Vibration System Mechanical
Due to massive development in the computers and their related softwares, Vibration analysis and suppression became an important task since 1960. [1].
In order to study the effects of vibrations in the right way, we should check first of all the reasons which cause that vibration. For this purpose, the analysis of dynamic behavior of the mechanical system and devices operation should be carried out. This task is not an easy task because of complexity of the mechanical systems and the associated devices . the mechanical systems are composed of many parts with many degrees of freedom, complicated structure and with closed, opened or branched kinematics. They are characterized by holonomic or nonholonomic constraints, elastic elements, elements with variable mass with clearances in kinematics pairs, etc.
There are many sources of the vibrations in the mechanical systems and their associated devices but identifying and allocating theses sources is not an easy task. The reasons of vibrations which disturb a mechanical system operation are different. Some of them come out from the realization of the technological process. The other result from the abnormal assembly, wear and tear of parts, etc. Beside that some reasons come out from the external influence related to the environment.
Vibration is affection the mechanical system due to the disturbances, it is affecting the environemt because of the nosie which result from the vibration,.
Vibrations suppression and control deals with two main tasks, the mechanical system operation protection, and Minimizing the undesirable effects.
2.2 Methods of vibration reduction
Recently, many methods an approache has been presented to minimize and control the vibration of the mechanical systems. These methods could be classified to two main groups which are passive and active methods [33].
The protection of vibration reasons, parametric modifications, Structural modifications, and Vibration damping are considered as a passive methods
The protection of vibration reasons consist in elimination of additional energy sources, elimination or decrease input forces and isolation from external disturbances e.g. balancing, decrease of colliding bodies mass, substitution of rolling bearings by slide ones, etc. The parametric modifications lead mainly to changes of mass and stiffness elements. The structural modifications deal with introducing additional constraints to the system or tearing of existing ones by adding vibration eliminators. The damping is also important but it comes second in the analaysis. It refers to mechanical energy dissipation which is exchanged to heat. It causes the decrease of general efficiency of machines and devices. The ideal device performance should run with minimal damping value. In case when the undesirable vibrations cannot be eliminated via constructional or parameters changes the damping should be introduced. This additional damping consist in the use of: constructional materials with appropriate damping value, frictional joints, additional dampers introducing e.g. hydraulic ones.
Residual vibration suppression is important in a broad range of mechanical engineering applications such as the deployment of space structures and cranes or the operation of machine tools and flexible robots. The traditional approaches to minimize the effect of residual vibrations are focused on either increasing the structural stiffness, which increases the system's size and weight or using closed loop control methods, which require accurate on-board electronics and increase the system's cost and complexity.
An alternative approach for suppressing residual vibrations is the proper conditioning of the prespecified excitation pattern, the so-called Guidance, so that the system moves exactly to the desired end position without any residual vibrations[3]. the methods in this category are traditionally considered to be quite sensitive to variations of the system dynamic parameters, significant research effort has been devoted to increase their robustness features. A brief survey of relevant methods has been performed by Antoniadis [4].
command shaping for vibration reduction is an old technique [34], however the field has been improved by notion that the technique can be used successfully even with a large uncertainty in the system parameters [5]. Input shaping has been successfully applied for controlling the vibration of the mechanical systems. Input shaping is implemented by convoluting a sequence of impulses with system command input to produce a shaped input which used to drive the system. This technique is become very popular due to its simplicity.
The effectiveness of the input shaping has been demonstrated on many different types of systems and many papers has been published on input shaping since its original presentation. Due to ease of implementation and robustness of minimize the vibration, input shaping has been implemented on applications ranging from the small machines to large cranes[8,9].
While input shaping methods present good performance in many applications, their robustness is limited in some cases, for instance around the system natural frequencies , to resolve that the total duration of the pulse sequence is to be increased. This will results in a delays in the total duration of the system motion. In a first attempt to extend the robustness of the vibration suppression method based on the convolution with a series of impulses, a general approach has been proposed by Antoniadis [4], leading to a set of three different methods for the design of the impulse sequence.
Input shaping has been used successfully in many applications for vibration suppression such as long reach manipulators, cranes and coordinate measuring machines [12-14]. It is widely employed in flexible aircraft [28] and helicopter control [29]. In these methodologies, a feedforward input signal is shaped so that it does not contain spectral components at the system's resonance frequencies. A significant amount of work on shaped command input based on filtering techniques has been reported. These include low-pass filters, band-stop filters and notch filters. Singer and Seering [5] have proposed an input-shaping strategy, which is currently receiving considerable attention in vibration control [5, 30, 31]. The method involves convolving a desired command with a sequence of impulses known as an input shaper. The shaped command that results from the convolution is then used to drive the system. Design objectives are to determine the amplitude and time locations of the impulses, so that the shaped command reduces the detrimental effects of system flexibility. These parameters are obtained from the natural frequencies and damping ratios of the system. Using this method, a response without vibration can be achieved. But with a slight time delay approximately equal to the length of the impulse sequence. The method has been shown to be the most effective in reducing motion-induced vibrations [32]. With more impulses, the system becomes more robust to flexible mode parameter changes, but this will result in a longer delay in the system response.
While input shaping methods present good performance in a variety of systems and applications, their robustness is limited in local areas around the system natural frequencies and can be increased only by increasing the total duration of the pulse sequence. This results in unnecessary delays of the total duration of the system motion. In a first attempt to extend the robustness of the vibration suppression method based on the convolution of the guidance function with a series of impulses, a general approach has been proposed, leading to a set of three different methods for the proper design of the impulse sequence [4].
The impulse sequence approach is significantly extended in [10], by establishing a theoretical framework, according to which the design of an appropriate guidance function can be transformed to the proper design of a conventional lowpass Finit Impulse Response (FIR) digital filter. Furthermore, in order to ensure the proper design of the filters, the .Delay-Error-Order (DEO) Curves concept has been proposed, as a filter design tool [15]. The effectiveness of FIR filters for residual vibration suppression has been studied thoroughly both theoretically and experimentally [11, 15].
The residual motion (vibration) in a flexible system is normally fast motion induced. The occurrence of any vibration after the commanded position has been reached will require additional settling time before the new maneuver can be initiated [3]. Therefore, in order to achieve a fast system response to command input signals, it
is imperative that this vibration is reduced. This feature is desirable in fast maneuvering systems, such as fighter aircraft. Various approaches have been proposed to reduce vibration in flexible systems. They can be broadly categorized as feedforward, feedback or a combination of both methods. Command shaping is one of the several methods used for feed-forward motion-induced vibration control.
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