1. Property of Roger Cortesi, MIT Precision Engineering Research Group. DO NOT COPY or TRANSMIT without written permission. The Standard MiniMill™ Stiffness Calculations Precision Engineering Research Group Massachusetts Institute of Technology, Mechanical Engineering Department Phone: (617) 253-1953 Fax: (617) 258-6427 http://pergatory.mit.edu/ Room 3-470 77 Massachusetts Ave. Cambridge, MA 02139 By: Roger Cortesi rcortesi@mit.edu http://pergatory.mit.edu/rcortesi/

2. Property of Roger Cortesi, MIT Precision Engineering Research Group. DO NOT COPY or TRANSMIT without written permission. Types of Stiffness Calculations Ball Screw Stiffness Servo Stiffness Carriage Translation Stiffness Carriage Roll Stiffness

3. Property of Roger Cortesi, MIT Precision Engineering Research Group. DO NOT COPY or TRANSMIT without written permission. Standard MiniMill™ Ball Screw Stiffness

4. Property of Roger Cortesi, MIT Precision Engineering Research Group. DO NOT COPY or TRANSMIT without written permission. Standard MiniMill™ Servo Stiffness The ball screw is really a wedge

5. Property of Roger Cortesi, MIT Precision Engineering Research Group. DO NOT COPY or TRANSMIT without written permission. Standard MiniMill™ Carriage Translation Stiffness The carriage stiffness in the UP DOWN and SIDE directions in 4 times the truck stiffness in each of these directions. Star Linear™ Steel Truck Short (left) and Standard Truck (right)

6. Property of Roger Cortesi, MIT Precision Engineering Research Group. DO NOT COPY or TRANSMIT without written permission. Standard MiniMill™ Carriage Roll Stiffness Tool Force 2 Trucks Center of Stiffness LtLt LbLb

7. Property of Roger Cortesi, MIT Precision Engineering Research Group. DO NOT COPY or TRANSMIT without written permission. Carriage Stiffness Comparison Between The Standard and Modified MiniMill™ Axial Stiffness 1 is the servo stiffness. Use if a linear encoder is used Axial Stiffness 2 is the stiffness of the ball screw, use if a rotary encoder is used See the Modified MiniMill™ Stiffness Presentation for the calculation of the its stiffness values

8. Property of Roger Cortesi, MIT Precision Engineering Research Group. DO NOT COPY or TRANSMIT without written permission. Overall Machine Stiffness Estimates Between The Standard and Modified MiniMill™ The Modified MiniMill™ has an estimated Machine Stiffness of: 5 N/micron (27,000 lbf/inch) The Standard MiniMill™ has an estimated Machine Stiffness of: 10 N/micron (57,000 lbf/inch) This can be doubled by upgrading from short trucks (0.02 C Preload) to Standard Trucks (0.08 C Preload) The machine stiffness was estimated from the deflection due to the rolling of Y Carriage and Deflection of the Z Axis. See the Modified MiniMill™ Stiffness Presentation for the calculation of the its stiffness values