The document presents a redesign of a ball screw mount for Accu-Router, a CNC refurbishing company. A team of mechanical engineering students were tasked with redesigning the mount to reduce costs. The current mount and ball screw both require expensive machining. The team developed several design concepts and conducted finite element analysis on the selected design. A prototype was fabricated and tested, with results analyzed. The goal was to develop a mount that maintains structural integrity at a lower price.

1.
University
of
Tennessee
Ball Screw Mount Design
Mechanical
Engineering
Senior
Design
in
conjunction
with
Accu-­‐Router
William
Brown,
Patirck
Connor,
Corey
Crumpton,
Skye
Jerrolds
12-­‐12-­‐2014

2. 1
Abstract
A
team
of
mechanical
engineering
seniors
from
the
University
of
Tennessee
have
partnered
with
Accu-­‐Router,
an
environment-­‐friendly
computer
numerically
controlled
(CNC)
refurbishing
company,
to
redesign
a
ball
screw
mount.
These
mounts
provide
both
the
support
structure
and
x-­‐axis
movement
for
several
different
CNC
tables
Accu-­‐Router
plans
to
refurbish.
However,
not
only
are
these
mounts
costly,
but
also
they
require
that
the
ball
screw
each
mount
supports
be
machined
and
threaded
as
well
–
further
adding
to
both
the
overall
cost
and
availability
of
these
two
parts.
As
a
company
that
values
timely
service
and
competitive
prices,
it
is
of
great
importance
that
the
team
can
produce
new
mounts
that
will
be
in
accordance
with
Accu-­‐
Router’s
standards.
The
intent
of
this
report
is
to
present
the
research,
redesign,
and
viability
of
the
new
and
improved
ball
screw
mount.
In
this
report,
the
background
of
the
project
is
discussed
in
more
detail,
design
specifications
for
current
mounts
are
explained,
several
different
designs
are
presented,
and
a
final
design
is
selected
as
the
prototype.
For
the
final
design,
a
finite
element
analysis
is
performed
through
Solidworks,
a
prototype
is
assembled
and
tested
during
the
spring
semester,
and
the
acquired
data
is
analyzed
and
documented.
This
team
believes
that
through
the
efforts
outlined
in
this
report,
a
superior
mount
design
will
successfully
be
implemented
into
Accu-­‐Router’s
line
of
CNC
machines.

3. 2
Table of Contents
Abstract
.......................................................................................................................................................
1
Background
of
Problem
...............................................................................................................................
3
Work
Statement
..........................................................................................................................................
3
Design
Specifications
...................................................................................................................................
4
Design
Concepts
..........................................................................................................................................
5
Design
A
...................................................................................................................................................
5
Design
B
...................................................................................................................................................
8
Design
C
.................................................................................................................................................
10
Evaluation
of
Concepts
..............................................................................................................................
13
Scoring
Process
......................................................................................................................................
14
Recommendation
..................................................................................................................................
14
Sponsor
Feedback
..................................................................................................................................
15
Finite
Element
Analysis
..............................................................................................................................
15
Fabrication
of
Prototype
............................................................................................................................
18
Economic
Impact
.......................................................................................................................................
22
Conclusion
and
Recommendations
...........................................................................................................
22
Appendix
....................................................................................................................................................
24
Gantt
Chart
............................................................................................................................................
24
September-­‐December
............................................................................................................................
24
January-­‐April
..........................................................................................................................................
26
January
..................................................................................................................................................
26
February
.................................................................................................................................................
27
March
....................................................................................................................................................
27
April
.......................................................................................................................................................
28
Engineering
Calculations
........................................................................................................................
29
Detailed
Shop
Drawings
.........................................................................................................................
30

4. 3
Background of Problem
Accu-­‐Router
is
a
small
business
that
specializes
in
“green
engineering,”
specifically
for
CNC,
or
computer
numerically
controlled,
machines.
They
buy
used
CNC
routers
and
refurbish
them
with
added
improvements
to
increase
the
longevity
of
the
machine.
Additionally,
the
company
also
builds
these
CNC
machines
from
the
ground
up.
Due
to
their
interest
in
reusing
materials,
it
would
be
beneficial
to
lower
costs
in
as
many
areas
as
possible.
One
area
of
high
cost
is
the
expense
of
having
both
the
ball
screw
mounts
and
the
corresponding
ball
screws
machined.
The
overall
cost
of
the
mount,
$494.49,
is
due
to
the
labor
involved
with
machining
very
tight
tolerances
for
the
bore
of
the
ball
screw.
The
cost
is
further
increased
because
the
ends
of
the
ball
screw
must
be
machined
not
only
to
match
the
inside
diameter
of
the
mount,
but
also
to
include
threads
that
will
secure
the
ball
screw
through
the
mount
with
a
lock
nut
on
the
outside.
Additionally,
having
the
ball
screw
machined
and
threaded
adds
a
significant
lead
time
to
the
availability
of
this
part.
This
down
time
is
of
great
concern
to
Accu-­‐Router,
and
having
a
ball
screw
that
requires
no
machining
would
be
highly
beneficial.
Work Statement
The
University
of
Tennessee’s
senior
design
group
is
dedicated
to
redesigning
and
producing
a
prototype
for
an
x-­‐axis
ball
screw
mount
for
Accu-­‐Router.
Through
the
team’s
design
process
and
engineering
analysis,
a
mount
will
be
produced
that
retains
both
the
integrity
of
the
original
design
as
well
as
a
reduced
price
for
an
overall
superior
product.
The
main
focus
of
this
project
is
to
take
an
existing
component
of
the
CNC
machine
and
redesign
it
to
produce
a
more
cost
effective
product.
This
redesign
process
integrates
previous
mounting
specifications,
maintains
the
structural
integrity
of
the
original
component,
and
accounts
for
material
and
labor
costs
of
producing
a
new
component.
The
team’s
preliminary
design
is
the
result
of
not
only
eliminating
unnecessary
material
associated
with
the
component,
but
also
complying
with
mounting
specification
requirements
in
order
to
implement
the
new
product
into
existing
CNC
tables.
Finally,
the
team
will
report
the
results
of
its
finite
element
analysis
and
prototype
testing
to
Accu-­‐Router
in
a
timely
manner
in
order
to
obtain
feedback
and
create
a
functional
component
that
meets
their
standards.

5. 4
Design Specifications
In
order
to
maximize
the
functionality
of
the
design,
the
new
prototype
needs
to
satisfy
the
following
criteria
depicted
in
Figure
1.
Figure
1:
Bolt-­‐Hole
Pattern
Of
Original
Mount
The
base
of
the
design
must
maintain
the
exact
dimensions
of
the
original
design,
5.25
inches
long,
4
inches
wide,
and
1
inch
high,
and
also
must
contain
the
four
original
bolt-­‐holes’
pattern.
The
location
of
these
bolt-­‐hole
centroids,
measured
from
the
bottom
left
corner
of
the
base,
are
as
follows:
0.5
inches
by
0.625
inches,
0.5
inches
by
3.375
inches,
4.75
inches
by
.625
inches,
and
4.75
inches
by
3.375
inches.
The
diameter
of
all
the
bolt-­‐holes
must
be
0.41
inches.
The
height
of
the
ball
screw
mount
and
its
centroid,
measured
from
the
base,
are
5
inches
and
3.75
inches
respectively.
The
centroid
of
the
mount
must
be
placed
2.625
inches
from
the
left
and
right
side
of
the
base.
Finally,
the
new
design
must
also
have
an
overall
lower
cost
than
the
original
design.
This
can
be
done
by
implementing
both
a
creative
alternative
to
not
only
machining
and
threading
the
ball
screw
mount,
but
also
by
fastening
the
ball
screw
with
a
large
lock
nut.
The
new
design
must
also
be
able
to
withstand
the
required
load
as
well
as
not
produce
any
axial,
lateral,
or
rotational
loading
on
the
ball
screw.

6. 5
Design Concepts
Design A
Features
The
team’s
first
design
(Design
A)
is
a
very
simple
design
requiring
only
two
pieces
to
be
machined.
Its
simplicity
also
allows
it
to
be
very
easily
produced,
resulting
in
a
reduction
of
the
cost
of
production.
This
design
uses
a
two-­‐screw
clamping
system
and
a
setscrew
to
keep
the
ball
screw
in
place.
The
most
important
feature
of
this
design
is
that
by
increasing
the
ball
screw
mount
bore,
there
is
no
longer
a
need
to
machine
down
and
thread
the
end
of
the
ball
screw
to
secure
it
in
the
mount.
It
accomplishes
this
while
also
meeting
all
of
the
requirements
set
forth
by
Accu-­‐Router,
including
retaining
all
original
bolt
hole
patterns,
meeting
the
height
requirement
of
5
inches,
and
retaining
the
height
of
the
ball
screw
bore’s
centroid
of
3.75
inches.
Additional
new
features
of
Design
A
are
listed
below.
-­‐ Removal
of
the
gussets
(triangular
steel
pieces)
that
were
welded
on
to
the
side
of
the
original
design.
The
team
concluded
that
these
gussets
not
only
served
little
purpose,
but
also
added
extra
cost
to
production.
-­‐ Increase
in
the
size
of
the
ball
screw
bore
to
1.97
inches
(50
mm).
This
will
allow
the
ball
screw
to
fit
into
the
mount
with
no
machining.
This
will
cut
down
on
the
amount
of
machining
and
the
overall
cost.
-­‐ Decrease
in
overall
volume.
This
was
achieved
by
shortening
the
length
of
the
neck.
The
team
determined
this
would
cut
down
on
material
cost.
-­‐ Increased
width
of
the
base
of
the
neck
to
accommodate
the
larger
ball
screw
bore.
-­‐ Changed
the
position
of
the
clamping
system.
This
was
done
to
meet
the
5-­‐inch
height
requirement.
The
team
removed
the
screws
from
the
top
of
the
ball
screw
bore
and
instead
placed
them
vertically,
perpendicular
to
the
base,
and
next
to
the
ball
screw
bore
(Figure
5).
They
lay
flush
with
the
topside
of
the
mount
due
to
a
counter
bore.
Benefits
Design
A
is
a
very
simple
design
that
is
similar
to
the
original
mount.
One
of
the
benefits
of
such
a
simple
design
is
that
it
will
require
a
minimal
amount
of
machining
to
complete
the
part,
thus
cutting
down
on
overall
cost.
This
design
also
cuts
cost
since
the
addition
of
the
setscrew
allows
the
ball
screw
to
be
clamped
into
the
mount
without
any
machining
or
threading.
Design
A
is
a
practical
solution
to
the
problem
set
forth
by
Accu-­‐Router
as
it
cuts
down
on
price
while
still
meeting
the
standards
and
requirements
expected.
Feasibility
Design
A
has
a
very
high
feasibility
because
it
is
a
simple
design;
it
meets
all
the
requirements
and
functions
as
specified
by
Accu-­‐Router,
and
it
is
similar
to
the
original
design.
All
of
the
features
and
benefits
specified
above
will
help
reduce
costs
and
make
this
design
a
very
practical
option
for
replacing
Accu-­‐Router’s
current
ball
screw
mount.

7. 6
Figure
2:
Design
A
Isometric
View
Figure
3:
Design
A
Front
View

8. 7
Figure
4:
Design
A
Top
View
Figure
5:
Design
A
Section
View
Note:
Not
final
rendering
of
models

9. 8
Design B
Features
The
second
design
is
comprised
of
two
components
machined
on
a
mill
and
welded
together
at
the
specified
location.
The
bolt-­‐hole
pattern
and
base
dimensions
are
the
same
as
the
original
assembly,
however,
the
height
of
the
base
has
been
reduced
to
one-­‐half
of
an
inch.
The
milled
pocket
on
the
top
face
of
the
base
piece
provides
a
means
of
precisely
attaching
the
neck
of
the
assembly.
The
pocket
is
130
thousandths
of
an
inch
deep,
and
has
been
designed
to
be
milled
with
an
end
mill
no
larger
than
half
of
an
inch
in
diameter,
therefore
all
internal
radii
are
greater
than
one-­‐quarter
of
an
inch.
Two
of
the
sides
provide
orthogonal
faces
that
the
orthogonal
sides
of
the
neck
can
rest
against,
providing
a
quick
and
simple
way
to
align
the
neck
of
the
mount
perpendicularly
during
the
welding
process.
The
neck
of
the
assembly
is
4.63
inches
tall
and
rests
on
the
face
created
by
the
pocket.
This
keeps
the
assembly
within
the
vertical
restriction
of
5
inches.
The
cross
section
of
the
neck
is
a
2-­‐inch
by
2.93-­‐inch
rectangle.
The
neck
of
Design
B
is
reduced
compared
to
the
design
of
the
original
neck
in
order
to
save
material
and
machining
costs.
The
bore
is
50
millimeters
in
diameter
in
order
to
house
the
non-­‐
machined
ball
screw.
The
top
face
of
the
neck
contains
a
bolt-­‐hole
protruding
into
the
bore
that
is
meant
to
hold
a
set
screw,
which
prevents
twist
of
the
ball
screw
as
well
as
movement
in
the
axial
direction.
Since
the
bore
diameter
is
increased,
the
clamping
bolts
are
placed
on
the
side
instead
of
the
top
due
to
the
height
restriction
of
5
inches.
The
bolts’
axial
direction
is
therefore
oriented
to
the
assembly’s
vertical
direction.
The
bolt
heads
will
rest
in
the
counter
bore,
allowing
the
head
to
be
below
flush
with
the
top
face
of
the
neck,
resulting
in
no
bolt
resting
above
5
inches
in
the
vertical
direction.
Benefits
The
cost
of
welding
for
this
design
is
reduced
since
the
neck
can
easily
be
located
on
the
base.
There
will
be
a
reduced
cost
of
material
since
the
overall
volume
has
been
decreased.
The
cost
of
machining
the
mount
will
be
reduced
since
only
a
base
and
neck
need
to
be
machined
instead
of
a
base,
a
neck,
and
two
gussets.
The
cost
of
machining
the
ball
screw
will
also
be
reduced
since
only
a
tapped
hole
for
a
set
screw
will
require
machining
instead
of
thread
on
the
outer
diameter
of
the
ball
screw
requiring
machining.
In
addition
to
the
reduced
costs,
the
design
is
still
able
to
withstand
the
required
load.
Feasibility
This
design
is
a
simple
concept
that
meets
all
requirements
and
functions
specified
by
Accu-­‐
Router.
This
design
is
very
similar
to
the
original
design,
and
therefore
would
be
very
easy
to
implement
on
current
and
future
systems.

10. 9
Figure
6:
Design
B
Isometric
View
Figure
7:
Design
B
Cross-­‐Sectional
View

11. 10
Design C
Features
The
third
design
is
comprised
of
four
components
that
are
machined
and
bolted
together
at
the
specified
locations.
The
bolt-­‐hole
pattern
and
base
dimensions
are
the
same
as
the
original
assembly,
however,
the
height
of
the
base
has
been
reduced
to
one-­‐half
of
an
inch.
The
neck
of
the
assembly
is
1.72
inches
tall
and
rests
symmetrically
on
the
top
face
of
the
base.
The
cross
section
of
the
neck
is
a
0.75-­‐inch
by
2-­‐inch
rectangle.
The
neck
of
Design
C
is
reduced
compared
to
the
design
of
the
original
neck
in
order
to
save
material
and
machining
costs.
The
neck
attaches
to
the
base
via
two
bolts
that
are
run
from
the
bottom
of
the
base.
The
neck
supports
the
bottom
of
the
clamping
head.
The
clamping
head
is
attached
to
the
neck
via
two
bolts
that
are
run
from
the
top
of
the
bottom
clamping
head.
The
clamping
head
contains
a
cylindrical
extruded
cut
that
is
used
to
house
and
center
the
ball
screw.
The
bore
will
be
increased
to
50
millimeters
in
diameter
in
order
to
house
the
non-­‐machined
ball
screw.
The
top
clamping
head
is
attached
to
the
bottom
clamping
head
via
four
bolts
on
the
four
corners
of
the
clamping
heads.
The
two
heads
do
not
come
into
contact,
and
instead
has
a
cylindrical
bore
that
houses
the
ball
screw.
The
bolts
then
provide
the
clamping
force
that
the
clamping
heads
produce
on
the
ball
screw.
The
top
face
of
the
clamping
head
contains
a
bolt-­‐hole
protruding
into
the
bore
that
is
meant
to
hold
a
set
screw,
which
will
prevent
twist
of
the
ball
screw
as
well
as
movement
in
the
axial
direction.
The
bottom
clamping
head’s
dimensions
are
2.9
inches
long,
2
inches
wide,
and
1.15
inches
high
with
the
exception
of
the
bore
and
bolt
holes.
The
top
clamping
head’s
dimensions
are
2.9
inches
long,
2
inches
wide,
and
1
inch
high
with
the
exception
of
the
bore
and
bolt
holes.
Benefits
This
design
eliminates
the
cost
of
welding
since
the
components
are
now
attached
via
bolts.
The
cost
of
material
is
reduced
since
the
overall
volume
has
been
decreased.
The
cost
of
machining
the
ball
screw
is
also
reduced.
Only
a
tapped
hole
for
a
set
screw
will
need
to
be
machined
instead
of
thread
on
the
outer
diameter
of
the
ball
screw.
In
addition
to
the
reduced
costs,
the
design
is
still
able
to
withstand
the
required
load.
Feasibility
This
design
is
a
relatively
simple
concept
that
meets
all
requirements
and
functions
specified
by
Accu–Router.
In
order
to
implement
the
design,
the
user
would
simply
apply
a
thread-­‐locker
to
the
bolts
as
they
are
placed
in
the
appropriate
locations.
The
mount
is
then
placed
in
the
appropriate
location
as
the
ball
screw
is
located
and
mounted.

12. 11
Figure
8:
Design
C
Isometric
View
Figure
9:
Design
C
Cross
Sectional
View
Section
A-­‐A

13. 12
Figure
10:
Design
C
Cross
Sectional
View
Section
B-­‐B

14. 13
Evaluation of Concepts
In
order
to
determine
the
team’s
ideal
design,
a
Pugh
chart
was
created
that
evaluates
the
benefits
and
drawbacks
of
the
three
designs.
The
two
main
criteria
of
the
Pugh
chart
are
cost
and
safety,
and
each
criterion
is
given
50%
total
weight.
Figure
11
shows
the
details
of
the
Pugh
chart.
Priority
Design
A
Design
B
Design
C
0.5
Safety
0.1
Load
Capacity
3
3
2
0.4
Torque
Resistance
3
3
2
0.5
Cost
0.2
Welding
1
2
3
0.1
Machining
2
2
1
0.1
Assembly
2
3
2
0.1
Material
1
1
3
Total
2.2
2.5
2.2
*Total
=
priority*ranking
*Rankings
on
1-­‐3
scale
Figure
11:
Matrix
Decision
Pugh
Chart
Within
the
safety
category,
the
two
subcategories
were
load
capacity
and
torque
resistance.
Torque
resistance
was
given
40%
weight
due
to
the
continuous
rotational
forces
the
motor
applies
to
the
ball
screw
while
it
is
in
use.
The
load
capacity
was
given
10%
weight
since
the
ball
screw
only
experiences
minimal
axial
forces
that
are
transmitted
to
the
mounts.
Within
the
cost
category,
the
four
subcategories
were
welding,
machining,
assembly,
and
material.
Machining
was
given
20%
weight
due
to
the
major
considerations
of
machining
both
the
mounts
and
the
ball
screw.
A
design
that
could
successfully
accommodate
a
non-­‐machined
ball
screw
would
decrease
cost
and
availability
time
significantly;
therefore
this
category
was
weighted
with
more
importance
compared
to
the
other
cost
categories.
Although
the
labor
costs
for
welding
are
generally
higher
than
machining,
each
design
concept
requires
no
more
welding
than
the
original
design,
and
thus
welding
was
only
given
10%
weight.
Assembly
was
given
10%
weight
as
well
to
account
for
the
differences
between
the
assembly
of
the
original
design,
Design
A,
Design
B,
and
Design
C.
Finally,
material
costs
were
also
given
10%
weight
because
the
team
intends
to
use
the
same
material
as
the
current
mounts.

15. 14
Scoring Process
The
scoring
process
took
each
design
and
rated
all
of
the
categories
on
a
1
to
3
scale,
where
1
represents
a
poor
performance
and
3
represents
an
excellent
performance.
Each
score
given
was
an
estimate
based
on
the
knowledge
that
the
team
has
of
both
general
machine
design
and
the
original
design.
The
rest
of
this
section
will
highlight
the
strengths
and
weaknesses
of
each
design.
Design
A
was
scored
a
3
in
each
safety
category
since
Design
A
varied
only
slightly
from
the
original
design,
and
the
original
design
had
an
exceptional
safety
performance.
In
the
cost
section,
Design
A
scored
a
2
in
the
machining
and
assembly
categories
since
the
gussets
are
removed
from
the
original
design.
Finally,
Design
A
scored
a
1
in
the
welding
and
material
categories.
Although
the
welding
and
material
requirements
for
Design
A
were
less
than
the
original
design,
they
required
significantly
more
welding
and
material
than
the
other
design
concepts.
Similar
to
Design
A,
Design
B
scored
a
3
in
each
safety
category
since
Design
B
also
closely
resembles
the
original
design.
In
the
cost
section,
Design
B
scored
a
3
in
assembly
because
it
only
requires
the
attachment
of
the
base
plate
to
the
mount
itself.
However,
this
design
scored
a
2
in
machining
and
welding
since
it
requires
a
great
deal
of
machining
for
the
milled
cutout
so
both
the
alignment
of
the
mount
and
welding
of
the
mount
into
the
cutout.
Finally,
Design
B
scored
a
1
in
material
because,
similar
to
Design
A,
it
requires
more
material
than
design
C.
Finally,
Design
C
scored
a
2
in
each
safety
category
due
to
the
unique
design’s
unknown
reliability,
caused
from
its
slender
neck
not
being
able
to
withstand
the
rotational
forces
applied
to
the
mount.
In
the
cost
section,
Design
C
scored
a
3
in
material
and
welding
since
it
requires
very
little
material
as
well
as
no
welding.
This
design
scored
a
2
in
assembly
since
the
user
is
required
to
assemble
the
entire
mount.
Finally,
this
design
scored
a
1
in
machining
since
each
component
requires
individual
machining,
thus
increasing
the
cost
of
the
mount.
Recommendation
Originally,
the
team
recommended
Design
B
since
its
overall
score
on
the
Pugh
chart
was
a
2.5,
while
the
other
designs
each
scored
a
2.2.
Based
on
the
assumption
that
Design
B
was
similar
to
the
original
design,
the
team
was
confident
it
would
not
only
be
reliable,
but
also
reduce
costs
due
to
the
simplicity
of
accurately
aligning
the
neck
onto
the
base
via
the
milled
cutout.
However,
in
case
Design
B
was
not
sufficient,
the
team
decided
that
Design
A
would
be
the
next
best
option,
despite
that
both
Design
A
and
Design
C
scored
a
2.2
on
the
Pugh
chart.
The
justification
behind
this
decision
was
that
Design
A
was
closer
to
the
original
design
than
Design
C,
and
therefore
would
have
less
safety
risks.

16. 15
Sponsor Feedback
Although
Design
B
was
recommended
to
Accu-­‐Router,
they
informed
the
team
that
there
is
a
high
risk
of
the
steel
distorting
when
being
welded
into
a
milled
piece.
Therefore,
they
decided
that
Design
A
would
be
the
best
choice
among
the
three
designs.
Based
on
the
decision
matrix
and
scoring
process,
the
team
supported
their
decision.
Since
Design
A
is
similar
to
the
original
design,
it
would
create
the
least
amount
of
unknown
variables
when
the
part
is
tested.
Finite Element Analysis
The
team
decided
to
do
a
finite
element
analysis
(FEA)
to
determine
the
maximum
stresses
and
the
factor
of
safety
of
the
ball
screw
mount.
To
do
the
FEA,
the
decision
was
made
to
create
a
model
assembly
of
the
ball
screw
mount,
the
ball
screw,
and
the
setscrew
within
Solidworks.
The
team
ran
into
difficulties
replicating
the
ball
screw
and
setscrew,
so
the
decision
was
made
to
model
them
as
cylinders.
The
simulated
ball
screw
was
a
cylinder
with
a
diameter
of
50
millimeters
and
a
length
of
12
inches.
The
simulated
setscrew
was
a
cylinder
modeled
after
an
8-­‐32
and
5/16
inch
set
screw.
However,
the
team
later
learned
that
the
8-­‐32
set
screw
had
problems
breaking
after
use,
and
therefore
was
changed
to
a
¼-­‐20
sized
screw
instead.
After
assembling
these
models,
the
simulation
program
in
Solidworks
was
used
to
run
the
analysis.
During
the
simulation
program,
a
torque
and
an
axial
force
was
applied
on
the
ball
screw
(see
Figure
12).
The
torque
was
found
using
the
motor
specs
that
were
acquired
from
Accu-­‐Router.
The
axial
force
was
found
using
the
maximum
speed
of
the
table,
the
time
it
takes
to
reach
the
maximum
speed,
and
the
weight
of
the
table.
The
torque
applied
was
70
N-­‐m
(51.6
ft-­‐lb),
and
the
axial
force
applied
was
414
lbs.
To
simulate
the
mount
being
bolted
on
to
the
machine,
the
bottom
face
of
the
mount
was
fixed.
In
an
iterative
process,
the
team
simulated
tightening
the
bolts
down
and
deforming
the
top
face
of
the
mount
by
up
to
2mm.
Figure
12:
FEA
Model
Assembly

17. 16
Once
all
of
the
forces
were
applied,
a
mesh
was
created
of
the
assembly
and
the
simulation
was
performed.
Several
variables
attained
from
the
analysis
include
the
maximum
stresses,
the
location
of
the
maximum
stresses
(see
Figure
13),
and
the
factor
of
safety
(see
Figure
14).
All
of
these
values
are
located
on
Table
1.
The
team
was
also
interested
in
finding
out
if
the
setscrew
would
be
able
to
withstand
the
shear
and
axial
forces
applied,
as
well
as
determining
what
type
and
size
of
weld
would
be
appropriate
to
use.
Figure
13:
FEA
Stress
Diagram
Figure
14:
FEA
Factor
of
Safety
Diagram

18. 17
After
running
the
simulation
and
analyzing
the
acquired
data,
the
team
determined
that
the
setscrew
would
be
able
to
withstand
the
required
shear
and
axial
forces.
This
data
was
also
used
to
determine
the
appropriate
type
and
size
of
weld
to
connect
the
base
plate
and
the
neck.
After
analyzing
the
data
and
researching
different
welds,
it
was
determined
that
a
¼
inch,
E
6011
welding
rod
used
in
a
fillet
weld
would
produce
the
best
results.
This
welding
rod
was
chosen
because
it
has
a
high
maximum
strength
(60
kpsi)
and
it
has
a
high
tolerance
for
combining
imperfect
joints.
Table
1:
FEA
Data
Max.
Stresses
(FEA)
1.64
kpsi
Location
of
Max.
Stresses
Along
weld,
bolt
counter
bores,
where
mount
contacts
ball
screw
Factor
of
Safety
(Min.)
22
Factor
of
Safety
(Max.)
50
(max.
on
team
scale)
Factor
of
Safety
(Avg.)
36
Recommended
Setscrew
¼
-­‐
20
5/16”
Recommended
Weld
¼
“
E6011
fillet
weld

19. 18
Fabrication of Prototype
Before
the
first
prototypes
were
produced,
a
few
changes
were
made
to
the
mounts
within
Solidworks.
After
the
small
modifications
were
completed,
Accu-­‐Router
was
contacted
and
the
final
detailed
shop
drawings
were
sent.
Accu-­‐Router
officially
put
in
the
work
order
for
the
mount
at
the
end
of
December.
Once
the
prototype
was
delivered
a
few
tests
were
developed
to
run
on
the
mounts.
These
tests
were
developed
to
see
if
the
requirements
set
by
Accu-­‐
Router
were
met.
The
requirements
included:
the
ball
screw
must
fit
in
the
mount,
the
ball
screw
must
not
twist
in
the
mount,
and
the
ball
screw
must
not
push
or
pull
within
the
mount.
Fig.
15
Prototype
Special Considerations, Issues in Building Prototype
The
original
plan
was
to
tap
the
ball
screw
to
allow
the
setscrew,
located
on
top
of
the
mount,
to
screw
in
to
the
ball
screw
ensuring
no
twist
within
the
mount
occurred.
When
the
team
approached
the
machine
shop
to
tap
the
ball
screw,
it
was
brought
to
the
team’s
attention
that
unless
the
mount
and
the
ball
screw
were
tapped
at
the
same
time,
the
threads
would
not
match
up.
The
solution
was
to
drill
a
hole
in
the
ball
screw
with
a
diameter
of
(0.25
in.),
which
is
the
major
diameter
of
the
setscrew,
see
Fig.
16,
in
order
to
use
the
set
screw
as
a
pin.

20. 19
Fig.
16
End
of
Ball
screw
with
hole
Design of Test Apparatus and Test Procedure
Before
the
prototype
was
tested
on
a
machine,
a
simple
test
was
designed
to
ensure
that
the
mount
met
the
requirements
set
forth
by
Accu-­‐Router,
which
were:
the
mount
must
house
the
ball
screw,
the
ball
screw
must
not
twist
within
the
mount,
and
the
ball
screw
must
not
move
axially
within
the
mount.
The
team
was
given
some
values
for
external
forces
that
would
be
applied
to
the
ball
screw,
including
a
70
N*m
torque,
and
a
1400
N
axial
force.
In
order
to
apply
the
torque
on
the
ball
screw,
a
hexagonal
nut
was
welded
to
the
end
of
the
ball
screw,
see
Fig.
17.
This
was
done
so
that
the
team
could
take
a
wrench
and
apply
a
torque
to
the
ball
screw.
To
simulate
the
conditions
the
mount
would
most
likely
see
when
placed
on
an
operating
machine,
the
test
needed
to
fix
the
base
of
the
mount,
insert
the
ball
screw,
and
apply
our
external
forces.
Fig.
17
Welded
Nut

21. 20
For
the
first
test,
the
base
of
the
ball
screw
was
fixed
to
a
workbench
using
3
medium
sized
C-­‐
clamps.
A
two-­‐foot
section
of
the
ball
screw
was
then
inserted
into
the
mount.
To
secure
the
ball
screw
within
the
mount,
two
clamping
bolts
and
a
setscrew
were
inserted
and
tightened.
Once
the
forces
were
applied,
it
was
determined
if
any
twisting,
or
pushing/
pulling
occurred
within
the
mount.
To
apply
the
loads,
a
wrench
was
used
that
was
approximately
a
foot
long.
The
wrench
was
oriented
as
close
to
horizontal
as
possible
in
order
to
ensure
the
greatest
amount
of
torque,
and
then
a
weight
of
160
pounds
was
hung
from
the
end.
This
resulted
in
a
moment
slightly
more
than
three
times
the
given
value
of
70
N*m.
Fig.
18
Simple
Test
in
Estabrook
After
the
simple
test
was
completed,
the
team
traveled
to
the
Accu-­‐Router
plant
in
Morrison,
TN.
The
purpose
of
this
visit
was
to
test
the
mounts
on
the
machines
that
the
mounts
would
be
used
on.
Once
the
mounts
were
bolted
onto
the
CNC
machine,
a
full-­‐length
ball
screw
was
inserted
and
supported
solely
by
the
newly
designed
mounts.
The
clamping
bolts
were
inserted
and
tightened,
and
it
was
decided
that
the
first
test
would
be
completed
without
the
use
of
the
setscrew.
If
needed,
a
second
test
would
be
run
with
a
set
screw
inserted.
An
accelerometer
was
also
placed
on
the
table
to
get
a
more
accurate
value
for
the
axial
force
applied
to
the
ball
screw.

22. 21
Fig.
19
Accu-­‐Router
Test
1&2
Fig.
20
Accu-­‐Router
Test
3
Test Results
Preliminary Testing
This
test
involved
tightening
the
clamping
screws,
as
well
as
inserting
the
setscrew.
After
applying
approximately
three
times
the
given
load
of
70
N*m
torque
to
the
end
of
the
ball
screw,
there
was
no
visible
twisting
or
axial
movement
within
the
mount.
Real World Testing
This
test
involved
bolting
the
prototype
mounts
to
the
machines
in
which
they
would
be
used
on.
For
this
test
we
only
tightened
the
clamping
bolts
and
did
not
include
the
setscrew.
After
the
machine
was
run,
there
was
no
twisting,
pushing,
or
pulling
of
the
ball
screw
within
the

23. 22
mount.
The
data
recorded
by
the
accelerometer
provided
an
acceleration
of
the
table
of
36.702
ft/s.
Using
the
acceleration
data,
along
with
the
weight
of
the
table
(1200
lb
or
37.267
slugs),
the
axial
force
was
calculated
at
1367.77
lbf.
This
is
greater
than
the
predicted
axial
force
due
to
the
fact
that
Accu-­‐Router
uses
a
bell
shaped
curve
to
model
the
acceleration
rate.
This
curve
was
unavailable
to
the
team
previous
to
the
site
testing,
and
therefore
constant
acceleration
had
to
be
assumed.
The
tests
ran
on
the
prototypes
show
that
the
new
mounts
can
withstand
the
maximum
loads
without
allowing
any
movement
of
the
ball
screw.
It
was
also
found
that
the
mounts
secure
the
ball
screw
with
or
with
out
the
setscrew
inserted.
The
tests
also
showed
that
the
ball
screw
could
be
secured
without
having
to
machine
the
ends
down.
Ultimately,
the
testing
showed
that
meet
all
requirements
set
forth
by
Accu-­‐Router.
Economic Impact
Since
the
main
objective
of
this
design
was
to
decrease
the
overall
costs
associated
with
the
mount,
economic
impact
played
a
significant
role
in
designing
of
the
model.
Two
ways
the
overall
cost
was
decreased
was
by
removing
the
gussets
off
the
side
of
the
mount
as
well
as
increasing
the
bore
diameter
in
order
to
reduce
the
machining
cost
of
the
ball
screw.
The
result
is
a
price
reduction
of
375
dollars.
Excluding
the
additional
costs
of
turning
the
ball
screw,
the
original
mount’s
quote
is
495
dollars.
The
newly
designed
mount’s
quote
is
120
dollars.
This
quote
also
excludes
the
cost
of
machining
the
ball
screw,
however
immensely
less
machining
is
involved;
therefore,
there
will
be
a
significant
price
reduction
associated
with
the
ball
screw
as
well.
Since
the
new
design
decreases
the
cost
by
a
factor
of
4.125
(or
a
price
reduction
of
75.8%),
the
design
has
an
undisputable
positive
impact.
Conclusion and Recommendations
The
objective
of
this
design
project
was
to
design
a
cheaper
mount
for
a
CNC
ball
screw
that
still
withstands
the
maximum
loads
on
the
ball
screw
without
allowing
the
ball
screw
to
rotate
or
move
axially.
This
was
achieved
via
computer
animated
design
software,
finite
element
analysis
software,
and
the
fabrication
of
a
prototype
to
ensure
the
design
works.
The
results
of
the
finite
element
analysis
show
that
the
model
withstands
the
maximum
axial
and
torsional
loads.
The
test
of
the
prototype
also
showed
that
the
model
withstands
the
maximum
loads
without
allowing
rotation
or
axial
movement.
In
addition
to
withstanding
the
maximum
loads,
the
model
is
also
cheaper
than
the
original
design.
This
is
due
to
the
decreased
machining
costs

24. 23
of
the
components
involved
as
well
as
significantly
less
machining
to
the
ball
screw
itself.
The
result
is
a
cheaper,
yet
functional
model.
During
the
prototype
testing,
the
ball
screw
was
mounted
on
two
of
the
designed
mounts.
Neither
side
of
the
ball
screw
had
a
setscrew
in
place.
Based
on
this
lack
of
a
set
screw
as
well
as
the
results
in
the
testing,
the
design
team
from
the
University
of
Tennessee
observes
that
a
set
screw
is
not
needed,
which
would
further
decrease
the
cost
of
the
mount
and
screw
assembly.
However
the
team
recommends
the
use
of
this
set
screw.
While
both
ends
do
not
need
one,
the
assembly
is
more
reliable
and
can
withstand
more
loads
over
time
with
the
setscrew
in
place.

25. 24
Appendix
Gantt Chart
September-­‐December
September
Task
Start
Date
End
Date
#
of
Days
16-­‐
Sep
17-­‐
Sep
18-­‐
Sep
19-­‐
Sep
20-­‐
Sep
21-­‐
Sep
22-­‐
Sep
23-­‐
Sep
24-­‐
Sep
25-­‐
Sep
26-­‐
Sep
27-­‐
Sep
28-­‐
Sep
29-­‐
Sep
30-­‐
Sep
Func.
and
Req.
Docu-­‐
ment
9/16/14
9/23/14
8
Design
Con-­‐
cepts
9/23/14
9/25/14
3
Pugh
Chart
9/25/14
9/30/14
6
During
the
month
of
September,
the
team
focused
on
planning
the
initial
design
ideas
and
evaluated
the
pros
and
cons
of
each
design
by
creating
a
Pugh
Chart.
A
functions
and
requirements
document
was
also
prepared
that
details
the
specifications
for
each
design.
October
Task
Start
Date
End
Date
#
of
Days
1-­‐
Oct
2-­‐
Oct
3-­‐
Oct
4-­‐
Oct
5-­‐
Oct
6-­‐
Oct
7-­‐
Oct
8-­‐
Oct
9-­‐
Oct
10-­‐
Oct
11-­‐
Oct
12-­‐
Oct
13-­‐
Oct
14-­‐
Oct
15-­‐
Oct
16-­‐
Oct
Pugh
Chart
10/1/14
10/7/14
7
1st
Design
Review
10/7/14
10/7/14
1
Final
Design
Decision
10/7/14
10/21/14
15
3-­‐D
Model
10/21/14
10/31/14
11
Assembly
Drawing
10/21/14
10/31/14
11
Design
of
Subsystems
10/21/14
10/31/14
11

26. 25
Task
Start
Date
End
Date
#
of
Days
17-­‐
Oct
18-­‐
Oct
19-­‐
Oct
20-­‐
Oct
21-­‐
Oct
22-­‐
Oct
23-­‐
Oct
24-­‐
Oct
25-­‐
Oct
26-­‐
Oct
27-­‐
Oct
28-­‐
Oct
29-­‐
Oct
30-­‐
Oct
31-­‐
Oct
Pugh
Chart
10/1/14
10/7/14
7
1
st
Design
Review
10/7/14
10/7/14
1
Final
Design
Decision
10/7/14
10/21/1
4
15
3-­‐D
Model
10/21/14
10/31/1
4
11
Assembly
Drawing
10/21/14
10/31/1
4
11
Design
of
Subsystems
10/21/14
10/31/1
4
11
During
the
month
of
October,
the
team
presented
each
of
the
three
designs
to
Accu-­‐Router,
and
a
mutual
decision
to
pursue
Design
A
was
reached
after
evaluating
the
pros
and
cons
of
each
design.
After
the
final
design
was
determined,
a
3D
model
and
an
assembly
drawing
of
the
new
design
were
created
in
Solidworks.
November
Task
Start
Date
End
Date
#
of
Days
1-­‐
Nov
2-­‐
Nov
3-­‐
Nov
4-­‐
Nov
5-­‐
Nov
6-­‐
Nov
7-­‐
Nov
8-­‐
Nov
9-­‐
Nov
10-­‐
Nov
11-­‐
Nov
12-­‐
Nov
13-­‐
Nov
14-­‐
Nov
15-­‐
Nov
3-­‐D
Model
11/1/14
11/15/14
15
Assembly
Drawing
11/1/14
11/15/14
15
Design
of
Sub-­‐
systems
11/1/14
11/15/14
15
2
nd
Design
Review
11/7/14
11/20/14
14
Design
Report
11/1/14
11/31/14
31
Task
Start
Date
End
Date
#
of
Days
16-­‐
Nov
17-­‐
Nov
18-­‐
Nov
19-­‐
Nov
20-­‐
Nov
21-­‐
Nov
22-­‐
Nov
23-­‐
Nov
24-­‐
Nov
25-­‐
Nov
26-­‐
Nov
27-­‐
Nov
28-­‐
Nov
29-­‐
Nov
30-­‐
Nov
3-­‐D
Model
11/1/14
11/15/14
16
Assembly
Drawing
11/1/14
11/15/14
16
Design
of
Sub-­‐
systems
11/1/14
11/15/14
16
2
nd
Design
Review
11/7/14
11/20/14
14
Design
Report
11/1/14
11/31/14
31

27. 26
During
the
month
of
November,
the
team
continued
to
work
on
the
3D
model
and
assembly
drawing
of
the
new
design.
An
FEA
analysis
was
completed
in
Solidworks
to
determine
if
the
new
part
could
bear
both
the
required
load
and
torque
while
maintaining
a
high
safety
factor.
Once
this
was
completed,
the
team
prepared
to
present
the
acquired
data
to
Accu-­‐Router
for
the
second
design
presentation
at
the
beginning
of
December.
December
Task
Start
Date
End
Date
#
of
Days
1-­‐Dec
2-­‐Dec
3-­‐Dec
4-­‐Dec
5-­‐Dec
6-­‐Dec
7-­‐Dec
8-­‐Dec
9-­‐Dec
10-­‐Dec
11-­‐Dec
2nd
Design
Presentation
12/3/14
12/3/14
1
First
Prototype
12/1/14
12/3/14
3
Spring
Gant
Chart
12/1/14
12/11/14
11
During
the
month
of
December,
the
team
presented
the
acquired
data
to
Accu-­‐Router
to
show
that
the
new
design
would
be
both
reliable
and
cost
efficient.
Plans
for
next
semester’s
work
were
laid
out,
and
a
completed
final
report
on
the
team’s
progress
during
this
semester
was
submitted.
January-­‐April
January
Task
Start
Date
End
Date
#
of
Days
7-­‐Jan
8-­‐Jan
9-­‐Jan
10-­‐Jan
11-­‐Jan
12-­‐Jan
13-­‐Jan
14-­‐Jan
15-­‐Jan
16-­‐Jan
17-­‐Jan
18-­‐Jan
Adjust
Part
to
be
Re-­‐
manufactured
(If
Needed)
1/7/15
1/21/15
15
Manufacturing
of
Ball
Screw
Mount
by
Accu-­‐
Router*
1/7/15
2/21/15
46
Task
Start
Date
End
Date
#
of
Days
19-­‐Jan
20-­‐Jan
21-­‐Jan
22-­‐Jan
23-­‐Jan
24-­‐Jan
25-­‐Jan
26-­‐Jan
27-­‐Jan
28-­‐Jan
29-­‐Jan
30-­‐Jan
Adjust
Part
to
be
Re-­‐
manufactured
(If
Needed)
1/7/15
1/21/15
15
Manufacturing
of
Ball
Screw
Mount
by
Accu-­‐
Router*
1/7/15
2/21/15
46

28. 27
February
Task
Start
Date
End
Date
#
of
Days
1-­‐
Feb
2-­‐
Feb
3-­‐
Feb
4-­‐
Feb
5-­‐
Feb
6-­‐
Feb
7-­‐
Feb
8-­‐
Feb
9-­‐
Feb
10-­‐
Feb
11-­‐
Feb
12-­‐
Feb
13-­‐
Feb
14-­‐
Feb
Manufacturing
of
Ball
Screw
Mount
by
Accu-­‐Router*
1/7/15
2/21/15
39
Strain
Test
-­‐
Prototype
2/1/15
2/21/15
21
Vibration
Test
-­‐
Prototype
2/7/15
2/28/15
21
Report
-­‐
Special
Considerations
/
Issues
in
Building
Prototype
2/1/15
2/28/15
28
Task
Start
Date
End
Date
#
of
Days
15-­‐
Feb
16-­‐
Feb
17-­‐
Feb
18-­‐
Feb
19-­‐
Feb
20-­‐
Feb
21-­‐
Feb
22-­‐
Feb
23-­‐
Feb
24-­‐
Feb
25-­‐
Feb
26-­‐
Feb
27-­‐
Feb
28-­‐
Feb
Manufacturing
of
Ball
Screw
Mount
by
Accu-­‐Router*
1/7/15
2/21/15
39
Strain
Test
-­‐
Prototype
2/1/15
2/21/15
21
Vibration
Test
-­‐
Prototype
2/7/15
2/28/15
21
Report
-­‐
Special
Considerations
/
Issues
in
Building
Prototype
2/1/15
2/28/15
28
*Accu-­‐Router
is
given
21
extra
days
to
manufacture
the
ball
screw
mount
in
case
of
unexpected
delays
March
Task
Start
Date
End
Date
#
of
Days
1-­‐
Mar
2-­‐
Mar
3-­‐
Mar
4-­‐
Mar
5-­‐
Mar
6-­‐
Mar
7-­‐
Mar
8-­‐
Mar
9-­‐
Mar
10-­‐
Mar
11-­‐
Mar
12-­‐
Mar
13-­‐
Mar
14-­‐
Mar
15-­‐
Mar
Report
-­‐
Design
of
Test
Apparatus
and
Test
Procedure
3/1/15
3/7/15
7
Analyze
Data
From
Testing
3/1/15
3/15/15
15

29. 28
Task
Start
Date
End
Date
#
of
Days
16-­‐
Mar
17-­‐
Mar
18-­‐
Mar
19-­‐
Mar
20-­‐
Mar
21-­‐
Mar
22-­‐
Mar
23-­‐
Mar
24-­‐
Mar
25-­‐
Mar
26-­‐
Mar
27-­‐
Mar
28-­‐
Mar
29-­‐
Mar
30-­‐
Mar
31-­‐
Mar
Report
-­‐
Test
Results
3/16/15
3/22/15
7
Report
-­‐
Economic
Impact
3/23/15
3/31/15
9
Presentation
Preparation
3/16/15
3/31/15
16
April
Task
Start
Date
End
Date
#
of
Days
1-­‐
Apr
2-­‐
Apr
3-­‐
Apr
4-­‐
Apr
5-­‐
Apr
6-­‐
Apr
7-­‐
Apr
8-­‐
Apr
9-­‐
Apr
10-­‐
Apr
11-­‐
Apr
12-­‐
Apr
13-­‐
Apr
14-­‐
Apr
15-­‐
Apr
Presentation
(Date
Tentative
for
Early
April)
4/1/15
4/1/15
1
Final
Report
4/1/15
4/15/15
15

30. 29
Engineering Calculations
Calculated
Axial
Force
Table
! = 1600 !!!
Table
Velocity
! = 3000
!"
!"#
in
0.5!
Table
Acceleration
! = 8.33
!"
!!
Axial
Force
! = !" =
!
!
∗ ! =
!"##
!".!
∗ 8.33 = 414.9 !!!
Measured
Axial
Force
Table
! = 1200 !!!
From
accelerometer
Gravity
=
658 !"
Table’s
Acceleration
= 750 !"
! =
!"#$%
!"#$%&'
∗ ! =
!"#
!"#
∗ 32.2 = 36.702
!"
!!
Axial
Force
! = !" =
!
!
∗ ! =
!"##
!".!
∗ 36.702 = 1367.77 !!!
Cost
Old
$495
New
$120
$495 − $120 = $375
Decrease
in
price
!"#!!"#
!"#
∗ 100% = 75.8%
Reduction
in
cost

31. 30
Detailed Shop Drawings