Experimental and Numerical Investigation of Contact Parameters in a Dovetail Type of Blade Root Joints

this paper focuses on the contact characteristics of the blade root joints subjected to the dry friction damping under periodic excitation. The numerical method and experimental procedure are combined to trace the contact behavior in the nonlinear vibration conditions. In experimental procedure, a novel excitation method alongside the accurate measurements is used to determine the frequencies of the blade under different axial loads. In numerical simulations, local behavior of contact areas is investigated using the reduction method as a reliable and fast solver. Subsequently, by using both experimental measurements and numerical outcomes in a developed code, the global stiffness matrix is calculated. This leads to find the normal and tangential stiffness in the contact areas of a dovetail blade root joints. The results indicate that the proposed method can provide an accurate quantitative assessment for investigation the dynamic response of the joints with focusing the contact areas.

Study on the influence of radial stiffness on the nonlinear vibration of brake system

Purpose A dynamic model of the brake system considering the tangential and radial motion of the pad, and the torsion and wobbling motion of the disk is established in this paper. The influence of radial stiffness on the brake system is investigated under different tribological conditions. This paper aims to prove that sufficient radial stiffness is indispensable in the design of the brake system with good tribological performance. Design/methodology/approach By using the lumped mass method, a dynamic model of the brake system is established. A Stribeck-type friction model is applied to this model to correlate the frictional velocity, pressure and friction force. The stability of pad vibration is analysed by analysis methods. A new stability evaluation parameter is proposed to study the influence of radial stiffness on stability of pad vibration in a certain friction coefficient brake pressure range. Findings The findings show that the tangential vibration of the pad transits from periodic motion to quasi-periodic motion under a low tangential stiffness. The influence of radial stiffness on motion stability is stronger under a low nominal brake radius. The stability of the brake system can be ensured when the brake radius and radial stiffness are sufficient. Originality/value The influence of tangential stiffness of pad on stability of the brake system has been researched for decades. The insufficiency of stiffness in radial direction may also generate certain levels of instabilities but has not been fully investigated by modelling approach. This paper reveals that this parameter is also strongly correlated to nonlinear vibration of the brake pad.

Vibration and Derailment Analyses of Trains Moving on Curved and Cant Rails

A moving axle finite element (FE) was developed to study the contact between a wheel and curved rail, where the FE can simulate multi-point contact with sticking, sliding, and separation modes. The possible contact region is inputted as a number of nodes along the wheel and rail surfaces, while the wheel nodes are simulated as cubic-splines. The rail node to wheel cubic-splines contact method is then used to find the normal and shear forces, where the normal and tangential stiffness values obtained from the three-dimensional (3D) FE analysis for an actual wheel and rail are used to model the force–displacement relationship. A simple theoretical solution for curved railways was used to validate the proposed FE in 3D analyses. The results show that good agreement with the theoretical and FE solutions for the contact normal force, shear force, wheel sliding, and wheel separation under various train speeds, curve radius, cant angles, and friction coefficients. This FE can be used in combination with other elements to simulate a train traveling on a curved track system, in which only the standard Newton–Raphson and Newmark’s methods are required in the FE main program.

A study on the vibration dissipation mechanism of the rotating blade with dovetail joint

The vibration dissipation mechanism of the rotating blade with a dovetail joint is studied in this paper. Dry friction damping plays an indispensable role in the direction of vibration reduction. The vibration level is reduced by consuming the total energy of the turbine blade with the dry friction device on the blade-root in the paper. The mechanism of the vibration reduction is revealed by the variation of the friction force and the energy dissipation ratio of dry friction. In this paper, the flexible blade with a dovetail interface feature is discretized by using the spatial beam element based on the finite element theory. Then the classical Coulomb-spring friction model is introduced to obtain the dry friction model on the contact interfaces of the tenon-mortise structure. What is more, the effects of the system parameters (such as the rotating speed, the friction coefficient, the installation angle of the tenon) and the excitation level on blade damping characteristics are discussed, respectively. The results show that the variation of the system parameters leads to a significant change of damping characteristics of the blade. The variation of the tangential stiffness and the position of the external excitation will affect the nonlinear characteristics and vibration damping characteristics.

Rate of deformation in the cross section of a spatially curved rod with various assumptions

The article considers incremental relations connecting the changes in the kinematic parameters of the rod cross section with the deformation rate. These relations allow assessing the deformation rate on the elemental areas of a spatially curved rod, as well as considering the distortion of cross-section in its plane due to shear and torsion. Assessment of such relations between deformation rates and the rates of kinematic parameters allows developing the method of nonlinear calculation of rod systems based on integral expressions. Subsequently, these relations will be used for assessing the tangential stiffness of the rod element cross-section subjected to elastic-plastic calculation.

Emergence of tangential stiffness through the use of inclined orthotropic material

A flexible bearing support structure is effective for stabilizing the self-excited vibration of a bearing, such as oil whirl. The stabilization effect is increased if the structure has static tangential stiffness, where the reaction force is perpendicular to the displacement. In this study, it is shown that a support component made of inclined orthotropic material, which exhibits shear–extension coupling, can have tangential stiffness. The circumferential average of the tangential stiffness was found to vanish with a rotationally symmetric configuration of these components because the tangential forces of each component cancel out. However, the tangential force was recovered by allowing separation on the contact surface. A circular formation of an inclined orthotropic sheet that shows an axisymmetric stiffness matrix is proposed. Theoretical and numerical analyses clarified the effects of the friction coefficient, fitting interference, and degree of anisotropy of the material. Zero interference was found to be the best condition to maximize tangential stiffness.

In Situ Investigation of Load-Dependent Nonlinearities in Tangential Stiffness and Damping of Spherical Contacts

Seemingly stationary (pre-sliding) interfaces between different materials, parts, and components are major sources of compliance and damping in structures. Classical pre-sliding contact models assume smooth elastic contact and predict that frictional slip leads to a well-defined set of stiffness and damping nonlinearities. However, reported data deviate from those predictions, and literature lacks a conclusive evidence leading to those deviations. In this work, the authors measure tangential stiffness and damping capacities inside a scanning electron microscope (SEM) while monitoring contacts between a rigid spherical probe and two materials (high-density polyethylene (HDPE) and polyurethane elastomer). Measured force, displacement, contact area, stiffness, and damping are then compared with predictions of classical models. In situ SEM images synchronized to the tangential force–displacement responses are utilized to relate the degree of plasticity and geometric alterations to stiffness and damping nonlinearities. In agreement with the classical models, increasing tangential loads cause softening in contacts under light normal preloads. In contrast, stiffness for HDPE increases with increasing tangential loads at heavy normal preloads due to plasticity and pileups over the contact. Material damping is prevalent for all loading cases in polyurethane samples thanks to nearly fully adhered contact, whereas for only light tangential loads in HDPE. With increasing tangential loading, specific damping capacity of HDPE contacts increases tenfold. This nonlinear increase is due to plastic shearing and frictional losses induced by tangential loading. Those findings suggest that predictive interface models should include geometric alterations of contact, plasticity, and material damping.

A Coupled Eulerian–Lagrangian Model for Sliding Inception of Elastic–Plastic Spherical Contact

Currently existing finite element (FE) Lagrangian models of elastic–plastic spherical contact are costly in terms of computing time to reach vanishing tangential stiffness at sliding inception. A coupled Eulerian–Lagrangian (CEL) model with explicit dynamic analysis and power-law hardening is proposed to resolve this problem. The CEL model also avoids convergence problem caused by excessive distortion of elements in Lagrangian models. Static friction coefficient at sliding inception is investigated and compared with available experimental results. It is found that the proposed new CEL model is more efficient and accurate compared to previously published results of Lagrangian models.

Torsional Stiffness Model of an Industrial Robotic Joint Using Fractal Theory

It is known that mechanical connections have great influence on the dynamic characteristic of the assembly. In existing methods, the torsional stiffness of the robotic joint is calculated only considering the stiffness of components of the system, which largely reduces the prediction accuracy of the joint stiffness. In the paper, to predict the joint stiffness more accurately, a model is proposed considering influences of the stiffness of all connections existed in a joint system. The normal and tangential stiffness of the contact surface of each connection are calculated by combining the equilibrium analysis of the force and the fractal theory. Then the total stiffness of one robotic joint can be modelled by putting the torsional stiffness of all connections and that of the RV reducer and gear pair in parallel. To verify the proposed model, its simulation result is compared to the stiffness based on the previous technique without considering the influence of connections. The comparison result shows that the proposed model can improve the stiffness-prediction accuracy. This study can be extended to the stiffness modeling of other joint systems and provides a theoretical basis for the dynamic analysis of the robotic system.