5.8
MOTORCYCLE CRANKSHAFT, TETRAHEDRON NO. 16
Copy the sample file
B11_G.COS to the Z88 input file Z88G.COS.
We want to compute a
crankshaft for a monocylinder motorcycle engine and put a force of -5,000 N
onto the piston. The meshing will do Pro/ENGINEER.
The boundary conditions are
a bit tricky for this example: Put a reference (or datum) point to the center
of the face of the crankshaft. We'll need this point to fix the crankshaft in Z
direction, i.e. lengthwise.
The ball bearings, which
allow always some angular movement, and, thus, should be regarded as moment-
free supports, are fastened to the larger shaft axises. The flange facings of
the shaft axises are to be fixed in X and Y direction. Because whole surfaces
are fixed, don't allow one ore more of these surfaces to be fixed in Z
direction, too. This would result in blocking the angular movement - try it, if
you won't believe it.
A total force of -5,000 N
will be put onto the peripheral surface of the crankshaft journal.
The mesh is automatically
generated by Pro/MECHANICA featuring parabolic tetrahedrons. After storing the
COSMOS file, a Z88 session may start:
Copy B11_G.COS to
Z88G.COS, the COSMOS file for the converter Z88G
Start converting Z88G.COS
with Z88G
(Windows: COSMOS
converter Z88G. Looks quite similar on UNIX machines)
and proceed with the
Cuthill- McKee algorithm Z88H, because we'll expect a very bad node-
numbering for the parabolic tetrahedrons.
(Windows: Cuthill- McKee
program Z88H. Looks quite similar on UNIX machines)
The first line of Z88I1.TXT tells you the following values:
MAXKOI must have as a
minimum 3,941 elements * 10 nodes per element = 39,410.
Thus, Z88.DYN should look as follows:
MAXGS when
starting, any value
MAXKOI minimum
39410
MAXK minimum
6826
MAXE minimum
3941
MAXNFG minimum
20478
MAXNEG minimum
1
Proceed with a look at the
structure with Z88O (or
with Z88P ).
The computing time with Z88F is about 1,5 minutes on a PC (900
MHz AMD- processor, 512 MByte memory). Enter a value of about 11,400,000 for
MAXGS..
See the deflected structure
with Z88O. The
angular deflection of the axises is quite amazing. Now you would read off the
deflections of distinguished nodes, multiply with the appropriate lever arms
and check with the bearing catalogue if your ball bearings will allow this
angular movement without problems.
(Windows: Computing
deflections with Z88F. Looks quite similar on UNIX machines)
(Windows: Plot programm
Z88O, deflected structure)
Now we'll launch the
iteration solver Z88I1 and Z88I2. To begin with, we'll try some values for MAXSOR and MAXPUF in Z88.DYN (you may also enter, for example,
50,000,000 for MAXSOR and 5,000,000 for MAXPUF, if you want):
COMMON
START
MAXGS
11500000 has
for Z88I1 no meaning !
MAXKOI 40000 must
always be large enough !
MAXK 7000
read
off from Z88I1.TXT
MAXE 4000
read
off from Z88I1.TXT
MAXNFG
21000 read
off from Z88I1.TXT
MAXNEG 1 read
off from Z88I1.TXT
MAXSOR
2000000 important for Z88I1
MAXPUF
500000 important
for Z88I1
COMMON
END
Our entries did work
properly (otherwise, you would have to increase MAXSOR and MAXPUF) and the
sorting times was about 15 seconds on a PC (900 MHz AMD- processor, 512 MByte memory).
Read off for MAXGS:
768,687, rounded up 770,000. This looks fairly better than the direct Cholesky
solver Z88F with its need of 11,381,064 8- Byte elements = 87 Mbyte. The second
part of the iteration solver, i.e. Z88I2, will only need 768,687 8- Bytes
elements = 6 MByte.
Thus, we would adjust the
memory in Z88.DYN as
follows (feel free to enter even bigger values):
COMMON
START
MAXGS
770000 important !
MAXKOI
40000 must
always be large enough !
MAXK 7000
read
off from Z88I1.TXT
MAXE 4000
read
off from Z88I1.TXT
MAXNFG
21000 read
off from Z88I1.TXT
MAXNEG 1 read
off from Z88I1.TXT
MAXSOR
2000000 not
used by Z88I2
MAXPUF
500000 not
used by Z88I2
COMMON
END
If you adjust the iteration
parameters in Z88I4.TXT
(chapter 3.6) as follows:
10000 1e-7 1.
i.e. a maximum of 10,000
iterations, EPS with 1E-7 and RP (here Omega) with 1, then
this results in a computing time of about 1 minute on a PC (900 MHz AMD-
processor, 512 MByte memory).
In this case, both the
iteration solver and the direct Cholesky solver need about the same time, but
the iteration solver needs fewer than one tenth of memory. For large
structures, things get even worse for the Cholesky solver! But pay attention to
the fact, that you can't really compare the computing times. Try other entries
for EPS, for example 1E-5 (resulting in 303 iterations and 45 seconds)
or 1E-10 (resulting in 474 iterations and 1:08 minutes), and see the different
computing times.
(Windows: The iteration
solver Part 2, i.e. Z88I2)
However, a very nice
experiment is this:
Start from the very
beginning, run Z88G, but not the Cuthill- McKee algorithm Z88H. Launch
directly after Z88G a test run with Z88F (UNIX: z88f -t):
(Windows: The direct
Cholesky solver in test mode)
Gee, see the faces falling:
now we would need 184,122,663 8- Byte elements = 1,4 GByte. Absolutely no need
for this!
However, run again the
iteration solver part 1, i.e. Z88I1. This will again result in only 768,687
elements for the total stiffness matrix. Calculate, please:
184,122,663 : 768,687 = 240
: 1
The second part of the iteration solver, i.e. Z88I2, needs now some more iterations (451 in contrary to 415 with an equal EPS of 1E-7), because the matrix features the same number of non- zero elements, though, but the condition is worse because of the very bad node- numbering of Pro/MECHANICA. That means: When using the iteration solver you don't need to run the Cuthill- McKee algorithm Z88H for reducing the storage needs of the iteration solver (in contrary to the direct Cholesky solver Z88F, which may depend heavily on Z88H for larger structures!). However, Z88H may improve the matrix condition anyway.