Transient Contact Problem Research Articles

Numerical Approach for Detecting the Resonance Effects of Drilling during Assembly of Aircraft Structures

This paper is devoted to the development of a numerical approach that allows quick detection of the conditions favorable for the beginning of noticeable vibrations during drilling. The main novelty of the proposed approach lies in taking into account the deviations of the assembled compliant parts during non-stationary contact analysis by means of variation simulation. The approaches to stationary analysis of assembly quality are expanded and generalized for modeling such non-stationary effects as vibration and resonance. The numerical procedure is based on modeling the stress–strain state of the assembled structures by solving the corresponding transient contact problem. The use of Guyan reduction, the node-to-node contact model and the application of the generalized α method allow the reformulation of the contact problem in terms of a series of quadratic programming problems. The algorithm is thoroughly tested and validated with commercial software. The efficiency of the developed numerical procedure is illustrated by analysis of the test joints of two aircraft panels. The unsteady process of drilling the panels with periodic drilling force was simulated. The influence of deviations in the shape of the parts on the non-stationary interlayer gap was modeled by setting different initial gaps between parts. It is shown that the oscillation amplitudes of the interlayer gap depend on the initial gaps and do not correlate with the mean value of the stationary residual gap. Thus, non-stationary analysis provides new information about the quality of the assembly process, and it should be applied if the assembly process includes periodic impact on the assembled parts.

Finite-element transient calculation of a bell struck by a clapper

A finite-element calculation of a bell struck by the bell clapper was performed as a transient contact problem. The geometry of the bell was taken from a real bell which was carved especially in behalf of this research. The eigenmodes and eigenfrequencies of the bell were calculated in advance, being in good agreement with the measured frequencies. The clapper/bell contact time and impulse shape show the expected behavior. The impulse shape is a Gaussian impulse with a tendency of a sharper attack slope and a softer decay slope. The periodical shape of the spectrum of this impulse caused by its finite width with zero values for some frequencies is shown. Nevertheless, this spectrum also drives the frequencies of the bell within the low-amplitude region of the driving impulse with expected and measured strength. The reason for this mode energy transfer is discussed. Furthermore, the sound of the bell is calculated as radiation from its surface and analyzed with signal-processing tools like wavelet transforms or autoregressive models.

Finite element modelling of local contact conditions in gear teeth

The aim of the paper is to propose appropriate numerical methods and constitutive models for solution of the gear dynamic contact problem. This has been done through comparison with international gear standards. Such solution techniques are necessary for an accurate analysis of stress state and resultant design improvement of the complex gear configurations. This paper consists of two parts. The first part presents a solution of the general transient contact problem when the stress state of the tooth is studied. This has been carried out in two phases, initially using a coarse multiple-tooth finite element model to establish contact conditions and subsequently using a refined single-tooth-pair finite element model. Differences of up to 163 per cent were found between various international gear standards and the computed results. Various reasons for this have been discussed. The second part of the paper presents results from two types of local analysis which model viscoplasticity in the surface layer and defect generation respectively. These studies achieve a fuller understanding of the stress distribution in the contact zone, its deviation from the classical Hertzian closed-form solution and provide a firm basis for modelling the effect of gear dynamics on local damage, wear and failure. All the computations are made for single-tooth contact and procedures for optimizing the integration time step are used.

Effect of time-dependent speed on frictional heat generation and wear in transient axisymmetrical contact of sliding

A transient contact problem with frictional heating and wear for two nonuniform sliding half-spaces is considered. One of the two half-spaces is assumed to be slightly curved to give a Hertzian initial pressure distribution: the other is a rigid nonconductor. Under the assumption that the contact pressure distribution could be described by Hertz formulas during all the process of interaction, the problem is formulated in terms of one integral equation of Volterra type with unknown radius of contact area. A numerical solution of this equation is obtained using a piecewise-constant presentation of an unknown function. The influence of operating parameters on the contact temperature and the radius of the contact area is studied.

Resultant reactions in the transient contact problem for an anisotropic elastic half-space

The resultant contact forces and moments are determined for the initial stage of the interaction between an absolutely rigid smooth convex punch and an anisotropic elastic half-space within the framework of the three-dimensional transient problem, unlike the case of vertical indentation considered in [1].

Axi-symmetrical transient contact problem for sliding bodies with heat generation

A transient contact problem with frictional heating for two sliding half-spaces is considered. One of the two half-spaces is assumed to be slightly curved to give a Hertzian initial pressure distribution; the other is a rigid non-conductor. The problem is formulated in terms of one integral equation with unknown heat flux at the interface. The equation is solved numerically, using appropriately chosen Green's functions. Contact pressure and temperatures are found for various values of an independent parameter—the ratio of initial width of contact to the width in the steady state.

The plane transient contact problem for rough sliding bodies with wear and heat generation

Experimental investigation [1] corroborates the interdependence of processes and phenomena taking place in the contact of solids. Previous publications [2,3] are concerned with simultaneous calculation of the microgeometry of surfaces of bodies, their wear and the heat due to friction in the contact zone in steady contact problems. In the present paper an analogous contact problem has been considered. The model employs the Archard law of wear, in which the rate of material removal is proportional to pressure and speed of sliding. Contact pressure and temperatures at the interface are found from the solution of two governing integral equations. Green's functions are used to investigate the stresses and temperatures inside the two elastic bodies for a variety of material combinations and operating conditions.

Transient thermoelastic contact problem of two sliding half-planes

A transient contact problem with frictional heating for two sliding halfplanes is considered. One of the half-planes is slightly rounded to give a hertzian initial pressure distribution; the other is a rigid non-conductor. It is shown that if the ratio of initial width of contact to the width in the steady state is less than some critical value, the contact area shrinks smoothly until the steady state is reached. Otherwise the pressure distribution develops a wavy perturbation and eventually bifurcates. Results are compared with previous approximate solutions.