Nonlinear Dynamics of a Blade Rotor with Coupled Rubbing of Labyrinth Seal and Tip Seal

The dynamic response and its stability of a blade rotor with coupled rubbing in the labyrinth seal and tip seal are investigated. The dynamic equations are established based on the Hertz contact rubbing force at the labyrinth seal and the tip rubbing force considering both the contact deformation of the tip seal and the bending deformation of the blade. Numerical simulations show that the coupled rubbing response includes periodic motions, almost periodic motions, and chaotic motions. Compared with the single rubbing fault, coupled rubbing increases the range of rotation velocity of contact. A new continuation shooting method is used in the solution and stability analysis of the periodic response to give the bifurcation diagrams. The paths of the system for entering and exiting chaos are analyzed.

Determination of non!contact deformation of a material under the orbital action of an indenter

The influence of kinematic loading schemes on the formation of an elastoplastic wave under the orbital action of an indenter is considered. A mathematical model of hardening is presented, which determines the size and stressstrain state of the wave. The loading parameters influencing the wave size are determined. Keywords: kinematic diagram, orbital loading, deforming element, elastoplastic deformation, non-contact deformation, elastoplastic wave [email protected]

Indentation Measurement in Thin Plates under Bending Using 3D Digital Image Correlation

In the current paper, a novel experimental methodology to characterize the contact behavior on thin plates under bending is presented. The method is based on the experimental measurement of the indentation observed during contact experiments. Tests were conducted using aluminum thin plates and a steel sphere to evaluate the effect of thickness and bending during contact. For this purpose, a non-contact optical technique, 3D Digital Image Correlation (3D-DIC), has been employed to measure the out-of-plane displacements experienced at the rear face of the specimens (opposite where the contact is occurring). An indirect measurement of the experimental contact law is obtained for different plate thicknesses (2 mm, 3 mm, 4 mm, 5 mm and 6 mm) as the contact load increases. An energy balance performed during contact experiments made it possible to evaluate and quantify the applied energy to generate bending and contact deformation. When the specimen thickness increases from 2 mm to 6 mm, contact deformation reaches higher values from the total applied energy. In addition, it is also possible to evaluate the portion of the elastically recovered energy for contact and bending deformation during the unloading. It has been observed that thicker specimens show a lower elastic energy recovery due to bending and a higher elastic energy recovery due to contact. Results clearly show how the ratio between absorbed and applied energy changes as the specimen thickness increases, highlighting the relevance of the proposed method for the characterization of contact behavior in thin plates.

Investigation of the Transmission Accuracy of Ball Screw Considering Errors and Preloading Level

Transmission accuracy is one of the most important parameters in ball screw mechanism (BSM), however, very few researches can be found on the transmission accuracy modelling for BSM. Therefore, this paper proposes a novel model to predicate the transmission accuracy of BSM considering the manufacturing errors, installation errors, as well as the errors due to the contact deformation under different loading status. Meanwhile, the transmission accuracy of a typical BSM under five different preloading levels is measured on the basis of a transmission accuracy measuring system. The experimental results show that the difference is 21.6% under no preload condition, and is less than 11% under different preload conditions, largely owing to the uneven distribution of clearance can increase the travel deviation. Further analysis shows that the eccentricity error, which belongs to the installation error, is the most important factor, mainly generating the periodic fluctuation and amplitude of the transmission error. More importantly, the travel deviation increases with the increase of the preload, which indicates that the transmission accuracy of the BSM deteriorates when the load is increased.

The Limits of Applicability of the Method of Discontinuous Solutions in the Study of Pipe Drawing Processes

Introduction. Non-contact deformation of the workpiece material, which occurs along the boundaries of the deformation zone, is one of the main factors determining the energy-power parameters of pipe reduction processes. The most widespread practice in the design of metal forming processes is the method of discontinuous solutions, which makes it quite simple to take into account non-contact deformation in numerical simulation of processes. However, for most processes in the technical literature there are no systematic practical recommendations on the application of this method, which inevitably leads to a mismatch of theoretical principles and practice. The aim of the work is to determine the limits of applicability of the method of discontinuous solutions for processes of faultless drawing of pipes through a conical die, depending on the geometric parameters of the workpiece, tool, as well as the degree of deformation and hardening of the processed material. Research Methods. The model of the deformation zone for the process of flawless drawing is considered in two versions: by the method of discontinuous solutions and taking into account non-contact bends of the pipe wall. From the condition of the balance of the shear forces acting on the conditional shear surface and the bending moments caused by the bending of the pipe wall, under various deformation conditions, the boundary values of the thickness parameter are determined, at which it is advisable to carry out numerical simulation of the drawing processes using the discontinuous solution method. In this case, the calculations are performed separately for two sections of the deformation zone corresponding to the bending of the pipe wall at the entrance to and exit from the die. Results and discussions. The numerical implementation of the obtained dependences showed that at the entrance to the deformation zone, the boundary value of the thickness parameter increases with an increase in the taper angle of the die and the hood for the transition, but decreases with an increase in the anti-tension stress and the thickness parameter of the initial workpiece. At the exit from the deformation zone, the boundary value of the thick-walled parameter increases with an increase in the taper angle of the die and decreases with an increase in the stretch coefficient for the transition and the thick-walled parameter of the initial billet. If the parameter of the thickness of the initial billet exceeds the boundary value, then in numerical modeling it is advisable to use the method of discontinuous solutions. If it does not exceed, then other methods and models should be used. The results of a theoretical study can be used in the design of pipe drawing processes.