V. Spitas

Optimum Gear Tooth Geometry for Minimum Fillet Stress Using BEM and Experimental Verification With Photoelasticity

This paper introduces the concept of nondimensional gear teeth to be used in gear stress minimization problems. The proposed method of modeling reduces the computational time significantly when compared to other existing methods by essentially reducing the total number of design variables. Instead of modeling the loaded gear tooth and running BEA to calculate the maximum root stress at every iterative step of the optimization procedure, the stress is calculated by interpolation of tabulated values, which were calculated previously by applying the BEM on nondimensional models corresponding to different combinations of the design parameters. The complex algorithm is used for the optimization and the root stresses of the optimum gears are compared with the stresses of the standard gears for the same transmitted torque. Reduction in stress up to 36.5% can be achieved in this way. This reduction in stress has been confirmed experimentally with two-dimensional photoelasticity.

A FEM Study of the Bending Strength of Circular Fillet Gear Teeth Compared to Trochoidal Fillets Produced with Enlarged Cutter Tip Radius

Abstract Circular fillet (CF) gears have been proven to possess a higher bending strength than their standard trochoidal fillet (TF) counterparts. However, stronger nonstandard variants of the TF are already possible to produce by increasing the tip radius of the cutters used for gear generation (racks, hobs, pinion cutters), affording competitive results. In this paper a comparison of the bending strength is made between the CF and the nonstandard large tip radius TF designs spanning the entire usable tooth number range using FEA. The results suggest a systematic advantage of the CF over the stronger variants of the TF for numbers less than 17 teeth, which is the undercut limit for the 20° involute gear system.

Modeling of the Elastic Damping Response of a Carbon Nanotube–Polymer Nanocomposite in the Stress-Strain Domain Using an Elastic Energy Release Approach Based on Stick-Slip

A representative volume element (RVE) involving a single carbon nanotube (CNT) embedded in a plastic matrix is used to model the elastic behavior of the nanocomposite using finite elements. When the RVE is loaded axially, the maximum shear stress at the CNT-matrix interface can exceed the interfacial shear strength causing slippage of the CNT inside the matrix. Cyclic loading causes hysteretic stress-strain behavior of the nanocomposite and dependencies on the interfacial strength, geometry, relative elastic properties of the CNT and the matrix, and volume fraction of the CNTs are investigated.

Four-Parametric Design Study of the Bending Strength of Circular-Fillet Versus Trochoidal-Fillet in Gear Tooth Design Using BEM

Abstract Circular fillet pinions are designs of superior bending strength evolved as substitutes to the standard trochoidal fillet design. However this has only been verified considering gears of nominal thickness coefficient and addendum. This paper makes a comparative four-parametric study of the achieved bending strength of the two designs (circular fillet/trochoidal fillet) taking into consideration the large range of pinion and gear numbers used in engineering practice. The results are calculated using an automated BEM process and presented in generalised diagrams, called ‘stress map’, which are used to observe optimal application and usage restrictions of each design.

Effect of Cutter Pressure Angle on the Undercutting Risk and Bending Strength of 20° Involute Pinions Cut with Equivalent Nonstandard Cutters #

Abstract Recent research by the authors has shown that it is possible to generate fully interchangeable 20° involute gears using nonstandard module and pressure angle cutter geometry. Gear teeth cut by this method have working profiles that are identical to standard teeth, but notably different trochoidal fillets. In this paper the possibility to use this method to derive teeth with improved bending resistance is investigated numerically using Finite Element Method (FEM) for the entire possible range of values of the cutter pressure angle, thus providing a parametric mapping and a first suggestion for optimal design.

Direct analytical solution of the inverse gear tooth contact analysis problem

Despite the advances in gear tooth contact analysis and the existence of many competent theories, the fundamental inverse problem of determining the gear profile form that produces a desired kinematical response, or function of transmission errors, remains to be solved. This is because the usually employed form of the equations governing tooth contact is so complex and implicit, that it is impossible to solve inversely. To bypass this handicap, current design methodologies have to rely on indirect calculations, often requiring substantial computational effort. Here, a new more versatile formulation of the fundamental surface contact equations is proposed, leading to a set of meshing equations that allows the direct analytical solution of the inverse problem. The solution itself is in elegant vector-matrix form and it is explicit and fast. Applications of the proposed solution are discussed.

Coupled multi-DOF dynamic contact analysis model for the simulation of intermittent gear tooth contacts, impacts and rattling considering backlash and variable torque

Variable torque conditions in geared powertrain applications are known to lead to tooth contact loss, contact reversal, tooth impacts, rattling vibration and noise. Displacements/ deflections dominate the low-torque high-vibration responses and, besides backlash, the real-time dynamic lateral deflections of the gear bodies and the occurrence of simultaneous double-sided tooth contact influence the instantaneous mesh excitation strongly. The faster deterministic and stochastic analytical models do not consider this coupling, whereas the numerical models that do so implicitly by simulating the contact of discretised tooth surfaces/ volumes are significantly limited by the accuracy and computational overhead of their discrete meshes. To provide a both fast and accurate solution of the contact problem, especially in displacement-dominated operating conditions, this work analyses the dynamic contact of gears starting from basic principles and derives an accurate analytical model for the coupling between the compliance, contact geometry, the backlash, and the torsional and lateral displacements and deflections in the general three-dimensional multi-DOF system. This serves as a foundation for a series of dynamical simulations of a single-stage spur gear transmission under different variable-torque excitations to predict tooth contact loss and contact reversal and the basic interactions that lead to impacts and rattling vibration. This approach can be used to predict critical torque fluctuation levels, beyond which these phenomena emerge.

Reduction of Tooth Fillet Stresses Using Novel One-Sided Involute Asymmetric Gear Design

Abstract For increasing the load carrying capacity of geared power transmissions several tooth designs alternative to the standard involute have been proposed. The use of non-involute teeth has a number of disadvantages and for this reason asymmetric involute-type teeth have been studied as a promising alternative. In this article the idea of one-sided involute asymmetric spur gear teeth is introduced to increase load carrying capacity and combine the good meshing properties of the driving involute and the increased strength of non-involute curves. These novel teeth are intended for constant direction of rotation, although they can be used in a limited way for reverse rotation. Both profiles are fully generated by a hob, the design of which is also investigated. The increase in load carrying capacity can reach up to 28{%} compared to the standard 20° involute teeth.

Experimental Evaluation of Stress Intensity Factors in Spur Gear Teeth

In most engineering applications, gears are the most widely used machine elements for the transmission of power and motion from one shaft to another. Hence it is evident that there is a need for reliability and longer service-life, which requires precise knowledge of the stress field developed in the gear tooth. However this stress analysis becomes more complex when a small crack appears after overloading or fatigue conditions. It is therefore critical to calculate either the remaining life of the cracked gear under the same loading conditions, or the new maximum failsafe operating load to cover the initially calculated service time.

Shear Testing of Al and Al-Al4C3 Materials at Elevated Temperatures

The shear creep properties of the A1-A14C3 composite material were investigated for the first time at different temperatures ranging from 523 Κ to 773 Κ and different shear stress levels ranging from 25 to 40 MPa in comparison to pure aluminum. The specimens were loaded in pure shear using a specially designed patented specimen geometry and a prototype shear-testing machine. The experimental results indicate that the AI4C3 composite aluminum exhibits shear creep resistance more than four orders of magnitude higher than that of the unalloyed aluminum and can be loaded at shear stress levels exceeding two times those of the pure aluminum material. K e y w o r d s : Shear creep testing, Al, AI-AI4C3 composite, elevated temperature, F.E. analysis