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Modified MiniMill™ Stiffness Analysis

Room 3-470 77 Massachusetts Ave. Cambridge, MA 02139. Phone: (617) 253-1953 Fax: (617) 258-6427 http://pergatory.mit.edu/. Modified MiniMill™ Stiffness Analysis. By: Roger Cortesi rcortesi@mit.edu http://pergatory.mit.edu/rcortesi/. Precision Engineering Research Group

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Modified MiniMill™ Stiffness Analysis

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  1. Room 3-470 77 Massachusetts Ave. Cambridge, MA 02139 Phone: (617) 253-1953 Fax: (617) 258-6427 http://pergatory.mit.edu/ Modified MiniMill™ Stiffness Analysis By: Roger Cortesi rcortesi@mit.edu http://pergatory.mit.edu/rcortesi/ Precision Engineering Research Group Massachusetts Institute of Technology, Mechanical Engineering Department

  2. 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

  3. Tool Force Lt Lb 2 Air Bearings Center of Stiffness 2 Air Bearings Modified MiniMill™ Quick Check of Bearing Compliance

  4. 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?

  5. 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.

  6. 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

  7. Solutions to Modified MiniMill™Y 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 casting’s 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.

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