Properties Analysis of Disk Spring with Effects of Asymmetric Variable Friction

The primary objective of this fundamental research is to investigate the mechanical properties of the disk spring when the friction at the contact edges is asymmetric and varies with the load. The contact mechanics study shows that the static friction and static friction coefficient on fractal surfaces change depending on the normal load. In this paper, a fractal contact model based on the W-M function is used to explore the connection between the static friction and the normal load. Subsequently, taking into account the asymmetry of the contact surface at the edge, the variable static friction coefficient is brought into the existing model to obtain an improved static model of the disk spring. Different fractal dimensions, frictional states and free heights are considered under quasi-static loading condition, the relative errors between this paper and the method using Coulomb friction are also calculated, and experimental validation was performed. The static stiffness and force hysteresis of the disk spring for different forms of asymmetric variable friction are discussed. It is shown that using the variable friction model can improve the computational accuracy of the disk spring model under small loads and help to improve the design and control accuracy of preload and vibration isolation equipment using the disk spring as a component.

Nonlinear behavior of disk spring with complex contact state

Disk springs are widely used as preload and isolation due to their unique mechanical properties. In the prior research, the effect of linear friction on the disk spring was considered, but contact stiffness, another nonlinear contact factor, is ignored. Accordingly, in this paper, the asymmetric displacements of the contact edges are first derived, and the accurate friction dissipations are obtained, as a way to evaluate the effect of friction on the system. Then the velocity of the edges was obtained to establish a dynamic friction model. Meanwhile, the contact displacement and contact stiffness of the edge are obtained by fractal contact theory. Then the nonlinear static and dynamic models of disk spring with friction and contact stiffness are established by the energy method. The load–deflection relationship, stiffness, and hysteresis of disk spring are studied with different contact states. The results show that the model considering contact stiffness and asymmetric friction dissipation can effectively evaluate the static properties of the disk spring. Friction reinforces the nonlinear behavior of the system, while contact stiffness weakens the nonlinearity of the system. And due to the influence of nonlinear contact factors, the transmissibility curves produce multiple resonance peaks.

An Analytical Model for the Stiffness of Slotted Disk Springs

The slotted disk spring is an important part of ultrasonic motors. Its mechanical properties directly affect the running stability of the motor. In this study, an analytical model is developed to solve the preload problem for slotted disk springs used in ultrasonic motors. The outer conical ring of the slotted disk spring is modeled using the conical shell theory. The inner separated teeth are modeled by the cantilever beam theory. An analytical mechanical model for the force-displacement relationship of the entire slotted disk spring is then developed. The results of the experiment based on a force-displacement transducer and the results from the analytical model, a finite element calculation, and the Schremmer formula are compared to validate the analytical model. The results show that the proposed model has the highest accuracy. Parameter-sensitivity analysis for the slotted disk spring is finally performed, and a new slotted disk spring with a long zero-stiffness interval is designed for a 40[Formula: see text]mm traveling wave rotary ultrasonic motor.

Analytical Calculation, Numerical Structural Analysis and Design Optimization of the Diaphragm Spring of a Mechanical Clutch

This paper considers the diaphragm spring of a mechanical clutch being composed by a conical disk spring and trapezoidal lamellar springs attached to the disk spring. After analytical calculation of the disk spring a numerical structural analysis was performed in order to validate the 3D model of the disk spring. A design optimization with 4 design variables was done for the disk spring and, based on the optimized design, the 3D model of the diaphragm spring was built. A 6 design variables model of the diaphragm spring was proposed for design optimization analysis having as design objective the minimization of the maximum equivalent stress during disengaging the clutch.

Reinforcement of Underground Excavation with Expansion Shell Rock Bolt Equipped with Deformable Component

The basic type of rock mass reinforcement method for both preparatory and operational workings in underground metal ore mines, both in Poland and in different countries across the world, is the expansion shell or adhesive-bonded rock bolt. The article discusses results of static loading test of the expansion shell rock bolts equipped with originally developed deformable component. This component consists of two profiled rock bolt washers, two disk springs, and three guide bars. The disk spring and disk washer material differs in stiffness. The construction materials ensure that at first the springs under loading are partially compressed, and then the rock bolt washer is plastically deformed. The rock bolts tested were installed in blocks simulating a rock mass with rock compressive strength of 80 MPa. The rock bolt was loaded statically until its ultimate loading capacity was exceeded. The study presents the results obtained under laboratory conditions in the test rig allowing testing of the rock bolts at their natural size, as used in underground metal ore mines. The stress-strain/displacement characteristics of the expansion shell rock bolt with the deformable component were determined experimentally. The relationships between the geometric parameters and specific strains or displacements of the bolt rod were described, and the percentage contribution of those values in total displacements, resulting from the deformation of rock bolt support components (washer, thread) and the expansion shell head displacements, were estimated. The stiffness of the yielded and stiff bolts was empirically determined, including stiffness parameters of every individual part (deformable component, steel rod). There were two phases of displacement observed during the static tension of the rock bolt which differed in their intensity.

Theoretical Design and Characteristics Analysis of a Quasi-Zero Stiffness Isolator Using a Disk Spring as Negative Stiffness Element

This paper presents a novel quasi-zero stiffness (QZS) isolator designed by combining a disk spring with a vertical linear spring. The static characteristics of the disk spring and the QZS isolator are investigated. The optimal combination of the configurative parameters is derived to achieve a wide displacement range around the equilibrium position in which the stiffness has a low value and changes slightly. By considering the overloaded or underloaded conditions, the dynamic equations are established for both force and displacement excitations. The frequency response curves (FRCs) are obtained by using the harmonic balance method (HBM) and confirmed by the numerical simulation. The stability of the steady-state solution is analyzed by applying Floquet theory. The force, absolute displacement, and acceleration transmissibility are defined to evaluate the isolation performance. Effects of the offset displacement, excitation amplitude, and damping ratio on the QZS isolator and the equivalent system (ELS) are studied. The results demonstrate that the QZS isolator for overloaded or underloaded can exhibit different stiffness characteristics with changing excitation amplitude. If loaded with an appropriate mass, excited by not too large amplitude, and owned a larger damper, the QZS isolator can possess better isolation performance than its ELS in low frequency range.