Belleville Washers Research Articles

Experimental lap-shear tests on friction dampers with single and double slotted holes

Several experimental lap shear tests have been performed to assess the initial values of the slip resistance and their evolution during a cyclic loading history. Both friction dampers with parallel slotted holes and double slotted holes have been investigated. Friction devices with shims made of a previously tested material, called M4, have been tested and the tribological behaviour, the degradation of the friction coefficient, the influence of the bolts’ preload and the effect of Belleville washers have also been investigated. Moreover, a phenomenological model for the force-displacement response has been calibrated for the modelling of the cyclic response of the friction device. This is particularly important for the development of non-linear dynamic analyses of seismic resistant frames equipped with friction joints aiming at an accurate prediction of the structural response during a seismic event. Finally, a quality control of the friction properties of different batches of friction shims has been performed by means of the Fisher-Berens and Snedecor tests.

Design of Special Equipment for the Mechanical Testing of Runway Light Fixtures

Runway lights are essential components of the airstrip. However, there is currently no international standard that outlines methods for the testing of runway light fixtures. In this study, a novel testing method is developed to simulate the forces exerted on the lights during landing. The testing equipment is specifically designed to be easily mounted on a standard hydraulic press commonly used for tensile tests. This system allows for the regulation of the normal force between the aircraft tire and the fixture of the runway lighting system. To minimize load fluctuations during part sliding, Belleville washers are employed. The overall compliance of the system is validated through finite element analysis. Tests carried out by means of the proposed testing equipment allow the effective description of the variations in load at different positions during sliding. The system presented in this paper can be used to investigate the effects of landing on various combinations of cap design and tire material.

Exact shell solutions for conical springs. II. Radial cylindric curb

Actual manuscript examines the disk springs with constant material thickness. The kinematic hypothesis is used for modelling. Motivating feature is the possibility to calculate the disk springs of with free gliding edges and the edges with the constrained radial movement. Variation formulations are used for derivation. The developed equations are suitable for springs made of isotropic materials, as spring steel and light metal alloys. The advantage of the methodology is the derivation of closed form solutions with restrictions on radial movement of inner and outer edges. The developed formulas are recommended for industrial calculations of free and restricted Belleville washers.

A study of hybrid self-centring beam-to-beam connections equipped with shape-memory-alloy-plates and washers

This paper examined the hysteretic performance of a novel hybrid self-centring beam-to-beam connection equipped with shape memory alloy (SMA) plates and SMA Belleville washers. An experimental programme employing three proof-of-concept test specimens with varied SMA plate geometries and connection configurations was conducted. The test connections showed recentring performance with controllable residual deformations. The encouraging energy dissipation capacity of the test connections accompanied by excellent ductility was also confirmed. Subsequently, a numerical study was carried out to help interpret the test results and to further examine the connection's load carrying mechanism. In the numerical work, a hybrid finite element (FE) modelling technique enabling reproducing the residual strain development of SMA plates under hysteretic loading was developed and verified. The test and numerical study showed that the self-centring ability of the connection was appreciably affected by the hysteretic behaviour of SMA plates. The FE results also confirmed that the connection behaviour was sensitive to the connection configuration, and a minor gap between the beam segments could initiate intense buckling of the SMA plates. Nevertheless, the lateral deflection of the SMA plates can be suppressed by effective buckling restraints. To facilitate practical application, a theoretical prediction model enabling the quantification of a bilinear skeleton response of the connection was proposed, and the adequacy of the prediction model was evidenced by the correlation among the results of the tests, FE simulations and design predictions.

Belleville Washer Search and enhanced Papilionoidea Optimization Algorithms for real power loss reduction

Belleville Washer Search and enhanced Papilionoidea Optimization Algorithms for real power loss reduction

Measurements of Static and Dynamic Load Performance of a 102 MM Carbon-Graphite Porous Surface Tilting-Pad Gas Journal Bearing

Abstract Aerostatic journal bearings with porous tilting pads enable shaft support with minute drag power losses. To date archival information on the static and dynamic load performance of this bearing type is scant. Thus, the paper presents measurements conducted with an air lubricated bearing with diameter d = 102 mm and comprising four tilting pads made of porous carbon-graphite, each with length L = 76 mm. Two nested Belleville washers resting on spherical pivots support each pad. At ambient temperature of ∼ 21 °C, as the air supply pressure into the bearing pads increases, so does the bearing aerostatic specific load (F/(L·d)) that reaches 58% of the pressure difference, supply minus ambient. With an air supply pressure of 7.8 bar(a), the test bearing static stiffness KS = 13.1 MN/m, is independent of both shaft speed and static load. KS is just 63% of the washers' stiffness KP = 20.6 MN/m (during loading). While operating with shaft speeds equal to 6 krpm and 9 krpm (150 Hz) and under specific loads to 115 kPa and 101 kPa, respectively, dynamic load experiments with excitation frequencies up to 342 Hz show the test bearing supplied with air at 7.8 bar(a) has frequency independent stiffness (K) and damping (C) coefficients. For rotor speeds equaling 0, 6 and 9 krpm, the bearing direct stiffnesses KXX ∼ KYY range from 13.6 MN/m to 32.7 MN/m as the specific load increases from 0 kPa to 115 kPa. The direct damping coefficients CXX ∼ CYY are as large as 5.8 kN·s/m, though having a large experimental uncertainty. Bearing cross-coupled force coefficients are insignificant. The test porous gas bearing reached its intended load capacity, demonstrated a dynamically stable operation and produced force coefficients mainly affected by the pads' pivot supports and the magnitude of air supply pressurization.

PRELIMINARY STUDY ON NOVEL BEAM-TO-COLUMN CONNECTION BASED ON SMA PLATE

A novel beam-to-column connection equipped with shape memory alloy (SMA) plates has been proposed to realize resilient performance under low-to-medium seismic actions. In this conference paper, the detailed 3D numerical technique calibrated by the previous paper is adopted to examine the hysteretic behavior of the novel connection. A parametric study covering a reasonable range of parameters including the thickness of the SMA plate, friction coefficient between SMA plate and beam flange and pre-load of the bolt was carried out and the influence of the parameters was characterized. In addition, the effect of the SMA Belleville washer on the connection performance was also studied. The results of the numerical study showed that the initial connection stiffness and the energy-dissipation capacity of the novel connection can be enhanced with the increase of the thickness of the SMA plate. In addition, the initial connection stiffness and energy-dissipation behavior of the novel connection can be improved by increasing the friction coefficient or pre-load of bolts, whereas the increased friction level could compromise the self-centering behavior of the connection. The hysteretic curves of the numerical models of the connection also implied that the SMA washers may contribute to optimizing the connection behavior by increasing the connection stiffness and energy-dissipation capacity without sacrificing the self-centering behavior.

Compressive osseointegration for endoprosthetic reconstruction.

This review summarizes the biomechanical concepts, clinical outcomes and limitations of compressive osseointegration fixation for endoprosthetic reconstruction. Compressive osseointe - gration establishes stable fixation and integration through a novel mechanism; a Belleville washer system within the spindle applies 400-800 PSI force at the boneimplant interface. Compressive osseointegration can be used whenever standard endoprosthetic reconstruction is indicated. However, its mode of fixation allows for a shorter spindle that is less limited by the length of remaining cortical bone. Most often compressive osseointegration is used in the distal femur, proximal femur, proximal tibia, and humerus but these devices have been customized for use in less traditional locations. Aseptic mechanical failure occurs earlier than with standard endoprosthetic reconstruction, most often within the first two years. Compressive osseointegration has repeatedly been proven to be non-inferior to standard endoprosthetic reconstruction in terms of aseptic mechanical failure. No demographic, device specific, oncologic variables have been found to be associated with increased risk of aseptic mechanical failure. While multiple radiographic parameters are used to assess for aseptic mechanical failure, no suitable method of evaluation exists. The underlying pathology associated with aseptic mechanical failure demonstrates avascular bone necrosis. This is in comparison to the bone hypertrophy and ingrowth at the boneprosthetic interface that seals the endosteal canal, preventing aseptic loosening.

Cross-laminated timber rocking walls with slip-friction connections

Construction of tall-wood buildings is increasing in North America. Cross-laminated timber (CLT) is one of the dominant structural mass-timber products and is a high strength, lightweight, value-added, wood-composite panel suited for shear walls. The advent of tall-wood buildings necessitates further connection development for increased seismic resiliency to meet life-safety and performance-based design objectives. A novel slip-friction connection (SFC) was tested on six 1.52 m by 3.04 m CLT walls subject to static and pseudo-static cyclic loading. The SFC used Belleville springs and brass shims to provide stable slip forces and equivalent-viscous damping ratios between 0.28 and 0.63. Half of the wall tests included a short post-tensioned restoring rod with Belleville washers. Inclined self-tapping screws (STS) were used to connect the SFCs to the CLT walls, and the SFCs were designed to reliably dissipate energy while protecting the rocking walls from damage. The wall’s response followed the idealized parallelogram, or flag shaped, hysteretic models observed in other slip friction systems. Results indicate repeatable performance and structural protection at least 2.5 times STS design loads. Self-centering and partially-centering wall conditions were tested by changing the SFC slip forces, while maintaining an initial 23 kN restoring force. Based on these experiments designers will be able to apply SFCs to CLT rocking walls.

Large thermal hysteresis NiTi Belleville washer fabricated by metal injection moulding

ABSTRACT In this work, Ni49.4Ti50.6 Belleville washers are prepared by metal injection moulding (MIM). The martensitic transition temperatures and service performance of washers were investigated. The thermal hysteresis has reached 63.1–71.6°C, which is much higher than documented data in binary NiTi alloys. Ti2Ni and Ni4Ti3 phase are observed in XRD patterns, which is responsible for the large thermal hysteresis. In the service tests, the restoring forces are higher than 40 kN, which are sufficient to ensure a tight connection of the fasteners. The loop resistance and high-current test have proved the safety of MIM NiTi Belleville washers compared to traditional steel spring washers, which can meet the challenge in complex outdoor circumstances.

Investigation of energy storage in bolted joint components and the development of a geometry selection design tool for Belleville washers

Despite the advantages and widespread use of bolted joints in manufacturing, one major problem is their tendency to loosen, which can ultimately cause the joint to fail. This research evaluates strain energy storage in the Belleville washer, to determine how the washer's design could be modified to counteract relaxation in the bolt, which causes loosening. Finite Element Analysis (FEA) is used to study the strain energy, bolt preload, deflections, and other parameters of various geometric configurations of Belleville washers and shows that the strain energy is not optimally utilized with conventional Belleville washers, which have constant wall thickness. Tapering the Belleville washer reduces its weight significantly, thereby increasing the washer's energy storage capacity. The FEA data are used to develop a tool for helping to design Belleville washer geometry that can prevent bolt loosening. One of the tool's inputs is the bolt deflection relaxation within the acceptable bolt preload window. This work opens further research avenues for analyzing anti-loosening joints from the perspective of the elastic energy stored in the joint and thereby predicting when the joint might fail.

A study of hybrid self-centring connections equipped with shape memory alloy washers and bolts

This paper presents an innovative type of hybrid self-centring extended end-plate connections incorporating high strength bolts and two basic SMA elements, namely, SMA Belleville washers and SMA bolts. The fundamental mechanical characteristics of the individual SMA elements were first understood via cyclic tests, and subsequently a comprehensive test programme on of four proof-of-concept connections with varying bolt dimensions and washer arrangements was conducted. The connection specimens exhibited flag-shape hysteretic responses with good self-centring ability and cyclic loading repeatability. Satisfactory ductility accompanied by moderate energy dissipation capacity was also shown, and it was found that the SMA washers contributed evidently to the strength, stiffness, and energy dissipation of the connections. A numerical investigation was subsequently performed to enable a more in-depth understanding of the connection behaviour, and it was further shown that increasing the preload levels of either the SMA washers or the SMA bolts could effectively increase the connection stiffness. A design model was finally proposed which enables an idealised bi-linear description of the moment-rotation responses of the hybrid self-centring connections. The design stiffness and strength obtained from the proposed models were found to agree reasonably well with the test results and numerical predictions.

Performance Comparison of Belleville Washer under Compressive Load using Experimental and Simulation Methods

Belleville washers are used in the different engineering applications with standard design parameters. The present work shows the behavior of stress and deflection of the standard Belleville washer compared to the non-standard design parameter as per the industrial needs. Belleville washer (or) disk spring with higher height to thickness ratio i.e. (h/t) is made with a bearing flat at upper Inner Diameter (I.D) and lower Outer Diameter (I.D) with appropriate radius over edge. The Belleville washer design parameter is analyzed by numerical, experimental and LS-Dyna FEM simulation. FEM simulations were performed by using commercial simulation software LS-Dyna to study the behaviors of stress and deflection of the standard and non-standard Belleville washer. During the study it was observed that variation between simulation and experimental results. The difference was reduced by using element formation criterion available in LS-Dyna. Finally the simulation and experiment results were matched by using particular element formation of 8 node hexagonal elements.

11.30: Experimental behaviour of base plate joints equipped with self‐centering system and friction dampers

ABSTRACTA FREE from DAMage friction connection is a connection where friction dampers are introduced by adding friction pads, sliding on slotted steel plates, pre‐stressed with high strength bolts. Even though such a technology provides great advantages in terms of removal of damage to the structural elements, it has the main drawback to provide a limited re‐centering capability. In fact, during a seismic loading history, FREEDAM joints rotate concentrating the dissipation in the friction interface but, due to their high stiffness, after the end of the ground motion, they remain in a deformed position, leaving also the structure with residual drifts resulting in out‐of‐plumbs.The goal of the work is to propose an approach to provide FREEDAM structures with a self‐centering capacity by studying particular devices, to be installed in beam‐to‐column joints or column base joints. In this paper, the attention is focused on the problem of re‐centering of base plate joints studying a detail consisting in a connection located at the base of the columns of the first storey equipped with friction dampers and threaded bars. The threaded bars work as elastic springs thanks to sets of Belleville washers used to increase the deformability and to allow the opening of a gap in the connection. The main breakthrough of the proposed technology with respect to the existing literature, aside from the methodology employed for the design of the friction connection, is that the self‐centering capability is obtained with re‐centering elements (threaded bars and Belleville springs) which are not conceived to be extended up to the end of the column at the top storey of the building, but they have a size similar to the column splice's cover plates. The work reports the results of a preliminary experimental investigation on this joint detail which has regarded cyclic and pseudo‐dynamic tests. The experimental results presented seems very encouraging towards the possible development of base plate joints with self‐centering capacity combined with friction dampers.

Validation of Constant Load C-Ring Apex Stresses for Stress Corrosion Cracking Testing in Supercritical Water

In selecting the materials for the Canadian supercritical water-cooled reactor (SCWR), the effects and extent of stress corrosion cracking (SCC) on candidate alloys of construction, under various operational conditions, must be considered. Several methods of applying stress to a corroding material are available for investigating SCC and each have their benefits and drawbacks; for simplicity of the experimental setup at University of New Brunswick (UNB), a constant load C-ring assembly has been used with Inconel 718 Belleville washers acting as a spring to deliver a near-constant load to the sample. To predict the stress at the apex of the C-ring, a mechanistic model has been developed to determine the force applied by the spring due to the thermal expansion of each component constrained within a fixed length when the temperature of the assembly is increased from ambient conditions to SCWR operational temperatures. In an attempt to validate the mechanistic model, trials to measure the force applied by the washers as the assembly thermally expanded were performed using an Instron machine and an environmental chamber. Accounting for the thermal expansion of the pull rods, the force was measured as temperature was increased while maintaining a constant displacement between the platens holding the C-ring. Results showed the initial model to be insufficient as it could not predict the force measured through this simple experiment. The revised model presented here considers the thermal expansion of the C-ring and all the components of the testing apparatus including the tree, backing washers, and Belleville washers. Further validation using the commercial finite element (FE) package abaqus is presented, as are preliminary results from the use of the apparatus to study the SCC of a zirconium-modified 310 s SS exposed to supercritical water.

Investigation into the Numerical Model Behaviour of Belleville Washers in Cold Roll Forming

With the steady increase in demand for roll formed products, due to their application in fields such as automotive, construction, architecture, etc., roll forming companies are challenged with rising customer demands. Companies are struggling to bring a product through from design to manufacture at improved rates, whilst achieving tighter tolerances. The roll forming process may also induce undesirable forming defects such as twist, distortion and straightness problems. Over the years, numerical simulations have been deployed to assist with the geometric validation of these effects. For the purpose of this paper, an investigation shall focus on an individual parameter within the finite element analysis of the cold roll forming process, i.e. the ’unknown’ spring effect acting of the top roll during the forming process due to the implementation of Belleville washers in the pillar set up. This parameter is assessed over a range of applied loads and compared with a standard friction model with fixed top and bottom rolls. The longitudinal strains on the final profile, the geometric accuracy and thickness variation are observed and presented in this paper. Reasoning is also provided to explain why the final profile bows in the vertical direction.

Superelastic SMA Belleville washers for seismic resisting applications: experimental study and modelling strategy

This study sheds considerable light on the potential of superelastic shape memory alloy Belleville washers for innovative seismic resisting applications. A series of experimental studies were conducted on washers with different stack combinations under varying temperatures and loading scenarios. The washers showed satisfactory self-centring and energy dissipation capacities at room temperature, although slight degradations of the hysteretic responses accompanied by residual deformations were induced. The hysteretic loops became stable after a few number of cycles, indicating good repeatability. The washers also showed good flexibility in terms of load resistance and deformation, which could be easily varied via changes in the stack combination. Compromised self-centring responses were observed at temperatures below 0 °C or above 40 °C, and a numerical study, validated by the experimental results, was adopted to further investigate the deformation mechanism of the washers. A further phenomenological model, taking account of the degradation effects under varied temperatures, was developed to enable effective and accurate simulation of devices incorporating the washers. Good agreements were observed between the test and simulation results, and the model was shown to have good numerical robustness for wide engineering applications.

Modeling and simulation of the thermo-mechanical response of NiTi-based Belleville springs

Nickel–titanium (NiTi) Belleville washers exhibit unique mechanical and functional features due to the reversible stress-induced and/or thermally induced phase transition mechanism of NiTi alloys. In this article, the thermo-mechanical response of such washers has been analyzed by finite element simulations as well as by a special semi-analytical model, which is based on a modified literature approach. The effects of the geometrical configuration of the washers as well as of different thermo-mechanical loading conditions, under stress-induced phase transformation regime, have been analyzed. The results highlighted a marked hysteretic response, in terms of force–deflection curve, due to the hysteresis in the stress–strain behavior of NiTi alloys. In addition, a marked influence of the geometry, as well as of the temperature, has been observed on the thermo-mechanical response of the washer.

Numerical study and practical design of beam-to-column connections with shape memory alloys

This paper reports a comprehensive numerical study on end-plate beam-to-column connections equipped with NiTi shape memory alloys (SMAs). The numerical modelling strategy is first validated through comparisons with seven full scale tests conducted by the authors. The FE predictions correlate well with the test results, especially in terms of the deformation mode, strain reading, moment–rotation response, residual deformation, and equivalent viscous damping. Following the validation study, a parametric study is performed considering the effects of bolt layout, bolt length/diameter, beam-to-connection strength ratio, end-plate thickness, column web panel deformation, and shear resisting mechanism. In order to overcome a major issue identified from the parametric study, i.e. shear slippage, an improved HS-SMA hybrid solution is proposed. One of the novel concepts is the employment of HS bolts in collaboration with SMA Belleville washers, where the latter are used to absorb the bolt row deformation, to enable connection recentring, and to offer supplementary energy dissipation. A detailed FE model is established to confirm the feasibility of the HS-SMA hybrid connection, and an analytical model is also developed for normal design of such connections. A set of design rules for practical use are also proposed, and the required future studies are finally identified.

Improving Belleville Washer Spring Characteristics Using Elastomer Filling

Abstract Belleville washer steel springs are characterized by a long fatigue life, better space utilization, low creep tendency, and high force bearing capacity with a small spring deflection. In the case of thicker springs, a greater force bearing and greater stiffness are obtained, but the deflection of the spring is reduced. In such a case, the fatigue life is reduced and there is a very high probability that a Belleville washer spring may fail in a brittle manner, causing additional damage to machinery. In order to prevent such a fracture of a Belleville washer, an elastomeric filling was used on both free surfaces of the spring. Experimental testing and numerical analyses show that enhanced loading characteristics were obtained when the elastomer filling was increasingly involved in the force bearing process. When the elastomer filling is compressed, the stresses in the Belleville washer steel are reduced, because the majority of the deflection stress is shared by the elastomer instead of the steel.