tasks based on kinematic information from the other arm joints. To do this, the position and orientation of the hand, forearm, arm, and back were recorded from five subjects during transport of a cylindrical and a spherical object between four different locations on a vertical shelf. The rotation angles in the arm joints were obtained from the records and used to train feed-forward neural networks (FFNNs) and time-delay neural networks (TDNNs) in order to predict wrist rotations (flexion/extension, abduction/adduction, and pronation/supination) based on the angles at the elbow and shoulder. Correlation coefficients between actual and predicted angles of 0.88 for the FFNN and 0.94 for the TDNN were obtained. These correlations improved when object information was added to the network or when it was trained separately for each object (0.94 for the FFNN, 0.96 for the TDNN). Similarly, it improved when the network was trained specifically for each subject. These results suggest that it would be feasible to reduce compensatory movements in prosthetic hands for specific tasks by using motorized wrists and automating their rotation based on kinematic information obtained with sensors appropriately positioned in the prosthesis and the subject’s body.This publication is part of the R&D project PID2020-118021RB-I00 funded by MICIN/AEI/ 10.13039/501100011033