Verification of a Finite Element Model of a Rotating Tippler Structure by Means of Strain Gauge Measurements

 

 

P.J.A. van Zyl; N.D.L. Burger; P.R. de Wet

Department of Mechanical Engineering, University of Pretoria, South Africa, Email: pieter.vz@9dot.co.za

 

 

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ABSTRACT

The complex rotational working of a tippler structure complicates the analytical evaluation of the structure. A further complication is the ever-changing boundary conditions while the structure rotates, together with the weight reduction of the coal in the wagons when the wagons are offloaded. Both these factors need to be taken into account when determining the stress levels in the structure while operational. To verify the accuracy of a finite element simulation of a tipping cycle, strain gauge measurements obtained from the actual tippler structure was compared with stress results obtained from linear static finite element analyses of the structure, simulating different tip positions at set time intervals. The results obtained from the comparison indicated an accurate simulation of the tipping cycle by means of the finite element simulation.

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1. Introduction

Tippler structures experience varying load or force inputs combined with changing boundary conditions during each increment of the tip cycle. These load variations and changing boundary conditions, induce varying stress levels in the structure while operating. To accurately simulate these stress levels in the structure by means of a finite element model, the model would need to allow for the changing loads and boundary conditions for each of an infinite number of positions. However, the cost and time consumed by such an analysis would render the benefits of the analysis inappropriate. For this reason, it was decided to investigate the possibility of simulating the complete tippler load and tip cycle by means of a small number of linear static finite element models, each model representing a 10-degree interval of the tip cycle, and then verifying the stress results obtained from the analysis by means of comparison with calculated stress results determined from strain gauge readings obtained from the actual tippler structure. The measured results were obtained by applying strain gauges at selected positions and measuring the strain levels and calculating the stress levels during consecutive tip cycles. By comparing the finite element results and the measured results the accuracy of the analysis method was established.

 

2. Tippler terminology

A tippler structure consists of two drum-like cages resting on eight support roller assemblies through which the coal wagons are driven, clamped and then rolled over or tipped to offload the coal. The coal falls onto a conveyor system which transports it away. Figure 1 shows the process layout.

 

 

Each cage consists of two end rings, a platform structure, a cross beam at the back and a side beam at the front. Mounted on the cross beam is a clamp assembly that clamps the wagon onto the rail during the tip cycle. The layout of the ingo cage and its clamp detail is shown in Figure 2.

 

 

The ingoing and outgoing cages are of similar construction and are referred to as the ingo cage and the outgo cage. Each cage has two end rings, which are referred to as the ingo ingo end ring for the ingo side end ring on the ingo cage and the ingo outgo end ring for the outgo side end ring on the ingo cage. Similarly, the outgo cage's end rings are referred to as the outgo ingo end ring for the ingo end ring on the outgo side cage and the outgo outgo end ring for the outgo side end ring of the outgo cage.

The clamp system consists of two clamps mounted to two clamp arms which are in turn mounted to the back of the cross beam. The clamp arm is further connected by means of a tie rod to a clamp mechanism. This clamp mechanism incorporates a counterweight. The clamping process is completely mechanical and there are no outside forces (hydraulic or electrical) that contribute to the clamping action.

During the tip cycle the wagons are tipped towards the side beam by means of two pinion gears that drive the two ring gears situated on the ingo ingo end ring and the outgo outgo end ring of the two cages. The drives of the two cages are not mechanically coupled and the two cages can tip separately. The tip angle is through 160 degrees and the total tip cycle takes approximately 40 seconds. The complete load and tip cycle takes approximately 110 seconds to complete. The terminology stated was used throughout the study.

 

3. Analysis procedure

The model verification analysis was completed in two components and the results of these components were compared to determine the accuracy of the simulation method. The first step in the analysis consisted of strain measurements on the structure analysed. The stress results calculated from the strain values were compared with the stress results obtained from the finite element analysis for the positions where the strain gauges were applied.

3.1 Strain gauge analysis

The rotation of the tippler structure during operation complicates strain gauge measurements when using conventional wiring methods. It was therefore decided to make use of wireless strain gauge amplifiers.

The positions selected for strain gauge application were selected based on the expected stress patterns in the structure. Only positions on main structural components where one-directional stresses and no stress concentrations were expected, were selected for the study. The selected strain gauge positions used for comparison purposes are shown in Figures 3 to 5. Also note the direction of the strain measurement. Some additional positions were strain-gauged to determine the magnitude of internal stress levels in the structure during the tip cycle. These measurements were, however not used in the model comparison. The positions of these strain gauges are shown in Figures 6 and 7.

 

 

 

 

 

 

 

 

 

 

For the application, a half-bridge strain gauge arrangement was used. This arrangement compensates for temperature changes that may influence the strain gauge readings during operation. In this application, the water sprayed in the air to reduce coal dust during the tip cycle may have caused temperature fluctuations that could influence the readings. Note that local bending on the strain-gauged plates was ruled out because of the section size of the structure where the strain gauges were applied. The properties of the strain gauges used are listed in Table 1.

 

 

The strain gauge amplifiers' outputs were set to zero with no wagons positioned on the platform. The sampling frequency used for the analysis was estimated from a sample reading taken during set-up recording of a tip cycle as shown in Figures 8 and 9. For the reading a sampling frequency of 50 Hz was used. This method was used as no known stress frequency data for the structure was available and the accepted industry standard of using a sample frequency of at least ten times the structure frequency¹ could therefore not be applied. The stress data obtained from the test readings showed that no peak data values were lost during the recording, indicating that the sample frequency was adequate.

 

 

 

 

Strain readings were then obtained for two complete loading cycles, i.e. the first positioning of the wagons on the platform and then for 25 consecutive tip cycles. The strain data obtained was translated to stress values which were then compared with the stress data obtained from the finite element analysis.

3.2 Finite element analysis

In order to obtain comparative stress data for the analysis, linear static finite element models were constructed, representing each 10-degree interval of the tipping cycle. It was decided to use the linear static analysis method for the analysis as this method is simpler, faster to complete, and the software used is readily available and less costly. For a linear analysis to hold true, the material properties, geometry and boundary conditions should be linear throughout the analysis. For the material properties, this means that the stress levels should be of such nature that no yielding takes place during the analysis. Furthermore, no geometric stiffening should take place during the analysis and the boundary conditions should not change from the original application to the final deformed shape. The loads applied should furthermore remain constant in magnitude, direction and distribution².

The method used in which the tippler's tip action is broken down into seventeen intervals and where each interval is dealt with as a linear static analysis with its own set of static boundary conditions therefore meets the criteria of a linear static analysis.

3.2.1 Finite element model preparation

The surface and solid components of the tippler structure were constructed using IDEAS NX software and each component was meshed separately. A shell model was constructed for the main structural components and a solid model for the primary compensating beam and support rollers. Based on an evaluation of some of the curved surface edges in the model, the decision was made to use second-order elements as these elements have the advantage of providing more accurate results on curved geometries³. Fewer elements could therefore be used and accurate results would still be obtained from a smaller model size. For the cage assembly, a second-order or parabolic quadrilateral thin shell mesh was used with an average element length of 150 millimetres. Where needed the element length was reduced and triangular elements were used. For the solid model components, a second-order tetrahedral element with an element length of 40 millimetres was used. The rollers were map-meshed with second-order solid parabolic bricks.

The meshed surface model of the cage structure is shown in Figure 10 and that of the roller assembly in Figure 11. The different colours applied to the model indicate the different plate thicknesses used in the construction of the structure.

 

 

 

 

To simulate the rail section mounted to the platform structure, beam elements with the same cross-sectional profile as the rail indicated on the structural drawings were used. The rail was tied to the platform structure by means of rigid elements to simulate the rail on platform interface. No relative movement is possible between the rail and the platform.

All pins, shafts and damping springs were simulated by means of rigid elements to reduce model set-up times. This assumption was made as the effect of shaft or pin-bending or the stress levels obtained in these components would have no influential effect on the stress levels in the tippler structure.

The main advantage of building a model of the complete cage assembly lies in the accurate weight distribution and stiffness representation that the model provides. Each of these factors could influence the stress results obtained with the models during the rotation simulation. Where two plates are bolted together in the assembly the connection was simulated as one plate with the combined thickness of the two plates. The difference in model stiffness created by simulating the bolted connections as a single plate of representing thickness would not influence the stress results as these connections are situated far from the strain gauge positions. Where possible all short surfaces, broken edges and scarred surfaces were removed from the models to reduce the possibility of generating badly shaped elements during the meshing process.

The next step in the model construction process was to combine the different structural meshes into one assembly mesh for each of the 10-degree tip intervals. To reduce model construction time, the I-DEAS "mesh from assembly" function was used. This function allows the user to mesh all assembly components separately and then combine all the separate meshes into one assembly mesh that represents the assembly orientation used. This process sped up the mesh-generation process for all the tipping positions investigated. In total 17 models were constructed. Figure 12 shows the assembly mesh of the tippler structure in the 60-degree position.

 

 

The element thicknesses selected for the wagon do not represent the actual construction of the wagon structure, but provide an accurate estimation of the wagon with its centre of gravity at a height of 933 mm above the rail as indicated in the wagon specification. Additional stiffness was added to the wagon structure by means of rigid elements that do not contribute to the weight of the wagon. The main functions of the wagon model are to simulate the weight of the empty wagon, provide the force transfer points from the wagon to the tippler structure and provide clamping areas for the clamps on the wagons.

All access covers in the structure were left open as the bolt connections on these covers are normally not preloaded and the cover is sealed with water-resistant putty which is applied between the cover and the structure. The covers would therefore not provide any structural stiffness to the tippler structure. Furthermore, no handrail, walkway structures or piping on the structure allowed for. The structural weight contribution of these components is negligible.

3.2.2 Boundary conditions

To accurately simulate component interfaces in the models, the boundary conditions applied should be able to transfer all translations and rotations needed from the one component to the other and vice versa. This is made possible by using coupled degrees of freedom, which is a set of nodes linked in specific directions and rotations. No frictional forces can, however, be simulated by these connections and were therefore not allowed for in this analysis.

All pinned connections were simulated by means of coupled degrees of freedom. Where the connection pins are not able to transfer moments the rotational constraints around the pin centrelines were disabled allowing the components to rotate freely around these centrelines. The support roller shafts were constrained by means of rigid elements and were not allowed to rotate around their centrelines. This would have no effect on the results, as the rollers are free to slide on the rail interface in the directions allowed for. The rails are, however, not allowed to slide in the horizontal direction on the grooved rollers but can slide on the non-grooved rollers. Any sliding on the non-grooved rollers would simulate play that exists in the support roller assemblies of the tippler structure. It would furthermore simulate relative slip that occurs between the rail and the rollers during the rotational motion of the cage when the static friction coefficient is overcome.

For the rail/roller interface, a coupled degree of freedom was applied that simulates the perpendicular reaction force that would be generated by the rollers on the rail. The applied coupled degrees of freedom are shown in Figure 13. The cage is free to rotate around its own centreline to allow for twisting during the analysis.

 

 

The wagon wheel interface on the platform rail was also simulated with coupled degrees of freedom. This method only transfers the vertical load to the rail and the side force generated by the wheel flange on the rail when the cage is rotating. The constraints would not affect the bending pattern of the platform structure. The constraints used on the wagon assembly are shown in Figure 14. Note, however, that these constraints change when the cage rotates. From an inspection of the wear plate on the side beam during the strain gauge installation process, it was clear that the wagons lean against the plates during the tip cycle. This would suggest that the wheels on the back rail of the platform would reduce their reaction force on the rail or even lift from the rail when the wagon leans against the wear plate.

 

 

The estimated angle at which the wagon would start to lean over was calculated from the available data for the wagons at approximately 17°. To simulate this situation the coupled degrees of freedom were removed between the rail and the wagon and applied between the wagon and the side-beam wear plates for all positions after the 20-degree rotation interval.

The support roller assembly bases were constrained in all directions on the surface interfacing with the concrete foundation. Furthermore, the cage was constrained against rotation at the pinion/ring gear interface on the ingo side end ring.

The main forces contributing to the stress in the tippler structure are the gravitational force and the forces introduced to the structure by means of the wagon and coal load. A gravitational acceleration value of 9.81 m/s² was used for analysis.

To simulate the reduction in the weight of coal in the wagon during the tip cycle a constant load curve was assumed as shown in Figure 15. This approach was selected to eliminate the complexity of estimating the weight of coal in the wagon at each tip angle simulated. From video material taken of the tip cycle and the angle of repose of coal of between 30 and 40 degrees⁴, it was estimated that the first coal would start dumping at a tip angle of between 30 and 40 degrees. The lower value of 30 degrees was selected for analysis purposes to allow for all possible angles of repose. The weight of coal in the wagon was reduced by 6 000 kg for each 10-degree interval rotated up to the 160-degree interval. For the return cycle the wagon was simulated as empty.

 

 

The weight of the coal as obtained from the graph was applied as a point load at the CG position of the wagon. Although this boundary condition could influence the structural stresses for certain tip intervals, applying this condition to all the tip intervals the error introduced is constant for all tip intervals. The data was therefore still valid for evaluating stress trends in the structure during the tip cycle.

The seventeen FEA models simulating the different tip intervals were solved, each model solution taking approximately 40 minutes on a Windows-based workstation. An additional analysis was also done on the ingo cage with no wagon positioned on the platform. The results of this analysis were used to determine the mean stress in the structure caused by gravity alone.

The strain gauge data obtained earlier does not take into account the stress in the structure caused by gravity and can therefore not directly be compared to the FEA results.

 

4. Results comparison

As previously described, a finite element model was constructed and solved for each 10-degree interval of the tipping cycle. The finite element results for a specific tip interval should, however, be compared with the strain gauge data for the exact time step when the tippler cage rotates through the set angle used in the finite element analysis. To be able to perform this comparison the time steps at the different tip angles had to be determined. Further, note that the cage will pass each interval angle twice during the tip cycle, the first time with a loaded wagon and the second time with an empty wagon.

From the strain gauge results, the total tip cycle time was determined as approximately 40 seconds. This Figure was verified by means of short video clips recorded on the day the strain gauge analysis was done. Furthermore, the tippler cage ramp-up and ramp-down intervals were set at 3 seconds. No further cycle detail was, however, available. Figure 16 shows the speed / time graph for the cage calculated for a 160-degree tip angle to be completed in 17 sec with the 3-sec ramp-up and ramp-down intervals included. The area under graph represents the 160 degrees rotated. From this graph, the time intervals at each 10-degree tip angle were calculated from the slope of the graph and the area underneath the graph.

 

 

From this data the time increments for stress data comparison were calculated and are shown in Figure 17. These time steps were used as reference to compare the stress values calculated from the strain gauge data to the stress values obtained from the FEA results angles.

 

 

Two data verifications were done to verify the accuracy of the FEA method used. For the first verification, the tippler results for an empty and loaded cage were compared. For the second verification, the strain gauge data and FEA data for the different tip intervals were compared. From these results, the accuracy of the FEA method was determined.

a) Loaded and unloaded tippler structure

The stress results obtained from the finite element models of the empty and loaded cages were compared with the strain gauge results obtained for the same load cases and with values obtained from a basic calculation done on the platform structure. The comparative data is shown in Table 2. The FEA values used for the comparison are shown in Figures 18 to 25.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

The largest stress difference between the measured and FEA results is 11.7%. This is for the back strain gauge where the full wagon replaces the empty wagon on the platform.

Figures 18 to 20 show the stress results obtained from the FEA for three load cases, i.e.:

□ The tippler cage empty with only gravitational forces applied

□ An empty wagon positioned on the platform

□ A loaded wagon positioned on the platform

The results used for the strain gauge comparison are shown in Figures 21 and 22.

To compare the stress values with the calculated and stress levels from strain gauge readings the Case I stress was deducted from the Case III stress simulating a full wagon being loaded onto the platform. The Case II stress was deducted from the Case III stress to simulate the difference in stress for an empty and loaded wagon on the platform. Note for all three Figures the stress scale was kept the same.

The data for the comparison between the FEA model and the stress levels determined from strain gauge readings differs by 11.7% at most. This indicates the model is representative of the actual conditions when the tippler is loaded with wagons.

b) Stress comparison for full tip cycle

The stress values obtained from finite element models for the positions where the strain gauges were applied were compared with the stress values calculated from the strain gauge readings. The comparison was done per time interval as calculated earlier. Figure 23 shows a comparison of the stress readings obtained for non-consecutive tip cycles. Note the difference in stress levels between the different tip cycles. These variations are caused by internal forces generated in the structure during the rotational motion of the cage. The existence of these forces was confirmed by the measurements taken with the strain gauges applied at the positions as indicated in Figures 6 and 7. The results of these readings are shown in Figures 24 and 25.

To compensate for the internal stress variations in the cage the stress values used for the comparison were calculated by averaging the stress readings obtained from non-consecutive tip cycles, i.e. the results as shown in Figure 23.

The first two sets of data as shown in Figures 26 and 27 show the calculated stress comparison for the two strain gauges applied to the platform structure. The deviation between the stress values at the maximum stress values is approximately 11.0% for the front strain gauge and 5.0% for the back strain gauge.

 

 

 

 

The data for the strain gauge on the cross beam is indicated in Figure 28. There is a slight deviation in the stress pattern between the two data sets. This is caused by a difference in the time of contact between the clamps and wagon, in the FEA model and the actual occurrence. The maximum deviation at the highest stress for the cross beam is approximately 9.4%.

 

 

The last comparison is between the stress values calculated from the strain gauge readings on the clamp arm and the FEA results obtained for the similar position. The results are shown in Figure 29 and have a maximum difference in value of approximately 8.8%.

 

 

The difference between the measured and FEA results can be contributed to effects such as differences in the boundary conditions applied, ramp-up and ramp-down speeds of the tippler structure, weight distribution or other effects not simulated in the FEA model. The largest difference in the measured and FEA data is seen for the cross beam data. This may be caused by the fact that the spring assembly in the clamp arm mechanism was simulated by means of a rigid element. The deviation is, however, only seen in the shape of the signal and not the maximum stress levels obtained. The data therefore indicates that the method applied to simulate the tip cycle by means of multiple linear static finite element analyses does provide an accurate representation of the actual stresses obtained during the tip cycle.

 

5. Results discussion

The FEA model results compare well with the strain gauge readings obtained from the tippler structure. The maximum error between the readings and the model is approximately 11.0% at the front strain gauge position on the platform structure. This indicates that the rotational motion of a tippler structure can be simulated accurately by using linear static finite element models solved for set intervals. The method would provide a good estimation of the stress values observed during the tip process and would therefore be suitable for the calculation of structural design stresses or fatigue life estimations.

 

References

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