Archive of Mechanical Engineering

In this obituary, we present the life and achievements of an outstanding Polish scientist, Professor Jan Kruszewski-Majewski, who passed away in 2012. Professor Kruszewski-Majewski was one of the pioneers in introducing modern numerical methods in mechanics. He created and developed an original, Polish method of modelling called the rigid finite element method. He was not only an outstanding scientist, but also a person of great charisma and moral rectitude.

In the paper, the authors describe the method of reduction of a model of rotor system. The proposed approach makes it possible to obtain a low order model including e.g. non-proportional damping or the gyroscopic effect. This method is illustrated using an example of a rotor system. First, a model of the system is built without gyroscopic and damping effects by using the rigid finite element method. Next, this model is reduced. Finally, two identical, low order, reduced models in two perpendicular planes are coupled together by means of gyroscopic and damping interaction to form one model of the system. Thus a hybrid model is obtained. The advantage of the presented method is that the number of gyroscopic and damping interactions does not affect the model range.

An original method of skeletal system modelling is presented in detail. Using DICOM images obtained from CT and PET tests, shell models of nine bones were created (humerus, radius, ulna, scapula, clavicle, femur, tibia, fibula, pelvis). Two methods of bone behaviour are also proposed, the first method treating the bone as a solid structure and the second method treating the bone as a complex porous structure. The behaviour of model parts is numerically examined by using the finite element method.

The paper concerns development of original method of optimal control at energy performance index and its application to dynamic processes surveillance of some mechatronic systems. The latter concerns chatter vibration surveillance during highspeed slender milling of rigid details, as well as motion control of two-wheeled mobile platform. Results of on-line computer simulations and real performance on the target objects reflect a great efficiency of the processes surveillance.

In the paper, a mechanical set composed of a robot (manipulator) and of an elastic beam is considered. The beam is fixed to the top of the robot structure. In most of similar cases, undesired vibrations can be excited in the beam. They create an especially significant problem when dynamics in the robot braking period is examined. In the paper, estimation and modification of length of the braking period is proposed, in order to reduce the undesired vibrations. Investigations are restricted to numerical models, only. The rigid finite elements modelling and the multibody modelling are used together to obtain the numerical model required for the system. Instead of the classical rigid finite elements, its modified version is used, where some of the relative deformations are locked between the neighbour elements. As a result, sizes of the obtained matrices can be reduced as well as the time of the numerical calculations.

The paper presents a model of an articulated vehicle with a flexible frame of a semi-trailer. The rigid finite element method in a modified formulation is used for discretisation of the frame. In order to carry out effective numerical simulation, a reduced model with a considerably smaller number of degrees of freedom is proposed. The parameters of the reduced model are chosen in an optimization process by using a genetic algorithm. To this end, it is assumed that the full and reduced model have to be similar in the range of static deflections and frequencies of free vibrations. Numerical simulations are concerned with the influence of the flexibility of the frame on the motion of the articulated vehicle during an overtaking maneuver. Results are presented and discussed.

The paper presents an application of the modified rigid finite element method to analysis of the dynamics of slender structures. The equations of motion are formulated for a system discretized by means of the method, and discussion is limited to planar systems and large deformations. Slender elements can be found in offshore engineering as lines, cables and risers. In these cases the hydrostatic influence of water and sea currents has to be taken into account. While analyzing dynamics of risers it may also be necessary to consider the flow of fluid inside the riser. The influence of hydrodynamic coefficients and the velocity of the internal flow of fluid on displacements and forces is presented.

Dry electrostatic precipitators (ESPs) are widely used for purification of exhaust gases in industrial applications. Maintenance of their high efficiency depends primarily on periodical cleaning of the collecting electrodes (CEs). Dust removal (regeneration of CEs) is realized by inducing periodical vibrations of the electrodes. The paper presents results of vibration modelling of a system of CEs; the results were obtained by means of the finite element method, the hybrid finite element method, the finite strip method and a model formulated using Abaqus. Numerical results are compared with those obtained from experimental measurements. Conclusions concerning numerical effectiveness and exactness of the methods are formulated and reasons for differences are discussed.

In offshore pedestal cranes one may distinguish three components of considerable length: a pedestal, a boom and a frame present in some designs. It is often necessary in dynamical analyses to take into account their flexibility. A convenient and efficient method for modelling them is the rigid finite element method in a modified form. The rigid finite element method allows us to take into account the flexibility of the beam system in selected directions while introducing a relatively small number of additional degrees of freedom to the system. This paper presents a method for modelling the pedestal, the frame and the boom of an offshore column crane, treating each of these components in a slightly different way. A custom approach is applied to the pedestal, using rigid finite elements of variable length. Results of sample numeric computations are included.