Hi Joe,
Too bad I missed you.
I wanted to ask you what can be done in Bend and especially in the
Cornin program to reduce the number of rulings from 50? to a smaller
number, perhaps as a variable (10 or so). The reason is that it may
be good enough for the use with finite elements programs like ANSYS
or TOSCA.
I tried to do it myself and got stuck in the Make file for the Cornin
program.
Any suggestions ?
Shlomo
I think that the simplest solution would be to modify CORNIN so that
it would select the desired number (e.g., 10) of cross sections for
output.
Alternatively one could do a search on the character string 'MAXMAX'
in BEND and
then change '=50' to '=10' wherever it ocurred. BEND was designed to
withstand just such an alteration but it might get a little messy
anyway, and besides, this would result in a less accurate solution
of the differential equation for the base curve so I think it would
be better to use the more accurate solution given by 50 points in
BEND and then lose some of the accuracy later in CORNIN.
Jeff,
How can the corner output from BEND be prepared for strain analysis in ANSYS?
In the corner files each cable is broken up into finite elements of a strange kind. Before deformation the straight cable is a prismatic bar (see line 9 on page 26 of your "Mechanics of Materials" text by R. C. Hibbeler) with a trapezoidal cross section. We take those cross sections slantwise instead of perpendicular but their four vertices still line up into four straight lines. They also decompose the cable into finite elements which are sort of prismatic in the sense that each element has four parallel straight edges, but each end is capped by a slantwise trapezoid instead of a perpendicular one.
Now in the corner file, after deformation, these slantwise trapezoids are still further skewed around, and the four line segments joining their corresponding vertices are no longer parallel.
My question is: Can ANSYS handle these skewed-up finite elements?
Does ANSYS just need nodes, the eight corner points of the element, without worrying about what kind of element they form?
Nine years ago Bob Wands was faced with this problem and he wrote: "The program works beautifully. The array xsec is very powerful once I understood all the indices. The resulting finite elements were not distorted badly enough to prevent execution, although the angular distortion generated several warnings. I am going to talk to the vendor and find out if that is serious; I routinely ignore distortions in structural problems without bad effect, and I imagine the magnetic solution will be as forgiving."
I don't know what happened with his proposed "talk to the vendor".
Anyway, if ANSYS can handle this then, according to Shlomo, Lorentz forces on the element can be found by TOSCA as body forces which ANSYS will then distribute out ot the eight vertices and go on from there.
Also ANSYS could be used to compute the forces (stresses) caused by deformations (strains) of the cable. The corner files give us the results of the deformation. To find the deformation itself we work backwards to find the undeformed cable as follows:
From the corner files we can get the heights of each slantwise trapezoid and because we know the height of the perpendicular trapezoid we can find the angle of slant and hence the orientation of the slantwise cross section in space. So to string them together to reform the original undeformed, straight prismatic bar we need only find out how far apart they are along the neutral axis which, I suppose, we might as well take to be the centroidal axis (see page 291, though a literature search, or maybe some original research (thinking), would probably allow us to do better than that). But the "how far apart" can be settled once we known Young's modulus for the cable which is easily measured, at least for the tensions used in the cable winding process.
So now we know the strains of the cable as wound. Shlomo says that enough of the rest of the stress-strain tensor is known that we can find all of its forces.
Then superimpose the Lorentz forces and we have a complete catalog.
Joe
Hi Joe,
Unfortunately, I did not really get a good answer to your questions. For one thing, Ansys has a very large instruction set, and we really did get only an "Introduction to Ansys". For another, there was an enormous amount of material to cover, and I was only able to get the instructor's attention for about 10 minutes on Friday afternoon.
Ansys would be easily able to build the solid model of the cables from the corner file - from a script that can be run within Ansys, or from an Iges translation of CAD geometry. Meshing the cables would appear to be no problem. Mesh elements should naturally be created that contain nodes that exist on the keypoints (corner points) of the solid model.
Ensuring a uniform element size and shape would be more difficult, because of the wide variation of space between corner points and the angular differences between rulings, however, our instructor thought that this could certainly be done.
Elements with large height/width ratios or small angles tend to dominate the stiffness of the FEA model and can affect results. Regarding Bob Wands' comment, I found that Ansys typically produces error messages regarding element shape, even in simple models and meshes that look very straight- forward. There are many ways to examine and correct "bad" elements.
Ansys would have no problem with the skewed trapezoids, and I don't think it even needs them to be straight lines. The instructor hesitated at my describtion of the winding, thinking I was looking for strains in going from straight to formed cables. Being a non-homogeneous, non-isotropic material, for which no real mechanical properties exist, I can understand why.
However, once the cables are formed, as in the corner files, all Ansys needs is a mesh of finite elements to apply additional forces. I can foresee some difficulties in making sure elements and nodes exist in meaningful places, and in making sure the loads are applied in the right way and in the right locations - also, the number one reason for solutions to be meaningless is improperly applied boundary conditions. All this will take some time, but once worked out, the solution should be straight-forward.Ansys is really an awesome package, and I hope to start spending some time every day getting to learn how to solve real problems with it. I will have to start simple, and compare results to things I can calculate to make sure I know what I'm doing. I am very busy right now with spools, but this project sounds very interesting to me. Maybe in the near future, I can start to spend some time on it.
An alternative would be for you to take some Ansys training. It is almost all written in Fortran, with some C. It is commonly linked into other Fortran programs, and could probably become a subroutine of BEND. Another option is to hire our instructor, who is a consultant. He was an excellent teacher, and is incredibly knowledgable about Ansys and FEA in general.
Bradford Knott ConsultingSee you soon,
Brad Knott - Principal Engineer
241 South Maple Avenue
Oak Park, Il, 60302
Phone: (708)660-0220
Fax: (708)660-0244
E-mail: bfkc@mediaone.net
4 calendar days later, I list the action items I recall from last friday's meeting on end parts:
A. JimK and Jeff to sit down, look at strain calculated by BEND as a
function of turn and length,
and see if it could be plotted in some sensible way which allowed
comparison to other designs
and to quench data.
Comments or corrections welcome. Thanks to Gianluca and Jeff.
jsk
Hi Jim,
I was able to rather easily graph the strain in a cable created by program BEND. I had saved a .cor (corner) file for each group of conductors I've created. A program Joe Cook wrote, called DELCOR, reads the corner file and outputs the strain (delta L / L) for each of four trapezoid points, at 48 of the 50 trapezoids for each cable.
The calculation needs a point on either side of the trapezoid being measured, and so must skip points 1 and 50. I have artificially entered zero for the delta L / L at point 1 in all the data, so that the graph points get mapped correctly.
Based on analysis of DELCOR output, Joe and I decided that only the outer(radius) near(nearest to the guiding strip), and outer(radius) far(farthest from the guiding strip) data are meaningful. The inner near and inner far points are subject to too much noise from the rulings being closer together.
I have created six Excel files, located in:
These files contain the DELCOR output from every group of interest in the two end designs studied. I have created a graph for many of the cables contained in these groups. The graphs are viewable and printable in the Excel files, and I have included many of the interesting graphs in a binder which I will give to you.
I will be happy to present or explain the data to the group, or we can discuss it at your convenience. Please note that many of the groups contain a localized spike that is of relatively large magnitude.
Joe Cook and I investigated this, and it is caused by the cable changing from being outer radius mounted on the inside corner, to being mounted on the outside corner. This produces a localized jog in the mathematical model that effects the strain calculation. Cables are affected in varying degrees by this jog, but the real cable does not experience this discontinuity.
This was a very interesting exercise for me, that makes me feel better about the level of hard-way bend strain present in our end designs. As shown in the graphs, when the points involved in the spike are ignored, the delta L / L's in most cables are very reasonable.
Jeff
Jeff,
Here is my next version of an explanation of the output from a run of BEND on May 7, 1999.
After discussing it with you, I will revise it, and would like to eventually put it up in the "Q&A" pages of the web site.
I have put an execute file BEND.exe in our anonymous ftp site. It runs OK on fnal (maybe only after executing 'chmod u+x BEND.exe'), where it was compiled, but it doesn't run on fnts08. I think it needs a missing FORTRAN run-time file.
The input file for this run was your q1ir03.xin:
Input file for IRQ It.#1 Inner Coil R.E. group 1 (0/3 18mm A-length) 1.9922520 outer radius 1.3779528 inner radius 9.4212348 outer starting angle of the guiding strip 10.9113266 initial edge angle of the guiding strip 0.06323718 mid-thickness of the cable 0.9771215 keystone angle of the cable 0.0 rounding of corners of the cable 0 3 numbers of cables on each side 1 choose INside group A-length ( 2 for OUTside) 0.708661417 A-length N do not choose the final edge angle of the guiding strip 8 estimated final edge angle of the guiding strip
Because I forgot to ask you for your values of expansion, shift and bluntness, I just left them at zero.
The output file is listed below, with my interpolated remarks offset by '>>' characters:
This is version April 14, 1994 of Program BEND,
last modified on March 6, 1995.
Please enter, on one line, the numbers of only those
options that you want to change from the default.
Option Default Alternate
------------------------------- --------- -----------
1 Input from an external file: No Yes
>> "No" : Program control info input by the user from the DOS command line.
>> "Yes": Program control info input from a user-constructed file.
2 Output to a journal file: No Yes
>> "Yes": Will echo all user input into a file which can then be read
>> back into the program during future runs so as to duplicate
>> the saved run except where the user chooses to override certain
>> values. NOT YET IMPLEMENTED
3 Units: British SI
>> If 3 is chosen, lengths should be input in millimeters.
>> Inside of the program these values are converted into SI units
>> and then reconverted back into millimeters for output.
>> I have checked this option by changing the inches in your input
>> file q1ir03.xin into millimeters and it seemed to run OK with
>> small differences attributable, I think, to the inaccuracy
>> of my input conversion. I'll show you the two outputs when we
>> meet.
4 Perturb group: No Yes
>> "Yes": Bulge the cable group azimuthally, a small amount, between
>> any two mesh points.
5 Cable cross section: Unchanged Change
>> "Change:" Allow run-time changes of the compile-time hard-coded
>> values of the cable-thickening and keystone-widening ratios.
6 Steepen rulings: No Yes
>> "Yes": Pull the rulings of the guiding strip, and hence of all
>> cables in the group, back towards more perpendicularity to
>> the base curve, or more away from it, depending on the whether
>> the user-chosen value is less than or greater than 1. This
>> option was part of a scheme to enable the user to move any
>> of the rulings around in any direction, smoothly but slightly,
>> but it is NOT DEBUGGED.
7 Automatic: No Yes
>> "Yes": Automate part of the design process, for now only by para-
>> meter sweeps and a simple one-parameter minimization of
>> a very crude figure of merit, -BADNESS.
8 Vary the base curve: No Yes
>> "Yes": Move the base curve slightly away from its least-strain
>> shape by smoothly varying its flexural rigidity along chosen
>> parts of its length.
9 Verbose terminal I/O: No Yes
>> "Yes": To the very limited extent that it has yet been implemented,
>> provide wordier prompts and explanations to new users that
>> more skilled users would rather skip over.
10 Debug: No Yes
>> "Yes": Output to the screen intermediate data values that the user
>> (or even the BEND programmer) might find useful in debugging
>> a run, even by altering them and rerunning parts of the cal-
>> culation. NOT YET IMPLEMENTED
11 Help: No Yes
>> "Yes": Only a little bit of online help is now available. This can
>> be greatly expanded as more experience with user questions
>> is obtained.
Please enter the complete file name for the disk file from which input is to be
read. (Include the file type and, if necessary, the version number,
with the separating punctuation "." and ";".)
The title of the input file is:
Input file for IRQ It.#1 Inner Coil R.E. group 1 (0/3 18mm A-length)
Please enter the file name for all output disk files.
(Include no file type or separating period).
The radius of the cylinder on which the base curve is wound
is 1.9922520 inches,
and the radius of the mandrel is 1.3779528 inches.
The width of the guiding strip is now 0.614299 inches, the difference
of these two numbers. What value would you prefer?
The outer starting angle for the guiding strip is 9.42123480 degrees.
The initial edge angle of the guiding strip is 10.91132660 degrees.
The mid-thickness of the cable is 0.06324.
The (uncorrected) keystone angle is 0.97712150 degrees.
The radius of curvature of corner-rounding is 0.000000.
There will be 0 cables inside the guiding strip and 3 outside.
The desired inside group A-length is 0.70866141700000
The estimate of the final edge angle of the guiding strip is, in degrees,
8.0000000000000
An initial guess at the guiding strip A-length is 0.7086614 inches.
The final edge angle of the guiding strip is now 7.7501534005432 degrees.
What angle would you prefer (degrees)?
The twist-spline starts at point number 2.
>>
>> When the guiding strip is twisted away from the rectifying developable
>> by SHIFT, BLUNT, etc., it may rotate the free edge laterally out beyond
>> that determined by its initial ruling, resulting in a (presumably small)
>> outward flaring of the strip. In that case the twisting is postponed
>> (in the above case from point 1 to point 2) until the guiding strip has
>> curved safely back around towards its final end.
>>
>> The same problem may occur up near the final end of the guiding strip.
>> Its free edge may rotate forward (slightly). In that case the twisting
>> is finished before the 50th point as announced by a message of the form:
>> "The twist-spline stops at point number ..."
>>
The overall Delta-L-Over-L is -0.0110.
Y-Z cross section cut by the vertical midplane at X = 0:
Lateral Surface: Inside Outside
--------------------- ---------------------
Z Y Z Y
At outer radius: 0.7086614 1.9922520 0.9172957 1.9922520 inches,
At inner radius: 0.7922655 1.3779528 0.9944748 1.3779528 inches,
Final edge angles: 7.75015340054 7.16099386925 degrees,
"A" Lengths: 0.70866141700 0.91729565726 inches.
The inside group A-length is now exactly correct!
The accepted value for the guiding strip A-length is
0.70866141700 inches.
The length of the base curve is 0.8792 inches.
The length of the free edge is 0.8790 inches.
The total twist of the developable strip is -13.14 degrees.
>>
>> The twist(-rate) of the strip at a given point is the rate at which
>> the ruling through that point is rotating about the base curve, per
>> unit of arc length. It will be different from the torsion of the
>> base curve if the strip has been twisted away from the rectifying
>> developable but it is still the twist as resisted by the torsional
>> rigidity of the cable, i.e., as "felt" by the cable.
>>
>> The total twist is the integral of the twist(-rate) with respect
>> to arc length along the entire base curve. It is intrinsic to the
>> shape of the strip and can not be computed just from the initial
>> and final rulings as two skew lines in space.
>>
The final edge angle of the guiding strip is now 7.7501534005432 degrees.
What angle would you prefer (degrees)?
The total twist of the guiding strip is now -14.63 degrees.
>>
>> Expansion, fixed, shift, bluntness and narrow are parameters which
>> determine the shape of the curve Phi(s), the amount of additional
>> twist given to the guiding strip over and above that amount which
>> it receives from the rectifying developable. That shape is deter-
>> mined by a cubic spline which can be modified by these parameters
>> as follows:
>>
>> SHIFT is the amount by which the shape of the curve Phi(s) is shifted
>> towards the beginning of the strip, if positive. Otherwise the
>> shape is shifted away from the beginning.
>> EXPAND is the amount by which the shape is expanded away from FIXED.
>> FIXED is the center of expansion, so it remains fixed during that
>> expansion.
>> BLUNT causes a broadening (when positive, narrowing when negative)
>> of the nose of the free edge.
>> NARROW causes a concentration of the effect of BLUNT on the nose of
>> the free edge, when positive. Otherwise it causes a concen-
>> tration near the beginning of the free edge. It has no effect
>> when BLUNT=0.
>>
The distribution of the twist angle is now given by
an expansion of amount 0.000
and a shift of amount 0.000
and added bluntness of 0.000.
What values would you prefer for:
Expansion?
Shift?
Bluntness?
Expansion = 0.000, fixed point = 0.500
shift = 0.000 and bluntness = 0.000
The twist-spline starts at point number 2.
The overall Delta-L-Over-L is -0.0110.
Step Length Delta-L Phi Curve Rad Curve Rad Twist Alpha
Number (Base) -Over-L (Base) (Free) Rate
------ ------ ------- ------ --------- --------- ------- ------
1 0.0000 -0.0017 1.49 28.54 29.35 0.0 90.00
2 0.2684 -0.0095 1.49 3.18 4.26 -2.4 93.51
3 0.3066 -0.0119 1.47 1.06 1.77 -5.4 94.96
5 0.3623 -0.0151 1.40 0.75 1.14 -11.0 96.94
10 0.4593 -0.0186 1.14 0.51 0.68 -22.7 99.95
15 0.5322 -0.0197 0.90 0.41 0.49 -31.6 101.48
17 0.5578 *-0.0197 0.80 0.39 0.43 -34.3 101.78
20 0.5937 -0.0195 0.67 0.36 0.36 -37.2 101.93
25 0.6485 -0.0185 0.48 0.33 0.27 * -39.1 101.47
30 0.6988 -0.0164 0.31 0.30 0.19 -37.1 100.20
40 0.7915 -0.0079 0.08 0.28 0.09 -22.9 95.81
48 0.8618 -0.0005 0.00 0.27 * 0.05 -4.9 91.21
49 0.8705 *-0.0001 0.00 0.27 0.08 -2.5 90.61
50 0.8792 ------ 0.00 0.40 0.08 0.0 90.00
>>
>> Phi is the angle by which a ruling is rotated about the base curve
>> as the guiding strip is twisted away from the rectifying developable.
>> Alpha is the angle that a ruling makes with (the tangent to) the base
>> curve at the point where it intersects it.
>>
Do you want to try different values of shift, bluntness, etc.? (N/Y)
Do you want the centroids of the current-densities
in the cables? (N/Y)
Do you want the corners of the cables? (N/Y)
Do you want all of the cable frames? (N/Y)
*********************** WARNING ***********************
There is a reversal of direction among the three coord-
inates (X, Y, and Z) of the four curves (inside-inner,
inside-outer, outside-inner, and outside-outer) deter-
mining the configuration of the group of cables:
Side Radii Coord Point Extremum Type
------ ----- ----- ----- -------- -------
Inside Inner Y 34 1.375014 Maximum
Inside Inner Y 50 1.374383 Final
Outside Inner X 3 0.379076 Minimum
Outside Inner X 4 0.379208 Maximum
Outside Inner X 50 0.000000 Final
-------------------------------------------------
>>
>> All three coordinates of a point moving along any one of the four
>> curves are supposed to vary monotonically, i.e., to be consistently
>> either non-decreasing or non-increasing functions of arc length.
>> X is supposed to decrease, and Y and Z are supposed to increase.
>> When this condition is violated, even though less than one-thousandth
>> of an inch as above, a WARNING is printed along with the value of the
>> offending coordinate and whether its irregularity was a local 'Maximum'
>> or 'Minimum', unless it was the first coordinate in which it was
>> designated 'Initial'. Whenever any irregularity is found the value
>> of the final coordinate is printed with the designation 'Final'.
>>
Press RETURN to continue ...
ANALYSIS
--------
---------------- On the inside lateral surface of the group ----------------
The length of the outer curve is 0.8792 inches.
Its worst curvature occurs at point number 49, 0.870 inches along the arc,
where its radius of curvature is 0.269 inches.
The length of the inner curve is 0.8697 inches.
Its worst curvature occurs at point number 48, 0.865 inches along the arc,
where its radius of curvature is 0.050 inches.
The overall Delta-L-Over-L of this surface is -0.0108.
The lowest Delta-L-Over-L is -0.1019 at point 50,
0.8792 inches along the outer curve.
The highest Delta-L-Over-L is -0.0001 at point 49,
0.8705 inches along the outer curve.
Press RETURN to continue ...
---------------- On the outside lateral surface of the group ----------------
The length of the outer curve is 1.2076 inches.
Its worst curvature occurs at point number 48, 1.1769 inches along the arc,
where its radius of curvature is 0.471 inches.
The length of the inner curve is 1.1784 inches.
Its worst curvature occurs at point number 49, 1.1714 inches along the arc,
where its radius of curvature is 0.220 inches.
The overall Delta-L-Over-L of this surface is -0.0242.
The lowest Delta-L-Over-L is -0.1783 at point 50,
1.2076 inches along the outer curve.
The highest Delta-L-Over-L is 0.0537 at point 7,
0.4456 inches along the outer curve.
************************* PROBLEM *************************
The free edge bulges out at point number 4 in the outside
strip of the group. Its amount is 0.13E-03 in.
If you nonetheless wish to continue, press RETURN.
(Otherwise, execute a program interrupt.)
>>
>> The X and Z coordinates of the free edge of any strip in the
>> group, in the above case on its outside surface, are checked
>> for monotonicity as a function of increasing arc length,
>> decreasing in the case of X and increasing in the case of Z.
>> When this condition is violated the user is given the option
>> of terminating execution, though usually the violation is so
>> small that the warning can be ignored.
>>
************************* PROBLEM *************************
There is a concavity along ruling number 2 in the outside
strip of the group. Its volume is 0.42E-05 cubic in.
If you nonetheless wish to continue, press RETURN.
(Otherwise, execute a program interrupt.)
>>
>> At any ruling of any strip in the group (as long as it is not the
>> first or last ruling in the strip) a parallelopiped can be formed
>> with edges the line segments connecting the free edge end of the
>> ruling with the two points on either side of it along the free edge,
>> and with the segment of that ruling within the group. The volume of
>> this parallelopiped is supposed to be always positive, otherwise a
>> 'PROBLEM' is announced, though usually the violating volume is so
>> small that it can be ignored.
>>
>> Along the line of intersection of rulings from any strip in the
>> group, the Z coordinate is supposed to increase monotonically.
>> Otherwise a 'POSSIBLE PROBLEM' is announced and the amount of
>> the 'wrinkle' printed.
>>
************************* PROBLEM *************************
There is a concavity along ruling number 3 in the outside
strip of the group. Its volume is 0.68E-05 cubic in.
If you nonetheless wish to continue, press RETURN.
(Otherwise, execute a program interrupt.)
Press RETURN to continue ...
----- On the internal lateral surfaces of the group -----
Low High
--------------------------- ---------------------------
Delta-L Point Cable Arc Delta-L Point Cable Arc
-Over-L # # Length -Over-L # # Length
------- ----- ----- ------ ------- ----- ----- ------
-0.2388 7 1 0.42 0.0472 3 1 0.31
-0.1577 50 2 1.10 0.0471 4 1 0.34
-0.1324 50 1 0.99 0.0411 5 1 0.37
-0.1151 49 2 1.08 0.0286 8 2 0.46
-0.1145 48 2 1.07 0.0284 7 2 0.43
-0.1135 47 2 1.06 0.0213 9 2 0.48
-0.1121 46 2 1.05 0.0209 10 2 0.50
-0.1104 45 2 1.03 0.0202 11 2 0.52
-0.1084 44 2 1.02 0.0197 6 2 0.41
-0.1060 43 2 1.01 0.0190 12 2 0.54
-0.1033 42 2 0.99 0.0175 13 2 0.56
-0.1002 41 2 0.98 0.0155 14 2 0.58
--------------------------- ---------------------------
Press RETURN to continue ...
Y-Z cross section cut by the vertical midplane at X = 0:
Lateral Surface: Inside Outside
--------------------- ---------------------
Z Y Z Y
At outer radius: 0.7086614 1.9922520 0.9172957 1.9922520 inches,
At inner radius: 0.7922655 1.3779528 0.9944748 1.3779528 inches,
Final edge angles: 7.75015340054 7.16099386925 degrees,
"A" Lengths: 0.70866141700 0.91729565726 inches.
Press RETURN to continue ...
X-Y cross section cut by the transverse plane at Z = 0:
Lateral Surface: Inside Outside
--------------------- ---------------------
X Y X Y
At outer radius: 0.3261149 1.9653796 0.5267278 1.9213604 inches,
Starting angles: 9.4212348 15.3306000 degrees,
At inner radius: 0.2097776 1.3618911 0.3796808 1.3246118 inches,
Starting angles: 8.7566784 15.9941821 degrees,
Side angles: 10.9113266 13.8426911 degrees.
Do you want a shelf under this group? (N/Y)
Do you want the inside lateral surface of this group? (N/Y)
Do you want the outside lateral surface of this group? (N/Y)
Do you want to continue, with interactive control
over variation of the free edge? (N/Y)
Do you want automatic control over variation
of the free edge? (N/Y)
********* Normal completion of program BEND *********
>> There is also a 'WARNING:' if an inner corner of a cable pokes itself
>> into the mandrel. As you suggested, this is usually caused by a choice
>> of the non-rounding option in the input file.
Joe