Variable Normal Load Research Articles

Optimal normal load variation in wedge-shaped Coulomb dampers

Wedge-shaped frictional dampers are widely used in civil, mechanical and aeronautical engineering with the purpose to limit and damp vibrations, increase component fatigue life, or resist seismic loads. The wedge shape induces normal load variations which complicates the analysis. Here, we study a model which can be considered a generalization of the Griffin model, originally devised for underplatform dampers in turbine blade attachments. The model has a mass element (the body whose vibrations are to be damped) linked to the wall by means of a spring and to a massless Coulomb damper via a “contact stiffness". In Griffin’s work the normal load acting on the Coulomb damper was kept constant. We introduce cyclic amplitude of the normal load, and phase shift between tangential and normal load. It is found that the optimization curves maintain the minimum for the mean normal load expected by Griffin’s model. However, a lower vibration amplitude is found for in-phase loading with respect to the constant load, over the entire frequency range. When the “contact stiffness" is higher than the structure stiffness (as it is generally expected), the maximum vibration decrement for in-phase loading is around 40%.

Steady-State Response of a Piping System Under Harmonic Excitations Considering Pipe-Support Friction With Variable Normal Loads

Dynamic loads in piping systems are mainly caused by transient phenomena generated by operating conditions or installed equipment. In most cases, these dynamic loads may be modeled as harmonic excitations, e.g., pulsating flow. On the other hand, when designing piping systems under dynamic loads, it is a common practice to neglect strong nonlinearities such as shocks and friction between pipe and support surfaces, mainly because of the excessive cost in terms of computational time and the complexity associated with the integration of the nonlinear equations of motion. However, disregarding these nonlinearities for some systems may result in overestimated dynamic amplitudes leading to incorrect analysis and designs. This paper presents a numerical approach to calculate the steady-state response amplitudes of a piping system subjected to harmonic excitations and considering dry friction between the pipe and the support surfaces, without performing a numerical integration. The proposed approach permits the analysis of three dimensional piping systems, where the normal forces may vary in time and is based in the hybrid frequency–time domain method (HFT). Results of the proposed approach are compared and discussed with those of a full integration scheme, confirming that HFT is a valid and computationally feasible option.

Effect of normal load variation on the frictional behavior of a simple Coulomb frictional oscillator

Various authors have studied the frictional contact problem for a simple concentrated mass under periodic forcing terms. In this paper, we give some additional closed form results for this problem for both the quasi-static limit and the full dynamic regime. We find in particular the regime where normal load is high enough to obtain a bounded displacement at all frequencies, which is of particular interest for “optimal” damping: in this case, the dynamic solution involves 2 stops of finite time. Contrary to the quasi-static prediction, the effect of normal load variation can decrease the peak displacement amplitude for in-phase loading up to the 80 percent. Moreover, similar to the quasi-static prediction, it can lead to a very large increase (up to more than 200 percent) for quadrature loading. Similar pattern is found for the frictional dissipation per cycle. For in-phase loading, therefore, the vibratory motion is damped more effectively, with additional beneficial effects on joint lifetime.

Rate-state friction in microelectromechanical systems interfaces: Experiment and theory

A microscale, multi-asperity frictional test platform has been designed that allows for wide variation of normal load, spring constant, and puller step frequency. Two different monolayer coatings have been applied to the surfaces—tridecafluorotris(dimethylamino)silane (FOTAS, CF3(CF2)5(CH2)2 Si(N(CH3)2)3) and octadecyltrichlorosilane (OTS, CH3(CH2)17SiCl3). Static friction aging was observed for both coatings. Simulating the platform using a modified rate-state model with discrete actuator steps results in good agreement with experiments over a wide control parameter subspace using system parameters extracted from experiments. Experimental and modeling results indicate that (1) contacts strengthen with rest time, exponentially approaching a maximum value and rejuvenating after inertial events, and (2) velocity strengthening is needed to explain the shorter than expected length of slips after the friction block transitions from a stick state. We suggest that aging occurs because tail groups in the monolayer coatings reconfigure readily upon initial contact with an opposing countersurface. The reconfiguration is limited by the constraint that head groups are covalently bound to the substrate.

Nonlinear Dynamics of Shrouded Turbine Blade System with Impact and Friction

Dry friction dampers are passive devices used to reduce the resonant vibration amplitudes in turbine bladed systems. In shrouded turbine blade systems, in addition to the stick- slip motion induced by dry friction during the contact state in the tangential direction, the interface also undergoes intermittent separation in the normal direction. The problem can thus be treated as a combination of impact and friction. In this work, the dynamics of dry friction damped oscillators which are representative models of dry friction damped bladed system is investigated. A one dimensional contact model which is capable of modeling the interface under constant and variable normal load is used. The steady state periodic solutions are obtained by multi - harmonic balance method (MHBM). Frequency response plots are generated for different values of normal load using the arc length continuation procedure. The MHBM solutions are validated using numerical integration. A single degree of freedom (dof) model under constant normal load with constant and variable friction coefficients, a dry friction damped two dof system under constant normal load and a two dof system under variable normal load are investigated. In the presence of variable normal load, the system shows multivalued frequency response and jump phenomenon. The optimal value of the normal load which gives minimum resonant response is also obtained.

Development of generalized Iwan model to simulate frictional contacts with variable normal loads

Most friction models are originally proposed to predict restoring forces in mechanical contacts with constant normal load. In practice the contact interface kinematics may involve normal motion in addition to the tangential displacements, leading to variation of the contact normal load. This phenomenon is observed most strongly in contacts with high lateral vibration amplitudes and is known as slap. The current study establishes a general friction model to account for variation in the normal load and enables one to predict the behavior of a contact more precisely. Iwan model (1966) [5] is a suitable candidate for contact interface modeling and is able to represent the stick-micro/macro slip behavior involved in a friction contact. This physical based model is employed in the current work and its physical parameters are generalized to include the normal load variation effects. The model is characterized by a slippage distribution density function and a linear stiffness at stick state. Both these parameters, defined in presence of constant normal load in the original model, are derived considering normal load variation leading to generalization of the contact model. Conventional models with constant normal loads produce symmetric contact interface hysteresis loops, but the developed generalized Iwan model is capable of generating asymmetric hysteresis loops similar to those frequently seen in experiments. The generalized contact model is employed to simulate the measured behavior of a beam with frictional support observed in an experimental test set-up. The contact slippage distribution function is first identified in a constant normal load condition. Next in low levels of contact preloads where variation of the normal load is significant, the identified distribution function in generalized form is employed to predict the experimental observations.

Dry Sliding Wear and Friction Behavior of Cu-SiC Nanocomposite Coating Prepared by Pulse Reverse Electrodeposition

The dry sliding wear and friction behavior of Cu-SiC nanocomposite coatings prepared by pulse-reverse co-electrodeposition technique has been evaluated using a ball-on-disk wear instrument. The effect of variation in normal load and sliding speed on wear and friction behavior was studied. This behavior was compared with two other pure specimens, one prepared under conditions similar to those of the composite and the other by casting and rolling. From the wear test it was observed that the wear rate of the nanocomposite increases with an increase in normal load, whereas it decreases with an increase in sliding speed. The coefficient of friction increases with an increase in sliding speed. However, with normal load variation, it shows a minimum at an intermediate load. In all tests the composite shows the lowest wear rate and coefficient of friction except at the highest load tested, where it is observed to show a coefficient of friction similar to that of the electrodeposited pure Cu.

Fracture Analysis of a Curvilinearly Stiffener Panel Subjected to Multiple Combined Loadings

A global–local finite element analysis was performed to study the damage tolerance of curvilinearly stiffened panels, fabricated using the modern additive-manufacturing process that can create so-called unitized structures. In the first step, a buckling analysis of panels was performed to determine whether the panels satisfied the buckling constraint in an undamaged state. In the second step, stress distributions in the panel were analyzed to determine the location of the critical stress under combined shear and compression loadings. Then, a fracture analysis of the curvilinearly stiffened panel with a crack designed at the earlier-obtained location of the critical stress, which was the common location with the maximum magnitude of the principal stresses and von Mises stress, was performed under combined shear and tensile loadings. A mesh-sensitivity analysis was performed to validate the choice of the mesh density near the crack tip. All analyses were performed using the global–local finite element method using MSC.Marc, and the global finite element methods using MSC.Marc and ABAQUS. A negligible difference in results and 94% savings in the CPU time were achieved using the global–local finite element method over the global finite element method by using a mesh density of 8.4 element/mm ahead of the crack tip. To study the influence of different loads on basic modes of fracture, the shear and normal (tensile) loads were varied differently. It was observed that the case with the fixed shear load but variable normal loads, and the case with the fixed normal load but variable shear loads were mode I. Under the maximum combined-loading condition, the largest effective stress-intensity factor was much smaller than the critical-stress-intensity factor.

Power loss minimization considering short‐circuit capacity in distribution system with decentralized distributed generation

AbstractIn the future, a large number of distributed generators are expected to be connected to the distribution system. However, with the connected capacity of distributed generation (DG) increasing, the problems of short‐circuit capacity (SCC) over the interrupting capacity of the circuit breaker (CB) and power loss increases due to reverse power flow from DG are inevitable. In this paper, a reconfiguration methodology based on an optimal algorithm is applied to the distribution system with DG to minimize power loss, taking into account the SCC. Moreover, in order to further reduce the loss, the daily load variation is also considered and the optimal model decided by calculations. Finally, to illustrate its application, the methodology is applied to a case study of a 33‐bus system with decentralized DG units. The results show that this method is obviously able to reduce power loss and make the network operate in the optimal mode with normal load variation, at the same time decreasing the SCC within the interrupting maximum of the faulty CB. Moreover, the whole voltage profile is also improved. © 2012 Institute of Electrical Engineers of Japan. Published by John Wiley & Sons, Inc.

A novel approach to measuring the frictional behaviour of human skin in vivo

Friction involving human skin plays a key role in human life. The availability of a portable tribometer improves the accessibility to large number of both subjects and anatomical sites. This is the first mobile device suitable to measure skin friction with a controlled and variable normal load (range 0.5–2N) and velocity (range 1–10mm/s) of a material of choice making a sliding rotational movement over the skin.The results of a pilot study, using stainless steel samples on the ventral forearm compare to results in the literature. The new device can be used for more extensive research to found these results and determine the effects of normal load or sliding velocity on the skin's frictional behaviour.

Modeling and identification of frictional forces at a contact interface experiencing micro-vibro-impacts

Modeling and identification of restoring forces at contact interfaces is an inevitable part of investigating the dynamic characteristics of mechanical systems. As the vibration amplitude increases, various nonlinear mechanisms such as micro/macro-slip and micro-impacts activate in the interface. This paper considers the nonlinear behavior of a frictional contact in situations where micro-impacts develop in the normal direction to the friction surface. It investigates the effect of variable normal load on the contact frictional forces, and defines a friction model capable of taking into account this effect. In an experimental case study, the contact is excited using a dual sine force to allow a reliable dual-mode identification procedure. The measured data and the normal modes of the corresponding linear system are employed to define the system nonlinear modes used to expand the system response. This provides a reduced order model containing dominant nonlinear effects in the contact interface. Force state mapping method is employed to identify the contact restoring forces. The experimentally obtained forces are employed to determine the parameters of a new friction law defied by modifying the Valanis model. It is shown the model is capable of predicting the main nonlinear characteristics of the contact interface and regenerates the experimental results at different vibration response levels.

An experimental study of the scratch properties of poly(methyl methacrylate) as a function of the concentration of added slip agent

A scratch test was performed on poly(methyl methacrylate) (PMMA) material that had been optimised for electronic products. In this study, the scratch properties of PMMA containing various concentrations of slip agent were investigated by performing scratch tests under two different load conditions, i.e., a static normal load and a variable normal load. The effects of the concentration of slip agent on the scratch properties of PMMA were characterised by some key tribological parameters, based on a new standard test methodology. Additionally, the damaged surfaces of the specimens were investigated to understand the variations in scratch mechanisms.

Wear behavior of aluminum matrix hybrid nanocomposites fabricated by powder metallurgy

Abstract In the present article, the dry sliding wear behavior of aluminum matrix nanocomposites containing various amounts of Al2O3–AlB12 (5, 10 and 15 wt.%) particles was investigated. All specimens were prepared by mechanical milling of Al and Al2O3–AlB12 nanocomposite powders, followed by hot pressing. Wear tests were carried out at room temperature in air using the pin-on-disc machine under variable normal loads. The counterface was an AISI 52100 steel pin with the hardness of 780 HV. Friction values and wear mechanisms are discussed based on scanning electron microscopy observations and energy-dispersive spectroscopy analysis of wear tracks and wear debris morphology. The average hardness of the nanocomposite increased with the percentage of added Al2O3–AlB12 particles. Results confirmed that worn surfaces of all nanocomposite samples tested under variable loads, covered by a mechanically mixed layer (MML), contained a considerable amount of oxygen and iron. The results indicated that higher Al2O3–AlB12 content in the nanocomposite promotes stronger material transfer from the counterface and oxidation reaction and, consequently, causes formation of protective MML with higher amount of oxide compounds content on the worn surface of nanocomposite, leading to the lower wear rate. After a certain sliding distance, the friction coefficient of the nanocomposites reduced and tended to attain a constant value. The formation of MML on the worn surface which can act as a lubricant seems to be responsible for this trend.

Dry wear of NiAl 3-reinforced mechanically alloyed aluminium with different microstructure

The tribological behaviour of mechanically alloyed (MA) aluminium-base materials reinforced by 2 vol.% NiAl 3, either as large lamellae (MA Al–Ni S) or as homogeneously dispersed rounded particles (MA Al–Ni S2) has been studied. The results are compared with that of nickel-free MA aluminium (MA Al S), taken as reference. All materials were prepared by mechanical milling of Al powder, eventually with the addition of 1 wt% Ni powder, followed by consolidation techniques of cold compaction and sintering. Tribological tests were carried out using the pin-on-disc configuration under variable normal load and temperature. MA Al–Ni S2 shows the highest wear reduction with respect to MA Al–Ni S at the highest load studied. At low load and high temperature, MA Al–Ni S2 shows the highest wear rate, probably due to severe abrasion of the steel counterpart. Friction values and wear mechanisms are discussed from SEM observations and EDS analysis of wear tracks, wear debris morphology and transfer tribolayers.

Fretting wear of SiAlON ceramic

Friction andwear properties of Si6- Z Al zO zN8- Z ( z = 0.5) were studied in case of fretting. SiAlON samples were prepared by hot pressing without any externally added liquid. The effect of running time, slip amplitude, and normal load on friction and wear were investigated. A constant coefficient of 0.45 was observed during running time; however, friction coefficient increased from 0.445 to 0.475 for normal load variation of 20N to 60N. Wear increased linearly with the increase in sliding time and normal load for both SiAlON and steel; however, it decreased with the increase in slip amplitude. Higher wear was observed at low amplitudes as compared with wear at higher amplitudes. Transition from higher wear to lower wear occurred at fretting amplitude of 100–150μm. Wear coefficient of 7.0 × 10−4 and 18 × 10−4 was observed for SiAlON and steel, respectively. Micrographs proved useful for understanding wear mechanism. The wear in SiAlON/steel tribopair was caused by a combination of third body abrasion, tribofilm formation, and minor scoring.

Effect of microstructure on slurry abrasion response of En-31 steel

Wear by slurry abrasion occurs in extruders, slurry pumps, and pipes carrying slurry of minerals and ores in mineral processing industries. The wear life of components used under slurry abrasion conditions is governed by the process parameters, properties of abrasive particles in slurry and material properties. In the present work slurry abrasion response of heat treated En-31 steel was studied. The quenched and tempered specimens of En-31 steel, tempered at different temperatures, were used in the present investigation. The slurry abrasion tests were performed using slurry abrasion test apparatus with silica sand as the abrasive medium. The effect of sliding distance, normal load and slurry concentration on volume loss was evaluated. The experiments were also carried with simultaneous variation of normal load and sliding distance. The results of the present work were explained by a model, V = ( K × S × L)/( H) 2/3, where V is the volume loss in slurry abrasion, S is the sliding distance, L is the normal load, H is the bulk hardness of the surface and K is wear coefficient. The morphology of the worn surfaces after slurry abrasion was studied under scanning electron microscope. The morphological studies of the worn surfaces revealed characteristic differences in the wear pattern under different test conditions. The operating mechanisms of material removal involved ploughing and cutting.

A microslip friction model with normal load variation induced by normal motion

A two-dimensional microslip friction model with normal load variation induced by normal motion is presented in this paper. The model is a distributed parameter model, which characterizes the stick-slip-separation of the contact interface and determines the resulting friction force, including its time variance and spatial distribution, between two elastic structures. When the relative motion is simple harmonic motion, the stick-slip-separation transition angles associated with any point in the contact area can be analytically determined within a cycle of motion. In addition, if the relative motion is given, stick-slip-separation transition boundaries inside the contact area and their time variances can be determined. Along with an iterative multi-mode solution approach utilizing harmonic balance method (HBM), the developed model can be employed to determine the forced response of frictionally constrained structures. In the approach, the forced response is constructed in terms of the free mode shapes of the structure; consequently, it can be determined at any excitation frequency and for any type of normal load distribution. Two examples, a one-dimensional beam like damper and a more realistic blade to ground damper, are employed to illustrate the predictive abilities of the developed model. It is shown that while employing a single mode model, transition boundaries for the beam like damper agrees with the results given in the literature, the developed method identifies the phase difference along the slip to stick transition boundary when a multi-mode model is employed. Moreover, while partial slip is illustrated in the two examples, typical softening and hardening effects, due to separation of the contact surface, are also predicted for the blade to ground damper.

Advanced Modeling of Underplatform Friction Dampers for Analysis of Bladed Disk Vibration

Advanced structural dynamic models for both wedge and split underplatform dampers have been developed. The new damper models take into account inertia forces and the effects of normal load variation on stick-slip transitions at the contact interfaces. The damper models are formulated for the general case of multiharmonic forced response analysis. An approach for using the new damper models in the dynamic analysis of large-scale finite element models of bladed disks is proposed and realized. Numerical investigations of bladed disks are performed to demonstrate the capabilities of the new models and an analysis of the influence of the damper parameters on the forced response of bladed disks is made.

Effects of Damping and Varying Contact Area at Blade-Disk Joints in Forced Response Analysis of Bladed Disk Assemblies

An approach is developed to analyze the multiharmonic forced response of large-scale finite element models of bladed disks taking account of the nonlinear forces acting at the contact interfaces of blade roots. Area contact interaction is modeled by area friction contact elements which allow for friction stresses under variable normal load, unilateral contacts, clearances, and interferences. Examples of application of the new approach to the analysis of root damping and forced response levels are given and numerical investigations of effects of contact conditions at root joints and excitation levels are explored for practical bladed disks.

Method for Direct Parametric Analysis of Nonlinear Forced Response of Bladed Disks With Friction Contact Interfaces

An effective method for direct parametric analysis of periodic nonlinear forced response of bladed disks with friction contact interfaces has been developed. The method allows, forced response levels to be calculated directly as a function of contact interface parameters such as the friction coefficient, contact surface stiffness (normal and tangential coefficients), clearances, interferences, and the normal stresses at the contact interfaces. The method is based on exact expressions for sensitivities of the multiharmonic interaction forces with respect to variation of all parameters of the friction contact interfaces. These novel expressions are derived in the paper for a friction contact model, accounting for the normal load variation and the possibility of separation-contact transitions. Numerical analysis of effects of the contact parameters on forced response levels has been performed using large-scale finite element models of a practical bladed turbine disk with underplatform dampers and with shroud contacts.