This paper presents an iterative method for calculating the effective contact ratio and the bending tooth stress for a pair of plastic/plastic and plastic/steel spur gears with an involute profile. In this method, the pinion and the gear are modeled, at each moment of the mesh cycle, as equivalent springs in parallel undergoing the same displacement along the line of action. This leads to the calculation of the bending stress by taking into account the number of teeth initially in contact and those which enter in contact prematurely. We also investigate the influence of certain gear parameters, such as, the number of teeth, the pressure angle, and the module on the behavior of a pair of meshed gears. In addition, the variation of the bending stress at the tooth fillet is investigated for a pair of plastic/plastic and a pair of plastic/steel spur gears, in order to determine the critical configurations for which the bending stress is maximum. In general, the results obtained from the present method also show that the stress variation in plastic/plastic gears differs markedly from that in plastic/steel gears.

Automation is conquering new fields on a daily basis. Aiming for faster and more reliable products, industrials as well as researchers are oriented into automation. Non-destructive testing as well as defect quantification is not an exception. In fact, decisions with minimum allowable error are sought in real-time when facing any potential defect. In this work, we suggest a comprehensive method based on model order reduction techniques to judge if a structure shall be salvaged. The real-time decision is based on multidimensional parametric simulation, performed offline, using the Proper Generalized Decomposition (PGD). The PGD is a model order reduction technique that allows circumventing the curse of dimensionality by using domain decomposition. Therefore, the 6D simulation illustrated in this paper is performed within a few minutes on a standard laptop. Later on, a stress concentration manifold is built and used online for decision-making. The manifold is validated on a few selected solutions solved analytically using an analytical procedure. The aforementioned procedure is developed, in this paper, to calculate the tangential stress around circular holes of different sizes, in an infinite isotropic plate containing any number of holes and subjected to in-plane pressure loading at the tip of the infinite plate. The procedure is based on determining two Muskhelishvili complex potentials in terms of complex Fourier series, and applying the Schwartz alternating method repeatedly until the boundary conditions on the contour of every hole are satisfied.

Automation is conquering new fields on a daily basis. Aiming for faster and more reliable products, industrials as well as researchers are oriented into automation. Non-destructive testing as well as defect quantification is not an exception. In fact, decisions with minimum allowable error are sought in real-time when facing any potential defect. In this work, we suggest a comprehensive method based on model order reduction techniques to judge if a structure shall be salvaged. The real-time decision is based on multidimensional parametric simulation, performed offline, using the Proper Generalized Decomposition (PGD). The PGD is a model order reduction technique that allows circumventing the curse of dimensionality by using domain decomposition. Therefore, the 6D simulation illustrated in this paper is performed within few minutes on a normal portable PC. Later on, a manifold is built and used online for decision-making.

A method for the calculation of the root and contact stresses for metal, spur and helical gears is presented in this work. The results of this method are verified by finite element calculations. This method enables the modeling of a pair of meshed gears during an interval of rotation by considering, for helical gears, a non-uniform load distribution along the lines of contact. Consequently, we were able to determine the parameters as well as the gear configurations for which the bending and contact stresses are maximum, in addition to relations directly yielding the critical bending and contact stress for a pair of mating spur and helical gears.

The Schwarz alternating method, along with Muskhelishvili's complex potential method, is used to calculate the stresses around non-intersecting circular holes in an infinite isotropic plate subjected to in-plane loads at infinity. The holes may have any size and may be disposed in any manner in the plate, and the loading may be in any direction.Complex Fourier series, whose coefficients are calculated using numerical integration, are incorporated within a Mathematica program for the determination of the tangential stress around any of the holes. The stress values obtained are then compared to published results in the literature and to results obtained using the finite element method.It is found that part of the results generated by the authors do not agree with some of the published ones, specifically, those pertaining to the locations and magnitudes of certain maximum stresses occurring around the contour of holes in a plate containing two holes at close proximity to each other. This is despite the fact that the results from the present authors' procedure have been verified several times by finite element calculations.The object of this paper is to present and discuss the results calculated using the authors' method and to underline the discrepancy mentioned above.

This paper presents a method for the calculation of the stresses around three non-intersecting identical circular holes in a row, in a thin and infinite isotropic plate subjected to in-plane longitudinal, transverse or biaxial tension at infinity. The calculation of the stresses around any of the three holes is obtained in terms of the stresses that would exist around and at the center of the contour of a third would-be hole in the plate, initially, containing two holes. The results from the present method are compared to finite element as well as to published results in the literature. It is seen that the method yields satisfactory results at key points around the contour of the holes.

Calculation methods of plastic helical gears with a real transverse contact ratio have never been studied in depth. The methods used in some references assume a uniform load distribution along the line of contact or don’t take into consideration the effect of premature mesh between one or more pair of teeth during engagement, which is not in good agreement with numerical results. This paper is focused on analysis of plastic helical gears. The nonuniform load distribution obtained from the proposed mathematical model is based on the calculation of the real contact ratio representing the real number of pairs of teeth in contact. This model also leads to the distribution of the tooth bending stress and the contact stress along the area of contact.

Analytical and finite element calculations are used to determine the mutual influence of three identical circular holes in a stressed isotropic plate. The plate is assumed to be infinitely long with a small thickness, and the loading consists of in-plane longitudinal, transverse or biaxial tension applied at infinity. The lines joining the centers of the holes form a triangle with sides that vary in length in order to study the influence of the holes proximity to each other on the stress field in the plate and on the stress concentration around the contour of any one of the holes. Furthermore, the finite element model is intended to corroborate results from an analytical method that the authors have previously developed.

The startling increase in performance, quality and sophistication in today's engineering products requires all agents participating in the process of product development to exchange information with one another through a product model, which enables the communication of the design between participants in the process of product development. The objective of this paper is to present a product model, which includes the assembly states to support various activities, involved in the assembly process. Because of its more comprehensive approach, this model both bridges the gap that exists in current Computer-Aided Design (CAD) and Manufacturing (CAM) systems and proves valuable in the design of all-inclusive systems combining various stages in the development of a product.

The objective of this work is to present a mathematical model which studies helical gears made of a material with a small modulus of elasticity, when one or more pairs of teeth mesh prematurely during engagement. This phenomenon may lead to the modification of the load distribution on the teeth which are initially in contact and to a kind of interference causing additional tooth wear of the gear. In this case, the calculation of the contact ratio must account for the real number of pairs of teeth in contact. This is especially important when large deformations occur as is confirmed in the results presented to confirm the validity of the proposed method.