In the particular NASTRAN application discussed here, a nut was attached to a stationary structure. The object of the analysis was to determine the vibration characteristics of the whole structure for various configurations; i.e., the evaluation of the mode shapes and frequencies when parts were moved to different mating positions. Details of the analysis are given

Butler, Thomas G.

English

NASA Technical Reports Server

 91-20511
MODELING A BALL SCREW/BALL NUT
IN SUBSTRUCTURING
Thomas G. Butler
BUTLER ANALYSES
INTRODUCTION
A ball screw/ball nut mechanism causes one part to move
with respect to another with a minimum of friction. Such a
structure is a good candidate for substructuring by assigning the
mating parts to two separate substructures. Figure 1 shows a
cut-away photograph of an assembled nut and screw. Matching
helical grooves in each share a continuous stream of steel balls
which are fed by the screw in the direction of travel through the
nut to a conduit that returns the balls to the trailing end for
continuous, smooth, quiet operation.
External Return
Nut
Ball Screw
Figure 1
Making a finite element model of this device and coor-
dinating the nut in one substructure with the screw in another
substructure is not straightforward. I made several stabs at
this before I was satisfied, and decided to share the toils of
this challenge at the NASTRAN Colloquium.
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https://ntrs.nasa.gov/search.jsp?R=19910011198 2020-03-19T18:32:39+00:00Z
BALL SCREW/BALL NUT
PLAN
In the particular application being discussed here, the
screw was attached to the moving structure and the nut was at-
tached to the stationery structure. The object of the overall
analysis was to determine the vibration characteristics of the
whole structure for various configurations; i.e. the evaluation
of the mode shapes and frequencies when parts were moved to
different mating positions. Therefore, it was necessary to
provide for the ball screw to be moved and reconnected to the
ball nut at a number of dlfferenct locations along its length.
The Substructure capability in NASTRAN makes it possible to
prescribe a connection with a COMBINE operation in Phase 2 and
perform an elgenvalue analysis for that configuration. Once
these results are catalogued, the analyst erases these results
and returns to the COMBINE operation for a new set of connections
and performs a second elgenvalue analysis. Succeeding runs can
be made for as many reposltionlngs as is desired. The challenge
is in modeling the nut so as to represent both the rigid body
relation of the helix plus the elastic relations of its members.
The scheme then is to model the nut and the screw so as to be
invarlant for any combination of positions, such that reposition-
inq is achieved by specifying that location on the screw that is
to be in contact with the nut in the Phase 2 COMBINE step.
MODEL
The first step is to represent the elastic parts in a
simple arrangement. The NUT will consist of two yokes at either
end of the nut and an axial tie between the two y_kes. The yoke
models the nut housing that connects the ball interface to the
stationary structure (P). The yoke consists of two bars
extending on either side of the screw (S) centroid to the bolts
in P. The sketch shows this simple arrangement.
45
BALL SCREW/BALLNUT
\
So far this is pretty boring. It will liven things up to
introduce the rotation of the screw vs. the translation of the
screw. There will be a string of grid points along the screw -
availaDle for connecting to the nut. The nut has 2 grid points
on line with the screw centroid. But these 2 grid points serve
only the elastic function so far. In order to get load into the
nut it needs to be endowed with some rather special things.
When the screw turns it will cause the scre W to advance
axially only as a result of its helix reacting the nut. So a
device is used to cause the screw rotation to advance the nu___!t
axially. This does not happen in reality, but it is a device to
provide a loading rate from screw into the nut. The
specifications for the ball nut/screw is one inch of advance for
one full rotation of the screw; i.e. one inch per 2_ radians.
This can be imposed with an MPC (Multi - Point - Constraint).
Relating this to the sketch, a unit translation in the Y
coordinate direction of the nut is constrained to 2w (6.2832)
radians of rotation about the Y axis of the screw. But now that
the nut is loaded with this displacement, it must be transformed
into an elastic force which will be reacted into structure P and
then back into an axial force in the screw. In effect what
46
BALL SCREW/BALL NUT
needs to be accomplished is to take a rotation of'the screw and
give it to the nut to intercede then deliver a translation back
into the screw. Just saying it, however, doesn't accomplish it,
because a number of needs of subsctructure analysis need to be
served.
The nut has to be self contained, if it is to be able to
be repositioned without having to be remodeled each time. One
way is to duplicate a point in the nut to represent the axial
rotation of the screw. Then duplicate another point to represent
the axial translation of the same point of the screw. Now the
helix constraint of the screw via the two special points of the
nut can be enacted with the MPC. It operates to connect the
translation of the helix elastically into the nut drive point
with a spring value equal to the compressibility of the set of
balls plus the stiffness of the lands of the helix. This rota-
tion of the screw causes the nut drive point to move axially.
Finally, the nut drive point axial translation connects back to
the screw axial translation, when the substructures are
COMBINE'd.
SUBSTRUCTURE COMMANDS
So far this discussion has been confined to a word
description, but more hurdles have to be overcome in finally
translating this scheme to problem data. A return to the sketch
will be helpful by embellishing it with the screw and assigning
numbers to the points. Point 2 of the NUT will connect transla-
tional dof's only in to point i0 of the SCREW and similarly point
5 of the NUT will connect translational dof's onl_to point ii of
the SCREW. However, GP's 2 & 5 will maintain all 6 dof's opera-
tional in order to support the link of the yokes to the station-
ary structure P. As a first step toward incorporating the heli-
cal action into the NUT, 2 new pairs of points are introduced.
47
BALL SCREH/BALL NUT
®
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Points 25 & 55 are added to pick up the rotations of SCRE-7_ points
i0 & ii. 0nly rotations about the ¥ axis will be enabled in GP's
25 & 55 by eliminating dof's i, 2, 3, 4, & 6 on the GRID bulk
card. The pair of points _ & =_.... are inserted to have transla-
tional freedom in the Y direction only by eliminating dof's i,
4 5 & 6 on the GRID bulk card The helix is put in place
_F • •
with MPC's between 25(5) and 22(2) and between 55(5) and 52(2) by
applying a factor of 2_ i.e.
MPC ID# 22 _ -i 0 25 5 6 oQ_o
MPC ID# 52 2 -I.0 55 5 6.2832.
Note that GP's 25 & 55 are retained as independent.
in order for them to be extant when NUT and SCREW
later.
This is done
are COMBINE'd
between
All is ready for the introduction of scalar springs
GP 22(2) and GP2(2) and between GP52(2) and GP5(2) to
48
BALL SCREW/BALL NUT
represent the drive resistance between SCRE_ and NUT which is
carried into the stationary structure by the bars connecting 2 &
5 to GP's I, 2, 4, & 6. The translational response of NUT drive
points 2 and 5 are ready for connecting back to the SCRE_ in a
COMBINE operation.
Now a word about Phase 2 COMBINE operations. If the
automatic option for COMBINE is chosen, it finds all dof's at the
same physical location and ties all like colocated dof's toqether
unless otherwise inhibited. The substructure control packet will
command that substructure P be COMBINE'd with substructrure S.
In this case the set of GP's 2, i0, 22, & 25 and the set of GP's
5, Ii, 52, & 55 are colocated. It is well to pause to tabulate
what the requirements are and what action is needed to implement
these desires.
I. Requirements
GP 2(1,2,3) should tie to GP 10(1,2,3)
Gp 5(1,2,3) should tie to GP 11(1,2,3).
Remedy
Note is taken that all 6 dof's are active at both points. In
order to limit the tie to only translations, the substructure
bulk data card called RELES is employed to command the release of
dof's 4, 5, & 6 during a COMBINE operation.
2. Requirements
GP 25(5) should tie to GP 10(5).
GP 55(5) should tie to GP 11(5).
Remedy
Since GP's 25 & 55 have only dof 5 active and singe the require-
ment is to tie them to dof 5 of GP's i0 & ii respectively, there
is no need to intercede. Allow the automatic option to proceed
unhindered.
. Requirements
GP 22(2) & 52(2)
substructure S.
should not tie to any part of
49
_L SCREW/_L NUT
Remedy
Impose a RELES on GP 22(2) & 52(2)
influence from substructure S.
to keep them free of any
SUMMARY
The action which will ensue from this model is as fol-
lows. NUT point GP 25(5) will pick up the rotation from SCREW
POINT GP 10(5). The MPC will advance the translation of NUT
point GP 22(2) from the rotation of GP 25(5) in the ratio of 1 :
2_. The translation of GP 22(2) will be opposed by the elastic
link to the NUT drive point GP 2(2). This helical loading will
be carried to the NUT houslng bars and reacted into the station-
ary substructure P. The net translation in all 3 coordinate
directions of NUT drive point GP 2 will be tied directly into the
3 translationals of SCREW substructure drive point I0. A paral-
lel set of actions will also take place between GP's SCREW ii to
NUT 55 to 52 to 5 to SCREW Ii. This completes the logic.
As a mathematician would say: "This is a pathological
case", in that such an elaborate device would not have had to be
resorted to for modeling a ball nut, if it were not for the
special requirement of having to reposition the NUT with respect
to the SCREW. The repositioning requirement demanded that the
NUT be self-contained so as to be independent of the relative
locations. Thus, in order to be self-contained, the NUT in
effect picked up the duties of the helical advancement from the
SCREW and carried them out internally in a highly artificial
manner in order to transmit the reaction into the parent struc-
ture before handing back the results of the helical advancement
to the SCREW. As a bonus, this modeling left the analyst free to
reposition the NUT at will along the SCREW merely by specifying
the coordinate transformation in moving the SCREW to a new posi-
tion and by specifyinq new GRID POINT numbers on the RELES cards.
This paper has shown an achievement of a simple set of
operating conditions to an otherwise complicated modeling task.
50


Modeling a ball screw/ball nut in substructuring

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