Vol. 1, No. 4 (2017): Regular Issue

PID control is widely used in electro-hydraulic systems. However, enhancing PID control performance in response to system nonlinearity, fluctuations of external load, and noise inevitably renders the chattering of the system that are also telltale indications of poor efficiency and dynamic instability. On the other hand, tuning down PID parameters would alleviate chatter at the expenses of reduced performance and inefficient use of resources. To address the particular issue, a novel controller concept termed as the time-frequency PID (TFPID) is developed. Firstly, a nonlinear electro-hydraulic dynamic model to be controlled is built for numerical and physical studies. Next, the working principle of the TFPID control is elaborated where the discrete wavelet transform is employed to decompose the error signal into high frequency error and low frequency error. Two unique PID controllers incorporating proportion, differential, and integral control are designed to mitigate the two error signals. The TFPID controller and system model are developed in MATLAB/Simulink to optimize the parameters and a hardware-in-the-loop test bench is employed to establish the performance of the system subject to interferences. Physical test results show that TFPID performs significantly better in anti-interference, stability, and dynamic response.

Tool-workpiece dynamics is characterized by aperiodic responses in- cluding period-doubling bifurcation and chaos. As a state signifying the extent of machining instability, tool chatter in longitudinal turn- ing operation is a function of nonlinear regenerative cutting force, instantaneous depth-of-cut (DOC), and workpiece whirling. The ef- fects of tool geometry and feed rate per revolution on cutting stability are investigated using a comprehensive model previously reported in References [1–3]. The model configuration allows the coupled tool- workpiece motion relative to the machining surface to be studied in the Cartesian space as a function of spindle speed, instantaneous DOC, rate of material removal, tool geometry, and material imbal- ance induced whirling. It is found that chatter can be eminent using one set of tool geometry while, at the same DOC, be sufficiently sup- pressed by employing tool inserts of different geometric parameters. Nonlinearity of tool structure is shown to have a dominant effect on tool vibration amplitude. High feed rate contributes to stability at high DOCs, thus indicating that feed rate is among the parameters that impact cutting stability.

Mechanical systems have traditionally provided a fertile area of study for researchers interested in nonlinear control, due to the inherent nonlinearities and the Lagrangian structure of these systems. Recently, a great deal of emphasis has been placed on studying systems with nonholonomic constraints, including mobile wheeled robots and multiple-trailer vehicles, where the wheels provide a no-slip velocity constraint. In this paper, a new methods in non-holonomic mechanics are applied to a problem of an ackerman steered car motion for the first time. This method of the geometrical theory of general nonholonomic constrained systems on fibered manifolds and their jet prolongations, based on so-called Chetaev-type constraint forces, was proposed and developed in the last decade by Krupkov´a in 1990’s. The relevance of this theory for general types of nonholonomic constraints, not only linear or affine ones, was then verified on appropriate models. Frequently considered constraints on real physical systems are based on rolling without sliding, i.e. they are holonomic, or semi-holonomic, i.e. integrable. Moreover, there exist some practical examples of systems subjected to true (non-integrable) nonholonomic constraint conditions. On the other hand, the equations of motion of an ackerman steered car are highly nonlinear and rolling without slipping condition can only be expressed by nonholonomic constraint equations. In this paper, the geometrical theory is applied to the above mentioned mechanical problem using the above mentioned Krupkov´a approach. The results of numerical solutions of constrained equations of motion, derived within the theory, are presented and thus they open the possibility of direct application of the theory to practical situations in engineers.

Flow-induced vibration of the flexible bottom wall in a lid-driven cavity is investigated numerically using a well-validated finite element scheme for fluid-structure interaction (FSI). First, the mechanical and mathematical models of a lid-driven cavity with flexible bottom are presented, and the corresponding FSI solution procedure is introduced briefly. Then, the accuracy and stability of the developed FSI scheme and code are examined and a grid independence test is carried out. Finally, using very fine increment, bifurcations of the flow-induced vibration (FIV) of the flexible bottom with respect to the structure rigidity and Reynolds number are studied in detail. The results could reveal more details of the benchmark FSI model involving a lid-driven cavity with flexible bottom, gaining a better understanding on other FIVs caused by the internal unsteady flows.

Unbalance is one of the most common mechanical faults in rotating machines. Although different balancing methods have been developed, most of them require balancing machine to perform unbalance correction. A method using accelerometers data and intricate vibration theories can eliminate the need of balancing machine, and the amplitude and phase of the machine’s vibrations can be identified. However it needs numerous measurements, and in some cases it is even impossible to be implemented. To overcome this problem, a novel approach with reduced number of measurements is presented in this paper. The proposed method requires only two measurements: one from original unbalanced condition, and the other from modified situation after adding an arbitrary trial mass to a marked location. The rotating rotor is being video recorded under original unbalanced and modified situations. The position of the marked area is identified when the amplitude of the sinusoidal vibration response reaches the maximum. The correction mass and its adding location are calculated using proposed method. To demonstrate the effectiveness of our method, an experiment is setup. Vibrations under healthy, unbalanced and balanced conditions are analyzed. The results demonstrated that the developed method is more cost effective with the same accuracy as the other contested balancing techniques.

In this paper, bifurcation trees of periodic motions to chaos in a periodically forced, time-delayed, twin-well Duffing oscillator are pre- dicted by a semi-analytical method. The twin-well Duffing oscilla tor is extensively used in physics and engineering. The bifurcation trees of periodic motions to chaos in nonlinear dynamical systems is very significant for determine motion complexity. Thus, the bi furcation trees for periodic motions to chaos in such a time-delayed, twin-well Duffing oscillator are obtained analytically. From the fi nite discrete Fourier series, harmonic frequency-amplitude character istics for period-1 to period-4 motions are analyzed. The stability and bifurcation behaviors of the time-delayed Duffing oscillator are different from the non-time-delayed Duffing oscillator. From the an alytical prediction, numerical illustrations of periodic motions in the time-delayed, twin-well Duffing oscillator are completed. The com plexity of period-1 motions to chaos in nonlinear dynamical systems are strongly dependent on the distributions and quantity levels of harmonic amplitudes. As a slowly varying excitation becomes very slow, the excitation amplitude will approach infinity for the infinite bifurcation trees of period-1 motion to chaos. Thus infinite bifurca tion trees of period-1 motion to chaos can be obtained.