Robert J. Rogers

Factors associated with support plate forces due to heat-exchanger tube vibratory contact

Abstract Studies have been made of several of the factors associated with the forces resulting from a heat-exchanger tube vibrating against its support plate. Finite element simulation results are compared with the behaviour of a cantilevered tube apparatus with two-dimensional sinusoidal excitation in air. The accuracy of the simulation technique is shown over a range of excitations. Simulations are then used to study the effects of varying the friction, damping, tube/annulus stiffness and clearance on the r.m.s. contact forces.

Combined Lagrangian multiplier and penalty function finite element technique for elastic impact analysis

Abstract A new finite element procedure which combines the Lagrangian multiplier method and the penalty function method for dynamic contact analysis with friction is presented in this paper. As a result of this combination, the whole contact system can be analyzed as one body in both contact and separation states. No displacement constraints are required on the striker and no extra stress due to gap elements is created. Coulombs friction law is employed to set up sliding and sticking conditions and discrete impact and release conditions are implemented. A two-dimensional analysis for the longitudinal impact of two rods is solved as a numerical example. The average values of stress and the time durations are very close to the theoretical solution.

An Experimental Study of Contact Forces During Oblique Elastic Impact

Low and high speed impacts frequently occur in many mechanical processes. Although widely studied, rarely are normal and tangential force time-waveforms measured, as generally these are very difficult measurements to do accurately. This paper presents, for the first time, a comprehensive set of experimentally obtained contact force waveforms during oblique elastic impact for a range of initial velocities and incidence angles. The experimental apparatus employed in this study was a simple pendulum consisting of a spherical steel striker suspended from a steel wire. The contact force time-waveforms were collected using a tri-axial piezoelectric force transducer sandwiched between a spherical target cap and a large block. The measured contact forces showed that loading was essentially limited to the normal and tangential directions in the horizontal plane. Analysis of the maximum normal and tangential forces for the near glancing angles of incidence indicated a friction coefficient that varies linearly with initial tangential velocity. The essential features of tangential force reversal during impact predicted by previous continuum models are confirmed by the experimental force results.

A NUMERICAL INVESTIGATION OF THE CHIP TOOL INTERFACE IN ORTHOGONAL MACHINING

A plane-strain thermo-elasto-viscoplastic finite element model has been developed and used to simulate orthogonal machining of 304L stainless steel using a ceramic tool. Simulations were carried out employing temperature-dependent physical properties. The model is used to investigate the effect of process parameters, tool geometry and edge preparation on the contact mechanics at the chip/tool interface. Stress and strain within the chip and the elastic tool are presented. Variables at the chip/tool interface such as contact length, sticking and sliding regions, normal and shear stresses, and frictional heat are investigated. Plastic deformation beneath the machined surface is compared for sharp and chamfered tools.

An Experimental Study of Friction During Planar Elastic Impact

Low-speed oblique elastic impacts frequently occur in heat exchangers and other equipment having loosely supported tubes or pipes. In order to experimentally study friction during such impacts, a pendulum-type impact apparatus was developed. A hardened steel sphere at the end of the pendulum collides with a flat steel surface for a range of approach velocities and angles. The present investigation examined eight velocities from 8 to 93 mm/s and impact angles (measured from the common normal) of 0 to 75 deg for each velocity. The normal and tangential contact force waveforms were measured using a triaxial piezoelectric force transducer which was dynamically calibrated. As expected, the results show that the tangential force is less than the limiting Amontons-Coulomb friction predictions at low impact angles. Two regimes of stick-slip and gross-slip friction are clearly distinguished by a new friction parameter called the specific traction ratio. Tangential force reversal was observed at low impact angles, indicating local tangential oscillations. The stick-slip results are consistent with a partial-slip model where the contact zone has a central sticking region surrounded by a ring area undergoing slip.

Analytical and experimental studies of tube/support interaction in multi-span heat exchanger tubes

Abstract Fretting damage of tubes in heat exchangers can be very costly and should be avoided. Information on vibratory responses and dynamic interaction between tubes and supports are prerequisites for understanding the relationship between frettingwear and tube vibration. A finite-element computation technique has been developed to predict the vibratory response and tube/support interaction of multi-span tubes. Experimental verficication of the computer prediction using a multi-span single tube apparatus has been performed in air and in water with clearance supports and with no-clearance supports. The natural frequencies, support impact forces and mid-span displacements of the experimental and analytical results were compared. The results are in fairly good agreement. An example is used to illustrate the application of the computation technique to a hypothetical heat exchanger tube. The life of the hypothetical heat exchanger tube is estimated based on the predicted support impact forces and existing wear data.

Proportional material damping in finite element impact analysis

Abstract A method is presented to implement proportional material damping into the combined Lagrangian multiplier and penalty function finite element technique for impact problems. The discrete impact and release conditions are modified to include extra structural damping terms. A two-dimensional analysis for the normal impact of a ring and a simulated spring is solved to illustrate the use of proportional material damping.

A Probabilistic Assessment Technique Applied to a Cracked Heat Exchanger Tube Subjected to Flow-Induced Vibration

Flow-induced vibration is a common phenomenon in shell-and-tube heat exchangers. The resulting vibration can lead to component failure by fretting wear due to tube-to-tube support impact or by fatigue. Due to manufacturing considerations, many parameters such as support clearance, alignment, and friction at the supports are not exactly known and are represented by statistical distributions. This makes the use of deterministic equations inaccurate. This paper presents a methodology that can be used during component operation to monitor known flaws and ensure safe operation. The methodology incorporates Monte Carlo simulations to predict remaining service life of a vibrating heat exchanger tube with a small circumferential through-wall crack next to the tube sheet. Vibration excitation includes turbulence and low-level fluid-elastic forces. Leakage calculations are made on the through-wall crack as it grows to fracture. A Weibull distribution is given for the time-to-fracture and for the time for the leak rate to reach a threshold value. This statistical information can then be used to assess the remaining service life and whether LBB criteria will be met.

Dynamic calibration of tri-axial piezoelectric force transducers

Applied dynamic loads are often difficult to measure accurately due to the dynamic response of the sensor used and the dependence of the sensors sensitivity on the mounting and loading details. For tri-axial force transducers, which are capable of measuring forces along the axial direction and along both directions of the transducers face, dynamic calibration is further complicated by the coupling of the sensors measurement directions. For this reason, a new apparatus for dynamic calibration of normal and tangential directions of a tri-axial piezoelectric force transducer has been constructed and tested. The calibration force is provided from a spring loaded uni-axial impulse hammer. The apparatus allows for calibration at a variety of calibration angles and speeds; the loading for all cases of a nonzero calibration angle is oblique, with the point of force application being eccentric to the centerline of the force transducers normal axis. As such, tangential loads are always accompanied by a normal load. The calibration results show that the normal direction correction factors have a systematic dependence on the calibration angle; the tangential correction factors show some scatter but do not appear to be dependent on the calibration angle.

An Analytical Solution for Shear Stress Distributions During Oblique Elastic Impact of Similar Spheres

A new solution method for the oblique elastic impact of similar spheres with Coulomb friction is presented. The solution uses approximations of the shear stress distributions at each time step during impact. These distributions are solved from analytical formulations and are able to account for both full sliding and partial-slip scenarios that may both be present for this problem due to inclusion of tangential compliance and friction effects. Comparison to previous continuum models in the literature shows very good agreement for the contact force wave forms obtained. The major advantage of this method is the drastic reduction in computation time required compared to previous solutions.