Modified MiniMill™ Stiffness Analysis

By: Roger Cortesi [email protected] http://pergatory.mit.edu/rcortesi/

Precision Engineering Research Group

Massachusetts Institute of Technology, Mechanical Engineering Department Room 3-470 77 Massachusetts Ave.

Cambridge, MA 02139 Phone: (617) 253-1953 Fax: (617) 258-6427 http://pergatory.mit.edu/ Property of Roger Cortesi, MIT Precision Engineering Research Group. DO NOT COPY or TRANSMIT without written permission.

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 Property of Roger Cortesi, MIT Precision Engineering Research Group. DO NOT COPY or TRANSMIT without written permission.

Modified MiniMill™ Quick Check of Bearing Compliance L b  275mm L t  500mm K  N 80  m F  30N Distance Between Bearing Centers Distance From Center of Stiffness to Tool Tip Stiffness of a Pair of Air Bearings Force Applied at Tool Tip L t 2  F   0.5 K  L b 2   2.5

 m Deflection at Tool Tip due to one set of bearings  machine  2   L b  machine  5  m  machine  2  10  4 in Deflection at Tool Tip due to both the Y and Z bearings L t Tool Force 2 Air Bearings 2 Air Bearings Center of Stiffness Property of Roger Cortesi, MIT Precision Engineering Research Group. DO NOT COPY or TRANSMIT without written permission.

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) The previous slide showed an estimate of 5  m for deflection at the tool tip. Did the extra 1.2  m come from the deflection of the Z axis itself?

30 N force

Property of Roger Cortesi, MIT Precision Engineering Research Group. DO NOT COPY or TRANSMIT without written permission.

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. Property of Roger Cortesi, MIT Precision Engineering Research Group. DO NOT COPY or TRANSMIT without written permission.

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



m Displacement due to carriage & axis roll 20



m Deflection of Way

Property of Roger Cortesi, MIT Precision Engineering Research Group. DO NOT COPY or TRANSMIT without written permission.

Solutions to Modified MiniMill™ Y Axis Displacement • Replace Polymer Concrete with Black Granite with will reduces the droop by half to roughly 10  m.

• 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.

Property of Roger Cortesi, MIT Precision Engineering Research Group. DO NOT COPY or TRANSMIT without written permission.