Experimental Measurement of Dynamic Characteristics of Structural Units

: The aim of this study is to investigate and optimize the dynamic properties of an entire structural unit. Using modal analysis and experimental measurements of the propulsion system, natural frequencies with close agreement were identiﬁed. The drive was able to work within the frequency range during start-up and normal operation, but due to various inﬂuences, including the inherent oscillations of structural elements, complex dynamic phenomena occurred. The presence of a conveyor with rubber and plastic wheels also affected the results. Important information on the input shaft, tooth frequency, driveline oscillation and output shaft was obtained. Research has identiﬁed resonant frequencies and increased drive oscillation that are created by the interaction between the input shaft and tooth frequency. The signiﬁcant frequency of bent screws in the conveyor pipe affects the shafts and the drive screw, which in turn causes problems with material fatigue and microcracks. Corrective measures include the possibility of replacing or balancing the screw and increasing the diameter of the pipe. Regular monitoring and diagnostics have a preventive nature and serve to minimize serious consequences. Implementing a controller with a PID system offers the potential to suppress oscillations and improve dynamic and strength characteristics, while accurate calibration of this implementation is of key importance.


Introduction
In technical practice, worm gears are frequently used elements of technical equipment in various spheres of industrial production where it is necessary to transmit torque.They are often combined with an electric motor, where they form a drive for various types of transport systems, either within production lines, for example in automotive or for the distribution of bulk materials such as sand.From a design point of view, these gears consist of a worm and a worm wheel, where these shafts are off-axis to each other, usually at 90 degrees.The worm gear and other structural parts (shafts, bearings, . ..) are stored in a gearbox, where more gear mechanisms and other types can be introduced, which are connected to each other and create a multi-stage gear [1][2][3].
In addition to the load-bearing function, the gearbox also fulfills a protective purpose, as it protects the gears themselves from dirt and also ensures effective lubrication.From a construction point of view, worm gears are manufactured as separate nodes, which are then joined into assemblies located on a common frame.According to the shape of the basic parts of the gears, we can divide worm gears into the following pairs: cylindrical worm-cylindrical worm wheel, cylindrical worm-globoid worm wheel and globoid wormgloboid worm wheel.Each of these types can be designed with any angle that its axes make [4][5][6].
The advantages of using worm gears include achieving high gear ratios, relatively quiet operation, high load capacity, smooth operation and the ability to self-lock when changing the direction of the torque, while this property can be used as a safety brake, for example, in lifting equipment.On the contrary, the disadvantage of using these types of gears is their relatively low efficiency, which in certain cases can reach only 70%, which is caused by high losses in the form of friction in the gearing.A high degree of friction between the teeth also causes the gearbox to overheat, which is related to the necessity of using additional cooling or oversizing the gearbox.The relatively expensive materials used for the production of worm wheels, which are usually alloys based on copper and tin, can also be considered a certain disadvantage [7][8][9][10].
Technical diagnostics deals with non-destructive methods of determining the technical condition of structural units in manufacturing engineering.Diagnostic methods for monitoring rotating machines evolve with technological progress and the development of computing and sensor technology.The reliability of diagnostics is determined by an optimal selection of sensors, their location and especially by processing measured data [11].A diagnostic algorithm is a set of actions which includes a mathematical model, selection of measured parameters, measuring devices, software, etc. Diagnostic models are also compiled for technical diagnostics and they are divided into physical and mathematical ones.A physical model is a real object and a mathematical model is defined as a system of hypotheses expressed by a system of equations and inequalities.The mechanical oscillation of structural nodes is a dynamic event with mass points performing a reciprocating motion around an equilibrium position [12,13].A solid body is, in technical diagnostics, presented as a whole replaced by a material point, and the motion of all body parts is the same at a given moment.The equivalent of oscillation is the concept of vibration.Vibration values are given by excitation force.Vibrations are defined by an amplitude and a phase at a given point in time.Machine vibrations are related to the dynamic stress of structural units and their technical condition [14].The vibrations are excited by both the rotating and linearly moving parts of machines; however, they are caused by impacts as well.Contact between two bodies in mutual motion occurs with a sudden change in gradient, determining the quantity of vibrations occurs during impact.Impact is caused by a transient oscillating event generated in a body by an impact wave [15].
Diagnostic tools can be divided into online systems, where the collection of diagnostic data takes place continuously during the operation of the device, and offline systems, when the measuring device does not collect data constantly, but either at fixed time intervals or if a change in behavior is observed during the operation of the system.Timely diagnosis of technical equipment enables the prevention of economic damage when the damage is detected and serviced in time [16].
One of the effective tools suitable for diagnosing transmission mechanisms is the use of vibrodiagnostics.Vibrodiagnostics enables the monitoring and capture of a wide variety of faults, such as misalignment of the rotating part, bearing faults, collisional interactions of individual parts, backlash, gear damage, etc.In the ideal case, the evaluation of signals is based on the principle that there are known data when the system works optimally, while if there is a change in behavior, based on the comparison of these modes, it is possible to determine the damaged part of the system.The diagnostic process itself can be divided into four basic parts: measurement, processing, selection of key features and diagnostics [16,17].
The essence of the analysis of vibrodiagnostic signals in the time domain (time domain analysis) is the evaluation of time course parameters of vibrodiagnostic signal-determining quantities such as deviation, velocity and acceleration.Instantaneous, mean and effective values of the signal are quickly evaluated in the time domain.This analysis in the time domain is suitable for motor starts and stops, impact responses, non-stationary signals with a variable function, non-linear system parameters and the stiffness transformation of oscillating structural units.The frequency analysis of vibrodiagnostic signal eliminates the deficiencies of the time analysis; i.e., it identifies emerging malfunctions of individual structural units.The Fourier transform is an important means of experimental analysis in processing of dynamic signals.Its essence is to replace any function x(t) with the sum of harmonic functions [18,19].
There are several studies and reviews dealing with vibrodiagnostic instruments and measurements, monitoring either complex rotating devices or their individual parts.Nithin et al. [20] dealt with the online monitoring of parameters as an element of preventive maintenance, where, in addition to vibrations, they also monitored temperature, noise, lubrication, etc.
The collective of authors Assaad et al. [21] investigated the wear of a multi-stage planetary gearbox used in lifting cranes.They drew the conclusion that the combination of cyclostationarity and autoregressive modeling increases the ability to detect mechanical wear in multi-stage transmissions.
In their overview study, the authors Malla and Panigrahi [22] deal with the problem of vibration analysis during bearing wear, analyzing 69 literary sources, from which they conclude that the diagnosis of a bearing fault is only possible in the time domain of the analysis, where it is not possible to identify the exact place of occurrence, which but it is possible to determine from the frequency characteristic.
In addition to the mentioned diagnostics, another step is also important, namely the optimization of the system based on the measured data.Optimization is a decision-making process; it is a set of all possible decisions in which the best evaluation is sought in terms of the chosen criterion, i.e., the extreme of a target function [23].Optimization is nowadays very important in the design of structural units.It contributes to their development and innovation.The choice of optimization criteria is related to the target function.An important criterion in optimizing the strength and dynamic characteristics of structural units is the evaluation of their lifetime and reliability.The lifetime and reliability of structural units can be understood differently, i.e., they include both static and dynamic analyses.Optimization methods are used for selection of the best possibility and they provide savings for manufacturing companies [24].However, it is only possible to optimize if there are several possibilities to choose from.This precondition is usually fulfilled when designing structural units.Optimization methods are also defined by algorithmic properties that are used in their programming.The issue of solving the given tasks is to define an optimization method.Its formulation is based on the following criteria: an optimality criterion, a mathematical model, a perturbation analysis, a choice of equipment and optimization system, a choice of optimization method and an optimization calculation.With the rapid development of artificial intelligence, machine learning and deep learning, it can be assumed that the needs of optimization tasks will take over these elements of Industry 4.0 [25,26].
In an issue on the use of "Intelligent Fault Diagnostics", the authors Lei et al. [27] published their overview study, while focusing on the development trends in this area and assuming the replacement of the human staff of the IFD.
Umbrajkaar et al. [28] focused their research on monitoring the state of non-alignment of the shaft, pointing out the possibilities of using machine learning and neural networks in the context of Industry 4.0, in which they discuss the results of their study in different misalignment conditions.
Singh et al. [29] also considered the elements of Industry 4.0, considering the use of artificial intelligence for monitoring and fault diagnosis, taking into account robust computing power and a lower need for qualified personnel.
The authors' motivation for their own experimental measurements of vibrations is rooted in the necessity to establish a knowledge base and acquire practical experience necessary for constructing a measurement setup intended to measure and diagnose various types of gear mechanisms in an accelerated mode.The measuring device should simulate the authentic load on the gearbox's structural node, inducing wear within a condensed time frame, typically spanning days.The monitored parameters that impact damage will precisely encompass the dynamic events during system start-up and rundown.Carrying out experimental measurements in practice is an essential intermediary step to accurately comprehend the dynamic events taking place during the lifecycle of gear mechanisms.This comprehension will subsequently assist in optimizing the subsequent design of the measurement system, appropriately incorporating various diagnostic tools.
The measuring device should be capable of handling variable loads, facilitating the alteration of drive type, speed and acceleration.The accelerated mode would be achieved through cyclic loading by modifying the movement direction or halting the transmission at a specific tooth.
The challenges that the authors will face in their future work will originate from the accurate selection of diagnostic tools, the placement of sensory technology on the device, the filtration of ambient noises that do not influence the measurements and the precise evaluation and interpretation of the collected data.The knowledge derived from the presented experimental measurements will also contribute to surmounting these challenges.

Materials and Methods
Our verification of theoretical knowledge in the field of research and optimization of the dynamic characteristics of the structural units in manufacturing engineering was applied to the RLN 200 screw conveyor (Flexicon Corporation, Bethlehem, PA, USA), the main component of which is an electric gearbox.The RLN 200 is shown in Figure 1, which is used for packaging bulk materials.The conveyor works on the principle of a freely rotating shaftless screw in a robust circular pipe.Material is transported by the screw rotating from the filling hopper towards the material discharge hole.The conveyor must be filled with material along its entire length in order to work optimally since it is constructed without bearings.The conveyor is made of stainless steel.The main parameters of the gearbox and conveyor are shown in Table 1.
accurately comprehend the dynamic events taking place during the lifecycle of gear mec anisms.This comprehension will subsequently assist in optimizing the subsequent desi of the measurement system, appropriately incorporating various diagnostic tools.
The measuring device should be capable of handling variable loads, facilitating t alteration of drive type, speed and acceleration.The accelerated mode would be achiev through cyclic loading by modifying the movement direction or halting the transmissi at a specific tooth.
The challenges that the authors will face in their future work will originate from t accurate selection of diagnostic tools, the placement of sensory technology on the devi the filtration of ambient noises that do not influence the measurements and the prec evaluation and interpretation of the collected data.The knowledge derived from the p sented experimental measurements will also contribute to surmounting these challeng

Materials and Methods
Our verification of theoretical knowledge in the field of research and optimization the dynamic characteristics of the structural units in manufacturing engineering was a plied to the RLN 200 screw conveyor (Flexicon Corporation, Bethlehem, PA, USA), t main component of which is an electric gearbox.The RLN 200 is shown in Figure 1, wh is used for packaging bulk materials.The conveyor works on the principle of a freely tating shaftless screw in a robust circular pipe.Material is transported by the screw rot ing from the filling hopper towards the material discharge hole.The conveyor must filled with material along its entire length in order to work optimally since it is construct without bearings.The conveyor is made of stainless steel.The main parameters of t gearbox and conveyor are shown in Table 1.The subject of this research into the dynamic characteristics of structural units in manufacturing engineering is the electric gearbox of the conveyor.It is used in this company during discontinuous operation due to the packaging of road salt in various sizes of the final products, namely 5 kg, 10 kg, 15 kg, 20 kg and 25 kg.Discontinuous operations, i.e., frequent switching off, switching on or reversing, cause faults in this defective structural unit, such as rapid wear of the gear mechanism and thus damage to the electric motor.The conveyor drive operates in two-shift or three-shift operations.The screw conveyor operates in an external working environment and the influence of packaging materials on the conveyor and the drive is obvious due to corrosion.Preventing undesirable conditions of manufacturing machines so they work reliably and in a trouble-free manner is very important.It is necessary to determine the state in which they operate not only safely but mainly without failures, which can result in the cessation of manufacturing and thus economic losses.Our experimental analysis as part of the dynamic analysis was performed on the drive of the screw conveyor.The vibration measurement was further subdivided into the measurement during the start operation of the unloaded drive, the measurement during operation and the measurement during the stop operation.
A universal NI 9234-4X+-5V/24 Bit analyzer (Pico Technology Ltd., St Neots, UK), shown in Figure 2, was used to measure vibrations.This device is a quick and mobile piece of equipment designed to obtain non-electrical characteristics in working conditions, the so-called in situ conditions of manufacturing machines.Preventing undesirable conditions of manufacturing machines so they and in a trouble-free manner is very important.It is necessary to determin which they operate not only safely but mainly without failures, which can cessation of manufacturing and thus economic losses.Our experimental an of the dynamic analysis was performed on the drive of the screw conveyor.measurement was further subdivided into the measurement during the star the unloaded drive, the measurement during operation and the measureme stop operation.

Total gear ratio
A universal NI 9234-4X+-5V/24 Bit analyzer (Pico Technology Ltd., S shown in Figure 2, was used to measure vibrations.This device is a quick and of equipment designed to obtain non-electrical characteristics in working c so-called in situ conditions of manufacturing machines.The parameters that can be obtained include: -Air flow velocity measurement; -Air temperature measurement; -Relative velocity measurement; -Luminosity measurement; -Luminous flux measurement; -Noise analysis, etc. The Wilcoxon Research sensor, model 736 (Wilcoxon Sensing Technologies, Frederick, MD, USA), which is shown in Figure 3, was used as the vibration acceleration sensor.The sensitivity of the sensor is 100 mV/g and the frequency measurements range from 2 Hz to 25 kHz.Figure 4 shows the experimental measurement of vibrations at the place of operation of the screw conveyor in situ.As can be seen from the figures, the accelerometer was placed on the conveyor drive, and a computer used to store the measured values was placed next to the conveyor.A scheme of the measuring device is provided in Figure 5.   Figure 4 shows the experimental measurement of vibrations at the place of operation of the screw conveyor in situ.As can be seen from the figures, the accelerometer was placed on the conveyor drive, and a computer used to store the measured values was placed next to the conveyor.A scheme of the measuring device is provided in Figure 5.
Processes 2023, 11, x FOR PEER REVIEW 6 of 18 The parameters that can be obtained include: -Air flow velocity measurement; -Air temperature measurement; -Relative velocity measurement; -Luminosity measurement; -Luminous flux measurement; -Noise analysis, etc.
The Wilcoxon Research sensor, model 736 (Wilcoxon Sensing Technologies, Frederick, MD, USA), which is shown in Figure 3, was used as the vibration acceleration sensor.The sensitivity of the sensor is 100 mV/g and the frequency measurements range from 2 Hz to 25 kHz.Figure 4 shows the experimental measurement of vibrations at the place of operation of the screw conveyor in situ.As can be seen from the figures, the accelerometer was placed on the conveyor drive, and a computer used to store the measured values was placed next to the conveyor.A scheme of the measuring device is provided in Figure 5.The Wilcoxon Research sensor, model 736 (Wilcoxon Sensing Technologies, ick, MD, USA), which is shown in Figure 3, was used as the vibration acceleration The sensitivity of the sensor is 100 mV/g and the frequency measurements range Hz to 25 kHz.Figure 4 shows the experimental measurement of vibrations at the place of op of the screw conveyor in situ.As can be seen from the figures, the accelerome placed on the conveyor drive, and a computer used to store the measured valu placed next to the conveyor.A scheme of the measuring device is provided in Fig

Modal Analysis
Ensuring the safety and reliability of structural units in manufacturing engineering is of paramount importance to prevent adverse situations within the manufacturing environment.Vibrations and resonance are among the critical factors that structural units must be designed to withstand.Modal analysis, as a powerful tool in dynamic analysis, plays a pivotal role in achieving this goal.In our quest for a deeper understanding of a structural unit's behavior and its resilience to vibrations and resonance, we turned to modal analysis.This indispensable technique allows us to delve into the dynamic response of a structure and determine its natural frequencies, which are instrumental in gauging its behavior under different operational conditions.The structural unit subjected to modal analysis was the drive mechanism, and we harnessed the capabilities of Autodesk Inventor 2023 software (Figure 6) for this purpose.The settings of modal analysis used are shown in Table 2. Modal analysis, a method employed for investigating the natural frequencies and mode shapes of a system, is a critical step in ensuring the integrity and reliability of any mechanical system.
Processes 2023, 11, x FOR PEER REVIEW

Modal Analysis
Ensuring the safety and reliability of structural units in manufacturing eng is of paramount importance to prevent adverse situations within the manufacturi ronment.Vibrations and resonance are among the critical factors that structu must be designed to withstand.Modal analysis, as a powerful tool in dynamic plays a pivotal role in achieving this goal.In our quest for a deeper understand structural unit's behavior and its resilience to vibrations and resonance, we tu modal analysis.This indispensable technique allows us to delve into the dyn sponse of a structure and determine its natural frequencies, which are instrum gauging its behavior under different operational conditions.The structural unit s to modal analysis was the drive mechanism, and we harnessed the capabilities desk Inventor 2023 software (Figure 6) for this purpose.The settings of modal used are shown in Table 2. Modal analysis, a method employed for investigating ural frequencies and mode shapes of a system, is a critical step in ensuring the and reliability of any mechanical system.The primary goal of our modal analysis was to identify the natural frequenci gear mechanism, which would serve as a basis for comparison with the frequen tained through experimental measurements.The analysis encompassed a total modes, each shedding light on different aspects of the drive's dynamic behavior sential to understand that the deformations observed during the modal analysis w

Curved mesh elements yes Fixation Bearings
The number of mesh elements 165,181 The shape of the mesh elements Tetra 10

Curved mesh elements yes
The primary goal of our modal analysis was to identify the natural frequencies of the gear mechanism, which would serve as a basis for comparison with the frequencies obtained through experimental measurements.The analysis encompassed a total of eight modes, each shedding light on different aspects of the drive's dynamic behavior.It is essential to understand that the deformations observed during the modal analysis were relative in nature and should not be taken as direct representations of real-world conditions.Rather, they provide valuable insights into the vibration characteristics of the drive.These insights are indispensable for optimizing the design, performance and safety of the structural unit.The results of our modal analysis are summarized in Table 3, offering a comprehensive overview of the natural frequencies and mode shapes we extracted from our investigation.These findings are instrumental in understanding and enhancing the drive's behavior and performance.To provide a more detailed perspective, let us delve deeper into the significance of modal analysis, the methodology we employed and the implications of our results.

Vibration Measurement via Accelerometer
The following measurements were recorded via the Wilcoxon Research 736 accelerometer and the universal vibration NI 9234-4X+-5V/24 Bit analyzer and they were evaluated via the software MATLAB & Simulink-Math Works R2022a.Figure 7 displays the dot chart of all measured values in the area of acceleration and acceleration derivative.Acceleration is defined as the first derivative of velocity against time.Very large deviations of the measured data can be clearly seen from the figure.The frequency spectrum was determined due to the analysis of dynamic characteristics and for a more accurate determination of the natural frequencies.The selected waveforms were also analyzed in a smaller frequency range in order to obtain more accurate representations.
Processes 2023, 11, x FOR PEER REVIEW 8 of 18 insights are indispensable for optimizing the design, performance and safety of the structural unit.The results of our modal analysis are summarized in Table 3, offering a comprehensive overview of the natural frequencies and mode shapes we extracted from our investigation.These findings are instrumental in understanding and enhancing the drive's behavior and performance.To provide a more detailed perspective, let us delve deeper into the significance of modal analysis, the methodology we employed and the implications of our results.

Vibration Measurement via Accelerometer
The following measurements were recorded via the Wilcoxon Research 736 accelerometer and the universal vibration NI 9234-4X+-5V/24 Bit analyzer and they were evaluated via the software MATLAB & Simulink-Math Works R2022a.Figure 7 displays the dot chart of all measured values in the area of acceleration and acceleration derivative.Acceleration is defined as the first derivative of velocity against time.Very large deviations of the measured data can be clearly seen from the figure.The frequency spectrum was determined due to the analysis of dynamic characteristics and for a more accurate determination of the natural frequencies.The selected waveforms were also analyzed in a smaller frequency range in order to obtain more accurate representations.The measured values shown in Figure 7 show certain elements of quatrefoil symmetry.However, this may be a random fluctuation of values.Thus, it is also clear from this representation that large oscillations occur during the operation of the drive.Figure 8 gives us a more detailed perspective on all recorded vibration values, with these values The measured values shown in Figure 7 show certain elements of quatrefoil symmetry.However, this may be a random fluctuation of values.Thus, it is also clear from this representation that large oscillations occur during the operation of the drive.Figure 8 gives us a more detailed perspective on all recorded vibration values, with these values displayed in three-dimensional space.We defined the acceleration parameter in the x-axis, the time parameter in the y-axis and the acceleration derivative parameter in the z-axis.The Interpolant-Biharmonic method was chosen via the already mentioned MATLAB software in this case; the category corresponds to the interpolation surfaces that pass through each measured value.This visualized display of the measured values clearly indicates to us that the drive is operating in a non-linear range.There are significant deviations associated with the measured data, indicating the complexity and dynamic variations that govern the results.Such a view allows us to perceive patterns and connections that would remain uncaptured in one-or two-dimensional representations.At the same time, this illustration confirms to us that the evaluation of vibrations requires sophisticated methods and a complex approach that takes into account a number of variables and factors influencing the behavior of the drive.
Processes 2023, 11, x FOR PEER REVIEW 9 of 18 The Interpolant-Biharmonic method was chosen via the already mentioned MATLAB software in this case; the category corresponds to the interpolation surfaces that pass through each measured value.This visualized display of the measured values clearly indicates to us that the drive is operating in a non-linear range.There are significant deviations associated with the measured data, indicating the complexity and dynamic variations that govern the results.Such a view allows us to perceive patterns and connections that would remain uncaptured in one-or two-dimensional representations.At the same time, this illustration confirms to us that the evaluation of vibrations requires sophisticated methods and a complex approach that takes into account a number of variables and factors influencing the behavior of the drive.Figure 9 presents a graph that shows all the measured data, namely the dependence of acceleration on time.This graph gives us a closer look at the significant interactions between the power-on, operation and shutdown of the drive, as it records the large interface of the measured values in these stages.Turning on the drive represents the most demanding moment for structural units, and therefore the measured values in this phase are several times higher than the values during the normal operation of the drive.Nevertheless, deviations are still visible even at regular intervals during steady-state operation, indicating the dynamic fluctuations and complex nature of the system.Figure 9 presents a graph that shows all the measured data, namely the dependence of acceleration on time.This graph gives us a closer look at the significant interactions between the power-on, operation and shutdown of the drive, as it records the large interface of the measured values in these stages.Turning on the drive represents the most demanding moment for structural units, and therefore the measured values in this phase are several times higher than the values during the normal operation of the drive.Nevertheless, deviations are still visible even at regular intervals during steady-state operation, indicating the dynamic fluctuations and complex nature of the system.
Such a detailed view of the behavior of the drive during different phases of the drive allows us not only to find out its basic trends, but also to analyze the effect of various conditions on its performance and stability.Further analysis of the measured data was carried out through a method known as "Wavelet".The concept of a "Wavelet" is basically a mathematical function that performs a conjunctive transform of Wavelets.This transformation makes it possible to recover even weak signals, which is important since the measured data can be prone to internal noise."Wavelet" works by dividing the measured values into different scales with assigned frequency ranges, which provides a more detailed view into the frequency structure of the signal.The use of "Wavelet" analysis in this context illustrates how sophisticated tools such as MATLAB can penetrate deeply into the characteristics of measured data to reveal structures and patterns that would be more difficult to recognize with conventional methods.
of acceleration on time.This graph gives us a closer look at the significant interactions between the power-on, operation and shutdown of the drive, as it records the large interface of the measured values in these stages.Turning on the drive represents the most demanding moment for structural units, and therefore the measured values in this phase are several times higher than the values during the normal operation of the drive.Nevertheless, deviations are still visible even at regular intervals during steady-state operation, indicating the dynamic fluctuations and complex nature of the system.Figure 10 shows a detailed analysis using the Wavelet method, which provides us with an overview of the time-frequency spectrum of the measured values of the conveyor drive.This analysis allows us to observe how the frequency content of the measured values changes depending on time.A distinct change, caused by vibrations when the drive is turned on, is clearly captured in these measured data.This burst activity is highlighted in red, giving us a strong visual indicator of this change.It is at this point that the drive changes from a mild state to an active mode, causing shock vibrations and increased dynamic activity.Another interesting aspect of this analysis concerns the steady mode of operation of the drive.Even after the transition to normal operation, there are still noticeable deviations at certain time intervals.These variations can be the result of various factors such as changing loads, changes in the environment or other dynamic influences.Such steady-state anomalies may indicate continuous variability in drive behavior and indicate that even at these moments the system is not completely stable.Overall, Figure 10 offers us an important insight into the time-frequency characteristics of the conveyor drive's vibrations, giving us a deeper insight into its dynamic behavior during different phases of operation.Such a detailed view of the behavior of the drive during different phases of the driv allows us not only to find out its basic trends, but also to analyze the effect of variou conditions on its performance and stability.Further analysis of the measured data wa carried out through a method known as "Wavelet".The concept of a "Wavelet" is basicall a mathematical function that performs a conjunctive transform of Wavelets.This transfor mation makes it possible to recover even weak signals, which is important since the meas ured data can be prone to internal noise."Wavelet" works by dividing the measured va ues into different scales with assigned frequency ranges, which provides a more detaile view into the frequency structure of the signal.The use of "Wavelet" analysis in this con text illustrates how sophisticated tools such as MATLAB can penetrate deeply into th characteristics of measured data to reveal structures and patterns that would be more dif ficult to recognize with conventional methods.
Figure 10 shows a detailed analysis using the Wavelet method, which provides u with an overview of the time-frequency spectrum of the measured values of the conveyo drive.This analysis allows us to observe how the frequency content of the measured va ues changes depending on time.A distinct change, caused by vibrations when the driv is turned on, is clearly captured in these measured data.This burst activity is highlighte in red, giving us a strong visual indicator of this change.It is at this point that the driv changes from a mild state to an active mode, causing shock vibrations and increased dy namic activity.Another interesting aspect of this analysis concerns the steady mode o operation of the drive.Even after the transition to normal operation, there are still notice able deviations at certain time intervals.These variations can be the result of various fac tors such as changing loads, changes in the environment or other dynamic influences Such steady-state anomalies may indicate continuous variability in drive behavior an indicate that even at these moments the system is not completely stable.Overall, Figur 10 offers us an important insight into the time-frequency characteristics of the conveyo drive's vibrations, giving us a deeper insight into its dynamic behavior during differen phases of operation.Figure 10 shows the amplitude of the vibration acceleration evaluated in the tim domain.An occurrence of an undesirable transient state from switching on the driv through operation to switching off the drive can be confirmed in this case as well.Th start-up, i.e., switching on the drive, has significantly higher measured values compare Figure 10 shows the amplitude of the vibration acceleration evaluated in the time domain.An occurrence of an undesirable transient state from switching on the drive through operation to switching off the drive can be confirmed in this case as well.The start-up, i.e., switching on the drive, has significantly higher measured values compared to further operation of the drive.The analysis of the acceleration of vibrations in the time domain clearly shows the repetition of the oscillating event in certain time intervals.Certain assumptions can be derived from the measured values during the drive operation in the time domain.There are dynamic events occurring in the drive that load the individual members of the structural unit.The shafts, keys, bearings, gears, screw and worm wheel oscillate at their own frequency, and thus also affect the resulting drive frequencies.The drive oscillates via forced oscillation.As the name implies, the electric gearbox consists of a two-stage gearbox; the first stage, with a gear ratio of 2, is the spur gear (the number of teeth on the pinion is 24 and the number of teeth on the wheel is 48) and the second-stage gear is a worm gear with a gear ratio of 14 (the screw is double-tracked and the worm wheel has 28 teeth).The resulting gear ratio is 28.The load is 38 Nm (based on the previously mentioned motor parameters: three-phase asynchronous motor of 3 kW, 1455 rpm).Based on the given parameters, the following frequencies listed in Table 4 were determined.

Analysis of Drive Start-Up without Load
Figures 11 and 12 show the start-up analysis concerning the switching on of the drive.The measured start-up values are displayed via the amplitude in the time domain.The given values were converted to the frequency domain using FFT, i.e., the Fast Fourier Transform, for their better analysis and identification.Fast Fourier Transform is a mathematical apparatus used for better searches of dominant amplitudes.
Via the analysis of switching on the drive, or the drive start-up, the amplitude values of frequencies up to 2.46 kHz were measured in the frequency range of the drive; hence, this can already be considered as an excessive oscillation of the drive.The frequency spectrum indicates a great demonstration of the dynamic events that occur in the drive during switching on, i.e., operation start-up.Each drive is generally more stressed during switching on than its during steady operation; however, in this case, its frequent switching on and switching off are undesirable events due to load type based on the amount of packaged salt or other bulk materials.An even greater load occurs if larger lumps of salt appear on a screw conveyor during transport; they sometimes occur there due to the fact that trucks transporting road salt intended for roads and highways during winter also transport rock salt intended for the utility industry.
"Zero-phase" is a special case of displaying measured values in which the actual impulse response is filtered.The given filter does not create phase distortion.The phase analysis of the drive start-up is important for expressing the application of the forces that act against the impact.It is basically an expression of displacement.The values are negative due to the fact that during the initial impact of the switched-on drive, there are forces which act against the forces that are at rest in the given structural unit.As can be seen from the analysis performed by MATLAB software, at a frequency of 0.123 kHz there is a displacement of −4 • ; however, at the frequency of 2.78 kHz, there is a displacement of up to −271 • .As can be seen from Figure 13, the analysis shows that there is a large number of displacements which have a negative effect on the properties of the drive; moreover, they are directly related to the strength and dynamic characteristics of the structural unit of the screw conveyor.

Analysis of Drive Start-Up without Load
Figures 11 and 12 show the start-up analysis concerning the switching on of the drive.The measured start-up values are displayed via the amplitude in the time domain.The given values were converted to the frequency domain using FFT, i.e., the Fast Fourier Transform, for their better analysis and identification.Fast Fourier Transform is a mathematical apparatus used for better searches of dominant amplitudes.Via the analysis of switching on the drive, or the drive start-up, the amplitude values of frequencies up to 2.46 kHz were measured in the frequency range of the drive; hence, this can already be considered as an excessive oscillation of the drive.The frequency spectrum indicates a great demonstration of the dynamic events that occur in the drive during switching on, i.e., operation start-up.Each drive is generally more stressed during switch-

Analysis of Steady-State Operation of Drive without Load
The time analysis shown in Figure 14 domain during the steady operation of the drive shows deviations in the measured data that can be seen at the first sight.There is a demonstration of the dynamic event based on the forced oscillation during the operation of the entire conveyor and drive at certain time intervals.The amplitude is non-linear and its increase and decrease is clear.The given amplitude is the resulting sum of the measured data, which is the result of the oscillations of all components in the gear; thus, it was converted by the FFT into the frequency domain for better analysis.This transformation is essentially a better representation of the measured data.It can be assumed that the nonlinearities occurring during the steady drive operation also result from the output speed of the screw, since the calculated values are close to the measured values of the output shaft.The cause is probably a bent screw.

Analysis of Steady-State Operation of Drive without Load
The time analysis shown in Figure 14 domain during the steady operation of the drive shows deviations in the measured data that can be seen at the first sight.There is a demonstration of the dynamic event based on the forced oscillation during the operation of the entire conveyor and drive at certain time intervals.The amplitude is non-linear and its increase and decrease is clear.The given amplitude is the resulting sum of the measured data, which is the result of the oscillations of all components in the gear; thus, it was converted by the FFT into the frequency domain for better analysis.This transformation is essentially a better representation of the measured data.It can be assumed that the non-linearities occurring during the steady drive operation also result from the output speed of the screw, since the calculated values are close to the measured values of the output shaft.The cause is probably a bent screw.

Analysis of Steady-State Operation of Drive without Load
The time analysis shown in Figure 14 domain during the steady operation of the drive shows deviations in the measured data that can be seen at the first sight.There is a demonstration of the dynamic event based on the forced oscillation during the operation of the entire conveyor and drive at certain time intervals.The amplitude is non-linear and its increase and decrease is clear.The given amplitude is the resulting sum of the measured data, which is the result of the oscillations of all components in the gear; thus, it was converted by the FFT into the frequency domain for better analysis.This transformation is essentially a better representation of the measured data.It can be assumed that the nonlinearities occurring during the steady drive operation also result from the output speed of the screw, since the calculated values are close to the measured values of the output shaft.The cause is probably a bent screw.The maximum frequency reached during the steady drive operation was 2.440 kHz (shown in Figure 15), which is essentially almost similar to the maximum of the analyzed drive start-up frequencies, with the frequency of 2.459 kHz being measured and evaluated.The frequencies during steady operation should naturally be lower than when switching on the drive.As shown in the analysis, there is also a complex oscillating event taking place during the steady operation of the drive.This event is the response of all the examined structural unit components, including the entire screw conveyor placed in the external environment on four wheels placed on an asphalt base.
Processes 2023, 11, x FOR PEER REVIEW 14 of 18 The maximum frequency reached during the steady drive operation was 2.440 kHz (shown in Figure 15), which is essentially almost similar to the maximum of the analyzed drive start-up frequencies, with the frequency of 2.459 kHz being measured and evaluated.The frequencies during steady operation should naturally be lower than when switching on the drive.As shown in the analysis, there is also a complex oscillating event taking place during the steady operation of the drive.This event is the response of all the examined structural unit components, including the entire screw conveyor placed in the external environment on four wheels placed on an asphalt base.

Analysis of Drive Rundown without Load
The conveyor and drive rundown are clearly visible from the amplitude in the analysis shown in Figure 16.Only the operation rundown time was selected for the accurate analysis.The repetitive dynamic event is also visible in the last measurement section, the rundown, and is probably caused by a defect in the screw of the conveyor or the drive which results from its speed frequency.Furthermore, the measured values were converted from the time to the frequency domain using FFT.

Analysis of Drive Rundown without Load
The conveyor and drive rundown are clearly visible from the amplitude in the analysis shown in Figure 16.Only the operation rundown time was selected for the accurate analysis.The repetitive dynamic event is also visible in the last measurement section, the rundown, and is probably caused by a defect in the screw of the conveyor or the drive which results from its speed frequency.Furthermore, the measured values were converted from the time to the frequency domain using FFT.
Processes 2023, 11, x FOR PEER REVIEW 14 of 18 The maximum frequency reached during the steady drive operation was 2.440 kHz (shown in Figure 15), which is essentially almost similar to the maximum of the analyzed drive start-up frequencies, with the frequency of 2.459 kHz being measured and evaluated.The frequencies during steady operation should naturally be lower than when switching on the drive.As shown in the analysis, there is also a complex oscillating event taking place during the steady operation of the drive.This event is the response of all the examined structural unit components, including the entire screw conveyor placed in the external environment on four wheels placed on an asphalt base.

Analysis of Drive Rundown without Load
The conveyor and drive rundown are clearly visible from the amplitude in the analysis shown in Figure 16.Only the operation rundown time was selected for the accurate analysis.The repetitive dynamic event is also visible in the last measurement section, the rundown, and is probably caused by a defect in the screw of the conveyor or the drive which results from its speed frequency.Furthermore, the measured values were converted from the time to the frequency domain using FFT.The maximum frequency of 2.31 kHz (shown in Figure 17) was measured in the frequency domain of the drive rundown analysis that again shows the repetition of a certain dynamic event in the measured data, as the repetitive maximum frequencies in previous analyses had very close frequency values.The other frequencies are the result of measurement and its transformation by FFT into the frequency domain.The maximum frequency of 2.31 kHz (shown in Figure 17) was measured in the frequency domain of the drive rundown analysis that again shows the repetition of a certain dynamic event in the measured data, as the repetitive maximum frequencies in previous analyses had very close frequency values.The other frequencies are the result of measurement and its transformation by FFT into the frequency domain.

Conclusions
The modal analysis of the drive yielded significant results that shed light on the behavior and characteristics of the system.By comparing the resulting natural frequencies with the measurements obtained through experimental testing, valuable insights were gained regarding the operational performance and potential issues of the drive.The first natural frequency of the drive was determined to be approximately 895.22 Hz, which closely aligned with the frequency of 915.63 Hz obtained during the second measurement using a vibrometer.This indicates that the drive operates within a specific frequency range and suggests that the system is functioning effectively in terms of its resonant behavior.These natural frequencies play a crucial role in understanding the dynamic response and behavior of the drive during various operational conditions.
It is worth mentioning that the natural frequencies were not only observed during steady-state operation but also during transient states, such as the start-up of the drive.This suggests that the system's resonance can occur during specific activities, leading to an increase in drive oscillation.For instance, the frequency of 2353 Hz, which was recorded when measuring the drive without a salt load, aligns with the sixth natural frequency.This observation further supports the presence of resonance or near-resonance conditions during certain drive activities.
The complexity of the dynamic events within the system adds another layer of understanding to the analysis.The resulting amplitude is influenced by a multitude of factors, including the unique oscillation frequencies of each structural unit.When these frequencies coincide, they can combine, resulting in significantly higher frequencies that contribute to the overall behavior of the system.Additionally, the external environment in which the conveyor is placed, with its four rubber and plastic wheels, has an impact on

Conclusions
The modal analysis of the drive yielded significant results that shed light on the behavior and characteristics of the system.By comparing the resulting natural frequencies with the measurements obtained through experimental testing, valuable insights were gained regarding the operational performance and potential issues of the drive.The first natural frequency of the drive was determined to be approximately 895.22 Hz, which closely aligned with the frequency of 915.63 Hz obtained during the second measurement using a vibrometer.This indicates that the drive operates within a specific frequency range and suggests that the system is functioning effectively in terms of its resonant behavior.These natural frequencies play a crucial role in understanding the dynamic response and behavior of the drive during various operational conditions.
It is worth mentioning that the natural frequencies were not only observed during steady-state operation but also during transient states, such as the start-up of the drive.This suggests that the system's resonance can occur during specific activities, leading to an increase in drive oscillation.For instance, the frequency of 2353 Hz, which was recorded when measuring the drive without a salt load, aligns with the sixth natural frequency.This observation further supports the presence of resonance or near-resonance conditions during certain drive activities.
The complexity of the dynamic events within the system adds another layer of understanding to the analysis.The resulting amplitude is influenced by a multitude of factors, including the unique oscillation frequencies of each structural unit.When these frequencies coincide, they can combine, resulting in significantly higher frequencies that contribute to the overall behavior of the system.Additionally, the external environment in which the conveyor is placed, with its four rubber and plastic wheels, has an impact on the results.These external factors introduce additional vibrations and influence the dynamics of the drive and conveyor system.
This study also provided valuable insights into other oscillations occurring within the system.The input shaft oscillation, which was measured at a frequency of approximately 24 Hz during the initial measurement with no load, provides crucial information about the behavior of this component.Additionally, the tooth frequency, calculated to be 582 Hz, was found to be present in the measured data, indicating its significance in the overall system dynamics.Moreover, the oscillation of the drive's second stage, specifically the tooth frequency of the screw drive, was observed to correspond with the input shaft frequency.This correlation suggests that the interaction between these two components can lead to increased drive oscillations and potentially impact the system's overall performance.The resulting frequency of the output shaft and the conveyor screw, measured at 0.866 Hz, was particularly noteworthy.This frequency remained dominant even during steady-state operation, indicating a potential issue with the conveyor screw.It is possible that the screw was bent, causing it to come into contact with the pipe at each turn.This abnormal contact generates additional vibrations and affects the performance and geometric characteristics of the shaft and drive screw.The bending of the conveyor screw, combined with the assumption of an input torque of 38 N•m and an output torque of approximately 1000 N•m, contributed to the observed increase in drive oscillation.The oscillation of the system causes fatigue strength, tearing of welds and the formation of micro cracks.These unfavorable events can be eliminated by replacing or straightening the internal screw in the conveyor or by increasing the diameter of the conveying pipe.Fatal consequences can also be prevented via continuous monitoring of dynamic events and their diagnosis during operation.Dynamic events that are also caused by impacts during operation of the drive can be eliminated by frequent start-ups.An elimination of the dynamic characteristics and the strength characteristics of the drive is also possible via the PID controller, which prevents oscillations in structural units.However, the PID controller must be set correctly in order to fulfil its function.The implementation of the PID controller was recommended to the operator of the technical equipment.In addition to the PID controller, it will also be necessary to replace the bent conveyor screw.After its implementation, system tuning and re-measurement should be followed in order to control the elimination of the problem.Another recommendation was the introduction of online measurements intended for predictive maintenance.Despite progress in technical systems, most machines are in operation without detailed monitoring of their operating parameters.Important equipment is regularly serviced as part of preventive maintenance, which increases equipment reliability, but at increased costs for spare parts and related activities.Predictive, or rather proactive, maintenance uses predictive diagnostics based on monitoring for early detection of emerging malfunctions and elimination of their causes.Maintenance costs vary significantly, e.g., according to the age of the operation and its equipment, but in any case it is an important factor to ensure the reliability or quality of production, as well as the economy and safety of the operation.Many industries are affected by crises, and therefore they cannot expect a large renewal of the machinery park, which often exceeds the planned lifetime and is also often overloaded in an effort to meet demanding production plans, or, in the case of replacements, of a production stoppage due to the failure of other equipment.A significant number of malfunctions occur without warning due to the lack of relevant information due to the lack of monitoring.At the same time, many disorders begin with the neglect of problems, the early solutions to which are simple and can prevent the development of greater damage.These are loose screws, imbalance and misalignment of machines, problems with lubrication and cleaning (filtration), etc. Monitoring systems are therefore part of early warning systems, but also systems for fault analysis.Individual key requirements taken into account when creating and deploying monitoring systems can be analyzed from several perspectives.Due to their large number, only the most important aspects are selected: flexibility-the possibility of quick reconfiguration of the system as part of the reflection of changed requirements; performance-sufficient quality of the measurement process; price reduction-material, human resources; reduction of dimensions-higher degree of integration and reduction of the number of compositional elements; and lifespan and upgradeability-use of standards enabling upgrades and servicing of the monitoring system.
The basic vision of the modern concept of industry is therefore a technical system that enables process monitoring through sensors directly built into devices or on their body; in our case, for example, material transport devices were able to make decentralized yet qualified decisions aimed at optimizing the process.
Gear ratio on the front gear Gear ratio on a worm gear Number of worm teeth The number of teeth of the worm wheel Number of pinion teeth Number of front wheel teeth Young's modulus (pinion, spur gear and worm) 20 Young's modulus (worm gear) this research into the dynamic characteristics of struc manufacturing engineering is the electric gearbox of the conveyor.It is use pany during discontinuous operation due to the packaging of road salt in v the final products, namely 5 kg, 10 kg, 15 kg, 20 kg and 25 kg.Discontinuo i.e., frequent switching off, switching on or reversing, cause faults in this d tural unit, such as rapid wear of the gear mechanism and thus damage to th tor.The conveyor drive operates in two-shift or three-shift operations.The sc operates in an external working environment and the influence of packagin the conveyor and the drive is obvious due to corrosion.

Figure 4 .
Figure 4. Placement of vibration sensor and experimental measurement in situ.

Figure 4 .
Figure 4. Placement of vibration sensor and experimental measurement in situ.

Figure 4 .
Figure 4. Placement of vibration sensor and experimental measurement in situ.

Figure 4 .
Figure 4. Placement of vibration sensor and experimental measurement in situ.

Figure 6 .
Figure 6.First natural shape of the drive oscillation at the frequency F1.

Figure 6 .
Figure 6.First natural shape of the drive oscillation at the frequency F1.

Figure 7 .
Figure 7. Display of unloaded drive measured values.

Figure 7 .
Figure 7. Display of unloaded drive measured values.

Figure 8 .
Figure 8. Display of measured values of unloaded drive in 3-D domain.

Figure 8 .
Figure 8. Display of measured values of unloaded drive in 3-D domain.

Figure 9 .
Figure 9. Point display of values measured during entire unloaded operating cycle.Figure 9. Point display of values measured during entire unloaded operating cycle.

Figure 9 .
Figure 9. Point display of values measured during entire unloaded operating cycle.Figure 9. Point display of values measured during entire unloaded operating cycle.

Figure 10 .
Figure 10.Measured values display of unloaded drive via Wavelet.

Figure 10 .
Figure 10.Measured values display of unloaded drive via Wavelet.

Figure 11 .
Figure 11.Time analysis of drive start-up.Figure 11.Time analysis of drive start-up.

Figure 11 . 18 Figure 12 .
Figure 11.Time analysis of drive start-up.Figure 11.Time analysis of drive start-up.Processes 2023, 11, x FOR PEER REVIEW 12 of 18

Figure 12 .
Figure 12.Frequency analysis of drive start-up.

Figure 13 .
Figure 13.Phase analysis of drive switching on.

Figure 14 .
Figure 14.Time analysis during steady drive operation.

Figure 13 .
Figure 13.Phase analysis of drive switching on.

Figure 14 .
Figure 14.Time analysis during steady drive operation.Figure 14.Time analysis during steady drive operation.

Figure 14 .
Figure 14.Time analysis during steady drive operation.Figure 14.Time analysis during steady drive operation.

Figure 15 .
Figure 15.Frequency analysis during steady drive operation.

Figure 16 .
Figure 16.Time analysis of drive rundown.

Figure 15 .
Figure 15.Frequency analysis during steady drive operation.

Figure 15 .
Figure 15.Frequency analysis during steady drive operation.

Figure 16 .
Figure 16.Time analysis of drive rundown.Figure 16.Time analysis of drive rundown.

Figure 16 .
Figure 16.Time analysis of drive rundown.Figure 16.Time analysis of drive rundown.

Figure 17 .
Figure 17.Frequency analysis of drive rundown.

Figure 17 .
Figure 17.Frequency analysis of drive rundown.

Table 1 .
The main parameters of the gearbox and conveyor.

Table 2 .
Parameters of modal analysis.

Table 2 .
Parameters of modal analysis.

Table 4 .
Frequencies of individual drive parts.