ANALYSIS OF AN AUTOMATIC WRAPPING MACHINE: NUMERICAL MODELS AND EXPERIMENTAL RESULTS

Transcription

1 THE 7 TH INTERNATIONAL CONFERENCE RESEARCH AND DEVELOPMENT OF MECHANICAL ELEMENTS AND SYSTEMS ANALYSIS OF AN AUTOMATIC WRAPPING MACHINE: NUMERICAL MODELS AND EXPERIMENTAL RESULTS Giangiacomo MINAK Zlatan ŠOŠKIĆ Snežana ĆIRIĆ KOSTIĆ Cristiano FRAGASSA Abstract: In this paper a study on the possibility of improving the performances of one automatic wrapping machine is shown. The productivity of this class of machines can be increased raising the rotational velocity of the wrapping system. A higher speed provokes in general higher centrifugal forces and consequently higher displacements and the strain and stress in critical points. The aim of this study is to analyze experimentally and numerically the actual system in order to be able to verify the structure and design new solutions. The conclusion of the research work is that the excessive displacement of some points was mainly due to rigid motion of structure parts rather than to their deformations. As a consequence, the proposed solution consists in the modification of the internal constraints positions and stiffness. Key words: Automatic machines, Strain Gages, FEM, Centrifugal force particularly in the static frame B to which the moving 1. INTRODUCTION structure is attached. Automatic wrapping machines were introduced in the 80s with the purpose of stabilizing the pallets load. Despite the widespread distribution of this kind of machines, their design is still based on a trial and error approach and on experience. Market pressure imposes now to improve the productivity of these wrappers, and this request results in the need of increasing the rotational speed of the moving parts. The consequence of the increased speeds is substantial increase of inertial and centrifugal forces, further leading to the necessity of a verification of the whole structure. In figure 1, the structure of the machine under study is shown and some important components are singled out: A is the main frame B is the stationary ring-hold frame C is the pre-stretch device D is the rotating ring E is the counter-weight for C F is the pallet being wrapped. During the work cycle, the pallet B is wrapped by a plastic film, held by the device C. In operation the ring D is put in rotary motion at rpm by means of a system of belts while the film is pre-stretched to the desired mechanical properties by C then attached to the pallet that is stationary. At the same time the frame B moves upwards and downwards to cover the whole pallet. Preliminary tests showed very high displacements of some critical points in the moving annular structure D and Fig. 1: Machine Structure This fact has no effect on machine functionality, but some issues on the machine durability, as regards in particular 69

2 fatigue life may arise and most of all too evident movements of some points of the machine can give to the customer the idea of a low quality product. The approach used by the company to modify this behaviour is to increase the components thickness and in general to increase the stiffness of the parts. This is generally correct for the static parts, while for the moving parts the results of this modification must be verified. Moreover the weight and the cost of the machine increase due to this approach. Therefore, the research aim was to assess the value of the stresses in the critical points in order to estimate the fatigue life and to find an alternative way to reduce the value of the displacements of the critical points. In order to determine the stresses an experimental approach has been used. Strains have been measure in selected critical points as a function of time under different loading conditions (rotational speed, weight of the moving masses). The measurement was performed by means of a wireless system and the results were analyzed both in the time and frequency domain Experimental results revealed the influence of the dead load and of the centrifugal forces on average stresses and amplitudes of stress variations in the considered points. The stress levels in all these selected points were well beneath the allowable one. In order to generalize the results and to provide a design tool, numerical FEM models were developed for all the substructures of interest. Preliminary modal analysis, confirmed by the experimental data, showed the possibility of neglecting dynamic effects and of performing a sequence of static analyses in different positions of the moving structure. The numerical results were in good accordance with experimental ones, allowing using the developed model for the necessary structural improvements of the wrapping machine architecture. 2. NUMERICAL MODEL The rotating ring and the associate mass is the cause of the displacements whose cause is studied. The first question to be answered is if the problem can be solved as a sequence of quasi-static cases or if dynamic effects are on the contrary important. To do that we need to compare the natural frequencies of the structures under study with the frequency of the excitation. For simple thin circular rings it is possible to find exact solutions [1] in particular cases. Qualitatively the vibration modes and simple formulas to calculate the natural frequencies of a free ring can be found in Figure 1. The possible modes are flexural in the plane, flexural out of plane, torsional and extensional. In our situation the problem is complicated by: 1) the presence of concentrated masses connected to the ring (C and E in Figure 1) 2) the presence on unilateral internal constrains that connect the ring D to the frame B 3) the loads acting on the ring (weight, traction from the belt, traction from the film, centrifugal forces). Due to this consideration we developed some numerical models by means of the commercial code Ansys Workbench. The machine is mainly composed by welded plates or thin components, so we chose to use shell elements for the analysis. Since we are interested in global behavior of the ring D and of the frame B, all the rest of the parts were simplified as much as it was possible. Fig. 2: Different vibration modes In figure 2 it is possible to se how the rotating ring is connected to the frame by means of unilateral vertical rollers (in the points A, B and C) and unilateral radial rollers in position shifted of 30 from the vertical ones. The constrains are not really unilateral, but the clearance is so high that for our purposes we should consider that condition. Fig. 3: System of internal contrains Unfortunaltely this was not possible with the developed model due to the limits of the software so from one side we found the natural frequencies considering of the ring and of the frame considered as complitely free, from the 70

3 other side we used bilateral constrains in two positions, one called T with the components C and E located in corrispondance of the points A1 and A2 of figure 3, and the second called W with the ring rotated of 90. In table 1 the first calculated natural frequency for each configuration is reported. It is possible to ses that there is litte influence of the load and the range in which the actual natural frequency of the ring should be is very narrow and far from the frequency of the exciting load that ranges Hz. In figure 4 it is possible to see that the first mode for the free ring, that has the lowest frequency, is flexural out-ofplane. Results in terms of Von Mises equivalent stress and deformed shape are shown in figure 7. The maximum stress is localized in one part that was not modelled realistically, so its value should be considered only as order of magnitude. It is worth noticing that the structure is weackly stressed and the main action on the ring is torsion in corrispondence of the hang masses while the effect of bending is limited due to the presence of rigid contrains. Table 1: Natural Frequencies of the rotating ring D. Condition\Case T W Free Hz Constrained C&Loaded Fig. 6: Loads and constrains utilized to analyze the rotating ring D. Fig. 4: First vibrating mode of the rotating ring D The first calculated natural frequency of the frame is over 85 Hz, much higher than the loading frequency. In figure 5 the first vibrational mode is shown. Also in this case it is is flexural out-of-plane. Fig. 7: Von Mises Stresses and deformed shape of the rotating ring D In figure 8 it is possible to see the trend of the axial and radial reaction as a function of the angular position of the concentrated masses. Fig. 5: First vibrating mode of the stationary frame B Due to the previous results the following analisys have been done considering a sequence of quasi-static conditions in which the position of the concentrated masses, corresponding to the elements C and E, is changed step by step. All the loads were applied simoultanously on the rotating ring, as it is possible to see in figure 6 and the constrains were considered perfectly rigid thus reducing calcunated the deplacement respect to the actual one. Fig. 8: Reactions in the internal constrains as function of the angular position of C and E These reactions were imposed as external load on the frame E toghether with an axial load provoked by a device that press down the pallet during the wrapping phase. In figure 9 the positions of the applied loads and the contrains (zero displacement in the corners) are shown. Finally in figure 10 the total deformation of the frame B in one angular position is shown as an example in which 71

4 is possible to appriciate the order of magnitude of the displacement. The maximum calculated displacement was in the points A1 and A2 of figure 3 equal to 0.23 mm. This value is far below what observed at naked eye even if the choice we made on internal contraints should lead to an overestimation of the stationary frame displacement and an underestimation od the rotating ring one. and precise timekeeping was provided by the microprocessors, which in turn were synchronized by the control computer. In order to study the behavior of characteristic parts of machine, strains were measured at measurement points selected both on rotational ring and on unmovable frame of the machine. Fig. 9: Loads and constrains utilized to analyze the stationary frame B. Fig. 10: Total deformation of the stationary frame B, an example. 3. EXPERIMENT In order to validate the FEM model and to obtain real data for the actual machine an experimental campaign was done. For the sake of experimental analysis of dynamical behavior of the considered machine, measurements of the strains arising on the structure during various experimental and exploitation regimes were performed. Experiment with 25 total test runs was designed with intention to provide data for analysis of influence of the following parameters: rotation speed of the rotating ring, mass of foil drum and foil stretching force. Strains were measured with standard strain gauges having resistance 120.0±0.5 Ω and strain gauge factor 2.04±0.01, and the electric signal proportional to the strain was "in situ" conditioned and converted to digital form by microprocessor attached in proximity of the strain gauge. The digital signal was then transmitted through wireless network to measurement control computer. The acquisition frequency of the measurement was 100 Hz, Fig. 11: Location of measurement ponts At the ring, the location of measurement points and the directions of measured stresses were as follows (Figure 11): at point A1, nearest to the drum with foil at bottom surface, strain was measured in circumferential direction; the strain was caused by flexural deformation of the ring and its extension due to centrifugal forces; at point A2-nearest to the electric motor at bottom surface, strain was measured in circumferential direction; the strain was also caused by flexural 72

5 deformation of the ring and its extension due to centrifugal forces; at points A3 and A4, at bottom surface at the ends of diameter normal to diameter A1-A2, strains were measured in circumferential direction; the strain was also caused by flexural deformation of the ring and its extension due to centrifugal forces; at point B1, at middle line of inner lateral side of rotation ring, closest to point A3, strain was measured in circumferential direction; the strain was caused by extension of the ring caused by centrifugal forces; At the frame, strain measurements were taken in points at the upper surface of the supporting frame at points C1 and C5, the middle points of the longer sides of the frame, were measured strains in direction parallel to the respective trusses, caused by flexural deformation; at points C3 and C4, the middle inner points of the shorter sides of the frame, were measured strains in direction parallel to the respective trusses, caused by flexural deformation; at point C2, the middle point of intermediary truss between points C1 and C3, was measured strain in direction parallel to the respective truss, caused by flexural deformation. From the point of view of geometry of the structure, points A3 and A4, then C1 and C5, and finally C2 and C4 can be considered as equivalent, and the results considering these points will be treated together. In order to study the influence of foil drum motion and forces caused by stretching of the foil, the following regimes of machine rotation were considered: without foil drum; with standard foil drum, having a mass of 20 kg, and foil NOT attached to load; with regular foil drum, having a mass of 20 kg, and foil attached to load, and hence stretched due to wrapping; with large foil drum, having a mass of 30 kg, and foil not stretched due to wrapping and foil not attached to load; with large foil drum, having a mass of 20 kg, and foil attached to load, and hence stretched due to wrapping. Test runs were performed so that 12 tests were performed without attaching the foil to a test load, and 13 tests were performed with the foil attached to a test load. Regarding the drum weight, 4 tests were performed without drum, 8 tests were performed with the standard drum, and 13 tests were performed with the large drum. In order to test influence of speed of rotation to dynamical behavior of the machine, runs were performed so that in stationary regime rotation speeds were 80 rpm, 72 rpm, 60 rpm and 40 rpm (100%, 90%, 75%, and 50% of maximal rotation speed). Two runs were performed with stationary speeds of 40 rpm, three runs were performed with the stationary speed of 60 rpm, four runs were performed with the stationary speed of 72 rpm and the remaining sixteen test runs were performed with stationary speed of 80 rpm. 4. DATA PROCESSING AND ANALYSIS The following assessment quantities were analyzed in order to provide for achievement of the previous goals were: sign of deformation; mean value of strain at measurement points; amplitude of strain; frequencies of natural vibrations; frequencies of driven oscillations. The assessment quantities were estimated by calculation of the following quantities probability function for strain distribution, leading to calculation of span and median value of measured stresses; frequency spectra of deformation in stationary regime, with absolute frequencies and relative to the rotation speed. While experimental results were free of electronic noise usually caused by commutation, they were still heavily influenced by presence of loading effects and electronic drift of amplifiers in condition units, electronic noise generated by electric motors driving the machine, and by heavy transmission losses. The data processing that separated strain dependent signal from other influences was extensive and will be presented in separated paper. The typical raw measurement data and a pre-processed data after removing the influences of loading, electronic drift and noise are shown in Figure 12. Fig. 12: Example of raw and pre-processed strain measurement data The obtained strain-dependent signal has initial and final values equal to zero, and hence their values measured during test runs are the consequence of the motion of the machine. The typical recorded variation of the stress has the shape shown in Figure 13. The stress signal shows three different phases of run, acceleration and deceleration of the wrapping mechanism which represent 73

6 transition machine regimes and stationary regime during which the rotational speed is constant. The figure also shows statistical quantities that are calculated by analysis of cumulative probability function. The statistical analysis was applied only to stationary regime, because only in the stationary regime the signal may be considered as random. Fig. 13: Example of typical measured signal with indication of regimes and calculated statistical quantities The separation between transition and stationary regime was performed using pattern recognition techniques which will be described elsewhere. The calculated statistical quantities, which are usually applied as statistically meaningful measures for characterization of random signals, are ε 0.15%, strain value higher than 0.15% of recorded data, used as estimation of lower limit of recorded signal, ε 99.85%, strain value higher than 99.85% of recorded data, used as estimation of lower limit of recorded signal, and ε 50%, strain value higher than 50% of recorded data, used as estimation of lower limit of recorded signal. From these statistical quantities were estimated two assessment quantities, ε m = ε 50% as a measure of mean value of the strain during stationary regime, and Δε=(ε 99.85% - ε 0.15% )/2, as a measure of variations of the strain during stationary regime. Other estimations are possible, like the calculation of true mean value or the most probable value of the measured strain, but their statistical and physical meaning would not be higher, due to random nature of the recorded signal. Measurement errors of calculated values were estimated by analyzing the results of repeated measurements taken under the same experimental conditions, and it was estimated that the total measurement variation was not higher than 10μD= The summary of the results of estimation of values ε m and Δε are given in the Table 2. The table enables the following conclusions considering mean values of measured strains: Strains have significant positive mean values in points on the rotation ring, while the mean values of the strains in points at frame are close to limits of estimation errors; positive sign of estimated mean values in points located on the rotation ring can be explained by extension due to centrifugal forces; Strains have significantly higher values in points A1 and A2 (close to drum and electric motor, respectively) then in points A3, A4 and B1, confirming further the conclusion of dominant role of centrifugal forces as driving mechanisms for the strains. Further analysis oriented towards identification of the main source of deformation was carried out to confirm the hypothesis that the mean value of strains in points A1 and A2 is predominantly caused by centrifugal forces: the strains at those points, observed at different rotation speeds, were fitted to the expression ε m =A+B ω 2 looking for the deviation from purely centrifugal form ε mcf =B ω 2. In point A1, using mass of the drum foil of 30 kg and rotation speeds of 60,72 and 80 rpm, one obtains parameters A=1.2±0.4μD, B=0.1746±0.0007μD/(rpm) 2, which leads to an estimation that not less than 98% of the strain is dependent on speed, and therefore, could be attributed to the centrifugal force. In point A2, with less experimental data, by the same procedure not less than 80% of the strain may be attributed to the centrifugal force. Table 2. Mean values and amplitudes of variation of measured strains Fig. 14: Comparison of calculated mean value of strains at the ring and the fit described in the paper Regarding the variable part of strain, the table offers the following conclusions: All points located at the bottom surface of the ring (A1-A4) have the same amplitude of variations of the 74

7 strain around μd, independent of speed and mass of drum with foil; at point B1, on inner lateral surface of the ring, the estimated variation of stress during rotation of the machine is approximately twice smaller; the machine, while the second feature is attributed to the natural vibrations of the rotation ring. Fig. 15: Comparison of calculated amplitude of variation of strains at the frame and the fit described in the paper In points C2,C3 and C4, located at the parts of the frame which is stiffened by ribs, the amplitude of the variations of the strains are small; The largest variations of the strains occur at points C1 and C5 located at the trusses on longer side of the frame; at these points are measured the largest strains at the whole structure, varying between -220 μd and +220 μd. Initial study of dependence of variation of strains in points C1 and C5 on working regimes show that the variation does not depend on mass of the drum with foil, but strongly depends on rotational speed of machine. Applying the same procedure with fitting as in the case of mean values of the strains, with parameters A=(11±7) μd and B=(0.030±0.002) μd/(rpm) 2 not less than 80% of the variation of the strain may be attributed to the centrifugal force. Further analysis of variation of strains during rotation of the machine was performed by frequency analysis of the variations. Due to the previously mentioned heavy transmission losses caused by electromagnetic induction, the acquired measurement data were not equidistant, so the standard FFT analysis was not applicable. Instead LSQ spectral analysis procedure [2] was performed, leading to Lomb's periodogram [3] instead of usual amplitude-frequency spectra. However, Lomb's periodogram is proportional to PSD spectra, so its application is straightforward. The only important difference that should be taken care about while analyzing Lomb's periodogram is that it represents normalized power spectra, so that conclusions about intensities of the same spectral lines of different spectra should be made carefully. Spectra of variation of strain at points located on rotational ring show two kinds of distinct features, as shown in Figure 16: peaks at frequencies 2f 0 and 6f 0, at positions that vary proportional to rotational speed (f 0 denotes frequency of rotation) and a peak in frequency range between 12 and 17 Hz, at positions that do not proportional to rotational speed. The first kind of features is attributed to the forced vibrations caused by rotation of Fig. 16: Spectra of strains at a point on the rotation ring of the machine The forced vibrations with the frequency 2f 0 can be attributed to the excitation due to motion of drum foil and counterweight, which have similar masses. Therefore, during the motion, it can be considered that after the rotation of the ring for a half of a circle the excitation repeats, meaning that the excitation caused by motion of drum foil and counterweight has frequency 2f 0. On the other hand, the forced vibrations with the frequency 6f 0 can be attributed to the excitation due to motion of supporting wheels, because the ring has six such wheels, and hence the rotation of the ring for a sixth of the circle repeats the excitation caused by the wheels. It is interesting to notice that with the increase of the speed of rotation, the relative importance of the two modes of forced vibrations changes, so that at higher rotation speeds vibrations of the ring caused by contact forces with wheels have more importance than at low rotation speeds, when vibrations caused by drum foil and counterweight are dominant mode of vibrations of the ring. Independence of the position of frequencies in range Hz suggests that they are response of the structure, and need further elaboration through modal analysis. It is also to be noticed that the vibrations have much weaker intensity compared to intensity of forced vibrations, suggesting that no mechanical resonance is observed in the system. 75

8 depends on the weight while the amplitude is a function of the centrifugal forces. In general the measured values of the strain are quite low confirming the numerical result that suggests to modify the internal constrains in order to reduce the displacement of the critical points. 6. CONCLUSION An automatic wrapping machine has been studied numerically and experimentally. From the analysis it can be concluded that the main part of the observed critical points displacements is due to rigid motion and to the clearances and the compliance of internal constrains. The stress level was well below the allowable one so the actual machine is over-dimensioned from this point of view. Improvements could involve the change of the position and of the type of connection between rotating ring D and stationary frame B. REFERENCES Fig. 17: Spectra of strains at a point on the machine frame The spectra of variations of strains at points on frame have one important difference comparing to the previously described spectra. As is shown in Figure 17, the spectra of strains at points on frame do not show spectral peaks at frequencies 6f 0, meaning that the contact forces between wheels and frame do not affect the motion of the frame. Forced vibrations of frame have frequency 2f0, and natural vibrations of the frame appear again the same frequency range Hz, implying that is, for the proper understanding of the dynamic behavior of the machine necessary to perform modal analyses of both ring and the frame of the machine, because interplay between natural vibrations of the structures may occur. In any of the considered cases, stretching of the foil did not show any influence on dynamic behavior of the structure. Similar to this, no conclusive influence of variation of the mass of the foil on a drum was observed. 5. DISCUSSION Combining the results of the numerical model and of the experimental activity it is possible to derive some directions for the design process of this class of machines. As regards the natural frequencies both methods indicates that the range is Hz. Forced vibrations are induced at frequencies double and six times the frequency of rotation, therefore the latter should be limited to 2Hz (120 rpm) in order to avoid resonance. The most stressed points during the cycle appear to be A1 and A2 on the rotating ring, near the concentrated masses. The mean value of the strain depends from the centrifugal force (hence from mass and speed) while the amplitude depends on the weight. On the frame the most stressed points are C1 and C5 and in this case the mean value [1] Lang T.E. (1962) Vibration of thin circular rings,nasa Report [2] Babu, P., Stoica, P. (2010) Spectral analysis of nonuniformly sampled data a review, Digital Signal Processing, Vol. 20, pp [3] Lomb, N.R., (1976) Least Squares Analysis of Unequally Spaced Data, Astrophysics and Space Science, Vol. 39, pp CORRESPONDENCE Prof. Dr Giangiacomo MINAK University of Bologna DIEM department viale Risorgimento Bologna, Italia giangiacomo.minak@unibo.it Dr Zlatan ŠOŠKIĆ University of Kragujevac Faculty of Mech. Eng. Kraljevo Dositejeva Kraljevo, Serbia soskic.z@mfkv.rs Snežana ĆIRIĆ KOSTIĆ University of Kragujevac Faculty of Mech. Eng. Kraljevo Dositejeva 19, Kraljevo, Serbia cirickostic.s@mfkv.rs Cristiano Fragassa, Dr Eng. University of Bologna DIEM department Viale Risorgimento Bologna, Italia cristiano.fragassa@unibo.it 76