Modified%20MiniMill

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Modified MiniMill Stiffness Analysis
By Roger Cortesi rcortesi_at_mit.edu
http//pergatory.mit.edu/rcortesi/
Precision Engineering Research Group Massachusetts
Institute of Technology, Mechanical Engineering
Department
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Modified MiniMill Stiffness Summary

• The MiniMill has a stiffness of about 5 N/micron
  (27,000 lbf/in)
• A 4 mm diameter 16 mm long carbide end mill has a
  stiffness of 0.6 N/micron (3300 lbf/in)
• A 4mm tool cutting at 110 W (5 of the spindle
  power) will require a cutting force of about 11 N
  (2.6 lbf)
• The Tool will deflect 20 Microns (0.0008 inches)
  under this load while the machine will deflect
  2.5 Microns (0.00007 in)

The following slides show the analysis
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Modified MiniMill Quick Check of Bearing
Compliance
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Modified MiniMill Displacement Due to Tool
Loading
A 30 Newton tool load was applied to the Z axis
at full extension in the negative X direction.
The FEA estimated 6.2 microns of displacement
with this load
This yields a machine stiffness of 5 N/micron
(27,000 lbf/in)
30 N force
The previous slide showed an estimate of 5 mm for
deflection at the tool tip. Did the extra 1.2 mm
come from the deflection of the Z axis itself?
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Checking the Compliance of the Z Axis
Bearing Pads Constraining Axis Here
30 N Force Applied Here
Under a 30 N force at full extension the Z Axis
deflects 1.6 microns.
This confirms that the quick check is reasonable
for bearing deflections.
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Modified MiniMill Deflection Due to Gravity

• There are two components
• The deflection of the Y way
• The Roll of the YZ Carriage

The deflection of the Y way is proportional to
the position of the YZ Carriage on the axis. When
the YZ Carriage is at the end of the Y way there
will be a deflection of about 20 microns for the
polymer concrete version. Solutions are listed on
the next slide. The Roll of the YZ Carriage is
independent of the either the YZ Carriage
Position or the Z Axis position, So it should not
effect the accuracy of the machine much.
16 mm Displacement due to carriage axis roll
20 mm Deflection of Way
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Solutions to Modified MiniMillY Axis
Displacement

• Replace Polymer Concrete with Black Granite with
  will reduces the droop by half to roughly 10mm.
• Embed 4 pieces of Steel Rebar in the polymer
  concrete castings corners. This should also
  reduce the droop by about half.
• A mapped servo controller that moves the z axis
  to compensate for the Y axis deflection.