Rigidity Of Shafts Research Articles

Experimental investigation of moving contact pattern in helical planetary gearboxes

Planetary gear sets combine the characteristics of high-power density and compact design which are beneficial for a wide range of high-performance applications. Embedded in the efforts for resource efficiency and cost reduction, new challenges arise regarding a lightweight design. An accurate prediction of the load sharing on the individual planetary gears and especially of the load distribution of the meshing gears is of major importance. A uniform load distribution enables the design of the individual tooth meshes without load increases and oversizing. However, a varying load distribution has been observed in planetary gearboxes with respect to the rotation of the carrier which is caused by misaligned central shafts of the gearbox. This behavior is influenced by several factors, such as manufacturing and assembly deviations, the rigidity of shafts, housing and bearings, the number of planets, the quality of the gear wheels and the operating conditions. To determine the exact load distribution, detailed simulations or extensive experimental prototype tests are required. In an early design phase, these detailed boundary conditions are not yet defined and their effect on a moving contact pattern therefore cannot be reliably considered.Thus, in this paper an experimental investigation of the influencing factors on a varying load distribution with regard to the carrier rotation is presented. Based on experimental data recommendations for the design of planetary gearboxes are derived.

Experimental investigation of the dynamic load sharing of planetary gearboxes

Due to their compactness and power density, planetary gearboxes are used for a wide range of high-performance applications in the automotive, aviation and marine sector. Aerospace applications in particular benefit from a full use of the load capacity potential to meet the requirements for lightweight construction and efficiency. Against this background, the load sharing between the individual planetary gears plays a decisive role. A uniform load sharing enables the design of the single tooth meshes without load increases and oversizing. However, due to manufacturing and assembly deviations, a perfect load sharing is technically not feasible. These load increases are taken into account in the standard calculation of the load capacity of planetary gearboxes by the mesh load factor Kγ. The load sharing in planetary gearboxes is influenced by a number of factors, such as the rigidity of shafts, housing and bearings, the number of planets, the quality of the gear wheels and the operating conditions. Detailed simulations or extensive experimental measurements are required to determine the exact load sharing. For new designs of planetary gearboxes, there are only simplified assumptions available, based on the number of planets and a rough estimation of the operating range. Especially additional dynamic forces, due to operation in high-speed ranges or near resonance frequencies, can lead to a considerable change of the dynamic load sharing compared to the static load sharing and cause an uncertainty in the design. Thus, in this paper the dynamic load sharing behaviour is investigated from 0 to 6800 rpm sun speed for different loads. Based on the experimental data recommendations for the design of planetary gearboxes under consideration of the operating conditions are derived.

Increase of bending rigidity of long-dimensional shaft by surface plastic deformation

The results of computer simulation of bending stiffness of cylindrical part are presented. The effect of residual stresses on the maximum bending is considered. It is established that the formation of residual stresses in the surface layers of a certain thickness have a positive effect on increasing the rigidity of the cylindrical pieces. The influence of the degree of relative deformation with the covering surface plastic deformation on the flexural rigidity of long shafts is determined. It is established that the degree of relative deformation in the range from 0.4 to 1.0% has a positive effect on the flexural rigidity of the shafts. The process in question can be implemented without the use of environmentally hazardous lubricating cooling technological means, which makes it possible to attribute it in the future to one of the types of green mechanical processing technologies.

Influence of surface plastic deformation on the flexural rigidity of shafts

In complete surface plastic deformation, the influence of the reduction on the residual stress and its distribution in long shafts is investigated.

Accuracy Control in the Machining of Low Rigidity Shafts

The study determines the most suitable pattern of alignment and fixing of low-rigidity shafts; it also presents factors that determine such choice. The part is fixed both by force closing and kinematic closing. A new method for machining low rigidity shafts is developed to control the elastic-deformable state of these shafts in a technological system and to produce parts with the required accuracy during turning. To implement this new developed method for low rigidity shafts, an apparatus is designed. The apparatus allows to increase the rigidity of shafts during machining by the application of axial tensile force to the workpiece. Rational prime costs of preparing technological alignment centers at the stage of production preparation are determined; knowing these costs, it is possible to select a suitable machining technology for low rigidity shafts, to produce a technology-oriented design, and to reduce the costs of machining these shafts.

A Recipe for Building the Torsional-Rigidity Bounds of Shafts Containing Multiply Coated Fibers with Imperfect Interfaces

This work is concerned with deriving the upper and lower bounds for the torsional rigidity of cylindrical shafts with arbitrary cross-section containing a number of multiply coated fibers with imperfect interfaces along the interfaces. Each multicoated fiber may have different constituents with different area fractions. In the formulation, we first extend our previous formulation, based on classical energy principles in elasticity, to construct torsional rigidity bounds for shafts containing simply coated fibers with two different kinds of imperfect interface. Next, based on the present results for shafts containing simply coated fibers and our previous findings for shafts containing homogeneous fibers with imperfectly bonded interfaces, we propose a concept of replacement fiber with an effective shear rigidity to replace the effect of fiber with imperfect bonding interface. In addition, we propose an equivalent shear rigidity to simulate the effect of a simply coated fiber. This replacement procedure allows us to construct the bounds, through a recursive procedure, for the torsional rigidity of shafts containing multiply coated fibers with possibly imperfect interfaces.

Bounds for the torsional rigidity of shafts with arbitrary cross-sections containing cylindrically orthotropic fibres or coated fibres

In this paper we derive bounds for the torsional rigidity of a cylindrical shaft with arbitrary transverse cross-section containing a number of cylindrically orthotropic fibres or coated fibres. The exact upper and lower bounds depend on the constituent shear rigidities, the area fractions, the locations of the reinforcements as well as the geometric shape of the cross-sections. Specific bounds are derived for circular shafts, elliptical shafts and cross-sections of equilateral triangle. Simplified expressions are also deduced for reinforcements with isotropic constituents. We verify that when additional constraints between the constituent properties of the phases are fulfilled, the upper and lower bounds will coincide. In the latter case, the fibres or coated fibres become neutral under torsion and the bounds recover the previously known exact torsional rigidity.

Method for calculating the rigidity of shafts of the reducer of rocking machines

Method for calculating the rigidity of shafts of the reducer of rocking machines

Bending Rigidity of Shafts with Transverse Grooves

Bending Rigidity of Shafts with Transverse Grooves

The Measurement of the Modulus of Rigidity of Intermediate Shafts

The accuracy of shaft horse power measured by torsion-meter depends upon those of both modulus of rigidity of shaft measured at land and torsional strain measured at sea. As the method of measuring the latter were already given by the Author in the Journal of Soc. N. A. Japan, No. 52, published on 1933, he intends to explain in this paper the accurate method of measuring the former and give the measured results on the modulus of rigidities of the intermediate shafts of thirty six merchant ships.