Influence of the longitudinal displacement on nonlinear principal parametric resonance of the woodworking bandsaw

The transverse vibrations of axially moving Timoshenko beam, as suitable mathematical models for woodworking bandsaws, are investigated. Special attention is paid to the influence of longitudinal displacement effect, as opposed to most models which can be usually encountered in the literature. This influence is introduced through the integro-partial differential equations. The expressions for the mode shapes in the case of hybrid supports with different torsion spring stiffness on the support points are also derived. The influence of mean beam velocity and axial tension on its natural frequencies and mode shapes is also investigated. Based on the nonlinear model, the amplitudes of the steady-state response are calculated for the case of principal parametric resonance. Developed program solution was tested on a number of earlier known examples. Present theoretical considerations, with the help of the program solution, is also used to analyse an example from industrial practice

The dynamics of mine hoist catenaries.

A Thesis Submitted to the Faculty of Engineering, University of the Witwatersrand, Johannesburg, South Africa for the Degree of Doctor of Philosophy.The dynamic analysis of catenary vibration of mine hoist ropes on South African mines is examined. This research has been preceded by studies in the mining industry, which have laid the foundation fot the definition of design guidelines of hoist systems to avoid catenary vibrations or rope whip. These guidelines are based on a classical linear analysis of a taut string, and in essence rely on ensuring that the frequency of excitation at the winder drum due to the coilingmechanism, does not coincide with the linear transverse natural frequency of the taut catenary. Such an approach neglects the nonlinear coupling between the lateral catenary motion and the longitudinal systern response. Although previous research sug gested the possibility of autoparametric coupling between the catenary and vertical rope, this was not developed further on a theoretical level.. The possibility of such behaviour is defined by considering the equations of motion of the coupled system. A design methodology is developed for determining the parameters of a mine hoist systern so as to avoid rope whip. The methodology accounts for the nonlinear coupling between the catenary and longitudinal system. In order to implement the proposed methodology, two phases of the analysis are developed. In the first phase the stability of the linear steady state motion is examined in the context of the nonlinear equations of motion, by applying a harmonic balance method. The stability analysis defines regions of secondary resonance, where it is shown that such regions may arise at sum and difference combinations of the linear lateral and longitudinal natural frequencies due to autoparametric excitation. Prior to this research, this phenomenon had not been appreciated in the context of the mine hoist system. A laboratory experiment was conducted to confirm the existence of these regions experimentally. In reality, the system is non-stationary since the dynamic characteristics of the system change during the winding cycle, and hence the steady state stability analysis can only describe potential regions of nonlinear interaction on a qualitative basis. The second phase of the analysis deals with a non-linear numerical simulation of the hoist system, which accounts for the non-stationary nature of the systems dynamic characteristics, and includes transient excitations induced during the wind. The methodology developed is assessed by considering the Kloof mine rope system, where rope whip was observed. This study demonstrates that although an appreciation of the steady state system characteristics is useful, the stability analysis alone is not sufficient. It is necessary to account for the non-stationary aspects of the winding cycle if a realistic interpretation of the observed behavlcur is to be achieved. To compliment this study, a motion analysis system was developed to record catenary response on an existing mine hoist installation. Such data has not been recorded before. This data provides direct evidence of the autoparametric nature of the coupled catenary/vertical rope system.AC201

Condition monitoring of belt based motion transmission systems

A key asset of Royal Mail Group consists of a nationwide network of sorting offices that forms a constituent component of the means through which the organisation provides an efficient nationwide postal service within the United Kingdom. It may be argued that the efficiency currently possessed by modem sorting offices is due to the utilisation of machines that automate the process of sorting items of mail. The modem letter-sorting machine possessed by Royal Mail can sort up to 30,000 letters per hour; such machines serve as an example of an achievement of the application of Mechatronics. The maintenance of letter sorting machines constitutes a large overhead for the organisation. In the face of competition from pervasive electronic media within the personal communications market and the prospect of deregulation, Royal Mail seeks to streamline its operation in part by the reduction of the overheads incurred through maintenance of letter sorting machinery. The adoption of condition based maintenance techniques and predictive maintenance, for letter sorting machine components such as belts and bearings, forms part of the strategy through which Royal Mail seeks to reduce this overhead. Utilisation of flat belts and timing belts for the implementation of key functions in letter sorting machinery, such as the transportation of items of mail within the mail sorting process, results in the use of many such components within letter sorting machinery. A direct link exists between the maintenance of peak performance of a sorting machine and the maintenance of belt drives; as such the maintenance of belt drives forms a substantial component of the maintenance overhead. The focus of this thesis consists of the condition monitoring of belt based motion transmission systems and in particular, flat belts. The research that forms the basis of this thesis consists of three elements. Firstly, consideration of current knowledge of belt based power transmission such as knowledge of the mechanics of the belt based power transmission process within the context of condition monitoring... [cont'd

An experimental and computational investigation of rotating flexible shaft system dynamics in rotary drilling assemblies for down hole drilling vibration mitigation

Rotary drilling system vibration has long been associated with damaging the bit, the bottom hole assembly (BHA) and drill string. Vibration has been traditionally measured in the bottom hole assembly, and been closely associated with the resonant behaviors. This research study proposes an improved physical laboratory model to explore the dynamic behaviors associated with vibration. This model includes contact with the borehole wall allowing a range of stabilization geometries while removing bit-formation interaction effects. The results of exercising the model help develop new insights into both vibration measurement diagnostics and mitigation strategy execution. Presented here is a review of other physical bottom hole assembly and drilling concepts, and a new novel model. Experimental investigation using the new model for a range of geometries is presented with recorded conditions, annotated video stills and analysis using regression and response surface methods. The analysis when compared to existing industry mitigation methods allows unique insight to the possible effectiveness of such methods. A numerical simulation of the system was also performed and its results compared to the laboratory tests. Results show that a shaft system alone can generate stick-slip and whirl behaviors. Such behaviors occur in distinct regions. Another conclusion of this work is that a popular method for inferring stick-slip from acceleration measures is not reliable for the system used in this study

Recent Developments in the Dynamic Stability of Elastic Structures

Dynamic instability in the mechanics of elastic structures is a fascinating topic, with many issues still unsettled. Accordingly, there is a wealth of literature examining the problems from different perspectives (analytical, numerical, experimental etc.), and coverings a wide variety of topics (bifurcations, chaos, strange attractors, imperfection sensitivity, tailor-ability, parametric resonance, conservative or non-conservative systems, linear or nonlinear systems, fluid-solid interaction, follower forces etc.). This paper provides a survey of selected topics of current research interest. It aims to collate the key recent developments and international trends, as well as describe any possible future challenges. A paradigmatic example of Ziegler's paradox on the destabilizing effect of small damping is also included

The dynamics of mine hoist catenaries.

A Thesis Submitted to the Faculty of Engineering, University of the Witwatersrand, Johannesburg, South Africa for the Degree of Doctor of Philosophy.The dynamic analysis of catenary vibration of mine hoist ropes on South African mines is examined. This research has been preceded by studies in the mining industry, which have laid the foundation fot the definition of design guidelines of hoist systems to avoid catenary vibrations or rope whip. These guidelines are based on a classical linear analysis of a taut string, and in essence rely on ensuring that the frequency of excitation at the winder drum due to the coilingmechanism, does not coincide with the linear transverse natural frequency of the taut catenary. Such an approach neglects the nonlinear coupling between the lateral catenary motion and the longitudinal systern response. Although previous research sug gested the possibility of autoparametric coupling between the catenary and vertical rope, this was not developed further on a theoretical level.. The possibility of such behaviour is defined by considering the equations of motion of the coupled system. A design methodology is developed for determining the parameters of a mine hoist systern so as to avoid rope whip. The methodology accounts for the nonlinear coupling between the catenary and longitudinal system. In order to implement the proposed methodology, two phases of the analysis are developed. In the first phase the stability of the linear steady state motion is examined in the context of the nonlinear equations of motion, by applying a harmonic balance method. The stability analysis defines regions of secondary resonance, where it is shown that such regions may arise at sum and difference combinations of the linear lateral and longitudinal natural frequencies due to autoparametric excitation. Prior to this research, this phenomenon had not been appreciated in the context of the mine hoist system. A laboratory experiment was conducted to confirm the existence of these regions experimentally. In reality, the system is non-stationary since the dynamic characteristics of the system change during the winding cycle, and hence the steady state stability analysis can only describe potential regions of nonlinear interaction on a qualitative basis. The second phase of the analysis deals with a non-linear numerical simulation of the hoist system, which accounts for the non-stationary nature of the systems dynamic characteristics, and includes transient excitations induced during the wind. The methodology developed is assessed by considering the Kloof mine rope system, where rope whip was observed. This study demonstrates that although an appreciation of the steady state system characteristics is useful, the stability analysis alone is not sufficient. It is necessary to account for the non-stationary aspects of the winding cycle if a realistic interpretation of the observed behavlcur is to be achieved. To compliment this study, a motion analysis system was developed to record catenary response on an existing mine hoist installation. Such data has not been recorded before. This data provides direct evidence of the autoparametric nature of the coupled catenary/vertical rope system.AC201

Machine generated vertical vibration in elevators

Vertical vibration deteriorates passenger comfort during an elevator travel. The drive system is a source of vertical vibration as well as the source of energy of the system. This report presents the results of a study of car vertical vibrations generated at the drive system in elevator installations. The elevator system can be considered as a translating assembly of inertia elements coupled and constrained by one-dimensional slender continua. The inertia elements are the car assembly, the counterweight, the traction sheave and other rotating components of the system. According to the roping arrangement and to the ratio of the tangential velocity of the traction sheave to the velocity of the car, the traction elevators can be classified as roped 1:1 or multiple reeving systems: the types examined in the present work are 1:1 and 2:1 traction elevators. Distributed- and lumped-parameter models (DPM and LPM respectively) are developed to calculate the natural frequencies and mode shapes of stationary elevator systems and their results compared. A non-stationary model of a 1:1 roping configuration elevator is developed as well to simulate the elevator acceleration response. The model accommodates the drive system dynamics: it includes the electric motor and the torque and velocity controllers, which ensure that the car follows a prescribed kinematic profile, so that good ride quality of the elevator is achieved. The machine parameters are computed by means of the Finite Element Method simulation software FLUX. With respect to the carcounterweight-sheave-ropes assembly, a LPM and a novel DPM are developed. The elevator dynamics represented by the DPM is described by a partial differential equation set that is discretised by expanding the vertical displacements in terms of the linear stationary mode shapes of a system composed of three masses constrained by the suspension rope. The models are implemented in the MATLAB/Simulink computational environment and the system response is determined through numerical simulation. It is shown that the LPM forms a good approximation of the DPM. Experimental tests are carried out on laboratory models. The elasticity modulus of the rope and the friction coefficients at the guide rail contact and at the machine are estimated. The acceleration response at the suspended masses and at the drive machine, the machine shaft velocity and the three phase current intensities supplied to the machine are measured during several travels. The machine torque is estimated from the current intensities. The computed and measured accelerations are compared either in time or frequency domain and it is demonstrated that the elevator car vibrates at frequencies generated at the machine, especially when they are close to the system natural frequencies. The proposed simulation models can be used as design and analysis tools in the development of high-performance elevator systems

Investigation of internal damping in carbon fiber and steel cables

The characterization of cable damping is important for the stability and performance of structures deployed in space using cables. However, literature available for the analysis of carbon fiber cable damping and its effect on dynamical behavior of deployable space structure is scarce. The objective of this work is to examine the variation of cable damping involving different cable properties and the ambient environments through several carefully instrumented tests. An analytical model to predict damping based on internal forces and variable cable geometry is developed and compared with those of tests. An experimental set-up for the measurement of cable damping is described. Cables in different lengths (0.2032m, 0.3048m and 0.5080m), constructions (20.71turns/m, 41.42tutns/m and 62.13turns/m), temperatures (20\u2103 and 4\u2103) and air pressures (normal and vacuum) are tested under five different tensile forces (111.25N, 222.50N, 333.75N, 445.00N and 578.50N). In addition, the effect of sensor mass, the support and test apparatus on damping are investigated. The damping is identified by the half-power bandwidth\u27 method and the \u27logarithmic decrement\u27 method. The results indicate that, typically, damping decreases as the length, tension and the number of turns of the tested cable increases. Also, temperature and air pressure contribute to the variation of damping. To explore the use of finite elements method (FEM) to simulate cable vibration and damping, the COMBIN14 and MASS21 elements in ANSYS13.0 are used. The finite element simulation results agree well with the test results on vibration frequency and time history response. This demonstrates that the selected elements are capable of modeling the dynamic response of cables using the Rayleigh damping constants. Using simplified mechanistic assumptions, an analytical approach is proposed to model cable damping. The proposed method and related issues are discussed considering numerical examples. It is shown that this method can predict the damping variation trend as observed in the tests of carbon fiber cables.\u2