Belleville Springs Research Articles

Experimental, numerical, and theoretical analysis of tapered belleville spring

Uniform thickness belleville springs(UBS) are a suitable replacement for coil springs in many applications due to their ability to take higher loads and their relatively small and compact size. This paper presents an experimental, numerical and theoretical analysis of the taper belleville spring(TBS). Experimental results on a normal taper belleville spring (NTBS), fabricated from stainless steel alloy (SS304), are presented. Non linear elastic-plastic finite element simulations support the experimental behaviour reasonably well. A correction factor based on Timoshenko’s theory of plates, to match the finite element analysis(FEA) results for NTBS, is presented. Reverse taper belleville spring (RTBS) analysis shows that it can store more elastic strain energy than UBS and NTBS. An optimisation study on TBS geometrical parameters is performed to attain maximum energy absorption for the null stiffness region.

ANALYSIS OF UNCONTROLLED WEAR IN THE AREA OFA BELLEVILLE SPRING OF A FRICTION TORSIONAL VIBRATIONDAMPER IN A MOTOR VEHICLE CLUTCH

The article describes the problem of excessive tribological wear of a torsional vibration damper built intoa single-disc friction clutch of a truck vehicle. In contrast to the controlled, design-based wear of damper’sfriction rings, i.e., wear whose kinetics are known and predictable, uncontrolled wear at Belleville springcontact surfaces effects in a premature decrease in the damper’s friction torque and, consequently, loss ofdurability. As a result of the analyses and experimental work, the causes of accelerated wear were identified.Sets of springs and friction rings from the 10 used vibration dampers that worked under similar operatingconditions but with different operating periods were used as the basic research material. The influence ofabrasive wear of Belleville springs on their load-deflection characteristic was identified. A comparativeanalysis of the characteristics of the new spring and the used springs is also presented to illustrate changes inthe axial load in the assemblies of the analyzed dampers.

Weak axis low-damage performance of seismic resilient rocking steel column base with friction connection

Rocking column bases with friction connections are a critical technology employed in the low-damage design of steel structures. In this study, cyclic loading tests were conducted along the weak axis of the column, incorporating INITIAL, AFTERSHOCK, and REPAIR cases, with a maximum drift ratio of 3%. In the AFTERSHOCK case, both the sliding and maximum moments at the column base exhibited a significant decrease of 67% and 16%, respectively. To address the decrease in sliding strength attributed to the loss of bolt tension, Belleville Springs (BeSs) were employed, and the bolts were maintained within the elastic range. The results demonstrate that the hysteretic curves of the column base almost perfectly align in all three cases, revealing a strength loss of less than 2% and a significant enhancement in seismic resilience. This low-damage column base proves well-suited for deployment in regions with high seismic risk, especially for buildings subjected to continuous seismic excitation. A finite element analysis (FEA) model was developed to quantitatively evaluate the damage, sliding, bolt tension loss, and energy dissipation performance of the column base. Finally, a simplified flag-shaped analytical model was proposed to guide the design of such low-damage column bases, providing a basis for their integration into overall structural analyses.

Metoda eksperymentalnego badania charakterystyki siła-odkszałcenie sprężyn Beleville w zespole odcinającym zasuwy klinowej

The article presents research methods and appropriate equipment for conducting experiments, as well as the analysis of the results. Studies on the hardness of the microstructure, elastic deformation and parts and samples were carried out using hardness testers, microscopes PMT-3, MIM-8 and devices for measuring the “force-strain” characteristic. The results of the study wer used to establish the dependence of the elastic properties of Belleville springs on the heat treatment modes, while also determining the microstructure and layer depth using various research methods. Every work studying the elastic properties and measurement of the static compressive force of a spring at a given strain value has been studied theoretically. Depending on the operating conditions, disc springs can be installed singly or assembled into packages, forming an elastic element working under compression. The research materials will be used in the work to improve the tightness of straight-through valves and the durability of the shut-off assembly parts. The dependence of the spring compression force and its deformation on the geometrical parameters of the disc springs has been established. Comparison of experimental and theoretical dependences has been made. It has been established that the residual deformation of the Belleville spring after captivity has a negative effect on the tightness of the shut-off valve assembly. The influence of various technological processes and modes of thermal treatment of disc springs on their elastic properties has been studied. Practical recommendations for improving the technological process of thermal treatment of Belleville springs have been proposed. The tasks of further research and implementation of the obtained results have been determined. Search work has been carried out to improve the technology of hardening processing of parts of the shut-off unit (gate and seat) of direct-flow valves. The possibility of using accelerated nitrocarburizing in a triethanolamine medium with induction heating by high-frequency currents at a temperature range of 950°С for boriding and borochroming has been established. Samples were made from standard steel grades 40, 40Kh and 38Kh2MYuA, subjected to hardening by the considered methods, and a study was made of the hardness, depth and microstructure of the hardened layer. Research in this direction should be continued in order to study the tribological characteristics (friction coefficient and wear resistance) of hardened parts. Each operation of the spring manufacturing technology has been studied, and deviations that have a significant impact on the operation of the spring and the sealing of the shut-off valve assembly have been identified.

Exact shell solutions for conical springs. III. Belleville springs with variable thickness

PurposeIn the current manuscript, the authors examine the Belleville spring with the variable thickness. The thickness is assumed to be variable along the meridional and parallel coordinates of conical coordinate system. The calculation of the Belleville springs includes the cases of the free gliding edges and the edges on cylindric curbs, which constrain the radial movement. The equations developed here are based on common assumptions and are simple enough to be applied to the industrial calculations.Design/methodology/approachIn the current manuscript, the authors examine the Belleville spring with the variable thickness. The calculation of the Belleville springs investigates the free gliding edges and the edges on cylindric curbs with the constrained radial movement. The equations developed here are based on common assumptions and are simple enough to be applied to the industrial calculations.FindingsThe developed equations demonstrate that the shift of the inversion point to the inside edge does not influence the bending of the cone. On the contrary, the character of the extensional deformation (circumferential strain) of the middle surface alternates significantly. The extension of the middle surface of free gliding spring occurs outside the inversion. The middle surface of the free gliding spring squeezes inside the inversion point. Contrarily, the complete middle surface of the disk spring on the cylindric curb extends. This behavior influences considerably the function of the spring.Research limitations/implicationsA slotted disk spring consists of two segments: a disk segment and a number of lever arm segments. Currently, the calculation of slotted disk spring is based on the SAE formula (SAE, 1996). This formula is limited to a straight slotted disk spring with freely gliding inner and outer edges.Practical implicationsThe equations developed here are based on common assumptions and are simple enough to be applied to the industrial calculations. The developed method is applicable for disk springs with radially constrained edges. The vertical displacements of a disk spring result from an axial load uniformly distributed on inner and outer edges. The method could be directly applied for calculation of slotted disk springs.Originality/valueThe nonlinear governing equations for the of Belleville spring centres were derived. The equations describe the deformation and stresses of thin and moderately thick washers. The variation method is applicable for the disc springs with free gliding and rigidly constrained edges. The developed method is applicable for Belleville spring with radially constrained edges. The vertical displacements of a disc spring result from an axial load uniformly distributed on inner and outer edges.

Improvement of the design of the plow-subsoiler-fertilizer to increase soil fertility

The use of intensive technologies for the cultivation of agricultural crops provides for the application of fertilizers in the process of tillage. This reduces the compaction of the soil, increases its fertility and the quality of the crop. The purpose of these studies is to develop a universal working tool that allows you to combine several technological operations in one pass of the unit. The authors have developed an original design of a plow-subsoiler-fertilizer. This combined working body includes a reversible plow and a vibratory subsoiler with fertilizer ducts. This solution allows you to combine the application of fertilizers when plowing the field, loosening the subsoil layer and mixing the soil. As a result of the work, the dependences of the geometric dimensions of the structure on the traction resistance to movement in the soil were obtained. To implement the developed idea into a real design, the main parameters of the plow-subsoiler-fertilizer are determined. Particular attention is paid to the calculation of the spring mechanism that ensures the vibration of the subsoiler. The optimal number and location of belleville springs in the block and shock absorber were selected, at which the subsoiler will perform self-oscillations with a given amplitude.

Arrangement of Belleville Springs on Endplates Combined with Optimal Cross-Sectional Shape in PEMFC Stack Using Equivalent Beam Modeling and FEA

A set of Belleville springs integrated into an endplate plays a key role in a proton exchange membrane fuel cell (PEMFC) stack, which makes the applied assembly force smoother, resulting from the absorbed vibration and thermal expansion. The appropriate arrangement of Belleville springs is important in PEMFC stack design. The aim of this study is to establish an equivalent beam model to optimize the numbers and positions of Belleville springs to minimize endplate deformation. Based on this, a finite element analysis (FEA) model of the PEMFC stack is proposed to further optimize the cross-sectional shape of the endplate. For the endplate with two, three and four groups of Belleville springs, its optimal positions correspond to 0.17lin, 0.27lin and 0.5lin (lin is the equal distance between steel belts). In addition, the low thickness should be 2/3 of the high thickness of the curved endplate for a uniform contact pressure distribution as well as the high-volume-specific power. However, the curvature radius of the endplate arc is negative to the uniformity of the contact pressure distribution, and particularly the internal cells of the PEMFC stack. This study provides a design direction for endplates combined with Belleville springs in large fuel cell stacks clamped with steel belts.

Experimental Study on Seismic Behavior of Steel Column Base Connections with Arc End-Plates Slip-Friction

This paper proposes a new type of steel slip-friction column base connections with arc end-plates. Two arc end-plates of the steel column base, which can slide between each other to some extent, were set at the position where the column base is subject to plastic deformation. Thus, the sliding-friction energy dissipation between the arc end-plates can effectively minimize or eliminate the energy dissipation of the traditional column base connections. Cyclic loading tests were conducted to study the hysteretic performance and energy consumption performance of the proposed connections. Considerations have been given to different axial compression ratios, Belleville springs (Bes), brass plates, and horizontal loading protocols. The test results show no obvious deformation or damage during the radial cyclic loading test. The curve shape of the test measurement approximates a parallelogram, showing good force performance. The proposed connections with the increasing axial compression force can increase the energy dissipation ability and load-carrying capacity. Therefore, the proposed connection has perfect seismic behavior.

Low‐prestressing, self‐centering energy dissipative brace

AbstractSelf‐centering energy dissipative (SCED) braces are designed to limit the maximum story drifts in buildings during earthquakes and to nearly eliminate residual drifts. SCED braces that have been developed in the past face three major challenges: they require high levels of prestressing force, they have limited elongation capacity, and their energy dissipative systems have inadequate reliability or excessive complexity. This paper proposes a new SCED brace that addresses these three challenges with the use of a mild‐steel dissipative element that never experiences compression, so it will not buckle. The feasibility of the new system was demonstrated with a set of experiments in a configuration that uses a series combination of post‐tensioned steel tendon and Belleville springs for re‐centering. The paper develops equations that govern the brace's performance, identifies key parameters and develops a numerical modeling method. The design of an example building shows that the new brace only requires approximately 6% of the prestressing force required for existing SCED braces to achieve similar hysteretic relationships. Numerical analysis confirms that a braced frame equipped with the new brace would control the maximum response to about the same extent as would for existing SCED braces and buckling‐restrained braces, while effectively eliminating residual drift under severe earthquakes. Meanwhile, the new system generates 18–26% smaller axial forces than existing SCED braces and appears to have a large elongation capacity. Based on these findings, it is concluded that the proposed brace successfully addresses the major challenges of previous SCED braces.

Use of the Belleville spring package in the vibration protection mechanism of the operator’s seat

Reducing the vibration effects on the operator of a construction, road and other machines is a relevant objective, since its accomplishing improves the efficiency and accuracy of the work performed by machines and reduces the risk of operators’ occupational diseases. Vibration protection systems with the effect of quasi-zero stiffness are promising. To produce this effect, Belleville springs packages can be used. They are a way to create a simple, reliable and inexpensive passive mechanism of the vibration protection system of the operator’s seat. The influence of the static characteristic center slope of two Belleville springs packages on the maximum acceleration of the load under the sinusoidal kinematic excitation of the seat base movements is investigated. The static characteristic center slope of the spring packages was characterized by the coefficient that affects the type of the static characteristic according to the known analytical expressions for the separate spring force. To obtain the chair acceleration values in a fixed coordinate system, we used a simulation mathematical model developed in the Simscape Multibody package for modeling mechanical systems of the MATLAB mathematical system. The model used blocks of a fixed coordinate system, a sliding joint and a rigid body forming a chain. The maximum acceleration of the chair in a fixed coordinate system was defined during a predetermined period of time at the end of the transition process under the steady state oscillations. When conducting the computational experiment, the specified oscillations amplitude of the chair base and the angular frequency of these oscillations varied. For a proper comparison of the experimental results in the form of graphical dependencies of the maximum acceleration on the amplitude and frequency, the ranges of acceptable and unacceptable arguments combinations were selected for the two spring packages. The combinations of amplitude and frequency were considered unacceptable when the maximum deformation of the spring package went beyond the static characteristic maximum. For the two packages of springs, the acceptable regions were different, therefore their intersection used for the comparative analysis, was obtained. The springs package with a relatively high stiffness in the center of the static characteristic is found out to generally provide better vibration protection of the chair in the entire acceptable range of arguments. Simultaneously, a package with lower stiffness in the center of the characteristic dampens vibrations better in the small amplitudes area, i.e. when operating in the quasi-zero stiffness area.

Analysis of electrical energy harvesting from piezoelectric integrated shallow conical composite shells in metastable configurations using mixed formulation

This article presents a study of energy harvesting from smart composite Belleville springs, which are truncated conical shallow shells bonded with piezoelectric patches. When the springs subject to mechanical loading–unloading cycles, electrical energy is generated from the integrated piezoelectric elements via the direct piezoelectric effect. A mixed strong and weak form mathematical model composed of strain energy and electric enthalpy is formulated to analyze the electro-elastic performance of the shells. Undergoing snap-through and snap-back buckling when loaded and unloaded in compression, the smart Belleville springs in metastable configurations exhibit unprecedented complex electromechanical behaviors, which can be applied to enhance energy scavenging. The developed model is firstly validated with the finite-element method using ABAQUS™ and the responses from both approaches are in excellent agreement. Parametric studies on the spring geometry are systematically conducted to determine geometrical effects on stored electrical energy in the piezoelectric patches. The numerical results obtained from the mixed-form model show that snap buckling in the metastable conical shells can be used to harvest a relatively large amount of electrical energy. Conclusions of this study lay down a design guideline for energy extraction from the smart composite Belleville springs with a variety of geometric and kinematic constraints.

Novel Hierarchical Energy Dissipation Systems for Seismic Protection of Buildings

ABSTRACT The methodology of installing energy dissipation devices is a key point in structural seismic design. This paper proposes three novel hierarchical energy dissipation (HED) systems, using miniature bar-typed structural fuses (MBSFs) of different installation constructions, i.e., making MBSF lengths varied, installing Belleville springs, and enabling the anchor device to slide frictionally. Verification tests and corresponding simulations were conducted to examine the feasibilities of these constructions. The results showed that BSC and FSC systems dissipated energy hierarchically as expected. Time-history dynamic analysis on single-degree-of-freedom (SDOF) models was then conducted, according to which a displacement-based design method was established and recommended.

Experimental analysis on stacking of Belleville spring

Belleville springs are frusto-conical in shape, can support high load with small deflection. Load-Deflection characteristics of a Belleville spring can be altered by stacking of springs. In this research work, Finite Element Analysis (FEA) of Belleville spring was carried out and compared against experimental analysis using strain gauge. FEA was carried out on a plain spring and results were compared with theoretical analysis. Experimental investigation was carried out using strain gauges for different configuration of Belleville springs such as plain spring and spring with stacking. From the studies it was concluded that theoretical, Finite Elemental and Experimental analyses were in good agreement. Spring stacking was done up to 6 numbers, and deflection was significantly altered from 1.46 mm to 8.14 mm (Deflection from one spring to six springs). With the stacking of springs, change in the magnitude of maximum stress was 1.5%. Thus, required load- deflection characteristics can be achieved by stacking of springs when space is not a constraint and large deflection is required.

The Static Response of Axisymmetric Conical Shells Exhibiting Bistable Behavior

Abstract Belleville springs are widely used in a variety of mechanical systems. Recent advances in the field of multi-stable structures suggest that these conical axisymmetric washers may be extremely useful as bistable building blocks for multi-stable architected metamaterials. In this paper, we examine the ability of existing analytical models to accurately predict the bistable behavior of Belleville springs, namely, a nonmonotonous force–displacement relation with two branches of positive stiffness separated by a branch of negative stiffness. By comparing with results of finite element (FE) simulations, we find that current analytical models may suffer from significant inaccuracies associated with the assumption of rigid rotation. According to this assumption, adopted by all analytical models of Belleville springs, the cross section of the spring rotates without bending, i.e., maintains zero curvature as the spring deforms. Motivated by this insight, we relax the rigid-rotation assumption and approximate the radial displacement field by a linear relation in terms of the distance from the spring axis. We find, based on extensive finite element simulations, that the functional dependence of the radial displacement on the geometry of the springs is indifferent to the stage of deformation and can be expressed in terms of three geometrical parameters. These findings enable us to derive closed-form expressions that are simple and straightforward to use, yet are significantly more accurate than existing analytical models.

PROBLEMS OF FREE ROLLING OF THE PILGER HEAD AND WAYS OF THEIR SOLUTION

A feature of the process of hot pilgring rolling of pipes is the presence of an under-roll of the rear end of the sleeve, which forms the so-called pilger head, which is due to the presence of a front support on the sleeve from the mandrel head of the feeding apparatus. Pilgerghead refers to the technologically inevitable loss of metal in the pilger mill, especially when rolling thin-walled (D / S = 12.5 - 40) and especially thin-walled (D / S > 40) pipes. At the same time, when rolling thick-walled pipes (D / S = 6-12.5), in practice, the methods of butt-end rolling of sleeves and free rolling of the pilger head are used, and the latter is used quite limited and only as an addition to the butt-to-butt rolling method of the last sleeve in a batch or in case of disturbance this process. The presence of a pilger head is one of the main factors of increased metal consumption at pilgrim mills. The analysis of the problems of the process of free rolling of the pilger head is carried out and the ways of their solution are proposed. One of the main problems of this process is the impossibility of its use when rolling out thin-walled (D / S = 12.5-40) and especially thin-walled (D / S > 40) pipes, which is due to the peculiarities of removing the pipe from the mandrel using a gate device and a feeder.To solve this problem, a new technology has been proposed, which provides for rolling the pilger head to such a wall thickness at the end, which ensures the removal of thin-walled (D / S = 12.5-40) and especially thin-walled (D / S > 40) pipes from the mandrel. New solutions have been proposed to reduce the displacement of the roll along the mandrel in the first rolling cycles of the pilger head, the theoretical study of which made it possible to recommend a method of reducing the speed during its rolling in comparison with the steady-state process by 40-50%, as the simplest and most effective. Two new methods have been proposed for removing the pipe from the mandrel after full or partial rolling of the pilger head, the first of which is distinguished by the simultaneous convergence of the upper and lower gates, and the second - by holding the rolling by the press dies. To hold the mandrel ring at the mandrel head, two new solutions have been proposed, according to the first, permanent magnets are mounted in the ring, according to the second, both halves of the ring are connected using Belleville springs, which create the necessary adhesion to the mandrel.

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.

Experimental investigation of a self‐centering precast concrete beam‐to‐column connection with top and bottom friction energy dissipaters

SummaryThe new friction material, non‐asbestos organic, and Belleville springs are applied to the friction energy dissipaters (FEDs) to improve its friction performance. The new high‐performance FEDs are placed in the top and bottom parts of the self‐centering precast concrete (SCPC) beam‐to‐column connections, which have inherently reduced residual deformation caused by posttensioned tendons, to enhance energy dissipation efficiency. Besides, the reasonable design of the connection between FEDs and backbone members makes it easy for the disassembly of all members, which significantly enhances the repair efficiency after a major earthquake. Theoretical analyses and 14 tests were performed on a full‐scale specimen, which were assembled two times, and the friction pads were replaced one time, to investigate the effects of various parameters on the performance of such FED‐SCPC beam‐to‐column connections. The influence of key design parameters on the hysteretic behaviors, such as stiffness, loss of posttensioned tendons force, self‐centering capacity, and energy dissipation capacity, has been analyzed. The test results indicate that the FED‐SCPC beam‐to‐column connections can achieve significant and reliable energy dissipation levels while maintaining self‐centering capabilities. The experimental and theoretical results can provide certain references for the seismic design and assembly of such structures.

Optimization of Belleville Spring by Inspecting Parameter Impacts

Clutch disc transmits the torque by frictional forces from the engine to transmission. For this purpose, clutch disc includes some components such a Belleville spring to provide vibration dampening. Belleville springs are used in order to perform hysteresis function of disc assembly by creating frictional torque into clutch system. Hysteresis function of disc is needed to absorb oscillations and prevent noise issues. Belleville spring geometrical shape is critically important and it defines load characteristic. A load of Belleville spring mainly depends on dimensions of inner diameter, outer diameter, thickness, angle, and slot dimensions. This study investigates the single and multi-objective optimization methodology in the automotive clutch system design. This novel methodology presents the design development approach to powertrain system components.

Experimental studies on Belleville springs use in the sliding hinge joint connection

The Sliding hinge joint (SHJ) is a low damage beam-to-column connection developed for and widely used in seismic moment-resisting steel frames (MRSFs). The asymmetric friction connection (AFC) is the SHJ's friction sliding energy dissipating component, which has also been used in other seismic resisting structural systems. In current practice, the AFC bolts are yielded at installation by the method of bolt tightening, and they are subjected to moment, shear, and axial force (MVP) interaction during stable sliding. Hence the AFC bolts tension, and as a result, SHJ elastic strength will be reduced after sliding cycles. A remedy to this post-sliding strength reduction could be installing the AFC bolts in the elastic range in conjunction with using Belleville springs (BeSs) to maintain the clamping force, but at the potential cost of deteriorating the SHJ self-centering capability. This paper describes nine real-scale SHJ's AFC component tests at quasi-static and dynamic rates of displacement controlled loading, with bolts either tightened in the elastic range using no BeSs as well as with four different configurations of BeSs which are deliberately not fully deflected at installation, to avoid the system self-centering capability deterioration and to minimize the additional imposed tension on the AFC bolts during stable sliding. It is concluded that using partially deflected BeSs with sufficient axial deformation to reach the installed bolt tension, with these being installed at both head and nut sides of the AFC bolts, will reduce the post-sliding clamping force loss, improve the self-centering capability, increase the system coefficient of friction, reduce the additional imposed tension on the AFC bolts during stable sliding due to prying actions and/or MVP interactions, and reduce the severity of the sliding surfaces' wearing.

Polymer composite Belleville springs for an automotive application

This paper investigates mathematical modelling and manufacturing of polymer composite Belleville springs, and their potential application. The original expression for load carrying capacity developed for metal springs is refined by considering the variation of elastic modulus and Poisson’s ratio of laminates in polar coordinates. A novel series spring stacking arrangement is proposed to achieve complex stiffness variation by progressive action. The experimental results show consistent effect of number of plies on the spring rate and compare well with the theoretical predictions. Although handmade, the variations in load carrying capacity is very small (∼10%) confirming manufacturing viability. It is shown that a smooth, variable spring rate curve can be produced by reducing slip-stick frictional forces with the use of spacers within the spring stacks. In one application, the composite springs are shown to offer significant vehicle dynamic performance improvement through reduction of the tyre contact patch force variation and vehicle body acceleration.