A n Exa Exam mpl ple e of a New New V ictaul ctauliic M odel deling Using A utoP utoPI PE 2004
1. General introduction Previous flexible Victaulic coupling modeling was based on the article “Flexible coupling: modeling of bi-linear moment rotation relationships in AutoPIPE” by Nasir Zulflqar. The idea from Nasir Zulflqar was to set up two rigid frames and use tie-link supports to control the two frame’s movements to simulate flexible coupling’s movements. Discrepancies of Nasir’s modeling are that spring stiffness has to be defined to obtain the exact moments and rotations at the centre of the flexible joint, and anchored rigid frame and the moveable rigid frame will limit the modeling application as well. In order to set up a more efficient and applicable coupling system, a new Victaulic coupling modeling is now available, which is different from the one created by Nasir Zulflqar but carries the same idea.
2. Method of modeling 2.1 Input data Let us consider a titanium pipe with each end connected between two tanks. One tank A00 has a 6 mm relative settlement (Y2 = -6 mm) and the other tank B04 has no movements. A vertical support is in the middle of the pipe which is connected to tank A00. Two Victaulic couplings were installed at the each end of the pipe. Both tank nozzles are L3 = 0.5 m long and connected with the each end of pipe through Victaulic couplings. The pipe is standard NPS 24 and is 1.2 meters long (L = 1200 mm). Two Victaulic flexible couplings (style 77) are needed to absorb the thermal expansion of the pipe and tank settlement. The modeling data will be based on the Victaulic’s bulletin 06.04. Suppose the design pressure of this piping system is 116 (KPa) and design temperature is 100 ( C). Ambient temperature is 17 ( C) from PV project site conditions. o
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2.2 Allowable movements Every Victaulic coupling has limited gap to allow pipe end movement inside the housing, which is the reason of absorbing the tank settlement and thermal expansion. For 24” coupling, the maximum allowable cut-grooved pipe end movement is G = 3.2*2*0.75 = 4.8 (mm). We can calculate the maximum allowable misalignment Y that the two couplings are able to bear without damage damage based on Victaulic Victaulic Design Data 26.01 shown shown in Figure 1 and 2. 2.
Figure 1 Maximum Allowable Misalignment Y (from Victaulic Design Data 26.01)
Figure 2 Relationship of L, Y, and G in this modeling
We need to pay attention to the value D here. I n AutoPI PE modeling, weshall model the coupling housing diameter as the pipe end diameter. Hence the diameter of the pipe end is the outside dimensions of the 24” coupling D =794 mm (rounded to 800 mm) from Victaulic bulletin 06.04, instead of the pipe diameter of 609.6 mm. Therefore, the maximum misalignment, i.e., the maximum settlement will be Y = G*L/D = 4.8*1200/800 = 7.2 (mm), which is larger than the tank settlement Ytank = 6 (mm).
Partially deflected joints will provide some portions of linear movements. o
However, this piping system will produce a thermal expansion displacement from 17 ( C) to100 ( C) as well. o
We can calculate the expansion displacement G1 = thermal coefficient * ∆T* L1 Here L1 = L + 2* L3 = 2.2 (meter) -6
Thermal expansion for this titanium material is 8.6*10 ∆T = 100-17 = 83 ( C) o
G1 = 8.6*10
-6
*83*2200 = 1.57 (mm)
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(mm/mm/ C);
Although we have the two couplings, the equivalent allowable settlement is combined displacement of the two couplings. We need to calculate the equivalent pipe end movement G2 due to the tank settlement. From above formula, we have G2 = D*Y2/L = 800*6/1200 = 4.0 (mm) ……………………………………….(2) Therefore, the actual total pipe end movement G’ = G1+G2 = 1.57 + 4 = 5.62 (mm), which is larger than the maximum allowable pipe end movement G = 4.8 (mm), therefore the supposed tank settlement shall be calculated again to meet the requirement. Using this method, we can find the Maximum allowable tank settlement Ya. Ya = (G – G1)*L/D = (4.8 – 1.57)*1200/800 = 4.85 (mm) Therefore, we have to change the settlement value for the tank from -6 mm to -4.85 mm, otherwise the two Victaulic couplings may fail or the system may suffer from large expansion stress and loads. 3. Modeling method 3.1 Modeling the expansion joint Now let us set up the modeling step by step. Set up an anchor A00 and input settlement DY = 4.85 mm. Create a 500 mm long tank nozzle from A00 to A01. Then create expansion joint from A01 to A02, which is shown in Figure 3.
Figure 3 Expansion Joint
Figure 4 Inputs of expansion joint We will input the length of the expansion joint as the maximum allowable pipe end movement of Victaulic coupling (see Figure 4). The relative movements of the two ends of Victaulic couplings are forbidden to prevent the end-break of the coupling. Therefore, we input Y and Z shear stiffness as rigid to make sure that the two ends of the coupling will move together. The Victaulic couplings are allowed to move in axial direction, rotate, and bend in Y and Z directions. 10 N/mm can be used as axial stiffness to simulate the smooth movement in this direction; 1000 N.m/degree can be used as torsional stiffness, Y and Z bending stiffness. No
zero values shall be input for stiffness, which will lead to unstable system errors shown as “E801-1: FATAL ERROR: Unstable system”. As a usual, zero will be input to the pressure area due to the minus profile changes during operation. 3.2 Coupling modeling From Victaulic bulletin 06.04, we can find that the outside dimensions of the 24” coupling is 794 (mm), and let us round it to 800 (mm). Therefore we can create four rigid fr ames V01, V02, V03, V04, which are 800/2 = 400 (mm) from the centre point to the top as left rigid part of flexible couplings (see Figure 5). And then create another four rigid frames V11, V12, V13, V14, which have the same dimensions as right part of flexible couplings. The input sheet from Figure 5 shows us the way to establish the frame beam
M8 from center A02 to V14 in the negative x direction. Here DX = -400. Choose the “Rigid” selection in “Table Name”, and input zero to Beta angle, Rigid Length End-I and J items. No weights will be considered for the rigid frames as the weight of the coupling has been defined in the expansion joint (see Figure 4). The two rigid frames created as the two ends of the pipes in the coupling housing, which are able to move and rotate at limited values. Tie-link supports will be used to control the relative movements of the two rigid frame ends, which is the simulation of the movements of the two pipes in the Victaulic coupling housing. The tie-link supports (in green) are shown in Figure 5. Rigid fr ame V01 and rigid frame V11 will be connected through tie-link supports. We put spring rate as rigid and zero friction coefficient to simulate the movements of the two pipe ends in the coupling housing. The maximum allowable pipe end movement is 4.8 mm. Because we do not know the exact movement direction of pipes in the coupling housing, as a conservative way, we can suppose the gap backward and forward movements be half of 4.8 mm, i.e., 2.4 mm. In this way, the actual pipe expansion may be shrunk into half of the allowable axial movements and may produce considerable expansion stress on the systems. No weights are considered here, so the gap setting will be weightless. Altogether four tie-link supports will be created to control the relative movements of the two pipe ends.
Figure 5 Frames of the Victaulic coupling modeling
Figure 6 Inputs of tie-link supports 3.3 Method of modeling insertion or copying Continue the pipe modeling from A02 to A03 for 600 mm and add a vertical support which connects to the tank A00 as shown in Figure 7. We the call the file as “system to be inserted.dat”. We can insert a similar coupling modeling instead of creating the second coupling modeling. A uniform Victaulic coupling modeling can be created shown in Figure 8 and is ready to be inserted whenever needed. We call the file as “modeling to insert.dat” . A bare coupling modeling will lead to “ N527-23” error, because bend or component cannot be used as a connection point. At least one piece of pipe (A00 to A01) connected to the modeling shall be given in order to insert successfully. The proper procedure for inserting can be done as f ollows.
Open the AutoPIPE dat file “system to be inserted.dat”, and select the insert point A04. Click the “insert” button on the top, select AutoPIPE model, then find “modeling to insert.dat”, open it, select the connecting point A00 and finally click “ok”. The new coupling modeling has been
Inserted into the system, which is shown in Figure 9. The inserted portion is numbering as segment B.
Figure 7 System with one Victaulic Coupling 4. Modeling outputs 4.1 Displacement outputs The displacement outputs of the modeling are shown in Figure 11. Since we input the allowable 2.4 mm for all the tie-link supports, the relative displacements of A01 and A02, and B01 and B02 should be verified. The maximum axial relative displacement of the first coupling (A01 and A02) is 0.34 -(-0.36) = 0.7 mm which is less than 2.4 mm. The maximum axial relative displacement of the second coupling (B01 and B02) is 0.46 (-0.34) = 0.8 mm which is less than 2.4 mm. Check the vertical movement of the system, and we find that maximum DY = -4.85, which is the exact maximum allowable tank settlement Ya we calculated in item 2.2. Therefore, the system outputs for modeling displacements are satisfied. 4.2 Load outputs The load outputs of the modeling are shown in Figure 12. The maximum load on the tank nozzles is the gravity weight, 8.18 (KN), which is quite reasonable for NPS24 pipe. The
support load is 5 (KN), which is the portion of the pipe and fluid weight. Therefore, the system outputs for modeling loads are satisfied.
Figure 8 Victaulic Coupling modeling for inserting 4.3 Stress outputs The stress outputs of the modeling are shown in Figure 13. The maximum stress is coming from the tank nozzles, which is only 10 percent of the allowable. This is because of the function on coupling axial and vertical movements.
Figure 9 Victaulic Coupling Modeling Inserted in the system
Figure 10 Example of Victaulic Coupling
Figure 11 Tables of Displacement Outputs of the Modeling
Figure 12 Load outputs of the Modeling
Figure 12 Load outputs of the Modeling
Figure 13 Stress outputs of the Modeling
5. Discussion 5.1 Change the support connection We may find totally different results if the support A03 is connected to the fixed tank B04, as shown in Figure 14. The loads are extremely large and stresses are huge. Half portion of the pipe from A03 to Bo4 will not going down due to the support, which is connecting to the fixed tank B04. Hence the maximum allowable tank settlement will be less than the value Ya from item 2.2. And the combined axial displacements for only one coupling will decrease the settlement as well. In addition, the upward intendance of the support will change the movements of the pipe. The formula specified in Figure 1 need to be revised. Therefore in this case, the tank settlement needs to be cut down to around 1 mm.
5.2 Tank rising instead of settling When the tank A00 has a growing up displacement Ya = 4.85 mm instead of settlement, the support shall be connected to B04 to get similar results as the case of settlement and support connection to A00, which shows in Figure 15.
Figure 14 Different results from changing the support connection.
Figure 15 Similar results for settlement and support connection to A00
Figure 15 Similar results for settlement and support connection to A00
5.3 Tank radial thermal expansion Suppose the two tanks (A00 and B04) are concrete tanks, which will have radial thermal expansion. If the concrete thermal expansion coefficient C = 9.9 E-6 (mm/mm / C) and the each tank radius R = 1200 (mm), we have the total tank thermal expansion displacement G2’ as follows. o
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G2’ = 9.9 E-6 [mm/ (mm* C)] * (100-17) C * 1200 mm = 1 mm Both of the two tanks will have the thermal expansion displacement 1mm. So the equivalent thermal expansion will be G2 = 2.0 (mm). Using the method stated in item 2.2, we can find the Maximum allowable tank settlement Ya considering the tank radial thermal expansion.
Ya = (G – G1-G2)*L/D = (4.8 -1.57- 2.0)*1200/800 = 1.845 (mm) The displacement outputs for this case are shown in Figure 16.
Figure 16 Displacement output for the tank thermal expansion case
Figure 16 Displacement output for the tank thermal expansion case
The maximum axial relative displacement of the first coupling (A01 and A02) is 1.34 (-0.37) = 1.71 mm which is less than 2.4 mm. The maximum axial relative displacement of the second coupling (B01 and B02) is 0.45 -(-1.34) = 1.79 mm which is less than 2.4 mm. Check the vertical movement of the system, and we find that maximum DY = -1.85, which is the exact maximum allowable tank settlement Ya we calculated in item 2.2. Therefore, the system outputs for modeling displacements are satisfied. The loads outputs for this case are shown in Figure 17. The load outputs of the modeling are shown in Figure 12. The maximum load on the tank nozzles is the gravity weight, 8.18 (KN), which is quite reasonable for NPS24 pipe. The support load is 5.69 (KN), which is the portion of the pipe and fluid weight. Therefore, the system outputs for modeling loads are satisfied.
Figure 17 Load outputs for the tank thermal expansion case The stress outputs for this case are shown in Figure 18. The maximum stress is coming from the weight of the pipe, which is only 0.04 percent of the allowable. This is because of the function on coupling axial and vertical movements.
Figure 18 Stress outputs for the tank thermal expansion case
Figure 19 Zero gaps in the tie-link support.
6. Modeling Verification In order to check the modeling, we can reduce the tie‐link support gap to zero as shown in Figure 19. Then the modeling shall act as a rigid flange on the pipe, the bending stress will be high due to the settlements of the tank, as shown in Figure 20.
Figure 20 Stress results of zero gap tie-link support of modeling
The maximum axial relative displacement of the first coupling (A01 and A02) is 4.2 – 4.18 = 0.02 mm and the maximum axial relative displacement of the second coupling (B01 and B02) is 0.66- 0.65 = 0.01 mm, which are almost zero. The loads outputs for this case are shown in Figure 17. The load outputs of the modeling are shown in Figure 12. The maximum load on the tank nozzles is the bending force, which is 1242 KN due to the settlement. And the bending stress value will be 0.79 allowable, as shown in Figure 20. Now let us delete the modeling and put the pipe instead as shown in Figure 21. The zero gap modeling shall be approximately the same results as the one of the bare pipe to show the correction of this modeling. From the analysis results, stress results are the same, as shown in Figure 22. The maximum nozzle loads are 1242 KN for zero gap coupling modeling and 1274 KN for the bare pipe system.
Figure 21 Pipe systems without coupling modeling
Figure 22 Stress results of pipe system without coupling modeling Figure 22 Stress results of pipe system without coupling modeling
7. Conclusion Normally, there are some minus differences between the Victaulic coupling modeling and the bare pipe modeling. That is because the zero gaps coupling modeling may have some extent of rotation. Therefore the maximum force will be a little bit smaller than the bare pipe modeling. However, from the stress analysis point of view, the Victaulic coupling modeling is good enough to calculate the loads, stresses and displacements of piping systems.
8. Reference A. B.
NASIR ZUFIQAR, Flexible Coupling: modeling of bi-linear moment rotation relationship in AutoPIPE Victaulic Coupling bulletin 06.04, 26.01. from http://www.victaulic.com
