How to prevent radial displacement under torsional load

[faremusai]

I am trying to model a hollow steel shaft with the following configuration:
- one end fixed
- the other end is free to rotate about and move along the z-axis. The end cap surface is rigidly fixed to another stiff component so that radial displacement of the inside and outside rim are restricted.
- subject to a torsional torque load acting on the end cap surface about the centre line (z-axis)

Analysis result shown that the free end bulged outward like the mouth of a trumpet. The torque seemd to have casue radial displacement.

I prefer the free end cap surface node to be free to rotate/swivel like a self-align bearing but radial displacement of the cap surface node must be restricted.

What sort of constraint(s) should be added to prevent the radial displacement at the free end?

http://files.engineering.com/getfil...cantilever-Subject_to_torsion_at_free_end.jpg

http://files.engineering.com/getfil...ect_to_torsion_at_free_end-Deformed_shape.jpg

 

[BlasMolero]

Hello!,
Simply apply a radial constraint TR=0 in the end cap surface using the cylindrical coordinate system. You need to orient your model to have the global Z-axis in the axial direction of the cylinder, or define a local coordinate system of type CYLINDRICAL with the X axis being the darial and Z axis being the axial to used it to prescribe the local constraint in the end cap surface, OK?.

Regarding deformed shape, do not get confused, all is scaled, not matter is you prescribe the radial constraint (Tradial=0), if in the deformed output vector you select TOTAL TRANSLATION then you will see a total translation deformed model.

The best way to see that you are doing things correctly is to list the nodal displacement in the end cap surface: in the nodes at the plane Y=0 you will have resultant displacement TX=0, do not get confused with the deformed shape, OK?

List Output Standard
1 Node(s) Selected...
Femap with NX Nastran Version 11.22
Model   : D:\MODELOS\TEST\cylinder-hollow-radial=0.modfem   Report :  Node
Format  : NASTRAN Displacement
 
Output Set 1 - NX NASTRAN Case 1
                                            D I S P L A C E M E N T   V E C T O R

      POINT ID.                 T1             T2             T3             R1             R2             R3
          241      G                 0.    5.409732E-4  -5.513489E-11             0.             0.             0.

Best regards,
Blas.

~~~~~~~~~~~~~~~~~~~~~~
Blas Molero Hidalgo
Ingeniero Industrial
Director

IBERISA
48004 BILBAO (SPAIN)
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[rb1957]

why do you not want radial displacement ? warping is real.

if you want to keep the shell circular, add a web (fill in the tube) or a ring frame.

another day in paradise, or is paradise one day closer ?

 

[faremusai]

Thank BlasMolero and rb1957 for the advices.

The reason for restriction on radial displacement is that there is a large diametre rigid sprocket fit on the free end, similar to interference fit. As a result, I expect the free end can rotate/swivel but cannot wrap outward along the radial direction.

I want the free end to be free to rotate, slide along the z-axis and swivel about the centre at free end due to eccentricity of load on the sprocket.

 

[rb1957]

so model the sprocket, reinforcing the open end of the tube

another day in paradise, or is paradise one day closer ?

 

[faremusai]

A local cylindrical CSys (ID 3) at the centre of the free end cap surface (r-axis parallel to Global X-axis, t-axis
coincide with Global Y-axis) was created.

A "TR" (radial displacement) contraint was added to the end cap surface using CSys ID 3.
Then, listing of nodes on the end cap surface shows that they all have "DefCS=0, OutCS=3 Display CSys=OutCS"

The following nodal displacement result for nodes on outer circumference was obtained (listed using "-1: Nodal Output
Coordinate System"):

ID CSys ID 1..Total Translation 2..T1 Translation 3..T2 Translation 4..T3 Translation
277 3 0.0003717754 -0 0.0003717754 5.155416e-010
278 3 0.0003717757 -2.21917e-012 0.0003717757 5.32948e-010
279 3 0.0003717752 2.166257e-012 0.0003717751 6.309728e-010
280 3 0.000371774 5.790012e-012 0.000371774 3.835967e-010
281 3 0.0003717752 -1.770755e-012 0.0003717751 1.196298e-010
282 3 0.0003717756 -9.211705e-012 0.0003717756 2.524407e-010
283 3 0.0003717744 3.794732e-012 0.0003717744 9.401047e-011
284 3 0.0003717754 9.631209e-013 0.0003717754 -3.495831e-011
285 3 0.0003717751 1.870703e-018 0.0003717751 -3.497996e-011
286 3 0.000371775 2.239907e-012 0.000371775 -1.156286e-010
287 3 0.0003717752 7.029679e-012 0.0003717752 -1.493956e-010
288 3 0.0003717748 4.955722e-012 0.0003717748 -2.162235e-010
289 3 0.000371775 1.526691e-012 0.000371775 -3.079048e-010
290 3 0.0003717751 -8.483479e-012 0.0003717751 -3.47616e-010
291 3 0.0003717753 -4.977859e-013 0.0003717753 -3.556272e-010
292 3 0.000371775 1.382444e-013 0.000371775 -3.619223e-010
293 3 0.000371775 0 0.000371775 -4.33991e-010
560 3 0.0003717761 -3.864843e-012 0.0003717761 4.30784e-010
561 3 0.0003717749 2.936823e-013 0.0003717749 2.939721e-010
562 3 0.0003717749 -4.633303e-012 0.0003717749 4.351028e-010
563 3 0.0003717754 -1.905272e-011 0.0003717754 3.199456e-010
564 3 0.0003717749 4.845997e-012 0.0003717749 1.737752e-010
565 3 0.0003717749 -9.117068e-012 0.0003717749 2.506169e-010
566 3 0.0003717761 -2.350758e-012 0.0003717761 4.840162e-011
567 3 0.0003717753 -6.396779e-018 0.0003717753 -6.871453e-011
568 3 0.0003717758 3.414271e-012 0.0003717758 -1.238376e-010
569 3 0.0003717753 1.816636e-012 0.0003717753 -3.067882e-010
570 3 0.0003717743 -2.500366e-012 0.0003717743 -1.976774e-010
571 3 0.0003717755 -1.770408e-012 0.0003717755 -1.057971e-010
572 3 0.000371776 1.17365e-011 0.000371776 -4.210776e-010
573 3 0.0003717748 3.68101e-012 0.0003717748 -4.613355e-010
574 3 0.0003717753 -1.227051e-012 0.0003717753 -4.383943e-010

The magnitude of "T1 Translation" has an order of E-12. I think it can be treated as no radial displacement (typical
magnitude for the same surface without TR constriant is about E-07). But why not all nodes simply has a "0" magnitude for T1 Translation, only node 277 (left hand side on Global X-axis and Y=0) and 293 (right hand side on Global X-axis and Y=0) has a "0" magnitude instead?

I still cannot get the desired deformed shape correctly displayed in Global Rectangular CSys (ID 0). The actual deformed shape should be a twisted tube with constant diameter and showing the twisting of mesh. But a trumpet shape was displayed no matter which CSys was selected in the Deform / Transform option in "Postprocessing Toolbox".

How the "Deform" in Postprecessing Toolbox should be set in order to get the desired deforned shape similar to the
picture "6-Shaft under torsion-Desired deformed shape.jpg"?

Position of node_277&293

http://files.engineering.com/getfil...78c1eaa71&file=1-Position_of_node_277&293.jpg

Deformed shape-CSys_0

http://files.engineering.com/getfil...3adc4cdfdad6&file=2-Deformed_shape-CSys_0.jpg

Deformed shape-CSys_3_R-on

http://files.engineering.com/getfil...4af86c8&file=3-Deformed_shape-CSys_3_R-on.jpg

Deformed shape-CSys_3_RT-on

http://files.engineering.com/getfil...88a910&file=4-Deformed_shape-CSys_3_RT-on.jpg

Deformed shape-CSys_3_RTZ-on

http://files.engineering.com/getfil...701f0&file=5-Deformed_shape-CSys_3_RTZ-on.jpg

Shaft under torsion-Desired deformed shape

http://files.engineering.com/getfil...haft_under_torsion-Desired_deformed_shape.jpg