# Enhancing Vibration Analysis in Hydraulic Presses: A Case Study Evaluation
## 2 State of the Art  
Measurement is defined as a cognitive process involving the comparison, through physical experience, of a given quantity with a certain reference value accepted as the unit. This definition can be expanded to acknowledge that some automatic measuring instruments also fulfill executive tasks [13]. Measurement is thus the process of receiving and transforming information about the measured quantity in order to obtain, by comparison with a measurement unit, a quantitative result in a form most convenient for perception by human senses, transmission in space or time (registration), mathematical processing, or utilization for control purposes [14]. Conducting such measurements is necessary for the following [15; 16; 17]:  
* Determining vibration waveforms and their parameters over time to identify the type of vibrations and their characteristic magnitudes, and for conducting detailed analysis;
* Detecting sources of vibrations, i.e., identifying the cause of vibration occurrence and their locations;
* Determining characteristic features of mechanical systems (e.g., determining variations in loads over time during vibrations and their dependence on object parameters, shapes, dimensions, material properties, etc. );
* Isolating and reducing harmful vibrations for the reliable operation of equipment and the wellbeing of operators;
* Assessing the harmfulness of occurring vibrations for the operation of mechanical equipment and carrying out certain preventive measures. Often, it is crucial to determine the waveforms of natural and forced vibrations of mechanical systems. Only for simple systems can these waveforms be determined analytically. For more complex systems, these waveforms result from the superposition of natural vibrations, and they must be experimentally determined based on measurements at various points in the system. The waveforms of natural vibrations depend on the initial conditions and mechanical parameters of the system. The waveforms of forced vibrations depend on changes in excitation over time. Based on the obtained vibration waveforms, their type (periodic, random, non-stationary, etc.) can be determined, and an analysis can be conducted [18]. The aim of the analysis is to obtain information about the vibration parameters of a given system. An important aspect is to determine the nodes of vibration (points, lines, or surfaces that do not participate in vibrations) and points where the vibration amplitudes are highest for a given frequency. The set of vibration amplitudes of individual points in the system represents the shape (waveform) of the vibrations. These issues are the subject of geometric analysis [19; 20; 21]. Time-domain analysis involves determining how various quantities (linear displacement, velocity, acceleration, deformation, etc.) change over time [22]. If the changes are periodic, their frequency is also determined. If the changes are random, statistical methods are used for analysis [23; 24]. Insightful conclusions can also be drawn from a frequency-domain analysis, which involves determining characteristic changes in quantities and parameters as a function of frequency. Sources of vibrations can arise from constructional reasons (e.g., crank mechanisms, cam mechanisms, and other devices performing movements, such as drives of vibratory machines), technological reasons (imperfections in the manufacturing and assembly of machinery, e.g., imbalance of rotating masses, ovalization of bearing elements and rotating parts, unwanted clearances, and other defects), or operational reasons (due to wear of components and surface distortions during motion) [25; 26; 27]. By measuring the vibrations of individual elements of the examined object, it is possible to identify a subset that is the source of harmful vibrations. Often, replacing this subset can significantly reduce the vibrations of the entire object.