Common to liquids, solids and substances in between the former two is that if a stress is applied to them, they will strain. Stress may be visualized by placing a small amount of fluid between two parallel plates. When one plate slides over the other, forces act on the fluid dependent upon the rate of the plate movement. This causes a shear stress on the liquid. Recall laminar flow of fluids through a tubular vessel. Strain is the response to the stress. If solids are elastic, they deform and return to their original shape. Since fluids are not elastic and, hence, viscous, their deformation is irreversible.

Introduction to rheology

Mesh stiffness calculation of a spur gear pair with tooth profile modification and tooth root crack

The paper presents a review of multiaxial fatigue failure criteria based on the critical plane concept. The criteria have been divided into three groups, according to the fatigue damage parameter used in the criterion, i.e. (i) stress, (ii) strain and (iii) strain energy density criteria. Each criterion was described mainly by the critical plane orientation. Multiaxial fatigue criteria based on the critical plane concept usually apply different loading parameters in the critical plane whose orientation is determined by (a) only shear loading parameters (crack Mode II or III), (b) only normal loading parameters (crack Mode I) or sometimes (c) mixed loading parameters (mixed crack Mode). There are also criteria based on few critical plane orientations and criteria based on critical plane orientations determined by a weighted averaging process of rotating principal stress axes.

A Review of Critical Plane Orientations in Multiaxial Fatigue Failure Criteria of Metallic Materials

This paper presents a method for estimating high-cycle fatigue strength under multiaxial loading conditions. The physical interpretation of the fatigue damage is based on the theory of cyclic deformation in single crystals. Such a theory is also used to single out those stress components which can be considered significant for crack nucleation and growth in the so-called Stage I regime. Fatigue life estimates are carried out by means of a modified Wohler curve which can be applied to both smooth and blunt notched components, subjected to either in-phase or out-of-phase loads. The modified Wohler curve plots the fatigue strength in terms of the maximum macroscopic shear stress amplitudes, the reference plane - where such amplitudes have to be evaluated - being thought of as coincident with the fatigue microcrack initiation plane. The position of the fatigue strength curve also depends on the stress component normal to such a plane and the phase angle as well. About 450 experimental data taken from the literature are used to check the accuracy of the method under multiaxial fatigue conditions.

A bi-parametric Wöhler curve for high cycle multiaxial fatigue assessment

Critical plane approaches are useful methods when designing against long-term fatigue of machine components made from metals. Somewhat surprisingly, the very basic problem of the evaluation of the amplitude and mean value of the shear stress acting on the critical plane is still not resolved satisfactorily for non-proportional cyclic loading conditions. In the present paper, existing proposals for solving this problem are briefly reviewed and their weaknesses highlighted. Then it is shown, through particular examples, that application of these proposals can lead to ambiguous results. Therefore, new definitions of the amplitude and mean value of the shear stress acting on the critical plane are formulated here. These new definitions are free from any ambiguity because they are based on the construction of the unique minimum-circumscribed circle to the path described by the shear stress on the critical plane. The centre of this circle defines the mean shear stress, whereas its radius provides the corresponding shear stress amplitude. The algorithm yielding this minimum-circumscribed circle is presented in some detail.

https://onlinelibrary.wiley.com/doi/pdf/10.1046/j.1460-2695.1998.00459.x

Critical plane approaches in high-cycle fatigue : On the definition of the amplitude and mean value of the shear stress acting on the critical plane

A comparative study of multiaxial high-cycle fatigue criteria for metals

Compared with common speed reducers, the cycloidal ones (also known as cycloid drives) cover a wider range of transmission ratios, have a higher load-carrying capacity, are smaller, exhibit a smoother running and a good efficiency. These characteristics make them attractive for industrial applications, especially for robotics applications, machine tools and linear axis positioning in assembly machinery. In this paper, a theoretical and experimental investigation on an innovative cycloidal speed reducer will be presented. The typical cycloid drive has a planet wheel, the profile of which is the inner offset of an epitrochoid, meshing with cylindrical rollers connected to the case. This reducer, on the contrary, has an external ring gear, the transverse profile of which is the external offset of an epitrochoid, and engages with the planet wheel by means of cylindrical rollers. This paper will investigate the structural characteristics and the kinematical principles of this type of reducer. A theoretical approach based on the envelope theory (following Litvin’s approach) will be developed and compared with a development of Blanche and Yang’s approach. Furthermore, a simplified procedure to calculate force distribution on cycloid drive elements, as well as its power losses and theoretical mechanical efficiency will be presented. The effects of design parameters on the values of the forces will be studied, for an optimal design of this type of reducer. The theoretical model will be then tuned using the results of tests on a specific rig. As a result of the experimental tests, the reducer mechanical efficiency dependency on speed and torque will be described. The aim of this work is to perform the fine tuning of a theoretical model in order to predict the operating behavior of the cycloid drive, and to improve its design procedure.Copyright © 2007 by ASME

Theoretical and Experimental Analysis of a Cycloidal Speed Reducer

Numerical modeling of the power losses in geared transmissions: Windage, churning and cavitation simulations with a new integrated approach that drastically reduces the computational effort

Nowadays, the basic requirements of gear transmissions are not limited to resistance and reliability, but often include good efficiency and low vibration and noise emissions. This article i...

Carlo Gorla

Papers

A comparative study of multiaxial high-cycle fatigue criteria for metals

Theoretical and Experimental Analysis of a Cycloidal Speed Reducer

Numerical modeling of the power losses in geared transmissions: Windage, churning and cavitation simulations with a new integrated approach that drastically reduces the computational effort

The effects of the shape of tooth profile modifications on the transmission error, bending, and contact stress of spur gears:

Hydraulic losses of a gearbox: CFD analysis and experiments